Subgroups — C₂×C₅₃×#3534 #27270233

Order 13568.

8166 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3534	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#562	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₃×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₃×#551	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#546	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#546	C₂	1	2	yes	maximal, complemented
9	C₂×D₄²×C₅₃	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#539	C₂	1	2	yes	maximal, complemented
13	C₂×C₅₃×#538	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#534	C₂	1	2	yes	maximal, complemented
17	C₂×C₅₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
25	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
26	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
27	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#562	C₂²	1	32	yes	complemented
30	C₅₃×#560	C₂²	1	32	yes	complemented
31	C₅₃×#553	C₂²	1	32	yes	complemented
32	C₅₃×#551	C₂²	1	32	yes	complemented
33	C₅₃×#546	C₂²	1	32	yes	complemented
34	C₅₃×#546	C₂²	1	32	yes	complemented
35	C₅₃×#546	C₂²	1	32	yes	complemented
36	D₄²×C₅₃	C₂²	1	32	yes	complemented
37	C₅₃×#540	C₂²	1	32	yes	complemented
38	C₅₃×#539	C₂²	1	32	yes	complemented
39	C₅₃×#539	C₂²	1	16	yes	complemented
40	C₅₃×#538	C₂²	1	16	yes	complemented
41	C₅₃×#538	C₂²	1	32	yes	complemented
42	C₅₃×#537	C₂²	1	16	yes	complemented
43	C₅₃×#534	C₂²	1	32	yes	complemented
44	C₅₃×#534	C₂²	1	16	yes	complemented
45	C₂×#127×C₅₃	C₂²	1	2	yes	complemented
46	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
47	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
48	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
49	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
50	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
51	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
52	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
53	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
54	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
55	C₅₃×#525	C₂²	1	16	yes	complemented
56	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
57	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
58	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
59	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
60	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
61	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
62	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
63	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
64	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
65	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
66	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
67	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
68	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
69	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
70	C₂×#123×C₅₃	C₂²	1	16	yes	complemented
71	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
73	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
75	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
76	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
77	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	C₂×#121×C₅₃	C₂²	1	2	yes	—
79	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
80	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
82	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
83	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
84	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
85	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
87	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
88	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
89	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
90	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
91	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
92	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
93	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
94	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
95	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
96	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
97	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
99	C₂×#121×C₅₃	C₂²	1	16	yes	complemented
100	C₂×#120×C₅₃	C₂²	1	2	yes	—
101	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
102	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
103	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
104	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
105	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
106	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
107	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
109	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
110	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
111	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
112	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
113	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
114	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
115	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
116	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
117	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
122	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
126	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
127	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
128	C₂⁵×C₅₃	C₂³	1	2	yes	—
129	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
130	C₂⁵×C₅₃	C₂³	1	2	yes	—
131	C₂×#41×C₅₃	—	4	4	no	—
132	C₂×#41×C₅₃	—	4	8	no	—
133	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
134	C₂×#41×C₅₃	C₂³	1	16	yes	complemented
135	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
136	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₅₃	—	4	4	no	—
138	C₂²×D₄×C₅₃	—	4	4	no	—
139	C₂²×D₄×C₅₃	—	4	8	no	—
140	C₂²×D₄×C₅₃	—	4	8	no	—
141	C₂²×D₄×C₅₃	—	4	8	no	—
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
148	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
149	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
151	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
157	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
158	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
159	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
161	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
162	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
163	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
164	C₂²×D₄×C₅₃	C₂³	1	16	yes	complemented
165	C₂²×D₄×C₅₃	C₂³	1	16	yes	complemented
166	C₂²×D₄×C₅₃	C₂³	1	16	yes	complemented
167	C₂³×C₄×C₅₃	—	4	4	no	—
168	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
169	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
171	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
172	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
173	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
176	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
177	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
178	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
179	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
182	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
183	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₅₃	C₂³	1	8	yes	complemented
185	#127×C₅₃	C₂³	1	16	yes	complemented
186	#126×C₅₃	C₂³	1	16	yes	complemented
187	#126×C₅₃	C₂³	1	16	yes	complemented
188	#126×C₅₃	C₂³	1	16	yes	complemented
189	#126×C₅₃	C₂³	1	16	yes	complemented
190	#125×C₅₃	C₂³	1	16	yes	complemented
191	#125×C₅₃	C₂³	1	16	yes	complemented
192	#124×C₅₃	C₂³	1	16	yes	complemented
193	#124×C₅₃	C₂³	1	16	yes	complemented
194	#124×C₅₃	C₂³	1	16	yes	complemented
195	#123×C₅₃	C₂³	1	16	yes	complemented
196	#123×C₅₃	C₂³	1	16	yes	complemented
197	#123×C₅₃	C₂³	1	16	yes	complemented
198	#123×C₅₃	C₂³	1	16	yes	complemented
199	#123×C₅₃	C₂³	1	16	yes	complemented
200	#123×C₅₃	C₂³	1	16	yes	complemented
201	#123×C₅₃	C₂³	1	16	yes	complemented
202	#123×C₅₃	C₂³	1	16	yes	complemented
203	#123×C₅₃	C₂³	1	16	yes	complemented
204	#123×C₅₃	C₂³	1	16	yes	complemented
205	#123×C₅₃	C₂³	1	16	yes	complemented
206	#123×C₅₃	C₂³	1	16	yes	complemented
207	#123×C₅₃	C₂³	1	16	yes	complemented
208	#123×C₅₃	C₂³	1	16	yes	complemented
209	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
210	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
211	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
212	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
213	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
214	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
215	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
216	#121×C₅₃	C₂³	1	8	yes	—
217	#121×C₅₃	C₂³	1	16	yes	—
218	#121×C₅₃	C₂³	1	8	yes	complemented
219	#121×C₅₃	C₂³	1	8	yes	complemented
220	#121×C₅₃	C₂³	1	8	yes	complemented
221	#121×C₅₃	C₂³	1	16	yes	complemented
222	#121×C₅₃	C₂³	1	16	yes	complemented
223	#121×C₅₃	C₂³	1	8	yes	complemented
224	#121×C₅₃	C₂³	1	8	yes	complemented
225	#121×C₅₃	C₂³	1	16	yes	complemented
226	#121×C₅₃	C₂³	1	16	yes	complemented
227	#121×C₅₃	C₂³	1	16	yes	complemented
228	#121×C₅₃	C₂³	1	16	yes	complemented
229	#121×C₅₃	C₂³	1	16	yes	complemented
230	#121×C₅₃	C₂³	1	16	yes	complemented
231	#121×C₅₃	C₂³	1	16	yes	complemented
232	#121×C₅₃	C₂³	1	16	yes	complemented
233	#121×C₅₃	C₂³	1	16	yes	complemented
234	#121×C₅₃	C₂³	1	16	yes	complemented
235	#121×C₅₃	C₂³	1	16	yes	complemented
236	#121×C₅₃	C₂³	1	16	yes	complemented
237	#120×C₅₃	C₂³	1	16	yes	—
238	#120×C₅₃	C₂³	1	16	yes	complemented
239	#120×C₅₃	C₂³	1	16	yes	complemented
240	#120×C₅₃	C₂³	1	16	yes	complemented
241	#120×C₅₃	C₂³	1	16	yes	complemented
242	#120×C₅₃	C₂³	1	16	yes	complemented
243	#120×C₅₃	C₂³	1	16	yes	complemented
244	#120×C₅₃	C₂³	1	16	yes	complemented
245	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
246	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
247	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
248	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
249	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
250	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
251	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
252	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
253	#117×C₅₃	C₂³	1	8	yes	complemented
254	#117×C₅₃	C₂³	1	16	yes	complemented
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
306	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
307	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
308	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
309	C₂⁴×C₅₃	—	2	4	no	—
310	C₂⁴×C₅₃	—	2	4	no	—
311	C₂⁴×C₅₃	—	2	4	no	—
312	C₂⁴×C₅₃	—	2	8	no	—
313	C₂⁴×C₅₃	—	4	2	no	—
314	C₂⁴×C₅₃	—	4	2	no	—
315	C₂⁴×C₅₃	—	4	4	no	—
316	C₂⁴×C₅₃	—	4	4	no	—
317	C₂⁴×C₅₃	—	4	4	no	—
318	C₂⁴×C₅₃	—	4	2	no	—
319	C₂⁴×C₅₃	—	4	4	no	—
320	C₂⁴×C₅₃	—	4	4	no	—
321	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
322	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
323	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
325	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
326	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
327	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
330	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
331	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
332	#41×C₅₃	—	4	16	no	—
333	#41×C₅₃	—	4	32	no	—
334	C₂×Q₈×C₅₃	—	4	2	no	—
335	C₂×Q₈×C₅₃	—	4	4	no	—
336	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
337	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
338	C₂×D₄×C₅₃	—	2	8	no	—
339	C₂×D₄×C₅₃	—	2	8	no	—
340	C₂×D₄×C₅₃	—	2	8	no	—
341	C₂×D₄×C₅₃	—	2	8	no	—
342	C₂×D₄×C₅₃	—	2	8	no	—
343	C₂×D₄×C₅₃	—	4	2	no	—
344	C₂×D₄×C₅₃	—	4	4	no	—
345	C₂×D₄×C₅₃	—	4	2	no	—
346	C₂×D₄×C₅₃	—	4	4	no	—
347	C₂×D₄×C₅₃	—	4	4	no	—
348	C₂×D₄×C₅₃	—	4	4	no	—
349	C₂×D₄×C₅₃	—	4	4	no	—
350	C₂×D₄×C₅₃	—	4	4	no	—
351	C₂×D₄×C₅₃	—	4	4	no	—
352	C₂×D₄×C₅₃	—	4	4	no	—
353	C₂×D₄×C₅₃	—	4	16	no	—
354	C₂×D₄×C₅₃	—	4	4	no	—
355	C₂×D₄×C₅₃	—	4	4	no	—
356	C₂×D₄×C₅₃	—	4	4	no	—
357	C₂×D₄×C₅₃	—	4	2	no	—
358	C₂×D₄×C₅₃	—	4	4	no	—
359	C₂×D₄×C₅₃	—	4	16	no	—
360	C₂×D₄×C₅₃	—	4	32	no	—
361	C₂×D₄×C₅₃	—	4	32	no	—
362	C₂×D₄×C₅₃	—	4	32	no	—
363	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
364	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
365	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
368	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
369	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
373	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
374	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
375	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
376	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
377	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
378	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
379	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
380	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
381	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
382	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₅₃	—	2	4	no	—
384	C₂²×C₄×C₅₃	—	2	4	no	—
385	C₂²×C₄×C₅₃	—	2	4	no	—
386	C₂²×C₄×C₅₃	—	4	2	no	—
387	C₂²×C₄×C₅₃	—	4	2	no	—
388	C₂²×C₄×C₅₃	—	4	2	no	—
389	C₂²×C₄×C₅₃	—	4	2	no	—
390	C₂²×C₄×C₅₃	—	4	16	no	—
391	C₂²×C₄×C₅₃	—	4	2	no	—
392	C₂²×C₄×C₅₃	—	4	4	no	—
393	C₂²×C₄×C₅₃	—	4	2	no	—
394	C₂²×C₄×C₅₃	—	4	4	no	—
395	C₂²×C₄×C₅₃	—	4	4	no	—
396	C₂²×C₄×C₅₃	—	4	4	no	—
397	C₂²×C₄×C₅₃	—	4	4	no	—
398	C₂²×C₄×C₅₃	—	4	4	no	—
399	C₂²×C₄×C₅₃	—	4	4	no	—
400	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
401	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
402	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
403	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
410	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
416	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
417	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
418	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
419	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
420	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
421	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
422	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
423	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
424	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
426	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
427	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
428	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
430	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
431	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
432	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
433	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
434	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
435	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
436	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
438	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
439	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
444	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
447	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
453	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
454	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
455	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
456	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
457	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
458	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
459	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
460	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
461	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
463	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
464	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
465	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
466	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
467	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
468	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
469	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
470	C₄²×C₅₃	C₂⁴	1	8	yes	—
471	C₄²×C₅₃	C₂⁴	1	8	yes	—
472	C₄²×C₅₃	C₂⁴	1	8	yes	—
473	C₂³×C₅₃	—	2	2	no	—
474	C₂³×C₅₃	—	2	2	no	—
475	C₂³×C₅₃	—	2	2	no	—
476	C₂³×C₅₃	—	2	2	no	—
477	C₂³×C₅₃	—	2	8	no	—
478	C₂³×C₅₃	—	2	2	no	—
479	C₂³×C₅₃	—	2	4	no	—
480	C₂³×C₅₃	—	2	4	no	—
481	C₂³×C₅₃	—	2	4	no	—
482	C₂³×C₅₃	—	2	4	no	—
483	C₂³×C₅₃	—	2	4	no	—
484	C₂³×C₅₃	—	2	4	no	—
485	C₂³×C₅₃	—	2	4	no	—
486	C₂³×C₅₃	—	2	8	no	—
487	C₂³×C₅₃	—	2	2	no	—
488	C₂³×C₅₃	—	2	4	no	—
489	C₂³×C₅₃	—	2	4	no	—
490	C₂³×C₅₃	—	2	2	no	—
491	C₂³×C₅₃	—	2	4	no	—
492	C₂³×C₅₃	—	2	4	no	—
493	C₂³×C₅₃	—	2	4	no	—
494	C₂³×C₅₃	—	2	8	no	—
495	C₂³×C₅₃	—	2	16	no	—
496	C₂³×C₅₃	—	4	4	no	—
497	C₂³×C₅₃	—	4	4	no	—
498	C₂³×C₅₃	—	4	8	no	—
499	C₂³×C₅₃	—	4	8	no	—
500	C₂³×C₅₃	—	4	8	no	—
501	C₂³×C₅₃	—	4	4	no	—
502	C₂³×C₅₃	—	4	8	no	—
503	C₂³×C₅₃	—	4	8	no	—
504	C₂³×C₅₃	—	4	16	no	—
505	C₂³×C₅₃	—	8	16	no	—
506	C₂³×C₅₃	—	8	8	no	—
507	C₂³×C₅₃	—	8	16	no	—
508	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
509	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
510	C₂³×C₅₃	C₂⁵	1	2	yes	—
511	C₂³×C₅₃	C₂⁵	1	4	yes	—
512	C₂³×C₅₃	C₂⁵	1	4	yes	—
513	C₂³×C₅₃	C₂⁵	1	4	yes	—
514	C₂³×C₅₃	C₂⁵	1	4	yes	—
515	C₂³×C₅₃	C₂⁵	1	2	yes	—
516	C₂³×C₅₃	C₂⁵	1	2	yes	—
517	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
518	Q₈×C₅₃	—	4	4	no	—
519	Q₈×C₅₃	—	4	8	no	—
520	D₄×C₅₃	—	2	16	no	—
521	D₄×C₅₃	—	2	16	no	—
522	D₄×C₅₃	—	2	16	no	—
523	D₄×C₅₃	—	2	16	no	—
524	D₄×C₅₃	—	2	16	no	—
525	D₄×C₅₃	—	4	4	no	—
526	D₄×C₅₃	—	4	8	no	—
527	D₄×C₅₃	—	4	4	no	—
528	D₄×C₅₃	—	4	8	no	—
529	D₄×C₅₃	—	4	8	no	—
530	D₄×C₅₃	—	4	8	no	—
531	D₄×C₅₃	—	4	8	no	—
532	D₄×C₅₃	—	4	8	no	—
533	D₄×C₅₃	—	4	8	no	—
534	D₄×C₅₃	—	4	8	no	—
535	D₄×C₅₃	—	4	8	no	—
536	D₄×C₅₃	—	4	8	no	—
537	D₄×C₅₃	—	4	8	no	—
538	D₄×C₅₃	—	4	4	no	—
539	D₄×C₅₃	—	4	8	no	—
540	C₂×C₄×C₅₃	—	2	2	no	—
541	C₂×C₄×C₅₃	—	2	8	no	—
542	C₂×C₄×C₅₃	—	2	2	no	—
543	C₂×C₄×C₅₃	—	2	2	no	—
544	C₂×C₄×C₅₃	—	2	2	no	—
545	C₂×C₄×C₅₃	—	2	4	no	—
546	C₂×C₄×C₅₃	—	2	8	no	—
547	C₂×C₄×C₅₃	—	2	8	no	—
548	C₂×C₄×C₅₃	—	2	4	no	—
549	C₂×C₄×C₅₃	—	2	4	no	—
550	C₂×C₄×C₅₃	—	2	4	no	—
551	C₂×C₄×C₅₃	—	2	4	no	—
552	C₂×C₄×C₅₃	—	2	4	no	—
553	C₂×C₄×C₅₃	—	2	4	no	—
554	C₂×C₄×C₅₃	—	2	4	no	—
555	C₂×C₄×C₅₃	—	4	4	no	—
556	C₂×C₄×C₅₃	—	4	4	no	—
557	C₂×C₄×C₅₃	—	4	4	no	—
558	C₂×C₄×C₅₃	—	4	4	no	—
559	C₂×C₄×C₅₃	—	4	4	no	—
560	C₂×C₄×C₅₃	—	4	8	no	—
561	C₂×C₄×C₅₃	—	4	4	no	—
562	C₂×C₄×C₅₃	—	4	8	no	—
563	C₂×C₄×C₅₃	—	4	8	no	—
564	C₂×C₄×C₅₃	—	4	8	no	—
565	C₂×C₄×C₅₃	—	4	8	no	—
566	C₂×C₄×C₅₃	—	4	8	no	—
567	C₂×C₄×C₅₃	—	4	8	no	—
568	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
569	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
570	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
571	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
572	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
573	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
574	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
575	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
576	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
577	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
578	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
579	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
580	C₂×#3534	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
581	C₂²×C₅₃	—	2	2	no	—
582	C₂²×C₅₃	—	2	2	no	—
583	C₂²×C₅₃	—	2	2	no	—
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	8	no	—
586	C₂²×C₅₃	—	2	8	no	—
587	C₂²×C₅₃	—	2	2	no	—
588	C₂²×C₅₃	—	2	4	no	—
589	C₂²×C₅₃	—	2	4	no	—
590	C₂²×C₅₃	—	2	4	no	—
591	C₂²×C₅₃	—	2	4	no	—
592	C₂²×C₅₃	—	2	4	no	—
593	C₂²×C₅₃	—	2	4	no	—
594	C₂²×C₅₃	—	2	4	no	—
595	C₂²×C₅₃	—	2	2	no	—
596	C₂²×C₅₃	—	2	4	no	—
597	C₂²×C₅₃	—	2	4	no	—
598	C₂²×C₅₃	—	2	2	no	—
599	C₂²×C₅₃	—	2	4	no	—
600	C₂²×C₅₃	—	2	4	no	—
601	C₂²×C₅₃	—	2	4	no	—
602	C₂²×C₅₃	—	4	16	no	—
603	C₂²×C₅₃	—	4	4	no	—
604	C₂²×C₅₃	—	4	8	no	—
605	C₂²×C₅₃	—	4	8	no	—
606	C₂²×C₅₃	—	4	8	no	—
607	C₂²×C₅₃	—	4	8	no	—
608	C₂²×C₅₃	—	8	16	no	—
609	C₂²×C₅₃	—	8	8	no	—
610	C₂²×C₅₃	—	8	16	no	—
611	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
612	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
613	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
614	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
615	C₂²×C₅₃	#585	1	2	yes	—
616	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
617	C₄×C₅₃	—	2	2	no	—
618	C₄×C₅₃	—	2	2	no	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	—	2	2	no	—
621	C₄×C₅₃	—	2	4	no	—
622	C₄×C₅₃	—	2	4	no	—
623	C₄×C₅₃	—	2	4	no	—
624	C₄×C₅₃	—	2	4	no	—
625	C₄×C₅₃	—	2	4	no	—
626	C₄×C₅₃	—	2	4	no	—
627	C₄×C₅₃	—	2	4	no	—
628	C₄×C₅₃	—	2	4	no	—
629	#3534	C₂×C₅₃	1	32	yes	direct product factor
630	C₂×#562	C₂×C₅₃	1	2	yes	complemented
631	C₂×#560	C₂×C₅₃	1	2	yes	complemented
632	C₂×#553	C₂×C₅₃	1	2	yes	complemented
633	C₂×#551	C₂×C₅₃	1	2	yes	complemented
634	C₂×#546	C₂×C₅₃	1	2	yes	complemented
635	C₂×#546	C₂×C₅₃	1	2	yes	complemented
636	C₂×#546	C₂×C₅₃	1	2	yes	complemented
637	C₂×D₄²	C₂×C₅₃	1	2	yes	complemented
638	C₂×#540	C₂×C₅₃	1	2	yes	complemented
639	C₂×#539	C₂×C₅₃	1	2	yes	complemented
640	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
641	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
642	C₂×#538	C₂×C₅₃	1	2	yes	complemented
643	C₂×#537	C₂×C₅₃	1	1	yes	characteristic, complemented
644	C₂×#534	C₂×C₅₃	1	2	yes	complemented
645	C₂×#534	C₂×C₅₃	1	1	yes	characteristic, complemented
646	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
647	C₂²×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
648	C₂²×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
649	C₂×C₅₃	—	2	4	no	—
650	C₂×C₅₃	—	2	4	no	—
651	C₂×C₅₃	—	4	2	no	—
652	C₂×C₅₃	—	4	4	no	—
653	C₂×C₅₃	—	4	4	no	—
654	C₂×C₅₃	—	4	4	no	—
655	C₂×C₅₃	—	4	4	no	—
656	C₂×C₅₃	#3534	1	4	yes	direct product factor
657	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
660	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
662	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
663	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	C₂³×D₄	C₂²×C₅₃	1	2	yes	complemented
665	C₂³×D₄	C₂²×C₅₃	1	2	yes	complemented
666	C₂³×D₄	C₂²×C₅₃	1	2	yes	complemented
667	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#562	C₂²×C₅₃	1	32	yes	complemented
669	#560	C₂²×C₅₃	1	32	yes	complemented
670	#553	C₂²×C₅₃	1	32	yes	complemented
671	#551	C₂²×C₅₃	1	32	yes	complemented
672	#546	C₂²×C₅₃	1	32	yes	complemented
673	#546	C₂²×C₅₃	1	32	yes	complemented
674	#546	C₂²×C₅₃	1	32	yes	complemented
675	D₄²	C₂²×C₅₃	1	32	yes	complemented
676	#540	C₂²×C₅₃	1	32	yes	complemented
677	#539	C₂²×C₅₃	1	32	yes	complemented
678	#539	C₂²×C₅₃	1	16	yes	complemented
679	#538	C₂²×C₅₃	1	16	yes	complemented
680	#538	C₂²×C₅₃	1	32	yes	complemented
681	#537	C₂²×C₅₃	1	16	yes	complemented
682	#534	C₂²×C₅₃	1	32	yes	complemented
683	#534	C₂²×C₅₃	1	16	yes	complemented
684	C₂×#127	C₂²×C₅₃	1	2	yes	complemented
685	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
686	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
687	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
688	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
689	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
690	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
691	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
692	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
693	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
694	#525	C₂²×C₅₃	1	16	yes	complemented
695	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
696	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
697	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
698	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
699	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
700	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
701	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
702	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
703	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
704	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
705	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
706	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
707	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
708	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
709	C₂×#123	C₂²×C₅₃	1	16	yes	complemented
710	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
713	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
714	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
715	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
716	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
717	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
718	C₂×#121	C₂²×C₅₃	1	2	yes	—
719	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
723	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
724	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
725	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
727	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
728	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
729	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
730	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
731	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
732	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
733	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
734	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
735	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
736	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
737	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
738	C₂×#121	C₂²×C₅₃	1	16	yes	complemented
739	C₂×#120	C₂²×C₅₃	1	2	yes	—
740	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
741	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
742	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
743	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
744	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
745	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
746	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
747	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
748	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
749	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
750	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
751	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
752	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
753	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
754	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
755	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
757	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
759	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
761	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
765	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
766	C₅₃	C₂×#3534	1	1	yes	characteristic, direct product factor, Sylow
767	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
768	C₂⁵	C₂³×C₅₃	1	2	yes	—
769	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
770	C₂⁵	C₂³×C₅₃	1	2	yes	—
771	C₂×#41	—	4	4	no	—
772	C₂×#41	—	4	8	no	—
773	C₂×#41	C₂³×C₅₃	1	8	yes	complemented
774	C₂×#41	C₂³×C₅₃	1	16	yes	complemented
775	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
776	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
777	C₂²×D₄	—	4	4	no	—
778	C₂²×D₄	—	4	4	no	—
779	C₂²×D₄	—	4	8	no	—
780	C₂²×D₄	—	4	8	no	—
781	C₂²×D₄	—	4	8	no	—
782	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
783	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
784	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
785	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
786	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
787	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
788	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
789	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
790	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
791	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
792	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
793	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
795	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
796	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
797	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
798	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
799	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
801	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
802	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
803	C₂²×D₄	C₂³×C₅₃	1	8	yes	complemented
804	C₂²×D₄	C₂³×C₅₃	1	16	yes	complemented
805	C₂²×D₄	C₂³×C₅₃	1	16	yes	complemented
806	C₂²×D₄	C₂³×C₅₃	1	16	yes	complemented
807	C₂³×C₄	—	4	4	no	—
808	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
809	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
810	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
811	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
812	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
813	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
814	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
815	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
816	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
817	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
818	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
819	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
820	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
821	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
822	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
823	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
824	C₂³×C₄	C₂³×C₅₃	1	8	yes	complemented
825	#127	C₂³×C₅₃	1	16	yes	complemented
826	#126	C₂³×C₅₃	1	16	yes	complemented
827	#126	C₂³×C₅₃	1	16	yes	complemented
828	#126	C₂³×C₅₃	1	16	yes	complemented
829	#126	C₂³×C₅₃	1	16	yes	complemented
830	#125	C₂³×C₅₃	1	16	yes	complemented
831	#125	C₂³×C₅₃	1	16	yes	complemented
832	#124	C₂³×C₅₃	1	16	yes	complemented
833	#124	C₂³×C₅₃	1	16	yes	complemented
834	#124	C₂³×C₅₃	1	16	yes	complemented
835	#123	C₂³×C₅₃	1	16	yes	complemented
836	#123	C₂³×C₅₃	1	16	yes	complemented
837	#123	C₂³×C₅₃	1	16	yes	complemented
838	#123	C₂³×C₅₃	1	16	yes	complemented
839	#123	C₂³×C₅₃	1	16	yes	complemented
840	#123	C₂³×C₅₃	1	16	yes	complemented
841	#123	C₂³×C₅₃	1	16	yes	complemented
842	#123	C₂³×C₅₃	1	16	yes	complemented
843	#123	C₂³×C₅₃	1	16	yes	complemented
844	#123	C₂³×C₅₃	1	16	yes	complemented
845	#123	C₂³×C₅₃	1	16	yes	complemented
846	#123	C₂³×C₅₃	1	16	yes	complemented
847	#123	C₂³×C₅₃	1	16	yes	complemented
848	#123	C₂³×C₅₃	1	16	yes	complemented
849	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
850	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
851	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
852	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
853	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
854	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
855	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
856	#121	C₂³×C₅₃	1	8	yes	—
857	#121	C₂³×C₅₃	1	16	yes	—
858	#121	C₂³×C₅₃	1	8	yes	complemented
859	#121	C₂³×C₅₃	1	8	yes	complemented
860	#121	C₂³×C₅₃	1	8	yes	complemented
861	#121	C₂³×C₅₃	1	16	yes	complemented
862	#121	C₂³×C₅₃	1	16	yes	complemented
863	#121	C₂³×C₅₃	1	8	yes	complemented
864	#121	C₂³×C₅₃	1	8	yes	complemented
865	#121	C₂³×C₅₃	1	16	yes	complemented
866	#121	C₂³×C₅₃	1	16	yes	complemented
867	#121	C₂³×C₅₃	1	16	yes	complemented
868	#121	C₂³×C₅₃	1	16	yes	complemented
869	#121	C₂³×C₅₃	1	16	yes	complemented
870	#121	C₂³×C₅₃	1	16	yes	complemented
871	#121	C₂³×C₅₃	1	16	yes	complemented
872	#121	C₂³×C₅₃	1	16	yes	complemented
873	#121	C₂³×C₅₃	1	16	yes	complemented
874	#121	C₂³×C₅₃	1	16	yes	complemented
875	#121	C₂³×C₅₃	1	16	yes	complemented
876	#121	C₂³×C₅₃	1	16	yes	complemented
877	#120	C₂³×C₅₃	1	16	yes	—
878	#120	C₂³×C₅₃	1	16	yes	complemented
879	#120	C₂³×C₅₃	1	16	yes	complemented
880	#120	C₂³×C₅₃	1	16	yes	complemented
881	#120	C₂³×C₅₃	1	16	yes	complemented
882	#120	C₂³×C₅₃	1	16	yes	complemented
883	#120	C₂³×C₅₃	1	16	yes	complemented
884	#120	C₂³×C₅₃	1	16	yes	complemented
885	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
886	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
887	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
888	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
889	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
890	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
891	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
892	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
893	#117	C₂³×C₅₃	1	8	yes	complemented
894	#117	C₂³×C₅₃	1	16	yes	complemented
895	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
896	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
899	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
900	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
901	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
902	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
904	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
906	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
907	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
908	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
909	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
910	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
911	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
912	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
913	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
914	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
915	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
916	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
917	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
918	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
919	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
920	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
921	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
922	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
923	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
924	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
925	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
926	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
928	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
929	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
930	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
931	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
932	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
933	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
934	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
935	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
936	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
937	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
938	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
939	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
940	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	complemented
941	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
942	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
943	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
944	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	complemented
945	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	complemented
946	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
947	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
948	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
949	C₂⁴	—	2	4	no	—
950	C₂⁴	—	2	4	no	—
951	C₂⁴	—	2	4	no	—
952	C₂⁴	—	2	8	no	—
953	C₂⁴	—	4	2	no	—
954	C₂⁴	—	4	2	no	—
955	C₂⁴	—	4	4	no	—
956	C₂⁴	—	4	4	no	—
957	C₂⁴	—	4	4	no	—
958	C₂⁴	—	4	2	no	—
959	C₂⁴	—	4	4	no	—
960	C₂⁴	—	4	4	no	—
961	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
962	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
963	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
965	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
966	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
967	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
969	C₂⁴	C₂⁴×C₅₃	1	8	yes	—
970	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
971	C₂⁴	C₂⁴×C₅₃	1	8	yes	—
972	#41	—	4	16	no	—
973	#41	—	4	32	no	—
974	C₂×Q₈	—	4	2	no	—
975	C₂×Q₈	—	4	4	no	—
976	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
977	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
978	C₂×D₄	—	2	8	no	—
979	C₂×D₄	—	2	8	no	—
980	C₂×D₄	—	2	8	no	—
981	C₂×D₄	—	2	8	no	—
982	C₂×D₄	—	2	8	no	—
983	C₂×D₄	—	4	2	no	—
984	C₂×D₄	—	4	4	no	—
985	C₂×D₄	—	4	2	no	—
986	C₂×D₄	—	4	4	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	—	4	4	no	—
989	C₂×D₄	—	4	4	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	4	no	—
993	C₂×D₄	—	4	16	no	—
994	C₂×D₄	—	4	4	no	—
995	C₂×D₄	—	4	4	no	—
996	C₂×D₄	—	4	4	no	—
997	C₂×D₄	—	4	2	no	—
998	C₂×D₄	—	4	4	no	—
999	C₂×D₄	—	4	16	no	—
1000	C₂×D₄	—	4	32	no	—
1001	C₂×D₄	—	4	32	no	—
1002	C₂×D₄	—	4	32	no	—
1003	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1004	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1005	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1006	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1007	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1008	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1009	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1010	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1011	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1012	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1013	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1014	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1015	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1016	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1017	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1018	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1019	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1020	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1021	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1022	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1023	C₂²×C₄	—	2	4	no	—
1024	C₂²×C₄	—	2	4	no	—
1025	C₂²×C₄	—	2	4	no	—
1026	C₂²×C₄	—	4	2	no	—
1027	C₂²×C₄	—	4	2	no	—
1028	C₂²×C₄	—	4	2	no	—
1029	C₂²×C₄	—	4	2	no	—
1030	C₂²×C₄	—	4	16	no	—
1031	C₂²×C₄	—	4	2	no	—
1032	C₂²×C₄	—	4	4	no	—
1033	C₂²×C₄	—	4	2	no	—
1034	C₂²×C₄	—	4	4	no	—
1035	C₂²×C₄	—	4	4	no	—
1036	C₂²×C₄	—	4	4	no	—
1037	C₂²×C₄	—	4	4	no	—
1038	C₂²×C₄	—	4	4	no	—
1039	C₂²×C₄	—	4	4	no	—
1040	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1041	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1043	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1044	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1045	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1046	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1047	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1048	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1049	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1053	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1054	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1055	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1056	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1057	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1058	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1059	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1060	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1061	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1062	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1063	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1064	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1065	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1066	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1067	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1068	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1069	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1070	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1071	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1072	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1073	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1074	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1075	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1076	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1077	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1078	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1079	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1080	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1081	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1082	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1083	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1084	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1085	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1086	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1087	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1088	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1089	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1090	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1091	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1092	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1093	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1094	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1095	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1096	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1097	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1098	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1099	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1100	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1101	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1102	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1103	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1104	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1105	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1106	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1107	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1108	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1109	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1110	C₄²	C₂⁴×C₅₃	1	8	yes	—
1111	C₄²	C₂⁴×C₅₃	1	8	yes	—
1112	C₄²	C₂⁴×C₅₃	1	8	yes	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	2	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	8	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	4	no	—
1120	C₂³	—	2	4	no	—
1121	C₂³	—	2	4	no	—
1122	C₂³	—	2	4	no	—
1123	C₂³	—	2	4	no	—
1124	C₂³	—	2	4	no	—
1125	C₂³	—	2	4	no	—
1126	C₂³	—	2	8	no	—
1127	C₂³	—	2	2	no	—
1128	C₂³	—	2	4	no	—
1129	C₂³	—	2	4	no	—
1130	C₂³	—	2	2	no	—
1131	C₂³	—	2	4	no	—
1132	C₂³	—	2	4	no	—
1133	C₂³	—	2	4	no	—
1134	C₂³	—	2	8	no	—
1135	C₂³	—	2	16	no	—
1136	C₂³	—	4	4	no	—
1137	C₂³	—	4	4	no	—
1138	C₂³	—	4	8	no	—
1139	C₂³	—	4	8	no	—
1140	C₂³	—	4	8	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	8	no	—
1143	C₂³	—	4	8	no	—
1144	C₂³	—	4	16	no	—
1145	C₂³	—	8	16	no	—
1146	C₂³	—	8	8	no	—
1147	C₂³	—	8	16	no	—
1148	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
1149	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
1150	C₂³	C₂⁵×C₅₃	1	4	yes	—
1151	C₂³	C₂⁵×C₅₃	1	4	yes	—
1152	C₂³	C₂⁵×C₅₃	1	2	yes	—
1153	C₂³	C₂⁵×C₅₃	1	4	yes	—
1154	C₂³	C₂⁵×C₅₃	1	4	yes	—
1155	C₂³	C₂⁵×C₅₃	1	2	yes	—
1156	C₂³	C₂⁵×C₅₃	1	2	yes	—
1157	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1158	Q₈	—	4	4	no	—
1159	Q₈	—	4	8	no	—
1160	D₄	—	2	16	no	—
1161	D₄	—	2	16	no	—
1162	D₄	—	2	16	no	—
1163	D₄	—	2	16	no	—
1164	D₄	—	2	16	no	—
1165	D₄	—	4	4	no	—
1166	D₄	—	4	8	no	—
1167	D₄	—	4	4	no	—
1168	D₄	—	4	8	no	—
1169	D₄	—	4	8	no	—
1170	D₄	—	4	8	no	—
1171	D₄	—	4	8	no	—
1172	D₄	—	4	8	no	—
1173	D₄	—	4	8	no	—
1174	D₄	—	4	8	no	—
1175	D₄	—	4	8	no	—
1176	D₄	—	4	8	no	—
1177	D₄	—	4	8	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	8	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	8	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	4	no	—
1186	C₂×C₄	—	2	8	no	—
1187	C₂×C₄	—	2	8	no	—
1188	C₂×C₄	—	2	4	no	—
1189	C₂×C₄	—	2	4	no	—
1190	C₂×C₄	—	2	4	no	—
1191	C₂×C₄	—	2	4	no	—
1192	C₂×C₄	—	2	4	no	—
1193	C₂×C₄	—	2	4	no	—
1194	C₂×C₄	—	2	4	no	—
1195	C₂×C₄	—	4	4	no	—
1196	C₂×C₄	—	4	4	no	—
1197	C₂×C₄	—	4	4	no	—
1198	C₂×C₄	—	4	4	no	—
1199	C₂×C₄	—	4	4	no	—
1200	C₂×C₄	—	4	8	no	—
1201	C₂×C₄	—	4	4	no	—
1202	C₂×C₄	—	4	8	no	—
1203	C₂×C₄	—	4	8	no	—
1204	C₂×C₄	—	4	8	no	—
1205	C₂×C₄	—	4	8	no	—
1206	C₂×C₄	—	4	8	no	—
1207	C₂×C₄	—	4	8	no	—
1208	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1209	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1210	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1211	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1212	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1213	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1214	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1215	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1216	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1217	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1218	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1219	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1220	C₂²	—	2	8	no	—
1221	C₂²	—	2	8	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	4	no	—
1228	C₂²	—	2	4	no	—
1229	C₂²	—	2	4	no	—
1230	C₂²	—	2	4	no	—
1231	C₂²	—	2	4	no	—
1232	C₂²	—	2	4	no	—
1233	C₂²	—	2	4	no	—
1234	C₂²	—	2	2	no	—
1235	C₂²	—	2	4	no	—
1236	C₂²	—	2	4	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	4	no	—
1239	C₂²	—	2	4	no	—
1240	C₂²	—	2	4	no	—
1241	C₂²	—	4	16	no	—
1242	C₂²	—	4	4	no	—
1243	C₂²	—	4	8	no	—
1244	C₂²	—	4	8	no	—
1245	C₂²	—	4	8	no	—
1246	C₂²	—	4	8	no	—
1247	C₂²	—	8	16	no	—
1248	C₂²	—	8	8	no	—
1249	C₂²	—	8	16	no	—
1250	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	4	yes	—
1251	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	4	yes	—
1252	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1253	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1254	C₂²	C₅₃×#585	1	2	yes	—
1255	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1256	C₄	—	2	2	no	—
1257	C₄	—	2	2	no	—
1258	C₄	—	2	2	no	—
1259	C₄	—	2	2	no	—
1260	C₄	—	2	4	no	—
1261	C₄	—	2	4	no	—
1262	C₄	—	2	4	no	—
1263	C₄	—	2	4	no	—
1264	C₄	—	2	4	no	—
1265	C₄	—	2	4	no	—
1266	C₄	—	2	4	no	—
1267	C₄	—	2	4	no	—
1268	C₂	—	2	4	no	—
1269	C₂	—	2	4	no	—
1270	C₂	—	4	2	no	—
1271	C₂	—	4	4	no	—
1272	C₂	—	4	4	no	—
1273	C₂	—	4	4	no	—
1274	C₂	—	4	4	no	—
1275	C₂	C₅₃×#3534	1	4	yes	direct product factor
1276	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1277	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1278	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3534	C₂	direct (N × H)
2. C₂×C₅₃×#562	C₂	semidirect
3. C₂×C₅₃×#560	C₂	semidirect
4. C₂×C₅₃×#553	C₂	semidirect
5. C₂×C₅₃×#551	C₂	semidirect
6. C₂×C₅₃×#546	C₂	semidirect
7. C₂×C₅₃×#546	C₂	semidirect
8. C₂×C₅₃×#546	C₂	semidirect
9. C₂×D₄²×C₅₃	C₂	semidirect
10. C₂×C₅₃×#540	C₂	semidirect
11. C₂×C₅₃×#539	C₂	semidirect
12. C₂×C₅₃×#539	C₂	semidirect
13. C₂×C₅₃×#538	C₂	semidirect
14. C₂×C₅₃×#538	C₂	semidirect
15. C₂×C₅₃×#537	C₂	semidirect
16. C₂×C₅₃×#534	C₂	semidirect
17. C₂×C₅₃×#534	C₂	semidirect
18. C₂×C₅₃×#525	C₂	semidirect
19. C₂²×#123×C₅₃	C₂	semidirect
20. C₂²×#121×C₅₃	C₂	semidirect
21. C₂²×#41×C₅₃	C₂²	semidirect
22. C₂²×#41×C₅₃	C₂²	semidirect
24. C₂³×D₄×C₅₃	C₂²	semidirect
25. C₂³×D₄×C₅₃	C₂²	semidirect
26. C₂³×D₄×C₅₃	C₂²	semidirect
27. C₂³×D₄×C₅₃	C₂²	semidirect
28. C₂⁴×C₄×C₅₃	C₂²	semidirect
29. C₅₃×#562	C₂²	semidirect
30. C₅₃×#560	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
32. C₅₃×#551	C₂²	semidirect
33. C₅₃×#546	C₂²	semidirect
34. C₅₃×#546	C₂²	semidirect
35. C₅₃×#546	C₂²	semidirect
36. D₄²×C₅₃	C₂²	semidirect
37. C₅₃×#540	C₂²	semidirect
38. C₅₃×#539	C₂²	semidirect
39. C₅₃×#539	C₂²	semidirect
40. C₅₃×#538	C₂²	semidirect
41. C₅₃×#538	C₂²	semidirect
42. C₅₃×#537	C₂²	semidirect
43. C₅₃×#534	C₂²	semidirect
44. C₅₃×#534	C₂²	semidirect
45. C₂×#127×C₅₃	C₂²	semidirect
46. C₂×#126×C₅₃	C₂²	semidirect
47. C₂×#126×C₅₃	C₂²	semidirect
48. C₂×#126×C₅₃	C₂²	semidirect
49. C₂×#126×C₅₃	C₂²	semidirect
50. C₂×#125×C₅₃	C₂²	semidirect
51. C₂×#125×C₅₃	C₂²	semidirect
52. C₂×#124×C₅₃	C₂²	semidirect
53. C₂×#124×C₅₃	C₂²	semidirect
54. C₂×#124×C₅₃	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
56. C₂×#123×C₅₃	C₂²	semidirect
57. C₂×#123×C₅₃	C₂²	semidirect
58. C₂×#123×C₅₃	C₂²	semidirect
59. C₂×#123×C₅₃	C₂²	semidirect
60. C₂×#123×C₅₃	C₂²	semidirect
61. C₂×#123×C₅₃	C₂²	semidirect
62. C₂×#123×C₅₃	C₂²	semidirect
63. C₂×#123×C₅₃	C₂²	semidirect
64. C₂×#123×C₅₃	C₂²	semidirect
65. C₂×#123×C₅₃	C₂²	semidirect
66. C₂×#123×C₅₃	C₂²	semidirect
67. C₂×#123×C₅₃	C₂²	semidirect
68. C₂×#123×C₅₃	C₂²	semidirect
69. C₂×#123×C₅₃	C₂²	semidirect
70. C₂×#123×C₅₃	C₂²	semidirect
71. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
72. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
73. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
74. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
75. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
76. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
77. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
80. C₂×#121×C₅₃	C₂²	semidirect
81. C₂×#121×C₅₃	C₂²	semidirect
82. C₂×#121×C₅₃	C₂²	semidirect
83. C₂×#121×C₅₃	C₂²	semidirect
84. C₂×#121×C₅₃	C₂²	semidirect
85. C₂×#121×C₅₃	C₂²	semidirect
86. C₂×#121×C₅₃	C₂²	semidirect
87. C₂×#121×C₅₃	C₂²	semidirect
88. C₂×#121×C₅₃	C₂²	semidirect
89. C₂×#121×C₅₃	C₂²	semidirect
90. C₂×#121×C₅₃	C₂²	semidirect
91. C₂×#121×C₅₃	C₂²	semidirect
92. C₂×#121×C₅₃	C₂²	semidirect
93. C₂×#121×C₅₃	C₂²	semidirect
94. C₂×#121×C₅₃	C₂²	semidirect
95. C₂×#121×C₅₃	C₂²	semidirect
96. C₂×#121×C₅₃	C₂²	semidirect
97. C₂×#121×C₅₃	C₂²	semidirect
98. C₂×#121×C₅₃	C₂²	semidirect
99. C₂×#121×C₅₃	C₂²	semidirect
101. C₂×#120×C₅₃	C₂²	semidirect
102. C₂×#120×C₅₃	C₂²	semidirect
103. C₂×#120×C₅₃	C₂²	semidirect
104. C₂×#120×C₅₃	C₂²	semidirect
105. C₂×#120×C₅₃	C₂²	semidirect
106. C₂×#120×C₅₃	C₂²	semidirect
107. C₂×#120×C₅₃	C₂²	semidirect
108. C₂×C₄×D₄×C₅₃	C₂²	semidirect
109. C₂×C₄×D₄×C₅₃	C₂²	semidirect
110. C₂×C₄×D₄×C₅₃	C₂²	semidirect
111. C₂×C₄×D₄×C₅₃	C₂²	semidirect
112. C₂×C₄×D₄×C₅₃	C₂²	semidirect
113. C₂×C₄×D₄×C₅₃	C₂²	semidirect
114. C₂×C₄×D₄×C₅₃	C₂²	semidirect
115. C₂×C₄×D₄×C₅₃	C₂²	semidirect
116. C₂×#117×C₅₃	C₂²	semidirect
117. C₂×#117×C₅₃	C₂²	semidirect
118. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
119. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
120. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
121. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
122. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
123. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
124. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
125. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
133. C₂×#41×C₅₃	C₂³	semidirect
134. C₂×#41×C₅₃	C₂³	semidirect
163. C₂²×D₄×C₅₃	C₂³	semidirect
164. C₂²×D₄×C₅₃	C₂³	semidirect
165. C₂²×D₄×C₅₃	C₂³	semidirect
166. C₂²×D₄×C₅₃	C₂³	semidirect
184. C₂³×C₄×C₅₃	C₂³	semidirect
185. #127×C₅₃	C₂³	semidirect
186. #126×C₅₃	C₂³	semidirect
187. #126×C₅₃	C₂³	semidirect
188. #126×C₅₃	C₂³	semidirect
189. #126×C₅₃	C₂³	semidirect
190. #125×C₅₃	C₂³	semidirect
191. #125×C₅₃	C₂³	semidirect
192. #124×C₅₃	C₂³	semidirect
193. #124×C₅₃	C₂³	semidirect
194. #124×C₅₃	C₂³	semidirect
195. #123×C₅₃	C₂³	semidirect
196. #123×C₅₃	C₂³	semidirect
197. #123×C₅₃	C₂³	semidirect
198. #123×C₅₃	C₂³	semidirect
199. #123×C₅₃	C₂³	semidirect
200. #123×C₅₃	C₂³	semidirect
201. #123×C₅₃	C₂³	semidirect
202. #123×C₅₃	C₂³	semidirect
203. #123×C₅₃	C₂³	semidirect
204. #123×C₅₃	C₂³	semidirect
205. #123×C₅₃	C₂³	semidirect
206. #123×C₅₃	C₂³	semidirect
207. #123×C₅₃	C₂³	semidirect
208. #123×C₅₃	C₂³	semidirect
209. C₂²⋊Q₈×C₅₃	C₂³	semidirect
210. C₂²⋊Q₈×C₅₃	C₂³	semidirect
211. C₂²⋊Q₈×C₅₃	C₂³	semidirect
212. C₂²⋊Q₈×C₅₃	C₂³	semidirect
213. C₂²⋊Q₈×C₅₃	C₂³	semidirect
214. C₂²⋊Q₈×C₅₃	C₂³	semidirect
215. C₂²⋊Q₈×C₅₃	C₂³	semidirect
218. #121×C₅₃	C₂³	semidirect
219. #121×C₅₃	C₂³	semidirect
220. #121×C₅₃	C₂³	semidirect
221. #121×C₅₃	C₂³	semidirect
222. #121×C₅₃	C₂³	semidirect
223. #121×C₅₃	C₂³	semidirect
224. #121×C₅₃	C₂³	semidirect
225. #121×C₅₃	C₂³	semidirect
226. #121×C₅₃	C₂³	semidirect
227. #121×C₅₃	C₂³	semidirect
228. #121×C₅₃	C₂³	semidirect
229. #121×C₅₃	C₂³	semidirect
230. #121×C₅₃	C₂³	semidirect
231. #121×C₅₃	C₂³	semidirect
232. #121×C₅₃	C₂³	semidirect
233. #121×C₅₃	C₂³	semidirect
234. #121×C₅₃	C₂³	semidirect
235. #121×C₅₃	C₂³	semidirect
236. #121×C₅₃	C₂³	semidirect
238. #120×C₅₃	C₂³	semidirect
239. #120×C₅₃	C₂³	semidirect
240. #120×C₅₃	C₂³	semidirect
241. #120×C₅₃	C₂³	semidirect
242. #120×C₅₃	C₂³	semidirect
243. #120×C₅₃	C₂³	semidirect
244. #120×C₅₃	C₂³	semidirect
245. C₄×D₄×C₅₃	C₂³	semidirect
246. C₄×D₄×C₅₃	C₂³	semidirect
247. C₄×D₄×C₅₃	C₂³	semidirect
248. C₄×D₄×C₅₃	C₂³	semidirect
249. C₄×D₄×C₅₃	C₂³	semidirect
250. C₄×D₄×C₅₃	C₂³	semidirect
251. C₄×D₄×C₅₃	C₂³	semidirect
252. C₄×D₄×C₅₃	C₂³	semidirect
253. #117×C₅₃	C₂³	semidirect
254. #117×C₅₃	C₂³	semidirect
272. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
273. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
274. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
300. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
301. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
302. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
303. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
304. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
305. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
580. C₂×#3534	C₅₃	direct (N × H)
629. #3534	C₂×C₅₃	direct (N × H)
630. C₂×#562	C₂×C₅₃	semidirect
631. C₂×#560	C₂×C₅₃	semidirect
632. C₂×#553	C₂×C₅₃	semidirect
633. C₂×#551	C₂×C₅₃	semidirect
634. C₂×#546	C₂×C₅₃	semidirect
635. C₂×#546	C₂×C₅₃	semidirect
636. C₂×#546	C₂×C₅₃	semidirect
637. C₂×D₄²	C₂×C₅₃	semidirect
638. C₂×#540	C₂×C₅₃	semidirect
639. C₂×#539	C₂×C₅₃	semidirect
640. C₂×#539	C₂×C₅₃	semidirect
641. C₂×#538	C₂×C₅₃	semidirect
642. C₂×#538	C₂×C₅₃	semidirect
643. C₂×#537	C₂×C₅₃	semidirect
644. C₂×#534	C₂×C₅₃	semidirect
645. C₂×#534	C₂×C₅₃	semidirect
646. C₂×#525	C₂×C₅₃	semidirect
647. C₂²×#123	C₂×C₅₃	semidirect
648. C₂²×#121	C₂×C₅₃	semidirect
656. C₂×C₅₃	#3534	direct (N × H)
660. C₂²×#41	C₂²×C₅₃	semidirect
661. C₂²×#41	C₂²×C₅₃	semidirect
663. C₂³×D₄	C₂²×C₅₃	semidirect
664. C₂³×D₄	C₂²×C₅₃	semidirect
665. C₂³×D₄	C₂²×C₅₃	semidirect
666. C₂³×D₄	C₂²×C₅₃	semidirect
667. C₂⁴×C₄	C₂²×C₅₃	semidirect
668. #562	C₂²×C₅₃	semidirect
669. #560	C₂²×C₅₃	semidirect
670. #553	C₂²×C₅₃	semidirect
671. #551	C₂²×C₅₃	semidirect
672. #546	C₂²×C₅₃	semidirect
673. #546	C₂²×C₅₃	semidirect
674. #546	C₂²×C₅₃	semidirect
675. D₄²	C₂²×C₅₃	semidirect
676. #540	C₂²×C₅₃	semidirect
677. #539	C₂²×C₅₃	semidirect
678. #539	C₂²×C₅₃	semidirect
679. #538	C₂²×C₅₃	semidirect
680. #538	C₂²×C₅₃	semidirect
681. #537	C₂²×C₅₃	semidirect
682. #534	C₂²×C₅₃	semidirect
683. #534	C₂²×C₅₃	semidirect
684. C₂×#127	C₂²×C₅₃	semidirect
685. C₂×#126	C₂²×C₅₃	semidirect
686. C₂×#126	C₂²×C₅₃	semidirect
687. C₂×#126	C₂²×C₅₃	semidirect
688. C₂×#126	C₂²×C₅₃	semidirect
689. C₂×#125	C₂²×C₅₃	semidirect
690. C₂×#125	C₂²×C₅₃	semidirect
691. C₂×#124	C₂²×C₅₃	semidirect
692. C₂×#124	C₂²×C₅₃	semidirect
693. C₂×#124	C₂²×C₅₃	semidirect
694. #525	C₂²×C₅₃	semidirect
695. C₂×#123	C₂²×C₅₃	semidirect
696. C₂×#123	C₂²×C₅₃	semidirect
697. C₂×#123	C₂²×C₅₃	semidirect
698. C₂×#123	C₂²×C₅₃	semidirect
699. C₂×#123	C₂²×C₅₃	semidirect
700. C₂×#123	C₂²×C₅₃	semidirect
701. C₂×#123	C₂²×C₅₃	semidirect
702. C₂×#123	C₂²×C₅₃	semidirect
703. C₂×#123	C₂²×C₅₃	semidirect
704. C₂×#123	C₂²×C₅₃	semidirect
705. C₂×#123	C₂²×C₅₃	semidirect
706. C₂×#123	C₂²×C₅₃	semidirect
707. C₂×#123	C₂²×C₅₃	semidirect
708. C₂×#123	C₂²×C₅₃	semidirect
709. C₂×#123	C₂²×C₅₃	semidirect
710. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
711. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
712. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
713. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
714. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
715. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
716. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
719. C₂×#121	C₂²×C₅₃	semidirect
720. C₂×#121	C₂²×C₅₃	semidirect
721. C₂×#121	C₂²×C₅₃	semidirect
722. C₂×#121	C₂²×C₅₃	semidirect
723. C₂×#121	C₂²×C₅₃	semidirect
724. C₂×#121	C₂²×C₅₃	semidirect
725. C₂×#121	C₂²×C₅₃	semidirect
726. C₂×#121	C₂²×C₅₃	semidirect
727. C₂×#121	C₂²×C₅₃	semidirect
728. C₂×#121	C₂²×C₅₃	semidirect
729. C₂×#121	C₂²×C₅₃	semidirect
730. C₂×#121	C₂²×C₅₃	semidirect
731. C₂×#121	C₂²×C₅₃	semidirect
732. C₂×#121	C₂²×C₅₃	semidirect
733. C₂×#121	C₂²×C₅₃	semidirect
734. C₂×#121	C₂²×C₅₃	semidirect
735. C₂×#121	C₂²×C₅₃	semidirect
736. C₂×#121	C₂²×C₅₃	semidirect
737. C₂×#121	C₂²×C₅₃	semidirect
738. C₂×#121	C₂²×C₅₃	semidirect
740. C₂×#120	C₂²×C₅₃	semidirect
741. C₂×#120	C₂²×C₅₃	semidirect
742. C₂×#120	C₂²×C₅₃	semidirect
743. C₂×#120	C₂²×C₅₃	semidirect
744. C₂×#120	C₂²×C₅₃	semidirect
745. C₂×#120	C₂²×C₅₃	semidirect
746. C₂×#120	C₂²×C₅₃	semidirect
747. C₂×C₄×D₄	C₂²×C₅₃	semidirect
748. C₂×C₄×D₄	C₂²×C₅₃	semidirect
749. C₂×C₄×D₄	C₂²×C₅₃	semidirect
750. C₂×C₄×D₄	C₂²×C₅₃	semidirect
751. C₂×C₄×D₄	C₂²×C₅₃	semidirect
752. C₂×C₄×D₄	C₂²×C₅₃	semidirect
753. C₂×C₄×D₄	C₂²×C₅₃	semidirect
754. C₂×C₄×D₄	C₂²×C₅₃	semidirect
755. C₂×#117	C₂²×C₅₃	semidirect
756. C₂×#117	C₂²×C₅₃	semidirect
757. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
758. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
759. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
760. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
761. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
762. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
763. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
764. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
765. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
766. C₅₃	C₂×#3534	direct (N × H)
773. C₂×#41	C₂³×C₅₃	semidirect
774. C₂×#41	C₂³×C₅₃	semidirect
803. C₂²×D₄	C₂³×C₅₃	semidirect
804. C₂²×D₄	C₂³×C₅₃	semidirect
805. C₂²×D₄	C₂³×C₅₃	semidirect
806. C₂²×D₄	C₂³×C₅₃	semidirect
824. C₂³×C₄	C₂³×C₅₃	semidirect
825. #127	C₂³×C₅₃	semidirect
826. #126	C₂³×C₅₃	semidirect
827. #126	C₂³×C₅₃	semidirect
828. #126	C₂³×C₅₃	semidirect
829. #126	C₂³×C₅₃	semidirect
830. #125	C₂³×C₅₃	semidirect
831. #125	C₂³×C₅₃	semidirect
832. #124	C₂³×C₅₃	semidirect
833. #124	C₂³×C₅₃	semidirect
834. #124	C₂³×C₅₃	semidirect
835. #123	C₂³×C₅₃	semidirect
836. #123	C₂³×C₅₃	semidirect
837. #123	C₂³×C₅₃	semidirect
838. #123	C₂³×C₅₃	semidirect
839. #123	C₂³×C₅₃	semidirect
840. #123	C₂³×C₅₃	semidirect
841. #123	C₂³×C₅₃	semidirect
842. #123	C₂³×C₅₃	semidirect
843. #123	C₂³×C₅₃	semidirect
844. #123	C₂³×C₅₃	semidirect
845. #123	C₂³×C₅₃	semidirect
846. #123	C₂³×C₅₃	semidirect
847. #123	C₂³×C₅₃	semidirect
848. #123	C₂³×C₅₃	semidirect
849. C₂²⋊Q₈	C₂³×C₅₃	semidirect
850. C₂²⋊Q₈	C₂³×C₅₃	semidirect
851. C₂²⋊Q₈	C₂³×C₅₃	semidirect
852. C₂²⋊Q₈	C₂³×C₅₃	semidirect
853. C₂²⋊Q₈	C₂³×C₅₃	semidirect
854. C₂²⋊Q₈	C₂³×C₅₃	semidirect
855. C₂²⋊Q₈	C₂³×C₅₃	semidirect
858. #121	C₂³×C₅₃	semidirect
859. #121	C₂³×C₅₃	semidirect
860. #121	C₂³×C₅₃	semidirect
861. #121	C₂³×C₅₃	semidirect
862. #121	C₂³×C₅₃	semidirect
863. #121	C₂³×C₅₃	semidirect
864. #121	C₂³×C₅₃	semidirect
865. #121	C₂³×C₅₃	semidirect
866. #121	C₂³×C₅₃	semidirect
867. #121	C₂³×C₅₃	semidirect
868. #121	C₂³×C₅₃	semidirect
869. #121	C₂³×C₅₃	semidirect
870. #121	C₂³×C₅₃	semidirect
871. #121	C₂³×C₅₃	semidirect
872. #121	C₂³×C₅₃	semidirect
873. #121	C₂³×C₅₃	semidirect
874. #121	C₂³×C₅₃	semidirect
875. #121	C₂³×C₅₃	semidirect
876. #121	C₂³×C₅₃	semidirect
878. #120	C₂³×C₅₃	semidirect
879. #120	C₂³×C₅₃	semidirect
880. #120	C₂³×C₅₃	semidirect
881. #120	C₂³×C₅₃	semidirect
882. #120	C₂³×C₅₃	semidirect
883. #120	C₂³×C₅₃	semidirect
884. #120	C₂³×C₅₃	semidirect
885. C₄×D₄	C₂³×C₅₃	semidirect
886. C₄×D₄	C₂³×C₅₃	semidirect
887. C₄×D₄	C₂³×C₅₃	semidirect
888. C₄×D₄	C₂³×C₅₃	semidirect
889. C₄×D₄	C₂³×C₅₃	semidirect
890. C₄×D₄	C₂³×C₅₃	semidirect
891. C₄×D₄	C₂³×C₅₃	semidirect
892. C₄×D₄	C₂³×C₅₃	semidirect
893. #117	C₂³×C₅₃	semidirect
894. #117	C₂³×C₅₃	semidirect
912. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
913. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
914. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
940. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
941. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
942. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
943. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
944. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
945. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
1275. C₂	C₅₃×#3534	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3534	2
C₂×C₅₃×#562	2
C₂×C₅₃×#560	2
C₂×C₅₃×#553	2
C₂×C₅₃×#551	2
C₂×C₅₃×#546	2
C₂×D₄²×C₅₃	2
C₂×C₅₃×#540	2
C₂×C₅₃×#539	2
C₂×C₅₃×#538	2
C₂×C₅₃×#537	2
C₂×C₅₃×#534	2
C₂×C₅₃×#525	2
C₂²×#123×C₅₃	2
C₂²×#121×C₅₃	2
C₂×#3534	53

Subgroups — C2×C53×#3534 #27270233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3534 #27270233