Subgroups — C₂×C₅₃×#3505 #27270279

Order 13568.

8082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3505	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#553	C₂	1	4	yes	maximal, complemented
3	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₃×#552	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₃×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₅₃×#548	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#539	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#538	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#534	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₃×#529	C₂	1	2	yes	maximal, complemented
12	C₂×C₅₃×#525	C₂	1	2	yes	maximal, complemented
13	C₂²×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#518	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
18	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₅₃	C₂²	1	2	yes	—
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#553	C₂²	1	32	yes	complemented
25	C₅₃×#553	C₂²	1	64	yes	complemented
26	C₅₃×#552	C₂²	1	32	yes	complemented
27	C₅₃×#551	C₂²	1	64	yes	complemented
28	C₅₃×#548	C₂²	1	32	yes	complemented
29	C₅₃×#546	C₂²	1	32	yes	complemented
30	C₅₃×#539	C₂²	1	32	yes	complemented
31	C₅₃×#538	C₂²	1	32	yes	complemented
32	C₅₃×#534	C₂²	1	32	yes	complemented
33	C₅₃×#529	C₂²	1	32	yes	complemented
34	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
35	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
36	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
37	C₂×#125×C₅₃	C₂²	1	4	yes	complemented
38	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
39	C₂×#124×C₅₃	C₂²	1	4	yes	complemented
40	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
41	C₅₃×#525	C₂²	1	32	yes	complemented
42	C₂×#123×C₅₃	C₂²	1	4	yes	—
43	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
44	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
45	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
46	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
47	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
48	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
49	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
50	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
51	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
52	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
53	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	16	yes	complemented
54	C₂×#121×C₅₃	C₂²	1	2	yes	—
55	C₂×#121×C₅₃	C₂²	1	2	yes	—
56	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
57	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
58	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
59	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
60	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
61	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
62	C₂×#121×C₅₃	C₂²	1	16	yes	complemented
63	C₂×#120×C₅₃	C₂²	1	4	yes	—
64	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
65	C₅₃×#518	C₂²	1	32	yes	complemented
66	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
67	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
68	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
69	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
70	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
71	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
72	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
73	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
74	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
75	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
76	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
77	C₂×C₄×D₄×C₅₃	C₂²	1	16	yes	complemented
78	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
79	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
80	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
81	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
85	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
86	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
87	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
88	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
89	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
90	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
91	C₂⁵×C₅₃	C₂³	1	2	yes	—
92	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
93	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×#41×C₅₃	—	4	8	no	—
95	C₂×#41×C₅₃	C₂³	1	16	yes	complemented
96	C₂²×Q₈×C₅₃	—	4	4	no	—
97	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₅₃	C₂³	1	8	yes	complemented
100	C₂²×D₄×C₅₃	—	2	8	no	—
101	C₂²×D₄×C₅₃	—	2	16	no	—
102	C₂²×D₄×C₅₃	—	4	4	no	—
103	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
105	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
108	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₅₃	C₂³	1	16	yes	—
110	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
111	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
112	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
114	C₂³×C₄×C₅₃	—	4	4	no	—
115	C₂³×C₄×C₅₃	—	4	4	no	—
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
129	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
130	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
133	C₂³×C₄×C₅₃	C₂³	1	8	yes	complemented
134	#126×C₅₃	C₂³	1	32	yes	complemented
135	#126×C₅₃	C₂³	1	32	yes	complemented
136	#126×C₅₃	C₂³	1	32	yes	complemented
137	#125×C₅₃	C₂³	1	16	yes	complemented
138	#125×C₅₃	C₂³	1	32	yes	complemented
139	#124×C₅₃	C₂³	1	16	yes	complemented
140	#124×C₅₃	C₂³	1	32	yes	complemented
141	#123×C₅₃	C₂³	1	32	yes	—
142	#123×C₅₃	C₂³	1	32	yes	complemented
143	#123×C₅₃	C₂³	1	32	yes	complemented
144	#123×C₅₃	C₂³	1	32	yes	complemented
145	#123×C₅₃	C₂³	1	32	yes	complemented
146	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
147	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
148	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
149	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	complemented
152	#121×C₅₃	C₂³	1	16	yes	—
153	#121×C₅₃	C₂³	1	16	yes	—
154	#121×C₅₃	C₂³	1	16	yes	complemented
155	#121×C₅₃	C₂³	1	16	yes	complemented
156	#121×C₅₃	C₂³	1	16	yes	complemented
157	#121×C₅₃	C₂³	1	32	yes	complemented
158	#121×C₅₃	C₂³	1	32	yes	complemented
159	#121×C₅₃	C₂³	1	32	yes	complemented
160	#120×C₅₃	C₂³	1	32	yes	—
161	#120×C₅₃	C₂³	1	32	yes	complemented
162	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
163	C₄×D₄×C₅₃	C₂³	1	16	yes	—
164	C₄×D₄×C₅₃	C₂³	1	16	yes	—
165	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
166	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
167	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
168	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
169	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
170	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
171	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
172	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
173	#117×C₅₃	C₂³	1	32	yes	complemented
174	#117×C₅₃	C₂³	1	16	yes	complemented
175	#117×C₅₃	C₂³	1	32	yes	complemented
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
192	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
197	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	—
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
209	C₂×C₂²⋊C₄×C₅₃	C₂³	1	32	yes	complemented
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	complemented
211	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
214	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
215	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
216	C₂⁴×C₅₃	—	2	4	no	—
217	C₂⁴×C₅₃	—	2	8	no	—
218	C₂⁴×C₅₃	—	4	2	no	—
219	C₂⁴×C₅₃	—	4	2	no	—
220	C₂⁴×C₅₃	—	4	2	no	—
221	C₂⁴×C₅₃	—	4	2	no	—
222	C₂⁴×C₅₃	—	4	4	no	—
223	C₂⁴×C₅₃	—	4	4	no	—
224	C₂⁴×C₅₃	#41	1	8	yes	complemented
225	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
226	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
227	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
230	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
231	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
232	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
233	#41×C₅₃	—	4	32	no	—
234	C₂×Q₈×C₅₃	—	2	8	no	—
235	C₂×Q₈×C₅₃	—	4	4	no	—
236	C₂×Q₈×C₅₃	—	4	16	no	—
237	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
238	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
239	C₂×D₄×C₅₃	—	2	8	no	—
240	C₂×D₄×C₅₃	—	2	16	no	—
241	C₂×D₄×C₅₃	—	2	8	no	—
242	C₂×D₄×C₅₃	—	2	16	no	—
243	C₂×D₄×C₅₃	—	2	32	no	—
244	C₂×D₄×C₅₃	—	2	64	no	—
245	C₂×D₄×C₅₃	—	2	8	no	—
246	C₂×D₄×C₅₃	—	4	16	no	—
247	C₂×D₄×C₅₃	—	4	4	no	—
248	C₂×D₄×C₅₃	—	4	8	no	—
249	C₂×D₄×C₅₃	—	4	8	no	—
250	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
251	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
252	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
253	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
254	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
255	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
256	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
257	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
258	C₂²×C₄×C₅₃	—	2	8	no	—
259	C₂²×C₄×C₅₃	—	2	4	no	—
260	C₂²×C₄×C₅₃	—	2	4	no	—
261	C₂²×C₄×C₅₃	—	2	4	no	—
262	C₂²×C₄×C₅₃	—	2	4	no	—
263	C₂²×C₄×C₅₃	—	2	8	no	—
264	C₂²×C₄×C₅₃	—	4	16	no	—
265	C₂²×C₄×C₅₃	—	4	16	no	—
266	C₂²×C₄×C₅₃	—	4	2	no	—
267	C₂²×C₄×C₅₃	—	4	4	no	—
268	C₂²×C₄×C₅₃	—	4	2	no	—
269	C₂²×C₄×C₅₃	—	4	2	no	—
270	C₂²×C₄×C₅₃	—	4	2	no	—
271	C₂²×C₄×C₅₃	—	4	2	no	—
272	C₂²×C₄×C₅₃	—	4	8	no	—
273	C₂²×C₄×C₅₃	—	4	4	no	—
274	C₂²×C₄×C₅₃	—	4	4	no	—
275	C₂²×C₄×C₅₃	—	4	8	no	—
276	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
282	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
295	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
298	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
299	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
312	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
315	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
316	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
317	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
318	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
322	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
323	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
328	C₄²×C₅₃	C₂⁴	1	8	yes	—
329	C₄²×C₅₃	C₂⁴	1	8	yes	—
330	C₄²×C₅₃	C₂⁴	1	16	yes	—
331	C₄²×C₅₃	C₂⁴	1	16	yes	—
332	C₂³×C₅₃	—	2	2	no	—
333	C₂³×C₅₃	—	2	2	no	—
334	C₂³×C₅₃	—	2	2	no	—
335	C₂³×C₅₃	—	2	2	no	—
336	C₂³×C₅₃	—	2	2	no	—
337	C₂³×C₅₃	—	2	2	no	—
338	C₂³×C₅₃	—	2	8	no	—
339	C₂³×C₅₃	—	2	4	no	—
340	C₂³×C₅₃	—	2	8	no	—
341	C₂³×C₅₃	—	2	4	no	—
342	C₂³×C₅₃	—	2	8	no	—
343	C₂³×C₅₃	—	2	8	no	—
344	C₂³×C₅₃	—	2	4	no	—
345	C₂³×C₅₃	—	2	16	no	—
346	C₂³×C₅₃	—	4	4	no	—
347	C₂³×C₅₃	—	4	4	no	—
348	C₂³×C₅₃	—	4	16	no	—
349	C₂³×C₅₃	—	4	4	no	—
350	C₂³×C₅₃	—	4	4	no	—
351	C₂³×C₅₃	—	4	8	no	—
352	C₂³×C₅₃	—	4	8	no	—
353	C₂³×C₅₃	—	4	16	no	—
354	C₂³×C₅₃	—	8	16	no	—
355	C₂³×C₅₃	C₂×#41	1	4	yes	—
356	C₂³×C₅₃	C₂×#41	1	4	yes	—
357	C₂³×C₅₃	C₂×#41	1	4	yes	—
358	C₂³×C₅₃	C₂×#41	1	16	yes	complemented
359	C₂³×C₅₃	C₂⁵	1	4	yes	—
360	C₂³×C₅₃	C₂⁵	1	8	yes	—
361	C₂³×C₅₃	C₂⁵	1	2	yes	—
362	C₂³×C₅₃	C₂⁵	1	2	yes	—
363	C₂³×C₅₃	C₂⁵	1	2	yes	—
364	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
365	Q₈×C₅₃	—	2	16	no	—
366	Q₈×C₅₃	—	4	8	no	—
367	D₄×C₅₃	—	2	16	no	—
368	D₄×C₅₃	—	2	32	no	—
369	D₄×C₅₃	—	2	16	no	—
370	D₄×C₅₃	—	2	32	no	—
371	D₄×C₅₃	—	2	16	no	—
372	D₄×C₅₃	—	4	8	no	—
373	D₄×C₅₃	—	4	16	no	—
374	D₄×C₅₃	—	4	16	no	—
375	C₂×C₄×C₅₃	—	2	16	no	—
376	C₂×C₄×C₅₃	—	2	8	no	—
377	C₂×C₄×C₅₃	—	2	8	no	—
378	C₂×C₄×C₅₃	—	2	4	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	4	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	8	no	—
384	C₂×C₄×C₅₃	—	2	4	no	—
385	C₂×C₄×C₅₃	—	2	8	no	—
386	C₂×C₄×C₅₃	—	2	8	no	—
387	C₂×C₄×C₅₃	—	2	8	no	—
388	C₂×C₄×C₅₃	—	2	8	no	—
389	C₂×C₄×C₅₃	—	2	16	no	—
390	C₂×C₄×C₅₃	—	4	4	no	—
391	C₂×C₄×C₅₃	—	4	8	no	—
392	C₂×C₄×C₅₃	—	4	4	no	—
393	C₂×C₄×C₅₃	—	4	4	no	—
394	C₂×C₄×C₅₃	—	4	4	no	—
395	C₂×C₄×C₅₃	—	4	4	no	—
396	C₂×C₄×C₅₃	—	4	16	no	—
397	C₂×C₄×C₅₃	—	4	8	no	—
398	C₂×C₄×C₅₃	—	4	8	no	—
399	C₂×C₄×C₅₃	—	4	16	no	—
400	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
401	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
402	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
403	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
404	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
405	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
406	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
407	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
408	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
409	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
410	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
411	C₂×#3505	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂²×C₅₃	—	2	2	no	—
413	C₂²×C₅₃	—	2	2	no	—
414	C₂²×C₅₃	—	2	2	no	—
415	C₂²×C₅₃	—	2	2	no	—
416	C₂²×C₅₃	—	2	2	no	—
417	C₂²×C₅₃	—	2	2	no	—
418	C₂²×C₅₃	—	2	8	no	—
419	C₂²×C₅₃	—	2	8	no	—
420	C₂²×C₅₃	—	2	8	no	—
421	C₂²×C₅₃	—	2	4	no	—
422	C₂²×C₅₃	—	2	8	no	—
423	C₂²×C₅₃	—	2	4	no	—
424	C₂²×C₅₃	—	2	8	no	—
425	C₂²×C₅₃	—	2	8	no	—
426	C₂²×C₅₃	—	2	4	no	—
427	C₂²×C₅₃	—	4	16	no	—
428	C₂²×C₅₃	—	4	16	no	—
429	C₂²×C₅₃	—	4	8	no	—
430	C₂²×C₅₃	—	4	16	no	—
431	C₂²×C₅₃	—	8	16	no	—
432	C₂²×C₅₃	C₂²×#41	1	4	yes	—
433	C₂²×C₅₃	C₂²×#41	1	4	yes	—
434	C₂²×C₅₃	C₂²×#41	1	4	yes	—
435	C₂²×C₅₃	C₂²×#41	1	2	yes	—
436	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₂²×C₅₃	#585	1	2	yes	—
438	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
439	C₄×C₅₃	—	2	8	no	—
440	C₄×C₅₃	—	2	4	no	—
441	C₄×C₅₃	—	2	2	no	—
442	C₄×C₅₃	—	2	4	no	—
443	C₄×C₅₃	—	2	2	no	—
444	C₄×C₅₃	—	2	2	no	—
445	C₄×C₅₃	—	2	8	no	—
446	C₄×C₅₃	—	2	4	no	—
447	C₄×C₅₃	—	2	8	no	—
448	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
449	#3505	C₂×C₅₃	1	32	yes	direct product factor
450	C₂×#553	C₂×C₅₃	1	2	yes	complemented
451	C₂×#553	C₂×C₅₃	1	4	yes	complemented
452	C₂×#552	C₂×C₅₃	1	2	yes	complemented
453	C₂×#551	C₂×C₅₃	1	4	yes	complemented
454	C₂×#548	C₂×C₅₃	1	2	yes	complemented
455	C₂×#546	C₂×C₅₃	1	2	yes	complemented
456	C₂×#539	C₂×C₅₃	1	2	yes	complemented
457	C₂×#538	C₂×C₅₃	1	2	yes	complemented
458	C₂×#534	C₂×C₅₃	1	2	yes	complemented
459	C₂×#529	C₂×C₅₃	1	2	yes	complemented
460	C₂×#525	C₂×C₅₃	1	2	yes	complemented
461	C₂²×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
462	C₂²×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
463	C₂×#518	C₂×C₅₃	1	2	yes	complemented
464	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
465	C₂×C₅₃	—	2	4	no	—
466	C₂×C₅₃	—	2	4	no	—
467	C₂×C₅₃	—	2	4	no	—
468	C₂×C₅₃	—	4	4	no	—
469	C₂×C₅₃	—	4	8	no	—
470	C₂×C₅₃	#3505	1	4	yes	direct product factor
471	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
472	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
475	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
476	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
477	C₂³×D₄	C₂²×C₅₃	1	2	yes	—
478	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
479	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
480	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
481	#553	C₂²×C₅₃	1	32	yes	complemented
482	#553	C₂²×C₅₃	1	64	yes	complemented
483	#552	C₂²×C₅₃	1	32	yes	complemented
484	#551	C₂²×C₅₃	1	64	yes	complemented
485	#548	C₂²×C₅₃	1	32	yes	complemented
486	#546	C₂²×C₅₃	1	32	yes	complemented
487	#539	C₂²×C₅₃	1	32	yes	complemented
488	#538	C₂²×C₅₃	1	32	yes	complemented
489	#534	C₂²×C₅₃	1	32	yes	complemented
490	#529	C₂²×C₅₃	1	32	yes	complemented
491	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
492	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
493	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
494	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
495	C₂×#125	C₂²×C₅₃	1	4	yes	complemented
496	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
497	C₂×#124	C₂²×C₅₃	1	4	yes	complemented
498	#525	C₂²×C₅₃	1	32	yes	complemented
499	C₂×#123	C₂²×C₅₃	1	4	yes	—
500	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
501	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
502	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
503	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
504	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
505	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
506	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
507	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
508	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
509	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	complemented
510	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	16	yes	complemented
511	C₂×#121	C₂²×C₅₃	1	2	yes	—
512	C₂×#121	C₂²×C₅₃	1	2	yes	—
513	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
514	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
515	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
516	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
517	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
518	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
519	C₂×#121	C₂²×C₅₃	1	16	yes	complemented
520	C₂×#120	C₂²×C₅₃	1	4	yes	—
521	C₂×#120	C₂²×C₅₃	1	4	yes	complemented
522	#518	C₂²×C₅₃	1	32	yes	complemented
523	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
524	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
525	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
526	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
527	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
528	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
529	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
530	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
531	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
532	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
533	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
534	C₂×C₄×D₄	C₂²×C₅₃	1	16	yes	complemented
535	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
536	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
537	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
538	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
539	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
540	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
541	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
542	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
543	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
544	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
545	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
546	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
547	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
548	C₅₃	C₂×#3505	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁵	C₂³×C₅₃	1	2	yes	—
550	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
551	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
552	C₂×#41	—	4	8	no	—
553	C₂×#41	C₂³×C₅₃	1	16	yes	complemented
554	C₂²×Q₈	—	4	4	no	—
555	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
556	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
557	C₂²×Q₈	C₂³×C₅₃	1	8	yes	complemented
558	C₂²×D₄	—	2	8	no	—
559	C₂²×D₄	—	2	16	no	—
560	C₂²×D₄	—	4	4	no	—
561	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
562	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
563	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
564	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
565	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
566	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
567	C₂²×D₄	C₂³×C₅₃	1	16	yes	—
568	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
569	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
570	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
571	C₂²×D₄	C₂³×C₅₃	1	8	yes	complemented
572	C₂³×C₄	—	4	4	no	—
573	C₂³×C₄	—	4	4	no	—
574	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
575	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
579	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
582	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
584	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
587	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
588	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
590	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
591	C₂³×C₄	C₂³×C₅₃	1	8	yes	complemented
592	#126	C₂³×C₅₃	1	32	yes	complemented
593	#126	C₂³×C₅₃	1	32	yes	complemented
594	#126	C₂³×C₅₃	1	32	yes	complemented
595	#125	C₂³×C₅₃	1	16	yes	complemented
596	#125	C₂³×C₅₃	1	32	yes	complemented
597	#124	C₂³×C₅₃	1	16	yes	complemented
598	#124	C₂³×C₅₃	1	32	yes	complemented
599	#123	C₂³×C₅₃	1	32	yes	—
600	#123	C₂³×C₅₃	1	32	yes	complemented
601	#123	C₂³×C₅₃	1	32	yes	complemented
602	#123	C₂³×C₅₃	1	32	yes	complemented
603	#123	C₂³×C₅₃	1	32	yes	complemented
604	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
605	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
606	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
607	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
608	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
609	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	complemented
610	#121	C₂³×C₅₃	1	16	yes	—
611	#121	C₂³×C₅₃	1	16	yes	—
612	#121	C₂³×C₅₃	1	16	yes	complemented
613	#121	C₂³×C₅₃	1	16	yes	complemented
614	#121	C₂³×C₅₃	1	16	yes	complemented
615	#121	C₂³×C₅₃	1	32	yes	complemented
616	#121	C₂³×C₅₃	1	32	yes	complemented
617	#121	C₂³×C₅₃	1	32	yes	complemented
618	#120	C₂³×C₅₃	1	32	yes	—
619	#120	C₂³×C₅₃	1	32	yes	complemented
620	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
621	C₄×D₄	C₂³×C₅₃	1	16	yes	—
622	C₄×D₄	C₂³×C₅₃	1	16	yes	—
623	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
624	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
625	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
626	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
627	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
628	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
629	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
630	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
631	#117	C₂³×C₅₃	1	32	yes	complemented
632	#117	C₂³×C₅₃	1	16	yes	complemented
633	#117	C₂³×C₅₃	1	32	yes	complemented
634	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
647	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
648	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
649	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	complemented
650	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
667	C₂×C₂²⋊C₄	C₂³×C₅₃	1	32	yes	complemented
668	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	complemented
669	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
671	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
672	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
674	C₂⁴	—	2	4	no	—
675	C₂⁴	—	2	8	no	—
676	C₂⁴	—	4	2	no	—
677	C₂⁴	—	4	2	no	—
678	C₂⁴	—	4	2	no	—
679	C₂⁴	—	4	2	no	—
680	C₂⁴	—	4	4	no	—
681	C₂⁴	—	4	4	no	—
682	C₂⁴	#41×C₅₃	1	8	yes	complemented
683	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
684	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
685	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
686	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
687	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
688	C₂⁴	C₂⁴×C₅₃	1	8	yes	—
689	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
690	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
691	#41	—	4	32	no	—
692	C₂×Q₈	—	2	8	no	—
693	C₂×Q₈	—	4	4	no	—
694	C₂×Q₈	—	4	16	no	—
695	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
696	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	16	no	—
699	C₂×D₄	—	2	8	no	—
700	C₂×D₄	—	2	16	no	—
701	C₂×D₄	—	2	32	no	—
702	C₂×D₄	—	2	64	no	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	4	16	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	8	no	—
707	C₂×D₄	—	4	8	no	—
708	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
709	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
710	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
711	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
712	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
713	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
714	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
715	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
716	C₂²×C₄	—	2	8	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	8	no	—
722	C₂²×C₄	—	4	16	no	—
723	C₂²×C₄	—	4	16	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	8	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	—	4	8	no	—
734	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
743	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
746	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
747	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
749	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
751	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
752	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
753	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
756	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
757	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
758	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
759	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
761	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
762	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
763	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
764	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
765	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
766	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
767	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
769	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
770	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
771	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
774	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
778	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
779	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
780	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
781	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
783	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
784	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
785	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
786	C₄²	C₂⁴×C₅₃	1	8	yes	—
787	C₄²	C₂⁴×C₅₃	1	8	yes	—
788	C₄²	C₂⁴×C₅₃	1	16	yes	—
789	C₄²	C₂⁴×C₅₃	1	16	yes	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	8	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	2	8	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	16	no	—
804	C₂³	—	4	4	no	—
805	C₂³	—	4	4	no	—
806	C₂³	—	4	16	no	—
807	C₂³	—	4	4	no	—
808	C₂³	—	4	4	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	16	no	—
812	C₂³	—	8	16	no	—
813	C₂³	C₂×#41×C₅₃	1	4	yes	—
814	C₂³	C₂×#41×C₅₃	1	4	yes	—
815	C₂³	C₂×#41×C₅₃	1	4	yes	—
816	C₂³	C₂×#41×C₅₃	1	16	yes	complemented
817	C₂³	C₂⁵×C₅₃	1	4	yes	—
818	C₂³	C₂⁵×C₅₃	1	8	yes	—
819	C₂³	C₂⁵×C₅₃	1	2	yes	—
820	C₂³	C₂⁵×C₅₃	1	2	yes	—
821	C₂³	C₂⁵×C₅₃	1	2	yes	—
822	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
823	Q₈	—	2	16	no	—
824	Q₈	—	4	8	no	—
825	D₄	—	2	16	no	—
826	D₄	—	2	32	no	—
827	D₄	—	2	16	no	—
828	D₄	—	2	32	no	—
829	D₄	—	2	16	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	16	no	—
832	D₄	—	4	16	no	—
833	C₂×C₄	—	2	16	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	8	no	—
847	C₂×C₄	—	2	16	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	16	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	4	16	no	—
858	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
859	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
860	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
861	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
862	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
863	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
864	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
865	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
866	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
867	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
868	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
869	C₂²	—	2	8	no	—
870	C₂²	—	2	8	no	—
871	C₂²	—	2	8	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	4	16	no	—
885	C₂²	—	4	16	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	4	16	no	—
888	C₂²	—	8	16	no	—
889	C₂²	C₂²×#41×C₅₃	1	4	yes	—
890	C₂²	C₂²×#41×C₅₃	1	4	yes	—
891	C₂²	C₂²×#41×C₅₃	1	4	yes	—
892	C₂²	C₂²×#41×C₅₃	1	2	yes	—
893	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
894	C₂²	C₅₃×#585	1	2	yes	—
895	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
896	C₄	—	2	8	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	8	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	8	no	—
905	C₄	C₂×H(5,𝔽₂)×C₅₃	1	4	yes	—
906	C₂	—	2	4	no	—
907	C₂	—	2	4	no	—
908	C₂	—	2	4	no	—
909	C₂	—	4	4	no	—
910	C₂	—	4	8	no	—
911	C₂	C₅₃×#3505	1	4	yes	direct product factor
912	C₂	C₂³×#41×C₅₃	1	1	yes	characteristic
913	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
914	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×#3505	C₂	direct (N × H)
2. C₂×C₅₃×#553	C₂	semidirect
3. C₂×C₅₃×#553	C₂	semidirect
4. C₂×C₅₃×#552	C₂	semidirect
5. C₂×C₅₃×#551	C₂	semidirect
6. C₂×C₅₃×#548	C₂	semidirect
7. C₂×C₅₃×#546	C₂	semidirect
8. C₂×C₅₃×#539	C₂	semidirect
9. C₂×C₅₃×#538	C₂	semidirect
10. C₂×C₅₃×#534	C₂	semidirect
11. C₂×C₅₃×#529	C₂	semidirect
12. C₂×C₅₃×#525	C₂	semidirect
13. C₂²×C₂²⋊Q₈×C₅₃	C₂	semidirect
14. C₂²×#121×C₅₃	C₂	semidirect
15. C₂×C₅₃×#518	C₂	semidirect
16. C₂²×C₄×D₄×C₅₃	C₂	semidirect
17. C₂²×#41×C₅₃	C₂²	semidirect
18. C₂³×Q₈×C₅₃	C₂²	semidirect
21. C₂³×D₄×C₅₃	C₂²	semidirect
23. C₂⁴×C₄×C₅₃	C₂²	semidirect
24. C₅₃×#553	C₂²	semidirect
25. C₅₃×#553	C₂²	semidirect
26. C₅₃×#552	C₂²	semidirect
27. C₅₃×#551	C₂²	semidirect
28. C₅₃×#548	C₂²	semidirect
29. C₅₃×#546	C₂²	semidirect
30. C₅₃×#539	C₂²	semidirect
31. C₅₃×#538	C₂²	semidirect
32. C₅₃×#534	C₂²	semidirect
33. C₅₃×#529	C₂²	semidirect
34. C₂×#126×C₅₃	C₂²	semidirect
35. C₂×#126×C₅₃	C₂²	semidirect
36. C₂×#126×C₅₃	C₂²	semidirect
37. C₂×#125×C₅₃	C₂²	semidirect
38. C₂×#125×C₅₃	C₂²	semidirect
39. C₂×#124×C₅₃	C₂²	semidirect
40. C₂×#124×C₅₃	C₂²	semidirect
41. C₅₃×#525	C₂²	semidirect
43. C₂×#123×C₅₃	C₂²	semidirect
44. C₂×#123×C₅₃	C₂²	semidirect
45. C₂×#123×C₅₃	C₂²	semidirect
46. C₂×#123×C₅₃	C₂²	semidirect
47. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
48. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
49. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
50. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
51. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
56. C₂×#121×C₅₃	C₂²	semidirect
57. C₂×#121×C₅₃	C₂²	semidirect
58. C₂×#121×C₅₃	C₂²	semidirect
59. C₂×#121×C₅₃	C₂²	semidirect
60. C₂×#121×C₅₃	C₂²	semidirect
61. C₂×#121×C₅₃	C₂²	semidirect
62. C₂×#121×C₅₃	C₂²	semidirect
64. C₂×#120×C₅₃	C₂²	semidirect
65. C₅₃×#518	C₂²	semidirect
66. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
69. C₂×C₄×D₄×C₅₃	C₂²	semidirect
70. C₂×C₄×D₄×C₅₃	C₂²	semidirect
71. C₂×C₄×D₄×C₅₃	C₂²	semidirect
72. C₂×C₄×D₄×C₅₃	C₂²	semidirect
73. C₂×C₄×D₄×C₅₃	C₂²	semidirect
74. C₂×C₄×D₄×C₅₃	C₂²	semidirect
75. C₂×C₄×D₄×C₅₃	C₂²	semidirect
76. C₂×C₄×D₄×C₅₃	C₂²	semidirect
77. C₂×C₄×D₄×C₅₃	C₂²	semidirect
78. C₂×#117×C₅₃	C₂²	semidirect
79. C₂×#117×C₅₃	C₂²	semidirect
80. C₂×#117×C₅₃	C₂²	semidirect
81. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
82. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
83. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
84. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
87. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
88. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
89. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
90. C₂²×C₄²×C₅₃	C₂²	semidirect
95. C₂×#41×C₅₃	C₂³	semidirect
99. C₂²×Q₈×C₅₃	C₂³	semidirect
113. C₂²×D₄×C₅₃	C₂³	semidirect
133. C₂³×C₄×C₅₃	C₂³	semidirect
134. #126×C₅₃	C₂³	semidirect
135. #126×C₅₃	C₂³	semidirect
136. #126×C₅₃	C₂³	semidirect
137. #125×C₅₃	C₂³	semidirect
138. #125×C₅₃	C₂³	semidirect
139. #124×C₅₃	C₂³	semidirect
140. #124×C₅₃	C₂³	semidirect
142. #123×C₅₃	C₂³	semidirect
143. #123×C₅₃	C₂³	semidirect
144. #123×C₅₃	C₂³	semidirect
145. #123×C₅₃	C₂³	semidirect
146. C₂²⋊Q₈×C₅₃	C₂³	semidirect
147. C₂²⋊Q₈×C₅₃	C₂³	semidirect
148. C₂²⋊Q₈×C₅₃	C₂³	semidirect
149. C₂²⋊Q₈×C₅₃	C₂³	semidirect
150. C₂²⋊Q₈×C₅₃	C₂³	semidirect
151. C₂²⋊Q₈×C₅₃	C₂³	semidirect
154. #121×C₅₃	C₂³	semidirect
155. #121×C₅₃	C₂³	semidirect
156. #121×C₅₃	C₂³	semidirect
157. #121×C₅₃	C₂³	semidirect
158. #121×C₅₃	C₂³	semidirect
159. #121×C₅₃	C₂³	semidirect
161. #120×C₅₃	C₂³	semidirect
162. C₄×Q₈×C₅₃	C₂³	semidirect
165. C₄×D₄×C₅₃	C₂³	semidirect
166. C₄×D₄×C₅₃	C₂³	semidirect
167. C₄×D₄×C₅₃	C₂³	semidirect
168. C₄×D₄×C₅₃	C₂³	semidirect
169. C₄×D₄×C₅₃	C₂³	semidirect
170. C₄×D₄×C₅₃	C₂³	semidirect
171. C₄×D₄×C₅₃	C₂³	semidirect
172. C₄×D₄×C₅₃	C₂³	semidirect
173. #117×C₅₃	C₂³	semidirect
174. #117×C₅₃	C₂³	semidirect
175. #117×C₅₃	C₂³	semidirect
188. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
189. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
190. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
191. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
208. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
209. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
210. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
215. C₂×C₄²×C₅₃	C₂³	semidirect
224. C₂⁴×C₅₃	#41	semidirect
358. C₂³×C₅₃	C₂×#41	semidirect
411. C₂×#3505	C₅₃	direct (N × H)
449. #3505	C₂×C₅₃	direct (N × H)
450. C₂×#553	C₂×C₅₃	semidirect
451. C₂×#553	C₂×C₅₃	semidirect
452. C₂×#552	C₂×C₅₃	semidirect
453. C₂×#551	C₂×C₅₃	semidirect
454. C₂×#548	C₂×C₅₃	semidirect
455. C₂×#546	C₂×C₅₃	semidirect
456. C₂×#539	C₂×C₅₃	semidirect
457. C₂×#538	C₂×C₅₃	semidirect
458. C₂×#534	C₂×C₅₃	semidirect
459. C₂×#529	C₂×C₅₃	semidirect
460. C₂×#525	C₂×C₅₃	semidirect
461. C₂²×C₂²⋊Q₈	C₂×C₅₃	semidirect
462. C₂²×#121	C₂×C₅₃	semidirect
463. C₂×#518	C₂×C₅₃	semidirect
464. C₂²×C₄×D₄	C₂×C₅₃	semidirect
470. C₂×C₅₃	#3505	direct (N × H)
474. C₂²×#41	C₂²×C₅₃	semidirect
475. C₂³×Q₈	C₂²×C₅₃	semidirect
478. C₂³×D₄	C₂²×C₅₃	semidirect
480. C₂⁴×C₄	C₂²×C₅₃	semidirect
481. #553	C₂²×C₅₃	semidirect
482. #553	C₂²×C₅₃	semidirect
483. #552	C₂²×C₅₃	semidirect
484. #551	C₂²×C₅₃	semidirect
485. #548	C₂²×C₅₃	semidirect
486. #546	C₂²×C₅₃	semidirect
487. #539	C₂²×C₅₃	semidirect
488. #538	C₂²×C₅₃	semidirect
489. #534	C₂²×C₅₃	semidirect
490. #529	C₂²×C₅₃	semidirect
491. C₂×#126	C₂²×C₅₃	semidirect
492. C₂×#126	C₂²×C₅₃	semidirect
493. C₂×#126	C₂²×C₅₃	semidirect
494. C₂×#125	C₂²×C₅₃	semidirect
495. C₂×#125	C₂²×C₅₃	semidirect
496. C₂×#124	C₂²×C₅₃	semidirect
497. C₂×#124	C₂²×C₅₃	semidirect
498. #525	C₂²×C₅₃	semidirect
500. C₂×#123	C₂²×C₅₃	semidirect
501. C₂×#123	C₂²×C₅₃	semidirect
502. C₂×#123	C₂²×C₅₃	semidirect
503. C₂×#123	C₂²×C₅₃	semidirect
504. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
505. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
506. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
507. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
508. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
509. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
510. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
513. C₂×#121	C₂²×C₅₃	semidirect
514. C₂×#121	C₂²×C₅₃	semidirect
515. C₂×#121	C₂²×C₅₃	semidirect
516. C₂×#121	C₂²×C₅₃	semidirect
517. C₂×#121	C₂²×C₅₃	semidirect
518. C₂×#121	C₂²×C₅₃	semidirect
519. C₂×#121	C₂²×C₅₃	semidirect
521. C₂×#120	C₂²×C₅₃	semidirect
522. #518	C₂²×C₅₃	semidirect
523. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
526. C₂×C₄×D₄	C₂²×C₅₃	semidirect
527. C₂×C₄×D₄	C₂²×C₅₃	semidirect
528. C₂×C₄×D₄	C₂²×C₅₃	semidirect
529. C₂×C₄×D₄	C₂²×C₅₃	semidirect
530. C₂×C₄×D₄	C₂²×C₅₃	semidirect
531. C₂×C₄×D₄	C₂²×C₅₃	semidirect
532. C₂×C₄×D₄	C₂²×C₅₃	semidirect
533. C₂×C₄×D₄	C₂²×C₅₃	semidirect
534. C₂×C₄×D₄	C₂²×C₅₃	semidirect
535. C₂×#117	C₂²×C₅₃	semidirect
536. C₂×#117	C₂²×C₅₃	semidirect
537. C₂×#117	C₂²×C₅₃	semidirect
538. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
539. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
540. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
541. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
544. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
545. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
546. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
547. C₂²×C₄²	C₂²×C₅₃	semidirect
548. C₅₃	C₂×#3505	direct (N × H)
553. C₂×#41	C₂³×C₅₃	semidirect
557. C₂²×Q₈	C₂³×C₅₃	semidirect
571. C₂²×D₄	C₂³×C₅₃	semidirect
591. C₂³×C₄	C₂³×C₅₃	semidirect
592. #126	C₂³×C₅₃	semidirect
593. #126	C₂³×C₅₃	semidirect
594. #126	C₂³×C₅₃	semidirect
595. #125	C₂³×C₅₃	semidirect
596. #125	C₂³×C₅₃	semidirect
597. #124	C₂³×C₅₃	semidirect
598. #124	C₂³×C₅₃	semidirect
600. #123	C₂³×C₅₃	semidirect
601. #123	C₂³×C₅₃	semidirect
602. #123	C₂³×C₅₃	semidirect
603. #123	C₂³×C₅₃	semidirect
604. C₂²⋊Q₈	C₂³×C₅₃	semidirect
605. C₂²⋊Q₈	C₂³×C₅₃	semidirect
606. C₂²⋊Q₈	C₂³×C₅₃	semidirect
607. C₂²⋊Q₈	C₂³×C₅₃	semidirect
608. C₂²⋊Q₈	C₂³×C₅₃	semidirect
609. C₂²⋊Q₈	C₂³×C₅₃	semidirect
612. #121	C₂³×C₅₃	semidirect
613. #121	C₂³×C₅₃	semidirect
614. #121	C₂³×C₅₃	semidirect
615. #121	C₂³×C₅₃	semidirect
616. #121	C₂³×C₅₃	semidirect
617. #121	C₂³×C₅₃	semidirect
619. #120	C₂³×C₅₃	semidirect
620. C₄×Q₈	C₂³×C₅₃	semidirect
623. C₄×D₄	C₂³×C₅₃	semidirect
624. C₄×D₄	C₂³×C₅₃	semidirect
625. C₄×D₄	C₂³×C₅₃	semidirect
626. C₄×D₄	C₂³×C₅₃	semidirect
627. C₄×D₄	C₂³×C₅₃	semidirect
628. C₄×D₄	C₂³×C₅₃	semidirect
629. C₄×D₄	C₂³×C₅₃	semidirect
630. C₄×D₄	C₂³×C₅₃	semidirect
631. #117	C₂³×C₅₃	semidirect
632. #117	C₂³×C₅₃	semidirect
633. #117	C₂³×C₅₃	semidirect
646. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
647. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
648. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
649. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
666. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
667. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
668. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
673. C₂×C₄²	C₂³×C₅₃	semidirect
682. C₂⁴	#41×C₅₃	semidirect
816. C₂³	C₂×#41×C₅₃	semidirect
911. C₂	C₅₃×#3505	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×#3505	2
C₂×C₅₃×#553	2
C₂×C₅₃×#552	2
C₂×C₅₃×#551	2
C₂×C₅₃×#548	2
C₂×C₅₃×#546	2
C₂×C₅₃×#539	2
C₂×C₅₃×#538	2
C₂×C₅₃×#534	2
C₂×C₅₃×#529	2
C₂×C₅₃×#525	2
C₂²×C₂²⋊Q₈×C₅₃	2
C₂²×#121×C₅₃	2
C₂×C₅₃×#518	2
C₂²×C₄×D₄×C₅₃	2
C₂×#3505	53

Subgroups — C2×C53×#3505 #27270279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3505 #27270279