Subgroups — C₂×C₅₃×#3494 #27270309

Order 13568.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#555	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₃×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₅₃×#547	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#546	C₂	1	4	yes	maximal, complemented
8	C₂×C₅₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#532	C₂	1	2	yes	maximal, complemented
13	C₂×C₅₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₅₃	C₂²	1	4	yes	complemented
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₅₃	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#555	C₂²	1	32	yes	complemented
25	C₅₃×#553	C₂²	1	32	yes	complemented
26	C₅₃×#553	C₂²	1	32	yes	complemented
27	C₅₃×#551	C₂²	1	64	yes	complemented
28	C₅₃×#547	C₂²	1	32	yes	complemented
29	C₅₃×#546	C₂²	1	64	yes	complemented
30	C₅₃×#544	C₂²	1	16	yes	complemented
31	C₅₃×#542	C₂²	1	32	yes	complemented
32	C₅₃×#540	C₂²	1	32	yes	complemented
33	C₅₃×#535	C₂²	1	16	yes	complemented
34	C₅₃×#532	C₂²	1	32	yes	complemented
35	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
36	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
37	C₂×#127×C₅₃	C₂²	1	2	yes	complemented
38	C₅₃×#529	C₂²	1	32	yes	complemented
39	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
40	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
41	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
42	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
43	C₂×#124×C₅₃	C₂²	1	4	yes	complemented
44	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
45	C₂×#124×C₅₃	C₂²	1	4	yes	complemented
46	C₅₃×#525	C₂²	1	16	yes	complemented
47	C₂×#123×C₅₃	C₂²	1	2	yes	—
48	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
49	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
50	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
51	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
52	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
53	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
55	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×#121×C₅₃	C₂²	1	2	yes	—
57	C₂×#121×C₅₃	C₂²	1	2	yes	—
58	C₂×#121×C₅₃	C₂²	1	2	yes	—
59	C₂×#121×C₅₃	C₂²	1	2	yes	—
60	C₂×#121×C₅₃	C₂²	1	16	yes	complemented
61	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
63	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
64	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
65	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
66	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
67	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#120×C₅₃	C₂²	1	2	yes	—
69	C₂×#120×C₅₃	C₂²	1	4	yes	—
70	C₅₃×#520	C₂²	1	16	yes	complemented
71	C₅₃×#518	C₂²	1	16	yes	complemented
72	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
73	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
74	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
75	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
76	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
78	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
79	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
83	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
84	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
85	C₂×#117×C₅₃	C₂²	1	2	yes	—
86	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
87	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
88	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
89	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
90	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
91	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#117×C₅₃	C₂²	1	16	yes	complemented
93	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
96	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
97	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
98	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
99	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
101	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
102	C₂⁵×C₅₃	C₂³	1	2	yes	—
103	C₂×#41×C₅₃	—	2	8	no	—
104	C₂×#41×C₅₃	—	4	16	no	—
105	C₂×#41×C₅₃	C₂³	1	8	yes	—
106	C₂×#41×C₅₃	C₂³	1	32	yes	complemented
107	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
109	C₂²×D₄×C₅₃	—	2	8	no	—
110	C₂²×D₄×C₅₃	—	4	8	no	—
111	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
118	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
120	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
121	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
122	C₂²×D₄×C₅₃	C₂³	1	16	yes	—
123	C₂³×C₄×C₅₃	—	2	8	no	—
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	2	yes	—
129	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
132	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
135	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
136	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
137	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
139	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
140	#127×C₅₃	C₂³	1	16	yes	complemented
141	#126×C₅₃	C₂³	1	32	yes	complemented
142	#126×C₅₃	C₂³	1	32	yes	complemented
143	#125×C₅₃	C₂³	1	16	yes	complemented
144	#125×C₅₃	C₂³	1	16	yes	complemented
145	#124×C₅₃	C₂³	1	16	yes	complemented
146	#124×C₅₃	C₂³	1	32	yes	complemented
147	#124×C₅₃	C₂³	1	32	yes	complemented
148	#123×C₅₃	C₂³	1	16	yes	—
149	#123×C₅₃	C₂³	1	32	yes	complemented
150	#123×C₅₃	C₂³	1	32	yes	complemented
151	#123×C₅₃	C₂³	1	32	yes	complemented
152	#123×C₅₃	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
155	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
156	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	complemented
157	#121×C₅₃	C₂³	1	16	yes	—
158	#121×C₅₃	C₂³	1	16	yes	—
159	#121×C₅₃	C₂³	1	16	yes	—
160	#121×C₅₃	C₂³	1	16	yes	—
161	#121×C₅₃	C₂³	1	8	yes	complemented
162	#121×C₅₃	C₂³	1	8	yes	complemented
163	#121×C₅₃	C₂³	1	32	yes	complemented
164	#121×C₅₃	C₂³	1	16	yes	complemented
165	#121×C₅₃	C₂³	1	16	yes	complemented
166	#121×C₅₃	C₂³	1	32	yes	complemented
167	#121×C₅₃	C₂³	1	32	yes	complemented
168	#120×C₅₃	C₂³	1	16	yes	—
169	#120×C₅₃	C₂³	1	32	yes	—
170	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
171	C₄×D₄×C₅₃	C₂³	1	32	yes	—
172	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
173	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
174	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
175	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
176	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
177	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
178	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
179	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
180	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
181	#117×C₅₃	C₂³	1	8	yes	—
182	#117×C₅₃	C₂³	1	8	yes	—
183	#117×C₅₃	C₂³	1	16	yes	—
184	#117×C₅₃	C₂³	1	8	yes	—
185	#117×C₅₃	C₂³	1	16	yes	complemented
186	#117×C₅₃	C₂³	1	8	yes	complemented
187	#117×C₅₃	C₂³	1	8	yes	complemented
188	#117×C₅₃	C₂³	1	16	yes	complemented
189	#117×C₅₃	C₂³	1	32	yes	complemented
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
209	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	—
216	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₅₃	C₂³	1	32	yes	—
220	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	—
222	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
234	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
235	C₂×C₄²×C₅₃	C₂³	1	16	yes	complemented
236	C₂⁴×C₅₃	—	2	4	no	—
237	C₂⁴×C₅₃	—	2	4	no	—
238	C₂⁴×C₅₃	—	2	8	no	—
239	C₂⁴×C₅₃	—	4	2	no	—
240	C₂⁴×C₅₃	—	4	4	no	—
241	C₂⁴×C₅₃	—	4	4	no	—
242	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
244	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
245	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
246	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
249	#41×C₅₃	—	2	32	no	—
250	#41×C₅₃	—	4	64	no	—
251	C₂×Q₈×C₅₃	—	2	4	no	—
252	C₂×Q₈×C₅₃	—	4	8	no	—
253	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₅₃	C₂⁴	1	16	yes	—
255	C₂×D₄×C₅₃	—	2	8	no	—
256	C₂×D₄×C₅₃	—	2	16	no	—
257	C₂×D₄×C₅₃	—	2	8	no	—
258	C₂×D₄×C₅₃	—	2	8	no	—
259	C₂×D₄×C₅₃	—	2	8	no	—
260	C₂×D₄×C₅₃	—	2	4	no	—
261	C₂×D₄×C₅₃	—	2	32	no	—
262	C₂×D₄×C₅₃	—	4	8	no	—
263	C₂×D₄×C₅₃	—	4	4	no	—
264	C₂×D₄×C₅₃	—	4	8	no	—
265	C₂×D₄×C₅₃	—	4	8	no	—
266	C₂×D₄×C₅₃	—	4	32	no	—
267	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
268	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
269	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
270	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
271	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
272	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
273	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
274	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
275	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
276	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
277	C₂²×C₄×C₅₃	—	2	4	no	—
278	C₂²×C₄×C₅₃	—	2	8	no	—
279	C₂²×C₄×C₅₃	—	2	4	no	—
280	C₂²×C₄×C₅₃	—	2	4	no	—
281	C₂²×C₄×C₅₃	—	2	4	no	—
282	C₂²×C₄×C₅₃	—	2	4	no	—
283	C₂²×C₄×C₅₃	—	2	8	no	—
284	C₂²×C₄×C₅₃	—	2	32	no	—
285	C₂²×C₄×C₅₃	—	4	8	no	—
286	C₂²×C₄×C₅₃	—	4	4	no	—
287	C₂²×C₄×C₅₃	—	4	4	no	—
288	C₂²×C₄×C₅₃	—	4	8	no	—
289	C₂²×C₄×C₅₃	—	4	8	no	—
290	C₂²×C₄×C₅₃	#41	1	8	yes	complemented
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	4	yes	—
295	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
296	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
307	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
311	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
312	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
321	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
322	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
323	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
325	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
329	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
331	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
334	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
338	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
339	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
340	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
342	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
343	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
344	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
345	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
348	C₄²×C₅₃	C₂⁴	1	8	yes	—
349	C₄²×C₅₃	C₂⁴	1	8	yes	—
350	C₄²×C₅₃	C₂⁴	1	8	yes	—
351	C₄²×C₅₃	C₂⁴	1	8	yes	—
352	C₄²×C₅₃	C₂⁴	1	8	yes	—
353	C₄²×C₅₃	C₂⁴	1	16	yes	—
354	C₂³×C₅₃	—	2	2	no	—
355	C₂³×C₅₃	—	2	2	no	—
356	C₂³×C₅₃	—	2	2	no	—
357	C₂³×C₅₃	—	2	2	no	—
358	C₂³×C₅₃	—	2	8	no	—
359	C₂³×C₅₃	—	2	2	no	—
360	C₂³×C₅₃	—	2	4	no	—
361	C₂³×C₅₃	—	2	8	no	—
362	C₂³×C₅₃	—	2	4	no	—
363	C₂³×C₅₃	—	2	8	no	—
364	C₂³×C₅₃	—	2	8	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	2	8	no	—
367	C₂³×C₅₃	—	2	4	no	—
368	C₂³×C₅₃	—	2	2	no	—
369	C₂³×C₅₃	—	2	16	no	—
370	C₂³×C₅₃	—	4	4	no	—
371	C₂³×C₅₃	—	4	8	no	—
372	C₂³×C₅₃	—	4	8	no	—
373	C₂³×C₅₃	—	4	16	no	—
374	C₂³×C₅₃	—	8	16	no	—
375	C₂³×C₅₃	C₂×#41	1	4	yes	—
376	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
377	C₂³×C₅₃	C₂⁵	1	4	yes	—
378	C₂³×C₅₃	C₂⁵	1	2	yes	—
379	C₂³×C₅₃	C₂⁵	1	8	yes	—
380	C₂³×C₅₃	C₂⁵	1	2	yes	—
381	C₂³×C₅₃	C₂⁵	1	2	yes	—
382	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
383	Q₈×C₅₃	—	2	8	no	—
384	Q₈×C₅₃	—	4	16	no	—
385	D₄×C₅₃	—	2	16	no	—
386	D₄×C₅₃	—	2	32	no	—
387	D₄×C₅₃	—	2	16	no	—
388	D₄×C₅₃	—	2	16	no	—
389	D₄×C₅₃	—	2	16	no	—
390	D₄×C₅₃	—	2	8	no	—
391	D₄×C₅₃	—	4	16	no	—
392	D₄×C₅₃	—	4	8	no	—
393	D₄×C₅₃	—	4	16	no	—
394	D₄×C₅₃	—	4	16	no	—
395	C₂×C₄×C₅₃	—	2	8	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	2	2	no	—
398	C₂×C₄×C₅₃	—	2	4	no	—
399	C₂×C₄×C₅₃	—	2	4	no	—
400	C₂×C₄×C₅₃	—	2	4	no	—
401	C₂×C₄×C₅₃	—	2	16	no	—
402	C₂×C₄×C₅₃	—	2	8	no	—
403	C₂×C₄×C₅₃	—	2	4	no	—
404	C₂×C₄×C₅₃	—	2	4	no	—
405	C₂×C₄×C₅₃	—	2	4	no	—
406	C₂×C₄×C₅₃	—	2	4	no	—
407	C₂×C₄×C₅₃	—	2	8	no	—
408	C₂×C₄×C₅₃	—	2	8	no	—
409	C₂×C₄×C₅₃	—	2	8	no	—
410	C₂×C₄×C₅₃	—	2	8	no	—
411	C₂×C₄×C₅₃	—	2	16	no	—
412	C₂×C₄×C₅₃	—	4	16	no	—
413	C₂×C₄×C₅₃	—	4	8	no	—
414	C₂×C₄×C₅₃	—	4	8	no	—
415	C₂×C₄×C₅₃	—	4	16	no	—
416	C₂×C₄×C₅₃	—	4	16	no	—
417	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
418	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
419	C₂×C₄×C₅₃	C₂×#41	1	16	yes	complemented
420	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
421	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
422	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
423	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
424	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
425	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
426	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
427	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
428	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
429	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
430	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
431	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
432	C₂×#3494	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
433	C₂²×C₅₃	—	2	2	no	—
434	C₂²×C₅₃	—	2	2	no	—
435	C₂²×C₅₃	—	2	2	no	—
436	C₂²×C₅₃	—	2	2	no	—
437	C₂²×C₅₃	—	2	8	no	—
438	C₂²×C₅₃	—	2	8	no	—
439	C₂²×C₅₃	—	2	2	no	—
440	C₂²×C₅₃	—	2	4	no	—
441	C₂²×C₅₃	—	2	8	no	—
442	C₂²×C₅₃	—	2	4	no	—
443	C₂²×C₅₃	—	2	8	no	—
444	C₂²×C₅₃	—	2	2	no	—
445	C₂²×C₅₃	—	2	8	no	—
446	C₂²×C₅₃	—	2	4	no	—
447	C₂²×C₅₃	—	2	2	no	—
448	C₂²×C₅₃	—	4	16	no	—
449	C₂²×C₅₃	—	4	8	no	—
450	C₂²×C₅₃	—	4	4	no	—
451	C₂²×C₅₃	—	4	16	no	—
452	C₂²×C₅₃	—	8	16	no	—
453	C₂²×C₅₃	C₂²×#41	1	4	yes	—
454	C₂²×C₅₃	C₂²×#41	1	2	yes	—
455	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
456	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²×C₅₃	#585	1	2	yes	—
458	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
459	C₄×C₅₃	—	2	2	no	—
460	C₄×C₅₃	—	2	2	no	—
461	C₄×C₅₃	—	2	4	no	—
462	C₄×C₅₃	—	2	4	no	—
463	C₄×C₅₃	—	2	4	no	—
464	C₄×C₅₃	—	2	8	no	—
465	C₄×C₅₃	—	2	4	no	—
466	C₄×C₅₃	—	2	4	no	—
467	C₄×C₅₃	—	2	4	no	—
468	C₄×C₅₃	—	2	4	no	—
469	C₄×C₅₃	C₂²×#41	1	4	yes	—
470	C₄×C₅₃	C₂²×#41	1	4	yes	—
471	#3494	C₂×C₅₃	1	32	yes	direct product factor
472	C₂×#555	C₂×C₅₃	1	2	yes	complemented
473	C₂×#553	C₂×C₅₃	1	2	yes	complemented
474	C₂×#553	C₂×C₅₃	1	2	yes	complemented
475	C₂×#551	C₂×C₅₃	1	4	yes	complemented
476	C₂×#547	C₂×C₅₃	1	2	yes	complemented
477	C₂×#546	C₂×C₅₃	1	4	yes	complemented
478	C₂×#544	C₂×C₅₃	1	1	yes	characteristic, complemented
479	C₂×#542	C₂×C₅₃	1	2	yes	complemented
480	C₂×#540	C₂×C₅₃	1	2	yes	complemented
481	C₂×#535	C₂×C₅₃	1	1	yes	characteristic, complemented
482	C₂×#532	C₂×C₅₃	1	2	yes	complemented
483	C₂×#529	C₂×C₅₃	1	2	yes	complemented
484	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
485	C₂²×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
486	C₂×#520	C₂×C₅₃	1	1	yes	characteristic, complemented
487	C₂×#518	C₂×C₅₃	1	1	yes	characteristic, complemented
488	C₂²×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
489	C₂×C₅₃	—	2	4	no	—
490	C₂×C₅₃	—	2	4	no	—
491	C₂×C₅₃	—	4	4	no	—
492	C₂×C₅₃	—	4	2	no	—
493	C₂×C₅₃	—	4	8	no	—
494	C₂×C₅₃	#3494	1	4	yes	direct product factor
495	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
496	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
498	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
499	C₂²×#41	C₂²×C₅₃	1	4	yes	complemented
500	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
501	C₂³×D₄	C₂²×C₅₃	1	2	yes	—
502	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
503	#555	C₂²×C₅₃	1	32	yes	complemented
504	#553	C₂²×C₅₃	1	32	yes	complemented
505	#553	C₂²×C₅₃	1	32	yes	complemented
506	#551	C₂²×C₅₃	1	64	yes	complemented
507	#547	C₂²×C₅₃	1	32	yes	complemented
508	#546	C₂²×C₅₃	1	64	yes	complemented
509	#544	C₂²×C₅₃	1	16	yes	complemented
510	#542	C₂²×C₅₃	1	32	yes	complemented
511	#540	C₂²×C₅₃	1	32	yes	complemented
512	#535	C₂²×C₅₃	1	16	yes	complemented
513	#532	C₂²×C₅₃	1	32	yes	complemented
514	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
515	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
516	C₂×#127	C₂²×C₅₃	1	2	yes	complemented
517	#529	C₂²×C₅₃	1	32	yes	complemented
518	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
519	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
520	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
521	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
522	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
523	C₂×#124	C₂²×C₅₃	1	4	yes	complemented
524	C₂×#124	C₂²×C₅₃	1	4	yes	complemented
525	#525	C₂²×C₅₃	1	16	yes	complemented
526	C₂×#123	C₂²×C₅₃	1	2	yes	—
527	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
528	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
529	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
530	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
531	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
532	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
533	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
534	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	complemented
535	C₂×#121	C₂²×C₅₃	1	2	yes	—
536	C₂×#121	C₂²×C₅₃	1	2	yes	—
537	C₂×#121	C₂²×C₅₃	1	2	yes	—
538	C₂×#121	C₂²×C₅₃	1	2	yes	—
539	C₂×#121	C₂²×C₅₃	1	16	yes	complemented
540	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
541	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
542	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
543	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
544	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
545	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
546	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
547	C₂×#120	C₂²×C₅₃	1	2	yes	—
548	C₂×#120	C₂²×C₅₃	1	4	yes	—
549	#520	C₂²×C₅₃	1	16	yes	complemented
550	#518	C₂²×C₅₃	1	16	yes	complemented
551	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
552	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
553	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
554	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
555	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
556	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
557	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
558	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
559	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
560	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
561	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
562	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
563	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
564	C₂×#117	C₂²×C₅₃	1	2	yes	—
565	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
566	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
567	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
568	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
569	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
570	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
571	C₂×#117	C₂²×C₅₃	1	16	yes	complemented
572	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
573	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
574	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
575	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
576	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
577	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
578	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
579	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
580	C₅₃	C₂×#3494	1	1	yes	characteristic, direct product factor, Sylow
581	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
582	C₂⁵	C₂³×C₅₃	1	2	yes	—
583	C₂×#41	—	2	8	no	—
584	C₂×#41	—	4	16	no	—
585	C₂×#41	C₂³×C₅₃	1	8	yes	—
586	C₂×#41	C₂³×C₅₃	1	32	yes	complemented
587	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
588	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
589	C₂²×D₄	—	2	8	no	—
590	C₂²×D₄	—	4	8	no	—
591	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
592	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
593	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
594	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
596	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
597	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
598	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
599	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
600	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
601	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
602	C₂²×D₄	C₂³×C₅₃	1	16	yes	—
603	C₂³×C₄	—	2	8	no	—
604	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
606	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
608	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
611	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
613	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
615	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
616	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
617	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
618	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
619	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
620	#127	C₂³×C₅₃	1	16	yes	complemented
621	#126	C₂³×C₅₃	1	32	yes	complemented
622	#126	C₂³×C₅₃	1	32	yes	complemented
623	#125	C₂³×C₅₃	1	16	yes	complemented
624	#125	C₂³×C₅₃	1	16	yes	complemented
625	#124	C₂³×C₅₃	1	16	yes	complemented
626	#124	C₂³×C₅₃	1	32	yes	complemented
627	#124	C₂³×C₅₃	1	32	yes	complemented
628	#123	C₂³×C₅₃	1	16	yes	—
629	#123	C₂³×C₅₃	1	32	yes	complemented
630	#123	C₂³×C₅₃	1	32	yes	complemented
631	#123	C₂³×C₅₃	1	32	yes	complemented
632	#123	C₂³×C₅₃	1	32	yes	complemented
633	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
634	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
635	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
636	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	complemented
637	#121	C₂³×C₅₃	1	16	yes	—
638	#121	C₂³×C₅₃	1	16	yes	—
639	#121	C₂³×C₅₃	1	16	yes	—
640	#121	C₂³×C₅₃	1	16	yes	—
641	#121	C₂³×C₅₃	1	8	yes	complemented
642	#121	C₂³×C₅₃	1	8	yes	complemented
643	#121	C₂³×C₅₃	1	32	yes	complemented
644	#121	C₂³×C₅₃	1	16	yes	complemented
645	#121	C₂³×C₅₃	1	16	yes	complemented
646	#121	C₂³×C₅₃	1	32	yes	complemented
647	#121	C₂³×C₅₃	1	32	yes	complemented
648	#120	C₂³×C₅₃	1	16	yes	—
649	#120	C₂³×C₅₃	1	32	yes	—
650	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
651	C₄×D₄	C₂³×C₅₃	1	32	yes	—
652	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
653	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
654	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
655	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
656	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
657	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
658	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
659	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
660	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
661	#117	C₂³×C₅₃	1	8	yes	—
662	#117	C₂³×C₅₃	1	8	yes	—
663	#117	C₂³×C₅₃	1	16	yes	—
664	#117	C₂³×C₅₃	1	8	yes	—
665	#117	C₂³×C₅₃	1	16	yes	complemented
666	#117	C₂³×C₅₃	1	8	yes	complemented
667	#117	C₂³×C₅₃	1	8	yes	complemented
668	#117	C₂³×C₅₃	1	16	yes	complemented
669	#117	C₂³×C₅₃	1	32	yes	complemented
670	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
673	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
680	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
684	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
685	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
686	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
688	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
689	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	complemented
690	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅₃	1	32	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
709	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
710	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
711	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
712	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
713	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
714	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
715	C₂×C₄²	C₂³×C₅₃	1	16	yes	complemented
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	2	4	no	—
718	C₂⁴	—	2	8	no	—
719	C₂⁴	—	4	2	no	—
720	C₂⁴	—	4	4	no	—
721	C₂⁴	—	4	4	no	—
722	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
724	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
725	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
726	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
727	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
728	C₂⁴	C₂⁴×C₅₃	1	8	yes	—
729	#41	—	2	32	no	—
730	#41	—	4	64	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	4	8	no	—
733	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
734	C₂×Q₈	C₂⁴×C₅₃	1	16	yes	—
735	C₂×D₄	—	2	8	no	—
736	C₂×D₄	—	2	16	no	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	8	no	—
739	C₂×D₄	—	2	8	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	32	no	—
742	C₂×D₄	—	4	8	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	8	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	32	no	—
747	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
748	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
749	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
750	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
751	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
752	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
753	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
754	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
755	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
756	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	8	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	8	no	—
764	C₂²×C₄	—	2	32	no	—
765	C₂²×C₄	—	4	8	no	—
766	C₂²×C₄	—	4	4	no	—
767	C₂²×C₄	—	4	4	no	—
768	C₂²×C₄	—	4	8	no	—
769	C₂²×C₄	—	4	8	no	—
770	C₂²×C₄	#41×C₅₃	1	8	yes	complemented
771	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
780	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
781	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
782	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
784	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
785	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
786	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
787	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
788	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
789	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
790	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
791	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
792	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
793	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
796	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
797	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
798	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
799	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
800	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
801	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
802	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
803	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
804	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
805	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
806	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
807	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
808	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
809	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
810	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
811	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
812	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
813	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
814	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
815	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
816	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
817	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
818	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
819	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
820	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
821	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
822	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
823	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
825	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
826	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
827	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
828	C₄²	C₂⁴×C₅₃	1	8	yes	—
829	C₄²	C₂⁴×C₅₃	1	8	yes	—
830	C₄²	C₂⁴×C₅₃	1	8	yes	—
831	C₄²	C₂⁴×C₅₃	1	8	yes	—
832	C₄²	C₂⁴×C₅₃	1	8	yes	—
833	C₄²	C₂⁴×C₅₃	1	16	yes	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	8	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	8	no	—
844	C₂³	—	2	8	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	8	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	16	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	8	no	—
852	C₂³	—	4	8	no	—
853	C₂³	—	4	16	no	—
854	C₂³	—	8	16	no	—
855	C₂³	C₂×#41×C₅₃	1	4	yes	—
856	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
857	C₂³	C₂⁵×C₅₃	1	2	yes	—
858	C₂³	C₂⁵×C₅₃	1	8	yes	—
859	C₂³	C₂⁵×C₅₃	1	4	yes	—
860	C₂³	C₂⁵×C₅₃	1	2	yes	—
861	C₂³	C₂⁵×C₅₃	1	2	yes	—
862	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	4	16	no	—
865	D₄	—	2	16	no	—
866	D₄	—	2	32	no	—
867	D₄	—	2	16	no	—
868	D₄	—	2	16	no	—
869	D₄	—	2	16	no	—
870	D₄	—	2	8	no	—
871	D₄	—	4	16	no	—
872	D₄	—	4	8	no	—
873	D₄	—	4	16	no	—
874	D₄	—	4	16	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	16	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	8	no	—
891	C₂×C₄	—	2	16	no	—
892	C₂×C₄	—	4	16	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	4	16	no	—
896	C₂×C₄	—	4	16	no	—
897	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
898	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
899	C₂×C₄	C₂×#41×C₅₃	1	16	yes	complemented
900	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
901	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
902	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
903	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
904	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
905	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
906	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
907	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
908	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
909	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
910	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
911	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	8	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	16	no	—
928	C₂²	—	4	4	no	—
929	C₂²	—	4	16	no	—
930	C₂²	—	4	8	no	—
931	C₂²	—	8	16	no	—
932	C₂²	C₂²×#41×C₅₃	1	4	yes	—
933	C₂²	C₂²×#41×C₅₃	1	2	yes	—
934	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	4	yes	—
935	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
936	C₂²	C₅₃×#585	1	2	yes	—
937	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	4	no	—
943	C₄	—	2	8	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	4	no	—
947	C₄	—	2	4	no	—
948	C₄	C₂²×#41×C₅₃	1	4	yes	—
949	C₄	C₂²×#41×C₅₃	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	2	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	8	no	—
954	C₂	—	4	4	no	—
955	C₂	C₅₃×#3494	1	4	yes	direct product factor
956	C₂	C₂³×#41×C₅₃	1	1	yes	characteristic
957	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
958	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×#3494	C₂	direct (N × H)
2. C₂×C₅₃×#555	C₂	semidirect
3. C₂×C₅₃×#553	C₂	semidirect
4. C₂×C₅₃×#553	C₂	semidirect
5. C₂×C₅₃×#551	C₂	semidirect
6. C₂×C₅₃×#547	C₂	semidirect
7. C₂×C₅₃×#546	C₂	semidirect
8. C₂×C₅₃×#544	C₂	semidirect
9. C₂×C₅₃×#542	C₂	semidirect
10. C₂×C₅₃×#540	C₂	semidirect
11. C₂×C₅₃×#535	C₂	semidirect
12. C₂×C₅₃×#532	C₂	semidirect
13. C₂×C₅₃×#529	C₂	semidirect
14. C₂×C₅₃×#525	C₂	semidirect
15. C₂²×#121×C₅₃	C₂	semidirect
16. C₂×C₅₃×#520	C₂	semidirect
17. C₂×C₅₃×#518	C₂	semidirect
18. C₂²×#117×C₅₃	C₂	semidirect
20. C₂²×#41×C₅₃	C₂²	semidirect
24. C₅₃×#555	C₂²	semidirect
25. C₅₃×#553	C₂²	semidirect
26. C₅₃×#553	C₂²	semidirect
27. C₅₃×#551	C₂²	semidirect
28. C₅₃×#547	C₂²	semidirect
29. C₅₃×#546	C₂²	semidirect
30. C₅₃×#544	C₂²	semidirect
31. C₅₃×#542	C₂²	semidirect
32. C₅₃×#540	C₂²	semidirect
33. C₅₃×#535	C₂²	semidirect
34. C₅₃×#532	C₂²	semidirect
35. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
37. C₂×#127×C₅₃	C₂²	semidirect
38. C₅₃×#529	C₂²	semidirect
39. C₂×#126×C₅₃	C₂²	semidirect
40. C₂×#126×C₅₃	C₂²	semidirect
41. C₂×#125×C₅₃	C₂²	semidirect
42. C₂×#125×C₅₃	C₂²	semidirect
43. C₂×#124×C₅₃	C₂²	semidirect
44. C₂×#124×C₅₃	C₂²	semidirect
45. C₂×#124×C₅₃	C₂²	semidirect
46. C₅₃×#525	C₂²	semidirect
48. C₂×#123×C₅₃	C₂²	semidirect
49. C₂×#123×C₅₃	C₂²	semidirect
50. C₂×#123×C₅₃	C₂²	semidirect
51. C₂×#123×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
54. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
60. C₂×#121×C₅₃	C₂²	semidirect
61. C₂×#121×C₅₃	C₂²	semidirect
62. C₂×#121×C₅₃	C₂²	semidirect
63. C₂×#121×C₅₃	C₂²	semidirect
64. C₂×#121×C₅₃	C₂²	semidirect
65. C₂×#121×C₅₃	C₂²	semidirect
66. C₂×#121×C₅₃	C₂²	semidirect
67. C₂×#121×C₅₃	C₂²	semidirect
70. C₅₃×#520	C₂²	semidirect
71. C₅₃×#518	C₂²	semidirect
72. C₂×C₄×Q₈×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×C₄×D₄×C₅₃	C₂²	semidirect
79. C₂×C₄×D₄×C₅₃	C₂²	semidirect
80. C₂×C₄×D₄×C₅₃	C₂²	semidirect
81. C₂×C₄×D₄×C₅₃	C₂²	semidirect
82. C₂×C₄×D₄×C₅₃	C₂²	semidirect
87. C₂×#117×C₅₃	C₂²	semidirect
88. C₂×#117×C₅₃	C₂²	semidirect
89. C₂×#117×C₅₃	C₂²	semidirect
90. C₂×#117×C₅₃	C₂²	semidirect
91. C₂×#117×C₅₃	C₂²	semidirect
92. C₂×#117×C₅₃	C₂²	semidirect
94. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
95. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
96. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
100. C₂²×C₄²×C₅₃	C₂²	semidirect
106. C₂×#41×C₅₃	C₂³	semidirect
138. C₄⋊Q₈×C₅₃	C₂³	semidirect
139. C₄⋊Q₈×C₅₃	C₂³	semidirect
140. #127×C₅₃	C₂³	semidirect
141. #126×C₅₃	C₂³	semidirect
142. #126×C₅₃	C₂³	semidirect
143. #125×C₅₃	C₂³	semidirect
144. #125×C₅₃	C₂³	semidirect
145. #124×C₅₃	C₂³	semidirect
146. #124×C₅₃	C₂³	semidirect
147. #124×C₅₃	C₂³	semidirect
149. #123×C₅₃	C₂³	semidirect
150. #123×C₅₃	C₂³	semidirect
151. #123×C₅₃	C₂³	semidirect
152. #123×C₅₃	C₂³	semidirect
154. C₂²⋊Q₈×C₅₃	C₂³	semidirect
155. C₂²⋊Q₈×C₅₃	C₂³	semidirect
156. C₂²⋊Q₈×C₅₃	C₂³	semidirect
161. #121×C₅₃	C₂³	semidirect
162. #121×C₅₃	C₂³	semidirect
163. #121×C₅₃	C₂³	semidirect
164. #121×C₅₃	C₂³	semidirect
165. #121×C₅₃	C₂³	semidirect
166. #121×C₅₃	C₂³	semidirect
167. #121×C₅₃	C₂³	semidirect
170. C₄×Q₈×C₅₃	C₂³	semidirect
172. C₄×D₄×C₅₃	C₂³	semidirect
173. C₄×D₄×C₅₃	C₂³	semidirect
174. C₄×D₄×C₅₃	C₂³	semidirect
175. C₄×D₄×C₅₃	C₂³	semidirect
176. C₄×D₄×C₅₃	C₂³	semidirect
177. C₄×D₄×C₅₃	C₂³	semidirect
178. C₄×D₄×C₅₃	C₂³	semidirect
179. C₄×D₄×C₅₃	C₂³	semidirect
180. C₄×D₄×C₅₃	C₂³	semidirect
185. #117×C₅₃	C₂³	semidirect
186. #117×C₅₃	C₂³	semidirect
187. #117×C₅₃	C₂³	semidirect
188. #117×C₅₃	C₂³	semidirect
189. #117×C₅₃	C₂³	semidirect
207. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
208. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
209. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
235. C₂×C₄²×C₅₃	C₂³	semidirect
290. C₂²×C₄×C₅₃	#41	semidirect
419. C₂×C₄×C₅₃	C₂×#41	semidirect
432. C₂×#3494	C₅₃	direct (N × H)
471. #3494	C₂×C₅₃	direct (N × H)
472. C₂×#555	C₂×C₅₃	semidirect
473. C₂×#553	C₂×C₅₃	semidirect
474. C₂×#553	C₂×C₅₃	semidirect
475. C₂×#551	C₂×C₅₃	semidirect
476. C₂×#547	C₂×C₅₃	semidirect
477. C₂×#546	C₂×C₅₃	semidirect
478. C₂×#544	C₂×C₅₃	semidirect
479. C₂×#542	C₂×C₅₃	semidirect
480. C₂×#540	C₂×C₅₃	semidirect
481. C₂×#535	C₂×C₅₃	semidirect
482. C₂×#532	C₂×C₅₃	semidirect
483. C₂×#529	C₂×C₅₃	semidirect
484. C₂×#525	C₂×C₅₃	semidirect
485. C₂²×#121	C₂×C₅₃	semidirect
486. C₂×#520	C₂×C₅₃	semidirect
487. C₂×#518	C₂×C₅₃	semidirect
488. C₂²×#117	C₂×C₅₃	semidirect
494. C₂×C₅₃	#3494	direct (N × H)
499. C₂²×#41	C₂²×C₅₃	semidirect
503. #555	C₂²×C₅₃	semidirect
504. #553	C₂²×C₅₃	semidirect
505. #553	C₂²×C₅₃	semidirect
506. #551	C₂²×C₅₃	semidirect
507. #547	C₂²×C₅₃	semidirect
508. #546	C₂²×C₅₃	semidirect
509. #544	C₂²×C₅₃	semidirect
510. #542	C₂²×C₅₃	semidirect
511. #540	C₂²×C₅₃	semidirect
512. #535	C₂²×C₅₃	semidirect
513. #532	C₂²×C₅₃	semidirect
514. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
515. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
516. C₂×#127	C₂²×C₅₃	semidirect
517. #529	C₂²×C₅₃	semidirect
518. C₂×#126	C₂²×C₅₃	semidirect
519. C₂×#126	C₂²×C₅₃	semidirect
520. C₂×#125	C₂²×C₅₃	semidirect
521. C₂×#125	C₂²×C₅₃	semidirect
522. C₂×#124	C₂²×C₅₃	semidirect
523. C₂×#124	C₂²×C₅₃	semidirect
524. C₂×#124	C₂²×C₅₃	semidirect
525. #525	C₂²×C₅₃	semidirect
527. C₂×#123	C₂²×C₅₃	semidirect
528. C₂×#123	C₂²×C₅₃	semidirect
529. C₂×#123	C₂²×C₅₃	semidirect
530. C₂×#123	C₂²×C₅₃	semidirect
532. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
533. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
534. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
539. C₂×#121	C₂²×C₅₃	semidirect
540. C₂×#121	C₂²×C₅₃	semidirect
541. C₂×#121	C₂²×C₅₃	semidirect
542. C₂×#121	C₂²×C₅₃	semidirect
543. C₂×#121	C₂²×C₅₃	semidirect
544. C₂×#121	C₂²×C₅₃	semidirect
545. C₂×#121	C₂²×C₅₃	semidirect
546. C₂×#121	C₂²×C₅₃	semidirect
549. #520	C₂²×C₅₃	semidirect
550. #518	C₂²×C₅₃	semidirect
551. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
553. C₂×C₄×D₄	C₂²×C₅₃	semidirect
554. C₂×C₄×D₄	C₂²×C₅₃	semidirect
555. C₂×C₄×D₄	C₂²×C₅₃	semidirect
556. C₂×C₄×D₄	C₂²×C₅₃	semidirect
557. C₂×C₄×D₄	C₂²×C₅₃	semidirect
558. C₂×C₄×D₄	C₂²×C₅₃	semidirect
559. C₂×C₄×D₄	C₂²×C₅₃	semidirect
560. C₂×C₄×D₄	C₂²×C₅₃	semidirect
561. C₂×C₄×D₄	C₂²×C₅₃	semidirect
566. C₂×#117	C₂²×C₅₃	semidirect
567. C₂×#117	C₂²×C₅₃	semidirect
568. C₂×#117	C₂²×C₅₃	semidirect
569. C₂×#117	C₂²×C₅₃	semidirect
570. C₂×#117	C₂²×C₅₃	semidirect
571. C₂×#117	C₂²×C₅₃	semidirect
573. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
574. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
575. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
579. C₂²×C₄²	C₂²×C₅₃	semidirect
580. C₅₃	C₂×#3494	direct (N × H)
586. C₂×#41	C₂³×C₅₃	semidirect
618. C₄⋊Q₈	C₂³×C₅₃	semidirect
619. C₄⋊Q₈	C₂³×C₅₃	semidirect
620. #127	C₂³×C₅₃	semidirect
621. #126	C₂³×C₅₃	semidirect
622. #126	C₂³×C₅₃	semidirect
623. #125	C₂³×C₅₃	semidirect
624. #125	C₂³×C₅₃	semidirect
625. #124	C₂³×C₅₃	semidirect
626. #124	C₂³×C₅₃	semidirect
627. #124	C₂³×C₅₃	semidirect
629. #123	C₂³×C₅₃	semidirect
630. #123	C₂³×C₅₃	semidirect
631. #123	C₂³×C₅₃	semidirect
632. #123	C₂³×C₅₃	semidirect
634. C₂²⋊Q₈	C₂³×C₅₃	semidirect
635. C₂²⋊Q₈	C₂³×C₅₃	semidirect
636. C₂²⋊Q₈	C₂³×C₅₃	semidirect
641. #121	C₂³×C₅₃	semidirect
642. #121	C₂³×C₅₃	semidirect
643. #121	C₂³×C₅₃	semidirect
644. #121	C₂³×C₅₃	semidirect
645. #121	C₂³×C₅₃	semidirect
646. #121	C₂³×C₅₃	semidirect
647. #121	C₂³×C₅₃	semidirect
650. C₄×Q₈	C₂³×C₅₃	semidirect
652. C₄×D₄	C₂³×C₅₃	semidirect
653. C₄×D₄	C₂³×C₅₃	semidirect
654. C₄×D₄	C₂³×C₅₃	semidirect
655. C₄×D₄	C₂³×C₅₃	semidirect
656. C₄×D₄	C₂³×C₅₃	semidirect
657. C₄×D₄	C₂³×C₅₃	semidirect
658. C₄×D₄	C₂³×C₅₃	semidirect
659. C₄×D₄	C₂³×C₅₃	semidirect
660. C₄×D₄	C₂³×C₅₃	semidirect
665. #117	C₂³×C₅₃	semidirect
666. #117	C₂³×C₅₃	semidirect
667. #117	C₂³×C₅₃	semidirect
668. #117	C₂³×C₅₃	semidirect
669. #117	C₂³×C₅₃	semidirect
687. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
688. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
689. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
715. C₂×C₄²	C₂³×C₅₃	semidirect
770. C₂²×C₄	#41×C₅₃	semidirect
899. C₂×C₄	C₂×#41×C₅₃	semidirect
955. C₂	C₅₃×#3494	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×#3494	2
C₂×C₅₃×#555	2
C₂×C₅₃×#553	2
C₂×C₅₃×#551	2
C₂×C₅₃×#547	2
C₂×C₅₃×#546	2
C₂×C₅₃×#544	2
C₂×C₅₃×#542	2
C₂×C₅₃×#540	2
C₂×C₅₃×#535	2
C₂×C₅₃×#532	2
C₂×C₅₃×#529	2
C₂×C₅₃×#525	2
C₂²×#121×C₅₃	2
C₂×C₅₃×#520	2
C₂×C₅₃×#518	2
C₂²×#117×C₅₃	2
C₂×#3494	53

Subgroups — C2×C53×#3494 #27270309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3494 #27270309