Subgroups — #28318548

Order 13568.

1246 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#435	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×#6157	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13133271	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×#6157	C₂	1	1	yes	maximal, characteristic
5	#20290516	C₂	1	1	yes	maximal, characteristic, complemented
6	#20290513	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290502	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290458	C₂	1	1	yes	maximal, characteristic, complemented
9	#20290455	C₂	1	1	yes	maximal, characteristic, complemented
10	#20290450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊#6157	C₂	1	1	yes	maximal, characteristic, complemented
12	#20290443	C₂	1	1	yes	maximal, characteristic, complemented
13	#20290443	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×#6157	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×D₅₃	C₂	1	1	yes	maximal, characteristic
16	C₂×D₅₃⋊M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×D₄×#6157	C₄	1	2	yes	—
19	C₂²×C₄×#6157	C₂²	1	1	yes	characteristic
20	C₂²×C₄×#6157	C₂²	1	1	yes	characteristic
21	#16811655	C₄	1	2	yes	complemented
22	#16811654	C₄	1	2	yes	complemented
23	#16811653	C₄	1	2	yes	complemented
24	#16811652	C₄	1	2	yes	complemented
25	D₅₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
26	D₅₃⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
27	D₅₃⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
28	M₁₆×#6157	—	2	4	no	—
29	#16811582	C₂²	1	1	yes	characteristic
30	C₂×#13133271	—	2	4	no	—
31	C₂×#13133271	C₂²	1	1	yes	characteristic
32	C₂×#13133271	C₂²	1	1	yes	characteristic
33	C₂×#13133271	C₂²	1	1	yes	characteristic
34	C₂×#13133271	C₂²	1	1	yes	characteristic
35	C₂×#13133271	C₂²	1	1	yes	characteristic
36	C₂×#13133271	C₂²	1	1	yes	characteristic
37	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
38	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
39	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
40	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
41	C₄⋊C₄×#6157	C₄	1	2	yes	—
42	C₄×C₄⋊#6157	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×#6157	C₄	1	2	yes	—
44	C₂²⋊C₄×#6157	C₄	1	2	yes	—
45	C₄×C₂²⋊#6157	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊#6157	C₂²	1	1	yes	characteristic
47	C₄²×#6157	C₂²	1	1	yes	characteristic
48	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
51	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
56	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
57	#16810697	C₄	1	1	yes	characteristic, complemented
58	#16810696	C₄	1	1	yes	characteristic, complemented
59	#16810695	C₄	1	1	yes	characteristic, complemented
60	#16810694	C₄	1	1	yes	characteristic, complemented
61	#16810693	C₄	1	1	yes	characteristic, complemented
62	#16810692	C₄	1	1	yes	characteristic, complemented
63	#16810691	C₄	1	1	yes	characteristic, complemented
64	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
65	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
66	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
67	#97×D₅₃	C₂²	1	1	yes	characteristic
68	C₅₃×#435	C₄	1	1	yes	characteristic, complemented
69	C₂³×#6157	C₂×C₄	1	2	yes	—
70	C₂³×#6157	C₂×C₄	1	2	yes	—
71	C₂×#11719936	C₂×C₄	1	2	yes	complemented
72	D₅₃⋊M₁₆	—	2	2	no	—
73	D₅₃⋊M₁₆	—	2	2	no	—
74	C₂×#11719940	C₂×C₄	1	2	yes	complemented
75	C₂×D₅₃⋊C₈	—	2	2	no	—
76	C₂×D₅₃⋊C₈	—	2	2	no	—
77	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	complemented
78	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×#88324	C₂×C₄	1	2	yes	complemented
83	D₄×#6157	—	2	8	no	—
84	C₂×C₄⋊#6157	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊#6157	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊#6157	C₂×C₄	1	2	yes	—
87	C₂×C₄×#6157	—	2	2	no	—
88	C₂×C₄×#6157	—	2	2	no	—
89	C₂×C₄×#6157	—	2	2	no	—
90	C₂×C₄×#6157	—	2	2	no	—
91	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
92	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
93	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
94	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
95	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
96	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
97	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
98	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
99	#13133284	C₂×C₄	1	2	yes	complemented
100	C₄⋊#88324	C₂×C₄	1	2	yes	complemented
101	#13133274	C₂×C₄	1	2	yes	complemented
102	#13133274	C₂×C₄	1	2	yes	complemented
103	C₂²⋊#88324	C₂×C₄	1	2	yes	complemented
104	C₂²⋊#88324	C₂×C₄	1	2	yes	complemented
105	#13133272	C₂×C₄	1	2	yes	complemented
106	#13133272	C₂×C₄	1	2	yes	complemented
107	#13133271	—	2	2	no	—
108	#13133271	—	2	2	no	—
109	#13133271	—	2	2	no	—
110	#13133271	—	2	2	no	—
111	#13133271	—	2	2	no	—
112	#13133271	D₄	1	4	yes	complemented
113	C₈×#6157	—	2	2	no	—
114	C₈×#6157	—	2	2	no	—
115	C₈×#6157	—	2	2	no	—
116	C₈×#6157	—	2	2	no	—
117	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
118	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
119	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
120	C₂×D₄×D₅₃	C₂×C₄	1	1	yes	characteristic
121	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
123	C₂×#11719917	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂×#11719912	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×#11719912	C₂×C₄	1	1	yes	characteristic, complemented
126	M₁₆×D₅₃	—	2	2	no	—
127	M₁₆×D₅₃	—	2	2	no	—
128	C₂²×#88322	C₂×C₄	1	1	yes	characteristic, complemented
129	C₂×C₈×D₅₃	—	2	2	no	—
130	C₂×C₈×D₅₃	—	2	2	no	—
131	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic, complemented
132	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic, complemented
133	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
134	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
135	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
136	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
137	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
138	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
139	#13133179	C₂×C₄	1	1	yes	characteristic
140	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
141	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
142	#13133177	C₂×C₄	1	1	yes	characteristic
143	#13133177	C₂×C₄	1	1	yes	characteristic
144	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
145	C₂²⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
146	C₂²⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
147	C₄²×D₅₃	C₂³	1	1	yes	characteristic
148	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic, complemented
149	#13133146	C₂×C₄	1	1	yes	characteristic, complemented
150	#13133146	C₂×C₄	1	1	yes	characteristic, complemented
151	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic, complemented
152	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic, complemented
153	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
154	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
155	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
156	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
157	#13133128	C₂×C₄	1	1	yes	characteristic, complemented
158	#13133127	C₂×C₄	1	1	yes	characteristic, complemented
159	#13133127	C₂×C₄	1	1	yes	characteristic, complemented
160	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
161	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
162	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
163	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
164	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
165	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
166	#97×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
167	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
168	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
169	C₂²×#6157	—	2	4	no	—
170	C₂²×#6157	—	2	4	no	—
171	C₂²×#6157	—	2	4	no	—
172	C₂²×#6157	—	2	4	no	—
173	C₂²×#6157	—	4	2	no	—
174	C₂²×#6157	—	4	2	no	—
175	C₂²×#6157	C₂²×C₄	1	2	yes	—
176	C₂²×#6157	C₂²×C₄	1	2	yes	—
177	C₂²×#6157	C₂²×C₄	1	2	yes	—
178	C₂²×#6157	C₂²×C₄	1	2	yes	—
179	C₂×D₄×C₅₃	C₄²	1	1	yes	characteristic
180	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
183	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
184	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
186	D₄×D₅₃	—	2	4	no	—
187	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
188	C₂×C₄×D₅₃	—	2	1	no	—
189	C₂×C₄×D₅₃	—	2	1	no	—
190	C₂×C₄×D₅₃	—	2	1	no	—
191	C₂×C₄×D₅₃	—	2	1	no	—
192	C₂×C₄×D₅₃	—	2	1	no	—
193	C₂×C₄×D₅₃	—	2	1	no	—
194	C₂×C₄×D₅₃	—	2	1	no	—
195	C₂×C₄×D₅₃	—	2	1	no	—
196	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
205	C₂²⋊#6157	—	2	4	no	—
206	C₂²⋊#6157	M₁₆	1	8	yes	complemented
207	#11719940	—	2	4	no	—
208	C₂×#88324	—	2	4	no	—
209	C₂×#88324	C₂²×C₄	1	2	yes	—
210	C₂×#88324	C₂²×C₄	1	2	yes	—
211	C₂×#88324	C₂²×C₄	1	2	yes	—
212	C₂×#88324	C₂²×C₄	1	2	yes	—
213	C₄⋊#6157	—	2	4	no	—
214	C₄×#6157	—	2	4	no	—
215	C₄×#6157	—	2	4	no	—
216	C₄×#6157	—	2	4	no	—
217	C₄×#6157	—	2	1	no	—
218	C₄×#6157	—	2	1	no	—
219	C₄×#6157	—	2	1	no	—
220	C₄×#6157	—	2	1	no	—
221	C₄×#6157	—	2	1	no	—
222	C₄×#6157	—	2	1	no	—
223	C₄×#6157	—	4	2	no	—
224	C₄×#6157	C₂×D₄	1	2	yes	—
225	C₄×#6157	#41	1	2	yes	—
226	#11719936	—	2	4	no	—
227	D₅₃⋊C₈	—	2	1	no	—
228	D₅₃⋊C₈	—	2	1	no	—
229	D₅₃⋊C₈	—	2	1	no	—
230	D₅₃⋊C₈	—	2	1	no	—
231	D₅₃⋊C₈	—	2	1	no	—
232	D₅₃⋊C₈	—	2	1	no	—
233	D₅₃⋊C₈	—	2	4	no	—
234	D₅₃⋊C₈	C₂×D₄	1	2	yes	—
235	D₅₃⋊C₈	#41	1	2	yes	—
236	M₁₆×C₅₃	—	2	2	no	—
237	C₂×C₈×C₅₃	—	2	2	no	—
238	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
242	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
243	C₂²⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
244	C₂²⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
245	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
246	C₂²⋊Dic₅₃	C₄²	1	1	yes	characteristic
247	C₂²⋊Dic₅₃	C₄²	1	1	yes	characteristic
248	#11719921	C₄²	1	1	yes	characteristic
249	#11719921	C₄²	1	1	yes	characteristic
250	#11719921	C₄²	1	1	yes	characteristic
251	#11719921	C₄²	1	1	yes	characteristic
252	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
253	#11719919	C₄²	1	1	yes	characteristic
254	#11719919	C₄²	1	1	yes	characteristic
255	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
256	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
257	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
258	#11719917	—	2	2	no	—
259	C₂×#88322	—	2	2	no	—
260	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
261	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
262	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
263	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
264	#11719912	—	2	2	no	—
265	#11719912	—	2	2	no	—
266	C₈×D₅₃	—	2	1	no	—
267	C₈×D₅₃	—	2	1	no	—
268	C₈×D₅₃	—	2	1	no	—
269	C₈×D₅₃	—	2	1	no	—
270	C₈×D₅₃	—	2	1	no	—
271	C₈×D₅₃	—	2	1	no	—
272	C₈×D₅₃	—	2	2	no	—
273	C₈×D₅₃	—	2	2	no	—
274	C₈×D₅₃	C₂×D₄	1	2	yes	—
275	C₈×D₅₃	#41	1	2	yes	—
276	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
277	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
278	C₂²×D₅₃	—	2	1	no	—
279	C₂²×D₅₃	—	2	1	no	—
280	C₂²×D₅₃	—	2	2	no	—
281	C₂²×D₅₃	—	2	1	no	—
282	C₂²×D₅₃	—	2	1	no	—
283	C₂²×D₅₃	—	2	2	no	—
284	C₂²×D₅₃	—	2	2	no	—
285	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
286	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
287	C₂²×D₅₃	C₂×M₁₆	1	4	yes	—
288	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
289	C₂×#6157	—	2	2	no	—
290	C₂×#6157	—	2	2	no	—
291	C₂×#6157	—	2	2	no	—
292	C₂×#6157	—	2	2	no	—
293	C₂×#6157	—	2	2	no	—
294	C₂×#6157	—	2	2	no	—
295	C₂×#6157	—	2	2	no	—
296	C₂×#6157	—	2	2	no	—
297	C₂×#6157	—	2	2	no	—
298	C₂×#6157	—	4	8	no	—
299	C₂×#6157	—	4	8	no	—
300	C₂×#6157	C₄×D₄	1	4	yes	—
301	C₂×#6157	C₂×M₁₆	1	4	yes	—
302	C₂×#6157	C₂×M₁₆	1	4	yes	—
303	D₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	1	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
309	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
310	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
311	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
312	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
313	C₂²⋊D₅₃	—	2	2	no	—
314	C₂²⋊D₅₃	—	2	2	no	—
315	C₂×Dic₅₃	—	2	1	no	—
316	C₂×Dic₅₃	—	2	1	no	—
317	C₂×Dic₅₃	—	2	1	no	—
318	C₂×Dic₅₃	—	2	1	no	—
319	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
320	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
321	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
322	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
323	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
324	D₂₁₂	—	2	2	no	—
325	C₄×D₅₃	—	2	1	no	—
326	C₄×D₅₃	—	2	1	no	—
327	C₄×D₅₃	—	2	1	no	—
328	C₄×D₅₃	—	2	1	no	—
329	C₄×D₅₃	—	2	2	no	—
330	C₄×D₅₃	—	2	2	no	—
331	C₄×D₅₃	—	2	1	no	—
332	C₄×D₅₃	—	2	1	no	—
333	C₄×D₅₃	—	2	1	no	—
334	C₄×D₅₃	—	2	1	no	—
335	C₄×D₅₃	—	2	1	no	—
336	C₄×D₅₃	—	2	1	no	—
337	C₄×D₅₃	—	2	1	no	—
338	C₄×D₅₃	—	2	1	no	—
339	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
340	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
341	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
342	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
343	#88324	—	2	2	no	—
344	#88324	—	2	2	no	—
345	#88324	—	2	2	no	—
346	#88324	C₄×D₄	1	4	yes	complemented
347	C₈×C₅₃	—	2	1	no	—
348	C₈×C₅₃	—	2	1	no	—
349	C₈×C₅₃	—	2	1	no	—
350	C₈×C₅₃	C₄×D₄	1	2	yes	complemented
351	#88322	—	2	1	no	—
352	#88322	—	2	1	no	—
353	#88322	—	2	1	no	—
354	#88322	C₄×D₄	1	2	yes	complemented
355	#20491	—	53	1	no	maximal, Sylow
356	C₂²×C₅₃	—	2	1	no	—
357	C₂²×C₅₃	—	2	1	no	—
358	C₂²×C₅₃	—	2	1	no	—
359	C₂²×C₅₃	—	2	1	no	—
360	C₂²×C₅₃	—	2	1	no	—
361	C₂²×C₅₃	C₄×M₁₆	1	2	yes	complemented
362	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
363	C₂×D₅₃	—	2	1	no	—
364	C₂×D₅₃	—	2	1	no	—
365	C₂×D₅₃	—	2	4	no	—
366	C₂×D₅₃	—	2	4	no	—
367	C₂×D₅₃	—	2	1	no	—
368	C₂×D₅₃	—	2	1	no	—
369	C₂×D₅₃	—	2	1	no	—
370	C₂×D₅₃	—	4	2	no	—
371	C₂×D₅₃	—	4	2	no	—
372	C₂×D₅₃	C₄×M₁₆	1	2	yes	complemented
373	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×D₅₃	C₄×#41	1	1	yes	characteristic
375	C₂×D₅₃	C₂²×M₁₆	1	2	yes	—
376	C₂×D₅₃	#568	1	2	yes	—
377	#6157	—	2	4	no	—
378	#6157	—	2	4	no	—
379	#6157	—	2	4	no	—
380	#6157	—	4	2	no	—
381	C₄×C₅₃	—	2	1	no	—
382	C₄×C₅₃	—	2	1	no	—
383	C₄×C₅₃	—	2	1	no	—
384	C₄×C₅₃	—	2	1	no	—
385	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
386	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
387	Dic₅₃	—	2	1	no	—
388	Dic₅₃	—	2	1	no	—
389	Dic₅₃	—	2	1	no	—
390	Dic₅₃	—	2	1	no	—
391	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
392	Dic₅₃	C₄×#41	1	1	yes	characteristic
393	C₂×#435	—	53	1	no	—
394	C₂×#435	—	53	1	no	—
395	C₂×C₄×M₁₆	—	53	1	no	—
396	C₂²×#97	—	53	1	no	—
397	C₄²×D₄	—	53	1	no	—
398	#1771	—	53	1	no	—
399	#1771	—	53	1	no	—
400	#1767	—	53	1	no	—
401	#1753	—	53	1	no	—
402	#1753	—	53	1	no	—
403	C₈×C₂²⋊C₄	—	53	1	no	—
404	C₈×C₂²⋊C₄	—	53	1	no	—
405	#1749	—	53	1	no	—
406	#1749	—	53	1	no	—
407	C₄×#97	—	53	1	no	—
408	C₂×C₅₃	—	2	2	no	—
409	C₂×C₅₃	—	4	1	no	—
410	C₂×C₅₃	C₄²×D₄	1	1	yes	characteristic
411	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
412	C₂×C₅₃	#2875	1	1	yes	characteristic
413	D₅₃	—	2	2	no	—
414	D₅₃	—	4	1	no	—
415	D₅₃	D₄×M₁₆	1	2	yes	—
416	D₅₃	#2970	1	2	yes	—
417	C₂²×M₁₆	—	53	1	no	—
418	C₂²×M₁₆	—	53	1	no	—
419	C₂³×C₈	—	53	1	no	—
420	C₂³×C₈	—	53	1	no	—
421	C₂×C₄×D₄	—	53	1	no	—
422	C₂×C₄×D₄	—	53	2	no	—
423	C₂²×C₄²	—	53	1	no	—
424	C₂²×C₄²	—	53	1	no	—
425	#435	—	53	2	no	—
426	#435	—	53	2	no	—
427	#435	—	53	2	no	—
428	#435	—	53	2	no	—
429	#435	—	53	1	no	—
430	#435	—	53	1	no	—
431	#435	—	53	1	no	—
432	#435	—	53	1	no	—
433	#435	—	53	1	no	—
434	#435	—	53	1	no	—
435	#435	—	53	1	no	—
436	#435	#6157	1	1	yes	characteristic, complemented
437	C₂×C₄⋊C₈	—	53	1	no	—
438	C₂×C₄⋊C₈	—	53	1	no	—
439	C₂×C₂²⋊C₈	—	53	1	no	—
440	C₂×C₂²⋊C₈	—	53	1	no	—
441	C₂×C₂²⋊C₈	—	53	1	no	—
442	C₂×C₂²⋊C₈	—	53	1	no	—
443	C₄×M₁₆	—	106	4	no	—
444	C₂×#97	—	53	1	no	—
445	C₂×#97	—	53	1	no	—
446	C₂×#97	—	53	1	no	—
447	C₂×#97	—	53	1	no	—
448	C₂×#97	—	53	1	no	—
449	C₂×#97	—	53	1	no	—
450	C₂×#97	—	53	1	no	—
451	C₂×#97	—	53	1	no	—
452	C₂×#97	—	106	4	no	—
453	C₂×C₄×C₈	—	53	1	no	—
454	C₂×C₄×C₈	—	53	1	no	—
455	C₂×C₄×C₈	—	53	1	no	—
456	C₂×C₄×C₈	—	53	1	no	—
457	C₄×C₄⋊C₄	—	53	1	no	—
458	C₄×C₄⋊C₄	—	53	2	no	—
459	C₄×C₂²⋊C₄	—	53	1	no	—
460	C₄×C₂²⋊C₄	—	53	1	no	—
461	C₄×C₂²⋊C₄	—	53	2	no	—
462	C₄×C₂²⋊C₄	—	53	2	no	—
463	C₄³	—	53	1	no	—
464	#336	—	53	1	no	—
465	#336	—	53	1	no	—
466	#336	—	53	1	no	—
467	#336	—	53	1	no	—
468	#336	—	53	1	no	—
469	#336	—	53	1	no	—
470	C₅₃	#20491	1	1	yes	characteristic, complemented, Sylow
471	C₂²×D₄	—	53	1	no	—
472	C₂³×C₄	—	53	1	no	—
473	C₂³×C₄	—	53	1	no	—
474	C₂³×C₄	—	53	2	no	—
475	C₂³×C₄	—	53	2	no	—
476	C₂×M₁₆	—	53	2	no	—
477	C₂×M₁₆	—	53	2	no	—
478	C₂×M₁₆	—	53	1	no	—
479	C₂×M₁₆	—	53	1	no	—
480	C₂×M₁₆	—	53	1	no	—
481	C₂×M₁₆	—	106	2	no	—
482	C₂×M₁₆	—	106	2	no	—
483	C₂×M₁₆	—	106	2	no	—
484	C₂×M₁₆	—	106	2	no	—
485	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic, complemented
486	C₂²×C₈	—	53	1	no	—
487	C₂²×C₈	—	53	1	no	—
488	C₂²×C₈	—	53	1	no	—
489	C₂²×C₈	—	53	2	no	—
490	C₂²×C₈	—	53	2	no	—
491	C₂²×C₈	—	53	1	no	—
492	C₂²×C₈	—	53	1	no	—
493	C₂²×C₈	—	53	1	no	—
494	C₂²×C₈	—	53	1	no	—
495	C₂²×C₈	—	53	1	no	—
496	C₂²×C₈	—	53	1	no	—
497	C₂²×C₈	—	53	1	no	—
498	C₂²×C₈	—	53	1	no	—
499	C₂²×C₈	—	106	2	no	—
500	C₂²×C₈	—	106	2	no	—
501	C₂²×C₈	—	106	2	no	—
502	C₂²×C₈	—	106	2	no	—
503	C₂²×C₈	C₂×#6157	1	1	yes	characteristic, complemented
504	C₄×D₄	—	53	1	no	—
505	C₄×D₄	—	53	1	no	—
506	C₄×D₄	—	53	1	no	—
507	C₄×D₄	—	53	1	no	—
508	C₄×D₄	—	53	1	no	—
509	C₄×D₄	—	53	1	no	—
510	C₄×D₄	—	53	1	no	—
511	C₄×D₄	—	106	8	no	—
512	C₄×D₄	C₂×#6157	1	1	yes	characteristic
513	C₂×C₄⋊C₄	—	53	1	no	—
514	C₂×C₄⋊C₄	—	53	2	no	—
515	C₂×C₂²⋊C₄	—	53	2	no	—
516	C₂×C₂²⋊C₄	—	53	1	no	—
517	C₂×C₂²⋊C₄	—	53	1	no	—
518	C₂×C₂²⋊C₄	—	53	2	no	—
519	C₂×C₄²	—	53	1	no	—
520	C₂×C₄²	—	53	1	no	—
521	C₂×C₄²	—	53	2	no	—
522	C₂×C₄²	—	53	1	no	—
523	C₂×C₄²	—	53	1	no	—
524	C₂×C₄²	—	53	1	no	—
525	C₂×C₄²	—	53	2	no	—
526	C₂×C₄²	—	53	2	no	—
527	C₂×C₄²	—	53	2	no	—
528	C₂×C₄²	—	106	2	no	—
529	C₂×C₄²	—	106	2	no	—
530	C₂×C₄²	—	106	2	no	—
531	C₂×C₄²	—	106	2	no	—
532	C₄⋊C₈	—	53	2	no	—
533	C₄⋊C₈	—	53	2	no	—
534	C₄⋊C₈	—	53	1	no	—
535	C₄⋊C₈	—	53	1	no	—
536	C₄⋊C₈	—	53	1	no	—
537	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic, complemented
538	C₂²⋊C₈	—	53	2	no	—
539	C₂²⋊C₈	—	53	2	no	—
540	C₂²⋊C₈	—	53	2	no	—
541	C₂²⋊C₈	—	53	2	no	—
542	C₂²⋊C₈	—	53	1	no	—
543	C₂²⋊C₈	—	53	1	no	—
544	C₂²⋊C₈	—	53	1	no	—
545	C₂²⋊C₈	—	53	1	no	—
546	C₂²⋊C₈	—	53	1	no	—
547	C₂²⋊C₈	—	53	1	no	—
548	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic, complemented
549	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic, complemented
550	#97	—	53	4	no	—
551	#97	—	53	2	no	—
552	#97	—	53	2	no	—
553	#97	—	53	1	no	—
554	#97	—	53	1	no	—
555	#97	—	53	1	no	—
556	#97	—	106	2	no	—
557	#97	—	106	2	no	—
558	#97	—	106	2	no	—
559	#97	—	106	2	no	—
560	#97	—	106	2	no	—
561	#97	C₂×#6157	1	1	yes	characteristic, complemented
562	C₄×C₈	—	106	2	no	—
563	C₄×C₈	—	106	2	no	—
564	C₄×C₈	—	106	2	no	—
565	C₄×C₈	—	106	2	no	—
566	#95	—	53	2	no	—
567	#95	—	53	2	no	—
568	#95	—	53	2	no	—
569	C₂⁴	—	53	1	no	—
570	C₂⁴	—	53	1	no	—
571	C₂×D₄	—	53	1	no	—
572	C₂×D₄	—	53	1	no	—
573	C₂×D₄	—	53	1	no	—
574	C₂×D₄	—	106	4	no	—
575	C₂×D₄	C₄×#6157	1	1	yes	characteristic
576	C₂²×C₄	—	53	1	no	—
577	C₂²×C₄	—	53	2	no	—
578	C₂²×C₄	—	53	2	no	—
579	C₂²×C₄	—	53	2	no	—
580	C₂²×C₄	—	53	1	no	—
581	C₂²×C₄	—	53	1	no	—
582	C₂²×C₄	—	53	1	no	—
583	C₂²×C₄	—	53	1	no	—
584	C₂²×C₄	—	53	1	no	—
585	C₂²×C₄	—	53	1	no	—
586	C₂²×C₄	—	53	1	no	—
587	C₂²×C₄	—	53	1	no	—
588	C₂²×C₄	—	53	1	no	—
589	C₂²×C₄	—	53	1	no	—
590	C₂²×C₄	—	53	2	no	—
591	C₂²×C₄	—	106	1	no	—
592	C₂²×C₄	—	106	1	no	—
593	C₂²×C₄	—	106	1	no	—
594	C₂²×C₄	—	106	1	no	—
595	C₂²×C₄	—	106	1	no	—
596	C₂²×C₄	—	106	1	no	—
597	C₂²×C₄	—	106	1	no	—
598	C₂²×C₄	—	106	1	no	—
599	C₂²×C₄	—	106	4	no	—
600	C₂²×C₄	—	106	4	no	—
601	C₂²×C₄	—	106	4	no	—
602	C₂²×C₄	—	106	4	no	—
603	C₂²×C₄	—	212	2	no	—
604	C₂²×C₄	—	212	2	no	—
605	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
606	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
607	M₁₆	—	2	2	no	—
608	M₁₆	—	106	2	no	—
609	M₁₆	—	106	2	no	—
610	M₁₆	—	106	4	no	—
611	M₁₆	—	106	4	no	—
612	M₁₆	—	106	2	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	53	2	no	—
615	C₂×C₈	—	53	2	no	—
616	C₂×C₈	—	53	2	no	—
617	C₂×C₈	—	53	1	no	—
618	C₂×C₈	—	53	2	no	—
619	C₂×C₈	—	53	2	no	—
620	C₂×C₈	—	53	2	no	—
621	C₂×C₈	—	53	2	no	—
622	C₂×C₈	—	53	2	no	—
623	C₂×C₈	—	53	1	no	—
624	C₂×C₈	—	53	1	no	—
625	C₂×C₈	—	53	1	no	—
626	C₂×C₈	—	106	2	no	—
627	C₂×C₈	—	106	1	no	—
628	C₂×C₈	—	106	1	no	—
629	C₂×C₈	—	106	1	no	—
630	C₂×C₈	—	106	1	no	—
631	C₂×C₈	—	106	1	no	—
632	C₂×C₈	—	106	1	no	—
633	C₂×C₈	—	106	2	no	—
634	C₂×C₈	—	106	4	no	—
635	C₂×C₈	—	106	4	no	—
636	C₂×C₈	—	106	1	no	—
637	C₂×C₈	—	106	1	no	—
638	C₂×C₈	—	106	1	no	—
639	C₂×C₈	—	106	1	no	—
640	C₂×C₈	—	106	1	no	—
641	C₂×C₈	—	106	1	no	—
642	C₂×C₈	—	106	2	no	—
643	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
644	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
645	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
646	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
647	C₄⋊C₄	—	53	1	no	—
648	C₄⋊C₄	—	53	1	no	—
649	C₄⋊C₄	—	53	1	no	—
650	C₄⋊C₄	—	106	4	no	—
651	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
652	C₂²⋊C₄	—	53	8	no	—
653	C₂²⋊C₄	—	53	1	no	—
654	C₂²⋊C₄	—	53	1	no	—
655	C₂²⋊C₄	—	53	1	no	—
656	C₂²⋊C₄	—	53	1	no	—
657	C₂²⋊C₄	—	53	1	no	—
658	C₂²⋊C₄	—	53	1	no	—
659	C₂²⋊C₄	—	106	4	no	—
660	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
661	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
662	C₄²	—	53	2	no	—
663	C₄²	—	53	2	no	—
664	C₄²	—	53	1	no	—
665	C₄²	—	53	1	no	—
666	C₄²	—	53	1	no	—
667	C₄²	—	106	1	no	—
668	C₄²	—	106	1	no	—
669	C₄²	—	106	1	no	—
670	C₄²	—	106	1	no	—
671	C₄²	—	106	1	no	—
672	C₄²	—	106	1	no	—
673	C₄²	—	106	4	no	—
674	C₄²	—	106	4	no	—
675	C₄²	—	106	4	no	—
676	C₄²	—	212	2	no	—
677	C₄²	C₂²×#6157	1	1	yes	characteristic
678	C₂³	—	53	1	no	—
679	C₂³	—	53	4	no	—
680	C₂³	—	53	1	no	—
681	C₂³	—	53	1	no	—
682	C₂³	—	106	1	no	—
683	C₂³	—	106	1	no	—
684	C₂³	—	106	2	no	—
685	C₂³	—	106	2	no	—
686	C₂³	—	106	1	no	—
687	C₂³	—	106	1	no	—
688	C₂³	—	106	2	no	—
689	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
690	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
691	D₄	—	2	2	no	—
692	D₄	—	106	2	no	—
693	D₄	—	106	2	no	—
694	D₄	—	106	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	53	1	no	—
700	C₂×C₄	—	53	1	no	—
701	C₂×C₄	—	53	1	no	—
702	C₂×C₄	—	53	1	no	—
703	C₂×C₄	—	53	1	no	—
704	C₂×C₄	—	53	4	no	—
705	C₂×C₄	—	53	4	no	—
706	C₂×C₄	—	53	4	no	—
707	C₂×C₄	—	53	1	no	—
708	C₂×C₄	—	53	1	no	—
709	C₂×C₄	—	53	1	no	—
710	C₂×C₄	—	53	1	no	—
711	C₂×C₄	—	106	1	no	—
712	C₂×C₄	—	106	1	no	—
713	C₂×C₄	—	106	1	no	—
714	C₂×C₄	—	106	1	no	—
715	C₂×C₄	—	106	1	no	—
716	C₂×C₄	—	106	1	no	—
717	C₂×C₄	—	106	2	no	—
718	C₂×C₄	—	106	2	no	—
719	C₂×C₄	—	106	1	no	—
720	C₂×C₄	—	106	1	no	—
721	C₂×C₄	—	106	1	no	—
722	C₂×C₄	—	106	1	no	—
723	C₂×C₄	—	106	1	no	—
724	C₂×C₄	—	106	1	no	—
725	C₂×C₄	—	106	2	no	—
726	C₂×C₄	—	106	2	no	—
727	C₂×C₄	—	106	2	no	—
728	C₂×C₄	—	106	2	no	—
729	C₂×C₄	—	106	2	no	—
730	C₂×C₄	—	106	2	no	—
731	C₂×C₄	—	106	1	no	—
732	C₂×C₄	—	106	1	no	—
733	C₂×C₄	—	106	1	no	—
734	C₂×C₄	—	106	1	no	—
735	C₂×C₄	—	106	2	no	—
736	C₂×C₄	—	106	2	no	—
737	C₂×C₄	—	106	2	no	—
738	C₂×C₄	—	212	8	no	—
739	C₂×C₄	—	212	8	no	—
740	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
741	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
742	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
743	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
744	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
745	C₈	—	2	1	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	53	4	no	—
749	C₈	—	53	2	no	—
750	C₈	—	106	2	no	—
751	C₈	—	106	2	no	—
752	C₈	—	106	2	no	—
753	C₈	—	106	1	no	—
754	C₈	—	106	1	no	—
755	C₈	—	106	1	no	—
756	C₈	D₄×#6157	1	2	yes	complemented
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	53	1	no	—
763	C₂²	—	53	1	no	—
764	C₂²	—	53	2	no	—
765	C₂²	—	53	2	no	—
766	C₂²	—	53	2	no	—
767	C₂²	—	106	4	no	—
768	C₂²	—	106	4	no	—
769	C₂²	—	106	1	no	—
770	C₂²	—	106	1	no	—
771	C₂²	—	106	1	no	—
772	C₂²	—	106	1	no	—
773	C₂²	—	106	1	no	—
774	C₂²	—	212	2	no	—
775	C₂²	—	212	2	no	—
776	C₂²	M₁₆×#6157	1	2	yes	complemented
777	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	53	1	no	—
783	C₄	—	53	1	no	—
784	C₄	—	106	4	no	—
785	C₄	—	106	4	no	—
786	C₄	—	106	4	no	—
787	C₄	—	106	1	no	—
788	C₄	—	106	1	no	—
789	C₄	—	106	1	no	—
790	C₄	—	106	1	no	—
791	C₄	—	212	2	no	—
792	C₄	C₂×D₄×#6157	1	1	yes	characteristic
793	C₄	#41×#6157	1	1	yes	characteristic
794	C₂	—	2	2	no	—
795	C₂	—	4	1	no	—
796	C₂	—	53	2	no	—
797	C₂	—	53	2	no	—
798	C₂	—	106	2	no	—
799	C₂	—	212	1	no	—
800	C₂	C₄×D₄×#6157	1	1	yes	characteristic
801	C₂	C₂×M₁₆×#6157	1	1	yes	characteristic
802	C₂	#20291285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#435	C₄
prime radical	C₂×D₄×D₅₃	C₂×C₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#435	#6157
hypocenter	C₅₃	#20491
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×#6157	C₂	semidirect
3. C₂²×#13133271	C₂	semidirect
5. #20290516	C₂	semidirect
6. #20290513	C₂	semidirect
7. #20290502	C₂	semidirect
8. #20290458	C₂	semidirect
9. #20290455	C₂	semidirect
10. #20290450	C₂	semidirect
11. C₈×C₂²⋊#6157	C₂	semidirect
12. #20290443	C₂	semidirect
13. #20290443	C₂	semidirect
14. #97×#6157	C₂	semidirect
21. #16811655	C₄	semidirect
22. #16811654	C₄	semidirect
23. #16811653	C₄	semidirect
24. #16811652	C₄	semidirect
57. #16810697	C₄	semidirect
58. #16810696	C₄	semidirect
59. #16810695	C₄	semidirect
60. #16810694	C₄	semidirect
61. #16810693	C₄	semidirect
62. #16810692	C₄	semidirect
63. #16810691	C₄	semidirect
68. C₅₃×#435	C₄	semidirect
71. C₂×#11719936	C₂×C₄	semidirect
74. C₂×#11719940	C₂×C₄	semidirect
77. C₂×D₅₃⋊C₈	C₂×C₄	semidirect
82. C₂²×#88324	C₂×C₄	semidirect
99. #13133284	C₂×C₄	semidirect
100. C₄⋊#88324	C₂×C₄	semidirect
101. #13133274	C₂×C₄	semidirect
102. #13133274	C₂×C₄	semidirect
103. C₂²⋊#88324	C₂×C₄	semidirect
104. C₂²⋊#88324	C₂×C₄	semidirect
105. #13133272	C₂×C₄	semidirect
106. #13133272	C₂×C₄	semidirect
112. #13133271	D₄	semidirect
123. C₂×#11719917	C₂×C₄	semidirect
124. C₂×#11719912	C₂×C₄	semidirect
125. C₂×#11719912	C₂×C₄	semidirect
128. C₂²×#88322	C₂×C₄	semidirect
131. C₂×C₈×D₅₃	C₂×C₄	semidirect
132. C₂×C₈×D₅₃	C₂×C₄	semidirect
148. C₄⋊#88322	C₂×C₄	semidirect
149. #13133146	C₂×C₄	semidirect
150. #13133146	C₂×C₄	semidirect
151. C₂²⋊#88322	C₂×C₄	semidirect
152. C₂²⋊#88322	C₂×C₄	semidirect
153. #13133129	C₂×C₄	semidirect
154. #13133129	C₂×C₄	semidirect
155. #13133129	C₂×C₄	semidirect
156. #13133129	C₂×C₄	semidirect
157. #13133128	C₂×C₄	semidirect
158. #13133127	C₂×C₄	semidirect
159. #13133127	C₂×C₄	semidirect
160. C₂×M₁₆×C₅₃	C₂×C₄	semidirect
161. C₂²×C₈×C₅₃	C₂×C₄	semidirect
163. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
164. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
165. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
166. #97×C₅₃	C₂×C₄	semidirect
206. C₂²⋊#6157	M₁₆	semidirect
346. #88324	C₄×D₄	semidirect
350. C₈×C₅₃	C₄×D₄	semidirect
354. #88322	C₄×D₄	semidirect
361. C₂²×C₅₃	C₄×M₁₆	semidirect
372. C₂×D₅₃	C₄×M₁₆	semidirect
436. #435	#6157	semidirect
470. C₅₃	#20491	semidirect
485. C₂×M₁₆	C₂×#6157	semidirect
503. C₂²×C₈	C₂×#6157	semidirect
537. C₄⋊C₈	C₂×#6157	semidirect
548. C₂²⋊C₈	C₂×#6157	semidirect
549. C₂²⋊C₈	C₂×#6157	semidirect
561. #97	C₂×#6157	semidirect
756. C₈	D₄×#6157	semidirect
776. C₂²	M₁₆×#6157	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#435	2
C₂×M₁₆×#6157	2
C₂²×#13133271	2
C₄×D₄×#6157	2
#20290516	2
#20290513	2
#20290502	2
#20290458	2
#20290455	2
#20290450	2
C₈×C₂²⋊#6157	2
#20290443	2
#97×#6157	2
#435×D₅₃	2
#20491	53