Subgroups — #28318825

Order 13568.

1118 conjugacy classes of subgroups.

The subgroup lattice has 792 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	C₄×D₄×#6157	C₂	1	1	yes	maximal, characteristic
3	#20290516	C₂	1	1	yes	maximal, characteristic, complemented
4	#20290513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×#6157	C₂	1	1	yes	maximal, characteristic, complemented
6	#20290458	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290455	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊#6157	C₂	1	1	yes	maximal, characteristic, complemented
10	#20290443	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²⋊C₈×#6157	C₂	1	1	yes	maximal, characteristic, complemented
12	#20290431	C₂	1	1	yes	maximal, characteristic, complemented
13	#20290377	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×(C₂×#6157)⋊C₈	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	#16811582	C₂²	1	1	yes	characteristic
29	C₂×#13133271	C₂²	1	1	yes	characteristic
30	C₂×#13133271	C₂²	1	1	yes	characteristic
31	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
32	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
33	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
34	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×#6157	C₄	1	2	yes	—
36	C₄×C₄⋊#6157	C₂²	1	1	yes	characteristic
37	C₂²⋊C₄×#6157	C₄	1	2	yes	—
38	C₂²⋊C₄×#6157	C₄	1	2	yes	—
39	C₄×C₂²⋊#6157	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊#6157	C₂²	1	1	yes	characteristic
41	C₄²×#6157	C₂²	1	1	yes	characteristic
42	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×#6157)⋊C₈	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×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
53	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
54	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
55	#16810697	C₄	1	1	yes	characteristic, complemented
56	#16810696	C₄	1	1	yes	characteristic, complemented
57	#16810695	C₄	1	1	yes	characteristic, complemented
58	#16810694	C₄	1	1	yes	characteristic, complemented
59	#16810693	C₄	1	1	yes	characteristic, complemented
60	#16810692	C₄	1	1	yes	characteristic, complemented
61	#16810691	C₄	1	1	yes	characteristic, complemented
62	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
63	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
64	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
65	#97×D₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#435	C₄	1	1	yes	characteristic, complemented
67	C₂³×#6157	C₂×C₄	1	2	yes	—
68	C₂³×#6157	C₂×C₄	1	2	yes	—
69	C₂×#11719936	C₂×C₄	1	2	yes	complemented
70	D₅₃⋊M₁₆	—	4	1	no	—
71	D₅₃⋊M₁₆	—	4	1	no	—
72	C₂×#11719940	C₂×C₄	1	2	yes	complemented
73	C₂×D₅₃⋊C₈	—	4	1	no	—
74	C₂×D₅₃⋊C₈	—	4	1	no	—
75	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	complemented
76	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×#88324	C₂×C₄	1	2	yes	complemented
81	D₄×#6157	—	2	8	no	—
82	C₂×C₄⋊#6157	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊#6157	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊#6157	C₂×C₄	1	2	yes	—
85	C₂×C₄×#6157	—	4	1	no	—
86	C₂×C₄×#6157	—	4	1	no	—
87	C₂×C₄×#6157	—	4	1	no	—
88	C₂×C₄×#6157	—	4	1	no	—
89	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
90	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
91	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
92	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
93	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
94	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
95	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
96	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
97	#13133284	C₂×C₄	1	2	yes	complemented
98	C₄⋊#88324	C₂×C₄	1	2	yes	complemented
99	#13133274	C₂×C₄	1	2	yes	complemented
100	#13133274	C₂×C₄	1	2	yes	complemented
101	C₂²⋊#88324	C₂×C₄	1	2	yes	complemented
102	C₂²⋊#88324	C₂×C₄	1	2	yes	complemented
103	#13133272	C₂×C₄	1	2	yes	complemented
104	#13133272	C₂×C₄	1	2	yes	complemented
105	#13133271	—	4	1	no	—
106	#13133271	—	4	1	no	—
107	C₈×#6157	—	4	1	no	—
108	C₈×#6157	—	4	1	no	—
109	C₈×#6157	—	4	1	no	—
110	C₈×#6157	—	4	1	no	—
111	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
112	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
113	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
114	C₂×D₄×D₅₃	C₂×C₄	1	1	yes	characteristic
115	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
117	C₂×#11719917	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×#11719912	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×#11719912	C₂×C₄	1	1	yes	characteristic, complemented
120	M₁₆×D₅₃	—	4	1	no	—
121	M₁₆×D₅₃	—	4	1	no	—
122	C₂²×#88322	C₂×C₄	1	1	yes	characteristic, complemented
123	C₂×C₈×D₅₃	—	4	1	no	—
124	C₂×C₈×D₅₃	—	4	1	no	—
125	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic, complemented
127	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
128	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
129	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
130	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
131	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
132	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
133	#13133179	C₂×C₄	1	1	yes	characteristic
134	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
135	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
136	#13133177	C₂×C₄	1	1	yes	characteristic
137	#13133177	C₂×C₄	1	1	yes	characteristic
138	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
141	C₄²×D₅₃	C₂³	1	1	yes	characteristic
142	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic, complemented
143	#13133146	C₂×C₄	1	1	yes	characteristic, complemented
144	#13133146	C₂×C₄	1	1	yes	characteristic, complemented
145	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic, complemented
146	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic, complemented
147	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
148	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
149	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
150	#13133129	C₂×C₄	1	1	yes	characteristic, complemented
151	#13133128	C₂×C₄	1	1	yes	characteristic, complemented
152	#13133127	C₂×C₄	1	1	yes	characteristic, complemented
153	#13133127	C₂×C₄	1	1	yes	characteristic, complemented
154	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
155	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
156	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
157	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
158	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
159	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
160	#97×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
161	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
162	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×#6157	—	2	4	no	—
164	C₂²×#6157	—	2	4	no	—
165	C₂²×#6157	—	2	4	no	—
166	C₂²×#6157	—	2	4	no	—
167	C₂²×#6157	—	4	2	no	—
168	C₂²×#6157	—	4	2	no	—
169	C₂²×#6157	C₂²×C₄	1	2	yes	—
170	C₂²×#6157	C₂²×C₄	1	2	yes	—
171	C₂²×#6157	C₂²×C₄	1	2	yes	—
172	C₂²×#6157	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₅₃	C₄²	1	1	yes	characteristic
174	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
177	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
178	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
180	D₄×D₅₃	—	2	4	no	—
181	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
182	C₂×C₄×D₅₃	—	2	1	no	—
183	C₂×C₄×D₅₃	—	2	1	no	—
184	C₂×C₄×D₅₃	—	2	1	no	—
185	C₂×C₄×D₅₃	—	2	1	no	—
186	C₂×C₄×D₅₃	—	2	1	no	—
187	C₂×C₄×D₅₃	—	2	1	no	—
188	C₂×C₄×D₅₃	—	2	1	no	—
189	C₂×C₄×D₅₃	—	2	1	no	—
190	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
199	C₂²⋊#6157	—	2	4	no	—
200	C₂²⋊#6157	M₁₆	1	8	yes	complemented
201	#11719940	—	4	2	no	—
202	C₂×#88324	—	4	2	no	—
203	C₂×#88324	C₂²×C₄	1	2	yes	—
204	C₂×#88324	C₂²×C₄	1	2	yes	—
205	C₂×#88324	C₂²×C₄	1	2	yes	—
206	C₂×#88324	C₂²×C₄	1	2	yes	—
207	C₄⋊#6157	—	2	4	no	—
208	C₄×#6157	—	2	4	no	—
209	C₄×#6157	—	2	4	no	—
210	C₄×#6157	—	2	1	no	—
211	C₄×#6157	—	2	1	no	—
212	C₄×#6157	—	2	1	no	—
213	C₄×#6157	—	2	1	no	—
214	C₄×#6157	—	2	1	no	—
215	C₄×#6157	—	2	1	no	—
216	C₄×#6157	—	2	1	no	—
217	C₄×#6157	—	2	1	no	—
218	C₄×#6157	—	4	2	no	—
219	C₄×#6157	—	4	2	no	—
220	#11719936	—	4	2	no	—
221	D₅₃⋊C₈	—	2	1	no	—
222	D₅₃⋊C₈	—	2	1	no	—
223	D₅₃⋊C₈	—	2	1	no	—
224	D₅₃⋊C₈	—	2	1	no	—
225	D₅₃⋊C₈	—	2	1	no	—
226	D₅₃⋊C₈	—	2	1	no	—
227	D₅₃⋊C₈	—	2	1	no	—
228	D₅₃⋊C₈	—	2	1	no	—
229	D₅₃⋊C₈	—	4	2	no	—
230	M₁₆×C₅₃	—	4	1	no	—
231	C₂×C₈×C₅₃	—	4	1	no	—
232	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
234	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
236	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
237	C₂²⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
238	C₂²⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
239	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
240	C₂²⋊Dic₅₃	C₄²	1	1	yes	characteristic
241	C₂²⋊Dic₅₃	C₄²	1	1	yes	characteristic
242	#11719921	C₄²	1	1	yes	characteristic
243	#11719921	C₄²	1	1	yes	characteristic
244	#11719921	C₄²	1	1	yes	characteristic
245	#11719921	C₄²	1	1	yes	characteristic
246	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
247	#11719919	C₄²	1	1	yes	characteristic
248	#11719919	C₄²	1	1	yes	characteristic
249	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
250	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
251	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
252	#11719917	—	4	1	no	—
253	C₂×#88322	—	4	1	no	—
254	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
255	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
256	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
257	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
258	#11719912	—	4	1	no	—
259	#11719912	—	4	1	no	—
260	C₈×D₅₃	—	2	1	no	—
261	C₈×D₅₃	—	2	1	no	—
262	C₈×D₅₃	—	2	1	no	—
263	C₈×D₅₃	—	2	1	no	—
264	C₈×D₅₃	—	2	1	no	—
265	C₈×D₅₃	—	2	1	no	—
266	C₈×D₅₃	—	2	1	no	—
267	C₈×D₅₃	—	2	1	no	—
268	C₈×D₅₃	—	4	1	no	—
269	C₈×D₅₃	—	4	1	no	—
270	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
271	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
272	C₂²×D₅₃	—	2	1	no	—
273	C₂²×D₅₃	—	2	1	no	—
274	C₂²×D₅₃	—	2	2	no	—
275	C₂²×D₅₃	—	2	1	no	—
276	C₂²×D₅₃	—	2	1	no	—
277	C₂²×D₅₃	—	2	2	no	—
278	C₂²×D₅₃	—	2	2	no	—
279	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
280	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
281	C₂²×D₅₃	C₂×M₁₆	1	4	yes	—
282	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
283	C₂×#6157	—	2	2	no	—
284	C₂×#6157	—	2	2	no	—
285	C₂×#6157	—	2	2	no	—
286	C₂×#6157	—	2	2	no	—
287	C₂×#6157	—	2	2	no	—
288	C₂×#6157	—	2	2	no	—
289	C₂×#6157	—	2	2	no	—
290	C₂×#6157	—	2	2	no	—
291	C₂×#6157	—	2	2	no	—
292	C₂×#6157	—	4	8	no	—
293	C₂×#6157	—	4	8	no	—
294	C₂×#6157	C₂×M₁₆	1	4	yes	—
295	C₂×#6157	C₂×M₁₆	1	4	yes	—
296	C₂×#6157	#131	1	4	yes	—
297	D₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	2	1	no	—
300	C₂×C₄×C₅₃	—	2	1	no	—
301	C₂×C₄×C₅₃	—	2	1	no	—
302	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
303	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
304	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
305	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
306	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
307	C₂²⋊D₅₃	—	2	2	no	—
308	C₂²⋊D₅₃	—	2	2	no	—
309	C₂×Dic₅₃	—	2	1	no	—
310	C₂×Dic₅₃	—	2	1	no	—
311	C₂×Dic₅₃	—	2	1	no	—
312	C₂×Dic₅₃	—	2	1	no	—
313	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
314	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
315	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
316	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
317	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
318	D₂₁₂	—	2	2	no	—
319	C₄×D₅₃	—	2	1	no	—
320	C₄×D₅₃	—	2	1	no	—
321	C₄×D₅₃	—	2	1	no	—
322	C₄×D₅₃	—	2	1	no	—
323	C₄×D₅₃	—	2	2	no	—
324	C₄×D₅₃	—	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	1	no	—
330	C₄×D₅₃	—	2	1	no	—
331	C₄×D₅₃	—	2	1	no	—
332	C₄×D₅₃	—	2	1	no	—
333	C₄×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
334	C₄×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
335	C₄×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
336	C₄×D₅₃	2₋¹⁺⁴	1	1	yes	characteristic
337	#88324	—	2	2	no	—
338	#88324	—	2	2	no	—
339	#88324	—	2	2	no	—
340	#88324	—	2	2	no	—
341	C₈×C₅₃	—	2	1	no	—
342	C₈×C₅₃	—	2	1	no	—
343	C₈×C₅₃	—	2	1	no	—
344	C₈×C₅₃	—	2	1	no	—
345	#88322	—	2	1	no	—
346	#88322	—	2	1	no	—
347	#88322	—	2	1	no	—
348	#88322	—	2	1	no	—
349	#20559	—	53	1	no	maximal, Sylow
350	C₂²×C₅₃	—	2	1	no	—
351	C₂²×C₅₃	—	2	1	no	—
352	C₂²×C₅₃	—	2	1	no	—
353	C₂²×C₅₃	—	2	1	no	—
354	C₂²×C₅₃	—	2	1	no	—
355	C₂²×C₅₃	C₄×M₁₆	1	2	yes	—
356	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
357	C₂×D₅₃	—	2	1	no	—
358	C₂×D₅₃	—	2	1	no	—
359	C₂×D₅₃	—	2	4	no	—
360	C₂×D₅₃	—	2	4	no	—
361	C₂×D₅₃	—	2	1	no	—
362	C₂×D₅₃	—	2	1	no	—
363	C₂×D₅₃	—	2	1	no	—
364	C₂×D₅₃	—	4	2	no	—
365	C₂×D₅₃	—	4	2	no	—
366	C₂×D₅₃	C₄×M₁₆	1	2	yes	—
367	C₂×D₅₃	#518	1	1	yes	characteristic
368	C₂×D₅₃	#520	1	1	yes	characteristic
369	C₂×D₅₃	C₂²×M₁₆	1	2	yes	—
370	C₂×D₅₃	C₂×#131	1	2	yes	—
371	#6157	—	2	4	no	—
372	#6157	—	2	4	no	—
373	#6157	—	2	4	no	—
374	#6157	—	4	2	no	—
375	C₄×C₅₃	—	2	1	no	—
376	C₄×C₅₃	—	2	1	no	—
377	C₄×C₅₃	—	2	1	no	—
378	C₄×C₅₃	—	2	1	no	—
379	C₄×C₅₃	#518	1	1	yes	characteristic
380	C₄×C₅₃	#520	1	1	yes	characteristic
381	Dic₅₃	—	2	1	no	—
382	Dic₅₃	—	2	1	no	—
383	Dic₅₃	—	2	1	no	—
384	Dic₅₃	—	2	1	no	—
385	Dic₅₃	#518	1	1	yes	characteristic
386	Dic₅₃	#520	1	1	yes	characteristic
387	C₂×#435	—	53	1	no	—
388	C₂×#435	—	53	1	no	—
389	C₄²×D₄	—	53	1	no	—
390	#1771	—	53	1	no	—
391	#1771	—	53	1	no	—
392	C₄×C₄⋊C₈	—	53	1	no	—
393	#1753	—	53	1	no	—
394	#1753	—	53	1	no	—
395	C₈×C₂²⋊C₄	—	53	1	no	—
396	C₈×C₂²⋊C₄	—	53	1	no	—
397	#1749	—	53	1	no	—
398	C₄×C₂²⋊C₈	—	53	1	no	—
399	#1745	—	53	1	no	—
400	#1728	—	53	1	no	—
401	C₂×#336	—	53	1	no	—
402	C₂×C₅₃	—	2	2	no	—
403	C₂×C₅₃	—	4	1	no	—
404	C₂×C₅₃	#2275	1	1	yes	characteristic
405	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
406	C₂×C₅₃	C₄×#131	1	1	yes	characteristic
407	D₅₃	—	2	2	no	—
408	D₅₃	—	4	1	no	—
409	D₅₃	#2974	1	2	yes	—
410	D₅₃	#2990	1	2	yes	—
411	C₂²×M₁₆	—	53	1	no	—
412	C₂²×M₁₆	—	53	1	no	—
413	C₂³×C₈	—	53	1	no	—
414	C₂³×C₈	—	53	1	no	—
415	C₂×C₄×D₄	—	53	1	no	—
416	C₂×C₄×D₄	—	53	2	no	—
417	C₂²×C₄²	—	53	1	no	—
418	C₂²×C₄²	—	53	1	no	—
419	#435	—	53	2	no	—
420	#435	—	53	2	no	—
421	#435	—	53	2	no	—
422	#435	—	53	2	no	—
423	#435	—	53	1	no	—
424	#435	—	53	1	no	—
425	#435	—	53	1	no	—
426	#435	—	53	1	no	—
427	#435	—	53	1	no	—
428	#435	—	53	1	no	—
429	#435	—	53	1	no	—
430	#435	#6157	1	1	yes	characteristic, complemented
431	C₂×C₄⋊C₈	—	53	1	no	—
432	C₂×C₄⋊C₈	—	53	1	no	—
433	C₂×C₂²⋊C₈	—	53	1	no	—
434	C₂×C₂²⋊C₈	—	53	1	no	—
435	C₂×C₂²⋊C₈	—	53	1	no	—
436	C₂×C₂²⋊C₈	—	53	1	no	—
437	C₂×#97	—	53	1	no	—
438	C₂×#97	—	53	1	no	—
439	C₂×#97	—	53	1	no	—
440	C₂×#97	—	53	1	no	—
441	C₂×C₄×C₈	—	53	1	no	—
442	C₂×C₄×C₈	—	53	1	no	—
443	C₂×C₄×C₈	—	53	1	no	—
444	C₂×C₄×C₈	—	53	1	no	—
445	C₄×C₄⋊C₄	—	53	1	no	—
446	C₄×C₄⋊C₄	—	53	2	no	—
447	C₄×C₂²⋊C₄	—	53	1	no	—
448	C₄×C₂²⋊C₄	—	53	1	no	—
449	C₄×C₂²⋊C₄	—	53	2	no	—
450	C₄×C₂²⋊C₄	—	53	2	no	—
451	C₄³	—	53	1	no	—
452	#336	—	53	1	no	—
453	#336	—	53	1	no	—
454	#336	—	53	1	no	—
455	#336	—	53	1	no	—
456	#336	—	53	1	no	—
457	#336	—	53	1	no	—
458	#336	—	53	1	no	—
459	#336	—	53	1	no	—
460	#336	—	53	1	no	—
461	#336	—	53	1	no	—
462	C₅₃	#20559	1	1	yes	characteristic, complemented, Sylow
463	C₂²×D₄	—	53	1	no	—
464	C₂³×C₄	—	53	1	no	—
465	C₂³×C₄	—	53	1	no	—
466	C₂³×C₄	—	53	2	no	—
467	C₂³×C₄	—	53	2	no	—
468	C₂×M₁₆	—	53	2	no	—
469	C₂×M₁₆	—	53	2	no	—
470	C₂×M₁₆	—	53	1	no	—
471	C₂×M₁₆	—	53	1	no	—
472	C₂×M₁₆	—	53	1	no	—
473	C₂×M₁₆	—	212	1	no	—
474	C₂×M₁₆	—	212	1	no	—
475	C₂×M₁₆	—	212	1	no	—
476	C₂×M₁₆	—	212	1	no	—
477	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic, complemented
478	C₂²×C₈	—	53	1	no	—
479	C₂²×C₈	—	53	1	no	—
480	C₂²×C₈	—	53	1	no	—
481	C₂²×C₈	—	53	1	no	—
482	C₂²×C₈	—	53	2	no	—
483	C₂²×C₈	—	53	2	no	—
484	C₂²×C₈	—	53	1	no	—
485	C₂²×C₈	—	53	1	no	—
486	C₂²×C₈	—	53	1	no	—
487	C₂²×C₈	—	53	1	no	—
488	C₂²×C₈	—	53	1	no	—
489	C₂²×C₈	—	53	1	no	—
490	C₂²×C₈	—	53	1	no	—
491	C₂²×C₈	—	212	1	no	—
492	C₂²×C₈	—	212	1	no	—
493	C₂²×C₈	—	212	1	no	—
494	C₂²×C₈	—	212	1	no	—
495	C₂²×C₈	C₂×#6157	1	1	yes	characteristic, complemented
496	C₄×D₄	—	53	1	no	—
497	C₄×D₄	—	53	1	no	—
498	C₄×D₄	—	53	1	no	—
499	C₄×D₄	—	53	1	no	—
500	C₄×D₄	—	53	1	no	—
501	C₄×D₄	—	53	1	no	—
502	C₄×D₄	—	53	1	no	—
503	C₄×D₄	—	106	8	no	—
504	C₄×D₄	C₂×#6157	1	1	yes	characteristic
505	C₂×C₄⋊C₄	—	53	1	no	—
506	C₂×C₄⋊C₄	—	53	2	no	—
507	C₂×C₂²⋊C₄	—	53	2	no	—
508	C₂×C₂²⋊C₄	—	53	1	no	—
509	C₂×C₂²⋊C₄	—	53	1	no	—
510	C₂×C₂²⋊C₄	—	53	2	no	—
511	C₂×C₄²	—	53	1	no	—
512	C₂×C₄²	—	53	2	no	—
513	C₂×C₄²	—	53	1	no	—
514	C₂×C₄²	—	53	1	no	—
515	C₂×C₄²	—	53	1	no	—
516	C₂×C₄²	—	53	1	no	—
517	C₂×C₄²	—	53	2	no	—
518	C₂×C₄²	—	53	2	no	—
519	C₂×C₄²	—	53	2	no	—
520	C₂×C₄²	—	212	1	no	—
521	C₂×C₄²	—	212	1	no	—
522	C₂×C₄²	—	212	1	no	—
523	C₂×C₄²	—	212	1	no	—
524	C₄⋊C₈	—	53	2	no	—
525	C₄⋊C₈	—	53	2	no	—
526	C₄⋊C₈	—	53	1	no	—
527	C₄⋊C₈	—	53	1	no	—
528	C₄⋊C₈	—	53	1	no	—
529	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic, complemented
530	C₂²⋊C₈	—	53	2	no	—
531	C₂²⋊C₈	—	53	2	no	—
532	C₂²⋊C₈	—	53	2	no	—
533	C₂²⋊C₈	—	53	2	no	—
534	C₂²⋊C₈	—	53	1	no	—
535	C₂²⋊C₈	—	53	1	no	—
536	C₂²⋊C₈	—	53	1	no	—
537	C₂²⋊C₈	—	53	1	no	—
538	C₂²⋊C₈	—	53	1	no	—
539	C₂²⋊C₈	—	53	1	no	—
540	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic, complemented
541	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic, complemented
542	#97	—	53	2	no	—
543	#97	—	53	2	no	—
544	#97	—	53	1	no	—
545	#97	—	53	1	no	—
546	#97	—	53	1	no	—
547	#97	—	212	1	no	—
548	#97	—	212	1	no	—
549	#97	C₂×#6157	1	1	yes	characteristic, complemented
550	C₄×C₈	—	212	1	no	—
551	C₄×C₈	—	212	1	no	—
552	C₄×C₈	—	212	1	no	—
553	C₄×C₈	—	212	1	no	—
554	#95	—	53	2	no	—
555	#95	—	53	2	no	—
556	#95	—	53	2	no	—
557	C₂⁴	—	53	1	no	—
558	C₂⁴	—	53	1	no	—
559	C₂×D₄	—	53	1	no	—
560	C₂×D₄	—	53	1	no	—
561	C₂×D₄	—	53	1	no	—
562	C₂×D₄	—	106	4	no	—
563	C₂×D₄	C₄×#6157	1	1	yes	characteristic
564	C₂²×C₄	—	53	1	no	—
565	C₂²×C₄	—	53	2	no	—
566	C₂²×C₄	—	53	2	no	—
567	C₂²×C₄	—	53	2	no	—
568	C₂²×C₄	—	53	1	no	—
569	C₂²×C₄	—	53	1	no	—
570	C₂²×C₄	—	53	1	no	—
571	C₂²×C₄	—	53	1	no	—
572	C₂²×C₄	—	53	1	no	—
573	C₂²×C₄	—	53	1	no	—
574	C₂²×C₄	—	53	1	no	—
575	C₂²×C₄	—	53	1	no	—
576	C₂²×C₄	—	53	1	no	—
577	C₂²×C₄	—	53	1	no	—
578	C₂²×C₄	—	53	2	no	—
579	C₂²×C₄	—	106	1	no	—
580	C₂²×C₄	—	106	1	no	—
581	C₂²×C₄	—	106	1	no	—
582	C₂²×C₄	—	106	1	no	—
583	C₂²×C₄	—	106	1	no	—
584	C₂²×C₄	—	106	1	no	—
585	C₂²×C₄	—	106	1	no	—
586	C₂²×C₄	—	106	1	no	—
587	C₂²×C₄	—	106	4	no	—
588	C₂²×C₄	—	106	4	no	—
589	C₂²×C₄	—	106	4	no	—
590	C₂²×C₄	—	106	4	no	—
591	C₂²×C₄	—	212	2	no	—
592	C₂²×C₄	—	212	2	no	—
593	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
594	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
595	M₁₆	—	4	1	no	—
596	M₁₆	—	212	1	no	—
597	M₁₆	—	212	1	no	—
598	M₁₆	—	212	1	no	—
599	M₁₆	—	212	2	no	—
600	M₁₆	—	212	2	no	—
601	C₂×C₈	—	4	1	no	—
602	C₂×C₈	—	53	2	no	—
603	C₂×C₈	—	53	2	no	—
604	C₂×C₈	—	53	2	no	—
605	C₂×C₈	—	53	2	no	—
606	C₂×C₈	—	53	1	no	—
607	C₂×C₈	—	53	1	no	—
608	C₂×C₈	—	53	1	no	—
609	C₂×C₈	—	53	1	no	—
610	C₂×C₈	—	106	1	no	—
611	C₂×C₈	—	106	1	no	—
612	C₂×C₈	—	106	1	no	—
613	C₂×C₈	—	106	1	no	—
614	C₂×C₈	—	106	1	no	—
615	C₂×C₈	—	106	1	no	—
616	C₂×C₈	—	106	1	no	—
617	C₂×C₈	—	106	1	no	—
618	C₂×C₈	—	106	1	no	—
619	C₂×C₈	—	106	1	no	—
620	C₂×C₈	—	106	1	no	—
621	C₂×C₈	—	106	1	no	—
622	C₂×C₈	—	106	1	no	—
623	C₂×C₈	—	106	1	no	—
624	C₂×C₈	—	106	1	no	—
625	C₂×C₈	—	106	1	no	—
626	C₂×C₈	—	212	1	no	—
627	C₂×C₈	—	212	1	no	—
628	C₂×C₈	—	212	1	no	—
629	C₂×C₈	—	212	2	no	—
630	C₂×C₈	—	212	2	no	—
631	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
632	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
633	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
634	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
635	C₄⋊C₄	—	53	1	no	—
636	C₄⋊C₄	—	53	1	no	—
637	C₄⋊C₄	—	53	1	no	—
638	C₄⋊C₄	—	106	4	no	—
639	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
640	C₂²⋊C₄	—	53	8	no	—
641	C₂²⋊C₄	—	53	1	no	—
642	C₂²⋊C₄	—	53	1	no	—
643	C₂²⋊C₄	—	53	1	no	—
644	C₂²⋊C₄	—	53	1	no	—
645	C₂²⋊C₄	—	53	1	no	—
646	C₂²⋊C₄	—	53	1	no	—
647	C₂²⋊C₄	—	106	4	no	—
648	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
649	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
650	C₄²	—	53	1	no	—
651	C₄²	—	53	1	no	—
652	C₄²	—	53	1	no	—
653	C₄²	—	106	1	no	—
654	C₄²	—	106	1	no	—
655	C₄²	—	106	1	no	—
656	C₄²	—	106	1	no	—
657	C₄²	—	106	1	no	—
658	C₄²	—	106	1	no	—
659	C₄²	—	106	4	no	—
660	C₄²	—	106	1	no	—
661	C₄²	—	106	1	no	—
662	C₄²	—	106	4	no	—
663	C₄²	—	212	2	no	—
664	C₄²	—	212	2	no	—
665	C₄²	C₂²×#6157	1	1	yes	characteristic
666	C₂³	—	53	1	no	—
667	C₂³	—	53	4	no	—
668	C₂³	—	53	1	no	—
669	C₂³	—	53	1	no	—
670	C₂³	—	106	1	no	—
671	C₂³	—	106	1	no	—
672	C₂³	—	106	2	no	—
673	C₂³	—	106	2	no	—
674	C₂³	—	106	1	no	—
675	C₂³	—	106	1	no	—
676	C₂³	—	106	2	no	—
677	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
678	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
679	D₄	—	2	2	no	—
680	D₄	—	106	2	no	—
681	D₄	—	106	2	no	—
682	D₄	—	106	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	53	1	no	—
688	C₂×C₄	—	53	1	no	—
689	C₂×C₄	—	53	1	no	—
690	C₂×C₄	—	53	1	no	—
691	C₂×C₄	—	53	1	no	—
692	C₂×C₄	—	53	4	no	—
693	C₂×C₄	—	53	4	no	—
694	C₂×C₄	—	53	4	no	—
695	C₂×C₄	—	53	1	no	—
696	C₂×C₄	—	53	1	no	—
697	C₂×C₄	—	53	1	no	—
698	C₂×C₄	—	53	1	no	—
699	C₂×C₄	—	106	1	no	—
700	C₂×C₄	—	106	1	no	—
701	C₂×C₄	—	106	1	no	—
702	C₂×C₄	—	106	1	no	—
703	C₂×C₄	—	106	2	no	—
704	C₂×C₄	—	106	2	no	—
705	C₂×C₄	—	106	1	no	—
706	C₂×C₄	—	106	1	no	—
707	C₂×C₄	—	106	1	no	—
708	C₂×C₄	—	106	1	no	—
709	C₂×C₄	—	106	1	no	—
710	C₂×C₄	—	106	1	no	—
711	C₂×C₄	—	106	1	no	—
712	C₂×C₄	—	106	1	no	—
713	C₂×C₄	—	106	2	no	—
714	C₂×C₄	—	106	2	no	—
715	C₂×C₄	—	106	2	no	—
716	C₂×C₄	—	106	2	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	2	no	—
724	C₂×C₄	—	106	2	no	—
725	C₂×C₄	—	106	2	no	—
726	C₂×C₄	—	212	8	no	—
727	C₂×C₄	—	212	8	no	—
728	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
729	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
730	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
731	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
732	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
733	C₈	—	2	1	no	—
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	1	no	—
737	C₈	—	106	2	no	—
738	C₈	—	106	2	no	—
739	C₈	—	106	2	no	—
740	C₈	—	106	2	no	—
741	C₈	—	106	1	no	—
742	C₈	—	106	1	no	—
743	C₈	—	106	1	no	—
744	C₈	—	106	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	53	1	no	—
751	C₂²	—	53	1	no	—
752	C₂²	—	53	2	no	—
753	C₂²	—	53	2	no	—
754	C₂²	—	53	2	no	—
755	C₂²	—	106	4	no	—
756	C₂²	—	106	4	no	—
757	C₂²	—	106	1	no	—
758	C₂²	—	106	1	no	—
759	C₂²	—	106	1	no	—
760	C₂²	—	106	1	no	—
761	C₂²	—	106	1	no	—
762	C₂²	—	212	2	no	—
763	C₂²	—	212	2	no	—
764	C₂²	M₁₆×#6157	1	2	yes	—
765	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	53	1	no	—
771	C₄	—	53	1	no	—
772	C₄	—	106	4	no	—
773	C₄	—	106	4	no	—
774	C₄	—	106	4	no	—
775	C₄	—	106	1	no	—
776	C₄	—	106	1	no	—
777	C₄	—	106	1	no	—
778	C₄	—	106	1	no	—
779	C₄	—	212	2	no	—
780	C₄	#16811690	1	1	yes	characteristic
781	C₄	#16811692	1	1	yes	characteristic
782	C₂	—	2	2	no	—
783	C₂	—	4	1	no	—
784	C₂	—	53	2	no	—
785	C₂	—	53	2	no	—
786	C₂	—	106	2	no	—
787	C₂	—	212	1	no	—
788	C₂	#20291154	1	1	yes	characteristic
789	C₂	C₂×M₁₆×#6157	1	1	yes	characteristic
790	C₂	#131×#6157	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	#20559
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
3. #20290516	C₂	semidirect
4. #20290513	C₂	semidirect
5. C₄⋊C₈×#6157	C₂	semidirect
6. #20290458	C₂	semidirect
7. #20290455	C₂	semidirect
8. #20290450	C₂	semidirect
9. C₈×C₂²⋊#6157	C₂	semidirect
10. #20290443	C₂	semidirect
11. C₂²⋊C₈×#6157	C₂	semidirect
12. #20290431	C₂	semidirect
13. #20290377	C₂	semidirect
14. C₂×(C₂×#6157)⋊C₈	C₂	semidirect
21. #16811655	C₄	semidirect
22. #16811654	C₄	semidirect
23. #16811653	C₄	semidirect
24. #16811652	C₄	semidirect
55. #16810697	C₄	semidirect
56. #16810696	C₄	semidirect
57. #16810695	C₄	semidirect
58. #16810694	C₄	semidirect
59. #16810693	C₄	semidirect
60. #16810692	C₄	semidirect
61. #16810691	C₄	semidirect
66. C₅₃×#435	C₄	semidirect
69. C₂×#11719936	C₂×C₄	semidirect
72. C₂×#11719940	C₂×C₄	semidirect
75. C₂×D₅₃⋊C₈	C₂×C₄	semidirect
80. C₂²×#88324	C₂×C₄	semidirect
97. #13133284	C₂×C₄	semidirect
98. C₄⋊#88324	C₂×C₄	semidirect
99. #13133274	C₂×C₄	semidirect
100. #13133274	C₂×C₄	semidirect
101. C₂²⋊#88324	C₂×C₄	semidirect
102. C₂²⋊#88324	C₂×C₄	semidirect
103. #13133272	C₂×C₄	semidirect
104. #13133272	C₂×C₄	semidirect
117. C₂×#11719917	C₂×C₄	semidirect
118. C₂×#11719912	C₂×C₄	semidirect
119. C₂×#11719912	C₂×C₄	semidirect
122. C₂²×#88322	C₂×C₄	semidirect
125. C₂×C₈×D₅₃	C₂×C₄	semidirect
126. C₂×C₈×D₅₃	C₂×C₄	semidirect
142. C₄⋊#88322	C₂×C₄	semidirect
143. #13133146	C₂×C₄	semidirect
144. #13133146	C₂×C₄	semidirect
145. C₂²⋊#88322	C₂×C₄	semidirect
146. C₂²⋊#88322	C₂×C₄	semidirect
147. #13133129	C₂×C₄	semidirect
148. #13133129	C₂×C₄	semidirect
149. #13133129	C₂×C₄	semidirect
150. #13133129	C₂×C₄	semidirect
151. #13133128	C₂×C₄	semidirect
152. #13133127	C₂×C₄	semidirect
153. #13133127	C₂×C₄	semidirect
154. C₂×M₁₆×C₅₃	C₂×C₄	semidirect
155. C₂²×C₈×C₅₃	C₂×C₄	semidirect
157. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
158. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
159. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
160. #97×C₅₃	C₂×C₄	semidirect
200. C₂²⋊#6157	M₁₆	semidirect
430. #435	#6157	semidirect
462. C₅₃	#20559	semidirect
477. C₂×M₁₆	C₂×#6157	semidirect
495. C₂²×C₈	C₂×#6157	semidirect
529. C₄⋊C₈	C₂×#6157	semidirect
540. C₂²⋊C₈	C₂×#6157	semidirect
541. C₂²⋊C₈	C₂×#6157	semidirect
549. #97	C₂×#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
C₄×D₄×#6157	2
#20290516	2
#20290513	2
C₄⋊C₈×#6157	2
#20290458	2
#20290455	2
#20290450	2
C₈×C₂²⋊#6157	2
#20290443	2
C₂²⋊C₈×#6157	2
#20290431	2
#20290377	2
C₂×(C₂×#6157)⋊C₈	2
#435×D₅₃	2
#20559	53