Subgroups — #30680531

Order 16768.

1032 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554066	C₂	1	2	yes	maximal, complemented
2	#22554056	C₂	1	2	yes	maximal, complemented
3	#22554035	C₂	1	2	yes	maximal, complemented
4	#22553985	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₂₆₂	C₂	1	2	yes	maximal, complemented
6	#22553971	C₂	1	2	yes	maximal, complemented
7	#22553958	C₂	1	2	yes	maximal, complemented
8	#22553937	C₂	1	2	yes	maximal, complemented
9	#22553933	C₂	1	2	yes	maximal, complemented
10	#22553928	C₂	1	4	yes	maximal, complemented
11	#22553899	C₂	1	2	yes	maximal, complemented
12	#22553888	C₂	1	2	yes	maximal, complemented
13	#22553869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16862234	C₂	1	1	yes	maximal, characteristic, complemented
15	#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523513	C₂²	1	2	yes	—
17	C₂²×Dic₂₆₂	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₆₂	C₂²	1	2	yes	complemented
19	C₂²×D₅₂₄	C₂²	1	1	yes	characteristic
20	#16862246	C₂²	1	1	yes	characteristic, complemented
21	#16862246	C₂²	1	1	yes	characteristic, complemented
22	#16862246	C₂²	1	2	yes	complemented
23	#16862245	C₂²	1	4	yes	complemented
24	#16862241	C₂²	1	4	yes	complemented
25	#16862241	C₂²	1	4	yes	complemented
26	#16862241	C₂²	1	4	yes	complemented
27	#16862238	C₂²	1	2	yes	complemented
28	#16862234	C₂²	1	2	yes	—
29	#16862234	C₂²	1	2	yes	—
30	#16862234	C₂²	1	2	yes	—
31	#16862234	C₂²	1	2	yes	—
32	#16862234	C₂²	1	2	yes	—
33	#16862232	C₂²	1	4	yes	complemented
34	#16862232	C₂²	1	4	yes	complemented
35	#16862231	C₂²	1	4	yes	—
36	#16862230	C₂²	1	4	yes	complemented
37	#16862230	C₂²	1	4	yes	complemented
38	#16862228	C₂²	1	4	yes	complemented
39	#16862226	C₂²	1	4	yes	complemented
40	#16862226	C₂²	1	4	yes	complemented
41	#16862225	C₂²	1	2	yes	—
42	#16862225	C₂²	1	2	yes	—
43	#16862225	C₂²	1	2	yes	complemented
44	#16862224	C₂²	1	4	yes	complemented
45	#16862224	C₂²	1	4	yes	complemented
46	#16862223	C₂²	1	4	yes	—
47	#16862223	C₂²	1	4	yes	complemented
48	#16862222	C₂²	1	4	yes	complemented
49	#16862220	C₂²	1	2	yes	—
50	#16862219	C₂²	1	4	yes	—
51	#16862218	C₂²	1	4	yes	complemented
52	#16862214	C₂²	1	4	yes	—
53	C₄×Dic₂₆₂	C₂²	1	2	yes	complemented
54	C₄×Dic₂₆₂	C₂²	1	2	yes	complemented
55	C₄×Dic₂₆₂	C₂²	1	2	yes	complemented
56	C₄×D₅₂₄	C₂²	1	2	yes	—
57	D₄×Dic₁₃₁	C₂²	1	4	yes	—
58	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	4	yes	complemented
59	#16862205	C₂²	1	2	yes	—
60	#16862204	C₂²	1	4	yes	complemented
61	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	2	yes	—
62	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₁₃₁	C₂²	1	4	yes	—
64	#126×C₁₃₁	C₂²	1	2	yes	complemented
65	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
66	#124×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
67	#123×C₁₃₁	C₂²	1	2	yes	—
68	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
69	#121×C₁₃₁	C₂²	1	1	yes	characteristic
70	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
72	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
73	#117×C₁₃₁	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
75	C₂³×D₁₃₁	C₂³	1	2	yes	—
76	#14523513	—	4	4	no	—
77	C₂×Dic₂₆₂	—	4	2	no	—
78	C₂×Dic₂₆₂	—	4	4	no	—
79	C₂×Dic₂₆₂	C₂³	1	2	yes	—
80	C₂×Dic₂₆₂	C₂³	1	2	yes	—
81	C₂×Dic₂₆₂	C₂³	1	2	yes	—
82	C₂×Dic₂₆₂	C₂³	1	4	yes	—
83	C₂×Dic₂₆₂	C₂³	1	2	yes	—
84	C₂×D₅₂₄	—	4	2	no	—
85	C₂×D₅₂₄	C₂³	1	2	yes	—
86	C₂×D₅₂₄	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₃₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₃₁	C₂³	1	4	yes	—
89	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
90	C₂²×Dic₁₃₁	C₂³	1	4	yes	—
91	C₂×C₄×D₁₃₁	C₂³	1	4	yes	—
92	C₂×C₄×D₁₃₁	C₂³	1	4	yes	—
93	C₄⋊Dic₁₃₁	C₂³	1	4	yes	—
94	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
95	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
96	C₄⋊Dic₁₃₁	C₂³	1	4	yes	—
97	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
98	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
99	Dic₁₃₁⋊C₄	C₂³	1	4	yes	—
100	Dic₁₃₁⋊C₄	C₂³	1	4	yes	—
101	Dic₁₃₁⋊C₄	C₂³	1	4	yes	—
102	Dic₁₃₁⋊C₄	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₃₁	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₃₁	C₂³	1	4	yes	—
105	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
106	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
111	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
113	C₄×Dic₁₃₁	C₂³	1	4	yes	—
114	C₄×Dic₁₃₁	C₂³	1	4	yes	—
115	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
117	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₁	C₂³	1	2	yes	—
119	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
127	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₄²×C₁₃₁	C₂³	1	2	yes	—
134	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
135	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₁₃₁	—	2	4	no	—
139	C₂²×D₁₃₁	—	4	2	no	—
140	C₂²×D₁₃₁	—	4	2	no	—
141	C₂²×D₁₃₁	C₂⁴	1	4	yes	—
142	Dic₂₆₂	—	2	4	no	—
143	Dic₂₆₂	—	2	4	no	—
144	Dic₂₆₂	—	4	4	no	—
145	Dic₂₆₂	—	4	2	no	—
146	Dic₂₆₂	—	4	2	no	—
147	D₅₂₄	—	2	4	no	—
148	D₅₂₄	—	4	2	no	—
149	C₂²⋊D₁₃₁	—	4	4	no	—
150	C₂²⋊D₁₃₁	—	4	4	no	—
151	C₂×Dic₁₃₁	—	4	4	no	—
152	C₂×Dic₁₃₁	—	4	2	no	—
153	C₂×Dic₁₃₁	C₂⁴	1	4	yes	—
154	C₂×Dic₁₃₁	C₂⁴	1	4	yes	—
155	C₂×Dic₁₃₁	C₂⁴	1	4	yes	—
156	C₄×D₁₃₁	—	4	4	no	—
157	C₄×D₁₃₁	—	4	4	no	—
158	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
159	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₃₁	—	4	1	no	—
161	D₄×C₁₃₁	—	2	4	no	—
162	D₄×C₁₃₁	—	4	1	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	2	2	no	—
165	C₂×C₄×C₁₃₁	—	2	4	no	—
166	C₂×C₄×C₁₃₁	—	4	1	no	—
167	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
176	C₂²×C₁₃₁	—	2	1	no	—
177	C₂²×C₁₃₁	—	2	1	no	—
178	C₂²×C₁₃₁	—	2	2	no	—
179	C₂²×C₁₃₁	—	2	2	no	—
180	C₂²×C₁₃₁	—	2	2	no	—
181	C₂²×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
182	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
183	C₂×D₁₃₁	—	2	4	no	—
184	C₂×D₁₃₁	—	2	4	no	—
185	C₂×D₁₃₁	—	2	4	no	—
186	C₂×D₁₃₁	—	8	4	no	—
187	C₄×C₁₃₁	—	2	2	no	—
188	C₄×C₁₃₁	—	2	1	no	—
189	C₄×C₁₃₁	—	2	1	no	—
190	C₄×C₁₃₁	—	2	1	no	—
191	C₄×C₁₃₁	—	2	2	no	—
192	C₄×C₁₃₁	—	2	1	no	—
193	C₄×C₁₃₁	—	2	1	no	—
194	C₄×C₁₃₁	—	2	2	no	—
195	C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
196	Dic₁₃₁	—	2	4	no	—
197	Dic₁₃₁	—	2	4	no	—
198	Dic₁₃₁	—	2	4	no	—
199	C₂×C₁₃₁	—	2	2	no	—
200	C₂×C₁₃₁	—	4	2	no	—
201	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₁₃₁	#585	1	1	yes	characteristic
204	D₁₃₁	—	4	4	no	—
205	C₁₃₁	#3561	1	1	yes	characteristic, complemented, Sylow
206	#3561	—	131	1	no	maximal, Sylow
207	#563	—	131	2	no	—
208	#562	—	131	2	no	—
209	#556	—	131	2	no	—
210	#551	—	131	4	no	—
211	D₄×Q₈	—	131	2	no	—
212	#548	—	131	2	no	—
213	#546	—	131	2	no	—
214	#543	—	131	2	no	—
215	#542	—	131	4	no	—
216	#542	—	131	2	no	—
217	#538	—	131	2	no	—
218	#536	—	131	2	no	—
219	#533	—	131	1	no	—
220	#529	D₁₃₁	1	1	yes	characteristic, complemented
221	C₂×#124	—	131	1	no	—
222	C₂×#41	—	131	2	no	—
223	C₂²×Q₈	—	131	1	no	—
224	C₂²×Q₈	—	131	2	no	—
225	C₂²×D₄	—	131	1	no	—
226	C₄⋊Q₈	—	131	4	no	—
227	C₄⋊Q₈	—	131	1	no	—
228	C₄⋊Q₈	—	131	1	no	—
229	C₄⋊Q₈	—	131	2	no	—
230	#126	—	131	4	no	—
231	#126	—	131	4	no	—
232	#126	—	131	4	no	—
233	#126	C₂×D₁₃₁	1	2	yes	complemented
234	#125	—	131	2	no	—
235	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
236	#124	—	131	4	no	—
237	#124	—	131	4	no	—
238	#124	—	131	2	no	—
239	#124	—	131	2	no	—
240	#124	—	131	2	no	—
241	#124	—	131	2	no	—
242	#124	—	131	2	no	—
243	#124	C₂×D₁₃₁	1	1	yes	characteristic, complemented
244	#123	—	131	4	no	—
245	#123	—	131	4	no	—
246	#123	—	131	4	no	—
247	#123	—	131	4	no	—
248	#123	C₂×D₁₃₁	1	2	yes	—
249	C₂²⋊Q₈	—	131	4	no	—
250	C₂²⋊Q₈	—	131	2	no	—
251	C₂²⋊Q₈	—	131	2	no	—
252	C₂²⋊Q₈	—	131	2	no	—
253	C₂²⋊Q₈	—	131	4	no	—
254	C₂²⋊Q₈	—	131	4	no	—
255	C₂²⋊Q₈	—	131	4	no	—
256	C₂²⋊Q₈	—	131	4	no	—
257	C₂²⋊Q₈	—	131	4	no	—
258	C₂²⋊Q₈	—	131	4	no	—
259	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
260	#121	—	131	4	no	—
261	#121	—	131	2	no	—
262	#121	—	131	4	no	—
263	#121	C₂×D₁₃₁	1	1	yes	characteristic
264	#120	—	131	4	no	—
265	C₄×Q₈	—	131	2	no	—
266	C₄×Q₈	—	131	2	no	—
267	C₄×Q₈	—	131	2	no	—
268	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
269	C₄×D₄	—	131	4	no	—
270	C₄×D₄	—	131	4	no	—
271	C₄×D₄	—	131	2	no	—
272	C₄×D₄	C₂×D₁₃₁	1	2	yes	—
273	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
274	#117	—	131	2	no	—
275	#117	—	131	4	no	—
276	#117	C₂×D₁₃₁	1	2	yes	complemented
277	C₂×C₂²⋊C₄	—	131	2	no	—
278	C₂×C₂²⋊C₄	—	131	2	no	—
279	C₂×C₂²⋊C₄	—	131	4	no	—
280	C₂×C₄²	C₂×D₁₃₁	1	1	yes	characteristic
281	C₂⁴	—	131	2	no	—
282	#41	—	524	4	no	—
283	C₂×Q₈	—	524	2	no	—
284	C₂×Q₈	—	524	4	no	—
285	C₂×Q₈	—	131	2	no	—
286	C₂×Q₈	—	131	2	no	—
287	C₂×Q₈	—	131	2	no	—
288	C₂×Q₈	—	131	4	no	—
289	C₂×Q₈	—	131	2	no	—
290	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
291	C₂×D₄	—	524	2	no	—
292	C₂×D₄	—	131	4	no	—
293	C₂×D₄	—	131	4	no	—
294	C₂×D₄	—	131	2	no	—
295	C₂×D₄	—	131	2	no	—
296	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
297	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
298	C₂²×C₄	—	131	2	no	—
299	C₂²×C₄	—	131	4	no	—
300	C₂²×C₄	—	131	4	no	—
301	C₂²×C₄	—	131	4	no	—
302	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₃₁	1	2	yes	—
305	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
306	C₄⋊C₄	—	131	4	no	—
307	C₄⋊C₄	—	131	4	no	—
308	C₄⋊C₄	—	131	4	no	—
309	C₄⋊C₄	—	131	4	no	—
310	C₄⋊C₄	—	131	4	no	—
311	C₄⋊C₄	—	131	2	no	—
312	C₄⋊C₄	—	131	2	no	—
313	C₄⋊C₄	—	131	2	no	—
314	C₄⋊C₄	—	131	4	no	—
315	C₄⋊C₄	—	131	2	no	—
316	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
317	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
318	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
319	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
320	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
321	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
322	C₂²⋊C₄	—	131	4	no	—
323	C₂²⋊C₄	—	131	4	no	—
324	C₂²⋊C₄	—	131	4	no	—
325	C₂²⋊C₄	—	131	4	no	—
326	C₂²⋊C₄	—	131	4	no	—
327	C₂²⋊C₄	—	131	4	no	—
328	C₂²⋊C₄	—	131	4	no	—
329	C₂²⋊C₄	—	131	4	no	—
330	C₂²⋊C₄	—	131	4	no	—
331	C₂²⋊C₄	—	131	4	no	—
332	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
333	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
334	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
335	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
336	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
337	C₄²	—	131	4	no	—
338	C₄²	—	131	4	no	—
339	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
340	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
341	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
342	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
343	C₄²	C₂²×D₁₃₁	1	2	yes	—
344	C₂³	—	262	4	no	—
345	C₂³	—	524	2	no	—
346	C₂³	—	524	2	no	—
347	C₂³	—	131	4	no	—
348	C₂³	C₂³×D₁₃₁	1	2	yes	—
349	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	262	4	no	—
352	Q₈	—	262	4	no	—
353	Q₈	—	524	4	no	—
354	Q₈	—	524	2	no	—
355	Q₈	—	524	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	1	no	—
358	D₄	—	262	4	no	—
359	D₄	—	524	2	no	—
360	D₄	—	524	4	no	—
361	D₄	—	524	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	524	4	no	—
367	C₂×C₄	—	524	4	no	—
368	C₂×C₄	—	524	4	no	—
369	C₂×C₄	—	524	2	no	—
370	C₂×C₄	—	131	4	no	—
371	C₂×C₄	—	131	4	no	—
372	C₂×C₄	—	131	4	no	—
373	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
375	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
380	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
381	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	262	4	no	—
388	C₂²	—	262	4	no	—
389	C₂²	—	262	4	no	—
390	C₂²	—	1048	4	no	—
391	C₂²	#16862293	1	2	yes	—
392	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	262	4	no	—
402	C₄	—	262	4	no	—
403	C₄	—	262	4	no	—
404	C₄	#16862292	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	4	2	no	—
407	C₂	—	524	4	no	—
408	C₂	C₂×#16862292	1	1	yes	characteristic
409	C₂	C₂×#16862293	1	1	yes	characteristic
410	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#529×C₁₃₁	C₂
hypercenter	#529	D₁₃₁
hypocenter	C₁₃₁	#3561
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #22554066	C₂	semidirect
2. #22554056	C₂	semidirect
3. #22554035	C₂	semidirect
4. #22553985	C₂	semidirect
5. D₄×Dic₂₆₂	C₂	semidirect
6. #22553971	C₂	semidirect
7. #22553958	C₂	semidirect
8. #22553937	C₂	semidirect
9. #22553933	C₂	semidirect
10. #22553928	C₂	semidirect
11. #22553899	C₂	semidirect
12. #22553888	C₂	semidirect
13. #22553869	C₂	semidirect
14. C₂×#16862234	C₂	semidirect
15. #529×C₁₃₁	C₂	semidirect
18. C₂²×Dic₂₆₂	C₂²	semidirect
20. #16862246	C₂²	semidirect
21. #16862246	C₂²	semidirect
22. #16862246	C₂²	semidirect
23. #16862245	C₂²	semidirect
24. #16862241	C₂²	semidirect
25. #16862241	C₂²	semidirect
26. #16862241	C₂²	semidirect
27. #16862238	C₂²	semidirect
33. #16862232	C₂²	semidirect
34. #16862232	C₂²	semidirect
36. #16862230	C₂²	semidirect
37. #16862230	C₂²	semidirect
38. #16862228	C₂²	semidirect
39. #16862226	C₂²	semidirect
40. #16862226	C₂²	semidirect
43. #16862225	C₂²	semidirect
44. #16862224	C₂²	semidirect
45. #16862224	C₂²	semidirect
47. #16862223	C₂²	semidirect
48. #16862222	C₂²	semidirect
51. #16862218	C₂²	semidirect
53. C₄×Dic₂₆₂	C₂²	semidirect
54. C₄×Dic₂₆₂	C₂²	semidirect
55. C₄×Dic₂₆₂	C₂²	semidirect
58. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
60. #16862204	C₂²	semidirect
64. #126×C₁₃₁	C₂²	semidirect
65. #125×C₁₃₁	C₂²	semidirect
66. #124×C₁₃₁	C₂²	semidirect
70. C₄×Q₈×C₁₃₁	C₂²	semidirect
72. C₄×D₄×C₁₃₁	C₂²	semidirect
73. #117×C₁₃₁	C₂²	semidirect
205. C₁₃₁	#3561	semidirect
220. #529	D₁₃₁	semidirect
233. #126	C₂×D₁₃₁	semidirect
235. #125	C₂×D₁₃₁	semidirect
243. #124	C₂×D₁₃₁	semidirect
268. C₄×Q₈	C₂×D₁₃₁	semidirect
273. C₄×D₄	C₂×D₁₃₁	semidirect
276. #117	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554066	2
#22554056	2
#22554035	2
#22553985	2
D₄×Dic₂₆₂	2
#22553971	2
#22553958	2
#22553937	2
#22553933	2
#22553928	2
#22553899	2
#22553888	2
#22553869	2
C₂×#16862234	2
#529×C₁₃₁	2
#3561	131