Subgroups — #44564937

Order 32128.

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	#30632437	C₂	1	2	yes	maximal, complemented
2	#30632431	C₂	1	2	yes	maximal, complemented
3	#30632406	C₂	1	2	yes	maximal, complemented
4	#30632363	C₂	1	4	yes	maximal, complemented
5	Q₈×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
6	#30632345	C₂	1	2	yes	maximal, complemented
7	#30632331	C₂	1	2	yes	maximal, complemented
8	#30632313	C₂	1	2	yes	maximal, complemented
9	#30632306	C₂	1	2	yes	maximal, complemented
10	#30632301	C₂	1	4	yes	maximal, complemented
11	#30632275	C₂	1	2	yes	maximal, complemented
12	#30632257	C₂	1	2	yes	maximal, complemented
13	#30632244	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632221	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#124×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860809	C₂²	1	2	yes	—
17	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	complemented
18	#22548715	C₂²	1	1	yes	characteristic, complemented
19	#22548715	C₂²	1	1	yes	characteristic, complemented
20	#22548713	C₂²	1	2	yes	complemented
21	#22548713	C₂²	1	4	yes	complemented
22	#22548709	C₂²	1	2	yes	complemented
23	#22548708	C₂²	1	4	yes	complemented
24	#22548708	C₂²	1	4	yes	complemented
25	#22548708	C₂²	1	4	yes	complemented
26	#22548707	C₂²	1	1	yes	characteristic, complemented
27	#22548707	C₂²	1	2	yes	complemented
28	#22548703	C₂²	1	1	yes	characteristic, complemented
29	#22548702	C₂²	1	2	yes	—
30	#22548701	C₂²	1	4	yes	complemented
31	#22548701	C₂²	1	4	yes	complemented
32	#22548699	C₂²	1	4	yes	complemented
33	#22548698	C₂²	1	2	yes	—
34	#22548697	C₂²	1	4	yes	complemented
35	#22548697	C₂²	1	4	yes	complemented
36	#22548696	C₂²	1	4	yes	—
37	#22548694	C₂²	1	1	yes	characteristic
38	#22548694	C₂²	1	2	yes	—
39	#22548694	C₂²	1	2	yes	—
40	#22548694	C₂²	1	4	yes	—
41	#22548692	C₂²	1	4	yes	complemented
42	#22548692	C₂²	1	4	yes	complemented
43	#22548692	C₂²	1	4	yes	complemented
44	#22548692	C₂²	1	4	yes	complemented
45	#22548692	C₂²	1	4	yes	complemented
46	#22548691	C₂²	1	4	yes	complemented
47	#22548691	C₂²	1	2	yes	complemented
48	#22548689	C₂²	1	1	yes	characteristic
49	#22548688	C₂²	1	4	yes	complemented
50	#22548687	C₂²	1	4	yes	—
51	#22548686	C₂²	1	2	yes	—
52	#22548684	C₂²	1	4	yes	—
53	Q₈×Dic₂₅₁	C₂²	1	2	yes	complemented
54	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
56	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
57	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₂₅₁	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₂₅₁	C₂²	1	4	yes	—
61	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
62	#22548674	C₂²	1	2	yes	—
63	#22548672	C₂²	1	2	yes	complemented
64	#22548671	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊Dic₂₅₁	C₂²	1	4	yes	—
66	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
67	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
68	#124×C₂₅₁	C₂²	1	2	yes	—
69	#124×C₂₅₁	C₂²	1	2	yes	—
70	#124×C₂₅₁	C₂²	1	2	yes	—
71	#124×C₂₅₁	C₂²	1	2	yes	—
72	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	—
73	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	—
74	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
75	#16860809	—	4	4	no	—
76	C₂×Dic₅₀₂	C₂³	1	2	yes	—
77	C₂×Dic₅₀₂	C₂³	1	4	yes	—
78	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
79	C₂×Dic₅₀₂	C₂³	1	2	yes	—
80	Q₈×D₂₅₁	—	4	4	no	—
81	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
83	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
85	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
86	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
87	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
88	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
89	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
90	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
91	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
92	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
93	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
94	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
95	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
96	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
97	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
98	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
99	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
100	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
101	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
102	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
103	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
105	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
106	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
107	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
108	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
109	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
110	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
111	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
112	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
113	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
114	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
116	C₄×Dic₂₅₁	C₂³	1	4	yes	—
117	C₄×Dic₂₅₁	C₂³	1	4	yes	—
118	C₄×Dic₂₅₁	C₂³	1	2	yes	—
119	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
120	C₂×Q₈×C₂₅₁	—	4	2	no	—
121	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
122	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
123	C₂×D₄×C₂₅₁	—	4	2	no	—
124	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
125	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
126	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
131	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
132	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
133	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
134	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
135	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
136	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
137	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
138	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
139	Dic₅₀₂	—	2	4	no	—
140	Dic₅₀₂	—	4	4	no	—
141	Dic₅₀₂	—	4	1	no	—
142	Dic₅₀₂	—	4	2	no	—
143	D₁₀₀₄	—	4	1	no	—
144	C₂²⋊D₂₅₁	—	2	4	no	—
145	C₂²⋊D₂₅₁	—	4	4	no	—
146	C₂²⋊D₂₅₁	—	4	4	no	—
147	C₂×Dic₂₅₁	—	4	4	no	—
148	C₂×Dic₂₅₁	—	4	4	no	—
149	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
150	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
151	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
152	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
153	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
154	C₄×D₂₅₁	—	2	4	no	—
155	C₄×D₂₅₁	—	4	4	no	—
156	C₂³×C₂₅₁	—	2	4	no	—
157	C₂³×C₂₅₁	—	4	2	no	—
158	C₂³×C₂₅₁	—	4	2	no	—
159	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
160	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
161	Q₈×C₂₅₁	—	2	4	no	—
162	Q₈×C₂₅₁	—	4	2	no	—
163	D₄×C₂₅₁	—	2	4	no	—
164	D₄×C₂₅₁	—	4	2	no	—
165	C₂×C₄×C₂₅₁	—	2	2	no	—
166	C₂×C₄×C₂₅₁	—	2	2	no	—
167	C₂×C₄×C₂₅₁	—	4	1	no	—
168	C₂×C₄×C₂₅₁	—	4	2	no	—
169	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
175	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
176	C₂²×C₂₅₁	—	2	1	no	—
177	C₂²×C₂₅₁	—	2	1	no	—
178	C₂²×C₂₅₁	—	2	4	no	—
179	C₂²×C₂₅₁	—	2	4	no	—
180	C₂²×C₂₅₁	—	2	4	no	—
181	C₂²×C₂₅₁	—	8	4	no	—
182	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
183	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
184	C₂×D₂₅₁	—	2	2	no	—
185	C₂×D₂₅₁	—	2	2	no	—
186	C₂×D₂₅₁	—	2	2	no	—
187	C₄×C₂₅₁	—	2	1	no	—
188	C₄×C₂₅₁	—	2	4	no	—
189	C₄×C₂₅₁	—	2	1	no	—
190	C₄×C₂₅₁	—	2	1	no	—
191	C₄×C₂₅₁	—	2	1	no	—
192	C₄×C₂₅₁	—	2	1	no	—
193	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
194	Dic₂₅₁	—	2	2	no	—
195	Dic₂₅₁	—	2	4	no	—
196	Dic₂₅₁	—	2	2	no	—
197	Dic₂₅₁	—	2	2	no	—
198	Dic₂₅₁	—	2	4	no	—
199	C₂×C₂₅₁	—	2	2	no	—
200	C₂×C₂₅₁	—	4	4	no	—
201	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₂₅₁	#585	1	1	yes	characteristic
204	D₂₅₁	—	4	2	no	—
205	C₂₅₁	#3561	1	1	yes	characteristic, complemented, Sylow
206	#3561	—	251	1	no	maximal, Sylow
207	#563	—	251	2	no	—
208	#562	—	251	2	no	—
209	#556	—	251	2	no	—
210	#551	—	251	4	no	—
211	D₄×Q₈	—	251	2	no	—
212	#548	—	251	2	no	—
213	#546	—	251	2	no	—
214	#543	—	251	2	no	—
215	#542	—	251	4	no	—
216	#542	—	251	2	no	—
217	#538	—	251	2	no	—
218	#536	—	251	2	no	—
219	#533	—	251	1	no	—
220	#529	—	251	1	no	—
221	C₂×#124	D₂₅₁	1	1	yes	characteristic, complemented
222	C₂×#41	—	251	2	no	—
223	C₂²×Q₈	—	251	2	no	—
224	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
225	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
226	C₄⋊Q₈	—	251	2	no	—
227	C₄⋊Q₈	—	251	4	no	—
228	C₄⋊Q₈	—	251	1	no	—
229	C₄⋊Q₈	—	251	1	no	—
230	#126	—	251	4	no	—
231	#126	—	251	4	no	—
232	#126	—	251	4	no	—
233	#126	—	251	2	no	—
234	#125	—	251	1	no	—
235	#125	—	251	2	no	—
236	#124	—	251	2	no	—
237	#124	—	251	4	no	—
238	#124	—	251	4	no	—
239	#124	—	251	1	no	—
240	#124	C₂×D₂₅₁	1	2	yes	—
241	#124	C₂×D₂₅₁	1	2	yes	—
242	#124	C₂×D₂₅₁	1	2	yes	—
243	#124	C₂×D₂₅₁	1	2	yes	—
244	#123	—	251	4	no	—
245	#123	—	251	2	no	—
246	#123	—	251	4	no	—
247	#123	—	251	4	no	—
248	#123	—	251	4	no	—
249	C₂²⋊Q₈	—	251	2	no	—
250	C₂²⋊Q₈	—	251	4	no	—
251	C₂²⋊Q₈	—	251	1	no	—
252	C₂²⋊Q₈	—	251	2	no	—
253	C₂²⋊Q₈	—	251	2	no	—
254	C₂²⋊Q₈	—	251	4	no	—
255	C₂²⋊Q₈	—	251	4	no	—
256	C₂²⋊Q₈	—	251	4	no	—
257	C₂²⋊Q₈	—	251	4	no	—
258	C₂²⋊Q₈	—	251	4	no	—
259	C₂²⋊Q₈	—	251	4	no	—
260	#121	—	251	2	no	—
261	#121	—	251	4	no	—
262	#121	—	251	1	no	—
263	#121	—	251	4	no	—
264	#120	—	251	4	no	—
265	C₄×Q₈	—	251	2	no	—
266	C₄×Q₈	—	251	1	no	—
267	C₄×Q₈	—	251	2	no	—
268	C₄×Q₈	—	251	2	no	—
269	C₄×D₄	—	251	2	no	—
270	C₄×D₄	—	251	2	no	—
271	C₄×D₄	—	251	4	no	—
272	C₄×D₄	—	251	4	no	—
273	C₄×D₄	—	251	1	no	—
274	#117	—	251	2	no	—
275	#117	—	251	4	no	—
276	#117	—	251	2	no	—
277	C₂×C₂²⋊C₄	—	251	4	no	—
278	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	—
280	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic
281	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
282	#41	—	1004	4	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	1004	4	no	—
285	C₂×Q₈	—	251	1	no	—
286	C₂×Q₈	—	251	2	no	—
287	C₂×Q₈	—	251	4	no	—
288	C₂×Q₈	—	251	2	no	—
289	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
290	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	251	4	no	—
293	C₂×D₄	—	251	4	no	—
294	C₂×D₄	—	251	2	no	—
295	C₂×D₄	—	251	1	no	—
296	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
297	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
298	C₂²×C₄	—	251	4	no	—
299	C₂²×C₄	—	251	4	no	—
300	C₂²×C₄	—	251	4	no	—
301	C₂²×C₄	—	251	2	no	—
302	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
306	C₄⋊C₄	—	251	2	no	—
307	C₄⋊C₄	—	251	2	no	—
308	C₄⋊C₄	—	251	4	no	—
309	C₄⋊C₄	—	251	2	no	—
310	C₄⋊C₄	—	251	2	no	—
311	C₄⋊C₄	—	251	2	no	—
312	C₄⋊C₄	—	251	4	no	—
313	C₄⋊C₄	—	251	4	no	—
314	C₄⋊C₄	—	251	2	no	—
315	C₄⋊C₄	—	251	4	no	—
316	C₄⋊C₄	—	251	4	no	—
317	C₄⋊C₄	—	251	2	no	—
318	C₄⋊C₄	—	251	1	no	—
319	C₄⋊C₄	—	251	1	no	—
320	C₄⋊C₄	—	251	4	no	—
321	C₄⋊C₄	—	251	2	no	—
322	C₂²⋊C₄	—	251	2	no	—
323	C₂²⋊C₄	—	251	4	no	—
324	C₂²⋊C₄	—	251	4	no	—
325	C₂²⋊C₄	—	251	4	no	—
326	C₂²⋊C₄	—	251	4	no	—
327	C₂²⋊C₄	—	251	4	no	—
328	C₂²⋊C₄	—	251	2	no	—
329	C₂²⋊C₄	—	251	2	no	—
330	C₂²⋊C₄	—	251	2	no	—
331	C₂²⋊C₄	—	251	2	no	—
332	C₂²⋊C₄	—	251	4	no	—
333	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
334	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
335	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
336	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
337	C₄²	—	251	4	no	—
338	C₄²	—	251	2	no	—
339	C₄²	—	251	4	no	—
340	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
341	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
342	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
343	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	251	2	no	—
348	C₂³	C₂³×D₂₅₁	1	4	yes	—
349	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
350	Q₈	—	2	4	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	1004	4	no	—
353	Q₈	—	1004	1	no	—
354	Q₈	—	1004	2	no	—
355	Q₈	—	502	4	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	2	no	—
358	D₄	—	1004	1	no	—
359	D₄	—	1004	4	no	—
360	D₄	—	1004	4	no	—
361	D₄	—	502	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	1004	4	no	—
367	C₂×C₄	—	1004	4	no	—
368	C₂×C₄	—	1004	4	no	—
369	C₂×C₄	—	502	4	no	—
370	C₂×C₄	—	251	2	no	—
371	C₂×C₄	—	251	4	no	—
372	C₂×C₄	—	251	2	no	—
373	C₂×C₄	—	251	4	no	—
374	C₂×C₄	—	251	2	no	—
375	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
377	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
380	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	8	4	no	—
388	C₂²	—	502	2	no	—
389	C₂²	—	502	2	no	—
390	C₂²	—	502	2	no	—
391	C₂²	#22548762	1	2	yes	—
392	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	4	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	502	2	no	—
400	C₄	—	502	4	no	—
401	C₄	—	502	2	no	—
402	C₄	—	502	2	no	—
403	C₄	—	502	4	no	—
404	C₄	#22548760	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	4	4	no	—
407	C₂	—	1004	2	no	—
408	C₂	C₂×#22548760	1	1	yes	characteristic
409	C₂	C₂×#22548762	1	1	yes	characteristic
410	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	C₂×#124×C₂₅₁	C₂
hypercenter	C₂×#124	D₂₅₁
hypocenter	C₂₅₁	#3561
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. #30632437	C₂	semidirect
2. #30632431	C₂	semidirect
3. #30632406	C₂	semidirect
4. #30632363	C₂	semidirect
5. Q₈×C₂²⋊D₂₅₁	C₂	semidirect
6. #30632345	C₂	semidirect
7. #30632331	C₂	semidirect
8. #30632313	C₂	semidirect
9. #30632306	C₂	semidirect
10. #30632301	C₂	semidirect
11. #30632275	C₂	semidirect
12. #30632257	C₂	semidirect
13. #30632244	C₂	semidirect
14. #30632221	C₂	semidirect
15. C₂×#124×C₂₅₁	C₂	semidirect
17. C₂×Q₈×D₂₅₁	C₂²	semidirect
18. #22548715	C₂²	semidirect
19. #22548715	C₂²	semidirect
20. #22548713	C₂²	semidirect
21. #22548713	C₂²	semidirect
22. #22548709	C₂²	semidirect
23. #22548708	C₂²	semidirect
24. #22548708	C₂²	semidirect
25. #22548708	C₂²	semidirect
26. #22548707	C₂²	semidirect
27. #22548707	C₂²	semidirect
28. #22548703	C₂²	semidirect
30. #22548701	C₂²	semidirect
31. #22548701	C₂²	semidirect
32. #22548699	C₂²	semidirect
34. #22548697	C₂²	semidirect
35. #22548697	C₂²	semidirect
41. #22548692	C₂²	semidirect
42. #22548692	C₂²	semidirect
43. #22548692	C₂²	semidirect
44. #22548692	C₂²	semidirect
45. #22548692	C₂²	semidirect
46. #22548691	C₂²	semidirect
47. #22548691	C₂²	semidirect
49. #22548688	C₂²	semidirect
53. Q₈×Dic₂₅₁	C₂²	semidirect
54. C₄×Dic₅₀₂	C₂²	semidirect
55. C₄×Dic₅₀₂	C₂²	semidirect
56. C₄×Dic₅₀₂	C₂²	semidirect
57. C₄×D₁₀₀₄	C₂²	semidirect
61. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
63. #22548672	C₂²	semidirect
64. #22548671	C₂²	semidirect
205. C₂₅₁	#3561	semidirect
221. C₂×#124	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632437	2
#30632431	2
#30632406	2
#30632363	2
Q₈×C₂²⋊D₂₅₁	2
#30632345	2
#30632331	2
#30632313	2
#30632306	2
#30632301	2
#30632275	2
#30632257	2
#30632244	2
#30632221	2
C₂×#124×C₂₅₁	2
#3561	251