Subgroups — #44552807

Order 32128.

696 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₂²⋊D₂₅₁)⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#22548671	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631580	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631571	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631569	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631563	C₂	1	1	yes	maximal, characteristic
8	#30631563	C₂	1	1	yes	maximal, characteristic
9	#30631561	C₂	1	1	yes	maximal, characteristic, complemented
10	#30631558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#30631534	C₂	1	1	yes	maximal, characteristic, complemented
14	#30631532	C₂	1	1	yes	maximal, characteristic, complemented
15	#388×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
17	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
21	(C₂²⋊D₂₅₁)⋊C₄	C₄	1	8	yes	complemented
22	#22548671	—	2	4	no	—
23	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
24	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
38	C₄²×D₂₅₁	—	2	4	no	—
39	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
40	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
41	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
42	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
43	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
44	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
45	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
46	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
51	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
52	#95×C₂₅₁	C₂²	1	1	yes	characteristic
53	#95×C₂₅₁	C₂²	1	1	yes	characteristic
54	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
55	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
56	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
57	C₂×C₂²⋊D₂₅₁	C₂×C₄	1	4	yes	—
58	C₂²×Dic₂₅₁	—	2	2	no	—
59	C₂²×Dic₂₅₁	—	2	2	no	—
60	C₂²×Dic₂₅₁	C₂×C₄	1	4	yes	complemented
61	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
62	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
63	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
64	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
65	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
66	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
67	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₂₅₁	—	2	2	no	—
69	C₂×C₄×D₂₅₁	—	2	2	no	—
70	C₂×C₄×D₂₅₁	—	2	2	no	—
71	C₂×C₄×D₂₅₁	—	2	2	no	—
72	C₂×C₄×D₂₅₁	—	2	2	no	—
73	C₂×C₄×D₂₅₁	—	2	2	no	—
74	C₂×C₄×D₂₅₁	—	2	2	no	—
75	C₂×C₄×D₂₅₁	—	2	2	no	—
76	C₂×C₄×D₂₅₁	C₂×C₄	1	4	yes	—
77	C₄⋊Dic₂₅₁	—	2	2	no	—
78	Dic₂₅₁⋊C₄	—	2	2	no	—
79	Dic₂₅₁⋊C₄	—	2	2	no	—
80	Dic₂₅₁⋊C₄	C₂×C₄	1	4	yes	complemented
81	C₂²⋊Dic₂₅₁	—	2	2	no	—
82	C₂²⋊Dic₂₅₁	—	2	2	no	—
83	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
84	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
85	(C₂×D₂₅₁)⋊C₄	C₂×C₄	1	4	yes	—
86	C₄×Dic₂₅₁	—	2	2	no	—
87	C₄×Dic₂₅₁	—	2	2	no	—
88	C₄×Dic₂₅₁	—	2	2	no	—
89	C₄×Dic₂₅₁	—	2	2	no	—
90	C₄×Dic₂₅₁	C₂×C₄	1	4	yes	complemented
91	C₄×Dic₂₅₁	D₄	1	4	yes	complemented
92	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₂₅₁	—	2	2	no	—
100	C₂²⋊C₄×C₂₅₁	—	2	2	no	—
101	C₂²⋊C₄×C₂₅₁	—	2	2	no	—
102	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	complemented
103	C₄²×C₂₅₁	—	2	2	no	—
104	C₂²×D₂₅₁	—	2	1	no	—
105	C₂²×D₂₅₁	—	2	1	no	—
106	C₂²×D₂₅₁	—	2	1	no	—
107	C₂²×D₂₅₁	—	2	1	no	—
108	C₂²×D₂₅₁	C₂²×C₄	1	2	yes	—
109	C₂²×D₂₅₁	#41	1	2	yes	—
110	C₂²×D₂₅₁	#41	1	2	yes	—
111	C₂²⋊D₂₅₁	—	2	8	no	—
112	C₂×Dic₂₅₁	—	2	1	no	—
113	C₂×Dic₂₅₁	—	2	1	no	—
114	C₂×Dic₂₅₁	—	2	1	no	—
115	C₂×Dic₂₅₁	—	2	1	no	—
116	C₂×Dic₂₅₁	—	2	1	no	—
117	C₂×Dic₂₅₁	—	2	1	no	—
118	C₂×Dic₂₅₁	—	2	1	no	—
119	C₂×Dic₂₅₁	—	2	1	no	—
120	C₂×Dic₂₅₁	—	2	8	no	—
121	C₂×Dic₂₅₁	—	2	1	no	—
122	C₂×Dic₂₅₁	—	2	1	no	—
123	C₂×Dic₂₅₁	—	2	1	no	—
124	C₂×Dic₂₅₁	—	2	1	no	—
125	C₂×Dic₂₅₁	—	2	1	no	—
126	C₂×Dic₂₅₁	—	2	1	no	—
127	C₂×Dic₂₅₁	C₂²×C₄	1	2	yes	—
128	C₂×Dic₂₅₁	C₂²×C₄	1	2	yes	—
129	C₂×Dic₂₅₁	C₂²×C₄	1	2	yes	—
130	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
131	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
132	C₂×Dic₂₅₁	#41	1	2	yes	—
133	C₂×Dic₂₅₁	#41	1	2	yes	—
134	C₄×D₂₅₁	—	2	8	no	—
135	C₄×D₂₅₁	—	2	8	no	—
136	C₄×D₂₅₁	—	2	8	no	—
137	C₂³×C₂₅₁	—	2	1	no	—
138	C₂³×C₂₅₁	—	2	1	no	—
139	C₂³×C₂₅₁	—	2	1	no	—
140	C₂³×C₂₅₁	—	2	1	no	—
141	C₂³×C₂₅₁	—	2	1	no	—
142	C₂³×C₂₅₁	—	2	1	no	—
143	C₂³×C₂₅₁	C₂²×C₄	1	2	yes	—
144	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
145	C₂×C₄×C₂₅₁	—	2	1	no	—
146	C₂×C₄×C₂₅₁	—	2	1	no	—
147	C₂×C₄×C₂₅₁	—	2	1	no	—
148	C₂×C₄×C₂₅₁	—	2	1	no	—
149	C₂×C₄×C₂₅₁	—	2	1	no	—
150	C₂×C₄×C₂₅₁	—	2	1	no	—
151	C₂×C₄×C₂₅₁	—	2	1	no	—
152	C₂×C₄×C₂₅₁	—	2	1	no	—
153	C₂×C₄×C₂₅₁	—	2	1	no	—
154	C₂×C₄×C₂₅₁	—	2	1	no	—
155	C₂×C₄×C₂₅₁	—	2	1	no	—
156	C₂×C₄×C₂₅₁	—	2	1	no	—
157	C₂×C₄×C₂₅₁	—	2	1	no	—
158	C₂×C₄×C₂₅₁	—	2	1	no	—
159	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
160	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
161	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
162	C₂×C₄×C₂₅₁	#41	1	2	yes	—
163	C₂²×C₂₅₁	—	2	2	no	—
164	C₂²×C₂₅₁	—	2	2	no	—
165	C₂²×C₂₅₁	—	2	2	no	—
166	C₂²×C₂₅₁	—	4	1	no	—
167	C₂²×C₂₅₁	—	4	1	no	—
168	C₂²×C₂₅₁	—	4	1	no	—
169	C₂²×C₂₅₁	—	4	1	no	—
170	C₂²×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
171	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
172	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
173	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
174	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
175	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
176	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
177	C₂×D₂₅₁	—	2	2	no	—
178	C₂×D₂₅₁	—	2	2	no	—
179	C₂×D₂₅₁	—	2	2	no	—
180	C₂×D₂₅₁	—	2	2	no	—
181	C₂×D₂₅₁	—	2	2	no	—
182	C₂×D₂₅₁	—	2	2	no	—
183	C₂×D₂₅₁	#117	1	4	yes	complemented
184	C₄×C₂₅₁	—	2	2	no	—
185	C₄×C₂₅₁	—	2	2	no	—
186	C₄×C₂₅₁	—	2	2	no	—
187	C₄×C₂₅₁	—	2	2	no	—
188	C₄×C₂₅₁	—	4	1	no	—
189	C₄×C₂₅₁	—	4	1	no	—
190	Dic₂₅₁	—	2	2	no	—
191	Dic₂₅₁	—	2	2	no	—
192	Dic₂₅₁	—	2	2	no	—
193	Dic₂₅₁	—	2	2	no	—
194	Dic₂₅₁	—	4	1	no	—
195	Dic₂₅₁	—	4	1	no	—
196	Dic₂₅₁	C₄×D₄	1	4	yes	—
197	C₂×C₂₅₁	—	4	2	no	—
198	C₂×C₂₅₁	C₂×#117	1	1	yes	characteristic
199	C₂×C₂₅₁	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂×C₂₅₁	C₄×#41	1	1	yes	characteristic
201	C₂×C₂₅₁	#525	1	1	yes	characteristic
202	C₂×C₂₅₁	#525	1	1	yes	characteristic
203	C₂×C₂₅₁	#529	1	1	yes	characteristic
204	C₂×C₂₅₁	#529	1	1	yes	characteristic
205	D₂₅₁	—	2	4	no	—
206	C₂₅₁	#2290	1	1	yes	characteristic, complemented, Sylow
207	#2290	—	251	1	no	maximal, Sylow
208	C₂×C₄×D₄	—	251	1	no	—
209	C₂×#117	—	251	1	no	—
210	C₂²×C₄²	—	251	1	no	—
211	#388	—	251	1	no	—
212	#388	D₂₅₁	1	1	yes	characteristic, complemented
213	#387	—	251	1	no	—
214	#387	—	251	1	no	—
215	#386	—	251	1	no	—
216	#386	—	251	1	no	—
217	#385	—	251	1	no	—
218	#385	—	251	1	no	—
219	C₄×C₄⋊C₄	—	251	1	no	—
220	C₄×C₂²⋊C₄	—	251	1	no	—
221	C₄×C₂²⋊C₄	—	251	1	no	—
222	#376	—	251	1	no	—
223	C₂²×D₄	—	251	1	no	—
224	C₂³×C₄	—	251	1	no	—
225	C₂³×C₄	—	251	1	no	—
226	C₂³×C₄	—	251	1	no	—
227	C₂³×C₄	—	251	1	no	—
228	C₄×D₄	—	251	8	no	—
229	#117	—	502	4	no	—
230	C₂×C₄⋊C₄	—	251	1	no	—
231	C₂×C₄⋊C₄	—	251	1	no	—
232	C₂×C₄⋊C₄	—	251	1	no	—
233	C₂×C₄⋊C₄	—	251	1	no	—
234	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	251	1	no	—
236	C₂×C₂²⋊C₄	—	251	1	no	—
237	C₂×C₂²⋊C₄	—	251	1	no	—
238	C₂×C₂²⋊C₄	—	251	1	no	—
239	C₂×C₂²⋊C₄	—	251	1	no	—
240	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
243	C₂×C₄²	—	502	4	no	—
244	C₂×C₄²	—	251	1	no	—
245	C₂×C₄²	—	251	1	no	—
246	C₂×C₄²	—	251	1	no	—
247	C₂×C₄²	—	251	1	no	—
248	C₂×C₄²	—	251	1	no	—
249	C₂×C₄²	—	251	1	no	—
250	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic
251	#95	—	251	1	no	—
252	#95	—	251	1	no	—
253	#95	—	251	1	no	—
254	#95	—	251	1	no	—
255	#95	—	251	1	no	—
256	#95	—	251	1	no	—
257	#95	—	251	1	no	—
258	#95	—	251	1	no	—
259	#95	C₂×D₂₅₁	1	1	yes	characteristic
260	#95	C₂×D₂₅₁	1	1	yes	characteristic
261	C₂⁴	—	251	1	no	—
262	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
263	C₂×D₄	—	502	2	no	—
264	C₂×D₄	—	502	2	no	—
265	C₂×D₄	—	251	4	no	—
266	C₂²×C₄	—	502	2	no	—
267	C₂²×C₄	—	502	2	no	—
268	C₂²×C₄	—	502	2	no	—
269	C₂²×C₄	—	502	2	no	—
270	C₂²×C₄	—	502	2	no	—
271	C₂²×C₄	—	502	2	no	—
272	C₂²×C₄	—	502	2	no	—
273	C₂²×C₄	—	502	2	no	—
274	C₂²×C₄	—	502	2	no	—
275	C₂²×C₄	—	502	2	no	—
276	C₂²×C₄	—	251	1	no	—
277	C₂²×C₄	—	251	1	no	—
278	C₂²×C₄	—	251	4	no	—
279	C₂²×C₄	—	251	1	no	—
280	C₂²×C₄	—	251	1	no	—
281	C₂²×C₄	—	251	1	no	—
282	C₂²×C₄	—	251	1	no	—
283	C₂²×C₄	—	251	4	no	—
284	C₂²×C₄	—	251	1	no	—
285	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	502	2	no	—
293	C₄⋊C₄	—	502	2	no	—
294	C₄⋊C₄	—	502	2	no	—
295	C₄⋊C₄	—	251	4	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	502	2	no	—
299	C₂²⋊C₄	—	502	2	no	—
300	C₂²⋊C₄	—	502	2	no	—
301	C₂²⋊C₄	—	502	2	no	—
302	C₂²⋊C₄	—	251	4	no	—
303	C₂²⋊C₄	C₄×D₂₅₁	1	4	yes	complemented
304	C₄²	—	2	2	no	—
305	C₄²	—	502	2	no	—
306	C₄²	—	502	2	no	—
307	C₄²	—	502	2	no	—
308	C₄²	—	502	2	no	—
309	C₄²	—	251	4	no	—
310	C₄²	—	251	4	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	502	1	no	—
318	C₂³	—	502	1	no	—
319	C₂³	—	502	1	no	—
320	C₂³	—	502	1	no	—
321	C₂³	—	251	2	no	—
322	C₂³	—	251	2	no	—
323	C₂³	—	251	2	no	—
324	C₂³	C₂×C₄×D₂₅₁	1	2	yes	—
325	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
326	D₄	—	502	8	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	502	8	no	—
342	C₂×C₄	—	502	8	no	—
343	C₂×C₄	—	502	8	no	—
344	C₂×C₄	—	502	1	no	—
345	C₂×C₄	—	502	1	no	—
346	C₂×C₄	—	502	1	no	—
347	C₂×C₄	—	502	1	no	—
348	C₂×C₄	—	502	1	no	—
349	C₂×C₄	—	502	1	no	—
350	C₂×C₄	—	502	1	no	—
351	C₂×C₄	—	502	1	no	—
352	C₂×C₄	—	502	1	no	—
353	C₂×C₄	—	502	1	no	—
354	C₂×C₄	—	502	1	no	—
355	C₂×C₄	—	502	1	no	—
356	C₂×C₄	—	502	1	no	—
357	C₂×C₄	—	502	1	no	—
358	C₂×C₄	—	502	8	no	—
359	C₂×C₄	—	251	2	no	—
360	C₂×C₄	—	251	2	no	—
361	C₂×C₄	—	251	2	no	—
362	C₂×C₄	—	251	2	no	—
363	C₂×C₄	—	251	2	no	—
364	C₂×C₄	—	251	2	no	—
365	C₂×C₄	—	251	2	no	—
366	C₂×C₄	C₂×C₄×D₂₅₁	1	2	yes	—
367	C₂×C₄	C₂×C₄×D₂₅₁	1	2	yes	—
368	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
369	C₂×C₄	#16860809	1	2	yes	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	502	2	no	—
378	C₂²	—	502	2	no	—
379	C₂²	—	502	2	no	—
380	C₂²	—	502	2	no	—
381	C₂²	—	502	2	no	—
382	C₂²	—	502	2	no	—
383	C₂²	—	251	4	no	—
384	C₂²	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
385	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
386	C₂²	#41×D₂₅₁	1	1	yes	characteristic
387	C₂²	#41×D₂₅₁	1	1	yes	characteristic
388	C₂²	#41×D₂₅₁	1	1	yes	characteristic
389	C₂²	#41×D₂₅₁	1	1	yes	characteristic
390	C₂²	C₂×#16860809	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	1004	1	no	—
398	C₄	—	1004	1	no	—
399	C₄	—	502	2	no	—
400	C₄	—	502	2	no	—
401	C₄	—	502	2	no	—
402	C₄	—	502	2	no	—
403	C₄	—	251	4	no	—
404	C₂	—	4	2	no	—
405	C₂	—	502	4	no	—
406	C₂	#117×D₂₅₁	1	1	yes	characteristic
407	C₂	C₄×D₄×D₂₅₁	1	1	yes	characteristic
408	C₂	C₄×#16860809	1	1	yes	characteristic
409	C₂	#30632195	1	1	yes	characteristic
410	C₂	#30632197	1	1	yes	characteristic
411	C₂	#30632216	1	1	yes	characteristic
412	C₂	#30632220	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₅₁
commutator	C₂²×C₂₅₁	C₂³×C₄
Fitting	#388×C₂₅₁	C₂
socle, cosocle	C₂³×C₂₅₁	C₂⁴
prime radical	C₂²×C₂²⋊D₂₅₁	C₂²
hypercenter	#388	D₂₅₁
hypocenter	C₂₅₁	#2290
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ #388

Complements

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

N	H ≅ G/N	type
2. C₂×#22548671	C₂	semidirect
3. C₂×C₄²×D₂₅₁	C₂	semidirect
4. #30631580	C₂	semidirect
5. #30631571	C₂	semidirect
6. #30631569	C₂	semidirect
9. #30631561	C₂	semidirect
10. #30631558	C₂	semidirect
11. C₄⋊C₄×Dic₂₅₁	C₂	semidirect
12. C₂²⋊C₄×Dic₂₅₁	C₂	semidirect
13. #30631534	C₂	semidirect
14. #30631532	C₂	semidirect
15. #388×C₂₅₁	C₂	semidirect
21. (C₂²⋊D₂₅₁)⋊C₄	C₄	semidirect
60. C₂²×Dic₂₅₁	C₂×C₄	semidirect
80. Dic₂₅₁⋊C₄	C₂×C₄	semidirect
90. C₄×Dic₂₅₁	C₂×C₄	semidirect
91. C₄×Dic₂₅₁	D₄	semidirect
102. C₂²⋊C₄×C₂₅₁	C₂×C₄	semidirect
183. C₂×D₂₅₁	#117	semidirect
206. C₂₅₁	#2290	semidirect
212. #388	D₂₅₁	semidirect
303. C₂²⋊C₄	C₄×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₂²⋊D₂₅₁)⋊C₄	2
C₂×#22548671	2
C₂×C₄²×D₂₅₁	2
#30631580	2
#30631571	2
#30631569	2
#30631563	2
#30631561	2
#30631558	2
C₄⋊C₄×Dic₂₅₁	2
C₂²⋊C₄×Dic₂₅₁	2
#30631534	2
#30631532	2
#388×C₂₅₁	2
#2290	251