Subgroups — #44553159

Order 32128.

532 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30631590	C₂	1	1	yes	maximal, characteristic
2	#30631586	C₂	1	1	yes	maximal, characteristic, complemented
3	#30631580	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631580	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631580	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631580	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631573	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631573	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631567	C₂	1	1	yes	maximal, characteristic
10	#30631562	C₂	1	1	yes	maximal, characteristic, complemented
11	#30631547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#123×C₂₅₁	C₂	1	1	yes	maximal, characteristic
16	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Dic₂₅₁	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×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
34	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
35	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
36	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
37	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
38	C₂₅₁⋊#95	C₂²	1	1	yes	characteristic
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	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
45	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
46	#123×C₂₅₁	C₄	1	8	yes	complemented
47	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊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×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
52	C₂²×Dic₂₅₁	—	2	2	no	—
53	C₂²×Dic₂₅₁	—	4	1	no	—
54	C₂²×Dic₂₅₁	—	4	1	no	—
55	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
56	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
57	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
58	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
59	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
60	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
61	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
62	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
63	C₄⋊Dic₂₅₁	—	2	2	no	—
64	C₄⋊Dic₂₅₁	—	4	1	no	—
65	C₄⋊Dic₂₅₁	—	4	1	no	—
66	C₄⋊Dic₂₅₁	—	4	1	no	—
67	C₄⋊Dic₂₅₁	—	4	1	no	—
68	C₂²⋊Dic₂₅₁	—	2	2	no	—
69	C₂²⋊Dic₂₅₁	—	2	2	no	—
70	C₂²⋊Dic₂₅₁	—	2	2	no	—
71	C₂²⋊Dic₂₅₁	—	4	1	no	—
72	C₂²⋊Dic₂₅₁	—	4	1	no	—
73	C₂²⋊Dic₂₅₁	—	4	1	no	—
74	C₂²⋊Dic₂₅₁	—	4	1	no	—
75	C₄×Dic₂₅₁	—	2	2	no	—
76	C₄×Dic₂₅₁	—	4	1	no	—
77	C₄×Dic₂₅₁	—	4	1	no	—
78	C₄×Dic₂₅₁	—	4	1	no	—
79	C₄×Dic₂₅₁	—	4	1	no	—
80	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
81	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₂₅₁	—	4	1	no	—
83	C₂×D₄×C₂₅₁	—	4	1	no	—
84	C₂×D₄×C₂₅₁	C₂×C₄	1	4	yes	—
85	C₂²×C₄×C₂₅₁	—	4	1	no	—
86	C₂²×C₄×C₂₅₁	—	4	1	no	—
87	C₂²×C₄×C₂₅₁	C₂×C₄	1	4	yes	complemented
88	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	complemented
94	C₄⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	complemented
95	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	—
96	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	—
97	C₂²⋊C₄×C₂₅₁	C₂×C₄	1	4	yes	complemented
98	C₂×Dic₂₅₁	—	2	1	no	—
99	C₂×Dic₂₅₁	—	2	1	no	—
100	C₂×Dic₂₅₁	—	2	1	no	—
101	C₂×Dic₂₅₁	—	2	1	no	—
102	C₂×Dic₂₅₁	—	2	1	no	—
103	C₂×Dic₂₅₁	—	2	1	no	—
104	C₂×Dic₂₅₁	—	2	1	no	—
105	C₂×Dic₂₅₁	—	2	1	no	—
106	C₂×Dic₂₅₁	—	2	1	no	—
107	C₂×Dic₂₅₁	—	2	1	no	—
108	C₂×Dic₂₅₁	—	2	1	no	—
109	C₂×Dic₂₅₁	—	2	1	no	—
110	C₂×Dic₂₅₁	—	2	1	no	—
111	C₂×Dic₂₅₁	—	2	1	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	—	4	4	no	—
121	C₂×Dic₂₅₁	#41	1	2	yes	—
122	C₂×Dic₂₅₁	#41	1	2	yes	—
123	C₂³×C₂₅₁	—	2	1	no	—
124	C₂³×C₂₅₁	—	2	1	no	—
125	C₂³×C₂₅₁	—	2	1	no	—
126	C₂³×C₂₅₁	—	2	1	no	—
127	C₂³×C₂₅₁	—	2	1	no	—
128	C₂³×C₂₅₁	—	2	1	no	—
129	C₂³×C₂₅₁	—	2	1	no	—
130	C₂³×C₂₅₁	—	2	1	no	—
131	C₂³×C₂₅₁	—	2	1	no	—
132	C₂³×C₂₅₁	—	2	1	no	—
133	C₂³×C₂₅₁	—	2	1	no	—
134	C₂³×C₂₅₁	—	2	1	no	—
135	C₂³×C₂₅₁	C₂²×C₄	1	2	yes	—
136	C₂³×C₂₅₁	C₂²×C₄	1	2	yes	—
137	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
138	D₄×C₂₅₁	—	4	4	no	—
139	C₂×C₄×C₂₅₁	—	2	1	no	—
140	C₂×C₄×C₂₅₁	—	2	1	no	—
141	C₂×C₄×C₂₅₁	—	2	1	no	—
142	C₂×C₄×C₂₅₁	—	2	1	no	—
143	C₂×C₄×C₂₅₁	—	2	1	no	—
144	C₂×C₄×C₂₅₁	—	2	1	no	—
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	—	4	4	no	—
150	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
151	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
152	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
153	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
154	C₂×C₄×C₂₅₁	C₂²×C₄	1	2	yes	—
155	C₂²×C₂₅₁	—	2	2	no	—
156	C₂²×C₂₅₁	—	2	2	no	—
157	C₂²×C₂₅₁	—	2	2	no	—
158	C₂²×C₂₅₁	—	2	2	no	—
159	C₂²×C₂₅₁	—	2	2	no	—
160	C₂²×C₂₅₁	—	2	2	no	—
161	C₂²×C₂₅₁	—	4	1	no	—
162	C₂²×C₂₅₁	—	4	1	no	—
163	C₂²×C₂₅₁	—	4	1	no	—
164	C₂²×C₂₅₁	—	4	1	no	—
165	C₂²×C₂₅₁	—	4	1	no	—
166	C₂²×C₂₅₁	—	4	1	no	—
167	C₂²×C₂₅₁	—	4	1	no	—
168	C₂²×C₂₅₁	—	4	1	no	—
169	C₂²×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
170	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
171	C₂²×C₂₅₁	C₂×#41	1	1	yes	characteristic
172	C₂²×C₂₅₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂²×C₂₅₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²×C₂₅₁	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²×C₂₅₁	2₋¹⁺⁴	1	1	yes	characteristic
176	C₄×C₂₅₁	—	2	2	no	—
177	C₄×C₂₅₁	—	2	2	no	—
178	C₄×C₂₅₁	—	2	2	no	—
179	C₄×C₂₅₁	—	2	2	no	—
180	C₄×C₂₅₁	—	2	2	no	—
181	Dic₂₅₁	—	2	2	no	—
182	Dic₂₅₁	—	2	2	no	—
183	Dic₂₅₁	—	4	1	no	—
184	Dic₂₅₁	—	4	1	no	—
185	Dic₂₅₁	—	4	1	no	—
186	Dic₂₅₁	—	4	1	no	—
187	Dic₂₅₁	—	4	1	no	—
188	Dic₂₅₁	—	4	1	no	—
189	C₂×C₂₅₁	—	4	2	no	—
190	C₂×C₂₅₁	—	4	2	no	—
191	C₂×C₂₅₁	C₄×#41	1	1	yes	characteristic
192	C₂×C₂₅₁	#518	1	1	yes	characteristic
193	C₂×C₂₅₁	#520	1	1	yes	characteristic
194	C₂×C₂₅₁	#538	1	1	yes	characteristic
195	C₂×C₂₅₁	#539	1	1	yes	characteristic
196	C₂×C₂₅₁	#540	1	1	yes	characteristic
197	C₂×C₂₅₁	#542	1	1	yes	characteristic
198	C₂₅₁	#2335	1	1	yes	characteristic, complemented, Sylow
199	#2335	—	251	1	no	maximal, Sylow
200	C₂×#123	D₂₅₁	1	1	yes	characteristic
201	#390	—	251	1	no	—
202	#389	—	251	1	no	—
203	#388	—	251	1	no	—
204	#388	—	251	1	no	—
205	#388	—	251	1	no	—
206	#388	—	251	1	no	—
207	#387	—	251	1	no	—
208	#387	—	251	1	no	—
209	#386	—	251	1	no	—
210	#385	—	251	1	no	—
211	#380	—	251	1	no	—
212	C₄×C₄⋊C₄	—	251	1	no	—
213	C₄×C₂²⋊C₄	—	251	1	no	—
214	C₄×C₂²⋊C₄	—	251	1	no	—
215	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
216	C₂³×C₄	—	251	1	no	—
217	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
218	#123	Dic₂₅₁	1	8	yes	complemented
219	C₂×C₄⋊C₄	—	251	1	no	—
220	C₂×C₄⋊C₄	—	251	1	no	—
221	C₂×C₄⋊C₄	—	251	1	no	—
222	C₂×C₄⋊C₄	—	251	1	no	—
223	C₂×C₄⋊C₄	—	251	1	no	—
224	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
226	C₂×C₂²⋊C₄	—	251	1	no	—
227	C₂×C₂²⋊C₄	—	251	1	no	—
228	C₂×C₂²⋊C₄	—	251	1	no	—
229	C₂×C₂²⋊C₄	—	251	1	no	—
230	C₂×C₂²⋊C₄	—	251	1	no	—
231	C₂×C₂²⋊C₄	—	251	1	no	—
232	C₂×C₂²⋊C₄	—	251	1	no	—
233	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
236	C₂×C₄²	—	251	1	no	—
237	C₂×C₄²	—	251	1	no	—
238	C₂×C₄²	—	251	1	no	—
239	C₂×C₄²	—	251	1	no	—
240	C₂×C₄²	—	251	1	no	—
241	#95	—	251	1	no	—
242	#95	—	251	1	no	—
243	#95	—	251	1	no	—
244	#95	—	251	1	no	—
245	#95	—	251	1	no	—
246	#95	—	251	1	no	—
247	#95	—	251	1	no	—
248	#95	—	251	1	no	—
249	#95	—	251	1	no	—
250	#95	—	251	1	no	—
251	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
252	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
253	C₂×D₄	—	4	1	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	C₂×Dic₂₅₁	1	4	yes	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	1004	1	no	—
259	C₂²×C₄	—	1004	1	no	—
260	C₂²×C₄	—	502	2	no	—
261	C₂²×C₄	—	251	1	no	—
262	C₂²×C₄	—	251	1	no	—
263	C₂²×C₄	—	251	1	no	—
264	C₂²×C₄	—	251	1	no	—
265	C₂²×C₄	—	251	1	no	—
266	C₂²×C₄	—	251	1	no	—
267	C₂²×C₄	—	251	1	no	—
268	C₂²×C₄	—	251	1	no	—
269	C₂²×C₄	C₂×Dic₂₅₁	1	4	yes	complemented
270	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
275	C₄⋊C₄	—	1004	1	no	—
276	C₄⋊C₄	—	1004	1	no	—
277	C₄⋊C₄	—	1004	1	no	—
278	C₄⋊C₄	—	1004	1	no	—
279	C₄⋊C₄	—	502	2	no	—
280	C₄⋊C₄	C₂×Dic₂₅₁	1	4	yes	complemented
281	C₄⋊C₄	C₂×Dic₂₅₁	1	4	yes	complemented
282	C₂²⋊C₄	—	1004	1	no	—
283	C₂²⋊C₄	—	1004	1	no	—
284	C₂²⋊C₄	—	1004	1	no	—
285	C₂²⋊C₄	—	1004	1	no	—
286	C₂²⋊C₄	—	502	2	no	—
287	C₂²⋊C₄	—	502	2	no	—
288	C₂²⋊C₄	—	502	2	no	—
289	C₂²⋊C₄	C₂×Dic₂₅₁	1	4	yes	—
290	C₂²⋊C₄	C₂×Dic₂₅₁	1	4	yes	—
291	C₂²⋊C₄	C₂×Dic₂₅₁	1	4	yes	complemented
292	C₄²	—	1004	1	no	—
293	C₄²	—	1004	1	no	—
294	C₄²	—	1004	1	no	—
295	C₄²	—	1004	1	no	—
296	C₄²	—	502	2	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	C₂²×Dic₂₅₁	1	2	yes	—
310	C₂³	C₂²×Dic₂₅₁	1	2	yes	—
311	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
312	D₄	—	4	4	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	1004	4	no	—
325	C₂×C₄	—	502	1	no	—
326	C₂×C₄	—	502	1	no	—
327	C₂×C₄	—	502	1	no	—
328	C₂×C₄	—	502	1	no	—
329	C₂×C₄	—	502	1	no	—
330	C₂×C₄	—	502	1	no	—
331	C₂×C₄	—	502	1	no	—
332	C₂×C₄	—	502	1	no	—
333	C₂×C₄	—	502	1	no	—
334	C₂×C₄	—	502	1	no	—
335	C₂×C₄	—	502	1	no	—
336	C₂×C₄	—	502	1	no	—
337	C₂×C₄	—	502	1	no	—
338	C₂×C₄	—	502	1	no	—
339	C₂×C₄	—	502	1	no	—
340	C₂×C₄	—	502	1	no	—
341	C₂×C₄	—	502	1	no	—
342	C₂×C₄	—	502	1	no	—
343	C₂×C₄	—	502	1	no	—
344	C₂×C₄	—	502	1	no	—
345	C₂×C₄	—	502	1	no	—
346	C₂×C₄	—	502	1	no	—
347	C₂×C₄	—	251	2	no	—
348	C₂×C₄	—	251	2	no	—
349	C₂×C₄	C₂²×Dic₂₅₁	1	2	yes	—
350	C₂×C₄	C₂²×Dic₂₅₁	1	2	yes	—
351	C₂×C₄	C₂²×Dic₂₅₁	1	2	yes	—
352	C₂×C₄	C₂²×Dic₂₅₁	1	2	yes	—
353	C₂×C₄	C₂²×Dic₂₅₁	1	2	yes	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	C₂³×Dic₂₅₁	1	1	yes	characteristic
369	C₂²	#41×D₂₅₁	1	1	yes	characteristic
370	C₂²	#41×D₂₅₁	1	1	yes	characteristic
371	C₂²	#22548760	1	1	yes	characteristic
372	C₂²	#22548760	1	1	yes	characteristic
373	C₂²	#22548761	1	1	yes	characteristic
374	C₂²	#22548762	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	1004	1	no	—
381	C₄	—	1004	1	no	—
382	C₄	—	1004	1	no	—
383	C₄	—	1004	1	no	—
384	C₄	—	1004	1	no	—
385	C₄	—	1004	1	no	—
386	C₄	—	502	2	no	—
387	C₄	—	502	2	no	—
388	C₂	—	4	2	no	—
389	C₂	—	4	2	no	—
390	C₂	#41×Dic₂₅₁	1	1	yes	characteristic
391	C₂	#30632162	1	1	yes	characteristic
392	C₂	#30632170	1	1	yes	characteristic
393	C₂	#30632273	1	1	yes	characteristic
394	C₂	#30632280	1	1	yes	characteristic
395	C₂	#30632289	1	1	yes	characteristic
396	C₂	#30632305	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₅₁
commutator	C₂²×C₂₅₁	C₂³×C₄
Fitting	C₂×#123×C₂₅₁	C₂
socle, cosocle	C₂³×C₂₅₁	C₂⁴
prime radical	C₂²×D₄×C₂₅₁	C₂²
hypercenter	C₂×#123	D₂₅₁
hypocenter	C₂₅₁	#2335
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
2. #30631586	C₂	semidirect
3. #30631580	C₂	semidirect
4. #30631580	C₂	semidirect
5. #30631580	C₂	semidirect
6. #30631580	C₂	semidirect
7. #30631573	C₂	semidirect
8. #30631573	C₂	semidirect
10. #30631562	C₂	semidirect
11. #30631547	C₂	semidirect
12. C₄⋊C₄×Dic₂₅₁	C₂	semidirect
13. C₂²⋊C₄×Dic₂₅₁	C₂	semidirect
14. C₄×C₂²⋊Dic₂₅₁	C₂	semidirect
46. #123×C₂₅₁	C₄	semidirect
87. C₂²×C₄×C₂₅₁	C₂×C₄	semidirect
93. C₄⋊C₄×C₂₅₁	C₂×C₄	semidirect
94. C₄⋊C₄×C₂₅₁	C₂×C₄	semidirect
97. C₂²⋊C₄×C₂₅₁	C₂×C₄	semidirect
198. C₂₅₁	#2335	semidirect
218. #123	Dic₂₅₁	semidirect
269. C₂²×C₄	C₂×Dic₂₅₁	semidirect
280. C₄⋊C₄	C₂×Dic₂₅₁	semidirect
281. C₄⋊C₄	C₂×Dic₂₅₁	semidirect
291. C₂²⋊C₄	C₂×Dic₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30631590	2
#30631586	2
#30631580	2
#30631573	2
#30631567	2
#30631562	2
#30631547	2
C₄⋊C₄×Dic₂₅₁	2
C₂²⋊C₄×Dic₂₅₁	2
C₄×C₂²⋊Dic₂₅₁	2
C₂×#123×C₂₅₁	2
#2335	251