Subgroups — #44564917

Order 32128.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632439	C₂	1	2	yes	maximal, complemented
2	#30632428	C₂	1	2	yes	maximal, complemented
3	#30632388	C₂	1	2	yes	maximal, complemented
4	#30632385	C₂	1	2	yes	maximal, complemented
5	#30632362	C₂	1	2	yes	maximal, complemented
6	#30632338	C₂	1	2	yes	maximal, complemented
7	#30632327	C₂	1	2	yes	maximal, complemented
8	#30632327	C₂	1	2	yes	maximal, complemented
9	#30632303	C₂	1	2	yes	maximal, complemented
10	#30632284	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632278	C₂	1	2	yes	maximal, complemented
12	#30632276	C₂	1	2	yes	maximal, complemented
13	#30632276	C₂	1	2	yes	maximal, complemented
14	#30632275	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632268	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632249	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632237	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632221	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#126×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16860810	C₂²	1	2	yes	complemented
21	C₂×#16860810	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
23	#22548715	C₂²	1	1	yes	characteristic, complemented
24	#22548714	C₂²	1	2	yes	complemented
25	#22548712	C₂²	1	1	yes	characteristic, complemented
26	#22548710	C₂²	1	2	yes	complemented
27	#22548710	C₂²	1	2	yes	complemented
28	#22548710	C₂²	1	2	yes	complemented
29	#22548709	C₂²	1	2	yes	complemented
30	#22548708	C₂²	1	2	yes	complemented
31	#22548707	C₂²	1	1	yes	characteristic, complemented
32	#22548706	C₂²	1	2	yes	complemented
33	#22548705	C₂²	1	2	yes	complemented
34	#22548703	C₂²	1	1	yes	characteristic, complemented
35	#22548703	C₂²	1	2	yes	complemented
36	#22548701	C₂²	1	2	yes	—
37	#22548701	C₂²	1	2	yes	—
38	#22548701	C₂²	1	2	yes	complemented
39	#22548700	C₂²	1	2	yes	complemented
40	#22548700	C₂²	1	2	yes	complemented
41	#22548700	C₂²	1	2	yes	complemented
42	#22548700	C₂²	1	2	yes	complemented
43	#22548700	C₂²	1	2	yes	complemented
44	#22548699	C₂²	1	2	yes	—
45	#22548699	C₂²	1	2	yes	—
46	#22548698	C₂²	1	2	yes	complemented
47	#22548698	C₂²	1	2	yes	complemented
48	#22548697	C₂²	1	2	yes	—
49	#22548697	C₂²	1	2	yes	—
50	#22548697	C₂²	1	2	yes	complemented
51	#22548695	C₂²	1	2	yes	complemented
52	#22548695	C₂²	1	2	yes	complemented
53	#22548694	C₂²	1	1	yes	characteristic, complemented
54	#22548693	C₂²	1	2	yes	complemented
55	#22548693	C₂²	1	2	yes	complemented
56	#22548693	C₂²	1	2	yes	complemented
57	#22548692	C₂²	1	2	yes	complemented
58	#22548692	C₂²	1	2	yes	complemented
59	#22548690	C₂²	1	2	yes	complemented
60	#22548690	C₂²	1	2	yes	complemented
61	#22548690	C₂²	1	2	yes	complemented
62	#22548690	C₂²	1	2	yes	complemented
63	#22548689	C₂²	1	1	yes	characteristic
64	#22548689	C₂²	1	1	yes	characteristic
65	#22548689	C₂²	1	2	yes	—
66	#22548689	C₂²	1	1	yes	characteristic, complemented
67	#22548689	C₂²	1	2	yes	complemented
68	#22548689	C₂²	1	2	yes	complemented
69	#22548688	C₂²	1	2	yes	—
70	#22548688	C₂²	1	2	yes	—
71	#22548688	C₂²	1	2	yes	—
72	#22548688	C₂²	1	2	yes	—
73	#22548688	C₂²	1	2	yes	complemented
74	#22548685	C₂²	1	2	yes	—
75	#22548685	C₂²	1	2	yes	—
76	#22548685	C₂²	1	2	yes	complemented
77	#22548685	C₂²	1	2	yes	complemented
78	#22548684	C₂²	1	2	yes	—
79	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
82	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
84	#22548677	C₂²	1	2	yes	complemented
85	#22548677	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
89	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
91	#22548673	C₂²	1	2	yes	complemented
92	#22548672	C₂²	1	2	yes	complemented
93	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
96	#126×C₂₅₁	C₂²	1	2	yes	complemented
97	#126×C₂₅₁	C₂²	1	2	yes	complemented
98	#126×C₂₅₁	C₂²	1	2	yes	complemented
99	#126×C₂₅₁	C₂²	1	2	yes	complemented
100	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
106	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₅₁	C₂³	1	2	yes	—
108	#16860810	—	4	4	no	—
109	#16860810	—	4	4	no	—
110	C₂×Dic₅₀₂	C₂³	1	2	yes	—
111	C₂×Dic₅₀₂	C₂³	1	2	yes	—
112	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
113	C₂×D₁₀₀₄	C₂³	1	2	yes	—
114	C₂×D₁₀₀₄	C₂³	1	2	yes	—
115	C₂×D₁₀₀₄	C₂³	1	2	yes	—
116	C₂×D₁₀₀₄	C₂³	1	2	yes	—
117	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
118	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
119	C₂×D₁₀₀₄	C₂³	1	2	yes	—
120	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
122	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
129	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
130	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
131	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
132	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
133	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
134	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
135	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
136	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
137	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
138	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
139	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
141	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
144	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
145	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
146	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
147	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
148	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
149	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
150	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
151	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
152	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
153	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
154	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
155	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
171	C₄×Dic₂₅₁	C₂³	1	2	yes	—
172	C₄×Dic₂₅₁	C₂³	1	2	yes	—
173	C₄×Dic₂₅₁	C₂³	1	2	yes	—
174	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
185	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
186	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
193	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
194	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
195	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
196	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
197	C₂²×D₂₅₁	—	4	2	no	—
198	C₂²×D₂₅₁	—	4	2	no	—
199	C₂²×D₂₅₁	—	4	2	no	—
200	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
201	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
202	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
203	Dic₅₀₂	—	4	1	no	—
204	Dic₅₀₂	—	4	2	no	—
205	Dic₅₀₂	—	4	2	no	—
206	D₁₀₀₄	—	4	2	no	—
207	D₁₀₀₄	—	4	2	no	—
208	D₁₀₀₄	—	4	2	no	—
209	D₁₀₀₄	—	4	1	no	—
210	D₁₀₀₄	—	4	1	no	—
211	D₁₀₀₄	—	4	1	no	—
212	D₁₀₀₄	—	4	2	no	—
213	D₁₀₀₄	—	4	2	no	—
214	C₂²⋊D₂₅₁	—	2	4	no	—
215	C₂²⋊D₂₅₁	—	2	4	no	—
216	C₂²⋊D₂₅₁	—	2	4	no	—
217	C₂²⋊D₂₅₁	—	4	2	no	—
218	C₂²⋊D₂₅₁	—	4	2	no	—
219	C₂²⋊D₂₅₁	—	4	2	no	—
220	C₂²⋊D₂₅₁	—	4	2	no	—
221	C₂×Dic₂₅₁	—	4	2	no	—
222	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
223	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
224	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
225	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
226	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
227	C₄×D₂₅₁	—	4	2	no	—
228	C₄×D₂₅₁	—	4	2	no	—
229	C₄×D₂₅₁	—	4	2	no	—
230	C₄×D₂₅₁	—	4	2	no	—
231	C₄×D₂₅₁	—	4	2	no	—
232	C₄×D₂₅₁	—	4	2	no	—
233	C₄×D₂₅₁	—	4	2	no	—
234	C₂³×C₂₅₁	—	2	2	no	—
235	C₂³×C₂₅₁	—	4	1	no	—
236	C₂³×C₂₅₁	—	4	1	no	—
237	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
238	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₂₅₁	—	2	2	no	—
240	C₂×C₄×C₂₅₁	—	2	2	no	—
241	C₂×C₄×C₂₅₁	—	4	1	no	—
242	C₂×C₄×C₂₅₁	—	4	1	no	—
243	C₂×C₄×C₂₅₁	—	4	1	no	—
244	C₂×C₄×C₂₅₁	—	4	1	no	—
245	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
254	C₂²×C₂₅₁	—	2	1	no	—
255	C₂²×C₂₅₁	—	2	1	no	—
256	C₂²×C₂₅₁	—	2	2	no	—
257	C₂²×C₂₅₁	—	2	2	no	—
258	C₂²×C₂₅₁	—	2	2	no	—
259	C₂²×C₂₅₁	—	8	2	no	—
260	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
261	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
262	C₂×D₂₅₁	—	2	2	no	—
263	C₂×D₂₅₁	—	2	2	no	—
264	C₂×D₂₅₁	—	2	2	no	—
265	C₂×D₂₅₁	—	2	2	no	—
266	C₂×D₂₅₁	—	2	2	no	—
267	C₂×D₂₅₁	—	2	2	no	—
268	C₂×D₂₅₁	—	2	2	no	—
269	C₂×D₂₅₁	—	2	2	no	—
270	C₂×D₂₅₁	—	2	2	no	—
271	C₂×D₂₅₁	—	8	4	no	—
272	C₄×C₂₅₁	—	2	1	no	—
273	C₄×C₂₅₁	—	2	2	no	—
274	C₄×C₂₅₁	—	2	1	no	—
275	C₄×C₂₅₁	—	2	1	no	—
276	C₄×C₂₅₁	—	2	2	no	—
277	C₄×C₂₅₁	—	2	2	no	—
278	C₄×C₂₅₁	—	2	1	no	—
279	C₄×C₂₅₁	—	2	1	no	—
280	C₄×C₂₅₁	—	2	1	no	—
281	Dic₂₅₁	—	2	2	no	—
282	Dic₂₅₁	—	2	2	no	—
283	Dic₂₅₁	—	2	2	no	—
284	Dic₂₅₁	—	2	2	no	—
285	Dic₂₅₁	—	2	2	no	—
286	C₂×C₂₅₁	—	2	2	no	—
287	C₂×C₂₅₁	—	4	2	no	—
288	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₂₅₁	#585	1	1	yes	characteristic
290	C₂×C₂₅₁	#585	1	1	yes	characteristic
291	D₂₅₁	—	4	2	no	—
292	D₂₅₁	—	4	2	no	—
293	D₂₅₁	—	4	2	no	—
294	C₂₅₁	#3560	1	1	yes	characteristic, complemented, Sylow
295	#3560	—	251	1	no	maximal, Sylow
296	#563	—	251	2	no	—
297	#560	—	251	2	no	—
298	#553	—	251	2	no	—
299	#553	—	251	2	no	—
300	#551	—	251	2	no	—
301	#547	—	251	2	no	—
302	#546	—	251	2	no	—
303	#546	—	251	2	no	—
304	#542	—	251	2	no	—
305	#539	—	251	2	no	—
306	#539	—	251	1	no	—
307	#538	—	251	2	no	—
308	#538	—	251	2	no	—
309	#538	—	251	1	no	—
310	#537	—	251	1	no	—
311	#534	—	251	1	no	—
312	#532	—	251	1	no	—
313	#529	—	251	1	no	—
314	C₂×#126	D₂₅₁	1	1	yes	characteristic, complemented
315	C₂×#41	—	251	2	no	—
316	C₂×#41	—	251	2	no	—
317	C₂²×D₄	—	251	2	no	—
318	C₄⋊Q₈	—	251	2	no	—
319	C₄⋊Q₈	—	251	1	no	—
320	#127	—	251	1	no	—
321	#126	—	251	2	no	—
322	#126	—	251	2	no	—
323	#126	—	251	2	no	—
324	#126	—	251	2	no	—
325	#126	—	251	2	no	—
326	#126	C₂×D₂₅₁	1	2	yes	complemented
327	#126	C₂×D₂₅₁	1	2	yes	complemented
328	#126	C₂×D₂₅₁	1	2	yes	complemented
329	#126	C₂×D₂₅₁	1	2	yes	complemented
330	#125	—	251	2	no	—
331	#125	—	251	2	no	—
332	#125	—	251	1	no	—
333	#124	—	251	2	no	—
334	#124	—	251	2	no	—
335	#124	—	251	2	no	—
336	#124	—	251	1	no	—
337	#124	—	251	2	no	—
338	#123	—	251	2	no	—
339	#123	—	251	2	no	—
340	#123	—	251	2	no	—
341	#123	—	251	2	no	—
342	#123	—	251	2	no	—
343	#123	—	251	2	no	—
344	#123	—	251	2	no	—
345	#123	—	251	2	no	—
346	#123	—	251	2	no	—
347	#123	—	251	2	no	—
348	#123	—	251	2	no	—
349	#123	—	251	2	no	—
350	C₂²⋊Q₈	—	251	1	no	—
351	C₂²⋊Q₈	—	251	2	no	—
352	C₂²⋊Q₈	—	251	2	no	—
353	C₂²⋊Q₈	—	251	2	no	—
354	C₂²⋊Q₈	—	251	2	no	—
355	C₂²⋊Q₈	—	251	2	no	—
356	C₂²⋊Q₈	—	251	2	no	—
357	C₂²⋊Q₈	—	251	2	no	—
358	#121	—	251	1	no	—
359	#121	—	251	1	no	—
360	#121	—	251	1	no	—
361	#121	—	251	2	no	—
362	#121	—	251	2	no	—
363	#121	—	251	2	no	—
364	#121	—	251	2	no	—
365	#121	—	251	2	no	—
366	#121	—	251	2	no	—
367	#121	—	251	2	no	—
368	#121	—	251	2	no	—
369	#121	—	251	2	no	—
370	#121	—	251	2	no	—
371	#121	—	251	2	no	—
372	#121	—	251	2	no	—
373	#120	—	251	2	no	—
374	#120	—	251	2	no	—
375	#120	—	251	2	no	—
376	#120	—	251	2	no	—
377	#120	—	251	2	no	—
378	C₄×Q₈	—	251	1	no	—
379	C₄×D₄	—	251	2	no	—
380	C₄×D₄	—	251	2	no	—
381	C₄×D₄	—	251	2	no	—
382	C₄×D₄	—	251	2	no	—
383	C₄×D₄	—	251	2	no	—
384	C₄×D₄	—	251	2	no	—
385	C₄×D₄	—	251	2	no	—
386	C₄×D₄	—	251	1	no	—
387	C₄×D₄	—	251	2	no	—
388	C₄×D₄	—	251	1	no	—
389	C₄×D₄	—	251	1	no	—
390	#117	—	251	2	no	—
391	#117	—	251	2	no	—
392	C₂×C₄⋊C₄	—	251	2	no	—
393	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
394	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
395	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
396	C₂×C₂²⋊C₄	—	251	2	no	—
397	C₂×C₂²⋊C₄	—	251	2	no	—
398	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
401	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
402	C₂⁴	—	251	2	no	—
403	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
404	#41	—	1004	4	no	—
405	#41	—	1004	4	no	—
406	C₂×Q₈	—	251	1	no	—
407	C₂×Q₈	—	251	2	no	—
408	C₂×Q₈	—	251	2	no	—
409	C₂×D₄	—	1004	4	no	—
410	C₂×D₄	—	251	2	no	—
411	C₂×D₄	—	251	2	no	—
412	C₂×D₄	—	251	2	no	—
413	C₂×D₄	—	251	2	no	—
414	C₂×D₄	—	251	2	no	—
415	C₂×D₄	—	251	2	no	—
416	C₂×D₄	—	251	2	no	—
417	C₂×D₄	—	251	2	no	—
418	C₂×D₄	—	251	1	no	—
419	C₂×D₄	—	251	1	no	—
420	C₂×D₄	—	251	2	no	—
421	C₂×D₄	—	251	2	no	—
422	C₂×D₄	—	251	1	no	—
423	C₂×D₄	—	251	2	no	—
424	C₂×D₄	—	251	2	no	—
425	C₂²×C₄	—	251	2	no	—
426	C₂²×C₄	—	251	2	no	—
427	C₂²×C₄	—	251	2	no	—
428	C₂²×C₄	—	251	2	no	—
429	C₂²×C₄	—	251	2	no	—
430	C₂²×C₄	—	251	2	no	—
431	C₂²×C₄	—	251	2	no	—
432	C₂²×C₄	—	251	2	no	—
433	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
434	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
439	C₄⋊C₄	—	251	2	no	—
440	C₄⋊C₄	—	251	2	no	—
441	C₄⋊C₄	—	251	2	no	—
442	C₄⋊C₄	—	251	2	no	—
443	C₄⋊C₄	—	251	2	no	—
444	C₄⋊C₄	—	251	2	no	—
445	C₄⋊C₄	—	251	2	no	—
446	C₄⋊C₄	—	251	2	no	—
447	C₄⋊C₄	—	251	2	no	—
448	C₄⋊C₄	—	251	2	no	—
449	C₄⋊C₄	—	251	1	no	—
450	C₄⋊C₄	—	251	2	no	—
451	C₄⋊C₄	—	251	1	no	—
452	C₄⋊C₄	—	251	1	no	—
453	C₄⋊C₄	—	251	1	no	—
454	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
455	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
456	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
457	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
458	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
459	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
460	C₂²⋊C₄	—	251	2	no	—
461	C₂²⋊C₄	—	251	2	no	—
462	C₂²⋊C₄	—	251	2	no	—
463	C₂²⋊C₄	—	251	2	no	—
464	C₂²⋊C₄	—	251	2	no	—
465	C₂²⋊C₄	—	251	2	no	—
466	C₂²⋊C₄	—	251	2	no	—
467	C₂²⋊C₄	—	251	2	no	—
468	C₂²⋊C₄	—	251	2	no	—
469	C₂²⋊C₄	—	251	2	no	—
470	C₂²⋊C₄	—	251	2	no	—
471	C₂²⋊C₄	—	251	2	no	—
472	C₂²⋊C₄	—	251	2	no	—
473	C₂²⋊C₄	—	251	2	no	—
474	C₂²⋊C₄	—	251	2	no	—
475	C₂²⋊C₄	—	251	2	no	—
476	C₂²⋊C₄	—	251	2	no	—
477	C₂²⋊C₄	—	251	2	no	—
478	C₂²⋊C₄	—	251	2	no	—
479	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
485	C₄²	—	251	2	no	—
486	C₄²	—	251	2	no	—
487	C₄²	—	251	2	no	—
488	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
489	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
490	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
491	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
492	C₂³	—	2	2	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	1004	2	no	—
496	C₂³	—	1004	2	no	—
497	C₂³	—	1004	2	no	—
498	C₂³	—	251	2	no	—
499	C₂³	—	251	2	no	—
500	C₂³	—	251	2	no	—
501	C₂³	C₂³×D₂₅₁	1	2	yes	—
502	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
503	Q₈	—	1004	2	no	—
504	Q₈	—	1004	2	no	—
505	Q₈	—	1004	1	no	—
506	D₄	—	1004	2	no	—
507	D₄	—	1004	2	no	—
508	D₄	—	1004	2	no	—
509	D₄	—	1004	2	no	—
510	D₄	—	1004	2	no	—
511	D₄	—	1004	1	no	—
512	D₄	—	1004	1	no	—
513	D₄	—	1004	1	no	—
514	D₄	—	1004	2	no	—
515	D₄	—	1004	2	no	—
516	D₄	—	1004	2	no	—
517	D₄	—	1004	2	no	—
518	D₄	—	502	4	no	—
519	D₄	—	502	4	no	—
520	D₄	—	502	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	1004	2	no	—
528	C₂×C₄	—	1004	2	no	—
529	C₂×C₄	—	1004	2	no	—
530	C₂×C₄	—	1004	2	no	—
531	C₂×C₄	—	1004	2	no	—
532	C₂×C₄	—	1004	2	no	—
533	C₂×C₄	—	1004	2	no	—
534	C₂×C₄	—	1004	2	no	—
535	C₂×C₄	—	251	2	no	—
536	C₂×C₄	—	251	2	no	—
537	C₂×C₄	—	251	2	no	—
538	C₂×C₄	—	251	2	no	—
539	C₂×C₄	—	251	2	no	—
540	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
541	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
542	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
543	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	2008	4	no	—
556	C₂²	—	502	2	no	—
557	C₂²	—	502	2	no	—
558	C₂²	—	502	2	no	—
559	C₂²	—	502	2	no	—
560	C₂²	—	502	2	no	—
561	C₂²	—	502	2	no	—
562	C₂²	—	502	2	no	—
563	C₂²	—	502	2	no	—
564	C₂²	—	502	2	no	—
565	C₂²	#22548761	1	2	yes	—
566	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	502	2	no	—
577	C₄	—	502	2	no	—
578	C₄	—	502	2	no	—
579	C₄	—	502	2	no	—
580	C₄	—	502	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	1004	2	no	—
584	C₂	—	1004	2	no	—
585	C₂	—	1004	2	no	—
586	C₂	C₂×#22548761	1	1	yes	characteristic
587	C₂	#30632523	1	1	yes	characteristic
588	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	C₂×#126×C₂₅₁	C₂
hypercenter	C₂×#126	D₂₅₁
hypocenter	C₂₅₁	#3560
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #30632439	C₂	semidirect
2. #30632428	C₂	semidirect
3. #30632388	C₂	semidirect
4. #30632385	C₂	semidirect
5. #30632362	C₂	semidirect
6. #30632338	C₂	semidirect
7. #30632327	C₂	semidirect
8. #30632327	C₂	semidirect
9. #30632303	C₂	semidirect
10. #30632284	C₂	semidirect
11. #30632278	C₂	semidirect
12. #30632276	C₂	semidirect
13. #30632276	C₂	semidirect
14. #30632275	C₂	semidirect
15. #30632268	C₂	semidirect
16. #30632249	C₂	semidirect
17. #30632237	C₂	semidirect
18. #30632221	C₂	semidirect
19. C₂×#126×C₂₅₁	C₂	semidirect
20. C₂×#16860810	C₂²	semidirect
21. C₂×#16860810	C₂²	semidirect
23. #22548715	C₂²	semidirect
24. #22548714	C₂²	semidirect
25. #22548712	C₂²	semidirect
26. #22548710	C₂²	semidirect
27. #22548710	C₂²	semidirect
28. #22548710	C₂²	semidirect
29. #22548709	C₂²	semidirect
30. #22548708	C₂²	semidirect
31. #22548707	C₂²	semidirect
32. #22548706	C₂²	semidirect
33. #22548705	C₂²	semidirect
34. #22548703	C₂²	semidirect
35. #22548703	C₂²	semidirect
38. #22548701	C₂²	semidirect
39. #22548700	C₂²	semidirect
40. #22548700	C₂²	semidirect
41. #22548700	C₂²	semidirect
42. #22548700	C₂²	semidirect
43. #22548700	C₂²	semidirect
46. #22548698	C₂²	semidirect
47. #22548698	C₂²	semidirect
50. #22548697	C₂²	semidirect
51. #22548695	C₂²	semidirect
52. #22548695	C₂²	semidirect
53. #22548694	C₂²	semidirect
54. #22548693	C₂²	semidirect
55. #22548693	C₂²	semidirect
56. #22548693	C₂²	semidirect
57. #22548692	C₂²	semidirect
58. #22548692	C₂²	semidirect
59. #22548690	C₂²	semidirect
60. #22548690	C₂²	semidirect
61. #22548690	C₂²	semidirect
62. #22548690	C₂²	semidirect
66. #22548689	C₂²	semidirect
67. #22548689	C₂²	semidirect
68. #22548689	C₂²	semidirect
73. #22548688	C₂²	semidirect
76. #22548685	C₂²	semidirect
77. #22548685	C₂²	semidirect
79. C₄×Dic₅₀₂	C₂²	semidirect
80. C₄×D₁₀₀₄	C₂²	semidirect
81. C₄×D₁₀₀₄	C₂²	semidirect
82. C₄×D₁₀₀₄	C₂²	semidirect
83. C₄×D₁₀₀₄	C₂²	semidirect
84. #22548677	C₂²	semidirect
85. #22548677	C₂²	semidirect
86. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
87. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
88. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
89. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
91. #22548673	C₂²	semidirect
92. #22548672	C₂²	semidirect
93. C₄⋊C₄×D₂₅₁	C₂²	semidirect
94. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
95. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
96. #126×C₂₅₁	C₂²	semidirect
97. #126×C₂₅₁	C₂²	semidirect
98. #126×C₂₅₁	C₂²	semidirect
99. #126×C₂₅₁	C₂²	semidirect
100. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
101. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
102. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
106. C₂×C₄²×C₂₅₁	C₂²	semidirect
294. C₂₅₁	#3560	semidirect
314. C₂×#126	D₂₅₁	semidirect
326. #126	C₂×D₂₅₁	semidirect
327. #126	C₂×D₂₅₁	semidirect
328. #126	C₂×D₂₅₁	semidirect
329. #126	C₂×D₂₅₁	semidirect
393. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
394. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
395. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
401. C₂×C₄²	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632439	2
#30632428	2
#30632388	2
#30632385	2
#30632362	2
#30632338	2
#30632327	2
#30632303	2
#30632284	2
#30632278	2
#30632276	2
#30632275	2
#30632268	2
#30632249	2
#30632237	2
#30632221	2
C₂×#126×C₂₅₁	2
#3560	251