Subgroups — #44564791

Order 32128.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 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	#30632425	C₂	1	2	yes	maximal, complemented
3	#30632402	C₂	1	2	yes	maximal, complemented
4	#30632381	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632375	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632372	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632360	C₂	1	2	yes	maximal, complemented
8	#30632346	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632343	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632334	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632332	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632290	C₂	1	2	yes	maximal, complemented
13	#30632289	C₂	1	2	yes	maximal, complemented
14	#30632276	C₂	1	2	yes	maximal, complemented
15	#30632270	C₂	1	2	yes	maximal, complemented
16	#30632268	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632266	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632263	C₂	1	1	yes	maximal, characteristic, complemented
19	#30632253	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632234	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632222	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632219	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860810	C₂²	1	1	yes	characteristic
25	C₂×#16860810	C₂²	1	1	yes	characteristic
26	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
27	C₂×#16860809	C₂²	1	1	yes	characteristic
28	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
30	#22548715	C₂²	1	2	yes	complemented
31	#22548714	C₂²	1	1	yes	characteristic, complemented
32	#22548711	C₂²	1	1	yes	characteristic
33	#22548711	C₂²	1	2	yes	—
34	#22548710	C₂²	1	2	yes	—
35	#22548710	C₂²	1	2	yes	—
36	#22548710	C₂²	1	2	yes	complemented
37	#22548709	C₂²	1	2	yes	complemented
38	#22548708	C₂²	1	2	yes	complemented
39	#22548706	C₂²	1	1	yes	characteristic, complemented
40	#22548706	C₂²	1	2	yes	complemented
41	#22548705	C₂²	1	2	yes	complemented
42	#22548703	C₂²	1	1	yes	characteristic
43	#22548703	C₂²	1	2	yes	—
44	#22548702	C₂²	1	1	yes	characteristic
45	#22548701	C₂²	1	1	yes	characteristic
46	#22548701	C₂²	1	2	yes	—
47	#22548701	C₂²	1	1	yes	characteristic, complemented
48	#22548701	C₂²	1	2	yes	complemented
49	#22548701	C₂²	1	2	yes	complemented
50	#22548700	C₂²	1	2	yes	—
51	#22548700	C₂²	1	2	yes	complemented
52	#22548699	C₂²	1	2	yes	—
53	#22548699	C₂²	1	2	yes	—
54	#22548699	C₂²	1	2	yes	complemented
55	#22548698	C₂²	1	2	yes	—
56	#22548697	C₂²	1	2	yes	—
57	#22548697	C₂²	1	2	yes	complemented
58	#22548697	C₂²	1	2	yes	complemented
59	#22548695	C₂²	1	1	yes	characteristic
60	#22548695	C₂²	1	1	yes	characteristic
61	#22548695	C₂²	1	1	yes	characteristic, complemented
62	#22548695	C₂²	1	1	yes	characteristic, complemented
63	#22548695	C₂²	1	1	yes	characteristic, complemented
64	#22548695	C₂²	1	2	yes	complemented
65	#22548694	C₂²	1	1	yes	characteristic, complemented
66	#22548693	C₂²	1	2	yes	complemented
67	#22548692	C₂²	1	2	yes	complemented
68	#22548692	C₂²	1	2	yes	complemented
69	#22548690	C₂²	1	1	yes	characteristic
70	#22548690	C₂²	1	1	yes	characteristic
71	#22548690	C₂²	1	1	yes	characteristic
72	#22548690	C₂²	1	2	yes	complemented
73	#22548689	C₂²	1	1	yes	characteristic
74	#22548689	C₂²	1	2	yes	—
75	#22548689	C₂²	1	2	yes	complemented
76	#22548689	C₂²	1	2	yes	complemented
77	#22548688	C₂²	1	1	yes	characteristic
78	#22548688	C₂²	1	1	yes	characteristic, complemented
79	#22548688	C₂²	1	2	yes	complemented
80	#22548688	C₂²	1	2	yes	complemented
81	#22548687	C₂²	1	2	yes	complemented
82	#22548687	C₂²	1	2	yes	complemented
83	#22548687	C₂²	1	2	yes	complemented
84	#22548686	C₂²	1	1	yes	characteristic
85	#22548686	C₂²	1	2	yes	—
86	#22548686	C₂²	1	1	yes	characteristic, complemented
87	#22548686	C₂²	1	2	yes	complemented
88	#22548685	C₂²	1	2	yes	—
89	#22548685	C₂²	1	2	yes	—
90	#22548683	C₂²	1	2	yes	—
91	#22548683	C₂²	1	2	yes	—
92	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
93	#22548680	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
95	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
96	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
97	#22548677	C₂²	1	1	yes	characteristic
98	#22548677	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
102	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
103	#22548674	C₂²	1	2	yes	complemented
104	#22548674	C₂²	1	2	yes	complemented
105	#22548673	C₂²	1	1	yes	characteristic
106	#22548673	C₂²	1	2	yes	complemented
107	#22548673	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
109	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
111	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
112	#126×C₂₅₁	C₂²	1	2	yes	complemented
113	#125×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
114	#123×C₂₅₁	C₂²	1	2	yes	complemented
115	#121×C₂₅₁	C₂²	1	1	yes	characteristic
116	#121×C₂₅₁	C₂²	1	1	yes	characteristic
117	#121×C₂₅₁	C₂²	1	2	yes	complemented
118	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
121	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₅₁	C₂³	1	2	yes	—
124	#16860810	—	4	2	no	—
125	#16860810	—	4	2	no	—
126	#16860810	—	4	2	no	—
127	#16860809	—	4	2	no	—
128	C₂×Dic₅₀₂	—	4	2	no	—
129	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₅₀₂	C₂³	1	2	yes	—
132	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
133	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
134	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
135	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
136	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
137	C₂×D₁₀₀₄	C₂³	1	2	yes	—
138	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
139	C₂×D₁₀₀₄	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
151	D₄×D₂₅₁	—	4	2	no	—
152	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
153	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
154	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
158	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
161	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
162	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
164	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
165	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
166	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
167	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
168	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
169	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
170	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
171	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
172	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
176	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
183	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
199	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₂₅₁	C₂³	1	2	yes	—
203	C₄×Dic₂₅₁	C₂³	1	2	yes	—
204	C₄×Dic₂₅₁	C₂³	1	2	yes	—
205	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
207	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
209	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
226	C₄²×C₂₅₁	C₂³	1	2	yes	—
227	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
228	C₂²×D₂₅₁	—	4	2	no	—
229	C₂²×D₂₅₁	—	4	2	no	—
230	C₂²×D₂₅₁	—	4	2	no	—
231	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
233	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
235	Dic₅₀₂	—	2	2	no	—
236	Dic₅₀₂	—	2	2	no	—
237	Dic₅₀₂	—	4	2	no	—
238	Dic₅₀₂	—	4	1	no	—
239	Dic₅₀₂	—	4	1	no	—
240	D₁₀₀₄	—	2	2	no	—
241	D₁₀₀₄	—	4	2	no	—
242	D₁₀₀₄	—	4	2	no	—
243	D₁₀₀₄	—	4	1	no	—
244	D₁₀₀₄	—	4	1	no	—
245	D₁₀₀₄	—	4	1	no	—
246	C₂²⋊D₂₅₁	—	4	2	no	—
247	C₂²⋊D₂₅₁	—	4	2	no	—
248	C₂²⋊D₂₅₁	—	4	2	no	—
249	C₂²⋊D₂₅₁	—	4	1	no	—
250	C₂²⋊D₂₅₁	—	4	1	no	—
251	C₂²⋊D₂₅₁	—	4	2	no	—
252	C₂²⋊D₂₅₁	—	4	1	no	—
253	C₂²⋊D₂₅₁	—	4	1	no	—
254	C₂²⋊D₂₅₁	—	4	1	no	—
255	C₂²⋊D₂₅₁	—	4	1	no	—
256	C₂²⋊D₂₅₁	—	4	2	no	—
257	C₂×Dic₂₅₁	—	4	2	no	—
258	C₂×Dic₂₅₁	—	4	2	no	—
259	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
262	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
265	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
266	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
267	C₄×D₂₅₁	—	2	2	no	—
268	C₄×D₂₅₁	—	2	2	no	—
269	C₄×D₂₅₁	—	2	2	no	—
270	C₄×D₂₅₁	—	4	2	no	—
271	C₄×D₂₅₁	—	4	1	no	—
272	C₄×D₂₅₁	—	4	1	no	—
273	C₄×D₂₅₁	—	4	2	no	—
274	C₄×D₂₅₁	—	4	2	no	—
275	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
276	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
277	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
278	D₄×C₂₅₁	—	2	2	no	—
279	D₄×C₂₅₁	—	4	2	no	—
280	D₄×C₂₅₁	—	4	2	no	—
281	D₄×C₂₅₁	—	4	1	no	—
282	C₂×C₄×C₂₅₁	—	2	2	no	—
283	C₂×C₄×C₂₅₁	—	2	2	no	—
284	C₂×C₄×C₂₅₁	—	4	2	no	—
285	C₂×C₄×C₂₅₁	—	4	2	no	—
286	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
289	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
291	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
293	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₂₅₁	—	2	1	no	—
295	C₂²×C₂₅₁	—	2	1	no	—
296	C₂²×C₂₅₁	—	2	2	no	—
297	C₂²×C₂₅₁	—	2	1	no	—
298	C₂²×C₂₅₁	—	2	2	no	—
299	C₂²×C₂₅₁	—	2	1	no	—
300	C₂²×C₂₅₁	—	2	1	no	—
301	C₂²×C₂₅₁	—	2	1	no	—
302	C₂²×C₂₅₁	—	2	2	no	—
303	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
304	C₂×D₂₅₁	—	2	1	no	—
305	C₂×D₂₅₁	—	2	1	no	—
306	C₂×D₂₅₁	—	2	1	no	—
307	C₂×D₂₅₁	—	2	2	no	—
308	C₂×D₂₅₁	—	2	1	no	—
309	C₂×D₂₅₁	—	2	1	no	—
310	C₂×D₂₅₁	—	2	2	no	—
311	C₂×D₂₅₁	—	2	1	no	—
312	C₂×D₂₅₁	—	2	1	no	—
313	C₂×D₂₅₁	—	2	1	no	—
314	C₂×D₂₅₁	—	2	2	no	—
315	C₂×D₂₅₁	—	2	1	no	—
316	C₂×D₂₅₁	—	8	4	no	—
317	C₄×C₂₅₁	—	2	1	no	—
318	C₄×C₂₅₁	—	2	1	no	—
319	C₄×C₂₅₁	—	2	1	no	—
320	C₄×C₂₅₁	—	2	2	no	—
321	C₄×C₂₅₁	—	2	2	no	—
322	C₄×C₂₅₁	—	2	2	no	—
323	C₄×C₂₅₁	—	2	1	no	—
324	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
325	Dic₂₅₁	—	2	1	no	—
326	Dic₂₅₁	—	2	1	no	—
327	Dic₂₅₁	—	2	1	no	—
328	Dic₂₅₁	—	2	2	no	—
329	Dic₂₅₁	—	2	2	no	—
330	Dic₂₅₁	—	2	1	no	—
331	Dic₂₅₁	—	2	1	no	—
332	Dic₂₅₁	—	2	2	no	—
333	C₂×C₂₅₁	—	4	2	no	—
334	C₂×C₂₅₁	—	4	1	no	—
335	C₂×C₂₅₁	—	4	1	no	—
336	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₂₅₁	#585	1	1	yes	characteristic
338	C₂×C₂₅₁	#585	1	1	yes	characteristic
339	D₂₅₁	—	4	1	no	—
340	D₂₅₁	—	4	1	no	—
341	D₂₅₁	—	4	2	no	—
342	D₂₅₁	—	4	1	no	—
343	C₂₅₁	#3551	1	1	yes	characteristic, complemented, Sylow
344	#3551	—	251	1	no	maximal, Sylow
345	#563	—	251	2	no	—
346	#560	—	251	2	no	—
347	#555	—	251	2	no	—
348	#553	—	251	1	no	—
349	#553	D₂₅₁	1	1	yes	characteristic, complemented
350	#552	—	251	1	no	—
351	#552	—	251	1	no	—
352	#551	—	251	2	no	—
353	#548	—	251	1	no	—
354	#548	—	251	1	no	—
355	#546	—	251	1	no	—
356	#546	—	251	1	no	—
357	#540	—	251	2	no	—
358	#540	—	251	2	no	—
359	#538	—	251	2	no	—
360	#538	—	251	2	no	—
361	#537	—	251	1	no	—
362	#537	—	251	1	no	—
363	#536	—	251	1	no	—
364	#535	—	251	1	no	—
365	#532	—	251	1	no	—
366	#529	—	251	1	no	—
367	#529	—	251	1	no	—
368	C₂×#41	—	251	1	no	—
369	C₂×#41	—	251	1	no	—
370	C₂×#41	—	251	1	no	—
371	C₂×#41	—	251	1	no	—
372	C₂²×Q₈	—	251	1	no	—
373	C₂²×D₄	—	251	1	no	—
374	C₄⋊Q₈	—	251	1	no	—
375	C₄⋊Q₈	—	251	2	no	—
376	#127	—	251	1	no	—
377	#127	—	251	2	no	—
378	#126	—	251	2	no	—
379	#126	—	251	2	no	—
380	#126	—	251	2	no	—
381	#126	—	251	2	no	—
382	#126	—	251	2	no	—
383	#126	C₂×D₂₅₁	1	2	yes	complemented
384	#125	—	251	1	no	—
385	#125	—	251	2	no	—
386	#125	—	251	2	no	—
387	#125	C₂×D₂₅₁	1	1	yes	characteristic, complemented
388	#124	—	251	1	no	—
389	#124	—	251	1	no	—
390	#124	—	251	1	no	—
391	#124	—	251	2	no	—
392	#124	—	251	2	no	—
393	#124	—	251	2	no	—
394	#124	—	251	1	no	—
395	#124	—	251	2	no	—
396	#123	—	251	2	no	—
397	#123	—	251	2	no	—
398	#123	—	251	2	no	—
399	#123	—	251	2	no	—
400	#123	—	251	2	no	—
401	#123	—	251	2	no	—
402	#123	—	251	2	no	—
403	#123	—	251	2	no	—
404	#123	—	251	2	no	—
405	#123	C₂×D₂₅₁	1	2	yes	complemented
406	C₂²⋊Q₈	—	251	1	no	—
407	C₂²⋊Q₈	—	251	1	no	—
408	C₂²⋊Q₈	—	251	1	no	—
409	C₂²⋊Q₈	—	251	1	no	—
410	C₂²⋊Q₈	—	251	1	no	—
411	C₂²⋊Q₈	—	251	1	no	—
412	C₂²⋊Q₈	—	251	2	no	—
413	C₂²⋊Q₈	—	251	2	no	—
414	C₂²⋊Q₈	—	251	2	no	—
415	C₂²⋊Q₈	—	251	2	no	—
416	#121	—	251	1	no	—
417	#121	—	251	1	no	—
418	#121	—	251	2	no	—
419	#121	—	251	2	no	—
420	#121	—	251	2	no	—
421	#121	—	251	2	no	—
422	#121	—	251	2	no	—
423	#121	—	251	1	no	—
424	#121	—	251	2	no	—
425	#121	—	251	2	no	—
426	#121	—	251	2	no	—
427	#121	—	251	1	no	—
428	#121	—	251	1	no	—
429	#121	—	251	2	no	—
430	#121	—	251	1	no	—
431	#121	—	251	1	no	—
432	#121	—	251	1	no	—
433	#121	—	251	2	no	—
434	#121	—	251	2	no	—
435	#121	C₂×D₂₅₁	1	1	yes	characteristic
436	#121	C₂×D₂₅₁	1	1	yes	characteristic
437	#121	C₂×D₂₅₁	1	2	yes	complemented
438	#120	—	251	2	no	—
439	#120	—	251	2	no	—
440	#120	—	251	2	no	—
441	#120	—	251	2	no	—
442	C₄×Q₈	—	251	1	no	—
443	C₄×Q₈	—	251	1	no	—
444	C₄×D₄	—	251	2	no	—
445	C₄×D₄	—	251	2	no	—
446	C₄×D₄	—	251	1	no	—
447	C₄×D₄	—	251	1	no	—
448	C₄×D₄	—	251	2	no	—
449	C₄×D₄	—	251	1	no	—
450	C₄×D₄	—	251	2	no	—
451	C₄×D₄	—	251	1	no	—
452	C₄×D₄	—	251	2	no	—
453	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
454	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
455	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
456	#117	—	251	2	no	—
457	#117	—	251	2	no	—
458	#117	—	251	2	no	—
459	#117	—	251	1	no	—
460	#117	—	251	2	no	—
461	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
462	C₂×C₄⋊C₄	—	251	1	no	—
463	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊C₄	—	251	2	no	—
465	C₂×C₂²⋊C₄	—	251	2	no	—
466	C₂×C₄²	—	251	1	no	—
467	C₂⁴	—	251	2	no	—
468	#41	—	1004	2	no	—
469	#41	—	1004	2	no	—
470	#41	—	1004	2	no	—
471	#41	—	1004	2	no	—
472	C₂×Q₈	—	1004	2	no	—
473	C₂×Q₈	—	251	1	no	—
474	C₂×Q₈	—	251	2	no	—
475	C₂×Q₈	—	251	1	no	—
476	C₂×Q₈	—	251	1	no	—
477	C₂×Q₈	—	251	1	no	—
478	C₂×D₄	—	1004	2	no	—
479	C₂×D₄	—	251	1	no	—
480	C₂×D₄	—	251	2	no	—
481	C₂×D₄	—	251	2	no	—
482	C₂×D₄	—	251	1	no	—
483	C₂×D₄	—	251	1	no	—
484	C₂×D₄	—	251	2	no	—
485	C₂×D₄	—	251	2	no	—
486	C₂×D₄	—	251	1	no	—
487	C₂×D₄	—	251	1	no	—
488	C₂×D₄	—	251	2	no	—
489	C₂×D₄	—	251	1	no	—
490	C₂×D₄	—	251	1	no	—
491	C₂×D₄	—	251	2	no	—
492	C₂×D₄	—	251	2	no	—
493	C₂×D₄	—	251	1	no	—
494	C₂×D₄	—	251	1	no	—
495	C₂×D₄	—	251	1	no	—
496	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
498	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
499	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
500	C₂²×C₄	—	251	2	no	—
501	C₂²×C₄	—	251	2	no	—
502	C₂²×C₄	—	251	1	no	—
503	C₂²×C₄	—	251	1	no	—
504	C₂²×C₄	—	251	2	no	—
505	C₂²×C₄	—	251	2	no	—
506	C₂²×C₄	—	251	2	no	—
507	C₂²×C₄	—	251	1	no	—
508	C₂²×C₄	—	251	1	no	—
509	C₂²×C₄	—	251	1	no	—
510	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
513	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
514	C₄⋊C₄	—	251	1	no	—
515	C₄⋊C₄	—	251	2	no	—
516	C₄⋊C₄	—	251	2	no	—
517	C₄⋊C₄	—	251	2	no	—
518	C₄⋊C₄	—	251	2	no	—
519	C₄⋊C₄	—	251	2	no	—
520	C₄⋊C₄	—	251	2	no	—
521	C₄⋊C₄	—	251	2	no	—
522	C₄⋊C₄	—	251	1	no	—
523	C₄⋊C₄	—	251	1	no	—
524	C₄⋊C₄	—	251	2	no	—
525	C₄⋊C₄	—	251	2	no	—
526	C₄⋊C₄	—	251	2	no	—
527	C₄⋊C₄	—	251	2	no	—
528	C₄⋊C₄	—	251	1	no	—
529	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
533	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
534	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
535	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
536	C₂²⋊C₄	—	251	2	no	—
537	C₂²⋊C₄	—	251	1	no	—
538	C₂²⋊C₄	—	251	2	no	—
539	C₂²⋊C₄	—	251	2	no	—
540	C₂²⋊C₄	—	251	1	no	—
541	C₂²⋊C₄	—	251	2	no	—
542	C₂²⋊C₄	—	251	1	no	—
543	C₂²⋊C₄	—	251	1	no	—
544	C₂²⋊C₄	—	251	2	no	—
545	C₂²⋊C₄	—	251	2	no	—
546	C₂²⋊C₄	—	251	2	no	—
547	C₂²⋊C₄	—	251	2	no	—
548	C₂²⋊C₄	—	251	1	no	—
549	C₂²⋊C₄	—	251	2	no	—
550	C₂²⋊C₄	—	251	2	no	—
551	C₂²⋊C₄	—	251	2	no	—
552	C₂²⋊C₄	—	251	1	no	—
553	C₂²⋊C₄	—	251	2	no	—
554	C₂²⋊C₄	—	251	2	no	—
555	C₂²⋊C₄	—	251	2	no	—
556	C₂²⋊C₄	—	251	2	no	—
557	C₂²⋊C₄	—	251	2	no	—
558	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
563	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
564	C₄²	—	251	1	no	—
565	C₄²	—	251	1	no	—
566	C₄²	—	251	1	no	—
567	C₄²	—	251	2	no	—
568	C₄²	—	251	2	no	—
569	C₄²	—	251	2	no	—
570	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
571	C₄²	C₂²×D₂₅₁	1	2	yes	—
572	C₂³	—	1004	2	no	—
573	C₂³	—	1004	2	no	—
574	C₂³	—	1004	2	no	—
575	C₂³	—	251	1	no	—
576	C₂³	—	251	2	no	—
577	C₂³	—	251	1	no	—
578	C₂³	—	251	1	no	—
579	C₂³	C₂³×D₂₅₁	1	2	yes	—
580	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
581	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
582	Q₈	—	1004	2	no	—
583	Q₈	—	1004	1	no	—
584	Q₈	—	1004	1	no	—
585	Q₈	—	502	2	no	—
586	Q₈	—	502	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	1	no	—
591	D₄	—	1004	1	no	—
592	D₄	—	1004	1	no	—
593	D₄	—	1004	2	no	—
594	D₄	—	1004	2	no	—
595	D₄	—	1004	1	no	—
596	D₄	—	1004	2	no	—
597	D₄	—	1004	1	no	—
598	D₄	—	1004	2	no	—
599	D₄	—	1004	2	no	—
600	D₄	—	1004	1	no	—
601	D₄	—	1004	1	no	—
602	D₄	—	1004	1	no	—
603	D₄	—	1004	1	no	—
604	D₄	—	1004	1	no	—
605	D₄	—	1004	2	no	—
606	D₄	—	1004	2	no	—
607	D₄	—	502	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	1004	2	no	—
613	C₂×C₄	—	1004	1	no	—
614	C₂×C₄	—	1004	2	no	—
615	C₂×C₄	—	1004	2	no	—
616	C₂×C₄	—	1004	1	no	—
617	C₂×C₄	—	1004	2	no	—
618	C₂×C₄	—	1004	2	no	—
619	C₂×C₄	—	502	2	no	—
620	C₂×C₄	—	502	2	no	—
621	C₂×C₄	—	502	2	no	—
622	C₂×C₄	—	251	1	no	—
623	C₂×C₄	—	251	1	no	—
624	C₂×C₄	—	251	2	no	—
625	C₂×C₄	—	251	1	no	—
626	C₂×C₄	—	251	1	no	—
627	C₂×C₄	—	251	2	no	—
628	C₂×C₄	—	251	2	no	—
629	C₂×C₄	—	251	1	no	—
630	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
632	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
635	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
636	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2008	4	no	—
648	C₂²	—	502	2	no	—
649	C₂²	—	502	1	no	—
650	C₂²	—	502	1	no	—
651	C₂²	—	502	1	no	—
652	C₂²	—	502	1	no	—
653	C₂²	—	502	1	no	—
654	C₂²	—	502	2	no	—
655	C₂²	—	502	1	no	—
656	C₂²	—	502	1	no	—
657	C₂²	—	502	1	no	—
658	C₂²	—	502	2	no	—
659	C₂²	—	502	1	no	—
660	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	502	1	no	—
669	C₄	—	502	2	no	—
670	C₄	—	502	2	no	—
671	C₄	—	502	1	no	—
672	C₄	—	502	1	no	—
673	C₄	—	502	1	no	—
674	C₄	—	502	1	no	—
675	C₄	—	502	2	no	—
676	C₄	#22548761	1	2	yes	—
677	C₂	—	4	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	1	no	—
680	C₂	—	1004	1	no	—
681	C₂	—	1004	2	no	—
682	C₂	—	1004	1	no	—
683	C₂	—	1004	1	no	—
684	C₂	C₂×#22548761	1	1	yes	characteristic
685	C₂	#30632522	1	1	yes	characteristic
686	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#553×C₂₅₁	C₂
hypercenter	#553	D₂₅₁
hypocenter	C₂₅₁	#3551
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #30632439	C₂	semidirect
2. #30632425	C₂	semidirect
3. #30632402	C₂	semidirect
4. #30632381	C₂	semidirect
5. #30632375	C₂	semidirect
6. #30632372	C₂	semidirect
7. #30632360	C₂	semidirect
8. #30632346	C₂	semidirect
9. #30632343	C₂	semidirect
10. #30632334	C₂	semidirect
11. #30632332	C₂	semidirect
12. #30632290	C₂	semidirect
13. #30632289	C₂	semidirect
14. #30632276	C₂	semidirect
15. #30632270	C₂	semidirect
16. #30632268	C₂	semidirect
17. #30632266	C₂	semidirect
18. #30632263	C₂	semidirect
19. #30632253	C₂	semidirect
20. #30632234	C₂	semidirect
21. #30632222	C₂	semidirect
22. #30632219	C₂	semidirect
23. #553×C₂₅₁	C₂	semidirect
26. C₂×#16860810	C₂²	semidirect
28. C₂²×Dic₅₀₂	C₂²	semidirect
30. #22548715	C₂²	semidirect
31. #22548714	C₂²	semidirect
36. #22548710	C₂²	semidirect
37. #22548709	C₂²	semidirect
38. #22548708	C₂²	semidirect
39. #22548706	C₂²	semidirect
40. #22548706	C₂²	semidirect
41. #22548705	C₂²	semidirect
47. #22548701	C₂²	semidirect
48. #22548701	C₂²	semidirect
49. #22548701	C₂²	semidirect
51. #22548700	C₂²	semidirect
54. #22548699	C₂²	semidirect
57. #22548697	C₂²	semidirect
58. #22548697	C₂²	semidirect
61. #22548695	C₂²	semidirect
62. #22548695	C₂²	semidirect
63. #22548695	C₂²	semidirect
64. #22548695	C₂²	semidirect
65. #22548694	C₂²	semidirect
66. #22548693	C₂²	semidirect
67. #22548692	C₂²	semidirect
68. #22548692	C₂²	semidirect
72. #22548690	C₂²	semidirect
75. #22548689	C₂²	semidirect
76. #22548689	C₂²	semidirect
78. #22548688	C₂²	semidirect
79. #22548688	C₂²	semidirect
80. #22548688	C₂²	semidirect
81. #22548687	C₂²	semidirect
82. #22548687	C₂²	semidirect
83. #22548687	C₂²	semidirect
86. #22548686	C₂²	semidirect
87. #22548686	C₂²	semidirect
92. C₄×Dic₅₀₂	C₂²	semidirect
93. #22548680	C₂²	semidirect
95. C₄×D₁₀₀₄	C₂²	semidirect
96. D₄×Dic₂₅₁	C₂²	semidirect
98. #22548677	C₂²	semidirect
100. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
101. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
102. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
103. #22548674	C₂²	semidirect
104. #22548674	C₂²	semidirect
106. #22548673	C₂²	semidirect
107. #22548673	C₂²	semidirect
108. C₄⋊C₄×D₂₅₁	C₂²	semidirect
111. C₄²×D₂₅₁	C₂²	semidirect
112. #126×C₂₅₁	C₂²	semidirect
113. #125×C₂₅₁	C₂²	semidirect
114. #123×C₂₅₁	C₂²	semidirect
117. #121×C₂₅₁	C₂²	semidirect
119. C₄×D₄×C₂₅₁	C₂²	semidirect
120. C₄×D₄×C₂₅₁	C₂²	semidirect
121. #117×C₂₅₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
343. C₂₅₁	#3551	semidirect
349. #553	D₂₅₁	semidirect
383. #126	C₂×D₂₅₁	semidirect
387. #125	C₂×D₂₅₁	semidirect
405. #123	C₂×D₂₅₁	semidirect
437. #121	C₂×D₂₅₁	semidirect
454. C₄×D₄	C₂×D₂₅₁	semidirect
455. C₄×D₄	C₂×D₂₅₁	semidirect
461. #117	C₂×D₂₅₁	semidirect
463. C₂×C₄⋊C₄	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
#30632425	2
#30632402	2
#30632381	2
#30632375	2
#30632372	2
#30632360	2
#30632346	2
#30632343	2
#30632334	2
#30632332	2
#30632290	2
#30632289	2
#30632276	2
#30632270	2
#30632268	2
#30632266	2
#30632263	2
#30632253	2
#30632234	2
#30632222	2
#30632219	2
#553×C₂₅₁	2
#3551	251