Subgroups — #44564783

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	#30632438	C₂	1	2	yes	maximal, complemented
2	#30632425	C₂	1	2	yes	maximal, complemented
3	#30632401	C₂	1	2	yes	maximal, complemented
4	#30632389	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632385	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632379	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632372	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632364	C₂	1	2	yes	maximal, complemented
9	#30632347	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632344	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632334	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632325	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632290	C₂	1	2	yes	maximal, complemented
14	#30632287	C₂	1	2	yes	maximal, complemented
15	#30632274	C₂	1	2	yes	maximal, complemented
16	#30632269	C₂	1	2	yes	maximal, complemented
17	#30632265	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632260	C₂	1	1	yes	maximal, characteristic, complemented
19	#30632253	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632233	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632223	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632218	C₂	1	1	yes	maximal, characteristic, complemented
23	#537×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×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
28	#22548714	C₂²	1	2	yes	complemented
29	#22548713	C₂²	1	1	yes	characteristic, complemented
30	#22548711	C₂²	1	1	yes	characteristic
31	#22548711	C₂²	1	2	yes	—
32	#22548710	C₂²	1	2	yes	—
33	#22548710	C₂²	1	2	yes	—
34	#22548710	C₂²	1	2	yes	complemented
35	#22548710	C₂²	1	2	yes	complemented
36	#22548708	C₂²	1	2	yes	complemented
37	#22548708	C₂²	1	2	yes	complemented
38	#22548706	C₂²	1	1	yes	characteristic, complemented
39	#22548706	C₂²	1	1	yes	characteristic, complemented
40	#22548706	C₂²	1	2	yes	complemented
41	#22548705	C₂²	1	2	yes	complemented
42	#22548704	C₂²	1	1	yes	characteristic
43	#22548704	C₂²	1	1	yes	characteristic
44	#22548702	C₂²	1	1	yes	characteristic
45	#22548702	C₂²	1	1	yes	characteristic, complemented
46	#22548702	C₂²	1	2	yes	complemented
47	#22548701	C₂²	1	2	yes	—
48	#22548701	C₂²	1	2	yes	—
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	complemented
54	#22548699	C₂²	1	2	yes	complemented
55	#22548698	C₂²	1	2	yes	—
56	#22548698	C₂²	1	2	yes	—
57	#22548697	C₂²	1	2	yes	—
58	#22548697	C₂²	1	2	yes	complemented
59	#22548696	C₂²	1	2	yes	complemented
60	#22548695	C₂²	1	1	yes	characteristic
61	#22548694	C₂²	1	1	yes	characteristic, complemented
62	#22548694	C₂²	1	1	yes	characteristic, complemented
63	#22548694	C₂²	1	2	yes	complemented
64	#22548693	C₂²	1	2	yes	complemented
65	#22548691	C₂²	1	1	yes	characteristic
66	#22548691	C₂²	1	2	yes	complemented
67	#22548690	C₂²	1	1	yes	characteristic
68	#22548689	C₂²	1	1	yes	characteristic
69	#22548689	C₂²	1	1	yes	characteristic
70	#22548689	C₂²	1	2	yes	complemented
71	#22548688	C₂²	1	2	yes	complemented
72	#22548687	C₂²	1	1	yes	characteristic
73	#22548687	C₂²	1	1	yes	characteristic
74	#22548687	C₂²	1	2	yes	—
75	#22548687	C₂²	1	1	yes	characteristic, complemented
76	#22548687	C₂²	1	1	yes	characteristic, complemented
77	#22548687	C₂²	1	2	yes	complemented
78	#22548687	C₂²	1	2	yes	complemented
79	#22548687	C₂²	1	2	yes	complemented
80	#22548686	C₂²	1	1	yes	characteristic
81	#22548686	C₂²	1	2	yes	—
82	#22548686	C₂²	1	2	yes	complemented
83	#22548686	C₂²	1	2	yes	complemented
84	#22548685	C₂²	1	2	yes	—
85	#22548683	C₂²	1	2	yes	—
86	#22548683	C₂²	1	2	yes	—
87	#22548683	C₂²	1	2	yes	—
88	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
89	#22548680	C₂²	1	1	yes	characteristic, complemented
90	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
91	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
92	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
93	#22548677	C₂²	1	1	yes	characteristic
94	#22548677	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
101	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
102	#22548674	C₂²	1	2	yes	complemented
103	#22548673	C₂²	1	1	yes	characteristic
104	#22548673	C₂²	1	2	yes	complemented
105	#22548673	C₂²	1	1	yes	characteristic, complemented
106	#22548671	C₂²	1	2	yes	complemented
107	#22548671	C₂²	1	2	yes	complemented
108	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
109	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
111	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
113	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
117	#121×C₂₅₁	C₂²	1	1	yes	characteristic
118	#121×C₂₅₁	C₂²	1	1	yes	characteristic
119	#121×C₂₅₁	C₂²	1	2	yes	complemented
120	#121×C₂₅₁	C₂²	1	2	yes	complemented
121	#121×C₂₅₁	C₂²	1	2	yes	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	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₅₀₂	C₂³	1	2	yes	—
128	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
129	Q₈×D₂₅₁	—	4	2	no	—
130	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
131	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
132	C₂×D₁₀₀₄	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
144	D₄×D₂₅₁	—	4	2	no	—
145	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
146	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
147	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
148	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
149	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
152	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
153	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
154	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
157	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
158	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
159	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
160	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
161	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
162	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
163	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
164	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
165	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
170	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
171	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
172	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
181	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₂₅₁)⋊C₄	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	2	yes	—
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	2	yes	—
191	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
195	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
196	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
197	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₅₁	C₂³	1	2	yes	—
200	C₄×Dic₂₅₁	C₂³	1	2	yes	—
201	C₄×Dic₂₅₁	C₂³	1	2	yes	—
202	C₄×Dic₂₅₁	C₂³	1	2	yes	—
203	#41×C₂₅₁	—	4	2	no	—
204	#41×C₂₅₁	—	4	2	no	—
205	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
209	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
210	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
211	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
218	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
222	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
223	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
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	Dic₅₀₂	—	2	2	no	—
235	Dic₅₀₂	—	4	2	no	—
236	Dic₅₀₂	—	4	1	no	—
237	D₁₀₀₄	—	2	2	no	—
238	D₁₀₀₄	—	4	2	no	—
239	D₁₀₀₄	—	4	1	no	—
240	C₂²⋊D₂₅₁	—	4	2	no	—
241	C₂²⋊D₂₅₁	—	4	2	no	—
242	C₂²⋊D₂₅₁	—	4	2	no	—
243	C₂²⋊D₂₅₁	—	4	1	no	—
244	C₂²⋊D₂₅₁	—	4	2	no	—
245	C₂²⋊D₂₅₁	—	4	1	no	—
246	C₂²⋊D₂₅₁	—	4	1	no	—
247	C₂²⋊D₂₅₁	—	4	1	no	—
248	C₂²⋊D₂₅₁	—	4	1	no	—
249	C₂²⋊D₂₅₁	—	4	1	no	—
250	C₂²⋊D₂₅₁	—	4	2	no	—
251	C₂×Dic₂₅₁	—	4	1	no	—
252	C₂×Dic₂₅₁	—	4	2	no	—
253	C₂×Dic₂₅₁	—	4	1	no	—
254	C₂×Dic₂₅₁	—	4	2	no	—
255	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
261	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
263	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
264	C₄×D₂₅₁	—	2	2	no	—
265	C₄×D₂₅₁	—	2	2	no	—
266	C₄×D₂₅₁	—	4	2	no	—
267	C₄×D₂₅₁	—	4	2	no	—
268	C₄×D₂₅₁	—	4	2	no	—
269	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
270	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
271	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
272	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
273	Q₈×C₂₅₁	—	2	2	no	—
274	Q₈×C₂₅₁	—	4	1	no	—
275	D₄×C₂₅₁	—	2	2	no	—
276	D₄×C₂₅₁	—	4	2	no	—
277	D₄×C₂₅₁	—	4	2	no	—
278	D₄×C₂₅₁	—	4	1	no	—
279	D₄×C₂₅₁	—	4	1	no	—
280	D₄×C₂₅₁	—	4	1	no	—
281	D₄×C₂₅₁	—	4	2	no	—
282	C₂×C₄×C₂₅₁	—	2	2	no	—
283	C₂×C₄×C₂₅₁	—	2	2	no	—
284	C₂×C₄×C₂₅₁	—	2	2	no	—
285	C₂×C₄×C₂₅₁	—	4	2	no	—
286	C₂×C₄×C₂₅₁	—	4	2	no	—
287	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	1	no	—
297	C₂²×C₂₅₁	—	2	2	no	—
298	C₂²×C₂₅₁	—	2	1	no	—
299	C₂²×C₂₅₁	—	2	1	no	—
300	C₂²×C₂₅₁	—	2	1	no	—
301	C₂²×C₂₅₁	—	2	2	no	—
302	C₂²×C₂₅₁	—	2	1	no	—
303	C₂²×C₂₅₁	—	2	1	no	—
304	C₂²×C₂₅₁	—	2	2	no	—
305	C₂²×C₂₅₁	—	2	1	no	—
306	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
307	C₂×D₂₅₁	—	2	1	no	—
308	C₂×D₂₅₁	—	2	1	no	—
309	C₂×D₂₅₁	—	2	2	no	—
310	C₂×D₂₅₁	—	2	2	no	—
311	C₂×D₂₅₁	—	2	1	no	—
312	C₂×D₂₅₁	—	2	2	no	—
313	C₂×D₂₅₁	—	2	1	no	—
314	C₂×D₂₅₁	—	2	1	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	H(5,𝔽₂)	1	2	yes	—
324	Dic₂₅₁	—	2	1	no	—
325	Dic₂₅₁	—	2	1	no	—
326	Dic₂₅₁	—	2	2	no	—
327	Dic₂₅₁	—	2	1	no	—
328	Dic₂₅₁	—	2	1	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	—	4	1	no	—
337	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₂₅₁	#585	1	1	yes	characteristic
339	C₂×C₂₅₁	#585	1	1	yes	characteristic
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	—	251	1	no	—
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	D₂₅₁	1	1	yes	characteristic, complemented
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	C₂×D₂₅₁	1	1	yes	characteristic
371	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
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	—	251	2	no	—
384	#125	—	251	1	no	—
385	#125	—	251	1	no	—
386	#125	—	251	2	no	—
387	#125	—	251	2	no	—
388	#124	—	251	1	no	—
389	#124	—	251	1	no	—
390	#124	—	251	1	no	—
391	#124	—	251	1	no	—
392	#124	—	251	2	no	—
393	#124	—	251	2	no	—
394	#124	—	251	2	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	—	251	2	no	—
406	C₂²⋊Q₈	—	251	1	no	—
407	C₂²⋊Q₈	—	251	2	no	—
408	C₂²⋊Q₈	—	251	1	no	—
409	C₂²⋊Q₈	—	251	1	no	—
410	C₂²⋊Q₈	—	251	2	no	—
411	C₂²⋊Q₈	—	251	1	no	—
412	C₂²⋊Q₈	—	251	2	no	—
413	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
414	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
415	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
416	#121	—	251	1	no	—
417	#121	—	251	1	no	—
418	#121	—	251	1	no	—
419	#121	—	251	1	no	—
420	#121	—	251	1	no	—
421	#121	—	251	2	no	—
422	#121	—	251	2	no	—
423	#121	—	251	2	no	—
424	#121	—	251	2	no	—
425	#121	—	251	2	no	—
426	#121	—	251	2	no	—
427	#121	—	251	2	no	—
428	#121	—	251	1	no	—
429	#121	—	251	1	no	—
430	#121	—	251	2	no	—
431	#121	—	251	1	no	—
432	#121	—	251	2	no	—
433	#121	C₂×D₂₅₁	1	1	yes	characteristic
434	#121	C₂×D₂₅₁	1	1	yes	characteristic
435	#121	C₂×D₂₅₁	1	2	yes	complemented
436	#121	C₂×D₂₅₁	1	2	yes	complemented
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	1	no	—
446	C₄×D₄	—	251	2	no	—
447	C₄×D₄	—	251	1	no	—
448	C₄×D₄	—	251	1	no	—
449	C₄×D₄	—	251	1	no	—
450	C₄×D₄	—	251	1	no	—
451	C₄×D₄	—	251	2	no	—
452	C₄×D₄	—	251	2	no	—
453	C₄×D₄	—	251	1	no	—
454	C₄×D₄	—	251	2	no	—
455	C₄×D₄	—	251	2	no	—
456	#117	—	251	2	no	—
457	#117	—	251	2	no	—
458	#117	—	251	1	no	—
459	#117	—	251	1	no	—
460	#117	—	251	2	no	—
461	#117	—	251	2	no	—
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	—	4	2	no	—
469	#41	—	4	2	no	—
470	#41	—	1004	2	no	—
471	#41	—	1004	2	no	—
472	C₂×Q₈	—	1004	2	no	—
473	C₂×Q₈	—	251	2	no	—
474	C₂×Q₈	—	251	1	no	—
475	C₂×Q₈	—	251	1	no	—
476	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
477	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
478	C₂×D₄	—	1004	2	no	—
479	C₂×D₄	—	251	1	no	—
480	C₂×D₄	—	251	1	no	—
481	C₂×D₄	—	251	2	no	—
482	C₂×D₄	—	251	2	no	—
483	C₂×D₄	—	251	2	no	—
484	C₂×D₄	—	251	1	no	—
485	C₂×D₄	—	251	1	no	—
486	C₂×D₄	—	251	1	no	—
487	C₂×D₄	—	251	2	no	—
488	C₂×D₄	—	251	2	no	—
489	C₂×D₄	—	251	1	no	—
490	C₂×D₄	—	251	2	no	—
491	C₂×D₄	—	251	1	no	—
492	C₂×D₄	—	251	1	no	—
493	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
495	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
496	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
497	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
499	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
500	C₂²×C₄	—	251	1	no	—
501	C₂²×C₄	—	251	1	no	—
502	C₂²×C₄	—	251	2	no	—
503	C₂²×C₄	—	251	2	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	C₂²×D₂₅₁	1	1	yes	characteristic
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	1	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	2	no	—
523	C₄⋊C₄	—	251	1	no	—
524	C₄⋊C₄	—	251	1	no	—
525	C₄⋊C₄	—	251	1	no	—
526	C₄⋊C₄	—	251	1	no	—
527	C₄⋊C₄	—	251	2	no	—
528	C₄⋊C₄	—	251	2	no	—
529	C₄⋊C₄	—	251	2	no	—
530	C₄⋊C₄	—	251	2	no	—
531	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
534	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
535	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
536	C₂²⋊C₄	—	251	2	no	—
537	C₂²⋊C₄	—	251	1	no	—
538	C₂²⋊C₄	—	251	1	no	—
539	C₂²⋊C₄	—	251	2	no	—
540	C₂²⋊C₄	—	251	1	no	—
541	C₂²⋊C₄	—	251	1	no	—
542	C₂²⋊C₄	—	251	2	no	—
543	C₂²⋊C₄	—	251	2	no	—
544	C₂²⋊C₄	—	251	2	no	—
545	C₂²⋊C₄	—	251	2	no	—
546	C₂²⋊C₄	—	251	1	no	—
547	C₂²⋊C₄	—	251	1	no	—
548	C₂²⋊C₄	—	251	2	no	—
549	C₂²⋊C₄	—	251	2	no	—
550	C₂²⋊C₄	—	251	2	no	—
551	C₂²⋊C₄	—	251	2	no	—
552	C₂²⋊C₄	—	251	2	no	—
553	C₂²⋊C₄	—	251	2	no	—
554	C₂²⋊C₄	—	251	2	no	—
555	C₂²⋊C₄	—	251	1	no	—
556	C₂²⋊C₄	—	251	1	no	—
557	C₂²⋊C₄	—	251	2	no	—
558	C₂²⋊C₄	—	251	2	no	—
559	C₂²⋊C₄	—	251	2	no	—
560	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
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	1	no	—
568	C₄²	—	251	2	no	—
569	C₄²	—	251	2	no	—
570	C₄²	—	251	2	no	—
571	C₄²	—	251	2	no	—
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	C₂³×D₂₅₁	1	2	yes	—
579	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
580	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
581	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
582	Q₈	—	2	2	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	1004	2	no	—
585	Q₈	—	1004	1	no	—
586	Q₈	—	502	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	1004	1	no	—
595	D₄	—	1004	2	no	—
596	D₄	—	1004	2	no	—
597	D₄	—	1004	2	no	—
598	D₄	—	1004	1	no	—
599	D₄	—	1004	1	no	—
600	D₄	—	1004	1	no	—
601	D₄	—	1004	1	no	—
602	D₄	—	1004	2	no	—
603	D₄	—	1004	1	no	—
604	D₄	—	1004	2	no	—
605	D₄	—	1004	2	no	—
606	D₄	—	1004	1	no	—
607	D₄	—	502	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	1004	2	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	1	no	—
619	C₂×C₄	—	1004	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	1	no	—
625	C₂×C₄	—	251	1	no	—
626	C₂×C₄	—	251	1	no	—
627	C₂×C₄	—	251	2	no	—
628	C₂×C₄	—	251	1	no	—
629	C₂×C₄	—	251	2	no	—
630	C₂×C₄	—	251	2	no	—
631	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
632	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
634	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
635	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
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	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2008	4	no	—
651	C₂²	—	502	1	no	—
652	C₂²	—	502	2	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	—	502	2	no	—
668	C₄	—	502	1	no	—
669	C₄	—	502	1	no	—
670	C₄	—	502	1	no	—
671	C₄	—	502	1	no	—
672	C₄	—	502	1	no	—
673	C₄	—	502	2	no	—
674	C₄	—	502	1	no	—
675	C₄	—	502	2	no	—
676	C₄	#22548760	1	2	yes	—
677	C₂	—	4	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	1004	1	no	—
682	C₂	—	1004	2	no	—
683	C₂	—	1004	1	no	—
684	C₂	C₂×#22548760	1	1	yes	characteristic
685	C₂	#30632522	1	1	yes	characteristic
686	C₂	#30632524	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#537×C₂₅₁	C₂
hypercenter	#537	D₂₅₁
hypocenter	C₂₅₁	#3551
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #30632438	C₂	semidirect
2. #30632425	C₂	semidirect
3. #30632401	C₂	semidirect
4. #30632389	C₂	semidirect
5. #30632385	C₂	semidirect
6. #30632379	C₂	semidirect
7. #30632372	C₂	semidirect
8. #30632364	C₂	semidirect
9. #30632347	C₂	semidirect
10. #30632344	C₂	semidirect
11. #30632334	C₂	semidirect
12. #30632325	C₂	semidirect
13. #30632290	C₂	semidirect
14. #30632287	C₂	semidirect
15. #30632274	C₂	semidirect
16. #30632269	C₂	semidirect
17. #30632265	C₂	semidirect
18. #30632260	C₂	semidirect
19. #30632253	C₂	semidirect
20. #30632233	C₂	semidirect
21. #30632223	C₂	semidirect
22. #30632218	C₂	semidirect
23. #537×C₂₅₁	C₂	semidirect
26. C₂×Q₈×D₂₅₁	C₂²	semidirect
28. #22548714	C₂²	semidirect
29. #22548713	C₂²	semidirect
34. #22548710	C₂²	semidirect
35. #22548710	C₂²	semidirect
36. #22548708	C₂²	semidirect
37. #22548708	C₂²	semidirect
38. #22548706	C₂²	semidirect
39. #22548706	C₂²	semidirect
40. #22548706	C₂²	semidirect
41. #22548705	C₂²	semidirect
45. #22548702	C₂²	semidirect
46. #22548702	C₂²	semidirect
49. #22548701	C₂²	semidirect
51. #22548700	C₂²	semidirect
53. #22548699	C₂²	semidirect
54. #22548699	C₂²	semidirect
58. #22548697	C₂²	semidirect
59. #22548696	C₂²	semidirect
61. #22548694	C₂²	semidirect
62. #22548694	C₂²	semidirect
63. #22548694	C₂²	semidirect
64. #22548693	C₂²	semidirect
66. #22548691	C₂²	semidirect
70. #22548689	C₂²	semidirect
71. #22548688	C₂²	semidirect
75. #22548687	C₂²	semidirect
76. #22548687	C₂²	semidirect
77. #22548687	C₂²	semidirect
78. #22548687	C₂²	semidirect
79. #22548687	C₂²	semidirect
82. #22548686	C₂²	semidirect
83. #22548686	C₂²	semidirect
88. Q₈×Dic₂₅₁	C₂²	semidirect
89. #22548680	C₂²	semidirect
91. D₄×Dic₂₅₁	C₂²	semidirect
92. D₄×Dic₂₅₁	C₂²	semidirect
94. #22548677	C₂²	semidirect
97. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
98. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
99. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
100. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
101. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
102. #22548674	C₂²	semidirect
104. #22548673	C₂²	semidirect
105. #22548673	C₂²	semidirect
106. #22548671	C₂²	semidirect
107. #22548671	C₂²	semidirect
108. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
111. C₂×C₄×Dic₂₅₁	C₂²	semidirect
113. C₂×#41×C₂₅₁	C₂²	semidirect
114. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
115. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
116. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
119. #121×C₂₅₁	C₂²	semidirect
120. #121×C₂₅₁	C₂²	semidirect
121. #121×C₂₅₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
343. C₂₅₁	#3551	semidirect
362. #537	D₂₅₁	semidirect
371. C₂×#41	C₂×D₂₅₁	semidirect
413. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
414. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
415. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
435. #121	C₂×D₂₅₁	semidirect
436. #121	C₂×D₂₅₁	semidirect
437. #121	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
#30632438	2
#30632425	2
#30632401	2
#30632389	2
#30632385	2
#30632379	2
#30632372	2
#30632364	2
#30632347	2
#30632344	2
#30632334	2
#30632325	2
#30632290	2
#30632287	2
#30632274	2
#30632269	2
#30632265	2
#30632260	2
#30632253	2
#30632233	2
#30632223	2
#30632218	2
#537×C₂₅₁	2
#3551	251