Subgroups — #44564611

Order 32128.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632441	C₂	1	2	yes	maximal, complemented
2	#30632439	C₂	1	2	yes	maximal, complemented
3	#30632376	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632375	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632372	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632361	C₂	1	2	yes	maximal, complemented
7	#30632360	C₂	1	2	yes	maximal, complemented
8	Q₈×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632350	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632350	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632317	C₂	1	2	yes	maximal, complemented
13	#30632315	C₂	1	2	yes	maximal, complemented
14	#30632300	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632295	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632281	C₂	1	2	yes	maximal, complemented
17	#30632278	C₂	1	2	yes	maximal, complemented
18	#30632263	C₂	1	1	yes	maximal, characteristic, complemented
19	#30632260	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632196	C₂	1	1	yes	maximal, characteristic
21	C₂×#22548695	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860810	C₂²	1	1	yes	characteristic
25	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
26	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
30	#22548715	C₂²	1	2	yes	complemented
31	#22548715	C₂²	1	1	yes	characteristic, complemented
32	#22548715	C₂²	1	2	yes	complemented
33	#22548714	C₂²	1	2	yes	complemented
34	#22548714	C₂²	1	2	yes	complemented
35	#22548714	C₂²	1	2	yes	complemented
36	#22548714	C₂²	1	2	yes	complemented
37	#22548713	C₂²	1	1	yes	characteristic, complemented
38	#22548710	C₂²	1	2	yes	—
39	#22548710	C₂²	1	2	yes	—
40	#22548710	C₂²	1	2	yes	—
41	#22548710	C₂²	1	2	yes	complemented
42	#22548710	C₂²	1	2	yes	complemented
43	#22548709	C₂²	1	2	yes	—
44	#22548708	C₂²	1	2	yes	complemented
45	#22548707	C₂²	1	2	yes	complemented
46	#22548707	C₂²	1	2	yes	complemented
47	#22548706	C₂²	1	2	yes	complemented
48	#22548706	C₂²	1	2	yes	complemented
49	#22548706	C₂²	1	1	yes	characteristic, complemented
50	#22548706	C₂²	1	2	yes	complemented
51	#22548705	C₂²	1	2	yes	complemented
52	#22548705	C₂²	1	2	yes	complemented
53	#22548703	C₂²	1	2	yes	—
54	#22548701	C₂²	1	2	yes	—
55	#22548700	C₂²	1	1	yes	characteristic
56	#22548700	C₂²	1	2	yes	—
57	#22548700	C₂²	1	2	yes	—
58	#22548699	C₂²	1	2	yes	—
59	#22548699	C₂²	1	2	yes	complemented
60	#22548698	C₂²	1	2	yes	—
61	#22548697	C₂²	1	1	yes	characteristic
62	#22548697	C₂²	1	2	yes	—
63	#22548697	C₂²	1	2	yes	complemented
64	#22548695	C₂²	1	1	yes	characteristic
65	#22548695	C₂²	1	1	yes	characteristic
66	#22548695	C₂²	1	1	yes	characteristic
67	#22548695	C₂²	1	2	yes	—
68	#22548695	C₂²	1	2	yes	—
69	#22548695	C₂²	1	1	yes	characteristic
70	#22548695	C₂²	1	1	yes	characteristic
71	#22548695	C₂²	1	2	yes	—
72	#22548695	C₂²	1	1	yes	characteristic, complemented
73	#22548695	C₂²	1	1	yes	characteristic, complemented
74	#22548695	C₂²	1	2	yes	complemented
75	#22548694	C₂²	1	1	yes	characteristic
76	#22548694	C₂²	1	1	yes	characteristic, complemented
77	#22548693	C₂²	1	1	yes	characteristic
78	#22548693	C₂²	1	2	yes	—
79	#22548693	C₂²	1	2	yes	—
80	#22548693	C₂²	1	2	yes	complemented
81	#22548692	C₂²	1	1	yes	characteristic
82	#22548692	C₂²	1	2	yes	—
83	#22548692	C₂²	1	2	yes	—
84	#22548692	C₂²	1	2	yes	—
85	#22548692	C₂²	1	2	yes	complemented
86	#22548692	C₂²	1	2	yes	complemented
87	#22548691	C₂²	1	1	yes	characteristic
88	#22548688	C₂²	1	1	yes	characteristic
89	#22548687	C₂²	1	1	yes	characteristic
90	#22548685	C₂²	1	1	yes	characteristic
91	#22548683	C₂²	1	1	yes	characteristic
92	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
93	#22548680	C₂²	1	1	yes	characteristic, complemented
94	#22548680	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
96	C₄×D₁₀₀₄	C₂²	1	2	yes	—
97	D₄×Dic₂₅₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
100	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
102	#22548674	C₂²	1	2	yes	—
103	#22548673	C₂²	1	2	yes	—
104	#22548673	C₂²	1	1	yes	characteristic, complemented
105	#22548672	C₂²	1	1	yes	characteristic
106	#22548672	C₂²	1	2	yes	—
107	C₂×C₄⋊Dic₂₅₁	C₂²	1	2	yes	—
108	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
109	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
110	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
112	#126×C₂₅₁	C₂²	1	2	yes	complemented
113	#125×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
114	#125×C₂₅₁	C₂²	1	2	yes	complemented
115	#123×C₂₅₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
120	#117×C₂₅₁	C₂²	1	2	yes	—
121	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
123	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
124	#16860810	—	4	2	no	—
125	C₂×Dic₅₀₂	—	4	2	no	—
126	C₂×Dic₅₀₂	—	4	2	no	—
127	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₀₂	C₂³	1	2	yes	—
131	C₂×Dic₅₀₂	C₂³	1	2	yes	—
132	C₂×Dic₅₀₂	C₂³	1	2	yes	—
133	C₂×Dic₅₀₂	C₂³	1	2	yes	—
134	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
135	Q₈×D₂₅₁	—	4	2	no	—
136	Q₈×D₂₅₁	—	4	2	no	—
137	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
138	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
143	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
144	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
145	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
146	C₂×C₄×D₂₅₁	—	4	2	no	—
147	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
151	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
154	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
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	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
162	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
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	1	yes	characteristic
167	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
168	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
169	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
170	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
173	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
174	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
176	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
178	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
179	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
180	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₂₅₁	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	1	yes	characteristic
194	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
200	C₄×Dic₂₅₁	C₂³	1	2	yes	—
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×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
210	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
225	C₄²×C₂₅₁	C₂³	1	2	yes	—
226	C₄²×C₂₅₁	C₂³	1	2	yes	—
227	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
228	C₂²×D₂₅₁	—	2	2	no	—
229	C₂²×D₂₅₁	—	2	2	no	—
230	C₂²×D₂₅₁	—	4	1	no	—
231	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
233	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
234	Dic₅₀₂	—	2	2	no	—
235	Dic₅₀₂	—	2	2	no	—
236	Dic₅₀₂	—	2	2	no	—
237	Dic₅₀₂	—	4	2	no	—
238	Dic₅₀₂	—	4	2	no	—
239	Dic₅₀₂	—	4	2	no	—
240	Dic₅₀₂	—	4	2	no	—
241	Dic₅₀₂	—	4	1	no	—
242	D₁₀₀₄	—	2	2	no	—
243	D₁₀₀₄	—	4	1	no	—
244	C₂²⋊D₂₅₁	—	2	2	no	—
245	C₂²⋊D₂₅₁	—	2	2	no	—
246	C₂²⋊D₂₅₁	—	4	1	no	—
247	C₂²⋊D₂₅₁	—	4	1	no	—
248	C₂×Dic₂₅₁	—	4	1	no	—
249	C₂×Dic₂₅₁	—	4	2	no	—
250	C₂×Dic₂₅₁	—	4	2	no	—
251	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
254	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
256	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
257	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
258	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
260	C₄×D₂₅₁	—	2	4	no	—
261	C₄×D₂₅₁	—	2	2	no	—
262	C₄×D₂₅₁	—	2	2	no	—
263	C₄×D₂₅₁	—	2	2	no	—
264	C₄×D₂₅₁	—	4	1	no	—
265	C₄×D₂₅₁	—	4	1	no	—
266	C₄×D₂₅₁	—	4	2	no	—
267	C₄×D₂₅₁	—	4	2	no	—
268	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
269	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
270	Q₈×C₂₅₁	—	2	2	no	—
271	D₄×C₂₅₁	—	2	2	no	—
272	C₂×C₄×C₂₅₁	—	2	4	no	—
273	C₂×C₄×C₂₅₁	—	2	2	no	—
274	C₂×C₄×C₂₅₁	—	2	2	no	—
275	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
279	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
280	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
282	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₂₅₁	—	2	1	no	—
285	C₂²×C₂₅₁	—	2	1	no	—
286	C₂²×C₂₅₁	—	2	1	no	—
287	C₂²×C₂₅₁	—	2	1	no	—
288	C₂²×C₂₅₁	—	2	1	no	—
289	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
290	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
291	C₂×D₂₅₁	—	2	1	no	—
292	C₂×D₂₅₁	—	2	1	no	—
293	C₂×D₂₅₁	—	2	1	no	—
294	C₂×D₂₅₁	—	2	1	no	—
295	C₂×D₂₅₁	—	2	1	no	—
296	C₂×D₂₅₁	—	2	1	no	—
297	C₂×D₂₅₁	—	2	1	no	—
298	C₂×D₂₅₁	—	2	1	no	—
299	C₂×D₂₅₁	—	4	4	no	—
300	C₂×D₂₅₁	2₋¹⁺⁴	1	2	yes	—
301	C₄×C₂₅₁	—	2	1	no	—
302	C₄×C₂₅₁	—	2	1	no	—
303	C₄×C₂₅₁	—	2	2	no	—
304	C₄×C₂₅₁	—	2	2	no	—
305	C₄×C₂₅₁	—	2	2	no	—
306	C₄×C₂₅₁	—	2	1	no	—
307	C₄×C₂₅₁	—	2	2	no	—
308	C₄×C₂₅₁	—	2	1	no	—
309	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
310	Dic₂₅₁	—	2	1	no	—
311	Dic₂₅₁	—	2	1	no	—
312	Dic₂₅₁	—	2	1	no	—
313	Dic₂₅₁	—	2	2	no	—
314	Dic₂₅₁	—	2	2	no	—
315	Dic₂₅₁	—	2	2	no	—
316	Dic₂₅₁	—	2	2	no	—
317	Dic₂₅₁	—	2	1	no	—
318	Dic₂₅₁	—	2	1	no	—
319	C₂×C₂₅₁	—	2	2	no	—
320	C₂×C₂₅₁	—	4	1	no	—
321	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	D₂₅₁	—	2	2	no	—
325	D₂₅₁	—	4	1	no	—
326	D₂₅₁	—	4	1	no	—
327	C₂₅₁	#3538	1	1	yes	characteristic, complemented, Sylow
328	#3538	—	251	1	no	maximal, Sylow
329	#563	—	251	2	no	—
330	#563	—	251	2	no	—
331	#552	—	251	1	no	—
332	#552	—	251	1	no	—
333	#552	—	251	1	no	—
334	#552	D₂₅₁	1	1	yes	characteristic, complemented
335	#551	—	251	2	no	—
336	#551	—	251	2	no	—
337	D₄×Q₈	—	251	1	no	—
338	D₄×Q₈	—	251	1	no	—
339	D₄×Q₈	—	251	1	no	—
340	D₄×Q₈	—	251	1	no	—
341	#544	—	251	2	no	—
342	#544	—	251	2	no	—
343	#541	—	251	1	no	—
344	#541	—	251	1	no	—
345	#539	—	251	2	no	—
346	#539	—	251	2	no	—
347	#536	—	251	1	no	—
348	#536	—	251	1	no	—
349	#525	—	251	1	no	—
350	C₂×C₂²⋊Q₈	—	251	1	no	—
351	C₂×C₂²⋊Q₈	—	251	1	no	—
352	C₂×#41	—	251	1	no	—
353	C₂²×Q₈	—	251	1	no	—
354	C₂²×Q₈	—	251	1	no	—
355	C₂²×Q₈	—	251	1	no	—
356	C₂²×Q₈	—	251	1	no	—
357	C₂³×C₄	—	251	1	no	—
358	C₄⋊Q₈	—	251	1	no	—
359	C₄⋊Q₈	—	251	2	no	—
360	C₄⋊Q₈	—	251	2	no	—
361	C₄⋊Q₈	—	251	2	no	—
362	C₄⋊Q₈	—	251	2	no	—
363	C₄⋊Q₈	—	251	2	no	—
364	C₄⋊Q₈	—	251	1	no	—
365	C₄⋊Q₈	—	251	2	no	—
366	#126	—	251	2	no	—
367	#126	—	251	2	no	—
368	#126	—	251	2	no	—
369	#126	—	251	2	no	—
370	#126	—	251	2	no	—
371	#126	—	251	2	no	—
372	#126	—	251	2	no	—
373	#126	C₂×D₂₅₁	1	2	yes	complemented
374	#125	—	251	2	no	—
375	#125	—	251	2	no	—
376	#125	—	251	2	no	—
377	#125	—	251	1	no	—
378	#125	—	251	2	no	—
379	#125	—	251	2	no	—
380	#125	—	251	2	no	—
381	#125	—	251	2	no	—
382	#125	C₂×D₂₅₁	1	1	yes	characteristic, complemented
383	#125	C₂×D₂₅₁	1	2	yes	complemented
384	#124	—	251	2	no	—
385	#124	—	251	2	no	—
386	#123	—	251	2	no	—
387	#123	—	251	1	no	—
388	#123	—	251	2	no	—
389	#123	—	251	2	no	—
390	#123	—	251	1	no	—
391	#123	—	251	2	no	—
392	#123	—	251	2	no	—
393	#123	—	251	2	no	—
394	#123	—	251	2	no	—
395	#123	C₂×D₂₅₁	1	2	yes	—
396	C₂²⋊Q₈	—	251	1	no	—
397	C₂²⋊Q₈	—	251	1	no	—
398	C₂²⋊Q₈	—	251	1	no	—
399	C₂²⋊Q₈	—	251	1	no	—
400	C₂²⋊Q₈	—	251	1	no	—
401	C₂²⋊Q₈	—	251	1	no	—
402	C₂²⋊Q₈	—	251	2	no	—
403	C₂²⋊Q₈	—	251	1	no	—
404	C₂²⋊Q₈	—	251	1	no	—
405	C₂²⋊Q₈	—	251	2	no	—
406	C₂²⋊Q₈	—	251	2	no	—
407	C₂²⋊Q₈	—	251	1	no	—
408	C₂²⋊Q₈	—	251	1	no	—
409	C₂²⋊Q₈	—	251	1	no	—
410	C₂²⋊Q₈	—	251	2	no	—
411	C₂²⋊Q₈	—	251	2	no	—
412	C₂²⋊Q₈	—	251	2	no	—
413	C₂²⋊Q₈	—	251	2	no	—
414	C₂²⋊Q₈	—	251	2	no	—
415	C₂²⋊Q₈	—	251	1	no	—
416	C₂²⋊Q₈	—	251	2	no	—
417	C₂²⋊Q₈	—	251	2	no	—
418	C₂²⋊Q₈	—	251	2	no	—
419	C₂²⋊Q₈	—	251	2	no	—
420	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
421	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
422	#121	—	251	1	no	—
423	#121	—	251	1	no	—
424	#120	—	251	1	no	—
425	#120	—	251	1	no	—
426	C₄×Q₈	—	251	1	no	—
427	C₄×Q₈	—	251	1	no	—
428	C₄×Q₈	—	251	1	no	—
429	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
430	C₄×D₄	—	251	2	no	—
431	C₄×D₄	—	251	1	no	—
432	C₄×D₄	—	251	1	no	—
433	C₄×D₄	—	251	2	no	—
434	C₄×D₄	—	251	2	no	—
435	C₄×D₄	—	251	1	no	—
436	C₄×D₄	—	251	2	no	—
437	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
438	#117	—	251	2	no	—
439	#117	—	251	1	no	—
440	#117	—	251	2	no	—
441	#117	—	251	1	no	—
442	#117	—	251	2	no	—
443	#117	C₂×D₂₅₁	1	2	yes	—
444	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	—	251	2	no	—
446	C₂×C₄⋊C₄	—	251	2	no	—
447	C₂×C₄⋊C₄	—	251	1	no	—
448	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	251	2	no	—
450	C₂×C₂²⋊C₄	—	251	2	no	—
451	C₂⁴	—	251	1	no	—
452	#41	—	1004	2	no	—
453	C₂×Q₈	—	1004	2	no	—
454	C₂×Q₈	—	1004	2	no	—
455	C₂×Q₈	—	1004	2	no	—
456	C₂×Q₈	—	1004	2	no	—
457	C₂×Q₈	—	251	2	no	—
458	C₂×Q₈	—	251	2	no	—
459	C₂×Q₈	—	251	2	no	—
460	C₂×Q₈	—	251	2	no	—
461	C₂×Q₈	—	251	1	no	—
462	C₂×Q₈	—	251	1	no	—
463	C₂×Q₈	—	251	1	no	—
464	C₂×Q₈	—	251	1	no	—
465	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
466	C₂×D₄	—	251	1	no	—
467	C₂×D₄	—	251	1	no	—
468	C₂×D₄	—	251	1	no	—
469	C₂×D₄	—	251	1	no	—
470	C₂×D₄	—	251	1	no	—
471	C₂×D₄	—	251	1	no	—
472	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
473	C₂²×C₄	—	1004	2	no	—
474	C₂²×C₄	—	251	2	no	—
475	C₂²×C₄	—	251	1	no	—
476	C₂²×C₄	—	251	2	no	—
477	C₂²×C₄	—	251	2	no	—
478	C₂²×C₄	—	251	1	no	—
479	C₂²×C₄	—	251	2	no	—
480	C₂²×C₄	—	251	1	no	—
481	C₂²×C₄	—	251	2	no	—
482	C₂²×C₄	—	251	1	no	—
483	C₂²×C₄	—	251	1	no	—
484	C₂²×C₄	—	251	1	no	—
485	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
486	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
488	C₄⋊C₄	—	251	1	no	—
489	C₄⋊C₄	—	251	2	no	—
490	C₄⋊C₄	—	251	2	no	—
491	C₄⋊C₄	—	251	2	no	—
492	C₄⋊C₄	—	251	2	no	—
493	C₄⋊C₄	—	251	2	no	—
494	C₄⋊C₄	—	251	2	no	—
495	C₄⋊C₄	—	251	2	no	—
496	C₄⋊C₄	—	251	2	no	—
497	C₄⋊C₄	—	251	1	no	—
498	C₄⋊C₄	—	251	1	no	—
499	C₄⋊C₄	—	251	2	no	—
500	C₄⋊C₄	—	251	2	no	—
501	C₄⋊C₄	—	251	2	no	—
502	C₄⋊C₄	—	251	2	no	—
503	C₄⋊C₄	—	251	2	no	—
504	C₄⋊C₄	—	251	2	no	—
505	C₄⋊C₄	—	251	2	no	—
506	C₄⋊C₄	—	251	1	no	—
507	C₄⋊C₄	—	251	1	no	—
508	C₄⋊C₄	—	251	2	no	—
509	C₄⋊C₄	—	251	2	no	—
510	C₄⋊C₄	—	251	2	no	—
511	C₄⋊C₄	—	251	2	no	—
512	C₄⋊C₄	—	251	2	no	—
513	C₄⋊C₄	—	251	1	no	—
514	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
516	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
519	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
520	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
521	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
522	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
524	C₂²⋊C₄	—	251	2	no	—
525	C₂²⋊C₄	—	251	1	no	—
526	C₂²⋊C₄	—	251	1	no	—
527	C₂²⋊C₄	—	251	2	no	—
528	C₂²⋊C₄	—	251	2	no	—
529	C₂²⋊C₄	—	251	2	no	—
530	C₂²⋊C₄	—	251	2	no	—
531	C₂²⋊C₄	—	251	2	no	—
532	C₂²⋊C₄	—	251	2	no	—
533	C₂²⋊C₄	—	251	2	no	—
534	C₂²⋊C₄	—	251	1	no	—
535	C₂²⋊C₄	—	251	1	no	—
536	C₂²⋊C₄	—	251	1	no	—
537	C₂²⋊C₄	—	251	1	no	—
538	C₂²⋊C₄	—	251	2	no	—
539	C₂²⋊C₄	—	251	1	no	—
540	C₂²⋊C₄	—	251	1	no	—
541	C₂²⋊C₄	—	251	2	no	—
542	C₂²⋊C₄	—	251	2	no	—
543	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
548	C₄²	—	251	2	no	—
549	C₄²	—	251	1	no	—
550	C₄²	—	251	2	no	—
551	C₄²	—	251	2	no	—
552	C₄²	—	251	2	no	—
553	C₄²	C₂²×D₂₅₁	1	2	yes	—
554	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
555	C₄²	C₂²×D₂₅₁	1	2	yes	—
556	C₂³	—	1004	1	no	—
557	C₂³	—	502	2	no	—
558	C₂³	—	502	2	no	—
559	C₂³	—	251	1	no	—
560	C₂³	—	251	1	no	—
561	C₂³	—	251	1	no	—
562	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
563	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	1004	2	no	—
566	Q₈	—	1004	2	no	—
567	Q₈	—	1004	2	no	—
568	Q₈	—	1004	2	no	—
569	Q₈	—	1004	1	no	—
570	Q₈	—	502	2	no	—
571	Q₈	—	502	2	no	—
572	Q₈	—	502	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	1004	1	no	—
575	D₄	—	1004	1	no	—
576	D₄	—	1004	1	no	—
577	D₄	—	502	2	no	—
578	D₄	—	502	2	no	—
579	D₄	—	502	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	1004	1	no	—
584	C₂×C₄	—	1004	1	no	—
585	C₂×C₄	—	1004	2	no	—
586	C₂×C₄	—	1004	2	no	—
587	C₂×C₄	—	1004	1	no	—
588	C₂×C₄	—	1004	2	no	—
589	C₂×C₄	—	1004	2	no	—
590	C₂×C₄	—	502	4	no	—
591	C₂×C₄	—	502	2	no	—
592	C₂×C₄	—	502	2	no	—
593	C₂×C₄	—	502	2	no	—
594	C₂×C₄	—	251	1	no	—
595	C₂×C₄	—	251	1	no	—
596	C₂×C₄	—	251	2	no	—
597	C₂×C₄	—	251	1	no	—
598	C₂×C₄	—	251	2	no	—
599	C₂×C₄	—	251	2	no	—
600	C₂×C₄	—	251	2	no	—
601	C₂×C₄	—	251	1	no	—
602	C₂×C₄	—	251	1	no	—
603	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
605	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
606	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
608	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
610	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	1004	4	no	—
618	C₂²	—	502	1	no	—
619	C₂²	—	502	1	no	—
620	C₂²	—	502	1	no	—
621	C₂²	—	502	1	no	—
622	C₂²	—	502	1	no	—
623	C₂²	—	502	1	no	—
624	C₂²	—	502	1	no	—
625	C₂²	—	502	1	no	—
626	C₂²	—	251	2	no	—
627	C₂²	#22548762	1	2	yes	—
628	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	502	1	no	—
638	C₄	—	502	1	no	—
639	C₄	—	502	2	no	—
640	C₄	—	502	2	no	—
641	C₄	—	502	2	no	—
642	C₄	—	502	1	no	—
643	C₄	—	502	2	no	—
644	C₄	—	502	1	no	—
645	C₄	—	502	1	no	—
646	C₄	#22548761	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	1004	1	no	—
650	C₂	—	1004	1	no	—
651	C₂	—	502	2	no	—
652	C₂	C₂×#22548761	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic
654	C₂	C₂×#22548762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#552×C₂₅₁	C₂
prime radical	#30632196	C₂
hypercenter	#552	D₂₅₁
hypocenter	C₂₅₁	#3538
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #30632441	C₂	semidirect
2. #30632439	C₂	semidirect
3. #30632376	C₂	semidirect
4. #30632375	C₂	semidirect
5. #30632372	C₂	semidirect
6. #30632361	C₂	semidirect
7. #30632360	C₂	semidirect
8. Q₈×D₁₀₀₄	C₂	semidirect
9. D₄×Dic₅₀₂	C₂	semidirect
10. #30632350	C₂	semidirect
11. #30632350	C₂	semidirect
12. #30632317	C₂	semidirect
13. #30632315	C₂	semidirect
14. #30632300	C₂	semidirect
15. #30632295	C₂	semidirect
16. #30632281	C₂	semidirect
17. #30632278	C₂	semidirect
18. #30632263	C₂	semidirect
19. #30632260	C₂	semidirect
21. C₂×#22548695	C₂	semidirect
22. C₂²⋊Q₈×D₂₅₁	C₂	semidirect
23. #552×C₂₅₁	C₂	semidirect
26. C₂²×Dic₅₀₂	C₂²	semidirect
28. C₂×Q₈×D₂₅₁	C₂²	semidirect
30. #22548715	C₂²	semidirect
31. #22548715	C₂²	semidirect
32. #22548715	C₂²	semidirect
33. #22548714	C₂²	semidirect
34. #22548714	C₂²	semidirect
35. #22548714	C₂²	semidirect
36. #22548714	C₂²	semidirect
37. #22548713	C₂²	semidirect
41. #22548710	C₂²	semidirect
42. #22548710	C₂²	semidirect
44. #22548708	C₂²	semidirect
45. #22548707	C₂²	semidirect
46. #22548707	C₂²	semidirect
47. #22548706	C₂²	semidirect
48. #22548706	C₂²	semidirect
49. #22548706	C₂²	semidirect
50. #22548706	C₂²	semidirect
51. #22548705	C₂²	semidirect
52. #22548705	C₂²	semidirect
59. #22548699	C₂²	semidirect
63. #22548697	C₂²	semidirect
72. #22548695	C₂²	semidirect
73. #22548695	C₂²	semidirect
74. #22548695	C₂²	semidirect
76. #22548694	C₂²	semidirect
80. #22548693	C₂²	semidirect
85. #22548692	C₂²	semidirect
86. #22548692	C₂²	semidirect
92. C₄×Dic₅₀₂	C₂²	semidirect
93. #22548680	C₂²	semidirect
94. #22548680	C₂²	semidirect
104. #22548673	C₂²	semidirect
112. #126×C₂₅₁	C₂²	semidirect
113. #125×C₂₅₁	C₂²	semidirect
114. #125×C₂₅₁	C₂²	semidirect
117. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
118. C₄×Q₈×C₂₅₁	C₂²	semidirect
121. #117×C₂₅₁	C₂²	semidirect
327. C₂₅₁	#3538	semidirect
334. #552	D₂₅₁	semidirect
373. #126	C₂×D₂₅₁	semidirect
382. #125	C₂×D₂₅₁	semidirect
383. #125	C₂×D₂₅₁	semidirect
421. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
429. C₄×Q₈	C₂×D₂₅₁	semidirect
444. #117	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632441	2
#30632439	2
#30632376	2
#30632375	2
#30632372	2
#30632361	2
#30632360	2
Q₈×D₁₀₀₄	2
D₄×Dic₅₀₂	2
#30632350	2
#30632317	2
#30632315	2
#30632300	2
#30632295	2
#30632281	2
#30632278	2
#30632263	2
#30632260	2
#30632196	2
C₂×#22548695	2
C₂²⋊Q₈×D₂₅₁	2
#552×C₂₅₁	2
#3538	251