Subgroups — #44565015

Order 32128.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632437	C₂	1	2	yes	maximal, complemented
2	#30632432	C₂	1	2	yes	maximal, complemented
3	#30632412	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632406	C₂	1	2	yes	maximal, complemented
5	#30632405	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632396	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632389	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632384	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632377	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632376	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632370	C₂	1	2	yes	maximal, complemented
12	#30632315	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632314	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632306	C₂	1	2	yes	maximal, complemented
15	#30632304	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632302	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632301	C₂	1	2	yes	maximal, complemented
18	#30632299	C₂	1	2	yes	maximal, complemented
19	#30632282	C₂	1	2	yes	maximal, complemented
20	#30632240	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632218	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632217	C₂	1	1	yes	maximal, characteristic, complemented
23	#555×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#22548715	C₂²	1	2	yes	—
25	#22548714	C₂²	1	1	yes	characteristic
26	#22548714	C₂²	1	1	yes	characteristic
27	#22548714	C₂²	1	1	yes	characteristic
28	#22548713	C₂²	1	2	yes	—
29	#22548713	C₂²	1	2	yes	—
30	#22548710	C₂²	1	1	yes	characteristic
31	#22548709	C₂²	1	2	yes	—
32	#22548708	C₂²	1	1	yes	characteristic
33	#22548708	C₂²	1	2	yes	—
34	#22548708	C₂²	1	2	yes	—
35	#22548708	C₂²	1	2	yes	—
36	#22548708	C₂²	1	2	yes	—
37	#22548708	C₂²	1	2	yes	—
38	#22548708	C₂²	1	2	yes	—
39	#22548708	C₂²	1	2	yes	—
40	#22548708	C₂²	1	2	yes	—
41	#22548707	C₂²	1	2	yes	—
42	#22548707	C₂²	1	1	yes	characteristic
43	#22548707	C₂²	1	2	yes	—
44	#22548706	C₂²	1	1	yes	characteristic
45	#22548706	C₂²	1	1	yes	characteristic
46	#22548706	C₂²	1	1	yes	characteristic
47	#22548706	C₂²	1	1	yes	characteristic
48	#22548705	C₂²	1	1	yes	characteristic
49	#22548705	C₂²	1	2	yes	—
50	#22548705	C₂²	1	2	yes	—
51	#22548705	C₂²	1	2	yes	—
52	#22548705	C₂²	1	2	yes	—
53	#22548702	C₂²	1	1	yes	characteristic
54	#22548702	C₂²	1	2	yes	—
55	#22548701	C₂²	1	1	yes	characteristic
56	#22548701	C₂²	1	2	yes	—
57	#22548701	C₂²	1	2	yes	—
58	#22548699	C₂²	1	1	yes	characteristic
59	#22548699	C₂²	1	2	yes	—
60	#22548698	C₂²	1	2	yes	—
61	#22548697	C₂²	1	2	yes	—
62	#22548696	C₂²	1	1	yes	characteristic
63	#22548696	C₂²	1	2	yes	—
64	#22548696	C₂²	1	2	yes	—
65	#22548696	C₂²	1	2	yes	—
66	#22548696	C₂²	1	2	yes	—
67	#22548695	C₂²	1	1	yes	characteristic
68	#22548694	C₂²	1	1	yes	characteristic
69	#22548694	C₂²	1	2	yes	—
70	#22548694	C₂²	1	2	yes	—
71	#22548694	C₂²	1	1	yes	characteristic
72	#22548693	C₂²	1	2	yes	—
73	#22548692	C₂²	1	1	yes	characteristic
74	#22548692	C₂²	1	2	yes	—
75	#22548692	C₂²	1	2	yes	—
76	#22548692	C₂²	1	2	yes	—
77	#22548692	C₂²	1	2	yes	—
78	#22548692	C₂²	1	2	yes	—
79	#22548692	C₂²	1	2	yes	—
80	#22548692	C₂²	1	2	yes	—
81	#22548691	C₂²	1	2	yes	—
82	#22548687	C₂²	1	1	yes	characteristic
83	#22548687	C₂²	1	2	yes	—
84	#22548686	C₂²	1	1	yes	characteristic
85	#22548686	C₂²	1	2	yes	—
86	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
87	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
88	C₄×Dic₅₀₂	C₂²	1	2	yes	—
89	C₄×Dic₅₀₂	C₂²	1	2	yes	—
90	C₄×Dic₅₀₂	C₂²	1	2	yes	—
91	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
92	#22548680	C₂²	1	1	yes	characteristic
93	#22548680	C₂²	1	1	yes	characteristic
94	D₄×Dic₂₅₁	C₂²	1	2	yes	—
95	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
96	D₄×Dic₂₅₁	C₂²	1	2	yes	—
97	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
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	#22548674	C₂²	1	1	yes	characteristic
102	#22548674	C₂²	1	1	yes	characteristic
103	#22548673	C₂²	1	1	yes	characteristic
104	#22548672	C₂²	1	1	yes	characteristic
105	#22548672	C₂²	1	2	yes	—
106	#22548671	C₂²	1	2	yes	—
107	#22548671	C₂²	1	2	yes	—
108	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
109	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	—
110	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
111	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
113	#124×C₂₅₁	C₂²	1	2	yes	—
114	#124×C₂₅₁	C₂²	1	2	yes	—
115	#121×C₂₅₁	C₂²	1	1	yes	characteristic
116	#121×C₂₅₁	C₂²	1	2	yes	—
117	#121×C₂₅₁	C₂²	1	1	yes	characteristic
118	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
120	#117×C₂₅₁	C₂²	1	1	yes	characteristic
121	#117×C₂₅₁	C₂²	1	2	yes	—
122	#117×C₂₅₁	C₂²	1	1	yes	characteristic
123	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
124	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
125	C₂×Dic₅₀₂	C₂³	1	2	yes	—
126	C₂×Dic₅₀₂	C₂³	1	2	yes	—
127	C₂×Dic₅₀₂	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
131	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
132	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
133	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
134	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
135	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
136	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
138	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
142	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
145	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
146	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
148	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
149	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
150	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
151	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
152	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
153	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
154	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
155	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
156	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
157	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
158	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
159	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
160	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
162	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
165	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
166	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
167	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
173	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
183	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
189	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
190	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
191	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
192	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
193	C₄×Dic₂₅₁	C₂³	1	2	yes	—
194	C₄×Dic₂₅₁	C₂³	1	2	yes	—
195	C₄×Dic₂₅₁	C₂³	1	2	yes	—
196	C₄×Dic₂₅₁	C₂³	1	2	yes	—
197	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₅₁	C₂³	1	2	yes	—
199	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
200	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
201	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
203	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
204	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
207	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
219	C₄²×C₂₅₁	C₂³	1	2	yes	—
220	C₄²×C₂₅₁	C₂³	1	2	yes	—
221	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
222	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
223	Dic₅₀₂	—	2	2	no	—
224	Dic₅₀₂	—	4	2	no	—
225	Dic₅₀₂	—	4	1	no	—
226	Dic₅₀₂	—	4	2	no	—
227	Dic₅₀₂	—	4	2	no	—
228	C₂²⋊D₂₅₁	—	4	1	no	—
229	C₂²⋊D₂₅₁	—	4	2	no	—
230	C₂²⋊D₂₅₁	—	4	1	no	—
231	C₂×Dic₂₅₁	—	4	2	no	—
232	C₂×Dic₂₅₁	—	4	2	no	—
233	C₂×Dic₂₅₁	—	4	1	no	—
234	C₂×Dic₂₅₁	—	4	2	no	—
235	C₂×Dic₂₅₁	—	4	1	no	—
236	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
237	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
238	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
244	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
246	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
247	C₄×D₂₅₁	—	2	2	no	—
248	C₄×D₂₅₁	—	4	2	no	—
249	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
250	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
251	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
252	Q₈×C₂₅₁	—	4	2	no	—
253	D₄×C₂₅₁	—	2	2	no	—
254	D₄×C₂₅₁	—	4	1	no	—
255	D₄×C₂₅₁	—	4	2	no	—
256	D₄×C₂₅₁	—	4	2	no	—
257	C₂×C₄×C₂₅₁	—	2	2	no	—
258	C₂×C₄×C₂₅₁	—	2	2	no	—
259	C₂×C₄×C₂₅₁	—	4	2	no	—
260	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
263	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
265	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
266	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₂₅₁	—	2	1	no	—
269	C₂²×C₂₅₁	—	2	1	no	—
270	C₂²×C₂₅₁	—	2	2	no	—
271	C₂²×C₂₅₁	—	2	2	no	—
272	C₂²×C₂₅₁	—	2	1	no	—
273	C₂²×C₂₅₁	—	2	2	no	—
274	C₂²×C₂₅₁	—	2	1	no	—
275	C₂²×C₂₅₁	—	2	1	no	—
276	C₂²×C₂₅₁	—	2	1	no	—
277	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
278	C₂×D₂₅₁	—	2	1	no	—
279	C₂×D₂₅₁	—	2	1	no	—
280	C₂×D₂₅₁	—	2	1	no	—
281	C₄×C₂₅₁	—	2	1	no	—
282	C₄×C₂₅₁	—	2	1	no	—
283	C₄×C₂₅₁	—	2	1	no	—
284	C₄×C₂₅₁	—	2	2	no	—
285	C₄×C₂₅₁	—	2	2	no	—
286	C₄×C₂₅₁	—	2	2	no	—
287	C₄×C₂₅₁	—	2	1	no	—
288	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
289	Dic₂₅₁	—	2	1	no	—
290	Dic₂₅₁	—	2	2	no	—
291	Dic₂₅₁	—	2	2	no	—
292	Dic₂₅₁	—	2	1	no	—
293	Dic₂₅₁	—	2	1	no	—
294	Dic₂₅₁	—	2	2	no	—
295	Dic₂₅₁	—	2	1	no	—
296	Dic₂₅₁	—	2	2	no	—
297	Dic₂₅₁	—	2	1	no	—
298	Dic₂₅₁	—	2	1	no	—
299	Dic₂₅₁	—	2	1	no	—
300	C₂×C₂₅₁	—	4	1	no	—
301	C₂×C₂₅₁	—	4	1	no	—
302	C₂×C₂₅₁	—	4	2	no	—
303	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂×C₂₅₁	#585	1	1	yes	characteristic
305	C₂×C₂₅₁	#585	1	1	yes	characteristic
306	D₂₅₁	—	4	1	no	—
307	C₂₅₁	#3565	1	1	yes	characteristic, complemented, Sylow
308	#3565	—	251	1	no	maximal, Sylow
309	#563	—	251	2	no	—
310	#562	—	251	2	no	—
311	#557	—	251	1	no	—
312	#556	—	251	2	no	—
313	#556	—	251	1	no	—
314	#555	D₂₅₁	1	1	yes	characteristic, complemented
315	#554	—	251	1	no	—
316	#553	—	251	1	no	—
317	#553	—	251	1	no	—
318	#552	—	251	1	no	—
319	#552	—	251	2	no	—
320	#552	—	251	1	no	—
321	#544	—	251	1	no	—
322	#544	—	251	1	no	—
323	#542	—	251	2	no	—
324	#542	—	251	2	no	—
325	#542	—	251	1	no	—
326	#542	—	251	1	no	—
327	#541	—	251	2	no	—
328	#539	—	251	2	no	—
329	#533	—	251	1	no	—
330	#529	—	251	1	no	—
331	#529	—	251	1	no	—
332	C₄⋊Q₈	—	251	2	no	—
333	C₄⋊Q₈	—	251	2	no	—
334	C₄⋊Q₈	—	251	1	no	—
335	C₄⋊Q₈	—	251	1	no	—
336	C₄⋊Q₈	—	251	1	no	—
337	C₄⋊Q₈	—	251	2	no	—
338	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
339	#126	—	251	1	no	—
340	#126	—	251	2	no	—
341	#126	—	251	1	no	—
342	#126	—	251	2	no	—
343	#126	—	251	2	no	—
344	#126	—	251	2	no	—
345	#126	—	251	2	no	—
346	#126	—	251	2	no	—
347	#126	—	251	2	no	—
348	#126	—	251	2	no	—
349	#126	—	251	2	no	—
350	#125	—	251	1	no	—
351	#125	—	251	1	no	—
352	#125	—	251	1	no	—
353	#125	—	251	1	no	—
354	#125	—	251	2	no	—
355	#125	—	251	2	no	—
356	#125	—	251	2	no	—
357	#125	—	251	2	no	—
358	#125	—	251	1	no	—
359	#125	—	251	2	no	—
360	#125	—	251	1	no	—
361	#125	—	251	2	no	—
362	#124	—	251	1	no	—
363	#124	—	251	2	no	—
364	#124	—	251	1	no	—
365	#124	—	251	2	no	—
366	#124	—	251	2	no	—
367	#124	C₂×D₂₅₁	1	2	yes	—
368	#124	C₂×D₂₅₁	1	2	yes	—
369	#123	—	251	1	no	—
370	#123	—	251	2	no	—
371	#123	—	251	2	no	—
372	#123	—	251	2	no	—
373	#123	—	251	2	no	—
374	#123	—	251	2	no	—
375	#123	—	251	1	no	—
376	#123	—	251	2	no	—
377	#123	—	251	2	no	—
378	C₂²⋊Q₈	—	251	2	no	—
379	C₂²⋊Q₈	—	251	1	no	—
380	C₂²⋊Q₈	—	251	2	no	—
381	C₂²⋊Q₈	—	251	2	no	—
382	C₂²⋊Q₈	—	251	1	no	—
383	C₂²⋊Q₈	—	251	1	no	—
384	C₂²⋊Q₈	—	251	2	no	—
385	C₂²⋊Q₈	—	251	1	no	—
386	C₂²⋊Q₈	—	251	2	no	—
387	C₂²⋊Q₈	—	251	2	no	—
388	C₂²⋊Q₈	—	251	2	no	—
389	C₂²⋊Q₈	—	251	2	no	—
390	C₂²⋊Q₈	—	251	2	no	—
391	C₂²⋊Q₈	—	251	2	no	—
392	C₂²⋊Q₈	—	251	2	no	—
393	#121	—	251	1	no	—
394	#121	—	251	1	no	—
395	#121	—	251	2	no	—
396	#121	—	251	2	no	—
397	#121	C₂×D₂₅₁	1	1	yes	characteristic
398	#121	C₂×D₂₅₁	1	2	yes	—
399	#121	C₂×D₂₅₁	1	1	yes	characteristic
400	C₄×Q₈	—	251	2	no	—
401	C₄×Q₈	—	251	1	no	—
402	C₄×Q₈	—	251	1	no	—
403	C₄×Q₈	—	251	1	no	—
404	C₄×Q₈	—	251	2	no	—
405	C₄×Q₈	—	251	2	no	—
406	C₄×Q₈	—	251	2	no	—
407	C₄×Q₈	—	251	1	no	—
408	C₄×D₄	—	251	2	no	—
409	C₄×D₄	—	251	1	no	—
410	C₄×D₄	—	251	2	no	—
411	C₄×D₄	—	251	1	no	—
412	C₄×D₄	—	251	1	no	—
413	C₄×D₄	—	251	1	no	—
414	C₄×D₄	—	251	2	no	—
415	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
416	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
417	#117	—	251	1	no	—
418	#117	—	251	1	no	—
419	#117	—	251	1	no	—
420	#117	—	251	2	no	—
421	#117	—	251	2	no	—
422	#117	—	251	1	no	—
423	#117	—	251	2	no	—
424	#117	C₂×D₂₅₁	1	1	yes	characteristic
425	#117	C₂×D₂₅₁	1	2	yes	—
426	#117	C₂×D₂₅₁	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	251	2	no	—
428	C₂×C₄⋊C₄	—	251	1	no	—
429	C₂×C₄⋊C₄	—	251	1	no	—
430	C₂×C₄²	—	251	1	no	—
431	C₂×Q₈	—	251	2	no	—
432	C₂×Q₈	—	251	2	no	—
433	C₂×Q₈	—	251	2	no	—
434	C₂×Q₈	—	251	1	no	—
435	C₂×Q₈	—	251	1	no	—
436	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
437	C₂×D₄	—	251	1	no	—
438	C₂×D₄	—	251	2	no	—
439	C₂×D₄	—	251	1	no	—
440	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
441	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
442	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
443	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
444	C₂²×C₄	—	251	1	no	—
445	C₂²×C₄	—	251	1	no	—
446	C₂²×C₄	—	251	2	no	—
447	C₂²×C₄	—	251	2	no	—
448	C₂²×C₄	—	251	2	no	—
449	C₂²×C₄	—	251	2	no	—
450	C₂²×C₄	—	251	1	no	—
451	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
454	C₄⋊C₄	—	251	1	no	—
455	C₄⋊C₄	—	251	2	no	—
456	C₄⋊C₄	—	251	1	no	—
457	C₄⋊C₄	—	251	1	no	—
458	C₄⋊C₄	—	251	1	no	—
459	C₄⋊C₄	—	251	2	no	—
460	C₄⋊C₄	—	251	2	no	—
461	C₄⋊C₄	—	251	2	no	—
462	C₄⋊C₄	—	251	2	no	—
463	C₄⋊C₄	—	251	2	no	—
464	C₄⋊C₄	—	251	2	no	—
465	C₄⋊C₄	—	251	1	no	—
466	C₄⋊C₄	—	251	2	no	—
467	C₄⋊C₄	—	251	2	no	—
468	C₄⋊C₄	—	251	1	no	—
469	C₄⋊C₄	—	251	1	no	—
470	C₄⋊C₄	—	251	1	no	—
471	C₄⋊C₄	—	251	1	no	—
472	C₄⋊C₄	—	251	2	no	—
473	C₄⋊C₄	—	251	1	no	—
474	C₄⋊C₄	—	251	1	no	—
475	C₄⋊C₄	—	251	2	no	—
476	C₄⋊C₄	—	251	2	no	—
477	C₄⋊C₄	—	251	2	no	—
478	C₄⋊C₄	—	251	2	no	—
479	C₄⋊C₄	—	251	2	no	—
480	C₄⋊C₄	—	251	2	no	—
481	C₄⋊C₄	—	251	2	no	—
482	C₄⋊C₄	—	251	2	no	—
483	C₄⋊C₄	—	251	1	no	—
484	C₄⋊C₄	—	251	2	no	—
485	C₄⋊C₄	—	251	2	no	—
486	C₄⋊C₄	—	251	2	no	—
487	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
492	C₂²⋊C₄	—	251	2	no	—
493	C₂²⋊C₄	—	251	1	no	—
494	C₂²⋊C₄	—	251	1	no	—
495	C₂²⋊C₄	—	251	2	no	—
496	C₂²⋊C₄	—	251	2	no	—
497	C₂²⋊C₄	—	251	1	no	—
498	C₂²⋊C₄	—	251	2	no	—
499	C₂²⋊C₄	—	251	2	no	—
500	C₂²⋊C₄	—	251	2	no	—
501	C₂²⋊C₄	—	251	1	no	—
502	C₂²⋊C₄	—	251	2	no	—
503	C₂²⋊C₄	—	251	2	no	—
504	C₂²⋊C₄	—	251	1	no	—
505	C₂²⋊C₄	—	251	1	no	—
506	C₂²⋊C₄	—	251	2	no	—
507	C₂²⋊C₄	—	251	1	no	—
508	C₂²⋊C₄	—	251	2	no	—
509	C₂²⋊C₄	—	251	1	no	—
510	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
517	C₄²	—	251	1	no	—
518	C₄²	—	251	1	no	—
519	C₄²	—	251	1	no	—
520	C₄²	—	251	1	no	—
521	C₄²	—	251	2	no	—
522	C₄²	—	251	2	no	—
523	C₄²	—	251	1	no	—
524	C₄²	—	251	2	no	—
525	C₄²	—	251	2	no	—
526	C₄²	—	251	2	no	—
527	C₄²	C₂²×D₂₅₁	1	2	yes	—
528	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
529	C₄²	C₂²×D₂₅₁	1	2	yes	—
530	C₂³	—	251	1	no	—
531	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
532	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
533	C₂³	C₂³×D₂₅₁	1	2	yes	—
534	Q₈	—	4	2	no	—
535	Q₈	—	1004	2	no	—
536	Q₈	—	1004	1	no	—
537	Q₈	—	1004	2	no	—
538	Q₈	—	1004	2	no	—
539	Q₈	—	502	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	1	no	—
544	D₄	—	1004	1	no	—
545	D₄	—	1004	2	no	—
546	D₄	—	1004	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	1004	2	no	—
551	C₂×C₄	—	1004	2	no	—
552	C₂×C₄	—	1004	1	no	—
553	C₂×C₄	—	1004	2	no	—
554	C₂×C₄	—	1004	1	no	—
555	C₂×C₄	—	1004	2	no	—
556	C₂×C₄	—	502	2	no	—
557	C₂×C₄	—	251	1	no	—
558	C₂×C₄	—	251	2	no	—
559	C₂×C₄	—	251	1	no	—
560	C₂×C₄	—	251	1	no	—
561	C₂×C₄	—	251	1	no	—
562	C₂×C₄	—	251	1	no	—
563	C₂×C₄	—	251	1	no	—
564	C₂×C₄	—	251	2	no	—
565	C₂×C₄	—	251	2	no	—
566	C₂×C₄	—	251	1	no	—
567	C₂×C₄	—	251	2	no	—
568	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
571	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
572	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
574	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
575	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	502	1	no	—
586	C₂²	—	502	1	no	—
587	C₂²	—	502	1	no	—
588	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	502	1	no	—
597	C₄	—	502	2	no	—
598	C₄	—	502	2	no	—
599	C₄	—	502	1	no	—
600	C₄	—	502	1	no	—
601	C₄	—	502	1	no	—
602	C₄	—	502	1	no	—
603	C₄	—	502	2	no	—
604	C₄	—	502	2	no	—
605	C₄	—	502	1	no	—
606	C₄	—	502	1	no	—
607	C₄	#22548762	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	2	no	—
611	C₂	—	1004	1	no	—
612	C₂	C₂×#22548762	1	1	yes	characteristic
613	C₂	#30632522	1	1	yes	characteristic
614	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#555×C₂₅₁	C₂
hypercenter	#555	D₂₅₁
hypocenter	C₂₅₁	#3565
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #30632437	C₂	semidirect
2. #30632432	C₂	semidirect
3. #30632412	C₂	semidirect
4. #30632406	C₂	semidirect
5. #30632405	C₂	semidirect
6. #30632396	C₂	semidirect
7. #30632389	C₂	semidirect
8. #30632384	C₂	semidirect
9. #30632377	C₂	semidirect
10. #30632376	C₂	semidirect
11. #30632370	C₂	semidirect
12. #30632315	C₂	semidirect
13. #30632314	C₂	semidirect
14. #30632306	C₂	semidirect
15. #30632304	C₂	semidirect
16. #30632302	C₂	semidirect
17. #30632301	C₂	semidirect
18. #30632299	C₂	semidirect
19. #30632282	C₂	semidirect
20. #30632240	C₂	semidirect
21. #30632218	C₂	semidirect
22. #30632217	C₂	semidirect
23. #555×C₂₅₁	C₂	semidirect
307. C₂₅₁	#3565	semidirect
314. #555	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632437	2
#30632432	2
#30632412	2
#30632406	2
#30632405	2
#30632396	2
#30632389	2
#30632384	2
#30632377	2
#30632376	2
#30632370	2
#30632315	2
#30632314	2
#30632306	2
#30632304	2
#30632302	2
#30632301	2
#30632299	2
#30632282	2
#30632240	2
#30632218	2
#30632217	2
#555×C₂₅₁	2
#3565	251