Subgroups — #44564644

Order 32128.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 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	#30632431	C₂	1	2	yes	maximal, complemented
3	#30632410	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632396	C₂	1	2	yes	maximal, complemented
5	#30632394	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632389	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632380	C₂	1	2	yes	maximal, complemented
8	#30632379	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₈×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632345	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632336	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632306	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632301	C₂	1	2	yes	maximal, complemented
14	#30632295	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632286	C₂	1	2	yes	maximal, complemented
16	#30632274	C₂	1	2	yes	maximal, complemented
17	#30632270	C₂	1	2	yes	maximal, complemented
18	#30632265	C₂	1	1	yes	maximal, characteristic, complemented
19	#30632260	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632197	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632196	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#22548691	C₂	1	1	yes	maximal, characteristic, complemented
23	#548×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860810	C₂²	1	1	yes	characteristic
25	C₂×#16860809	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
28	#22548715	C₂²	1	1	yes	characteristic, complemented
29	#22548714	C₂²	1	2	yes	complemented
30	#22548713	C₂²	1	1	yes	characteristic, complemented
31	#22548713	C₂²	1	2	yes	complemented
32	#22548710	C₂²	1	2	yes	—
33	#22548710	C₂²	1	2	yes	—
34	#22548710	C₂²	1	2	yes	—
35	#22548710	C₂²	1	2	yes	complemented
36	#22548709	C₂²	1	2	yes	—
37	#22548708	C₂²	1	2	yes	complemented
38	#22548708	C₂²	1	2	yes	complemented
39	#22548707	C₂²	1	2	yes	complemented
40	#22548706	C₂²	1	2	yes	complemented
41	#22548706	C₂²	1	2	yes	complemented
42	#22548706	C₂²	1	1	yes	characteristic, complemented
43	#22548705	C₂²	1	2	yes	complemented
44	#22548703	C₂²	1	2	yes	—
45	#22548701	C₂²	1	2	yes	—
46	#22548701	C₂²	1	2	yes	—
47	#22548701	C₂²	1	2	yes	—
48	#22548700	C₂²	1	1	yes	characteristic
49	#22548700	C₂²	1	2	yes	—
50	#22548699	C₂²	1	2	yes	—
51	#22548699	C₂²	1	2	yes	—
52	#22548699	C₂²	1	2	yes	complemented
53	#22548698	C₂²	1	2	yes	—
54	#22548697	C₂²	1	1	yes	characteristic
55	#22548697	C₂²	1	2	yes	—
56	#22548697	C₂²	1	2	yes	complemented
57	#22548696	C₂²	1	2	yes	complemented
58	#22548695	C₂²	1	1	yes	characteristic
59	#22548694	C₂²	1	1	yes	characteristic
60	#22548694	C₂²	1	2	yes	—
61	#22548694	C₂²	1	1	yes	characteristic, complemented
62	#22548694	C₂²	1	2	yes	complemented
63	#22548693	C₂²	1	1	yes	characteristic
64	#22548692	C₂²	1	1	yes	characteristic
65	#22548692	C₂²	1	2	yes	—
66	#22548692	C₂²	1	2	yes	complemented
67	#22548692	C₂²	1	2	yes	complemented
68	#22548692	C₂²	1	2	yes	complemented
69	#22548691	C₂²	1	1	yes	characteristic
70	#22548691	C₂²	1	1	yes	characteristic
71	#22548691	C₂²	1	2	yes	—
72	#22548691	C₂²	1	1	yes	characteristic
73	#22548691	C₂²	1	1	yes	characteristic
74	#22548691	C₂²	1	2	yes	—
75	#22548691	C₂²	1	1	yes	characteristic, complemented
76	#22548691	C₂²	1	2	yes	complemented
77	#22548689	C₂²	1	2	yes	—
78	#22548688	C₂²	1	1	yes	characteristic
79	#22548688	C₂²	1	2	yes	—
80	#22548687	C₂²	1	1	yes	characteristic
81	#22548687	C₂²	1	2	yes	—
82	#22548687	C₂²	1	2	yes	—
83	#22548687	C₂²	1	2	yes	—
84	#22548687	C₂²	1	2	yes	complemented
85	#22548686	C₂²	1	1	yes	characteristic
86	#22548686	C₂²	1	1	yes	characteristic, complemented
87	#22548685	C₂²	1	1	yes	characteristic
88	#22548683	C₂²	1	1	yes	characteristic
89	#22548683	C₂²	1	2	yes	—
90	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
93	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
94	D₄×Dic₂₅₁	C₂²	1	2	yes	—
95	D₄×Dic₂₅₁	C₂²	1	2	yes	—
96	D₄×Dic₂₅₁	C₂²	1	2	yes	—
97	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
101	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
103	#22548673	C₂²	1	1	yes	characteristic
104	#22548673	C₂²	1	1	yes	characteristic, complemented
105	#22548672	C₂²	1	1	yes	characteristic
106	#22548671	C₂²	1	2	yes	complemented
107	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
108	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
109	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	—
110	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
111	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
112	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
113	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
114	#124×C₂₅₁	C₂²	1	2	yes	complemented
115	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
118	#121×C₂₅₁	C₂²	1	1	yes	characteristic
119	#121×C₂₅₁	C₂²	1	2	yes	—
120	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
122	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
123	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
124	#16860810	—	4	2	no	—
125	#16860809	—	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	C₂×Dic₅₀₂	C₂³	1	2	yes	—
130	Q₈×D₂₅₁	—	4	2	no	—
131	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
132	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
140	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
141	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
142	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
143	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
144	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
145	C₂×C₄×D₂₅₁	—	4	2	no	—
146	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
151	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
152	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₂₅₁	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	1	yes	characteristic
161	C₄⋊Dic₂₅₁	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	2	yes	—
166	Dic₂₅₁⋊C₄	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	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	1	yes	characteristic
178	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
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	1	yes	characteristic
189	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
195	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₅₁	C₂³	1	2	yes	—
199	C₄×Dic₂₅₁	C₂³	1	2	yes	—
200	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₅₁	C₂³	1	2	yes	—
202	C₄×Dic₂₅₁	C₂³	1	2	yes	—
203	#41×C₂₅₁	—	4	2	no	—
204	C₂×Q₈×C₂₅₁	—	4	2	no	—
205	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
208	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
211	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
215	C₂²×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	1	yes	characteristic
221	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
226	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
227	C₄²×C₂₅₁	C₂³	1	2	yes	—
228	C₂²×D₂₅₁	—	2	2	no	—
229	C₂²×D₂₅₁	—	4	1	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	—	4	2	no	—
236	Dic₅₀₂	—	4	2	no	—
237	Dic₅₀₂	—	4	1	no	—
238	D₁₀₀₄	—	4	1	no	—
239	D₁₀₀₄	—	4	1	no	—
240	C₂²⋊D₂₅₁	—	2	2	no	—
241	C₂²⋊D₂₅₁	—	4	2	no	—
242	C₂²⋊D₂₅₁	—	4	1	no	—
243	C₂²⋊D₂₅₁	—	4	2	no	—
244	C₂²⋊D₂₅₁	—	4	2	no	—
245	C₂²⋊D₂₅₁	—	4	1	no	—
246	C₂²⋊D₂₅₁	—	4	1	no	—
247	C₂×Dic₂₅₁	—	4	1	no	—
248	C₂×Dic₂₅₁	—	4	2	no	—
249	C₂×Dic₂₅₁	—	4	2	no	—
250	C₂×Dic₂₅₁	—	4	2	no	—
251	C₂×Dic₂₅₁	—	4	2	no	—
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	1	yes	characteristic
256	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
257	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
259	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
260	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
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	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
268	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
269	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
270	Q₈×C₂₅₁	—	2	2	no	—
271	Q₈×C₂₅₁	—	2	2	no	—
272	Q₈×C₂₅₁	—	4	2	no	—
273	D₄×C₂₅₁	—	2	2	no	—
274	D₄×C₂₅₁	—	2	4	no	—
275	D₄×C₂₅₁	—	2	2	no	—
276	D₄×C₂₅₁	—	4	2	no	—
277	C₂×C₄×C₂₅₁	—	2	2	no	—
278	C₂×C₄×C₂₅₁	—	2	2	no	—
279	C₂×C₄×C₂₅₁	—	4	2	no	—
280	C₂×C₄×C₂₅₁	—	4	2	no	—
281	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
284	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
285	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
286	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₂₅₁	—	2	1	no	—
290	C₂²×C₂₅₁	—	2	1	no	—
291	C₂²×C₂₅₁	—	2	1	no	—
292	C₂²×C₂₅₁	—	2	2	no	—
293	C₂²×C₂₅₁	—	2	1	no	—
294	C₂²×C₂₅₁	—	2	2	no	—
295	C₂²×C₂₅₁	—	2	1	no	—
296	C₂²×C₂₅₁	—	2	2	no	—
297	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
298	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
299	C₂×D₂₅₁	—	2	1	no	—
300	C₂×D₂₅₁	—	2	1	no	—
301	C₂×D₂₅₁	—	2	1	no	—
302	C₂×D₂₅₁	—	2	1	no	—
303	C₂×D₂₅₁	—	2	1	no	—
304	C₂×D₂₅₁	—	2	1	no	—
305	C₂×D₂₅₁	—	2	1	no	—
306	C₂×D₂₅₁	—	2	1	no	—
307	C₂×D₂₅₁	—	2	1	no	—
308	C₂×D₂₅₁	—	4	4	no	—
309	C₄×C₂₅₁	—	2	1	no	—
310	C₄×C₂₅₁	—	2	1	no	—
311	C₄×C₂₅₁	—	2	2	no	—
312	C₄×C₂₅₁	—	2	2	no	—
313	C₄×C₂₅₁	—	2	1	no	—
314	C₄×C₂₅₁	—	2	2	no	—
315	C₄×C₂₅₁	—	2	1	no	—
316	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
317	Dic₂₅₁	—	2	1	no	—
318	Dic₂₅₁	—	2	1	no	—
319	Dic₂₅₁	—	2	1	no	—
320	Dic₂₅₁	—	2	2	no	—
321	Dic₂₅₁	—	2	1	no	—
322	Dic₂₅₁	—	2	2	no	—
323	Dic₂₅₁	—	2	1	no	—
324	Dic₂₅₁	—	2	2	no	—
325	Dic₂₅₁	—	2	2	no	—
326	C₂×C₂₅₁	—	2	2	no	—
327	C₂×C₂₅₁	—	4	1	no	—
328	C₂×C₂₅₁	—	4	2	no	—
329	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×C₂₅₁	#585	1	1	yes	characteristic
332	D₂₅₁	—	4	1	no	—
333	D₂₅₁	—	4	1	no	—
334	D₂₅₁	—	4	1	no	—
335	C₂₅₁	#3541	1	1	yes	characteristic, complemented, Sylow
336	#3541	—	251	1	no	maximal, Sylow
337	#563	—	251	2	no	—
338	#562	—	251	2	no	—
339	#556	—	251	1	no	—
340	#554	—	251	1	no	—
341	#554	—	251	2	no	—
342	#553	—	251	2	no	—
343	#553	—	251	1	no	—
344	#552	—	251	1	no	—
345	D₄×Q₈	—	251	1	no	—
346	#548	—	251	1	no	—
347	#548	D₂₅₁	1	1	yes	characteristic, complemented
348	#547	—	251	1	no	—
349	#542	—	251	2	no	—
350	#542	—	251	1	no	—
351	#541	—	251	1	no	—
352	#539	—	251	2	no	—
353	#538	—	251	2	no	—
354	#538	—	251	2	no	—
355	#537	—	251	1	no	—
356	#536	—	251	1	no	—
357	#525	—	251	1	no	—
358	#525	—	251	1	no	—
359	C₂×C₂²⋊Q₈	—	251	1	no	—
360	C₂×#41	—	251	1	no	—
361	C₂×#41	—	251	1	no	—
362	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
363	C₂²×Q₈	—	251	1	no	—
364	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
365	C₂³×C₄	—	251	1	no	—
366	C₄⋊Q₈	—	251	1	no	—
367	C₄⋊Q₈	—	251	2	no	—
368	C₄⋊Q₈	—	251	2	no	—
369	C₄⋊Q₈	—	251	1	no	—
370	#126	—	251	2	no	—
371	#126	—	251	2	no	—
372	#126	—	251	2	no	—
373	#126	—	251	2	no	—
374	#126	—	251	2	no	—
375	#126	—	251	2	no	—
376	#126	—	251	2	no	—
377	#125	—	251	2	no	—
378	#125	—	251	2	no	—
379	#125	—	251	1	no	—
380	#125	—	251	2	no	—
381	#125	—	251	2	no	—
382	#124	—	251	2	no	—
383	#124	—	251	2	no	—
384	#124	—	251	2	no	—
385	#124	—	251	2	no	—
386	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
387	#124	C₂×D₂₅₁	1	2	yes	complemented
388	#123	—	251	2	no	—
389	#123	—	251	2	no	—
390	#123	—	251	1	no	—
391	#123	—	251	2	no	—
392	#123	—	251	1	no	—
393	#123	—	251	2	no	—
394	#123	—	251	2	no	—
395	#123	—	251	2	no	—
396	#123	—	251	2	no	—
397	#123	—	251	2	no	—
398	C₂²⋊Q₈	—	251	1	no	—
399	C₂²⋊Q₈	—	251	1	no	—
400	C₂²⋊Q₈	—	251	2	no	—
401	C₂²⋊Q₈	—	251	1	no	—
402	C₂²⋊Q₈	—	251	1	no	—
403	C₂²⋊Q₈	—	251	2	no	—
404	C₂²⋊Q₈	—	251	1	no	—
405	C₂²⋊Q₈	—	251	2	no	—
406	C₂²⋊Q₈	—	251	1	no	—
407	C₂²⋊Q₈	—	251	1	no	—
408	C₂²⋊Q₈	—	251	2	no	—
409	C₂²⋊Q₈	—	251	2	no	—
410	C₂²⋊Q₈	—	251	1	no	—
411	C₂²⋊Q₈	—	251	1	no	—
412	C₂²⋊Q₈	—	251	1	no	—
413	C₂²⋊Q₈	—	251	2	no	—
414	C₂²⋊Q₈	—	251	2	no	—
415	C₂²⋊Q₈	—	251	2	no	—
416	C₂²⋊Q₈	—	251	2	no	—
417	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
418	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
419	#121	—	251	1	no	—
420	#121	—	251	1	no	—
421	#121	—	251	2	no	—
422	#121	—	251	1	no	—
423	#121	—	251	2	no	—
424	#121	—	251	2	no	—
425	#121	—	251	2	no	—
426	#121	—	251	2	no	—
427	#121	—	251	1	no	—
428	#121	—	251	2	no	—
429	#121	C₂×D₂₅₁	1	1	yes	characteristic
430	#121	C₂×D₂₅₁	1	2	yes	—
431	#120	—	251	1	no	—
432	#120	—	251	2	no	—
433	#120	—	251	1	no	—
434	C₄×Q₈	—	251	1	no	—
435	C₄×Q₈	—	251	1	no	—
436	C₄×Q₈	—	251	2	no	—
437	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
438	C₄×D₄	—	251	2	no	—
439	C₄×D₄	—	251	2	no	—
440	C₄×D₄	—	251	2	no	—
441	C₄×D₄	—	251	1	no	—
442	C₄×D₄	—	251	1	no	—
443	C₄×D₄	—	251	1	no	—
444	C₄×D₄	—	251	2	no	—
445	C₄×D₄	—	251	2	no	—
446	C₄×D₄	—	251	2	no	—
447	C₄×D₄	—	251	1	no	—
448	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
449	C₄×D₄	C₂×D₂₅₁	1	2	yes	—
450	#117	—	251	1	no	—
451	#117	—	251	1	no	—
452	#117	—	251	2	no	—
453	#117	—	251	1	no	—
454	C₂×C₄⋊C₄	—	251	2	no	—
455	C₂×C₄⋊C₄	—	251	1	no	—
456	C₂×C₄⋊C₄	—	251	1	no	—
457	C₂×C₄⋊C₄	—	251	2	no	—
458	C₂×C₂²⋊C₄	—	251	2	no	—
459	C₂⁴	—	251	1	no	—
460	#41	—	4	2	no	—
461	#41	—	1004	2	no	—
462	#41	—	1004	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	1004	2	no	—
465	C₂×Q₈	—	251	2	no	—
466	C₂×Q₈	—	251	1	no	—
467	C₂×Q₈	—	251	2	no	—
468	C₂×Q₈	—	251	1	no	—
469	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
470	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
472	C₂×D₄	—	251	1	no	—
473	C₂×D₄	—	251	2	no	—
474	C₂×D₄	—	251	2	no	—
475	C₂×D₄	—	251	2	no	—
476	C₂×D₄	—	251	1	no	—
477	C₂×D₄	—	251	1	no	—
478	C₂×D₄	—	251	1	no	—
479	C₂×D₄	—	251	1	no	—
480	C₂×D₄	—	251	1	no	—
481	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
482	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
485	C₂²×C₄	—	1004	2	no	—
486	C₂²×C₄	—	251	2	no	—
487	C₂²×C₄	—	251	1	no	—
488	C₂²×C₄	—	251	2	no	—
489	C₂²×C₄	—	251	2	no	—
490	C₂²×C₄	—	251	2	no	—
491	C₂²×C₄	—	251	2	no	—
492	C₂²×C₄	—	251	1	no	—
493	C₂²×C₄	—	251	1	no	—
494	C₂²×C₄	—	251	1	no	—
495	C₂²×C₄	—	251	1	no	—
496	C₂²×C₄	—	251	1	no	—
497	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
500	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
501	C₄⋊C₄	—	251	1	no	—
502	C₄⋊C₄	—	251	2	no	—
503	C₄⋊C₄	—	251	1	no	—
504	C₄⋊C₄	—	251	2	no	—
505	C₄⋊C₄	—	251	1	no	—
506	C₄⋊C₄	—	251	1	no	—
507	C₄⋊C₄	—	251	2	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	—	251	1	no	—
515	C₄⋊C₄	—	251	2	no	—
516	C₄⋊C₄	—	251	2	no	—
517	C₄⋊C₄	—	251	1	no	—
518	C₄⋊C₄	—	251	2	no	—
519	C₄⋊C₄	—	251	2	no	—
520	C₄⋊C₄	—	251	2	no	—
521	C₄⋊C₄	—	251	1	no	—
522	C₄⋊C₄	—	251	2	no	—
523	C₄⋊C₄	—	251	2	no	—
524	C₄⋊C₄	—	251	2	no	—
525	C₄⋊C₄	—	251	2	no	—
526	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
529	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
530	C₂²⋊C₄	—	251	1	no	—
531	C₂²⋊C₄	—	251	2	no	—
532	C₂²⋊C₄	—	251	1	no	—
533	C₂²⋊C₄	—	251	2	no	—
534	C₂²⋊C₄	—	251	2	no	—
535	C₂²⋊C₄	—	251	2	no	—
536	C₂²⋊C₄	—	251	2	no	—
537	C₂²⋊C₄	—	251	2	no	—
538	C₂²⋊C₄	—	251	2	no	—
539	C₂²⋊C₄	—	251	2	no	—
540	C₂²⋊C₄	—	251	2	no	—
541	C₂²⋊C₄	—	251	1	no	—
542	C₂²⋊C₄	—	251	2	no	—
543	C₂²⋊C₄	—	251	1	no	—
544	C₂²⋊C₄	—	251	2	no	—
545	C₂²⋊C₄	—	251	1	no	—
546	C₂²⋊C₄	—	251	1	no	—
547	C₂²⋊C₄	—	251	2	no	—
548	C₂²⋊C₄	—	251	1	no	—
549	C₂²⋊C₄	—	251	2	no	—
550	C₂²⋊C₄	—	251	1	no	—
551	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
557	C₄²	—	251	2	no	—
558	C₄²	—	251	1	no	—
559	C₄²	—	251	2	no	—
560	C₄²	—	251	2	no	—
561	C₄²	—	251	2	no	—
562	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
563	C₄²	C₂²×D₂₅₁	1	2	yes	—
564	C₂³	—	1004	1	no	—
565	C₂³	—	1004	1	no	—
566	C₂³	—	502	2	no	—
567	C₂³	—	251	1	no	—
568	C₂³	—	251	1	no	—
569	C₂³	—	251	1	no	—
570	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
571	C₂³	C₂³×D₂₅₁	1	2	yes	—
572	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	1004	2	no	—
577	Q₈	—	1004	1	no	—
578	Q₈	—	1004	2	no	—
579	Q₈	—	502	2	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	1004	1	no	—
585	D₄	—	1004	1	no	—
586	D₄	—	1004	1	no	—
587	D₄	—	1004	2	no	—
588	D₄	—	1004	1	no	—
589	D₄	—	1004	1	no	—
590	D₄	—	1004	2	no	—
591	D₄	—	1004	2	no	—
592	D₄	—	502	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	1004	1	no	—
598	C₂×C₄	—	1004	1	no	—
599	C₂×C₄	—	1004	2	no	—
600	C₂×C₄	—	1004	1	no	—
601	C₂×C₄	—	1004	2	no	—
602	C₂×C₄	—	1004	2	no	—
603	C₂×C₄	—	1004	2	no	—
604	C₂×C₄	—	1004	2	no	—
605	C₂×C₄	—	502	2	no	—
606	C₂×C₄	—	502	2	no	—
607	C₂×C₄	—	502	2	no	—
608	C₂×C₄	—	251	1	no	—
609	C₂×C₄	—	251	2	no	—
610	C₂×C₄	—	251	1	no	—
611	C₂×C₄	—	251	1	no	—
612	C₂×C₄	—	251	2	no	—
613	C₂×C₄	—	251	1	no	—
614	C₂×C₄	—	251	2	no	—
615	C₂×C₄	—	251	2	no	—
616	C₂×C₄	—	251	1	no	—
617	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
618	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
620	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
622	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	1004	4	no	—
634	C₂²	—	502	1	no	—
635	C₂²	—	502	1	no	—
636	C₂²	—	502	1	no	—
637	C₂²	—	502	1	no	—
638	C₂²	—	502	1	no	—
639	C₂²	—	502	1	no	—
640	C₂²	—	502	1	no	—
641	C₂²	—	502	1	no	—
642	C₂²	—	502	1	no	—
643	C₂²	#22548762	1	2	yes	—
644	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	502	1	no	—
653	C₄	—	502	1	no	—
654	C₄	—	502	2	no	—
655	C₄	—	502	1	no	—
656	C₄	—	502	1	no	—
657	C₄	—	502	2	no	—
658	C₄	—	502	1	no	—
659	C₄	—	502	2	no	—
660	C₄	—	502	2	no	—
661	C₄	#22548760	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	2	no	—
665	C₂	—	1004	1	no	—
666	C₂	—	1004	1	no	—
667	C₂	—	1004	1	no	—
668	C₂	C₂×#22548760	1	1	yes	characteristic
669	C₂	C₂×#22548762	1	1	yes	characteristic
670	C₂	#30632524	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#548×C₂₅₁	C₂
hypercenter	#548	D₂₅₁
hypocenter	C₂₅₁	#3541
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #30632438	C₂	semidirect
2. #30632431	C₂	semidirect
3. #30632410	C₂	semidirect
4. #30632396	C₂	semidirect
5. #30632394	C₂	semidirect
6. #30632389	C₂	semidirect
7. #30632380	C₂	semidirect
8. #30632379	C₂	semidirect
9. Q₈×C₂²⋊D₂₅₁	C₂	semidirect
10. #30632345	C₂	semidirect
11. #30632336	C₂	semidirect
12. #30632306	C₂	semidirect
13. #30632301	C₂	semidirect
14. #30632295	C₂	semidirect
15. #30632286	C₂	semidirect
16. #30632274	C₂	semidirect
17. #30632270	C₂	semidirect
18. #30632265	C₂	semidirect
19. #30632260	C₂	semidirect
20. #30632197	C₂	semidirect
21. #30632196	C₂	semidirect
22. C₂×#22548691	C₂	semidirect
23. #548×C₂₅₁	C₂	semidirect
26. C₂×Q₈×D₂₅₁	C₂²	semidirect
28. #22548715	C₂²	semidirect
29. #22548714	C₂²	semidirect
30. #22548713	C₂²	semidirect
31. #22548713	C₂²	semidirect
35. #22548710	C₂²	semidirect
37. #22548708	C₂²	semidirect
38. #22548708	C₂²	semidirect
39. #22548707	C₂²	semidirect
40. #22548706	C₂²	semidirect
41. #22548706	C₂²	semidirect
42. #22548706	C₂²	semidirect
43. #22548705	C₂²	semidirect
52. #22548699	C₂²	semidirect
56. #22548697	C₂²	semidirect
57. #22548696	C₂²	semidirect
61. #22548694	C₂²	semidirect
62. #22548694	C₂²	semidirect
66. #22548692	C₂²	semidirect
67. #22548692	C₂²	semidirect
68. #22548692	C₂²	semidirect
75. #22548691	C₂²	semidirect
76. #22548691	C₂²	semidirect
84. #22548687	C₂²	semidirect
86. #22548686	C₂²	semidirect
90. Q₈×Dic₂₅₁	C₂²	semidirect
91. C₄×Dic₅₀₂	C₂²	semidirect
92. C₄×Dic₅₀₂	C₂²	semidirect
97. D₄×Dic₂₅₁	C₂²	semidirect
102. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
104. #22548673	C₂²	semidirect
106. #22548671	C₂²	semidirect
108. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
110. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
112. C₂×#41×C₂₅₁	C₂²	semidirect
114. #124×C₂₅₁	C₂²	semidirect
115. #124×C₂₅₁	C₂²	semidirect
116. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
117. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
120. C₄×Q₈×C₂₅₁	C₂²	semidirect
335. C₂₅₁	#3541	semidirect
347. #548	D₂₅₁	semidirect
362. C₂×#41	C₂×D₂₅₁	semidirect
386. #124	C₂×D₂₅₁	semidirect
387. #124	C₂×D₂₅₁	semidirect
417. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
418. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
437. C₄×Q₈	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
#30632431	2
#30632410	2
#30632396	2
#30632394	2
#30632389	2
#30632380	2
#30632379	2
Q₈×C₂²⋊D₂₅₁	2
#30632345	2
#30632336	2
#30632306	2
#30632301	2
#30632295	2
#30632286	2
#30632274	2
#30632270	2
#30632265	2
#30632260	2
#30632197	2
#30632196	2
C₂×#22548691	2
#548×C₂₅₁	2
#3541	251