Subgroups — #44563967

Order 32128.

1242 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632421	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632391	C₂	1	2	yes	maximal, complemented
3	#30632382	C₂	1	2	yes	maximal, complemented
4	#30632380	C₂	1	2	yes	maximal, complemented
5	#30632368	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632365	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632364	C₂	1	2	yes	maximal, complemented
8	#30632326	C₂	1	2	yes	maximal, complemented
9	#30632324	C₂	1	2	yes	maximal, complemented
10	#30632319	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632233	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632217	C₂	1	2	yes	maximal, complemented
13	#30632215	C₂	1	2	yes	maximal, complemented
14	#30632196	C₂	1	2	yes	maximal, complemented
15	#30632194	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#16860809	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₂₅₁	C₂	1	2	yes	maximal, complemented
19	#525×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
21	C₂×#16860809	C₂²	1	2	yes	—
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
23	C₂×D₄×D₂₅₁	C₂²	1	2	yes	—
24	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₂₅₁	C₂²	1	2	yes	complemented
26	#22548713	C₂²	1	1	yes	characteristic, complemented
27	#22548711	C₂²	1	1	yes	characteristic
28	#22548710	C₂²	1	2	yes	complemented
29	#22548710	C₂²	1	2	yes	complemented
30	#22548708	C₂²	1	2	yes	complemented
31	#22548708	C₂²	1	2	yes	complemented
32	#22548705	C₂²	1	2	yes	complemented
33	#22548705	C₂²	1	2	yes	complemented
34	#22548704	C₂²	1	1	yes	characteristic, complemented
35	#22548702	C₂²	1	1	yes	characteristic, complemented
36	#22548701	C₂²	1	2	yes	complemented
37	#22548701	C₂²	1	2	yes	complemented
38	#22548700	C₂²	1	2	yes	complemented
39	#22548700	C₂²	1	2	yes	complemented
40	#22548699	C₂²	1	2	yes	complemented
41	#22548697	C₂²	1	2	yes	complemented
42	#22548697	C₂²	1	2	yes	complemented
43	#22548696	C₂²	1	1	yes	characteristic, complemented
44	#22548696	C₂²	1	1	yes	characteristic, complemented
45	#22548696	C₂²	1	2	yes	complemented
46	#22548693	C₂²	1	2	yes	complemented
47	#22548693	C₂²	1	2	yes	complemented
48	#22548692	C₂²	1	2	yes	complemented
49	#22548692	C₂²	1	2	yes	complemented
50	#22548691	C₂²	1	2	yes	complemented
51	#22548688	C₂²	1	2	yes	—
52	#22548688	C₂²	1	2	yes	complemented
53	#22548687	C₂²	1	2	yes	—
54	#22548687	C₂²	1	2	yes	complemented
55	#22548687	C₂²	1	2	yes	complemented
56	#22548687	C₂²	1	2	yes	complemented
57	#22548686	C₂²	1	2	yes	complemented
58	#22548685	C₂²	1	2	yes	—
59	#22548683	C₂²	1	1	yes	characteristic
60	#22548683	C₂²	1	1	yes	characteristic, complemented
61	#22548683	C₂²	1	2	yes	complemented
62	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
63	#22548680	C₂²	1	2	yes	complemented
64	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
65	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
66	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
67	#22548677	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
69	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
70	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
78	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
79	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
80	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
81	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
82	#22548674	C₂²	1	1	yes	characteristic, complemented
83	#22548673	C₂²	1	2	yes	complemented
84	#22548672	C₂²	1	2	yes	complemented
85	#22548671	C₂²	1	2	yes	complemented
86	#22548671	C₂²	1	2	yes	complemented
87	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
90	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₂₅₁	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
95	C₄²×D₂₅₁	C₂²	1	2	yes	complemented
96	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
98	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
99	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
101	#121×C₂₅₁	C₂²	1	2	yes	complemented
102	#120×C₂₅₁	C₂²	1	1	yes	characteristic
103	#120×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
105	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
106	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
108	C₂³×D₂₅₁	C₂³	1	2	yes	—
109	#16860810	—	4	2	no	—
110	#16860809	—	2	8	no	—
111	C₂×Dic₅₀₂	C₂³	1	2	yes	—
112	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
113	C₂×D₁₀₀₄	C₂³	1	2	yes	—
114	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
116	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
123	D₄×D₂₅₁	—	2	8	no	—
124	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
125	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
126	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
127	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
128	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₂₅₁	—	4	4	no	—
130	C₂×C₄×D₂₅₁	—	4	2	no	—
131	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
132	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
133	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
134	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
135	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
136	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
137	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
138	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
139	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
140	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
141	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
142	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
143	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
144	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
145	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
146	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
147	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
148	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
149	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
150	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
151	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
152	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
153	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
154	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
155	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
156	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
157	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
158	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
159	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
169	C₄×Dic₂₅₁	C₂³	1	2	yes	—
170	C₄×Dic₂₅₁	C₂³	1	2	yes	—
171	C₄×Dic₂₅₁	C₂³	1	2	yes	—
172	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
173	C₄×Dic₂₅₁	C₂³	1	2	yes	—
174	C₄×Dic₂₅₁	C₂³	1	2	yes	—
175	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
176	C₄×Dic₂₅₁	C₂³	1	2	yes	—
177	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
178	#41×C₂₅₁	—	4	2	no	—
179	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
181	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
182	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
184	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₂₅₁	—	4	2	no	—
186	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
187	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
191	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
193	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
194	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
196	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
197	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
201	C₄²×C₂₅₁	C₂³	1	2	yes	—
202	C₂²×D₂₅₁	—	2	4	no	—
203	C₂²×D₂₅₁	—	2	4	no	—
204	C₂²×D₂₅₁	—	2	4	no	—
205	C₂²×D₂₅₁	—	4	1	no	—
206	C₂²×D₂₅₁	—	4	2	no	—
207	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
208	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
209	Dic₅₀₂	—	2	4	no	—
210	Dic₅₀₂	—	4	1	no	—
211	D₁₀₀₄	—	2	4	no	—
212	D₁₀₀₄	—	4	1	no	—
213	C₂²⋊D₂₅₁	—	2	4	no	—
214	C₂²⋊D₂₅₁	—	2	4	no	—
215	C₂²⋊D₂₅₁	—	2	4	no	—
216	C₂²⋊D₂₅₁	—	2	4	no	—
217	C₂²⋊D₂₅₁	—	2	4	no	—
218	C₂²⋊D₂₅₁	—	4	2	no	—
219	C₂²⋊D₂₅₁	#41	1	8	yes	complemented
220	C₂×Dic₂₅₁	—	2	4	no	—
221	C₂×Dic₂₅₁	—	2	4	no	—
222	C₂×Dic₂₅₁	—	2	4	no	—
223	C₂×Dic₂₅₁	—	4	1	no	—
224	C₂×Dic₂₅₁	—	4	2	no	—
225	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
226	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
227	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
228	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
229	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
230	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
231	C₄×D₂₅₁	—	2	4	no	—
232	C₄×D₂₅₁	—	2	4	no	—
233	C₄×D₂₅₁	—	2	4	no	—
234	C₄×D₂₅₁	—	2	4	no	—
235	C₄×D₂₅₁	—	4	2	no	—
236	C₄×D₂₅₁	—	4	2	no	—
237	C₄×D₂₅₁	—	4	2	no	—
238	C₂³×C₂₅₁	—	2	4	no	—
239	C₂³×C₂₅₁	—	4	1	no	—
240	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
241	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
242	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
243	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
244	Q₈×C₂₅₁	—	4	1	no	—
245	D₄×C₂₅₁	—	2	4	no	—
246	D₄×C₂₅₁	—	2	4	no	—
247	D₄×C₂₅₁	—	4	1	no	—
248	D₄×C₂₅₁	—	4	1	no	—
249	D₄×C₂₅₁	—	4	1	no	—
250	C₂×C₄×C₂₅₁	—	2	2	no	—
251	C₂×C₄×C₂₅₁	—	2	4	no	—
252	C₂×C₄×C₂₅₁	—	2	2	no	—
253	C₂×C₄×C₂₅₁	—	2	2	no	—
254	C₂×C₄×C₂₅₁	—	4	2	no	—
255	C₂×C₄×C₂₅₁	—	4	1	no	—
256	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
257	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
258	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
259	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₂₅₁	—	2	2	no	—
264	C₂²×C₂₅₁	—	2	2	no	—
265	C₂²×C₂₅₁	—	2	2	no	—
266	C₂²×C₂₅₁	—	2	2	no	—
267	C₂²×C₂₅₁	—	2	2	no	—
268	C₂²×C₂₅₁	—	2	1	no	—
269	C₂²×C₂₅₁	—	2	1	no	—
270	C₂²×C₂₅₁	—	2	1	no	—
271	C₂²×C₂₅₁	—	4	4	no	—
272	C₂²×C₂₅₁	C₂×#41	1	4	yes	—
273	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
274	C₂×D₂₅₁	—	2	2	no	—
275	C₂×D₂₅₁	—	2	2	no	—
276	C₂×D₂₅₁	—	2	2	no	—
277	C₂×D₂₅₁	—	2	2	no	—
278	C₂×D₂₅₁	—	2	2	no	—
279	C₂×D₂₅₁	—	4	4	no	—
280	C₂×D₂₅₁	—	4	8	no	—
281	C₂×D₂₅₁	C₂×#41	1	4	yes	—
282	C₄×C₂₅₁	—	2	2	no	—
283	C₄×C₂₅₁	—	2	2	no	—
284	C₄×C₂₅₁	—	2	1	no	—
285	C₄×C₂₅₁	—	2	2	no	—
286	C₄×C₂₅₁	—	2	1	no	—
287	C₄×C₂₅₁	—	2	1	no	—
288	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
289	Dic₂₅₁	—	2	2	no	—
290	Dic₂₅₁	—	2	2	no	—
291	Dic₂₅₁	—	2	2	no	—
292	Dic₂₅₁	—	2	2	no	—
293	Dic₂₅₁	—	2	2	no	—
294	Dic₂₅₁	C₂×#41	1	4	yes	—
295	C₂×C₂₅₁	—	2	4	no	—
296	C₂×C₂₅₁	—	4	1	no	—
297	C₂×C₂₅₁	—	4	1	no	—
298	C₂×C₂₅₁	—	4	1	no	—
299	C₂×C₂₅₁	C₂²×#41	1	2	yes	—
300	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	D₂₅₁	—	2	4	no	—
302	D₂₅₁	—	4	2	no	—
303	C₂₅₁	#3481	1	1	yes	characteristic, complemented, Sylow
304	#3481	—	251	1	no	maximal, Sylow
305	#559	—	251	1	no	—
306	#554	—	251	2	no	—
307	#553	—	251	2	no	—
308	#553	—	251	2	no	—
309	#551	—	251	1	no	—
310	#551	—	251	2	no	—
311	#551	—	251	1	no	—
312	#546	—	251	2	no	—
313	#546	—	251	2	no	—
314	D₄²	—	251	1	no	—
315	#532	—	251	1	no	—
316	#529	—	251	2	no	—
317	#529	—	251	2	no	—
318	#525	—	251	1	no	—
319	#525	—	251	2	no	—
320	#525	D₂₅₁	1	1	yes	characteristic, complemented
321	C₄×#41	—	251	2	no	—
322	C₂×C₄×D₄	—	251	2	no	—
323	C₂×C₄×D₄	—	251	2	no	—
324	C₂×#41	—	251	2	no	—
325	C₂×#41	—	251	1	no	—
326	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
327	C₂²×D₄	—	251	2	no	—
328	C₂²×D₄	—	251	2	no	—
329	C₂³×C₄	—	251	2	no	—
330	C₂³×C₄	—	251	1	no	—
331	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	—	251	1	no	—
333	#127	—	251	1	no	—
334	#126	—	251	2	no	—
335	#126	—	251	2	no	—
336	#126	—	251	2	no	—
337	#126	—	251	2	no	—
338	#125	—	251	2	no	—
339	#125	—	251	2	no	—
340	#124	—	251	1	no	—
341	#124	—	251	1	no	—
342	#124	—	251	2	no	—
343	#124	—	251	2	no	—
344	#123	—	251	1	no	—
345	#123	—	251	1	no	—
346	#123	—	251	2	no	—
347	#123	—	251	2	no	—
348	#123	—	251	2	no	—
349	#123	—	251	2	no	—
350	#123	—	251	2	no	—
351	#123	—	251	2	no	—
352	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
353	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
354	C₂²⋊Q₈	—	251	2	no	—
355	C₂²⋊Q₈	—	251	2	no	—
356	C₂²⋊Q₈	—	251	2	no	—
357	C₂²⋊Q₈	—	251	2	no	—
358	C₂²⋊Q₈	—	251	2	no	—
359	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
360	#121	—	251	2	no	—
361	#121	—	251	2	no	—
362	#121	—	251	2	no	—
363	#121	—	251	2	no	—
364	#121	—	251	2	no	—
365	#121	—	251	2	no	—
366	#121	—	251	2	no	—
367	#121	C₂×D₂₅₁	1	2	yes	complemented
368	#120	—	251	1	no	—
369	#120	—	251	2	no	—
370	#120	—	251	1	no	—
371	#120	—	251	2	no	—
372	#120	C₂×D₂₅₁	1	1	yes	characteristic
373	#120	C₂×D₂₅₁	1	1	yes	characteristic, complemented
374	C₄×Q₈	—	251	2	no	—
375	C₄×Q₈	—	251	2	no	—
376	C₄×D₄	—	251	2	no	—
377	C₄×D₄	—	251	2	no	—
378	C₄×D₄	—	251	2	no	—
379	C₄×D₄	—	251	2	no	—
380	C₄×D₄	—	251	2	no	—
381	C₄×D₄	—	251	2	no	—
382	C₄×D₄	—	251	2	no	—
383	C₄×D₄	—	251	2	no	—
384	C₄×D₄	—	251	2	no	—
385	C₄×D₄	—	251	2	no	—
386	C₄×D₄	—	251	2	no	—
387	C₄×D₄	—	251	2	no	—
388	C₄×D₄	—	251	2	no	—
389	C₄×D₄	—	251	2	no	—
390	C₄×D₄	—	251	2	no	—
391	C₄×D₄	—	251	2	no	—
392	C₄×D₄	—	251	2	no	—
393	C₄×D₄	—	251	2	no	—
394	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
395	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
396	#117	—	251	1	no	—
397	#117	—	251	2	no	—
398	#117	—	251	2	no	—
399	#117	—	251	2	no	—
400	#117	—	251	2	no	—
401	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
402	C₂×C₄⋊C₄	—	251	2	no	—
403	C₂×C₄⋊C₄	—	251	2	no	—
404	C₂×C₂²⋊C₄	—	251	2	no	—
405	C₂×C₂²⋊C₄	—	251	2	no	—
406	C₂×C₂²⋊C₄	—	251	2	no	—
407	C₂×C₂²⋊C₄	—	251	2	no	—
408	C₂×C₄²	—	251	2	no	—
409	C₂×C₄²	—	251	1	no	—
410	C₂×C₄²	—	251	2	no	—
411	C₂⁴	—	251	1	no	—
412	C₂⁴	—	251	2	no	—
413	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
414	#41	—	4	2	no	—
415	#41	—	1004	2	no	—
416	#41	—	502	8	no	—
417	C₂×Q₈	—	251	1	no	—
418	C₂×Q₈	—	251	2	no	—
419	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
420	C₂×D₄	—	502	8	no	—
421	C₂×D₄	—	502	8	no	—
422	C₂×D₄	—	251	2	no	—
423	C₂×D₄	—	251	2	no	—
424	C₂×D₄	—	251	2	no	—
425	C₂×D₄	—	251	2	no	—
426	C₂×D₄	—	251	2	no	—
427	C₂×D₄	—	251	2	no	—
428	C₂×D₄	—	251	2	no	—
429	C₂×D₄	—	251	1	no	—
430	C₂×D₄	—	251	2	no	—
431	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
432	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
433	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	1004	4	no	—
438	C₂²×C₄	—	1004	2	no	—
439	C₂²×C₄	—	251	2	no	—
440	C₂²×C₄	—	251	1	no	—
441	C₂²×C₄	—	251	2	no	—
442	C₂²×C₄	—	251	2	no	—
443	C₂²×C₄	—	251	2	no	—
444	C₂²×C₄	—	251	2	no	—
445	C₂²×C₄	—	251	2	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	2	no	—
451	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
452	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
456	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
457	C₄⋊C₄	—	251	2	no	—
458	C₄⋊C₄	—	251	2	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	2	no	—
466	C₄⋊C₄	—	251	2	no	—
467	C₄⋊C₄	—	251	2	no	—
468	C₄⋊C₄	—	251	2	no	—
469	C₄⋊C₄	—	251	2	no	—
470	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
471	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
472	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
473	C₂²⋊C₄	—	251	2	no	—
474	C₂²⋊C₄	—	251	2	no	—
475	C₂²⋊C₄	—	251	2	no	—
476	C₂²⋊C₄	—	251	2	no	—
477	C₂²⋊C₄	—	251	2	no	—
478	C₂²⋊C₄	—	251	2	no	—
479	C₂²⋊C₄	—	251	1	no	—
480	C₂²⋊C₄	—	251	1	no	—
481	C₂²⋊C₄	—	251	2	no	—
482	C₂²⋊C₄	—	251	2	no	—
483	C₂²⋊C₄	—	251	2	no	—
484	C₂²⋊C₄	—	251	2	no	—
485	C₂²⋊C₄	—	251	2	no	—
486	C₂²⋊C₄	—	251	2	no	—
487	C₂²⋊C₄	—	251	2	no	—
488	C₂²⋊C₄	—	251	2	no	—
489	C₂²⋊C₄	—	251	2	no	—
490	C₂²⋊C₄	—	251	2	no	—
491	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
496	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
497	C₄²	—	251	1	no	—
498	C₄²	—	251	2	no	—
499	C₄²	—	251	2	no	—
500	C₄²	—	251	2	no	—
501	C₄²	—	251	2	no	—
502	C₄²	—	251	1	no	—
503	C₄²	—	251	2	no	—
504	C₄²	—	251	2	no	—
505	C₄²	C₂²×D₂₅₁	1	2	yes	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	1004	2	no	—
509	C₂³	—	1004	1	no	—
510	C₂³	—	502	4	no	—
511	C₂³	—	502	4	no	—
512	C₂³	—	502	4	no	—
513	C₂³	—	251	2	no	—
514	C₂³	—	251	2	no	—
515	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
516	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
517	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
518	C₂³	C₂³×D₂₅₁	1	2	yes	—
519	Q₈	—	4	1	no	—
520	Q₈	—	1004	1	no	—
521	Q₈	—	502	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	1004	1	no	—
528	D₄	—	1004	2	no	—
529	D₄	—	502	4	no	—
530	D₄	—	502	4	no	—
531	D₄	—	502	4	no	—
532	D₄	—	502	4	no	—
533	D₄	—	502	4	no	—
534	D₄	—	502	4	no	—
535	D₄	—	251	8	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	1004	2	no	—
543	C₂×C₄	—	1004	2	no	—
544	C₂×C₄	—	1004	2	no	—
545	C₂×C₄	—	1004	1	no	—
546	C₂×C₄	—	1004	2	no	—
547	C₂×C₄	—	502	4	no	—
548	C₂×C₄	—	502	4	no	—
549	C₂×C₄	—	502	4	no	—
550	C₂×C₄	—	502	4	no	—
551	C₂×C₄	—	502	4	no	—
552	C₂×C₄	—	502	4	no	—
553	C₂×C₄	—	502	4	no	—
554	C₂×C₄	—	251	2	no	—
555	C₂×C₄	—	251	2	no	—
556	C₂×C₄	—	251	2	no	—
557	C₂×C₄	—	251	2	no	—
558	C₂×C₄	—	251	2	no	—
559	C₂×C₄	—	251	2	no	—
560	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
561	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
563	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
564	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	1004	8	no	—
577	C₂²	—	1004	4	no	—
578	C₂²	—	502	2	no	—
579	C₂²	—	502	2	no	—
580	C₂²	—	502	2	no	—
581	C₂²	—	502	2	no	—
582	C₂²	—	502	2	no	—
583	C₂²	—	251	4	no	—
584	C₂²	#41×D₂₅₁	1	4	yes	—
585	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	502	2	no	—
593	C₄	—	502	2	no	—
594	C₄	—	502	2	no	—
595	C₄	—	502	2	no	—
596	C₄	—	502	2	no	—
597	C₄	—	251	4	no	—
598	C₄	#22548760	1	2	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	1004	2	no	—
604	C₂	—	502	4	no	—
605	C₂	C₂×#41×D₂₅₁	1	2	yes	—
606	C₂	C₂×#22548760	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	#525×C₂₅₁	C₂
hypercenter	#525	D₂₅₁
hypocenter	C₂₅₁	#3481
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #30632421	C₂	semidirect
2. #30632391	C₂	semidirect
3. #30632382	C₂	semidirect
4. #30632380	C₂	semidirect
5. #30632368	C₂	semidirect
6. #30632365	C₂	semidirect
7. #30632364	C₂	semidirect
8. #30632326	C₂	semidirect
9. #30632324	C₂	semidirect
10. #30632319	C₂	semidirect
11. #30632233	C₂	semidirect
12. #30632217	C₂	semidirect
13. #30632215	C₂	semidirect
14. #30632196	C₂	semidirect
15. #30632194	C₂	semidirect
16. C₄×#16860809	C₂	semidirect
17. C₂×C₄×C₂²⋊D₂₅₁	C₂	semidirect
18. C₄×D₄×D₂₅₁	C₂	semidirect
19. #525×C₂₅₁	C₂	semidirect
20. C₂×#16860810	C₂²	semidirect
24. C₂²×C₄×D₂₅₁	C₂²	semidirect
25. C₂²×C₄×D₂₅₁	C₂²	semidirect
26. #22548713	C₂²	semidirect
28. #22548710	C₂²	semidirect
29. #22548710	C₂²	semidirect
30. #22548708	C₂²	semidirect
31. #22548708	C₂²	semidirect
32. #22548705	C₂²	semidirect
33. #22548705	C₂²	semidirect
34. #22548704	C₂²	semidirect
35. #22548702	C₂²	semidirect
36. #22548701	C₂²	semidirect
37. #22548701	C₂²	semidirect
38. #22548700	C₂²	semidirect
39. #22548700	C₂²	semidirect
40. #22548699	C₂²	semidirect
41. #22548697	C₂²	semidirect
42. #22548697	C₂²	semidirect
43. #22548696	C₂²	semidirect
44. #22548696	C₂²	semidirect
45. #22548696	C₂²	semidirect
46. #22548693	C₂²	semidirect
47. #22548693	C₂²	semidirect
48. #22548692	C₂²	semidirect
49. #22548692	C₂²	semidirect
50. #22548691	C₂²	semidirect
52. #22548688	C₂²	semidirect
54. #22548687	C₂²	semidirect
55. #22548687	C₂²	semidirect
56. #22548687	C₂²	semidirect
57. #22548686	C₂²	semidirect
60. #22548683	C₂²	semidirect
61. #22548683	C₂²	semidirect
62. C₄×Dic₅₀₂	C₂²	semidirect
63. #22548680	C₂²	semidirect
64. C₄×D₁₀₀₄	C₂²	semidirect
65. D₄×Dic₂₅₁	C₂²	semidirect
66. D₄×Dic₂₅₁	C₂²	semidirect
67. #22548677	C₂²	semidirect
70. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
71. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
72. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
73. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
74. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
75. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
76. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
77. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
80. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
81. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
82. #22548674	C₂²	semidirect
83. #22548673	C₂²	semidirect
84. #22548672	C₂²	semidirect
85. #22548671	C₂²	semidirect
86. #22548671	C₂²	semidirect
87. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
88. C₄⋊C₄×D₂₅₁	C₂²	semidirect
89. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
90. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
91. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
92. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
93. C₂×C₄×Dic₂₅₁	C₂²	semidirect
94. C₂×C₄×Dic₂₅₁	C₂²	semidirect
95. C₄²×D₂₅₁	C₂²	semidirect
96. C₂×#41×C₂₅₁	C₂²	semidirect
97. C₂³×C₄×C₂₅₁	C₂²	semidirect
98. #123×C₂₅₁	C₂²	semidirect
99. #123×C₂₅₁	C₂²	semidirect
100. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
101. #121×C₂₅₁	C₂²	semidirect
103. #120×C₂₅₁	C₂²	semidirect
104. C₄×D₄×C₂₅₁	C₂²	semidirect
105. C₄×D₄×C₂₅₁	C₂²	semidirect
106. #117×C₂₅₁	C₂²	semidirect
219. C₂²⋊D₂₅₁	#41	semidirect
303. C₂₅₁	#3481	semidirect
320. #525	D₂₅₁	semidirect
326. C₂×#41	C₂×D₂₅₁	semidirect
331. C₂³×C₄	C₂×D₂₅₁	semidirect
352. #123	C₂×D₂₅₁	semidirect
353. #123	C₂×D₂₅₁	semidirect
359. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
367. #121	C₂×D₂₅₁	semidirect
373. #120	C₂×D₂₅₁	semidirect
394. C₄×D₄	C₂×D₂₅₁	semidirect
395. C₄×D₄	C₂×D₂₅₁	semidirect
401. #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
#30632421	2
#30632391	2
#30632382	2
#30632380	2
#30632368	2
#30632365	2
#30632364	2
#30632326	2
#30632324	2
#30632319	2
#30632233	2
#30632217	2
#30632215	2
#30632196	2
#30632194	2
C₄×#16860809	2
C₂×C₄×C₂²⋊D₂₅₁	2
C₄×D₄×D₂₅₁	2
#525×C₂₅₁	2
#3481	251