Subgroups — #44564773

Order 32128.

1002 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632439	C₂	1	2	yes	maximal, complemented
2	#30632438	C₂	1	2	yes	maximal, complemented
3	#30632420	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632419	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632417	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632409	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632406	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632404	C₂	1	2	yes	maximal, complemented
10	D₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632352	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632350	C₂	1	2	yes	maximal, complemented
13	#30632310	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632308	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632305	C₂	1	2	yes	maximal, complemented
16	#30632304	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632301	C₂	1	2	yes	maximal, complemented
18	#30632259	C₂	1	2	yes	maximal, complemented
19	#30632257	C₂	1	2	yes	maximal, complemented
20	#30632240	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632239	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632232	C₂	1	1	yes	maximal, characteristic
23	#542×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860809	C₂²	1	2	yes	—
25	C₂²×Dic₅₀₂	C₂²	1	2	yes	—
26	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	—
27	#22548715	C₂²	1	2	yes	—
28	#22548715	C₂²	1	1	yes	characteristic
29	#22548714	C₂²	1	1	yes	characteristic
30	#22548714	C₂²	1	1	yes	characteristic
31	#22548714	C₂²	1	1	yes	characteristic
32	#22548714	C₂²	1	1	yes	characteristic
33	#22548714	C₂²	1	2	yes	—
34	#22548714	C₂²	1	2	yes	—
35	#22548714	C₂²	1	1	yes	characteristic
36	#22548714	C₂²	1	2	yes	—
37	#22548714	C₂²	1	1	yes	characteristic
38	#22548713	C₂²	1	1	yes	characteristic
39	#22548713	C₂²	1	2	yes	—
40	#22548713	C₂²	1	2	yes	—
41	#22548711	C₂²	1	1	yes	characteristic
42	#22548710	C₂²	1	2	yes	—
43	#22548710	C₂²	1	2	yes	—
44	#22548710	C₂²	1	2	yes	—
45	#22548709	C₂²	1	2	yes	—
46	#22548708	C₂²	1	2	yes	—
47	#22548708	C₂²	1	2	yes	—
48	#22548708	C₂²	1	2	yes	—
49	#22548706	C₂²	1	1	yes	characteristic
50	#22548706	C₂²	1	1	yes	characteristic
51	#22548705	C₂²	1	2	yes	—
52	#22548704	C₂²	1	1	yes	characteristic
53	#22548703	C₂²	1	1	yes	characteristic
54	#22548702	C₂²	1	2	yes	—
55	#22548702	C₂²	1	1	yes	characteristic
56	#22548701	C₂²	1	2	yes	—
57	#22548701	C₂²	1	2	yes	—
58	#22548701	C₂²	1	2	yes	—
59	#22548701	C₂²	1	2	yes	—
60	#22548701	C₂²	1	2	yes	—
61	#22548699	C₂²	1	2	yes	—
62	#22548698	C₂²	1	2	yes	—
63	#22548697	C₂²	1	2	yes	—
64	#22548697	C₂²	1	2	yes	—
65	#22548697	C₂²	1	2	yes	—
66	#22548697	C₂²	1	2	yes	—
67	#22548696	C₂²	1	2	yes	—
68	#22548695	C₂²	1	2	yes	—
69	#22548694	C₂²	1	1	yes	characteristic
70	#22548694	C₂²	1	2	yes	—
71	#22548693	C₂²	1	2	yes	—
72	#22548693	C₂²	1	2	yes	—
73	#22548693	C₂²	1	2	yes	—
74	#22548693	C₂²	1	2	yes	—
75	#22548692	C₂²	1	2	yes	—
76	#22548692	C₂²	1	1	yes	characteristic
77	#22548692	C₂²	1	1	yes	characteristic
78	#22548692	C₂²	1	1	yes	characteristic
79	#22548692	C₂²	1	1	yes	characteristic
80	#22548692	C₂²	1	2	yes	—
81	#22548692	C₂²	1	2	yes	—
82	#22548692	C₂²	1	2	yes	—
83	#22548692	C₂²	1	2	yes	—
84	#22548691	C₂²	1	2	yes	—
85	#22548689	C₂²	1	1	yes	characteristic
86	#22548687	C₂²	1	2	yes	—
87	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic
88	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic
89	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
90	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
91	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
92	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
93	C₄×Dic₅₀₂	C₂²	1	2	yes	—
94	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
95	#22548680	C₂²	1	2	yes	—
96	#22548680	C₂²	1	1	yes	characteristic
97	#22548680	C₂²	1	1	yes	characteristic
98	#22548680	C₂²	1	2	yes	—
99	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
100	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
101	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
102	#22548677	C₂²	1	1	yes	characteristic
103	#22548677	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
105	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
106	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
107	#22548674	C₂²	1	1	yes	characteristic
108	#22548672	C₂²	1	2	yes	—
109	#22548671	C₂²	1	2	yes	—
110	#22548671	C₂²	1	2	yes	—
111	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
113	#126×C₂₅₁	C₂²	1	2	yes	—
114	#124×C₂₅₁	C₂²	1	2	yes	—
115	#124×C₂₅₁	C₂²	1	1	yes	characteristic
116	#123×C₂₅₁	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
119	#121×C₂₅₁	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
122	#117×C₂₅₁	C₂²	1	1	yes	characteristic
123	#16860809	—	4	4	no	—
124	C₂×Dic₅₀₂	—	4	4	no	—
125	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
126	C₂×Dic₅₀₂	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
135	Q₈×D₂₅₁	—	4	4	no	—
136	C₂×D₁₀₀₄	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	2	yes	—
140	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
141	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
142	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
143	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
144	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
145	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
146	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
147	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
153	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
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	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
159	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
160	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
166	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
171	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
174	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
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	(C₂×D₂₅₁)⋊C₄	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	2	yes	—
189	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
191	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
192	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
193	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
194	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
195	C₄×Dic₂₅₁	C₂³	1	2	yes	—
196	C₄×Dic₂₅₁	C₂³	1	2	yes	—
197	C₄×Dic₂₅₁	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
204	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
206	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
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	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	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	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
222	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
223	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
224	C₄²×C₂₅₁	C₂³	1	2	yes	—
225	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
226	Dic₅₀₂	—	2	2	no	—
227	Dic₅₀₂	—	2	2	no	—
228	Dic₅₀₂	—	2	4	no	—
229	Dic₅₀₂	—	2	2	no	—
230	Dic₅₀₂	—	2	2	no	—
231	Dic₅₀₂	—	2	2	no	—
232	Dic₅₀₂	—	4	2	no	—
233	Dic₅₀₂	—	4	2	no	—
234	Dic₅₀₂	—	4	2	no	—
235	Dic₅₀₂	—	4	2	no	—
236	D₁₀₀₄	—	2	2	no	—
237	C₂²⋊D₂₅₁	—	2	4	no	—
238	C₂²⋊D₂₅₁	—	4	2	no	—
239	C₂²⋊D₂₅₁	—	4	2	no	—
240	C₂×Dic₂₅₁	—	2	4	no	—
241	C₂×Dic₂₅₁	—	2	2	no	—
242	C₂×Dic₂₅₁	—	2	2	no	—
243	C₂×Dic₂₅₁	—	4	2	no	—
244	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
245	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
249	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
252	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
255	C₄×D₂₅₁	—	2	4	no	—
256	C₄×D₂₅₁	—	4	2	no	—
257	C₄×D₂₅₁	—	4	2	no	—
258	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
259	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
260	Q₈×C₂₅₁	—	2	2	no	—
261	Q₈×C₂₅₁	—	4	2	no	—
262	D₄×C₂₅₁	—	2	2	no	—
263	D₄×C₂₅₁	—	4	2	no	—
264	C₂×C₄×C₂₅₁	—	2	2	no	—
265	C₂×C₄×C₂₅₁	—	4	2	no	—
266	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
269	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
272	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
274	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₂₅₁	—	2	2	no	—
276	C₂²×C₂₅₁	—	2	1	no	—
277	C₂²×C₂₅₁	—	2	1	no	—
278	C₂²×C₂₅₁	—	2	2	no	—
279	C₂²×C₂₅₁	—	2	1	no	—
280	C₂²×C₂₅₁	—	2	2	no	—
281	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
282	C₂×D₂₅₁	—	2	2	no	—
283	C₂×D₂₅₁	—	2	2	no	—
284	C₂×D₂₅₁	—	2	2	no	—
285	C₄×C₂₅₁	—	2	1	no	—
286	C₄×C₂₅₁	—	2	2	no	—
287	C₄×C₂₅₁	—	2	2	no	—
288	C₄×C₂₅₁	—	2	1	no	—
289	C₄×C₂₅₁	—	2	1	no	—
290	C₄×C₂₅₁	—	2	2	no	—
291	C₄×C₂₅₁	—	2	1	no	—
292	C₄×C₂₅₁	—	2	1	no	—
293	C₄×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
294	Dic₂₅₁	—	2	1	no	—
295	Dic₂₅₁	—	2	2	no	—
296	Dic₂₅₁	—	2	1	no	—
297	Dic₂₅₁	—	2	2	no	—
298	Dic₂₅₁	—	2	1	no	—
299	Dic₂₅₁	—	2	1	no	—
300	Dic₂₅₁	—	2	1	no	—
301	Dic₂₅₁	—	2	1	no	—
302	Dic₂₅₁	—	2	2	no	—
303	Dic₂₅₁	H(5,𝔽₂)	1	2	yes	—
304	Dic₂₅₁	2₋¹⁺⁴	1	2	yes	—
305	C₂×C₂₅₁	—	4	2	no	—
306	C₂×C₂₅₁	—	4	1	no	—
307	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	D₂₅₁	—	4	2	no	—
311	C₂₅₁	#3550	1	1	yes	characteristic, complemented, Sylow
312	#3550	—	251	1	no	maximal, Sylow
313	#563	—	251	2	no	—
314	#563	—	251	2	no	—
315	#559	—	251	1	no	—
316	#559	—	251	1	no	—
317	Q₈²	—	251	1	no	—
318	Q₈²	—	251	1	no	—
319	#556	—	251	2	no	—
320	#556	—	251	1	no	—
321	#556	—	251	1	no	—
322	D₄×Q₈	—	251	1	no	—
323	D₄×Q₈	—	251	2	no	—
324	D₄×Q₈	—	251	1	no	—
325	#542	—	251	2	no	—
326	#542	—	251	2	no	—
327	#542	—	251	1	no	—
328	#542	—	251	1	no	—
329	#542	—	251	1	no	—
330	#542	D₂₅₁	1	1	yes	characteristic, complemented
331	#536	—	251	2	no	—
332	#536	—	251	2	no	—
333	#533	—	251	1	no	—
334	#533	—	251	1	no	—
335	#532	—	251	1	no	—
336	C₂×#41	—	251	2	no	—
337	C₂²×Q₈	—	251	2	no	—
338	C₂²×Q₈	—	251	2	no	—
339	C₄⋊Q₈	—	251	1	no	—
340	C₄⋊Q₈	—	251	2	no	—
341	C₄⋊Q₈	—	251	2	no	—
342	C₄⋊Q₈	—	251	1	no	—
343	C₄⋊Q₈	—	251	1	no	—
344	C₄⋊Q₈	—	251	1	no	—
345	C₄⋊Q₈	—	251	1	no	—
346	C₄⋊Q₈	—	251	2	no	—
347	C₄⋊Q₈	—	251	2	no	—
348	C₄⋊Q₈	—	251	2	no	—
349	C₄⋊Q₈	—	251	1	no	—
350	C₄⋊Q₈	—	251	1	no	—
351	C₄⋊Q₈	—	251	2	no	—
352	C₄⋊Q₈	—	251	1	no	—
353	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
354	#127	—	251	1	no	—
355	#126	—	251	2	no	—
356	#126	—	251	2	no	—
357	#126	—	251	2	no	—
358	#126	—	251	2	no	—
359	#126	—	251	2	no	—
360	#126	—	251	2	no	—
361	#126	—	251	2	no	—
362	#126	C₂×D₂₅₁	1	2	yes	—
363	#125	—	251	2	no	—
364	#125	—	251	1	no	—
365	#125	—	251	1	no	—
366	#124	—	251	1	no	—
367	#124	—	251	2	no	—
368	#124	—	251	1	no	—
369	#124	—	251	2	no	—
370	#124	—	251	2	no	—
371	#124	—	251	2	no	—
372	#124	—	251	2	no	—
373	#124	—	251	2	no	—
374	#124	—	251	1	no	—
375	#124	C₂×D₂₅₁	1	2	yes	—
376	#124	C₂×D₂₅₁	1	1	yes	characteristic
377	#123	—	251	2	no	—
378	#123	—	251	2	no	—
379	#123	—	251	2	no	—
380	#123	—	251	2	no	—
381	#123	—	251	2	no	—
382	#123	—	251	2	no	—
383	#123	—	251	2	no	—
384	#123	C₂×D₂₅₁	1	2	yes	—
385	C₂²⋊Q₈	—	251	2	no	—
386	C₂²⋊Q₈	—	251	1	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	C₂²⋊Q₈	—	251	2	no	—
394	C₂²⋊Q₈	—	251	1	no	—
395	C₂²⋊Q₈	—	251	1	no	—
396	C₂²⋊Q₈	—	251	1	no	—
397	C₂²⋊Q₈	—	251	1	no	—
398	C₂²⋊Q₈	—	251	2	no	—
399	C₂²⋊Q₈	—	251	2	no	—
400	C₂²⋊Q₈	—	251	2	no	—
401	C₂²⋊Q₈	—	251	2	no	—
402	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
403	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	—
404	#121	—	251	2	no	—
405	#121	—	251	1	no	—
406	#121	C₂×D₂₅₁	1	1	yes	characteristic
407	C₄×Q₈	—	251	1	no	—
408	C₄×Q₈	—	251	1	no	—
409	C₄×Q₈	—	251	2	no	—
410	C₄×Q₈	—	251	1	no	—
411	C₄×Q₈	—	251	2	no	—
412	C₄×Q₈	—	251	1	no	—
413	C₄×Q₈	—	251	1	no	—
414	C₄×Q₈	—	251	1	no	—
415	C₄×Q₈	—	251	1	no	—
416	C₄×Q₈	—	251	1	no	—
417	C₄×Q₈	—	251	2	no	—
418	C₄×Q₈	—	251	1	no	—
419	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
420	C₄×D₄	—	251	1	no	—
421	C₄×D₄	—	251	1	no	—
422	C₄×D₄	—	251	2	no	—
423	C₄×D₄	—	251	1	no	—
424	C₄×D₄	—	251	1	no	—
425	C₄×D₄	—	251	2	no	—
426	C₄×D₄	—	251	2	no	—
427	C₄×D₄	—	251	1	no	—
428	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
429	#117	—	251	1	no	—
430	#117	—	251	2	no	—
431	#117	—	251	2	no	—
432	#117	—	251	2	no	—
433	#117	C₂×D₂₅₁	1	1	yes	characteristic
434	C₂×C₄²	—	251	1	no	—
435	#41	—	1004	4	no	—
436	C₂×Q₈	—	1004	4	no	—
437	C₂×Q₈	—	1004	4	no	—
438	C₂×Q₈	—	251	2	no	—
439	C₂×Q₈	—	251	2	no	—
440	C₂×Q₈	—	251	2	no	—
441	C₂×Q₈	—	251	2	no	—
442	C₂×Q₈	—	251	1	no	—
443	C₂×Q₈	—	251	1	no	—
444	C₂×Q₈	—	251	1	no	—
445	C₂×Q₈	—	251	2	no	—
446	C₂×Q₈	—	251	1	no	—
447	C₂×Q₈	—	251	1	no	—
448	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
449	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
450	C₂×D₄	—	251	2	no	—
451	C₂×D₄	—	251	2	no	—
452	C₂×D₄	—	251	2	no	—
453	C₂×D₄	—	251	1	no	—
454	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
456	C₂²×C₄	—	251	2	no	—
457	C₂²×C₄	—	251	2	no	—
458	C₂²×C₄	—	251	2	no	—
459	C₂²×C₄	—	251	1	no	—
460	C₂²×C₄	—	251	1	no	—
461	C₂²×C₄	—	251	2	no	—
462	C₂²×C₄	—	251	2	no	—
463	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
465	C₄⋊C₄	—	251	2	no	—
466	C₄⋊C₄	—	251	1	no	—
467	C₄⋊C₄	—	251	1	no	—
468	C₄⋊C₄	—	251	2	no	—
469	C₄⋊C₄	—	251	2	no	—
470	C₄⋊C₄	—	251	1	no	—
471	C₄⋊C₄	—	251	1	no	—
472	C₄⋊C₄	—	251	1	no	—
473	C₄⋊C₄	—	251	1	no	—
474	C₄⋊C₄	—	251	2	no	—
475	C₄⋊C₄	—	251	2	no	—
476	C₄⋊C₄	—	251	1	no	—
477	C₄⋊C₄	—	251	1	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	1	no	—
485	C₄⋊C₄	—	251	1	no	—
486	C₄⋊C₄	—	251	1	no	—
487	C₄⋊C₄	—	251	1	no	—
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	1	no	—
493	C₄⋊C₄	—	251	1	no	—
494	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
499	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
500	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
501	C₂²⋊C₄	—	251	2	no	—
502	C₂²⋊C₄	—	251	1	no	—
503	C₂²⋊C₄	—	251	1	no	—
504	C₂²⋊C₄	—	251	2	no	—
505	C₂²⋊C₄	—	251	2	no	—
506	C₂²⋊C₄	—	251	2	no	—
507	C₂²⋊C₄	—	251	2	no	—
508	C₂²⋊C₄	—	251	2	no	—
509	C₂²⋊C₄	—	251	2	no	—
510	C₂²⋊C₄	—	251	2	no	—
511	C₂²⋊C₄	—	251	2	no	—
512	C₂²⋊C₄	—	251	2	no	—
513	C₂²⋊C₄	—	251	2	no	—
514	C₂²⋊C₄	—	251	2	no	—
515	C₂²⋊C₄	—	251	2	no	—
516	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
523	C₄²	—	251	1	no	—
524	C₄²	—	251	1	no	—
525	C₄²	—	251	1	no	—
526	C₄²	—	251	1	no	—
527	C₄²	—	251	1	no	—
528	C₄²	—	251	1	no	—
529	C₄²	—	251	2	no	—
530	C₄²	—	251	2	no	—
531	C₄²	—	251	2	no	—
532	C₄²	—	251	2	no	—
533	C₄²	—	251	2	no	—
534	C₄²	C₂²×D₂₅₁	1	2	yes	—
535	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
536	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
537	C₂³	—	251	2	no	—
538	C₂³	C₂³×D₂₅₁	1	2	yes	—
539	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
540	Q₈	—	2	2	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	1004	2	no	—
543	Q₈	—	1004	2	no	—
544	Q₈	—	1004	2	no	—
545	Q₈	—	1004	2	no	—
546	Q₈	—	502	2	no	—
547	Q₈	—	502	4	no	—
548	Q₈	—	502	2	no	—
549	Q₈	—	502	2	no	—
550	Q₈	—	502	2	no	—
551	Q₈	—	502	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	1004	2	no	—
555	D₄	—	1004	2	no	—
556	D₄	—	502	4	no	—
557	D₄	—	502	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	1004	2	no	—
561	C₂×C₄	—	1004	2	no	—
562	C₂×C₄	—	1004	2	no	—
563	C₂×C₄	—	502	4	no	—
564	C₂×C₄	—	502	4	no	—
565	C₂×C₄	—	502	2	no	—
566	C₂×C₄	—	502	2	no	—
567	C₂×C₄	—	251	1	no	—
568	C₂×C₄	—	251	1	no	—
569	C₂×C₄	—	251	2	no	—
570	C₂×C₄	—	251	1	no	—
571	C₂×C₄	—	251	2	no	—
572	C₂×C₄	—	251	1	no	—
573	C₂×C₄	—	251	1	no	—
574	C₂×C₄	—	251	2	no	—
575	C₂×C₄	—	251	1	no	—
576	C₂×C₄	—	251	1	no	—
577	C₂×C₄	—	251	1	no	—
578	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
579	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
582	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
583	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
587	C₂²	—	2	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	502	2	no	—
594	C₂²	—	502	2	no	—
595	C₂²	—	502	2	no	—
596	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	2	no	—
605	C₄	—	502	1	no	—
606	C₄	—	502	2	no	—
607	C₄	—	502	1	no	—
608	C₄	—	502	1	no	—
609	C₄	—	502	2	no	—
610	C₄	—	502	1	no	—
611	C₄	—	502	1	no	—
612	C₄	—	502	1	no	—
613	C₄	—	502	2	no	—
614	C₄	—	251	2	no	—
615	C₄	—	251	2	no	—
616	C₄	#22548762	1	2	yes	—
617	C₂	—	4	2	no	—
618	C₂	—	4	1	no	—
619	C₂	—	1004	2	no	—
620	C₂	H(5,𝔽₂)×D₂₅₁	1	1	yes	characteristic
621	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic
622	C₂	C₂×#22548762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#542×C₂₅₁	C₂
prime radical	#30632232	C₂
hypercenter	#542	D₂₅₁
hypocenter	C₂₅₁	#3550
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #30632439	C₂	semidirect
2. #30632438	C₂	semidirect
3. #30632420	C₂	semidirect
4. #30632419	C₂	semidirect
5. Q₈×Dic₅₀₂	C₂	semidirect
6. #30632417	C₂	semidirect
7. #30632409	C₂	semidirect
8. #30632406	C₂	semidirect
9. #30632404	C₂	semidirect
10. D₄×Dic₅₀₂	C₂	semidirect
11. #30632352	C₂	semidirect
12. #30632350	C₂	semidirect
13. #30632310	C₂	semidirect
14. #30632308	C₂	semidirect
15. #30632305	C₂	semidirect
16. #30632304	C₂	semidirect
17. #30632301	C₂	semidirect
18. #30632259	C₂	semidirect
19. #30632257	C₂	semidirect
20. #30632240	C₂	semidirect
21. #30632239	C₂	semidirect
23. #542×C₂₅₁	C₂	semidirect
311. C₂₅₁	#3550	semidirect
330. #542	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632439	2
#30632438	2
#30632420	2
#30632419	2
Q₈×Dic₅₀₂	2
#30632417	2
#30632409	2
#30632406	2
#30632404	2
D₄×Dic₅₀₂	2
#30632352	2
#30632350	2
#30632310	2
#30632308	2
#30632305	2
#30632304	2
#30632301	2
#30632259	2
#30632257	2
#30632240	2
#30632239	2
#30632232	2
#542×C₂₅₁	2
#3550	251