Subgroups — #44565149

Order 32128.

1412 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#22548762	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632503	C₂	1	4	yes	maximal, complemented
4	#30632501	C₂	1	4	yes	maximal, complemented
5	#30632497	C₂	1	4	yes	maximal, complemented
6	#30632494	C₂	1	4	yes	maximal, complemented
7	#30632485	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632483	C₂	1	4	yes	maximal, complemented
9	C₂×#22548748	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#22548745	C₂	1	1	yes	maximal, characteristic, complemented
11	#137×D₂₅₁	C₂	1	4	yes	maximal, complemented
12	#30632453	C₂	1	1	yes	maximal, characteristic, complemented
13	#575×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#22548763	C₂²	1	2	yes	complemented
15	#22548762	—	2	2	no	—
16	#22548762	—	2	2	no	—
17	#22548762	—	2	1	no	—
18	#22548762	C₂²	1	4	yes	complemented
19	#22548762	C₂²	1	4	yes	complemented
20	#22548762	C₂²	1	2	yes	complemented
21	#22548761	—	2	1	no	—
22	#22548761	C₂²	1	2	yes	complemented
23	#22548760	—	2	2	no	—
24	#22548760	C₂²	1	2	yes	complemented
25	C₂×#16860810	—	2	2	no	—
26	C₂×#16860810	—	2	1	no	—
27	C₂×#16860810	C₂²	1	1	yes	characteristic
28	C₂×#16860810	C₂²	1	1	yes	characteristic
29	C₂×#16860809	—	2	2	no	—
30	C₂×#16860809	C₂²	1	2	yes	complemented
31	#41×D₂₅₁	—	2	2	no	—
32	#41×D₂₅₁	C₂²	1	4	yes	—
33	C₂²×Dic₅₀₂	—	2	1	no	—
34	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
35	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	complemented
36	#22548748	C₂²	1	4	yes	complemented
37	#22548748	C₂²	1	4	yes	complemented
38	#22548747	C₂²	1	8	yes	complemented
39	#22548746	C₂²	1	2	yes	complemented
40	#22548745	C₂²	1	4	yes	complemented
41	#22548745	C₂²	1	4	yes	complemented
42	#22548745	C₂²	1	2	yes	complemented
43	#22548744	C₂²	1	8	yes	complemented
44	#22548744	C₂²	1	8	yes	complemented
45	#22548741	C₂²	1	2	yes	complemented
46	#22548740	C₂²	1	2	yes	complemented
47	#22548739	C₂²	1	8	yes	complemented
48	#22548736	C₂²	1	8	yes	complemented
49	#22548735	C₂²	1	4	yes	complemented
50	#22548734	C₂²	1	8	yes	complemented
51	C₂×Dic₁₀₀₄	C₂²	1	2	yes	complemented
52	C₂×#16860800	C₂²	1	2	yes	complemented
53	Q₁₆×D₂₅₁	C₂²	1	8	yes	complemented
54	C₂×#16860799	C₂²	1	2	yes	complemented
55	C₂×#16860798	C₂²	1	2	yes	complemented
56	SD₁₆×D₂₅₁	C₂²	1	8	yes	complemented
57	#22548723	C₂²	1	4	yes	complemented
58	#22548721	C₂²	1	4	yes	complemented
59	C₂×#16860794	C₂²	1	1	yes	characteristic, complemented
60	M₁₆×D₂₅₁	C₂²	1	4	yes	complemented
61	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
62	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
63	#137×C₂₅₁	C₂²	1	2	yes	complemented
64	#137×C₂₅₁	C₂²	1	2	yes	complemented
65	AGL(1,ℤ/8)×C₂₅₁	C₂²	1	2	yes	complemented
66	AGL(1,ℤ/8)×C₂₅₁	C₂²	1	2	yes	complemented
67	#135×C₂₅₁	C₂²	1	4	yes	complemented
68	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
69	#16860811	—	2	2	no	—
70	#16860811	C₂³	1	4	yes	—
71	#16860810	—	2	2	no	—
72	#16860810	—	2	2	no	—
73	#16860810	—	2	4	no	—
74	#16860810	—	2	4	no	—
75	#16860810	—	2	4	no	—
76	#16860810	—	2	4	no	—
77	#16860810	—	2	1	no	—
78	#16860810	—	2	1	no	—
79	#16860810	D₄	1	2	yes	—
80	#16860810	D₄	1	2	yes	—
81	#16860810	C₂³	1	2	yes	—
82	#16860810	C₂³	1	2	yes	—
83	#16860810	C₂³	1	2	yes	—
84	#16860810	C₂³	1	2	yes	—
85	#16860809	—	2	2	no	—
86	#16860809	—	2	4	no	—
87	#16860809	—	2	8	no	—
88	#16860809	—	2	8	no	—
89	#16860809	—	2	4	no	—
90	#16860809	—	2	4	no	—
91	#16860809	C₂³	1	8	yes	—
92	#16860809	C₂³	1	4	yes	—
93	C₂×Dic₅₀₂	—	2	4	no	—
94	C₂×Dic₅₀₂	—	2	4	no	—
95	C₂×Dic₅₀₂	—	2	2	no	—
96	C₂×Dic₅₀₂	—	2	2	no	—
97	C₂×Dic₅₀₂	—	2	1	no	—
98	C₂×Dic₅₀₂	—	2	1	no	—
99	C₂×Dic₅₀₂	—	2	1	no	—
100	C₂×Dic₅₀₂	D₄	1	1	yes	characteristic
101	C₂×Dic₅₀₂	C₂³	1	2	yes	—
102	C₂×Dic₅₀₂	C₂³	1	2	yes	—
103	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
104	C₂×Dic₅₀₂	C₂³	1	2	yes	—
105	Q₈×D₂₅₁	—	2	2	no	—
106	Q₈×D₂₅₁	—	2	4	no	—
107	Q₈×D₂₅₁	C₂³	1	4	yes	—
108	Q₈×D₂₅₁	C₂³	1	8	yes	—
109	C₂×D₁₀₀₄	—	2	2	no	—
110	C₂×D₁₀₀₄	D₄	1	1	yes	characteristic
111	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
113	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
114	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
115	C₂×C₂²⋊D₂₅₁	D₄	1	2	yes	—
116	D₄×D₂₅₁	—	2	4	no	—
117	D₄×D₂₅₁	—	2	2	no	—
118	D₄×D₂₅₁	—	2	4	no	—
119	D₄×D₂₅₁	C₂³	1	4	yes	—
120	C₂²×Dic₂₅₁	—	2	2	no	—
121	C₂²×Dic₂₅₁	—	2	1	no	—
122	C₂×C₄×D₂₅₁	—	2	2	no	—
123	C₂×C₄×D₂₅₁	—	2	4	no	—
124	C₂×C₄×D₂₅₁	—	2	1	no	—
125	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
126	Dic₁₀₀₄	C₂³	1	8	yes	—
127	#16860800	C₂³	1	8	yes	—
128	#16860800	C₂³	1	4	yes	—
129	#16860799	C₂³	1	8	yes	—
130	#16860798	C₂³	1	8	yes	—
131	#16860798	C₂³	1	4	yes	—
132	#16860797	C₂³	1	4	yes	—
133	#16860795	C₂³	1	4	yes	—
134	#16860794	C₂³	1	2	yes	—
135	#16860794	C₂³	1	2	yes	—
136	#16860793	C₂³	1	8	yes	—
137	C₂×C₂₅₁⋊C₈	C₂³	1	2	yes	—
138	C₈×D₂₅₁	C₂³	1	8	yes	—
139	#41×C₂₅₁	—	2	1	no	—
140	#41×C₂₅₁	—	2	1	no	—
141	#41×C₂₅₁	—	2	1	no	—
142	#41×C₂₅₁	—	2	1	no	—
143	#41×C₂₅₁	C₂³	1	2	yes	—
144	#41×C₂₅₁	C₂³	1	2	yes	—
145	#41×C₂₅₁	C₂³	1	2	yes	—
146	#41×C₂₅₁	C₂³	1	2	yes	—
147	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
148	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
149	C₂×D₄×C₂₅₁	—	2	1	no	—
150	C₂×D₄×C₂₅₁	—	2	1	no	—
151	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
152	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
153	C₂²×C₄×C₂₅₁	—	2	1	no	—
154	C₂²×C₄×C₂₅₁	—	2	1	no	—
155	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
156	Q₁₆×C₂₅₁	C₂³	1	4	yes	—
157	SD₁₆×C₂₅₁	C₂³	1	4	yes	—
158	SD₁₆×C₂₅₁	C₂³	1	4	yes	—
159	D₈×C₂₅₁	C₂³	1	4	yes	—
160	M₁₆×C₂₅₁	C₂³	1	2	yes	—
161	M₁₆×C₂₅₁	C₂³	1	2	yes	—
162	C₂×C₈×C₂₅₁	C₂³	1	2	yes	—
163	C₂²×D₂₅₁	—	2	1	no	—
164	C₂²×D₂₅₁	—	2	4	no	—
165	C₂²×D₂₅₁	C₂×D₄	1	2	yes	—
166	Dic₅₀₂	—	2	2	no	—
167	Dic₅₀₂	—	2	2	no	—
168	Dic₅₀₂	—	2	2	no	—
169	Dic₅₀₂	—	2	1	no	—
170	Dic₅₀₂	—	2	8	no	—
171	Dic₅₀₂	—	2	4	no	—
172	Dic₅₀₂	C₂×D₄	1	2	yes	—
173	Dic₅₀₂	C₂×D₄	1	2	yes	—
174	Dic₅₀₂	C₂⁴	1	4	yes	—
175	Dic₅₀₂	C₂⁴	1	2	yes	—
176	D₁₀₀₄	—	2	4	no	—
177	D₁₀₀₄	—	2	1	no	—
178	D₁₀₀₄	C₂×D₄	1	2	yes	—
179	D₁₀₀₄	C₂×D₄	1	2	yes	—
180	D₁₀₀₄	C₂⁴	1	2	yes	—
181	C₂²⋊D₂₅₁	—	2	2	no	—
182	C₂²⋊D₂₅₁	—	2	2	no	—
183	C₂²⋊D₂₅₁	—	2	4	no	—
184	C₂²⋊D₂₅₁	—	2	8	no	—
185	C₂²⋊D₂₅₁	—	2	4	no	—
186	C₂²⋊D₂₅₁	C₂×D₄	1	4	yes	—
187	C₂²⋊D₂₅₁	C₂×D₄	1	4	yes	—
188	C₂×Dic₂₅₁	—	2	2	no	—
189	C₂×Dic₂₅₁	—	2	1	no	—
190	C₂×Dic₂₅₁	—	2	2	no	—
191	C₂×Dic₂₅₁	—	2	2	no	—
192	C₂×Dic₂₅₁	—	2	4	no	—
193	C₂×Dic₂₅₁	—	2	8	no	—
194	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
195	C₄×D₂₅₁	—	2	4	no	—
196	C₄×D₂₅₁	—	2	8	no	—
197	C₄×D₂₅₁	—	2	2	no	—
198	C₄×D₂₅₁	—	2	2	no	—
199	C₄×D₂₅₁	—	2	4	no	—
200	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
201	C₄×D₂₅₁	C₂⁴	1	4	yes	—
202	C₂₅₁⋊C₈	C₂⁴	1	4	yes	—
203	C₂³×C₂₅₁	—	2	1	no	—
204	C₂³×C₂₅₁	—	2	1	no	—
205	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
206	Q₈×C₂₅₁	—	2	1	no	—
207	Q₈×C₂₅₁	—	2	1	no	—
208	Q₈×C₂₅₁	C₂⁴	1	2	yes	—
209	Q₈×C₂₅₁	C₂⁴	1	2	yes	—
210	D₄×C₂₅₁	—	2	2	no	—
211	D₄×C₂₅₁	—	2	2	no	—
212	D₄×C₂₅₁	—	2	2	no	—
213	D₄×C₂₅₁	—	2	2	no	—
214	D₄×C₂₅₁	—	2	1	no	—
215	D₄×C₂₅₁	—	2	1	no	—
216	D₄×C₂₅₁	C₂⁴	1	2	yes	—
217	D₄×C₂₅₁	C₂⁴	1	2	yes	—
218	C₂×C₄×C₂₅₁	—	2	1	no	—
219	C₂×C₄×C₂₅₁	—	2	1	no	—
220	C₂×C₄×C₂₅₁	—	2	2	no	—
221	C₂×C₄×C₂₅₁	—	2	2	no	—
222	C₂×C₄×C₂₅₁	—	2	2	no	—
223	C₂×C₄×C₂₅₁	—	2	2	no	—
224	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
225	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
226	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
227	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
230	C₈×C₂₅₁	C₂⁴	1	4	yes	—
231	C₂²×C₂₅₁	—	2	2	no	—
232	C₂²×C₂₅₁	—	2	2	no	—
233	C₂²×C₂₅₁	—	4	1	no	—
234	C₂²×C₂₅₁	—	4	2	no	—
235	C₂²×C₂₅₁	—	8	1	no	—
236	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
237	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
238	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×D₂₅₁	—	2	2	no	—
240	C₂×D₂₅₁	—	4	2	no	—
241	C₂×D₂₅₁	—	8	4	no	—
242	C₂×D₂₅₁	—	8	1	no	—
243	C₂×D₂₅₁	C₂²×D₄	1	4	yes	—
244	C₄×C₂₅₁	—	2	2	no	—
245	C₄×C₂₅₁	—	2	2	no	—
246	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
247	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
248	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
249	C₄×C₂₅₁	C₂⁵	1	1	yes	characteristic
250	Dic₂₅₁	—	2	2	no	—
251	Dic₂₅₁	—	2	4	no	—
252	Dic₂₅₁	C₂²×D₄	1	4	yes	—
253	C₂×C₂₅₁	—	2	1	no	—
254	C₂×C₂₅₁	—	2	1	no	—
255	C₂×C₂₅₁	—	2	1	no	—
256	C₂×C₂₅₁	—	4	2	no	—
257	C₂×C₂₅₁	—	4	2	no	—
258	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
259	D₂₅₁	—	2	4	no	—
260	D₂₅₁	—	4	2	no	—
261	C₂₅₁	#3586	1	1	yes	characteristic, complemented, Sylow
262	#3586	—	251	1	no	maximal, Sylow
263	#585	—	251	1	no	—
264	C₂×2₋¹⁺⁴	—	251	1	no	—
265	#578	—	251	4	no	—
266	#578	—	251	4	no	—
267	#577	—	251	4	no	—
268	#577	—	251	4	no	—
269	#575	—	251	1	no	—
270	#575	—	251	4	no	—
271	#575	D₂₅₁	1	1	yes	characteristic, complemented
272	C₂×#137	—	251	1	no	—
273	C₂×#137	—	251	4	no	—
274	C₂×#137	—	251	1	no	—
275	#568	—	251	1	no	—
276	2₋¹⁺⁴	—	502	2	no	—
277	2₋¹⁺⁴	—	502	2	no	—
278	2₋¹⁺⁴	—	502	1	no	—
279	2₋¹⁺⁴	—	251	4	no	—
280	2₋¹⁺⁴	—	251	4	no	—
281	2₋¹⁺⁴	—	251	2	no	—
282	2₋¹⁺⁴	—	251	2	no	—
283	H(5,𝔽₂)	—	502	2	no	—
284	H(5,𝔽₂)	—	502	1	no	—
285	H(5,𝔽₂)	—	251	2	no	—
286	H(5,𝔽₂)	—	251	2	no	—
287	C₂×#41	—	502	2	no	—
288	C₂×#41	—	502	1	no	—
289	C₂×#41	—	502	2	no	—
290	C₂×#41	—	502	2	no	—
291	C₂×#41	—	251	4	no	—
292	C₂×#41	—	251	2	no	—
293	C₂×#41	—	251	1	no	—
294	C₂×#41	—	251	1	no	—
295	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
296	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
297	C₂²×Q₈	—	502	1	no	—
298	C₂²×Q₈	—	251	2	no	—
299	C₂²×Q₈	—	251	1	no	—
300	#137	—	251	4	no	—
301	#137	—	251	4	no	—
302	#137	—	251	2	no	—
303	#137	—	251	2	no	—
304	#137	—	251	8	no	—
305	#137	—	251	8	no	—
306	#137	—	251	8	no	—
307	#137	—	251	4	no	—
308	#137	—	251	4	no	—
309	#137	C₂×D₂₅₁	1	2	yes	complemented
310	#137	C₂×D₂₅₁	1	2	yes	complemented
311	AGL(1,ℤ/8)	—	251	2	no	—
312	AGL(1,ℤ/8)	—	251	2	no	—
313	AGL(1,ℤ/8)	—	251	8	no	—
314	AGL(1,ℤ/8)	C₂×D₂₅₁	1	2	yes	complemented
315	AGL(1,ℤ/8)	C₂×D₂₅₁	1	2	yes	complemented
316	#135	—	251	4	no	—
317	#135	—	251	8	no	—
318	#135	—	251	8	no	—
319	#135	C₂×D₂₅₁	1	4	yes	complemented
320	C₂×Q₁₆	—	251	2	no	—
321	C₂×Q₁₆	—	251	8	no	—
322	C₂×Q₁₆	—	251	2	no	—
323	C₂×SD₁₆	—	251	2	no	—
324	C₂×SD₁₆	—	251	8	no	—
325	C₂×SD₁₆	—	251	2	no	—
326	#131	—	251	4	no	—
327	#131	—	251	4	no	—
328	C₂×M₁₆	—	251	1	no	—
329	C₂×M₁₆	—	251	4	no	—
330	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	2	1	no	—
334	#41	—	2	1	no	—
335	#41	—	502	2	no	—
336	#41	—	502	4	no	—
337	#41	—	502	2	no	—
338	#41	—	502	4	no	—
339	#41	—	502	4	no	—
340	#41	—	502	4	no	—
341	#41	—	502	2	no	—
342	#41	—	502	4	no	—
343	#41	—	502	8	no	—
344	#41	—	502	8	no	—
345	#41	—	502	2	no	—
346	#41	—	502	4	no	—
347	#41	—	502	4	no	—
348	#41	—	502	1	no	—
349	#41	—	502	1	no	—
350	#41	—	251	4	no	—
351	#41	—	251	8	no	—
352	#41	—	251	4	no	—
353	#41	—	251	2	no	—
354	#41	—	251	2	no	—
355	#41	—	251	2	no	—
356	#41	—	251	2	no	—
357	#41	—	251	2	no	—
358	#41	—	251	2	no	—
359	#41	C₂²×D₂₅₁	1	2	yes	—
360	#41	C₂²×D₂₅₁	1	2	yes	—
361	#41	C₂²×D₂₅₁	1	2	yes	—
362	#41	C₂²×D₂₅₁	1	2	yes	—
363	C₂×Q₈	—	502	4	no	—
364	C₂×Q₈	—	502	4	no	—
365	C₂×Q₈	—	502	2	no	—
366	C₂×Q₈	—	502	2	no	—
367	C₂×Q₈	—	502	2	no	—
368	C₂×Q₈	—	502	4	no	—
369	C₂×Q₈	—	502	1	no	—
370	C₂×Q₈	—	502	1	no	—
371	C₂×Q₈	—	502	1	no	—
372	C₂×Q₈	—	251	8	no	—
373	C₂×Q₈	—	251	4	no	—
374	C₂×Q₈	—	251	2	no	—
375	C₂×Q₈	—	251	2	no	—
376	C₂×Q₈	—	251	1	no	—
377	C₂×Q₈	—	251	2	no	—
378	C₂×Q₈	—	251	1	no	—
379	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
380	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	502	2	no	—
384	C₂×D₄	—	502	4	no	—
385	C₂×D₄	—	502	4	no	—
386	C₂×D₄	—	502	2	no	—
387	C₂×D₄	—	502	2	no	—
388	C₂×D₄	—	502	1	no	—
389	C₂×D₄	—	502	4	no	—
390	C₂×D₄	—	251	4	no	—
391	C₂×D₄	—	251	2	no	—
392	C₂×D₄	—	251	1	no	—
393	C₂×D₄	—	251	1	no	—
394	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
395	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	502	2	no	—
399	C₂²×C₄	—	502	4	no	—
400	C₂²×C₄	—	502	1	no	—
401	C₂²×C₄	—	502	2	no	—
402	C₂²×C₄	—	502	1	no	—
403	C₂²×C₄	—	251	2	no	—
404	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
405	Q₁₆	—	251	8	no	—
406	Q₁₆	—	251	4	no	—
407	Q₁₆	—	251	8	no	—
408	Q₁₆	C₂²×D₂₅₁	1	4	yes	—
409	SD₁₆	—	251	4	no	—
410	SD₁₆	—	251	8	no	—
411	SD₁₆	—	251	4	no	—
412	SD₁₆	—	251	8	no	—
413	SD₁₆	C₂²×D₂₅₁	1	4	yes	—
414	SD₁₆	C₂²×D₂₅₁	1	4	yes	—
415	D₈	—	251	4	no	—
416	D₈	C₂²×D₂₅₁	1	4	yes	—
417	M₁₆	—	251	2	no	—
418	M₁₆	—	251	2	no	—
419	M₁₆	—	251	8	no	—
420	M₁₆	C₂²×D₂₅₁	1	2	yes	—
421	M₁₆	C₂²×D₂₅₁	1	2	yes	—
422	C₂×C₈	—	251	2	no	—
423	C₂×C₈	—	251	8	no	—
424	C₂×C₈	C₂²×D₂₅₁	1	2	yes	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	502	4	no	—
428	C₂³	—	502	1	no	—
429	C₂³	—	251	2	no	—
430	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
431	Q₈	—	2	1	no	—
432	Q₈	—	2	1	no	—
433	Q₈	—	502	8	no	—
434	Q₈	—	502	4	no	—
435	Q₈	—	502	2	no	—
436	Q₈	—	502	2	no	—
437	Q₈	—	502	2	no	—
438	Q₈	—	502	1	no	—
439	Q₈	—	251	4	no	—
440	Q₈	—	251	2	no	—
441	Q₈	—	251	2	no	—
442	Q₈	—	251	2	no	—
443	Q₈	C₂³×D₂₅₁	1	2	yes	—
444	Q₈	C₂³×D₂₅₁	1	2	yes	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	1	no	—
450	D₄	—	2	1	no	—
451	D₄	—	502	4	no	—
452	D₄	—	502	4	no	—
453	D₄	—	502	8	no	—
454	D₄	—	502	2	no	—
455	D₄	—	502	2	no	—
456	D₄	—	502	4	no	—
457	D₄	—	502	1	no	—
458	D₄	—	251	4	no	—
459	D₄	—	251	4	no	—
460	D₄	—	251	2	no	—
461	D₄	—	251	2	no	—
462	D₄	—	251	2	no	—
463	D₄	C₂³×D₂₅₁	1	2	yes	—
464	D₄	C₂³×D₂₅₁	1	2	yes	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	502	4	no	—
472	C₂×C₄	—	502	8	no	—
473	C₂×C₄	—	502	4	no	—
474	C₂×C₄	—	502	2	no	—
475	C₂×C₄	—	502	1	no	—
476	C₂×C₄	—	502	2	no	—
477	C₂×C₄	—	502	2	no	—
478	C₂×C₄	—	502	4	no	—
479	C₂×C₄	—	502	8	no	—
480	C₂×C₄	—	502	2	no	—
481	C₂×C₄	—	502	2	no	—
482	C₂×C₄	—	251	2	no	—
483	C₂×C₄	—	251	4	no	—
484	C₂×C₄	—	251	4	no	—
485	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
486	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
487	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
488	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
489	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
490	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
491	C₈	—	251	4	no	—
492	C₈	C₂³×D₂₅₁	1	4	yes	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	2008	1	no	—
499	C₂²	—	2008	4	no	—
500	C₂²	—	1004	2	no	—
501	C₂²	—	502	2	no	—
502	C₂²	—	251	4	no	—
503	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
504	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
505	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	502	2	no	—
509	C₄	—	502	4	no	—
510	C₄	—	251	4	no	—
511	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
512	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
513	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
514	C₄	C₂⁴×D₂₅₁	1	1	yes	characteristic
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	4	2	no	—
519	C₂	—	4	2	no	—
520	C₂	—	1004	2	no	—
521	C₂	—	502	4	no	—
522	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₂₅₁
commutator, cosocle	C₄×C₂₅₁	C₂⁵
Frattini	C₄	C₂⁴×D₂₅₁
Fitting	#575×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂³×D₄
hypercenter	#575	D₂₅₁
hypocenter	C₂₅₁	#3586
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. #30632523	C₂	semidirect
2. C₂×#22548762	C₂	semidirect
3. #30632503	C₂	semidirect
4. #30632501	C₂	semidirect
5. #30632497	C₂	semidirect
6. #30632494	C₂	semidirect
7. #30632485	C₂	semidirect
8. #30632483	C₂	semidirect
9. C₂×#22548748	C₂	semidirect
10. C₂×#22548745	C₂	semidirect
11. #137×D₂₅₁	C₂	semidirect
12. #30632453	C₂	semidirect
13. #575×C₂₅₁	C₂	semidirect
14. #22548763	C₂²	semidirect
18. #22548762	C₂²	semidirect
19. #22548762	C₂²	semidirect
20. #22548762	C₂²	semidirect
22. #22548761	C₂²	semidirect
24. #22548760	C₂²	semidirect
30. C₂×#16860809	C₂²	semidirect
34. C₂²×Dic₅₀₂	C₂²	semidirect
35. C₂×Q₈×D₂₅₁	C₂²	semidirect
36. #22548748	C₂²	semidirect
37. #22548748	C₂²	semidirect
38. #22548747	C₂²	semidirect
39. #22548746	C₂²	semidirect
40. #22548745	C₂²	semidirect
41. #22548745	C₂²	semidirect
42. #22548745	C₂²	semidirect
43. #22548744	C₂²	semidirect
44. #22548744	C₂²	semidirect
45. #22548741	C₂²	semidirect
46. #22548740	C₂²	semidirect
47. #22548739	C₂²	semidirect
48. #22548736	C₂²	semidirect
49. #22548735	C₂²	semidirect
50. #22548734	C₂²	semidirect
51. C₂×Dic₁₀₀₄	C₂²	semidirect
52. C₂×#16860800	C₂²	semidirect
53. Q₁₆×D₂₅₁	C₂²	semidirect
54. C₂×#16860799	C₂²	semidirect
55. C₂×#16860798	C₂²	semidirect
56. SD₁₆×D₂₅₁	C₂²	semidirect
57. #22548723	C₂²	semidirect
58. #22548721	C₂²	semidirect
59. C₂×#16860794	C₂²	semidirect
60. M₁₆×D₂₅₁	C₂²	semidirect
62. C₂×#41×C₂₅₁	C₂²	semidirect
63. #137×C₂₅₁	C₂²	semidirect
64. #137×C₂₅₁	C₂²	semidirect
65. AGL(1,ℤ/8)×C₂₅₁	C₂²	semidirect
66. AGL(1,ℤ/8)×C₂₅₁	C₂²	semidirect
67. #135×C₂₅₁	C₂²	semidirect
68. C₂×M₁₆×C₂₅₁	C₂²	semidirect
261. C₂₅₁	#3586	semidirect
271. #575	D₂₅₁	semidirect
296. C₂×#41	C₂×D₂₅₁	semidirect
309. #137	C₂×D₂₅₁	semidirect
310. #137	C₂×D₂₅₁	semidirect
314. AGL(1,ℤ/8)	C₂×D₂₅₁	semidirect
315. AGL(1,ℤ/8)	C₂×D₂₅₁	semidirect
319. #135	C₂×D₂₅₁	semidirect
330. C₂×M₁₆	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632523	2
C₂×#22548762	2
#30632503	2
#30632501	2
#30632497	2
#30632494	2
#30632485	2
#30632483	2
C₂×#22548748	2
C₂×#22548745	2
#137×D₂₅₁	2
#30632453	2
#575×C₂₅₁	2
#3586	251