Subgroups — #44564592

Order 32128.

1134 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632434	C₂	1	4	yes	maximal, complemented
2	#30632394	C₂	1	2	yes	maximal, complemented
3	#30632346	C₂	1	2	yes	maximal, complemented
4	#30632341	C₂	1	2	yes	maximal, complemented
5	#30632333	C₂	1	2	yes	maximal, complemented
6	#30632324	C₂	1	4	yes	maximal, complemented
7	#30632312	C₂	1	2	yes	maximal, complemented
8	#30632308	C₂	1	2	yes	maximal, complemented
9	#30632286	C₂	1	2	yes	maximal, complemented
10	#30632274	C₂	1	2	yes	maximal, complemented
11	#30632265	C₂	1	2	yes	maximal, complemented
12	#30632264	C₂	1	2	yes	maximal, complemented
13	C₂×#22548694	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#22548689	C₂	1	1	yes	maximal, characteristic, complemented
15	#525×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860810	C₂²	1	2	yes	complemented
17	C₂×#16860809	C₂²	1	4	yes	complemented
18	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
21	#22548715	C₂²	1	2	yes	complemented
22	#22548710	C₂²	1	4	yes	complemented
23	#22548706	C₂²	1	4	yes	complemented
24	#22548703	C₂²	1	2	yes	complemented
25	#22548701	C₂²	1	4	yes	complemented
26	#22548701	C₂²	1	4	yes	complemented
27	#22548700	C₂²	1	4	yes	complemented
28	#22548699	C₂²	1	4	yes	complemented
29	#22548699	C₂²	1	4	yes	complemented
30	#22548697	C₂²	1	4	yes	complemented
31	#22548695	C₂²	1	4	yes	complemented
32	#22548694	C₂²	1	2	yes	—
33	#22548694	C₂²	1	2	yes	—
34	#22548694	C₂²	1	2	yes	complemented
35	#22548694	C₂²	1	2	yes	complemented
36	#22548694	C₂²	1	2	yes	complemented
37	#22548693	C₂²	1	4	yes	complemented
38	#22548693	C₂²	1	4	yes	complemented
39	#22548692	C₂²	1	4	yes	—
40	#22548692	C₂²	1	4	yes	complemented
41	#22548691	C₂²	1	4	yes	complemented
42	#22548689	C₂²	1	2	yes	—
43	#22548689	C₂²	1	2	yes	—
44	#22548689	C₂²	1	2	yes	—
45	#22548689	C₂²	1	2	yes	—
46	#22548689	C₂²	1	2	yes	complemented
47	#22548688	C₂²	1	4	yes	complemented
48	#22548687	C₂²	1	4	yes	complemented
49	#22548687	C₂²	1	4	yes	complemented
50	#22548687	C₂²	1	4	yes	complemented
51	#22548686	C₂²	1	4	yes	complemented
52	#22548683	C₂²	1	4	yes	—
53	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
54	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
55	D₄×Dic₂₅₁	C₂²	1	4	yes	—
56	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
57	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊Dic₂₅₁	C₂²	1	2	yes	complemented
59	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
60	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	—
62	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₂₅₁	C₂²	1	4	yes	—
64	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
65	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
66	#123×C₂₅₁	C₂²	1	2	yes	complemented
67	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
68	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
69	#121×C₂₅₁	C₂²	1	1	yes	characteristic
70	#121×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
71	#120×C₂₅₁	C₂²	1	2	yes	—
72	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
73	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
74	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₂₅₁	C₂³	1	2	yes	—
76	#16860810	—	4	4	no	—
77	#16860809	—	4	8	no	—
78	C₂×Dic₅₀₂	—	4	2	no	—
79	C₂×Dic₅₀₂	C₂³	1	2	yes	—
80	C₂×Dic₅₀₂	C₂³	1	2	yes	—
81	C₂×Dic₅₀₂	C₂³	1	4	yes	—
82	C₂×D₁₀₀₄	—	4	2	no	—
83	C₂×D₁₀₀₄	C₂³	1	2	yes	—
84	C₂×D₁₀₀₄	C₂³	1	2	yes	—
85	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
86	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
90	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
91	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
92	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
93	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
94	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
95	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
96	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
97	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
98	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
99	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
100	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
101	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
102	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
103	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
104	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
105	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
106	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
107	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
108	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
109	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
111	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
115	C₄×Dic₂₅₁	C₂³	1	4	yes	—
116	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
117	#41×C₂₅₁	—	4	2	no	—
118	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
119	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
120	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
121	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
122	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₂₅₁	—	4	2	no	—
124	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
127	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
134	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
137	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
140	C₄²×C₂₅₁	C₂³	1	2	yes	—
141	C₂²×D₂₅₁	—	2	4	no	—
142	C₂²×D₂₅₁	—	4	2	no	—
143	C₂²×D₂₅₁	—	4	2	no	—
144	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
145	Dic₅₀₂	—	2	4	no	—
146	Dic₅₀₂	—	4	2	no	—
147	Dic₅₀₂	—	4	4	no	—
148	D₁₀₀₄	—	2	4	no	—
149	D₁₀₀₄	—	4	2	no	—
150	C₂²⋊D₂₅₁	—	2	8	no	—
151	C₂²⋊D₂₅₁	—	4	4	no	—
152	C₂²⋊D₂₅₁	—	4	4	no	—
153	C₂²⋊D₂₅₁	—	4	4	no	—
154	C₂×Dic₂₅₁	—	2	4	no	—
155	C₂×Dic₂₅₁	—	4	2	no	—
156	C₂×Dic₂₅₁	—	4	2	no	—
157	C₂×Dic₂₅₁	—	4	4	no	—
158	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
159	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
160	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
161	C₄×D₂₅₁	—	4	4	no	—
162	C₄×D₂₅₁	—	4	4	no	—
163	C₂³×C₂₅₁	—	2	2	no	—
164	C₂³×C₂₅₁	—	2	2	no	—
165	C₂³×C₂₅₁	—	4	1	no	—
166	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
167	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
168	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
169	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
170	Q₈×C₂₅₁	—	4	1	no	—
171	D₄×C₂₅₁	—	2	4	no	—
172	D₄×C₂₅₁	—	2	4	no	—
173	D₄×C₂₅₁	—	4	1	no	—
174	D₄×C₂₅₁	—	4	2	no	—
175	C₂×C₄×C₂₅₁	—	2	2	no	—
176	C₂×C₄×C₂₅₁	—	2	2	no	—
177	C₂×C₄×C₂₅₁	—	2	2	no	—
178	C₂×C₄×C₂₅₁	—	2	4	no	—
179	C₂×C₄×C₂₅₁	—	4	1	no	—
180	C₂×C₄×C₂₅₁	—	4	1	no	—
181	C₂×C₄×C₂₅₁	—	4	1	no	—
182	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
183	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
184	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
187	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₂₅₁	—	2	1	no	—
190	C₂²×C₂₅₁	—	2	1	no	—
191	C₂²×C₂₅₁	—	2	1	no	—
192	C₂²×C₂₅₁	—	2	1	no	—
193	C₂²×C₂₅₁	—	2	1	no	—
194	C₂²×C₂₅₁	—	2	2	no	—
195	C₂²×C₂₅₁	—	2	2	no	—
196	C₂²×C₂₅₁	—	2	1	no	—
197	C₂²×C₂₅₁	—	2	2	no	—
198	C₂²×C₂₅₁	—	2	1	no	—
199	C₂²×C₂₅₁	—	4	4	no	—
200	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
201	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
202	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
203	C₂×D₂₅₁	—	2	4	no	—
204	C₂×D₂₅₁	—	2	4	no	—
205	C₂×D₂₅₁	—	2	4	no	—
206	C₂×D₂₅₁	—	8	4	no	—
207	C₄×C₂₅₁	—	2	1	no	—
208	C₄×C₂₅₁	—	2	1	no	—
209	C₄×C₂₅₁	—	2	1	no	—
210	C₄×C₂₅₁	—	2	2	no	—
211	C₄×C₂₅₁	—	2	2	no	—
212	C₄×C₂₅₁	—	2	2	no	—
213	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
214	Dic₂₅₁	—	2	4	no	—
215	Dic₂₅₁	—	2	4	no	—
216	Dic₂₅₁	—	2	4	no	—
217	C₂×C₂₅₁	—	2	2	no	—
218	C₂×C₂₅₁	—	2	2	no	—
219	C₂×C₂₅₁	—	4	2	no	—
220	C₂×C₂₅₁	—	4	1	no	—
221	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
224	D₂₅₁	—	4	4	no	—
225	C₂₅₁	#3536	1	1	yes	characteristic, complemented, Sylow
226	#3536	—	251	1	no	maximal, Sylow
227	#562	—	251	4	no	—
228	#554	—	251	2	no	—
229	#548	—	251	2	no	—
230	#547	—	251	2	no	—
231	#546	—	251	4	no	—
232	#546	—	251	2	no	—
233	#543	—	251	2	no	—
234	#542	—	251	2	no	—
235	#539	—	251	2	no	—
236	#538	—	251	2	no	—
237	#537	—	251	2	no	—
238	#537	—	251	2	no	—
239	#525	D₂₅₁	1	1	yes	characteristic, complemented
240	C₂×C₂²⋊Q₈	—	251	1	no	—
241	C₂×#121	—	251	1	no	—
242	C₂×#41	—	251	4	no	—
243	C₂×#41	—	251	2	no	—
244	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
245	C₂²×Q₈	—	251	1	no	—
246	C₂²×D₄	—	251	2	no	—
247	C₂²×D₄	—	251	1	no	—
248	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
249	C₄⋊Q₈	—	251	2	no	—
250	#126	—	251	4	no	—
251	#125	—	251	4	no	—
252	#124	—	251	4	no	—
253	#124	—	251	4	no	—
254	#124	—	251	2	no	—
255	#123	—	251	4	no	—
256	#123	—	251	4	no	—
257	#123	—	251	4	no	—
258	#123	—	251	4	no	—
259	#123	C₂×D₂₅₁	1	2	yes	complemented
260	C₂²⋊Q₈	—	251	4	no	—
261	C₂²⋊Q₈	—	251	2	no	—
262	C₂²⋊Q₈	—	251	2	no	—
263	C₂²⋊Q₈	—	251	2	no	—
264	C₂²⋊Q₈	—	251	2	no	—
265	C₂²⋊Q₈	—	251	2	no	—
266	C₂²⋊Q₈	—	251	4	no	—
267	C₂²⋊Q₈	—	251	4	no	—
268	C₂²⋊Q₈	—	251	4	no	—
269	C₂²⋊Q₈	—	251	4	no	—
270	C₂²⋊Q₈	—	251	4	no	—
271	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
272	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
273	#121	—	251	4	no	—
274	#121	—	251	4	no	—
275	#121	—	251	4	no	—
276	#121	—	251	4	no	—
277	#121	—	251	2	no	—
278	#121	—	251	2	no	—
279	#121	—	251	2	no	—
280	#121	—	251	2	no	—
281	#121	—	251	2	no	—
282	#121	—	251	4	no	—
283	#121	C₂×D₂₅₁	1	1	yes	characteristic
284	#121	C₂×D₂₅₁	1	1	yes	characteristic, complemented
285	#120	—	251	4	no	—
286	#120	C₂×D₂₅₁	1	2	yes	—
287	C₄×Q₈	—	251	2	no	—
288	C₄×D₄	—	251	4	no	—
289	C₄×D₄	—	251	4	no	—
290	C₄×D₄	—	251	2	no	—
291	C₄×D₄	C₂×D₂₅₁	1	2	yes	—
292	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
293	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
294	C₂×C₄⋊C₄	—	251	1	no	—
295	C₂×C₄⋊C₄	—	251	2	no	—
296	C₂×C₄⋊C₄	—	251	1	no	—
297	C₂×C₄⋊C₄	—	251	2	no	—
298	C₂×C₂²⋊C₄	—	251	2	no	—
299	C₂×C₂²⋊C₄	—	251	2	no	—
300	C₂×C₂²⋊C₄	—	251	4	no	—
301	C₂⁴	—	251	2	no	—
302	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
303	#41	—	4	2	no	—
304	#41	—	1004	4	no	—
305	#41	—	1004	8	no	—
306	C₂×Q₈	—	1004	2	no	—
307	C₂×Q₈	—	251	2	no	—
308	C₂×Q₈	—	251	4	no	—
309	C₂×Q₈	—	251	2	no	—
310	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
311	C₂×D₄	—	1004	2	no	—
312	C₂×D₄	—	1004	4	no	—
313	C₂×D₄	—	251	4	no	—
314	C₂×D₄	—	251	4	no	—
315	C₂×D₄	—	251	4	no	—
316	C₂×D₄	—	251	4	no	—
317	C₂×D₄	—	251	2	no	—
318	C₂×D₄	—	251	2	no	—
319	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
320	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
321	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
322	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	251	2	no	—
325	C₂²×C₄	—	251	2	no	—
326	C₂²×C₄	—	251	4	no	—
327	C₂²×C₄	—	251	4	no	—
328	C₂²×C₄	—	251	4	no	—
329	C₂²×C₄	—	251	2	no	—
330	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
332	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
335	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
337	C₄⋊C₄	—	251	2	no	—
338	C₄⋊C₄	—	251	2	no	—
339	C₄⋊C₄	—	251	4	no	—
340	C₄⋊C₄	—	251	4	no	—
341	C₄⋊C₄	—	251	2	no	—
342	C₄⋊C₄	—	251	4	no	—
343	C₄⋊C₄	—	251	2	no	—
344	C₄⋊C₄	—	251	4	no	—
345	C₄⋊C₄	—	251	4	no	—
346	C₄⋊C₄	—	251	4	no	—
347	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
350	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
351	C₂²⋊C₄	—	251	4	no	—
352	C₂²⋊C₄	—	251	4	no	—
353	C₂²⋊C₄	—	251	4	no	—
354	C₂²⋊C₄	—	251	4	no	—
355	C₂²⋊C₄	—	251	4	no	—
356	C₂²⋊C₄	—	251	4	no	—
357	C₂²⋊C₄	—	251	4	no	—
358	C₂²⋊C₄	—	251	4	no	—
359	C₂²⋊C₄	—	251	4	no	—
360	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
361	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
364	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
365	C₄²	—	251	4	no	—
366	C₄²	C₂²×D₂₅₁	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	1004	2	no	—
371	C₂³	—	1004	2	no	—
372	C₂³	—	502	4	no	—
373	C₂³	—	251	4	no	—
374	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
375	C₂³	C₂³×D₂₅₁	1	2	yes	—
376	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
377	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
378	Q₈	—	4	1	no	—
379	Q₈	—	1004	2	no	—
380	Q₈	—	1004	4	no	—
381	Q₈	—	502	4	no	—
382	D₄	—	2	4	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	1004	2	no	—
387	D₄	—	1004	4	no	—
388	D₄	—	1004	4	no	—
389	D₄	—	1004	4	no	—
390	D₄	—	502	8	no	—
391	D₄	—	502	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	1004	4	no	—
400	C₂×C₄	—	1004	4	no	—
401	C₂×C₄	—	1004	2	no	—
402	C₂×C₄	—	1004	2	no	—
403	C₂×C₄	—	1004	4	no	—
404	C₂×C₄	—	502	4	no	—
405	C₂×C₄	—	251	4	no	—
406	C₂×C₄	—	251	4	no	—
407	C₂×C₄	—	251	4	no	—
408	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
409	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
410	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
413	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	2008	4	no	—
427	C₂²	—	502	4	no	—
428	C₂²	—	502	4	no	—
429	C₂²	—	502	4	no	—
430	C₂²	#22548761	1	2	yes	—
431	C₂²	#22548762	1	2	yes	—
432	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	502	4	no	—
440	C₄	—	502	4	no	—
441	C₄	—	502	4	no	—
442	C₄	#22548760	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	1004	4	no	—
448	C₂	C₂×#22548760	1	1	yes	characteristic
449	C₂	C₂×#22548761	1	1	yes	characteristic
450	C₂	C₂×#22548762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#525×C₂₅₁	C₂
hypercenter	#525	D₂₅₁
hypocenter	C₂₅₁	#3536
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #30632434	C₂	semidirect
2. #30632394	C₂	semidirect
3. #30632346	C₂	semidirect
4. #30632341	C₂	semidirect
5. #30632333	C₂	semidirect
6. #30632324	C₂	semidirect
7. #30632312	C₂	semidirect
8. #30632308	C₂	semidirect
9. #30632286	C₂	semidirect
10. #30632274	C₂	semidirect
11. #30632265	C₂	semidirect
12. #30632264	C₂	semidirect
13. C₂×#22548694	C₂	semidirect
14. C₂×#22548689	C₂	semidirect
15. #525×C₂₅₁	C₂	semidirect
16. C₂×#16860810	C₂²	semidirect
17. C₂×#16860809	C₂²	semidirect
18. C₂²×Dic₅₀₂	C₂²	semidirect
21. #22548715	C₂²	semidirect
22. #22548710	C₂²	semidirect
23. #22548706	C₂²	semidirect
24. #22548703	C₂²	semidirect
25. #22548701	C₂²	semidirect
26. #22548701	C₂²	semidirect
27. #22548700	C₂²	semidirect
28. #22548699	C₂²	semidirect
29. #22548699	C₂²	semidirect
30. #22548697	C₂²	semidirect
31. #22548695	C₂²	semidirect
34. #22548694	C₂²	semidirect
35. #22548694	C₂²	semidirect
36. #22548694	C₂²	semidirect
37. #22548693	C₂²	semidirect
38. #22548693	C₂²	semidirect
40. #22548692	C₂²	semidirect
41. #22548691	C₂²	semidirect
46. #22548689	C₂²	semidirect
47. #22548688	C₂²	semidirect
48. #22548687	C₂²	semidirect
49. #22548687	C₂²	semidirect
50. #22548687	C₂²	semidirect
51. #22548686	C₂²	semidirect
53. C₄×Dic₅₀₂	C₂²	semidirect
54. C₄×D₁₀₀₄	C₂²	semidirect
56. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
58. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
59. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
60. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
64. C₂×#41×C₂₅₁	C₂²	semidirect
66. #123×C₂₅₁	C₂²	semidirect
68. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
70. #121×C₂₅₁	C₂²	semidirect
73. C₄×D₄×C₂₅₁	C₂²	semidirect
74. #117×C₂₅₁	C₂²	semidirect
225. C₂₅₁	#3536	semidirect
239. #525	D₂₅₁	semidirect
244. C₂×#41	C₂×D₂₅₁	semidirect
259. #123	C₂×D₂₅₁	semidirect
272. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
284. #121	C₂×D₂₅₁	semidirect
292. C₄×D₄	C₂×D₂₅₁	semidirect
293. #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
#30632434	2
#30632394	2
#30632346	2
#30632341	2
#30632333	2
#30632324	2
#30632312	2
#30632308	2
#30632286	2
#30632274	2
#30632265	2
#30632264	2
C₂×#22548694	2
C₂×#22548689	2
#525×C₂₅₁	2
#3536	251