Subgroups — #44564689

Order 32128.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632425	C₂	1	4	yes	maximal, complemented
2	#30632422	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632357	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632332	C₂	1	2	yes	maximal, complemented
5	#30632325	C₂	1	2	yes	maximal, complemented
6	D₄×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632322	C₂	1	2	yes	maximal, complemented
8	#30632321	C₂	1	2	yes	maximal, complemented
9	#30632290	C₂	1	2	yes	maximal, complemented
10	#30632288	C₂	1	2	yes	maximal, complemented
11	#30632251	C₂	1	2	yes	maximal, complemented
12	#30632250	C₂	1	2	yes	maximal, complemented
13	#30632245	C₂	1	4	yes	maximal, complemented
14	#127×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632224	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632219	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16860809	C₂²	1	2	yes	complemented
19	C₂²×D₁₀₀₄	C₂²	1	2	yes	complemented
20	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
21	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
22	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
23	C₂×D₄×D₂₅₁	C₂²	1	4	yes	complemented
24	C₂×D₄×D₂₅₁	C₂²	1	2	yes	complemented
25	#22548712	C₂²	1	1	yes	characteristic
26	#22548711	C₂²	1	2	yes	complemented
27	#22548711	C₂²	1	2	yes	complemented
28	#22548711	C₂²	1	2	yes	complemented
29	#22548711	C₂²	1	2	yes	complemented
30	#22548710	C₂²	1	2	yes	complemented
31	#22548708	C₂²	1	2	yes	complemented
32	#22548706	C₂²	1	1	yes	characteristic, complemented
33	#22548706	C₂²	1	1	yes	characteristic, complemented
34	#22548704	C₂²	1	1	yes	characteristic, complemented
35	#22548704	C₂²	1	2	yes	complemented
36	#22548703	C₂²	1	2	yes	complemented
37	#22548702	C₂²	1	1	yes	characteristic, complemented
38	#22548700	C₂²	1	2	yes	complemented
39	#22548700	C₂²	1	4	yes	complemented
40	#22548699	C₂²	1	4	yes	complemented
41	#22548698	C₂²	1	4	yes	complemented
42	#22548697	C₂²	1	2	yes	complemented
43	#22548697	C₂²	1	4	yes	complemented
44	#22548695	C₂²	1	1	yes	characteristic, complemented
45	#22548691	C₂²	1	1	yes	characteristic, complemented
46	#22548690	C₂²	1	1	yes	characteristic
47	#22548690	C₂²	1	2	yes	complemented
48	#22548689	C₂²	1	4	yes	complemented
49	#22548689	C₂²	1	4	yes	complemented
50	#22548689	C₂²	1	2	yes	complemented
51	#22548688	C₂²	1	4	yes	complemented
52	#22548687	C₂²	1	4	yes	complemented
53	#22548687	C₂²	1	4	yes	complemented
54	#22548687	C₂²	1	4	yes	complemented
55	#22548686	C₂²	1	1	yes	characteristic
56	#22548686	C₂²	1	2	yes	complemented
57	#22548686	C₂²	1	4	yes	complemented
58	#22548685	C₂²	1	4	yes	complemented
59	#22548685	C₂²	1	4	yes	complemented
60	#22548683	C₂²	1	4	yes	complemented
61	#22548683	C₂²	1	4	yes	complemented
62	#22548683	C₂²	1	4	yes	complemented
63	#22548683	C₂²	1	4	yes	complemented
64	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
66	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
68	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
69	#22548677	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
71	#22548674	C₂²	1	2	yes	complemented
72	#22548672	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	4	yes	complemented
74	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₂₅₁	C₂²	1	2	yes	complemented
76	#127×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
77	#127×C₂₅₁	C₂²	1	2	yes	complemented
78	#121×C₂₅₁	C₂²	1	4	yes	complemented
79	#121×C₂₅₁	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
83	C₂³×D₂₅₁	C₂³	1	4	yes	—
84	C₂³×D₂₅₁	C₂³	1	4	yes	—
85	#16860809	—	4	4	no	—
86	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
87	C₂×D₁₀₀₄	—	4	4	no	—
88	C₂×D₁₀₀₄	C₂³	1	2	yes	—
89	C₂×D₁₀₀₄	C₂³	1	2	yes	—
90	C₂×D₁₀₀₄	C₂³	1	2	yes	—
91	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
92	C₂×D₁₀₀₄	C₂³	1	2	yes	—
93	C₂×D₁₀₀₄	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
101	D₄×D₂₅₁	—	4	4	no	—
102	D₄×D₂₅₁	—	4	4	no	—
103	D₄×D₂₅₁	—	4	4	no	—
104	D₄×D₂₅₁	—	4	4	no	—
105	D₄×D₂₅₁	—	4	8	no	—
106	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
107	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
111	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
112	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
113	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
114	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
117	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
118	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
119	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
120	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
121	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
122	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
123	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
124	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
125	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
135	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
136	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
137	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
138	C₄×Dic₂₅₁	C₂³	1	2	yes	—
139	#41×C₂₅₁	—	4	4	no	—
140	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
143	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
144	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
145	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
146	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
147	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
148	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
149	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
154	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
155	C₄²×C₂₅₁	C₂³	1	2	yes	—
156	C₂²×D₂₅₁	—	2	8	no	—
157	C₂²×D₂₅₁	—	4	4	no	—
158	C₂²×D₂₅₁	—	4	4	no	—
159	C₂²×D₂₅₁	—	4	4	no	—
160	C₂²×D₂₅₁	—	4	4	no	—
161	C₂²×D₂₅₁	—	4	4	no	—
162	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
163	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
164	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
165	Dic₅₀₂	—	2	2	no	—
166	D₁₀₀₄	—	2	4	no	—
167	D₁₀₀₄	—	2	4	no	—
168	D₁₀₀₄	—	2	4	no	—
169	D₁₀₀₄	—	2	2	no	—
170	D₁₀₀₄	—	4	2	no	—
171	D₁₀₀₄	—	4	4	no	—
172	C₂²⋊D₂₅₁	—	2	4	no	—
173	C₂²⋊D₂₅₁	—	4	4	no	—
174	C₂²⋊D₂₅₁	—	4	4	no	—
175	C₂²⋊D₂₅₁	—	4	4	no	—
176	C₂²⋊D₂₅₁	—	4	4	no	—
177	C₂²⋊D₂₅₁	—	4	4	no	—
178	C₂²⋊D₂₅₁	—	4	4	no	—
179	C₂×Dic₂₅₁	—	4	4	no	—
180	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
184	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
185	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
186	C₄×D₂₅₁	—	2	2	no	—
187	C₄×D₂₅₁	—	2	2	no	—
188	C₄×D₂₅₁	—	2	2	no	—
189	C₄×D₂₅₁	—	2	4	no	—
190	C₄×D₂₅₁	—	4	4	no	—
191	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
192	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
193	Q₈×C₂₅₁	—	2	2	no	—
194	D₄×C₂₅₁	—	2	4	no	—
195	D₄×C₂₅₁	—	2	2	no	—
196	D₄×C₂₅₁	—	2	4	no	—
197	D₄×C₂₅₁	—	4	4	no	—
198	D₄×C₂₅₁	—	4	2	no	—
199	D₄×C₂₅₁	—	4	4	no	—
200	C₂×C₄×C₂₅₁	—	2	4	no	—
201	C₂×C₄×C₂₅₁	—	4	4	no	—
202	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
203	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
204	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
205	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
206	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
208	C₂²×C₂₅₁	—	2	2	no	—
209	C₂²×C₂₅₁	—	2	4	no	—
210	C₂²×C₂₅₁	—	2	4	no	—
211	C₂²×C₂₅₁	—	2	2	no	—
212	C₂²×C₂₅₁	—	2	2	no	—
213	C₂²×C₂₅₁	—	2	4	no	—
214	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
215	C₂×D₂₅₁	—	2	1	no	—
216	C₂×D₂₅₁	—	2	1	no	—
217	C₂×D₂₅₁	—	2	2	no	—
218	C₂×D₂₅₁	—	2	4	no	—
219	C₂×D₂₅₁	—	2	2	no	—
220	C₂×D₂₅₁	—	2	4	no	—
221	C₂×D₂₅₁	—	2	4	no	—
222	C₂×D₂₅₁	—	2	2	no	—
223	C₂×D₂₅₁	—	8	8	no	—
224	C₂×D₂₅₁	—	8	8	no	—
225	C₂×D₂₅₁	H(5,𝔽₂)	1	2	yes	—
226	C₄×C₂₅₁	—	2	2	no	—
227	C₄×C₂₅₁	—	2	2	no	—
228	C₄×C₂₅₁	—	2	1	no	—
229	C₄×C₂₅₁	—	2	2	no	—
230	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
231	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
232	Dic₂₅₁	—	2	2	no	—
233	Dic₂₅₁	—	2	1	no	—
234	Dic₂₅₁	—	2	1	no	—
235	Dic₂₅₁	—	2	1	no	—
236	Dic₂₅₁	—	2	2	no	—
237	Dic₂₅₁	—	2	2	no	—
238	C₂×C₂₅₁	—	4	2	no	—
239	C₂×C₂₅₁	—	4	4	no	—
240	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₂₅₁	—	2	2	no	—
244	D₂₅₁	—	4	2	no	—
245	D₂₅₁	—	4	4	no	—
246	C₂₅₁	#3543	1	1	yes	characteristic, complemented, Sylow
247	#3543	—	251	1	no	maximal, Sylow
248	#560	—	251	4	no	—
249	#559	—	251	1	no	—
250	#550	—	251	1	no	—
251	#550	D₂₅₁	1	1	yes	characteristic, complemented
252	#546	—	251	2	no	—
253	#546	—	251	2	no	—
254	D₄²	—	251	2	no	—
255	D₄²	—	251	2	no	—
256	D₄²	—	251	1	no	—
257	#540	—	251	2	no	—
258	#540	—	251	2	no	—
259	#535	—	251	2	no	—
260	#535	—	251	2	no	—
261	#534	—	251	4	no	—
262	C₂×#127	—	251	1	no	—
263	#529	—	251	1	no	—
264	#529	—	251	1	no	—
265	C₂×#41	—	251	2	no	—
266	C₂×#41	C₂×D₂₅₁	1	2	yes	complemented
267	C₂²×D₄	—	251	2	no	—
268	C₂²×D₄	—	251	2	no	—
269	C₂²×D₄	—	251	2	no	—
270	C₂²×D₄	—	251	4	no	—
271	C₂²×D₄	—	251	2	no	—
272	C₂²×D₄	—	251	2	no	—
273	#127	—	251	2	no	—
274	#127	—	251	2	no	—
275	#127	—	251	2	no	—
276	#127	—	251	2	no	—
277	#127	—	251	1	no	—
278	#127	C₂×D₂₅₁	1	1	yes	characteristic, complemented
279	#127	C₂×D₂₅₁	1	2	yes	complemented
280	#126	—	251	2	no	—
281	#126	—	251	2	no	—
282	#125	—	251	1	no	—
283	#125	—	251	1	no	—
284	#124	—	251	1	no	—
285	#124	—	251	2	no	—
286	#124	—	251	1	no	—
287	#124	—	251	2	no	—
288	#123	—	251	4	no	—
289	#123	—	251	2	no	—
290	#123	—	251	4	no	—
291	#123	—	251	2	no	—
292	#123	—	251	4	no	—
293	#123	—	251	4	no	—
294	C₂²⋊Q₈	—	251	1	no	—
295	C₂²⋊Q₈	—	251	1	no	—
296	#121	—	251	1	no	—
297	#121	—	251	4	no	—
298	#121	—	251	4	no	—
299	#121	—	251	4	no	—
300	#121	—	251	2	no	—
301	#121	—	251	4	no	—
302	#121	—	251	4	no	—
303	#121	—	251	4	no	—
304	#121	—	251	2	no	—
305	#121	—	251	1	no	—
306	#121	—	251	2	no	—
307	#121	—	251	4	no	—
308	#121	C₂×D₂₅₁	1	4	yes	complemented
309	#121	C₂×D₂₅₁	1	2	yes	complemented
310	#120	—	251	4	no	—
311	#120	—	251	4	no	—
312	#120	—	251	4	no	—
313	#120	—	251	4	no	—
314	#120	—	251	4	no	—
315	#120	—	251	4	no	—
316	C₄×Q₈	—	251	1	no	—
317	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
318	C₄×D₄	—	251	2	no	—
319	C₄×D₄	—	251	2	no	—
320	C₄×D₄	—	251	2	no	—
321	C₄×D₄	—	251	2	no	—
322	C₄×D₄	—	251	1	no	—
323	C₄×D₄	—	251	2	no	—
324	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
325	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
326	#117	—	251	2	no	—
327	#117	—	251	2	no	—
328	C₂×C₂²⋊C₄	—	251	4	no	—
329	C₂×C₄²	—	251	1	no	—
330	C₂⁴	—	251	4	no	—
331	C₂⁴	—	251	4	no	—
332	#41	—	4	4	no	—
333	#41	—	1004	4	no	—
334	C₂×Q₈	—	251	1	no	—
335	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
336	C₂×D₄	—	1004	4	no	—
337	C₂×D₄	—	1004	8	no	—
338	C₂×D₄	—	1004	4	no	—
339	C₂×D₄	—	1004	4	no	—
340	C₂×D₄	—	1004	4	no	—
341	C₂×D₄	—	1004	4	no	—
342	C₂×D₄	—	251	4	no	—
343	C₂×D₄	—	251	4	no	—
344	C₂×D₄	—	251	4	no	—
345	C₂×D₄	—	251	4	no	—
346	C₂×D₄	—	251	4	no	—
347	C₂×D₄	—	251	4	no	—
348	C₂×D₄	—	251	2	no	—
349	C₂×D₄	—	251	4	no	—
350	C₂×D₄	—	251	2	no	—
351	C₂×D₄	—	251	2	no	—
352	C₂×D₄	—	251	2	no	—
353	C₂×D₄	—	251	1	no	—
354	C₂×D₄	—	251	2	no	—
355	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
356	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
357	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
358	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
359	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
360	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
361	C₂²×C₄	—	251	4	no	—
362	C₂²×C₄	—	251	4	no	—
363	C₂²×C₄	—	251	1	no	—
364	C₂²×C₄	—	251	1	no	—
365	C₂²×C₄	—	251	1	no	—
366	C₂²×C₄	—	251	2	no	—
367	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
368	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	—
369	C₄⋊C₄	—	251	2	no	—
370	C₄⋊C₄	—	251	2	no	—
371	C₄⋊C₄	—	251	2	no	—
372	C₄⋊C₄	—	251	2	no	—
373	C₄⋊C₄	—	251	2	no	—
374	C₄⋊C₄	—	251	2	no	—
375	C₄⋊C₄	—	251	1	no	—
376	C₄⋊C₄	—	251	1	no	—
377	C₄⋊C₄	—	251	2	no	—
378	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
381	C₂²⋊C₄	—	251	2	no	—
382	C₂²⋊C₄	—	251	2	no	—
383	C₂²⋊C₄	—	251	2	no	—
384	C₂²⋊C₄	—	251	4	no	—
385	C₂²⋊C₄	—	251	2	no	—
386	C₂²⋊C₄	—	251	2	no	—
387	C₂²⋊C₄	—	251	4	no	—
388	C₂²⋊C₄	—	251	4	no	—
389	C₂²⋊C₄	—	251	2	no	—
390	C₂²⋊C₄	—	251	2	no	—
391	C₂²⋊C₄	—	251	2	no	—
392	C₂²⋊C₄	—	251	2	no	—
393	C₂²⋊C₄	—	251	4	no	—
394	C₂²⋊C₄	—	251	4	no	—
395	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
397	C₄²	—	251	1	no	—
398	C₄²	—	251	1	no	—
399	C₄²	—	251	1	no	—
400	C₄²	—	251	2	no	—
401	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
402	C₄²	C₂²×D₂₅₁	1	2	yes	—
403	C₂³	—	1004	4	no	—
404	C₂³	—	1004	4	no	—
405	C₂³	—	1004	4	no	—
406	C₂³	—	1004	4	no	—
407	C₂³	—	1004	4	no	—
408	C₂³	—	502	8	no	—
409	C₂³	—	251	4	no	—
410	C₂³	—	251	2	no	—
411	C₂³	—	251	1	no	—
412	C₂³	C₂³×D₂₅₁	1	2	yes	—
413	C₂³	C₂³×D₂₅₁	1	4	yes	—
414	Q₈	—	2	2	no	—
415	Q₈	—	502	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	1004	2	no	—
423	D₄	—	1004	4	no	—
424	D₄	—	1004	4	no	—
425	D₄	—	1004	4	no	—
426	D₄	—	1004	4	no	—
427	D₄	—	1004	4	no	—
428	D₄	—	1004	4	no	—
429	D₄	—	1004	4	no	—
430	D₄	—	502	4	no	—
431	D₄	—	502	4	no	—
432	D₄	—	502	2	no	—
433	D₄	—	502	4	no	—
434	D₄	—	502	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	1004	4	no	—
438	C₂×C₄	—	1004	4	no	—
439	C₂×C₄	—	502	2	no	—
440	C₂×C₄	—	502	2	no	—
441	C₂×C₄	—	502	2	no	—
442	C₂×C₄	—	502	4	no	—
443	C₂×C₄	—	251	1	no	—
444	C₂×C₄	—	251	1	no	—
445	C₂×C₄	—	251	1	no	—
446	C₂×C₄	—	251	2	no	—
447	C₂×C₄	—	251	2	no	—
448	C₂×C₄	—	251	2	no	—
449	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
451	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
452	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
453	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2008	8	no	—
462	C₂²	—	2008	8	no	—
463	C₂²	—	502	4	no	—
464	C₂²	—	502	2	no	—
465	C₂²	—	502	2	no	—
466	C₂²	—	502	4	no	—
467	C₂²	—	502	2	no	—
468	C₂²	—	502	4	no	—
469	C₂²	—	502	1	no	—
470	C₂²	—	502	1	no	—
471	C₂²	—	251	2	no	—
472	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	502	2	no	—
478	C₄	—	502	1	no	—
479	C₄	—	502	1	no	—
480	C₄	—	502	2	no	—
481	C₄	—	502	2	no	—
482	C₄	—	502	1	no	—
483	C₄	#22548760	1	2	yes	—
484	C₄	#22548761	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	—	4	4	no	—
487	C₂	—	1004	2	no	—
488	C₂	—	1004	4	no	—
489	C₂	—	502	2	no	—
490	C₂	H(5,𝔽₂)×D₂₅₁	1	1	yes	characteristic
491	C₂	C₂×#22548760	1	1	yes	characteristic
492	C₂	C₂×#22548761	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#550×C₂₅₁	C₂
hypercenter	#550	D₂₅₁
hypocenter	C₂₅₁	#3543
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #30632425	C₂	semidirect
2. #30632422	C₂	semidirect
3. #30632357	C₂	semidirect
4. #30632332	C₂	semidirect
5. #30632325	C₂	semidirect
6. D₄×D₁₀₀₄	C₂	semidirect
7. #30632322	C₂	semidirect
8. #30632321	C₂	semidirect
9. #30632290	C₂	semidirect
10. #30632288	C₂	semidirect
11. #30632251	C₂	semidirect
12. #30632250	C₂	semidirect
13. #30632245	C₂	semidirect
14. #127×D₂₅₁	C₂	semidirect
15. #30632224	C₂	semidirect
16. #30632219	C₂	semidirect
17. #550×C₂₅₁	C₂	semidirect
18. C₂×#16860809	C₂²	semidirect
19. C₂²×D₁₀₀₄	C₂²	semidirect
20. C₂×D₄×D₂₅₁	C₂²	semidirect
21. C₂×D₄×D₂₅₁	C₂²	semidirect
22. C₂×D₄×D₂₅₁	C₂²	semidirect
23. C₂×D₄×D₂₅₁	C₂²	semidirect
24. C₂×D₄×D₂₅₁	C₂²	semidirect
26. #22548711	C₂²	semidirect
27. #22548711	C₂²	semidirect
28. #22548711	C₂²	semidirect
29. #22548711	C₂²	semidirect
30. #22548710	C₂²	semidirect
31. #22548708	C₂²	semidirect
32. #22548706	C₂²	semidirect
33. #22548706	C₂²	semidirect
34. #22548704	C₂²	semidirect
35. #22548704	C₂²	semidirect
36. #22548703	C₂²	semidirect
37. #22548702	C₂²	semidirect
38. #22548700	C₂²	semidirect
39. #22548700	C₂²	semidirect
40. #22548699	C₂²	semidirect
41. #22548698	C₂²	semidirect
42. #22548697	C₂²	semidirect
43. #22548697	C₂²	semidirect
44. #22548695	C₂²	semidirect
45. #22548691	C₂²	semidirect
47. #22548690	C₂²	semidirect
48. #22548689	C₂²	semidirect
49. #22548689	C₂²	semidirect
50. #22548689	C₂²	semidirect
51. #22548688	C₂²	semidirect
52. #22548687	C₂²	semidirect
53. #22548687	C₂²	semidirect
54. #22548687	C₂²	semidirect
56. #22548686	C₂²	semidirect
57. #22548686	C₂²	semidirect
58. #22548685	C₂²	semidirect
59. #22548685	C₂²	semidirect
60. #22548683	C₂²	semidirect
61. #22548683	C₂²	semidirect
62. #22548683	C₂²	semidirect
63. #22548683	C₂²	semidirect
64. C₄×Dic₅₀₂	C₂²	semidirect
65. C₄×D₁₀₀₄	C₂²	semidirect
66. C₄×D₁₀₀₄	C₂²	semidirect
67. C₄×D₁₀₀₄	C₂²	semidirect
68. D₄×Dic₂₅₁	C₂²	semidirect
69. #22548677	C₂²	semidirect
70. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
71. #22548674	C₂²	semidirect
72. #22548672	C₂²	semidirect
73. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
74. C₄²×D₂₅₁	C₂²	semidirect
75. C₂×#41×C₂₅₁	C₂²	semidirect
76. #127×C₂₅₁	C₂²	semidirect
77. #127×C₂₅₁	C₂²	semidirect
78. #121×C₂₅₁	C₂²	semidirect
79. #121×C₂₅₁	C₂²	semidirect
80. C₄×Q₈×C₂₅₁	C₂²	semidirect
81. C₄×D₄×C₂₅₁	C₂²	semidirect
82. C₄×D₄×C₂₅₁	C₂²	semidirect
246. C₂₅₁	#3543	semidirect
251. #550	D₂₅₁	semidirect
266. C₂×#41	C₂×D₂₅₁	semidirect
278. #127	C₂×D₂₅₁	semidirect
279. #127	C₂×D₂₅₁	semidirect
308. #121	C₂×D₂₅₁	semidirect
309. #121	C₂×D₂₅₁	semidirect
317. C₄×Q₈	C₂×D₂₅₁	semidirect
324. C₄×D₄	C₂×D₂₅₁	semidirect
325. C₄×D₄	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632425	2
#30632422	2
#30632357	2
#30632332	2
#30632325	2
D₄×D₁₀₀₄	2
#30632322	2
#30632321	2
#30632290	2
#30632288	2
#30632251	2
#30632250	2
#30632245	2
#127×D₂₅₁	2
#30632224	2
#30632219	2
#550×C₂₅₁	2
#3543	251