Subgroups — #44563944

Order 32128.

1068 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632417	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632415	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632414	C₂	1	2	yes	maximal, complemented
4	#30632396	C₂	1	2	yes	maximal, complemented
5	#30632392	C₂	1	2	yes	maximal, complemented
6	#30632391	C₂	1	4	yes	maximal, complemented
7	D₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632350	C₂	1	2	yes	maximal, complemented
9	#30632243	C₂	1	2	yes	maximal, complemented
10	#30632242	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632239	C₂	1	2	yes	maximal, complemented
12	#30632239	C₂	1	4	yes	maximal, complemented
13	C₄×#16860809	C₂	1	1	yes	maximal, characteristic
14	C₄×#16860809	C₂	1	2	yes	maximal
15	C₂×#22548680	C₂	1	2	yes	maximal, complemented
16	C₄×Q₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#554×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16860809	C₂²	1	1	yes	characteristic
19	C₂²×Dic₅₀₂	C₂²	1	2	yes	—
20	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
21	#22548715	C₂²	1	1	yes	characteristic
22	#22548714	C₂²	1	4	yes	—
23	#22548714	C₂²	1	2	yes	—
24	#22548714	C₂²	1	2	yes	—
25	#22548714	C₂²	1	2	yes	—
26	#22548713	C₂²	1	2	yes	—
27	#22548713	C₂²	1	4	yes	—
28	#22548707	C₂²	1	2	yes	—
29	#22548706	C₂²	1	2	yes	—
30	#22548705	C₂²	1	4	yes	—
31	#22548705	C₂²	1	4	yes	—
32	#22548705	C₂²	1	4	yes	—
33	#22548695	C₂²	1	2	yes	—
34	#22548694	C₂²	1	2	yes	—
35	#22548694	C₂²	1	4	yes	—
36	#22548693	C₂²	1	4	yes	—
37	#22548693	C₂²	1	4	yes	—
38	#22548692	C₂²	1	4	yes	—
39	#22548692	C₂²	1	4	yes	—
40	#22548692	C₂²	1	4	yes	—
41	#22548691	C₂²	1	2	yes	—
42	Q₈×Dic₂₅₁	C₂²	1	2	yes	—
43	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic
44	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
45	C₄×Dic₅₀₂	C₂²	1	2	yes	—
46	C₄×Dic₅₀₂	C₂²	1	2	yes	—
47	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic
48	#22548680	C₂²	1	4	yes	—
49	#22548680	C₂²	1	2	yes	—
50	#22548680	C₂²	1	2	yes	—
51	#22548680	C₂²	1	4	yes	—
52	#22548680	C₂²	1	2	yes	—
53	#22548680	C₂²	1	4	yes	—
54	#22548680	C₂²	1	2	yes	—
55	#22548680	C₂²	1	1	yes	characteristic
56	#22548680	C₂²	1	1	yes	characteristic
57	#22548680	C₂²	1	2	yes	—
58	D₄×Dic₂₅₁	C₂²	1	2	yes	—
59	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₂₅₁	C₂²	1	4	yes	—
62	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	4	yes	—
63	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
64	#22548673	C₂²	1	2	yes	—
65	#22548673	C₂²	1	1	yes	characteristic
66	#22548671	C₂²	1	4	yes	—
67	#22548671	C₂²	1	2	yes	—
68	C₂×Dic₂₅₁⋊C₄	C₂²	1	4	yes	—
69	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
70	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
71	C₂×C₄×Dic₂₅₁	C₂²	1	2	yes	—
72	C₂×C₄×Dic₂₅₁	C₂²	1	4	yes	—
73	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
74	C₄²×D₂₅₁	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
76	#125×C₂₅₁	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	—
79	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	2	yes	—
83	#16860809	Q₈	1	8	yes	complemented
84	C₂×Dic₅₀₂	—	2	8	no	—
85	C₂×Dic₅₀₂	C₂³	1	2	yes	—
86	C₂×Dic₅₀₂	C₂³	1	4	yes	—
87	C₂×Dic₅₀₂	C₂³	1	2	yes	—
88	C₂×Dic₅₀₂	C₂³	1	4	yes	—
89	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
90	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
91	Q₈×D₂₅₁	—	2	4	no	—
92	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
93	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
94	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
95	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
96	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
97	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
100	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
102	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
104	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
106	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
107	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
108	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
109	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
110	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
111	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
112	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
113	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
114	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
115	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
116	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
117	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
118	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
119	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
120	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
121	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
123	C₄×Dic₂₅₁	C₂³	1	2	yes	—
124	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
125	C₄×Dic₂₅₁	C₂³	1	2	yes	—
126	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
127	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
128	C₄×Dic₂₅₁	C₂³	1	2	yes	—
129	C₄×Dic₂₅₁	C₂³	1	2	yes	—
130	C₄×Dic₂₅₁	C₂³	1	4	yes	—
131	C₄×Dic₂₅₁	C₂³	1	2	yes	—
132	C₄×Dic₂₅₁	C₂³	1	4	yes	—
133	C₄×Dic₂₅₁	C₂³	1	4	yes	—
134	C₄×Dic₂₅₁	C₂³	1	2	yes	—
135	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
136	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
137	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
139	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
140	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
142	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
143	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
145	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
146	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
147	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
148	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
149	C₄²×C₂₅₁	C₂³	1	2	yes	—
150	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
151	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
152	Dic₅₀₂	—	2	4	no	—
153	Dic₅₀₂	—	2	4	no	—
154	Dic₅₀₂	—	2	8	no	—
155	Dic₅₀₂	—	4	4	no	—
156	Dic₅₀₂	C₂×Q₈	1	4	yes	complemented
157	Dic₅₀₂	#41	1	4	yes	complemented
158	C₂²⋊D₂₅₁	C₂×Q₈	1	8	yes	complemented
159	C₂×Dic₂₅₁	—	2	8	no	—
160	C₂×Dic₂₅₁	—	4	2	no	—
161	C₂×Dic₂₅₁	C₂×Q₈	1	8	yes	complemented
162	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
164	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
165	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
166	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
167	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
169	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
170	C₄×D₂₅₁	—	2	2	no	—
171	C₄×D₂₅₁	—	2	4	no	—
172	C₄×D₂₅₁	—	4	1	no	—
173	C₄×D₂₅₁	—	4	2	no	—
174	C₄×D₂₅₁	C₂×Q₈	1	4	yes	complemented
175	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
176	Q₈×C₂₅₁	—	2	2	no	—
177	Q₈×C₂₅₁	—	4	2	no	—
178	D₄×C₂₅₁	C₂×Q₈	1	4	yes	complemented
179	C₂×C₄×C₂₅₁	—	2	4	no	—
180	C₂×C₄×C₂₅₁	—	4	4	no	—
181	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
182	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
184	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
185	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
186	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
188	C₂²×C₂₅₁	—	2	2	no	—
189	C₂²×C₂₅₁	—	2	2	no	—
190	C₂²×C₂₅₁	C₂²×Q₈	1	4	yes	—
191	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
192	C₂×D₂₅₁	—	2	1	no	—
193	C₂×D₂₅₁	—	2	1	no	—
194	C₂×D₂₅₁	C₂²×Q₈	1	2	yes	—
195	C₄×C₂₅₁	—	2	2	no	—
196	C₄×C₂₅₁	—	2	2	no	—
197	C₄×C₂₅₁	—	2	2	no	—
198	C₄×C₂₅₁	—	2	4	no	—
199	C₄×C₂₅₁	—	2	1	no	—
200	C₄×C₂₅₁	C₂²×Q₈	1	2	yes	—
201	C₄×C₂₅₁	C₂×#41	1	2	yes	—
202	Dic₂₅₁	—	2	1	no	—
203	Dic₂₅₁	—	2	4	no	—
204	Dic₂₅₁	—	2	1	no	—
205	Dic₂₅₁	—	2	2	no	—
206	Dic₂₅₁	—	2	2	no	—
207	Dic₂₅₁	C₂²×Q₈	1	2	yes	—
208	Dic₂₅₁	C₂²×Q₈	1	4	yes	—
209	Dic₂₅₁	C₂×#41	1	4	yes	—
210	C₂×C₂₅₁	—	2	4	no	—
211	C₂×C₂₅₁	C₂³×Q₈	1	1	yes	characteristic
212	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
213	C₂×C₂₅₁	#585	1	1	yes	characteristic
214	D₂₅₁	—	2	2	no	—
215	C₂₅₁	Q₈×#41	1	1	yes	characteristic, complemented, Sylow
216	Q₈×#41	—	251	1	no	maximal, Sylow
217	Q₈²	—	251	1	no	—
218	#557	—	251	2	no	—
219	#557	—	251	1	no	—
220	#554	—	251	4	no	—
221	#554	—	251	2	no	—
222	#554	—	251	2	no	—
223	#554	D₂₅₁	1	1	yes	characteristic, complemented
224	D₄×Q₈	—	251	2	no	—
225	D₄×Q₈	—	251	1	no	—
226	#533	—	251	1	no	—
227	#533	—	251	2	no	—
228	#533	—	251	2	no	—
229	#533	—	251	4	no	—
230	C₄×#41	—	251	2	no	—
231	C₄×#41	—	251	1	no	—
232	C₂×C₄×Q₈	—	251	1	no	—
233	C₂×C₄×Q₈	—	251	2	no	—
234	C₂×#41	—	251	1	no	—
235	C₂²×Q₈	—	251	1	no	—
236	C₂²×Q₈	—	251	2	no	—
237	C₄⋊Q₈	—	251	2	no	—
238	C₄⋊Q₈	—	251	4	no	—
239	C₄⋊Q₈	—	251	4	no	—
240	C₄⋊Q₈	—	251	2	no	—
241	C₄⋊Q₈	—	251	2	no	—
242	C₄⋊Q₈	—	251	2	no	—
243	C₄⋊Q₈	—	251	1	no	—
244	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
245	#125	—	251	4	no	—
246	#125	—	251	4	no	—
247	#125	—	251	4	no	—
248	#125	—	251	2	no	—
249	#125	—	251	2	no	—
250	#125	C₂×D₂₅₁	1	2	yes	—
251	C₂²⋊Q₈	—	251	2	no	—
252	C₂²⋊Q₈	—	251	2	no	—
253	C₂²⋊Q₈	—	251	4	no	—
254	C₂²⋊Q₈	—	251	4	no	—
255	C₂²⋊Q₈	—	251	2	no	—
256	C₂²⋊Q₈	—	251	4	no	—
257	C₂²⋊Q₈	—	251	4	no	—
258	C₂²⋊Q₈	—	251	4	no	—
259	C₂²⋊Q₈	—	251	4	no	—
260	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	—
261	C₂²⋊Q₈	C₂×D₂₅₁	1	4	yes	—
262	C₄×Q₈	—	251	1	no	—
263	C₄×Q₈	—	251	2	no	—
264	C₄×Q₈	—	251	1	no	—
265	C₄×Q₈	—	251	2	no	—
266	C₄×Q₈	—	251	2	no	—
267	C₄×Q₈	—	251	4	no	—
268	C₄×Q₈	—	251	2	no	—
269	C₄×Q₈	—	251	4	no	—
270	C₄×Q₈	—	251	2	no	—
271	C₄×Q₈	—	251	1	no	—
272	C₄×Q₈	—	251	2	no	—
273	C₄×Q₈	—	251	4	no	—
274	C₄×Q₈	—	251	1	no	—
275	C₄×Q₈	—	251	2	no	—
276	C₄×Q₈	—	251	2	no	—
277	C₄×Q₈	—	251	1	no	—
278	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
279	C₄×D₄	—	251	2	no	—
280	C₄×D₄	—	251	1	no	—
281	C₄×D₄	—	251	2	no	—
282	C₄×D₄	—	251	4	no	—
283	C₄×D₄	—	251	4	no	—
284	C₄×D₄	—	251	2	no	—
285	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
286	C₄×D₄	C₂×D₂₅₁	1	2	yes	—
287	#117	—	251	2	no	—
288	#117	—	251	1	no	—
289	#117	—	251	4	no	—
290	#117	—	251	2	no	—
291	C₂×C₄⋊C₄	—	251	4	no	—
292	C₂×C₄⋊C₄	—	251	2	no	—
293	C₂×C₄⋊C₄	—	251	1	no	—
294	C₂×C₄⋊C₄	C₂×D₂₅₁	1	2	yes	—
295	C₂×C₄²	—	251	2	no	—
296	C₂×C₄²	—	251	4	no	—
297	C₂×C₄²	—	251	1	no	—
298	C₂×C₄²	—	251	2	no	—
299	#41	—	251	8	no	—
300	C₂×Q₈	—	502	8	no	—
301	C₂×Q₈	—	502	4	no	—
302	C₂×Q₈	—	251	4	no	—
303	C₂×Q₈	—	251	2	no	—
304	C₂×Q₈	—	251	4	no	—
305	C₂×Q₈	—	251	2	no	—
306	C₂×Q₈	—	251	1	no	—
307	C₂×Q₈	—	251	1	no	—
308	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
309	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
310	C₂×D₄	—	251	2	no	—
311	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
312	C₂²×C₄	—	251	2	no	—
313	C₂²×C₄	—	251	1	no	—
314	C₂²×C₄	—	251	2	no	—
315	C₂²×C₄	—	251	4	no	—
316	C₂²×C₄	—	251	2	no	—
317	C₂²×C₄	—	251	1	no	—
318	C₂²×C₄	—	251	2	no	—
319	C₂²×C₄	—	251	1	no	—
320	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
321	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	—
322	C₄⋊C₄	—	251	2	no	—
323	C₄⋊C₄	—	251	4	no	—
324	C₄⋊C₄	—	251	4	no	—
325	C₄⋊C₄	—	251	2	no	—
326	C₄⋊C₄	—	251	4	no	—
327	C₄⋊C₄	—	251	2	no	—
328	C₄⋊C₄	—	251	2	no	—
329	C₄⋊C₄	—	251	1	no	—
330	C₄⋊C₄	—	251	4	no	—
331	C₄⋊C₄	—	251	2	no	—
332	C₄⋊C₄	—	251	2	no	—
333	C₄⋊C₄	—	251	4	no	—
334	C₄⋊C₄	—	251	2	no	—
335	C₄⋊C₄	—	251	1	no	—
336	C₄⋊C₄	—	251	4	no	—
337	C₄⋊C₄	—	251	4	no	—
338	C₄⋊C₄	—	251	4	no	—
339	C₄⋊C₄	—	251	2	no	—
340	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
341	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
342	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
343	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
344	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
345	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
347	C₂²⋊C₄	—	251	4	no	—
348	C₂²⋊C₄	—	251	2	no	—
349	C₂²⋊C₄	—	251	4	no	—
350	C₂²⋊C₄	—	251	2	no	—
351	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
352	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
353	C₄²	—	251	1	no	—
354	C₄²	—	251	2	no	—
355	C₄²	—	251	4	no	—
356	C₄²	—	251	2	no	—
357	C₄²	—	251	1	no	—
358	C₄²	—	251	2	no	—
359	C₄²	—	251	1	no	—
360	C₄²	—	251	2	no	—
361	C₄²	—	251	4	no	—
362	C₄²	—	251	2	no	—
363	C₄²	—	251	2	no	—
364	C₄²	—	251	4	no	—
365	C₄²	C₂²×D₂₅₁	1	2	yes	—
366	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
367	C₂³	—	251	1	no	—
368	C₂³	C₂³×D₂₅₁	1	2	yes	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	1004	4	no	—
372	Q₈	—	502	8	no	—
373	Q₈	—	502	4	no	—
374	Q₈	—	502	4	no	—
375	Q₈	—	251	4	no	—
376	Q₈	—	251	4	no	—
377	D₄	—	251	8	no	—
378	D₄	Q₈×D₂₅₁	1	4	yes	complemented
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	1004	2	no	—
382	C₂×C₄	—	1004	1	no	—
383	C₂×C₄	—	1004	2	no	—
384	C₂×C₄	—	502	4	no	—
385	C₂×C₄	—	502	8	no	—
386	C₂×C₄	—	502	2	no	—
387	C₂×C₄	—	251	1	no	—
388	C₂×C₄	—	251	1	no	—
389	C₂×C₄	—	251	4	no	—
390	C₂×C₄	—	251	2	no	—
391	C₂×C₄	—	251	2	no	—
392	C₂×C₄	—	251	8	no	—
393	C₂×C₄	—	251	1	no	—
394	C₂×C₄	—	251	2	no	—
395	C₂×C₄	—	251	2	no	—
396	C₂×C₄	—	251	4	no	—
397	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
398	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
399	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
400	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
402	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	502	1	no	—
407	C₂²	—	502	1	no	—
408	C₂²	—	251	2	no	—
409	C₂²	C₂×Q₈×D₂₅₁	1	4	yes	—
410	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	1	no	—
416	C₄	—	502	4	no	—
417	C₄	—	502	1	no	—
418	C₄	—	502	1	no	—
419	C₄	—	502	2	no	—
420	C₄	—	502	2	no	—
421	C₄	—	251	2	no	—
422	C₄	—	251	4	no	—
423	C₄	—	251	4	no	—
424	C₄	C₂×Q₈×D₂₅₁	1	2	yes	—
425	C₄	#41×D₂₅₁	1	2	yes	—
426	C₂	—	2	4	no	—
427	C₂	—	502	2	no	—
428	C₂	C₂²×Q₈×D₂₅₁	1	1	yes	characteristic
429	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
430	C₂	#30632522	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#554×C₂₅₁	C₂
prime radical	C₂×#16860809	C₂²
hypercenter	#554	D₂₅₁
hypocenter	C₂₅₁	Q₈×#41
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #30632417	C₂	semidirect
2. #30632415	C₂	semidirect
3. #30632414	C₂	semidirect
4. #30632396	C₂	semidirect
5. #30632392	C₂	semidirect
6. #30632391	C₂	semidirect
7. D₄×Dic₅₀₂	C₂	semidirect
8. #30632350	C₂	semidirect
9. #30632243	C₂	semidirect
10. #30632242	C₂	semidirect
11. #30632239	C₂	semidirect
12. #30632239	C₂	semidirect
15. C₂×#22548680	C₂	semidirect
16. C₄×Q₈×D₂₅₁	C₂	semidirect
17. #554×C₂₅₁	C₂	semidirect
83. #16860809	Q₈	semidirect
156. Dic₅₀₂	C₂×Q₈	semidirect
157. Dic₅₀₂	#41	semidirect
158. C₂²⋊D₂₅₁	C₂×Q₈	semidirect
161. C₂×Dic₂₅₁	C₂×Q₈	semidirect
174. C₄×D₂₅₁	C₂×Q₈	semidirect
178. D₄×C₂₅₁	C₂×Q₈	semidirect
215. C₂₅₁	Q₈×#41	semidirect
223. #554	D₂₅₁	semidirect
378. D₄	Q₈×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632417	2
#30632415	2
#30632414	2
#30632396	2
#30632392	2
#30632391	2
D₄×Dic₅₀₂	2
#30632350	2
#30632243	2
#30632242	2
#30632239	2
C₄×#16860809	2
C₂×#22548680	2
C₄×Q₈×D₂₅₁	2
#554×C₂₅₁	2
Q₈×#41	251