Subgroups — C₃₁×#34475 #21491234

Order 7936.

2280 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2381	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2378	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2368	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2353	C₂	1	2	yes	maximal
10	C₃₁×#2352	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2332	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2331	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2318	C₂	1	2	yes	maximal
20	C₃₁×#2310	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₃₁	C₄	1	16	yes	complemented
27	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#391	C₂²	1	1	yes	characteristic
45	C₃₁×#391	C₂²	1	1	yes	characteristic
46	C₃₁×#391	C₂²	1	2	yes	—
47	C₃₁×#391	C₂²	1	1	yes	characteristic
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#391	C₂²	1	2	yes	—
50	C₃₁×#391	C₂²	1	1	yes	characteristic
51	C₃₁×#391	C₂²	1	1	yes	characteristic
52	C₃₁×#391	C₂²	1	2	yes	—
53	C₃₁×#391	C₂²	1	2	yes	—
54	C₃₁×#391	C₂²	1	2	yes	—
55	C₃₁×#391	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	2	yes	—
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	2	yes	—
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	1	yes	characteristic
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#388	C₂²	1	1	yes	characteristic
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	1	yes	characteristic
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	1	yes	characteristic
89	C₃₁×#386	C₂²	1	1	yes	characteristic
90	C₃₁×#386	C₂²	1	2	yes	—
91	C₃₁×#386	C₂²	1	1	yes	characteristic
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	1	yes	characteristic
95	C₃₁×#385	C₂²	1	1	yes	characteristic
96	C₃₁×#383	C₂²	1	2	yes	—
97	C₃₁×#383	C₂²	1	2	yes	—
98	C₃₁×#382	C₂²	1	2	yes	—
99	C₃₁×#382	C₂²	1	1	yes	characteristic
100	C₃₁×#381	C₂²	1	2	yes	—
101	C₃₁×#381	C₂²	1	2	yes	—
102	C₃₁×#380	C₂²	1	2	yes	—
103	C₃₁×#380	C₂²	1	1	yes	characteristic
104	C₃₁×#380	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₃₁×#376	C₂²	1	1	yes	characteristic
121	C₃₁×#376	C₂²	1	2	yes	—
122	C₂×C₃₁×#95	C₂²	1	2	yes	—
123	C₂×C₃₁×#95	C₂²	1	2	yes	—
124	C₂²×Q₈×C₃₁	—	4	2	no	—
125	C₂²×Q₈×C₃₁	—	4	2	no	—
126	C₂²×Q₈×C₃₁	—	4	2	no	—
127	C₂²×Q₈×C₃₁	—	4	2	no	—
128	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	—
129	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
143	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
144	C₃₁×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
145	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
146	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
147	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
148	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
149	C₄×Q₈×C₃₁	—	4	2	no	—
150	C₄×Q₈×C₃₁	—	4	2	no	—
151	C₄×Q₈×C₃₁	—	4	2	no	—
152	C₄×Q₈×C₃₁	—	4	2	no	—
153	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
154	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
155	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	—
156	C₃₁×#117	—	4	2	no	—
157	C₃₁×#117	—	4	2	no	—
158	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	—	4	2	no	—
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	1	yes	characteristic
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	1	yes	characteristic
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	1	yes	characteristic
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	1	yes	characteristic
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	1	yes	characteristic
237	C₃₁×#95	C₂³	1	1	yes	characteristic
238	C₃₁×#95	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₃₁×#95	C₂³	1	1	yes	characteristic
244	C₃₁×#95	C₂³	1	2	yes	—
245	C₃₁×#95	C₂³	1	2	yes	—
246	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₃₁	—	2	2	no	—
249	C₂×Q₈×C₃₁	—	2	2	no	—
250	C₂×Q₈×C₃₁	—	2	2	no	—
251	C₂×Q₈×C₃₁	—	2	2	no	—
252	C₂×Q₈×C₃₁	—	2	2	no	—
253	C₂×Q₈×C₃₁	—	2	2	no	—
254	C₂×Q₈×C₃₁	—	4	2	no	—
255	C₂×Q₈×C₃₁	—	4	2	no	—
256	C₂×Q₈×C₃₁	—	4	2	no	—
257	C₂×Q₈×C₃₁	—	4	2	no	—
258	C₂×Q₈×C₃₁	—	4	16	no	—
259	C₂×Q₈×C₃₁	—	4	16	no	—
260	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
261	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
262	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
263	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
264	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
265	C₂×D₄×C₃₁	—	2	2	no	—
266	C₂×D₄×C₃₁	—	2	2	no	—
267	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
268	C₂²×C₄×C₃₁	—	2	2	no	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	2	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	4	no	—
275	C₂²×C₄×C₃₁	—	2	2	no	—
276	C₂²×C₄×C₃₁	—	4	1	no	—
277	C₂²×C₄×C₃₁	—	4	1	no	—
278	C₂²×C₄×C₃₁	—	4	1	no	—
279	C₂²×C₄×C₃₁	—	4	2	no	—
280	C₂²×C₄×C₃₁	—	4	2	no	—
281	C₂²×C₄×C₃₁	—	4	2	no	—
282	C₂²×C₄×C₃₁	—	4	2	no	—
283	C₂²×C₄×C₃₁	—	4	2	no	—
284	C₂²×C₄×C₃₁	—	4	2	no	—
285	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
286	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
287	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
288	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	4	2	no	—
316	C₄⋊C₄×C₃₁	—	4	1	no	—
317	C₄⋊C₄×C₃₁	—	4	2	no	—
318	C₄⋊C₄×C₃₁	—	4	2	no	—
319	C₄⋊C₄×C₃₁	—	4	1	no	—
320	C₄⋊C₄×C₃₁	—	4	1	no	—
321	C₄⋊C₄×C₃₁	—	4	2	no	—
322	C₄⋊C₄×C₃₁	—	4	2	no	—
323	C₄⋊C₄×C₃₁	—	4	2	no	—
324	C₄⋊C₄×C₃₁	—	4	2	no	—
325	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
326	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
327	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
328	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
330	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
331	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	2	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₃₁	—	4	1	no	—
338	C₂²⋊C₄×C₃₁	—	4	1	no	—
339	C₂²⋊C₄×C₃₁	—	4	1	no	—
340	C₂²⋊C₄×C₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
342	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
343	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
344	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
345	C₄²×C₃₁	—	2	2	no	—
346	C₄²×C₃₁	—	2	2	no	—
347	C₄²×C₃₁	—	2	2	no	—
348	C₄²×C₃₁	—	2	2	no	—
349	C₄²×C₃₁	—	2	4	no	—
350	C₄²×C₃₁	—	4	1	no	—
351	C₄²×C₃₁	—	4	1	no	—
352	C₄²×C₃₁	—	4	2	no	—
353	C₄²×C₃₁	—	4	2	no	—
354	C₄²×C₃₁	—	4	2	no	—
355	C₄²×C₃₁	—	4	2	no	—
356	C₄²×C₃₁	—	4	2	no	—
357	C₄²×C₃₁	—	4	2	no	—
358	C₄²×C₃₁	—	4	2	no	—
359	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
360	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
361	#34475	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂³×C₃₁	—	2	1	no	—
363	C₂³×C₃₁	—	2	1	no	—
364	C₂³×C₃₁	—	2	1	no	—
365	C₂³×C₃₁	—	2	1	no	—
366	C₂³×C₃₁	—	2	1	no	—
367	C₂³×C₃₁	—	2	1	no	—
368	C₂³×C₃₁	—	2	1	no	—
369	C₂³×C₃₁	—	2	1	no	—
370	C₂³×C₃₁	—	2	1	no	—
371	C₂³×C₃₁	—	2	1	no	—
372	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
373	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
374	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
375	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
376	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
377	Q₈×C₃₁	—	2	8	no	—
378	Q₈×C₃₁	—	2	8	no	—
379	Q₈×C₃₁	—	2	8	no	—
380	Q₈×C₃₁	—	4	8	no	—
381	Q₈×C₃₁	—	4	8	no	—
382	D₄×C₃₁	—	2	8	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	1	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	8	no	—
402	C₂×C₄×C₃₁	—	2	8	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	1	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	1	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	1	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	1	no	—
435	C₂×C₄×C₃₁	—	2	1	no	—
436	C₂×C₄×C₃₁	—	4	8	no	—
437	C₂×C₄×C₃₁	—	4	8	no	—
438	C₂×C₄×C₃₁	—	4	4	no	—
439	C₂×C₄×C₃₁	—	4	4	no	—
440	C₂×C₄×C₃₁	—	8	4	no	—
441	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
443	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
445	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
448	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
449	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
450	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
451	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
452	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
453	C₂×D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic
454	#2381	C₂×C₃₁	1	2	yes	complemented
455	#2378	C₂×C₃₁	1	2	yes	complemented
456	#2368	C₂×C₃₁	1	2	yes	complemented
457	#2365	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#2362	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#2360	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#2356	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#2353	C₂×C₃₁	1	2	yes	—
462	#2352	C₂×C₃₁	1	1	yes	characteristic
463	Q₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
464	Q₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#2332	C₂×C₃₁	1	2	yes	complemented
466	#2331	C₂×C₃₁	1	2	yes	complemented
467	#2329	C₂×C₃₁	1	2	yes	complemented
468	#2327	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#2323	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#2320	C₂×C₃₁	1	1	yes	characteristic, complemented
471	#2318	C₂×C₃₁	1	2	yes	—
472	#2310	C₂×C₃₁	1	1	yes	characteristic, complemented
473	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
474	C₂×#391	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#2290	C₂×C₃₁	1	1	yes	characteristic
476	C₂²×C₃₁	—	2	2	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	2	2	no	—
479	C₂²×C₃₁	—	2	2	no	—
480	C₂²×C₃₁	—	2	2	no	—
481	C₂²×C₃₁	—	2	2	no	—
482	C₂²×C₃₁	—	2	2	no	—
483	C₂²×C₃₁	—	2	2	no	—
484	C₂²×C₃₁	—	2	2	no	—
485	C₂²×C₃₁	—	4	1	no	—
486	C₂²×C₃₁	—	4	1	no	—
487	C₂²×C₃₁	—	4	1	no	—
488	C₂²×C₃₁	—	4	1	no	—
489	C₂²×C₃₁	#519	1	4	yes	—
490	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
491	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
495	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
496	C₂²×C₃₁	#585	1	1	yes	characteristic
497	C₄×C₃₁	—	2	2	no	—
498	C₄×C₃₁	—	2	2	no	—
499	C₄×C₃₁	—	2	4	no	—
500	C₄×C₃₁	—	2	4	no	—
501	C₄×C₃₁	—	2	4	no	—
502	C₄×C₃₁	—	2	2	no	—
503	C₄×C₃₁	—	2	4	no	—
504	C₄×C₃₁	—	2	2	no	—
505	C₄×C₃₁	—	2	2	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	—	4	1	no	—
508	C₄×C₃₁	—	4	1	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	1	no	—
511	C₄×C₃₁	—	4	1	no	—
512	C₄×C₃₁	—	4	1	no	—
513	C₄×C₃₁	—	4	2	no	—
514	C₄×C₃₁	—	4	1	no	—
515	C₄×C₃₁	—	4	2	no	—
516	C₄×C₃₁	—	4	2	no	—
517	C₄×C₃₁	#518	1	4	yes	—
518	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
519	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
520	D₄×Q₈	C₄×C₃₁	1	16	yes	complemented
521	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
522	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
523	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
524	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
525	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
527	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
528	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
529	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
531	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
533	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
534	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
535	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
536	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
537	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
538	#391	C₂²×C₃₁	1	1	yes	characteristic
539	#391	C₂²×C₃₁	1	1	yes	characteristic
540	#391	C₂²×C₃₁	1	2	yes	—
541	#391	C₂²×C₃₁	1	1	yes	characteristic
542	#391	C₂²×C₃₁	1	1	yes	characteristic
543	#391	C₂²×C₃₁	1	2	yes	—
544	#391	C₂²×C₃₁	1	1	yes	characteristic
545	#391	C₂²×C₃₁	1	1	yes	characteristic
546	#391	C₂²×C₃₁	1	2	yes	—
547	#391	C₂²×C₃₁	1	2	yes	—
548	#391	C₂²×C₃₁	1	2	yes	—
549	#391	C₂²×C₃₁	1	2	yes	—
550	#391	C₂²×C₃₁	1	2	yes	—
551	#391	C₂²×C₃₁	1	1	yes	characteristic
552	#391	C₂²×C₃₁	1	1	yes	characteristic
553	#391	C₂²×C₃₁	1	2	yes	—
554	#389	C₂²×C₃₁	1	1	yes	characteristic
555	#389	C₂²×C₃₁	1	1	yes	characteristic
556	#389	C₂²×C₃₁	1	2	yes	—
557	#389	C₂²×C₃₁	1	2	yes	—
558	#389	C₂²×C₃₁	1	2	yes	—
559	#388	C₂²×C₃₁	1	2	yes	—
560	#388	C₂²×C₃₁	1	2	yes	—
561	#388	C₂²×C₃₁	1	2	yes	—
562	#388	C₂²×C₃₁	1	1	yes	characteristic
563	#388	C₂²×C₃₁	1	2	yes	—
564	#388	C₂²×C₃₁	1	2	yes	—
565	#388	C₂²×C₃₁	1	1	yes	characteristic
566	#387	C₂²×C₃₁	1	2	yes	—
567	#387	C₂²×C₃₁	1	2	yes	—
568	#387	C₂²×C₃₁	1	2	yes	—
569	#387	C₂²×C₃₁	1	2	yes	—
570	#387	C₂²×C₃₁	1	2	yes	—
571	#387	C₂²×C₃₁	1	2	yes	—
572	#387	C₂²×C₃₁	1	2	yes	—
573	#387	C₂²×C₃₁	1	2	yes	—
574	#387	C₂²×C₃₁	1	2	yes	—
575	#387	C₂²×C₃₁	1	2	yes	—
576	#387	C₂²×C₃₁	1	1	yes	characteristic
577	#387	C₂²×C₃₁	1	2	yes	—
578	#387	C₂²×C₃₁	1	2	yes	—
579	#387	C₂²×C₃₁	1	2	yes	—
580	#387	C₂²×C₃₁	1	2	yes	—
581	#387	C₂²×C₃₁	1	2	yes	—
582	#387	C₂²×C₃₁	1	1	yes	characteristic
583	#386	C₂²×C₃₁	1	1	yes	characteristic
584	#386	C₂²×C₃₁	1	2	yes	—
585	#386	C₂²×C₃₁	1	1	yes	characteristic
586	#385	C₂²×C₃₁	1	2	yes	—
587	#385	C₂²×C₃₁	1	2	yes	—
588	#385	C₂²×C₃₁	1	1	yes	characteristic
589	#385	C₂²×C₃₁	1	1	yes	characteristic
590	#383	C₂²×C₃₁	1	2	yes	—
591	#383	C₂²×C₃₁	1	2	yes	—
592	#382	C₂²×C₃₁	1	2	yes	—
593	#382	C₂²×C₃₁	1	1	yes	characteristic
594	#381	C₂²×C₃₁	1	2	yes	—
595	#381	C₂²×C₃₁	1	2	yes	—
596	#380	C₂²×C₃₁	1	2	yes	—
597	#380	C₂²×C₃₁	1	1	yes	characteristic
598	#380	C₂²×C₃₁	1	2	yes	—
599	#380	C₂²×C₃₁	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
603	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
604	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
605	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
607	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
608	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
612	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
614	#376	C₂²×C₃₁	1	1	yes	characteristic
615	#376	C₂²×C₃₁	1	2	yes	—
616	C₂×#95	C₂²×C₃₁	1	2	yes	—
617	C₂×#95	C₂²×C₃₁	1	2	yes	—
618	C₂×C₃₁	—	2	4	no	—
619	C₂×C₃₁	—	4	2	no	—
620	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
621	C₂×C₃₁	C₂×#519	1	1	yes	characteristic
622	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
623	C₂×C₃₁	#3538	1	1	yes	characteristic
624	C₂×C₃₁	#3541	1	1	yes	characteristic
625	C₂×C₃₁	#3552	1	1	yes	characteristic
626	C₂×C₃₁	#3561	1	1	yes	characteristic
627	C₂²×Q₈	—	4	2	no	—
628	C₂²×Q₈	—	4	2	no	—
629	C₂²×Q₈	—	4	2	no	—
630	C₂²×Q₈	—	4	2	no	—
631	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	—
632	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
633	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
635	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
636	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
637	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
638	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
643	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
645	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
646	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
647	C₄⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
648	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
649	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	—
650	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
651	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
652	C₄×Q₈	—	4	2	no	—
653	C₄×Q₈	—	4	2	no	—
654	C₄×Q₈	—	4	2	no	—
655	C₄×Q₈	—	4	2	no	—
656	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
657	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
658	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	—
659	#117	—	4	2	no	—
660	#117	—	4	2	no	—
661	C₂×C₄⋊C₄	—	4	2	no	—
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	—	4	2	no	—
698	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
703	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
704	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
705	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
706	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
707	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
708	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
709	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
710	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	2	yes	—
716	#95	C₂³×C₃₁	1	2	yes	—
717	#95	C₂³×C₃₁	1	2	yes	—
718	#95	C₂³×C₃₁	1	2	yes	—
719	#95	C₂³×C₃₁	1	2	yes	—
720	#95	C₂³×C₃₁	1	2	yes	—
721	#95	C₂³×C₃₁	1	2	yes	—
722	#95	C₂³×C₃₁	1	1	yes	characteristic
723	#95	C₂³×C₃₁	1	2	yes	—
724	#95	C₂³×C₃₁	1	1	yes	characteristic
725	#95	C₂³×C₃₁	1	2	yes	—
726	#95	C₂³×C₃₁	1	1	yes	characteristic
727	#95	C₂³×C₃₁	1	1	yes	characteristic
728	#95	C₂³×C₃₁	1	1	yes	characteristic
729	#95	C₂³×C₃₁	1	1	yes	characteristic
730	#95	C₂³×C₃₁	1	2	yes	—
731	#95	C₂³×C₃₁	1	2	yes	—
732	#95	C₂³×C₃₁	1	2	yes	—
733	#95	C₂³×C₃₁	1	2	yes	—
734	#95	C₂³×C₃₁	1	2	yes	—
735	#95	C₂³×C₃₁	1	2	yes	—
736	#95	C₂³×C₃₁	1	2	yes	—
737	#95	C₂³×C₃₁	1	2	yes	—
738	#95	C₂³×C₃₁	1	2	yes	—
739	#95	C₂³×C₃₁	1	1	yes	characteristic
740	#95	C₂³×C₃₁	1	1	yes	characteristic
741	#95	C₂³×C₃₁	1	1	yes	characteristic
742	#95	C₂³×C₃₁	1	2	yes	—
743	#95	C₂³×C₃₁	1	2	yes	—
744	#95	C₂³×C₃₁	1	2	yes	—
745	#95	C₂³×C₃₁	1	2	yes	—
746	#95	C₂³×C₃₁	1	1	yes	characteristic
747	#95	C₂³×C₃₁	1	2	yes	—
748	#95	C₂³×C₃₁	1	2	yes	—
749	C₃₁	#34475	1	1	yes	characteristic, direct product factor, Sylow
750	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
751	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	2	no	—
760	C₂×Q₈	—	4	2	no	—
761	C₂×Q₈	—	4	2	no	—
762	C₂×Q₈	—	4	16	no	—
763	C₂×Q₈	—	4	16	no	—
764	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
765	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
766	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
767	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
768	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	4	1	no	—
781	C₂²×C₄	—	4	1	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
790	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
791	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
792	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	1	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	—	4	1	no	—
824	C₄⋊C₄	—	4	1	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
830	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
831	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
832	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
833	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
834	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
835	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	1	no	—
842	C₂²⋊C₄	—	4	1	no	—
843	C₂²⋊C₄	—	4	1	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
846	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
847	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
848	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	4	no	—
854	C₄²	—	4	1	no	—
855	C₄²	—	4	1	no	—
856	C₄²	—	4	2	no	—
857	C₄²	—	4	2	no	—
858	C₄²	—	4	2	no	—
859	C₄²	—	4	2	no	—
860	C₄²	—	4	2	no	—
861	C₄²	—	4	2	no	—
862	C₄²	—	4	2	no	—
863	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
864	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
876	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
877	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
878	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
879	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	2	8	no	—
882	Q₈	—	2	8	no	—
883	Q₈	—	4	8	no	—
884	Q₈	—	4	8	no	—
885	D₄	—	2	8	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	4	8	no	—
940	C₂×C₄	—	4	8	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	8	4	no	—
944	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
945	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
946	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
947	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
948	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
949	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
950	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
951	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
952	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
953	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
954	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
955	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	C₃₁×#519	1	4	yes	—
970	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
971	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
972	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
973	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
974	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
975	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
976	C₂²	C₃₁×#585	1	1	yes	characteristic
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	4	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	4	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	C₃₁×#518	1	4	yes	—
998	C₂	—	2	4	no	—
999	C₂	—	4	2	no	—
1000	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1001	C₂	C₂×C₃₁×#519	1	1	yes	characteristic
1002	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1003	C₂	C₃₁×#3538	1	1	yes	characteristic
1004	C₂	C₃₁×#3541	1	1	yes	characteristic
1005	C₂	C₃₁×#3552	1	1	yes	characteristic
1006	C₂	C₃₁×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2381	C₂	semidirect
3. C₃₁×#2378	C₂	semidirect
4. C₃₁×#2368	C₂	semidirect
5. C₃₁×#2365	C₂	semidirect
6. C₃₁×#2362	C₂	semidirect
7. C₃₁×#2360	C₂	semidirect
8. C₃₁×#2356	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₃₁	C₂	semidirect
12. Q₈×C₂²⋊C₄×C₃₁	C₂	semidirect
13. C₃₁×#2332	C₂	semidirect
14. C₃₁×#2331	C₂	semidirect
15. C₃₁×#2329	C₂	semidirect
16. C₃₁×#2327	C₂	semidirect
17. C₃₁×#2323	C₂	semidirect
18. C₃₁×#2320	C₂	semidirect
20. C₃₁×#2310	C₂	semidirect
21. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₃₁×#391	C₂	semidirect
26. D₄×Q₈×C₃₁	C₄	semidirect
129. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
143. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
144. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
147. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
148. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
153. C₄×Q₈×C₃₁	C₂×C₄	semidirect
361. #34475	C₃₁	direct (N × H)
454. #2381	C₂×C₃₁	semidirect
455. #2378	C₂×C₃₁	semidirect
456. #2368	C₂×C₃₁	semidirect
457. #2365	C₂×C₃₁	semidirect
458. #2362	C₂×C₃₁	semidirect
459. #2360	C₂×C₃₁	semidirect
460. #2356	C₂×C₃₁	semidirect
463. Q₈×C₂²⋊C₄	C₂×C₃₁	semidirect
464. Q₈×C₂²⋊C₄	C₂×C₃₁	semidirect
465. #2332	C₂×C₃₁	semidirect
466. #2331	C₂×C₃₁	semidirect
467. #2329	C₂×C₃₁	semidirect
468. #2327	C₂×C₃₁	semidirect
469. #2323	C₂×C₃₁	semidirect
470. #2320	C₂×C₃₁	semidirect
472. #2310	C₂×C₃₁	semidirect
473. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
474. C₂×#391	C₂×C₃₁	semidirect
520. D₄×Q₈	C₄×C₃₁	semidirect
632. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
646. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
647. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
650. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
651. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
656. C₄×Q₈	C₂×C₄×C₃₁	semidirect
749. C₃₁	#34475	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₃₁	2
C₃₁×#2381	2
C₃₁×#2378	2
C₃₁×#2368	2
C₃₁×#2365	2
C₃₁×#2362	2
C₃₁×#2360	2
C₃₁×#2356	2
C₃₁×#2353	2
C₃₁×#2352	2
Q₈×C₂²⋊C₄×C₃₁	2
C₃₁×#2332	2
C₃₁×#2331	2
C₃₁×#2329	2
C₃₁×#2327	2
C₃₁×#2323	2
C₃₁×#2320	2
C₃₁×#2318	2
C₃₁×#2310	2
C₄×C₃₁×C₂²⋊Q₈	2
C₂×C₃₁×#391	2
C₃₁×#2290	2
#34475	31

Subgroups — C31×#34475 #21491234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34475 #21491234