Subgroups — C₃₁×#35010 #21491769

Order 7936.

2930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2855	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2848	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2627	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2626	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2579	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2564	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2487	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2417	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2409	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2315	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2308	C₂	1	2	yes	maximal
14	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×C₂²⋊Q₈	—	2	8	no	—
20	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₃₁	—	2	8	no	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×#400	C₂²	1	4	yes	complemented
40	C₃₁×#399	C₂²	1	4	yes	complemented
41	C₃₁×#398	C₂²	1	8	yes	complemented
42	C₃₁×#396	C₂²	1	8	yes	complemented
43	C₃₁×#395	C₂²	1	4	yes	complemented
44	C₃₁×#393	C₂²	1	4	yes	complemented
45	C₃₁×#391	C₂²	1	4	yes	complemented
46	C₃₁×#389	C₂²	1	4	yes	complemented
47	C₃₁×#387	C₂²	1	8	yes	complemented
48	C₃₁×#386	C₂²	1	8	yes	—
49	C₃₁×#386	C₂²	1	4	yes	—
50	C₃₁×#386	C₂²	1	4	yes	—
51	C₃₁×#385	C₂²	1	4	yes	—
52	C₃₁×#385	C₂²	1	4	yes	—
53	C₃₁×#385	C₂²	1	8	yes	complemented
54	C₃₁×#385	C₂²	1	4	yes	complemented
55	C₃₁×#385	C₂²	1	4	yes	complemented
56	C₃₁×#381	C₂²	1	4	yes	—
57	C₃₁×#380	C₂²	1	2	yes	—
58	C₃₁×#380	C₂²	1	2	yes	—
59	C₃₁×#380	C₂²	1	8	yes	complemented
60	C₃₁×#380	C₂²	1	2	yes	complemented
61	C₃₁×#380	C₂²	1	4	yes	complemented
62	C₃₁×#380	C₂²	1	2	yes	complemented
63	C₃₁×#379	C₂²	1	4	yes	—
64	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
65	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
66	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₃₁	—	2	4	no	—
68	C₂²×Q₈×C₃₁	—	4	4	no	—
69	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
70	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
71	C₂²×D₄×C₃₁	—	2	4	no	—
72	C₂²×D₄×C₃₁	—	2	4	no	—
73	C₂²×D₄×C₃₁	Q₈	1	8	yes	complemented
74	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
76	C₂³×C₄×C₃₁	—	2	4	no	—
77	C₂³×C₄×C₃₁	—	4	4	no	—
78	C₂³×C₄×C₃₁	—	4	4	no	—
79	C₂³×C₄×C₃₁	D₄	1	8	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×C₂²⋊Q₈	—	2	8	no	—
95	C₃₁×C₂²⋊Q₈	—	2	8	no	—
96	C₃₁×C₂²⋊Q₈	—	2	8	no	—
97	C₃₁×C₂²⋊Q₈	—	2	8	no	—
98	C₃₁×C₂²⋊Q₈	—	4	8	no	—
99	C₄×D₄×C₃₁	—	2	8	no	—
100	C₄×D₄×C₃₁	—	2	8	no	—
101	C₄×D₄×C₃₁	—	2	8	no	—
102	C₄×D₄×C₃₁	—	2	8	no	—
103	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
105	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
106	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
118	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
131	C₂×C₄²×C₃₁	—	2	4	no	—
132	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
134	C₃₁×#95	C₂³	1	8	yes	—
135	C₃₁×#95	C₂³	1	4	yes	—
136	C₃₁×#95	C₂³	1	8	yes	—
137	C₃₁×#95	C₂³	1	8	yes	—
138	C₃₁×#95	C₂³	1	8	yes	—
139	C₃₁×#95	C₂³	1	4	yes	—
140	C₂⁴×C₃₁	—	2	2	no	—
141	C₂⁴×C₃₁	—	2	2	no	—
142	C₂⁴×C₃₁	—	4	2	no	—
143	C₂⁴×C₃₁	—	4	2	no	—
144	C₂⁴×C₃₁	—	4	2	no	—
145	C₂⁴×C₃₁	—	4	2	no	—
146	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
147	C₂⁴×C₃₁	C₂×Q₈	1	4	yes	—
148	C₂⁴×C₃₁	C₂×Q₈	1	4	yes	complemented
149	C₂⁴×C₃₁	#41	1	4	yes	—
150	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
151	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
153	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₃₁	—	2	4	no	—
155	C₂×Q₈×C₃₁	—	2	4	no	—
156	C₂×Q₈×C₃₁	—	2	8	no	—
157	C₂×Q₈×C₃₁	—	4	4	no	—
158	C₂×Q₈×C₃₁	—	4	16	no	—
159	C₂×D₄×C₃₁	—	2	32	no	—
160	C₂×D₄×C₃₁	—	2	4	no	—
161	C₂×D₄×C₃₁	—	2	4	no	—
162	C₂×D₄×C₃₁	—	2	4	no	—
163	C₂×D₄×C₃₁	—	2	4	no	—
164	C₂×D₄×C₃₁	C₂×Q₈	1	8	yes	—
165	C₂×D₄×C₃₁	C₂×Q₈	1	8	yes	complemented
166	C₂²×C₄×C₃₁	—	2	2	no	—
167	C₂²×C₄×C₃₁	—	2	2	no	—
168	C₂²×C₄×C₃₁	—	2	4	no	—
169	C₂²×C₄×C₃₁	—	2	4	no	—
170	C₂²×C₄×C₃₁	—	2	4	no	—
171	C₂²×C₄×C₃₁	—	2	2	no	—
172	C₂²×C₄×C₃₁	—	2	4	no	—
173	C₂²×C₄×C₃₁	—	2	2	no	—
174	C₂²×C₄×C₃₁	—	2	4	no	—
175	C₂²×C₄×C₃₁	—	2	8	no	—
176	C₂²×C₄×C₃₁	—	2	4	no	—
177	C₂²×C₄×C₃₁	—	2	4	no	—
178	C₂²×C₄×C₃₁	—	2	8	no	—
179	C₂²×C₄×C₃₁	—	4	16	no	—
180	C₂²×C₄×C₃₁	—	4	2	no	—
181	C₂²×C₄×C₃₁	—	4	2	no	—
182	C₂²×C₄×C₃₁	—	4	2	no	—
183	C₂²×C₄×C₃₁	—	4	4	no	—
184	C₂²×C₄×C₃₁	—	4	2	no	—
185	C₂²×C₄×C₃₁	—	4	4	no	—
186	C₂²×C₄×C₃₁	—	4	2	no	—
187	C₂²×C₄×C₃₁	—	4	4	no	—
188	C₂²×C₄×C₃₁	—	4	4	no	—
189	C₂²×C₄×C₃₁	—	4	4	no	—
190	C₂²×C₄×C₃₁	—	4	16	no	—
191	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	complemented
198	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₃₁	—	2	4	no	—
209	C₄⋊C₄×C₃₁	—	2	4	no	—
210	C₄⋊C₄×C₃₁	—	2	4	no	—
211	C₄⋊C₄×C₃₁	—	2	4	no	—
212	C₄⋊C₄×C₃₁	—	2	8	no	—
213	C₄⋊C₄×C₃₁	—	2	8	no	—
214	C₄⋊C₄×C₃₁	—	2	8	no	—
215	C₄⋊C₄×C₃₁	—	4	4	no	—
216	C₄⋊C₄×C₃₁	—	4	8	no	—
217	C₄⋊C₄×C₃₁	—	4	8	no	—
218	C₂²⋊C₄×C₃₁	—	2	4	no	—
219	C₂²⋊C₄×C₃₁	—	2	4	no	—
220	C₂²⋊C₄×C₃₁	—	2	8	no	—
221	C₂²⋊C₄×C₃₁	—	2	8	no	—
222	C₂²⋊C₄×C₃₁	—	2	8	no	—
223	C₂²⋊C₄×C₃₁	—	2	8	no	—
224	C₂²⋊C₄×C₃₁	—	2	4	no	—
225	C₂²⋊C₄×C₃₁	—	2	4	no	—
226	C₂²⋊C₄×C₃₁	—	4	8	no	—
227	C₂²⋊C₄×C₃₁	—	4	8	no	—
228	C₄²×C₃₁	—	2	4	no	—
229	C₄²×C₃₁	—	2	4	no	—
230	#35010	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₃₁	—	2	2	no	—
232	C₂³×C₃₁	—	2	2	no	—
233	C₂³×C₃₁	—	2	2	no	—
234	C₂³×C₃₁	—	2	2	no	—
235	C₂³×C₃₁	—	2	2	no	—
236	C₂³×C₃₁	—	2	2	no	—
237	C₂³×C₃₁	—	2	8	no	—
238	C₂³×C₃₁	—	2	2	no	—
239	C₂³×C₃₁	—	2	2	no	—
240	C₂³×C₃₁	—	2	4	no	—
241	C₂³×C₃₁	—	2	4	no	—
242	C₂³×C₃₁	—	4	4	no	—
243	C₂³×C₃₁	—	4	4	no	—
244	C₂³×C₃₁	—	4	8	no	—
245	C₂³×C₃₁	—	4	8	no	—
246	C₂³×C₃₁	—	4	8	no	—
247	C₂³×C₃₁	—	4	4	no	—
248	C₂³×C₃₁	—	4	4	no	—
249	C₂³×C₃₁	—	4	8	no	—
250	C₂³×C₃₁	C₂²⋊Q₈	1	16	yes	complemented
251	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
252	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
253	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
254	C₂³×C₃₁	C₂²×Q₈	1	4	yes	—
255	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
256	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
257	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
258	C₂³×C₃₁	C₂×#41	1	2	yes	—
259	C₂³×C₃₁	C₂×#41	1	2	yes	—
260	C₂³×C₃₁	C₂×#41	1	2	yes	—
261	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
262	Q₈×C₃₁	—	4	8	no	—
263	Q₈×C₃₁	—	4	8	no	—
264	D₄×C₃₁	—	2	16	no	—
265	D₄×C₃₁	—	2	16	no	—
266	C₂×C₄×C₃₁	—	2	8	no	—
267	C₂×C₄×C₃₁	—	2	2	no	—
268	C₂×C₄×C₃₁	—	2	2	no	—
269	C₂×C₄×C₃₁	—	2	2	no	—
270	C₂×C₄×C₃₁	—	2	2	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	8	no	—
273	C₂×C₄×C₃₁	—	2	8	no	—
274	C₂×C₄×C₃₁	—	2	8	no	—
275	C₂×C₄×C₃₁	—	2	2	no	—
276	C₂×C₄×C₃₁	—	2	4	no	—
277	C₂×C₄×C₃₁	—	2	2	no	—
278	C₂×C₄×C₃₁	—	2	4	no	—
279	C₂×C₄×C₃₁	—	2	8	no	—
280	C₂×C₄×C₃₁	—	2	8	no	—
281	C₂×C₄×C₃₁	—	2	8	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	8	no	—
284	C₂×C₄×C₃₁	—	2	8	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	4	4	no	—
287	C₂×C₄×C₃₁	—	4	4	no	—
288	C₂×C₄×C₃₁	—	4	4	no	—
289	C₂×C₄×C₃₁	—	4	8	no	—
290	C₂×C₄×C₃₁	—	4	8	no	—
291	C₂×C₄×C₃₁	—	4	4	no	—
292	C₂×C₄×C₃₁	—	4	4	no	—
293	C₂×C₄×C₃₁	—	4	8	no	—
294	C₂×C₄×C₃₁	—	4	8	no	—
295	C₂×C₄×C₃₁	—	8	8	no	—
296	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
301	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
302	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
303	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic
304	#2855	C₂×C₃₁	1	2	yes	complemented
305	#2848	C₂×C₃₁	1	2	yes	complemented
306	#2627	C₂×C₃₁	1	2	yes	complemented
307	#2626	C₂×C₃₁	1	2	yes	complemented
308	#2579	C₂×C₃₁	1	4	yes	complemented
309	#2564	C₂×C₃₁	1	4	yes	complemented
310	#2487	C₂×C₃₁	1	2	yes	complemented
311	#2417	C₂×C₃₁	1	4	yes	complemented
312	#2409	C₂×C₃₁	1	2	yes	complemented
313	#2315	C₂×C₃₁	1	2	yes	complemented
314	#2308	C₂×C₃₁	1	2	yes	—
315	C₂×#380	C₂×C₃₁	1	1	yes	characteristic, complemented
316	C₂²×C₃₁	—	2	2	no	—
317	C₂²×C₃₁	—	2	2	no	—
318	C₂²×C₃₁	—	2	2	no	—
319	C₂²×C₃₁	—	2	2	no	—
320	C₂²×C₃₁	—	2	2	no	—
321	C₂²×C₃₁	—	2	2	no	—
322	C₂²×C₃₁	—	2	4	no	—
323	C₂²×C₃₁	—	2	4	no	—
324	C₂²×C₃₁	—	2	4	no	—
325	C₂²×C₃₁	—	2	4	no	—
326	C₂²×C₃₁	—	2	4	no	—
327	C₂²×C₃₁	—	2	4	no	—
328	C₂²×C₃₁	—	2	4	no	—
329	C₂²×C₃₁	—	2	8	no	—
330	C₂²×C₃₁	—	4	16	no	—
331	C₂²×C₃₁	—	4	16	no	—
332	C₂²×C₃₁	—	4	2	no	—
333	C₂²×C₃₁	—	4	2	no	—
334	C₂²×C₃₁	—	4	4	no	—
335	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
336	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
337	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
338	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
339	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
340	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
342	C₂²×C₃₁	#585	1	2	yes	—
343	C₄×C₃₁	—	2	4	no	—
344	C₄×C₃₁	—	2	2	no	—
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	2	no	—
347	C₄×C₃₁	—	4	2	no	—
348	C₄×C₃₁	—	4	4	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	—	4	4	no	—
351	C₄×C₃₁	—	4	8	no	—
352	C₄×C₃₁	#534	1	4	yes	—
353	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
354	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
355	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
356	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	—	2	8	no	—
358	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
359	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
360	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
361	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
362	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
363	C₂×C₄×D₄	—	2	8	no	—
364	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
366	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
368	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
370	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
371	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
372	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
373	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
374	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
376	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
377	#400	C₂²×C₃₁	1	4	yes	complemented
378	#399	C₂²×C₃₁	1	4	yes	complemented
379	#398	C₂²×C₃₁	1	8	yes	complemented
380	#396	C₂²×C₃₁	1	8	yes	complemented
381	#395	C₂²×C₃₁	1	4	yes	complemented
382	#393	C₂²×C₃₁	1	4	yes	complemented
383	#391	C₂²×C₃₁	1	4	yes	complemented
384	#389	C₂²×C₃₁	1	4	yes	complemented
385	#387	C₂²×C₃₁	1	8	yes	complemented
386	#386	C₂²×C₃₁	1	8	yes	—
387	#386	C₂²×C₃₁	1	4	yes	—
388	#386	C₂²×C₃₁	1	4	yes	—
389	#385	C₂²×C₃₁	1	4	yes	—
390	#385	C₂²×C₃₁	1	4	yes	—
391	#385	C₂²×C₃₁	1	8	yes	complemented
392	#385	C₂²×C₃₁	1	4	yes	complemented
393	#385	C₂²×C₃₁	1	4	yes	complemented
394	#381	C₂²×C₃₁	1	4	yes	—
395	#380	C₂²×C₃₁	1	2	yes	—
396	#380	C₂²×C₃₁	1	2	yes	—
397	#380	C₂²×C₃₁	1	8	yes	complemented
398	#380	C₂²×C₃₁	1	2	yes	complemented
399	#380	C₂²×C₃₁	1	4	yes	complemented
400	#380	C₂²×C₃₁	1	2	yes	complemented
401	#379	C₂²×C₃₁	1	4	yes	—
402	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
403	C₂×C₃₁	—	2	4	no	—
404	C₂×C₃₁	—	2	4	no	—
405	C₂×C₃₁	—	2	4	no	—
406	C₂×C₃₁	—	4	4	no	—
407	C₂×C₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
408	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
409	C₂×C₃₁	#3449	1	1	yes	characteristic
410	C₂×C₃₁	#3501	1	2	yes	—
411	C₂×C₃₁	#3505	1	2	yes	—
412	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
413	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
414	C₂²×Q₈	—	2	4	no	—
415	C₂²×Q₈	—	4	4	no	—
416	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
417	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
418	C₂²×D₄	—	2	4	no	—
419	C₂²×D₄	—	2	4	no	—
420	C₂²×D₄	Q₈×C₃₁	1	8	yes	complemented
421	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
422	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
423	C₂³×C₄	—	2	4	no	—
424	C₂³×C₄	—	4	4	no	—
425	C₂³×C₄	—	4	4	no	—
426	C₂³×C₄	D₄×C₃₁	1	8	yes	—
427	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
428	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
435	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
436	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
437	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
438	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
441	C₂²⋊Q₈	—	2	8	no	—
442	C₂²⋊Q₈	—	2	8	no	—
443	C₂²⋊Q₈	—	2	8	no	—
444	C₂²⋊Q₈	—	2	8	no	—
445	C₂²⋊Q₈	—	4	8	no	—
446	C₄×D₄	—	2	8	no	—
447	C₄×D₄	—	2	8	no	—
448	C₄×D₄	—	2	8	no	—
449	C₄×D₄	—	2	8	no	—
450	C₂×C₄⋊C₄	—	2	4	no	—
451	C₂×C₄⋊C₄	—	2	4	no	—
452	C₂×C₄⋊C₄	—	2	8	no	—
453	C₂×C₄⋊C₄	—	4	4	no	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
464	C₂×C₂²⋊C₄	—	2	4	no	—
465	C₂×C₂²⋊C₄	—	2	8	no	—
466	C₂×C₂²⋊C₄	—	2	8	no	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
478	C₂×C₄²	—	2	4	no	—
479	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
480	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
481	#95	C₂³×C₃₁	1	4	yes	—
482	#95	C₂³×C₃₁	1	4	yes	—
483	#95	C₂³×C₃₁	1	8	yes	—
484	#95	C₂³×C₃₁	1	8	yes	—
485	#95	C₂³×C₃₁	1	8	yes	—
486	#95	C₂³×C₃₁	1	8	yes	—
487	C₃₁	#35010	1	1	yes	characteristic, direct product factor, Sylow
488	C₂⁴	—	2	2	no	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	4	2	no	—
491	C₂⁴	—	4	2	no	—
492	C₂⁴	—	4	2	no	—
493	C₂⁴	—	4	2	no	—
494	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
495	C₂⁴	C₂×Q₈×C₃₁	1	4	yes	—
496	C₂⁴	C₂×Q₈×C₃₁	1	4	yes	complemented
497	C₂⁴	#41×C₃₁	1	4	yes	—
498	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
499	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
501	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	8	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	16	no	—
507	C₂×D₄	—	2	32	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	C₂×Q₈×C₃₁	1	8	yes	—
513	C₂×D₄	C₂×Q₈×C₃₁	1	8	yes	complemented
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	8	no	—
527	C₂²×C₄	—	4	16	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	16	no	—
539	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
540	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
541	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
542	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
543	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
545	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	complemented
546	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
547	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	8	no	—
565	C₄⋊C₄	—	4	8	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	8	no	—
571	C₂²⋊C₄	—	2	8	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	4	8	no	—
575	C₂²⋊C₄	—	4	8	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	8	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	4	4	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	8	no	—
592	C₂³	—	4	8	no	—
593	C₂³	—	4	8	no	—
594	C₂³	—	4	4	no	—
595	C₂³	—	4	4	no	—
596	C₂³	—	4	8	no	—
597	C₂³	C₃₁×C₂²⋊Q₈	1	16	yes	complemented
598	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
599	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
600	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
601	C₂³	C₂²×Q₈×C₃₁	1	4	yes	—
602	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
603	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
604	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
605	C₂³	C₂×#41×C₃₁	1	2	yes	—
606	C₂³	C₂×#41×C₃₁	1	2	yes	—
607	C₂³	C₂×#41×C₃₁	1	2	yes	—
608	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
609	Q₈	—	4	8	no	—
610	Q₈	—	4	8	no	—
611	D₄	—	2	16	no	—
612	D₄	—	2	16	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	8	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	4	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	8	no	—
641	C₂×C₄	—	4	8	no	—
642	C₂×C₄	—	8	8	no	—
643	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
644	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
645	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
646	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
647	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
648	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	8	no	—
663	C₂²	—	4	16	no	—
664	C₂²	—	4	16	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	4	no	—
668	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
669	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
670	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
671	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
672	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
673	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
674	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
675	C₂²	C₃₁×#585	1	2	yes	—
676	C₄	—	2	4	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	4	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	4	no	—
684	C₄	—	4	8	no	—
685	C₄	C₃₁×#534	1	4	yes	—
686	C₂	—	2	4	no	—
687	C₂	—	2	4	no	—
688	C₂	—	2	4	no	—
689	C₂	—	4	4	no	—
690	C₂	C₂²×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
691	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
692	C₂	C₃₁×#3449	1	1	yes	characteristic
693	C₂	C₃₁×#3501	1	2	yes	—
694	C₂	C₃₁×#3505	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×C₂²⋊Q₈	C₂	semidirect
3. C₃₁×#2855	C₂	semidirect
4. C₃₁×#2848	C₂	semidirect
5. C₃₁×#2627	C₂	semidirect
6. C₃₁×#2626	C₂	semidirect
7. C₃₁×#2579	C₂	semidirect
8. C₃₁×#2564	C₂	semidirect
9. C₃₁×#2487	C₂	semidirect
10. C₃₁×#2417	C₂	semidirect
11. C₃₁×#2409	C₂	semidirect
12. C₃₁×#2315	C₂	semidirect
14. C₂×C₃₁×#380	C₂	semidirect
15. C₂³×Q₈×C₃₁	C₂²	semidirect
22. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₃₁×#400	C₂²	semidirect
40. C₃₁×#399	C₂²	semidirect
41. C₃₁×#398	C₂²	semidirect
42. C₃₁×#396	C₂²	semidirect
43. C₃₁×#395	C₂²	semidirect
44. C₃₁×#393	C₂²	semidirect
45. C₃₁×#391	C₂²	semidirect
46. C₃₁×#389	C₂²	semidirect
47. C₃₁×#387	C₂²	semidirect
53. C₃₁×#385	C₂²	semidirect
54. C₃₁×#385	C₂²	semidirect
55. C₃₁×#385	C₂²	semidirect
59. C₃₁×#380	C₂²	semidirect
60. C₃₁×#380	C₂²	semidirect
61. C₃₁×#380	C₂²	semidirect
62. C₃₁×#380	C₂²	semidirect
64. C₂×C₃₁×#95	C₂²	semidirect
73. C₂²×D₄×C₃₁	Q₈	semidirect
148. C₂⁴×C₃₁	C₂×Q₈	semidirect
165. C₂×D₄×C₃₁	C₂×Q₈	semidirect
197. C₂²×C₄×C₃₁	C₂×Q₈	semidirect
230. #35010	C₃₁	direct (N × H)
250. C₂³×C₃₁	C₂²⋊Q₈	semidirect
302. C₂²×C₂²⋊Q₈	C₂×C₃₁	semidirect
304. #2855	C₂×C₃₁	semidirect
305. #2848	C₂×C₃₁	semidirect
306. #2627	C₂×C₃₁	semidirect
307. #2626	C₂×C₃₁	semidirect
308. #2579	C₂×C₃₁	semidirect
309. #2564	C₂×C₃₁	semidirect
310. #2487	C₂×C₃₁	semidirect
311. #2417	C₂×C₃₁	semidirect
312. #2409	C₂×C₃₁	semidirect
313. #2315	C₂×C₃₁	semidirect
315. C₂×#380	C₂×C₃₁	semidirect
353. C₂³×Q₈	C₂²×C₃₁	semidirect
360. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
361. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
362. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
369. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
370. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
371. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
377. #400	C₂²×C₃₁	semidirect
378. #399	C₂²×C₃₁	semidirect
379. #398	C₂²×C₃₁	semidirect
380. #396	C₂²×C₃₁	semidirect
381. #395	C₂²×C₃₁	semidirect
382. #393	C₂²×C₃₁	semidirect
383. #391	C₂²×C₃₁	semidirect
384. #389	C₂²×C₃₁	semidirect
385. #387	C₂²×C₃₁	semidirect
391. #385	C₂²×C₃₁	semidirect
392. #385	C₂²×C₃₁	semidirect
393. #385	C₂²×C₃₁	semidirect
397. #380	C₂²×C₃₁	semidirect
398. #380	C₂²×C₃₁	semidirect
399. #380	C₂²×C₃₁	semidirect
400. #380	C₂²×C₃₁	semidirect
402. C₂×#95	C₂²×C₃₁	semidirect
420. C₂²×D₄	Q₈×C₃₁	semidirect
487. C₃₁	#35010	direct (N × H)
496. C₂⁴	C₂×Q₈×C₃₁	semidirect
513. C₂×D₄	C₂×Q₈×C₃₁	semidirect
545. C₂²×C₄	C₂×Q₈×C₃₁	semidirect
597. C₂³	C₃₁×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×C₂²⋊Q₈	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2855	2
C₃₁×#2848	2
C₃₁×#2627	2
C₃₁×#2626	2
C₃₁×#2579	2
C₃₁×#2564	2
C₃₁×#2487	2
C₃₁×#2417	2
C₃₁×#2409	2
C₃₁×#2315	2
C₃₁×#2308	2
C₂×C₃₁×#380	2
#35010	31

Subgroups — C31×#35010 #21491769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35010 #21491769