Subgroups — C₃₁×#17608 #21474367

Order 7936.

1298 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1516	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1513	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1511	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1508	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1504	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1501	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#328	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×2₋¹⁺⁴	C₄	1	1	yes	characteristic, complemented
13	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#131	—	2	1	no	—
15	D₄×Q₈×C₃₁	—	2	1	no	—
16	C₃₁×#548	—	2	1	no	—
17	C₃₁×#547	—	2	1	no	—
18	C₃₁×#547	—	2	2	no	—
19	C₃₁×#546	—	2	1	no	—
20	C₃₁×#546	—	2	2	no	—
21	C₃₁×#537	C₄	1	2	yes	complemented
22	C₃₁×#537	C₄	1	1	yes	characteristic, complemented
23	C₃₁×#536	C₄	1	1	yes	characteristic, complemented
24	C₃₁×#536	C₄	1	2	yes	complemented
25	C₃₁×#525	C₂²	1	1	yes	characteristic
26	C₃₁×#525	C₂²	1	2	yes	—
27	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃₁×#520	C₄	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₃₁	—	2	1	no	—
31	C₃₁×#408	—	2	2	no	—
32	C₃₁×#408	—	2	1	no	—
33	C₃₁×#407	C₂²	1	2	yes	—
34	C₃₁×#407	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₃₁×#391	—	2	1	no	—
38	C₃₁×#386	—	2	2	no	—
39	C₃₁×#381	C₂²	1	2	yes	—
40	C₃₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#95	C₂²	1	2	yes	—
43	C₃₁×#328	C₂²	1	1	yes	characteristic
44	C₃₁×#328	C₂²	1	2	yes	—
45	C₃₁×#328	C₂²	1	2	yes	—
46	C₃₁×#328	C₂²	1	2	yes	—
47	C₃₁×#328	C₂²	1	1	yes	characteristic
48	C₃₁×#328	C₂²	1	2	yes	—
49	C₃₁×#328	C₂²	1	2	yes	—
50	C₃₁×#327	C₂²	1	1	yes	characteristic
51	C₃₁×#327	C₂²	1	1	yes	characteristic
52	C₃₁×#327	C₂²	1	2	yes	—
53	C₃₁×2₋¹⁺⁴	—	4	4	no	—
54	C₂×#41×C₃₁	—	2	2	no	—
55	C₂×#41×C₃₁	—	2	1	no	—
56	C₂×#41×C₃₁	—	4	4	no	—
57	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
59	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic
60	C₂×#41×C₃₁	C₂×C₄	1	2	yes	complemented
61	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
63	C₂×#41×C₃₁	D₄	1	2	yes	—
64	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
65	C₂²×Q₈×C₃₁	—	2	1	no	—
66	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	complemented
68	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₃₁	D₄	1	2	yes	—
71	C₂³×C₄×C₃₁	—	2	2	no	—
72	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
73	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₃₁×#131	—	4	4	no	—
75	C₂×M₁₆×C₃₁	—	2	2	no	—
76	C₂×M₁₆×C₃₁	—	2	1	no	—
77	C₂²×C₈×C₃₁	—	2	2	no	—
78	C₂²×C₈×C₃₁	—	2	1	no	—
79	C₃₁×C₄⋊Q₈	—	2	1	no	—
80	C₃₁×C₄⋊Q₈	—	2	2	no	—
81	C₃₁×#124	—	2	1	no	—
82	C₃₁×#124	—	2	2	no	—
83	C₃₁×#123	—	2	2	no	—
84	C₃₁×#123	—	2	2	no	—
85	C₃₁×#123	—	2	2	no	—
86	C₃₁×#123	—	2	2	no	—
87	C₃₁×#123	—	2	1	no	—
88	C₃₁×C₂²⋊Q₈	—	2	1	no	—
89	C₃₁×C₂²⋊Q₈	—	2	2	no	—
90	C₃₁×C₂²⋊Q₈	—	2	1	no	—
91	C₃₁×C₂²⋊Q₈	—	2	2	no	—
92	C₃₁×C₂²⋊Q₈	—	2	1	no	—
93	C₃₁×C₂²⋊Q₈	—	2	2	no	—
94	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
95	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
96	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
97	C₃₁×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
98	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
99	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
101	C₃₁×#121	—	2	2	no	—
102	C₃₁×#121	—	2	2	no	—
103	C₃₁×#121	—	2	2	no	—
104	C₃₁×#121	—	2	1	no	—
105	C₃₁×#121	—	2	2	no	—
106	C₃₁×#121	C₂×C₄	1	1	yes	characteristic, complemented
107	C₃₁×#121	C₂×C₄	1	2	yes	complemented
108	C₃₁×#121	C₂³	1	1	yes	characteristic
109	C₃₁×#120	—	2	2	no	—
110	C₃₁×#120	—	2	1	no	—
111	C₄×Q₈×C₃₁	—	2	1	no	—
112	C₄×D₄×C₃₁	—	2	2	no	—
113	C₄×D₄×C₃₁	—	2	1	no	—
114	C₄×D₄×C₃₁	—	2	1	no	—
115	C₄×D₄×C₃₁	—	2	2	no	—
116	C₄×D₄×C₃₁	—	2	1	no	—
117	C₄×D₄×C₃₁	—	2	2	no	—
118	C₄×D₄×C₃₁	—	4	4	no	—
119	C₃₁×#117	C₂×C₄	1	1	yes	characteristic, complemented
120	C₃₁×#117	C₂×C₄	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
123	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	complemented
125	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
127	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
131	C₂×C₄²×C₃₁	—	2	1	no	—
132	C₃₁×C₂²⋊C₈	—	2	1	no	—
133	C₃₁×C₂²⋊C₈	—	2	2	no	—
134	C₃₁×C₂²⋊C₈	—	2	1	no	—
135	C₃₁×C₂²⋊C₈	—	2	2	no	—
136	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
138	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
139	C₃₁×#95	—	2	2	no	—
140	C₃₁×#95	—	2	2	no	—
141	C₃₁×#95	C₂³	1	1	yes	characteristic
142	C₃₁×#95	C₂³	1	2	yes	—
143	C₃₁×#95	C₂³	1	1	yes	characteristic
144	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
145	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
146	#41×C₃₁	—	2	4	no	—
147	#41×C₃₁	—	2	4	no	—
148	#41×C₃₁	—	4	4	no	—
149	#41×C₃₁	—	4	4	no	—
150	#41×C₃₁	—	4	2	no	—
151	#41×C₃₁	—	4	2	no	—
152	#41×C₃₁	—	4	4	no	—
153	#41×C₃₁	—	4	2	no	—
154	#41×C₃₁	—	4	8	no	—
155	#41×C₃₁	—	4	4	no	—
156	C₂×Q₈×C₃₁	—	2	2	no	—
157	C₂×Q₈×C₃₁	—	2	1	no	—
158	C₂×Q₈×C₃₁	—	4	2	no	—
159	C₂×Q₈×C₃₁	—	4	2	no	—
160	C₂×Q₈×C₃₁	—	4	4	no	—
161	C₂×Q₈×C₃₁	—	4	4	no	—
162	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×Q₈×C₃₁	C₂²⋊C₄	1	2	yes	—
165	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
166	C₂×Q₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	2	1	no	—
169	C₂×D₄×C₃₁	—	2	2	no	—
170	C₂×D₄×C₃₁	—	2	1	no	—
171	C₂×D₄×C₃₁	—	2	1	no	—
172	C₂×D₄×C₃₁	—	2	2	no	—
173	C₂×D₄×C₃₁	—	4	4	no	—
174	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
175	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
176	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
177	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
179	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
180	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×D₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₃₁	—	2	1	no	—
183	C₂²×C₄×C₃₁	—	2	2	no	—
184	C₂²×C₄×C₃₁	—	2	1	no	—
185	C₂²×C₄×C₃₁	—	2	1	no	—
186	C₂²×C₄×C₃₁	—	2	2	no	—
187	C₂²×C₄×C₃₁	—	2	2	no	—
188	C₂²×C₄×C₃₁	—	2	1	no	—
189	C₂²×C₄×C₃₁	—	2	1	no	—
190	C₂²×C₄×C₃₁	—	2	2	no	—
191	C₂²×C₄×C₃₁	—	4	2	no	—
192	C₂²×C₄×C₃₁	—	4	4	no	—
193	C₂²×C₄×C₃₁	—	4	4	no	—
194	C₂²×C₄×C₃₁	—	4	4	no	—
195	C₂²×C₄×C₃₁	—	8	2	no	—
196	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
197	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
207	M₁₆×C₃₁	—	4	4	no	—
208	M₁₆×C₃₁	—	4	2	no	—
209	C₂×C₈×C₃₁	—	2	1	no	—
210	C₂×C₈×C₃₁	—	2	1	no	—
211	C₂×C₈×C₃₁	—	2	2	no	—
212	C₂×C₈×C₃₁	—	4	4	no	—
213	C₂×C₈×C₃₁	—	4	2	no	—
214	C₄⋊C₄×C₃₁	—	2	2	no	—
215	C₄⋊C₄×C₃₁	—	2	2	no	—
216	C₄⋊C₄×C₃₁	—	2	2	no	—
217	C₄⋊C₄×C₃₁	—	2	2	no	—
218	C₄⋊C₄×C₃₁	—	2	1	no	—
219	C₄⋊C₄×C₃₁	—	2	1	no	—
220	C₄⋊C₄×C₃₁	—	2	2	no	—
221	C₄⋊C₄×C₃₁	—	2	1	no	—
222	C₄⋊C₄×C₃₁	—	2	2	no	—
223	C₄⋊C₄×C₃₁	—	4	2	no	—
224	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
225	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
226	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
227	C₂²⋊C₄×C₃₁	—	2	2	no	—
228	C₂²⋊C₄×C₃₁	—	2	2	no	—
229	C₂²⋊C₄×C₃₁	—	2	2	no	—
230	C₂²⋊C₄×C₃₁	—	2	1	no	—
231	C₂²⋊C₄×C₃₁	—	2	2	no	—
232	C₂²⋊C₄×C₃₁	—	2	1	no	—
233	C₂²⋊C₄×C₃₁	—	2	2	no	—
234	C₂²⋊C₄×C₃₁	—	2	1	no	—
235	C₂²⋊C₄×C₃₁	—	2	2	no	—
236	C₂²⋊C₄×C₃₁	—	2	1	no	—
237	C₂²⋊C₄×C₃₁	—	2	2	no	—
238	C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂²⋊C₄×C₃₁	—	4	2	no	—
240	C₂²⋊C₄×C₃₁	—	4	4	no	—
241	C₂²⋊C₄×C₃₁	—	8	1	no	—
242	C₄²×C₃₁	—	2	2	no	—
243	C₄²×C₃₁	—	2	1	no	—
244	C₄²×C₃₁	—	4	2	no	—
245	#17608	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₃₁	—	2	2	no	—
247	C₂³×C₃₁	—	2	2	no	—
248	C₂³×C₃₁	—	2	4	no	—
249	C₂³×C₃₁	—	2	1	no	—
250	C₂³×C₃₁	—	2	1	no	—
251	C₂³×C₃₁	—	2	1	no	—
252	C₂³×C₃₁	—	4	2	no	—
253	C₂³×C₃₁	—	4	1	no	—
254	C₂³×C₃₁	—	4	1	no	—
255	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₃₁	—	2	2	no	—
261	Q₈×C₃₁	—	2	2	no	—
262	Q₈×C₃₁	—	4	2	no	—
263	Q₈×C₃₁	—	4	2	no	—
264	Q₈×C₃₁	—	4	1	no	—
265	Q₈×C₃₁	—	4	4	no	—
266	Q₈×C₃₁	—	4	2	no	—
267	D₄×C₃₁	—	2	4	no	—
268	D₄×C₃₁	—	2	4	no	—
269	D₄×C₃₁	—	2	4	no	—
270	D₄×C₃₁	—	2	2	no	—
271	D₄×C₃₁	—	4	2	no	—
272	D₄×C₃₁	—	4	2	no	—
273	D₄×C₃₁	—	4	1	no	—
274	D₄×C₃₁	—	4	2	no	—
275	D₄×C₃₁	—	4	1	no	—
276	D₄×C₃₁	—	4	1	no	—
277	D₄×C₃₁	—	4	4	no	—
278	D₄×C₃₁	—	8	2	no	—
279	D₄×C₃₁	—	8	1	no	—
280	D₄×C₃₁	#99	1	4	yes	—
281	C₂×C₄×C₃₁	—	2	4	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	2	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	2	no	—
287	C₂×C₄×C₃₁	—	2	1	no	—
288	C₂×C₄×C₃₁	—	2	2	no	—
289	C₂×C₄×C₃₁	—	2	1	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	1	no	—
292	C₂×C₄×C₃₁	—	4	1	no	—
293	C₂×C₄×C₃₁	—	4	1	no	—
294	C₂×C₄×C₃₁	—	4	2	no	—
295	C₂×C₄×C₃₁	—	4	2	no	—
296	C₂×C₄×C₃₁	—	4	2	no	—
297	C₂×C₄×C₃₁	—	4	1	no	—
298	C₂×C₄×C₃₁	—	4	4	no	—
299	C₂×C₄×C₃₁	—	4	1	no	—
300	C₂×C₄×C₃₁	—	4	2	no	—
301	C₂×C₄×C₃₁	—	4	1	no	—
302	C₂×C₄×C₃₁	—	4	4	no	—
303	C₂×C₄×C₃₁	—	4	2	no	—
304	C₂×C₄×C₃₁	—	4	1	no	—
305	C₂×C₄×C₃₁	—	4	2	no	—
306	C₂×C₄×C₃₁	—	4	1	no	—
307	C₂×C₄×C₃₁	—	4	2	no	—
308	C₂×C₄×C₃₁	—	4	2	no	—
309	C₂×C₄×C₃₁	—	4	1	no	—
310	C₂×C₄×C₃₁	—	8	2	no	—
311	C₂×C₄×C₃₁	—	8	1	no	—
312	C₂×C₄×C₃₁	—	8	8	no	—
313	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
314	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
319	C₈×C₃₁	—	4	1	no	—
320	C₈×C₃₁	—	4	2	no	—
321	C₈×C₃₁	—	4	1	no	—
322	#3489	C₂×C₃₁	1	1	yes	characteristic
323	#2880	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#2339	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#1520	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#1516	C₂×C₃₁	1	2	yes	complemented
327	#1513	C₂×C₃₁	1	1	yes	characteristic, complemented
328	#1511	C₂×C₃₁	1	2	yes	complemented
329	#1508	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#1504	C₂×C₃₁	1	2	yes	complemented
331	#1501	C₂×C₃₁	1	1	yes	characteristic, complemented
332	C₂×#328	C₂×C₃₁	1	2	yes	complemented
333	C₂²×C₃₁	—	2	1	no	—
334	C₂²×C₃₁	—	2	2	no	—
335	C₂²×C₃₁	—	2	1	no	—
336	C₂²×C₃₁	—	2	2	no	—
337	C₂²×C₃₁	—	2	1	no	—
338	C₂²×C₃₁	—	2	1	no	—
339	C₂²×C₃₁	—	2	2	no	—
340	C₂²×C₃₁	—	2	2	no	—
341	C₂²×C₃₁	—	2	1	no	—
342	C₂²×C₃₁	—	2	1	no	—
343	C₂²×C₃₁	—	2	1	no	—
344	C₂²×C₃₁	—	2	2	no	—
345	C₂²×C₃₁	—	2	1	no	—
346	C₂²×C₃₁	—	4	4	no	—
347	C₂²×C₃₁	—	4	4	no	—
348	C₂²×C₃₁	—	4	1	no	—
349	C₂²×C₃₁	—	4	1	no	—
350	C₂²×C₃₁	—	4	1	no	—
351	C₂²×C₃₁	—	8	1	no	—
352	C₂²×C₃₁	—	8	1	no	—
353	C₂²×C₃₁	C₂×#99	1	4	yes	—
354	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
355	C₂²×C₃₁	#577	1	1	yes	characteristic
356	C₂²×C₃₁	#578	1	1	yes	characteristic
357	C₄×C₃₁	—	2	1	no	—
358	C₄×C₃₁	—	2	1	no	—
359	C₄×C₃₁	—	2	2	no	—
360	C₄×C₃₁	—	2	1	no	—
361	C₄×C₃₁	—	2	2	no	—
362	C₄×C₃₁	—	4	2	no	—
363	C₄×C₃₁	—	4	2	no	—
364	C₄×C₃₁	—	4	1	no	—
365	C₄×C₃₁	—	4	1	no	—
366	C₄×C₃₁	—	4	1	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	8	1	no	—
369	C₄×C₃₁	—	8	2	no	—
370	C₄×C₃₁	C₂×#99	1	2	yes	—
371	C₂×2₋¹⁺⁴	C₄×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
373	C₂×#131	—	2	1	no	—
374	D₄×Q₈	—	2	1	no	—
375	#548	—	2	1	no	—
376	#547	—	2	1	no	—
377	#547	—	2	2	no	—
378	#546	—	2	1	no	—
379	#546	—	2	2	no	—
380	#537	C₄×C₃₁	1	2	yes	complemented
381	#537	C₄×C₃₁	1	1	yes	characteristic, complemented
382	#536	C₄×C₃₁	1	1	yes	characteristic, complemented
383	#536	C₄×C₃₁	1	2	yes	complemented
384	#525	C₂²×C₃₁	1	1	yes	characteristic
385	#525	C₂²×C₃₁	1	2	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
388	#520	C₄×C₃₁	1	1	yes	characteristic, complemented
389	C₂×C₄×D₄	—	2	1	no	—
390	#408	—	2	2	no	—
391	#408	—	2	1	no	—
392	#407	C₂²×C₃₁	1	2	yes	—
393	#407	C₂²×C₃₁	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
395	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
396	#391	—	2	1	no	—
397	#386	—	2	2	no	—
398	#381	C₂²×C₃₁	1	2	yes	—
399	#380	C₂²×C₃₁	1	1	yes	characteristic
400	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×#95	C₂²×C₃₁	1	2	yes	—
402	#328	C₂²×C₃₁	1	1	yes	characteristic
403	#328	C₂²×C₃₁	1	2	yes	—
404	#328	C₂²×C₃₁	1	2	yes	—
405	#328	C₂²×C₃₁	1	2	yes	—
406	#328	C₂²×C₃₁	1	1	yes	characteristic
407	#328	C₂²×C₃₁	1	2	yes	—
408	#328	C₂²×C₃₁	1	2	yes	—
409	#327	C₂²×C₃₁	1	1	yes	characteristic
410	#327	C₂²×C₃₁	1	1	yes	characteristic
411	#327	C₂²×C₃₁	1	2	yes	—
412	C₂×C₃₁	—	2	1	no	—
413	C₂×C₃₁	—	2	1	no	—
414	C₂×C₃₁	—	2	4	no	—
415	C₂×C₃₁	—	4	2	no	—
416	C₂×C₃₁	—	4	1	no	—
417	C₂×C₃₁	—	4	1	no	—
418	C₂×C₃₁	—	8	1	no	—
419	C₂×C₃₁	C₂²×#99	1	1	yes	characteristic
420	C₂×C₃₁	#2898	1	1	yes	characteristic
421	C₂×C₃₁	#2901	1	1	yes	characteristic
422	2₋¹⁺⁴	—	4	4	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	—	4	4	no	—
426	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
427	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
428	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
429	C₂×#41	C₂×C₄×C₃₁	1	2	yes	complemented
430	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
431	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
432	C₂×#41	D₄×C₃₁	1	2	yes	—
433	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
434	C₂²×Q₈	—	2	1	no	—
435	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
436	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
437	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
438	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
439	C₂²×D₄	D₄×C₃₁	1	2	yes	—
440	C₂³×C₄	—	2	2	no	—
441	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
442	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
443	#131	—	4	4	no	—
444	C₂×M₁₆	—	2	2	no	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂²×C₈	—	2	2	no	—
447	C₂²×C₈	—	2	1	no	—
448	C₄⋊Q₈	—	2	1	no	—
449	C₄⋊Q₈	—	2	2	no	—
450	#124	—	2	1	no	—
451	#124	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	#123	—	2	2	no	—
455	#123	—	2	2	no	—
456	#123	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	—	2	2	no	—
463	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
464	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
465	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
466	C₂²⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
467	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
468	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
470	#121	—	2	2	no	—
471	#121	—	2	2	no	—
472	#121	—	2	2	no	—
473	#121	—	2	1	no	—
474	#121	—	2	2	no	—
475	#121	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
476	#121	C₂×C₄×C₃₁	1	2	yes	complemented
477	#121	C₂³×C₃₁	1	1	yes	characteristic
478	#120	—	2	2	no	—
479	#120	—	2	1	no	—
480	C₄×Q₈	—	2	1	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	1	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	4	4	no	—
488	#117	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
489	#117	C₂×C₄×C₃₁	1	2	yes	complemented
490	C₂×C₄⋊C₄	—	2	2	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	complemented
494	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
495	C₂×C₂²⋊C₄	—	2	2	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	2	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₄²	—	2	1	no	—
501	C₂²⋊C₈	—	2	1	no	—
502	C₂²⋊C₈	—	2	2	no	—
503	C₂²⋊C₈	—	2	1	no	—
504	C₂²⋊C₈	—	2	2	no	—
505	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
506	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
507	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
508	#95	—	2	2	no	—
509	#95	—	2	2	no	—
510	#95	C₂³×C₃₁	1	1	yes	characteristic
511	#95	C₂³×C₃₁	1	2	yes	—
512	#95	C₂³×C₃₁	1	1	yes	characteristic
513	C₃₁	#17608	1	1	yes	characteristic, direct product factor, Sylow
514	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
515	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
516	#41	—	2	4	no	—
517	#41	—	2	4	no	—
518	#41	—	4	4	no	—
519	#41	—	4	4	no	—
520	#41	—	4	2	no	—
521	#41	—	4	2	no	—
522	#41	—	4	4	no	—
523	#41	—	4	2	no	—
524	#41	—	4	8	no	—
525	#41	—	4	4	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	4	2	no	—
529	C₂×Q₈	—	4	2	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	—	4	4	no	—
532	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
533	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
534	C₂×Q₈	C₂²⋊C₄×C₃₁	1	2	yes	—
535	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
536	C₂×Q₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
545	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
546	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
547	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
548	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
549	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
550	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
551	C₂×D₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	4	no	—
563	C₂²×C₄	—	4	4	no	—
564	C₂²×C₄	—	4	4	no	—
565	C₂²×C₄	—	8	2	no	—
566	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
567	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
569	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
572	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
574	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
577	M₁₆	—	4	4	no	—
578	M₁₆	—	4	2	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	2	no	—
582	C₂×C₈	—	4	4	no	—
583	C₂×C₈	—	4	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
595	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
596	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	4	4	no	—
611	C₂²⋊C₄	—	8	1	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	4	2	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
625	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
626	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
627	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
628	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	4	no	—
635	Q₈	—	4	2	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	4	no	—
639	D₄	—	2	2	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	2	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	8	2	no	—
648	D₄	—	8	1	no	—
649	D₄	C₃₁×#99	1	4	yes	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	—	8	8	no	—
682	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
683	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
684	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
685	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
686	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
688	C₈	—	4	1	no	—
689	C₈	—	4	2	no	—
690	C₈	—	4	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	C₂×C₃₁×#99	1	4	yes	—
712	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
713	C₂²	C₃₁×#577	1	1	yes	characteristic
714	C₂²	C₃₁×#578	1	1	yes	characteristic
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	8	2	no	—
727	C₄	—	8	1	no	—
728	C₄	C₂×C₃₁×#99	1	2	yes	—
729	C₂	—	2	1	no	—
730	C₂	—	2	1	no	—
731	C₂	—	2	4	no	—
732	C₂	—	4	2	no	—
733	C₂	—	4	1	no	—
734	C₂	—	4	1	no	—
735	C₂	—	8	1	no	—
736	C₂	C₂²×C₃₁×#99	1	1	yes	characteristic
737	C₂	C₃₁×#2898	1	1	yes	characteristic
738	C₂	C₃₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2880	C₂	semidirect
3. C₃₁×#2339	C₂	semidirect
4. C₃₁×#1520	C₂	semidirect
5. C₃₁×#1516	C₂	semidirect
6. C₃₁×#1513	C₂	semidirect
7. C₃₁×#1511	C₂	semidirect
8. C₃₁×#1508	C₂	semidirect
9. C₃₁×#1504	C₂	semidirect
10. C₃₁×#1501	C₂	semidirect
11. C₂×C₃₁×#328	C₂	semidirect
12. C₂×C₃₁×2₋¹⁺⁴	C₄	semidirect
21. C₃₁×#537	C₄	semidirect
22. C₃₁×#537	C₄	semidirect
23. C₃₁×#536	C₄	semidirect
24. C₃₁×#536	C₄	semidirect
29. C₃₁×#520	C₄	semidirect
60. C₂×#41×C₃₁	C₂×C₄	semidirect
61. C₂×#41×C₃₁	C₂×C₄	semidirect
66. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
67. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
94. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
95. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
96. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
97. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
98. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
106. C₃₁×#121	C₂×C₄	semidirect
107. C₃₁×#121	C₂×C₄	semidirect
119. C₃₁×#117	C₂×C₄	semidirect
120. C₃₁×#117	C₂×C₄	semidirect
124. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
125. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
245. #17608	C₃₁	direct (N × H)
323. #2880	C₂×C₃₁	semidirect
324. #2339	C₂×C₃₁	semidirect
325. #1520	C₂×C₃₁	semidirect
326. #1516	C₂×C₃₁	semidirect
327. #1513	C₂×C₃₁	semidirect
328. #1511	C₂×C₃₁	semidirect
329. #1508	C₂×C₃₁	semidirect
330. #1504	C₂×C₃₁	semidirect
331. #1501	C₂×C₃₁	semidirect
332. C₂×#328	C₂×C₃₁	semidirect
371. C₂×2₋¹⁺⁴	C₄×C₃₁	semidirect
380. #537	C₄×C₃₁	semidirect
381. #537	C₄×C₃₁	semidirect
382. #536	C₄×C₃₁	semidirect
383. #536	C₄×C₃₁	semidirect
388. #520	C₄×C₃₁	semidirect
429. C₂×#41	C₂×C₄×C₃₁	semidirect
430. C₂×#41	C₂×C₄×C₃₁	semidirect
435. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
436. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
463. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
464. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
465. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
466. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
467. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
475. #121	C₂×C₄×C₃₁	semidirect
476. #121	C₂×C₄×C₃₁	semidirect
488. #117	C₂×C₄×C₃₁	semidirect
489. #117	C₂×C₄×C₃₁	semidirect
493. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
494. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
513. C₃₁	#17608	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3489	2
C₃₁×#2880	2
C₃₁×#2339	2
C₃₁×#1520	2
C₃₁×#1516	2
C₃₁×#1513	2
C₃₁×#1511	2
C₃₁×#1508	2
C₃₁×#1504	2
C₃₁×#1501	2
C₂×C₃₁×#328	2
#17608	31

Subgroups — C31×#17608 #21474367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17608 #21474367