Subgroups — C₃₁×#17547 #21474306

Order 7936.

1166 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2974	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1507	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1505	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1504	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1502	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1501	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1500	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#327	C₂	1	2	yes	maximal, complemented
12	C₃₁×#555	C₄	1	1	yes	characteristic, complemented
13	C₃₁×#554	C₄	1	1	yes	characteristic, complemented
14	C₃₁×#553	—	2	1	no	—
15	C₃₁×#553	C₄	1	2	yes	complemented
16	C₃₁×#550	C₄	1	1	yes	characteristic, complemented
17	C₃₁×#546	—	2	2	no	—
18	C₃₁×#546	C₄	1	2	yes	complemented
19	D₄²×C₃₁	—	2	1	no	—
20	D₄²×C₃₁	C₄	1	1	yes	characteristic, complemented
21	C₃₁×#540	—	2	1	no	—
22	C₃₁×#538	—	2	2	no	—
23	C₃₁×#532	C₂²	1	1	yes	characteristic
24	C₃₁×#529	C₂²	1	1	yes	characteristic
25	C₃₁×#525	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₃₁×#518	—	2	1	no	—
28	C₂×C₄×D₄×C₃₁	—	2	1	no	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#436	—	2	1	no	—
31	C₃₁×#435	—	2	2	no	—
32	C₈×D₄×C₃₁	—	2	1	no	—
33	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#407	C₂²	1	2	yes	complemented
36	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
37	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
38	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
40	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
41	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
43	C₃₁×#328	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#328	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#328	C₂²	1	2	yes	complemented
46	C₃₁×#327	C₂²	1	1	yes	characteristic
47	C₃₁×#327	C₂²	1	2	yes	—
48	C₃₁×#327	C₂²	1	1	yes	characteristic
49	C₃₁×#327	C₂²	1	2	yes	complemented
50	C₃₁×#327	C₂²	1	2	yes	complemented
51	C₃₁×#327	C₂²	1	2	yes	complemented
52	C₃₁×#327	C₂²	1	2	yes	complemented
53	C₂×#41×C₃₁	—	2	1	no	—
54	C₂×#41×C₃₁	C₂×C₄	1	2	yes	complemented
55	C₂²×D₄×C₃₁	—	2	2	no	—
56	C₂²×D₄×C₃₁	—	2	1	no	—
57	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	complemented
58	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₃₁	—	2	2	no	—
60	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₃₁	—	2	2	no	—
62	C₂²×C₈×C₃₁	—	2	2	no	—
63	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
64	C₃₁×#127	—	2	1	no	—
65	C₃₁×#127	C₂×C₄	1	1	yes	characteristic, complemented
66	C₃₁×#126	—	2	2	no	—
67	C₃₁×#126	—	2	1	no	—
68	C₃₁×#125	—	2	1	no	—
69	C₃₁×#125	C₂×C₄	1	1	yes	characteristic, complemented
70	C₃₁×#124	—	2	2	no	—
71	C₃₁×#124	—	2	1	no	—
72	C₃₁×#124	C₂×C₄	1	1	yes	characteristic, complemented
73	C₃₁×#123	—	2	2	no	—
74	C₃₁×#123	—	2	1	no	—
75	C₃₁×#123	—	2	2	no	—
76	C₃₁×#123	—	2	2	no	—
77	C₃₁×C₂²⋊Q₈	—	2	2	no	—
78	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
79	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
80	C₃₁×#121	—	2	2	no	—
81	C₃₁×#121	—	2	1	no	—
82	C₃₁×#121	—	2	2	no	—
83	C₃₁×#121	—	2	2	no	—
84	C₃₁×#121	—	2	1	no	—
85	C₃₁×#121	—	2	1	no	—
86	C₃₁×#121	—	2	2	no	—
87	C₃₁×#121	—	2	2	no	—
88	C₃₁×#121	C₂×C₄	1	2	yes	complemented
89	C₃₁×#121	C₂×C₄	1	2	yes	complemented
90	C₃₁×#121	C₂×C₄	1	2	yes	complemented
91	C₃₁×#121	C₂³	1	1	yes	characteristic
92	C₃₁×#121	C₂³	1	2	yes	—
93	C₃₁×#120	—	2	2	no	—
94	C₃₁×#120	—	2	2	no	—
95	C₃₁×#120	—	2	2	no	—
96	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
97	C₄×D₄×C₃₁	—	2	8	no	—
98	C₄×D₄×C₃₁	—	2	1	no	—
99	C₄×D₄×C₃₁	—	2	2	no	—
100	C₄×D₄×C₃₁	—	2	2	no	—
101	C₄×D₄×C₃₁	—	2	1	no	—
102	C₄×D₄×C₃₁	—	2	1	no	—
103	C₄×D₄×C₃₁	—	2	2	no	—
104	C₄×D₄×C₃₁	—	2	1	no	—
105	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
109	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	complemented
110	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
111	C₄×D₄×C₃₁	D₄	1	2	yes	—
112	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
113	C₃₁×#117	—	2	1	no	—
114	C₃₁×#117	—	2	1	no	—
115	C₃₁×#117	C₂×C₄	1	2	yes	complemented
116	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	complemented
118	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
120	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
121	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
122	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
123	C₂×C₄²×C₃₁	—	2	1	no	—
124	C₂×C₄²×C₃₁	—	2	1	no	—
125	C₂×C₄²×C₃₁	—	2	2	no	—
126	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊C₈	—	2	1	no	—
128	C₃₁×C₄⋊C₈	—	2	1	no	—
129	C₃₁×C₂²⋊C₈	—	2	2	no	—
130	C₃₁×C₂²⋊C₈	—	2	2	no	—
131	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
132	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
133	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
134	C₃₁×#97	—	2	1	no	—
135	C₄×C₈×C₃₁	—	2	1	no	—
136	C₃₁×#95	—	2	2	no	—
137	C₃₁×#95	—	2	1	no	—
138	C₃₁×#95	C₂³	1	1	yes	characteristic
139	C₃₁×#95	C₂³	1	2	yes	—
140	C₃₁×#95	C₂³	1	1	yes	characteristic
141	C₂⁴×C₃₁	—	2	2	no	—
142	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
143	#41×C₃₁	—	8	1	no	—
144	#41×C₃₁	—	8	1	no	—
145	#41×C₃₁	—	8	2	no	—
146	C₂×Q₈×C₃₁	—	2	1	no	—
147	C₂×Q₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₃₁	—	2	4	no	—
149	C₂×D₄×C₃₁	—	2	2	no	—
150	C₂×D₄×C₃₁	—	2	2	no	—
151	C₂×D₄×C₃₁	—	2	1	no	—
152	C₂×D₄×C₃₁	—	2	2	no	—
153	C₂×D₄×C₃₁	—	2	2	no	—
154	C₂×D₄×C₃₁	—	2	2	no	—
155	C₂×D₄×C₃₁	—	2	1	no	—
156	C₂×D₄×C₃₁	—	2	1	no	—
157	C₂×D₄×C₃₁	—	2	2	no	—
158	C₂×D₄×C₃₁	—	4	4	no	—
159	C₂×D₄×C₃₁	—	8	2	no	—
160	C₂×D₄×C₃₁	—	8	2	no	—
161	C₂×D₄×C₃₁	—	8	2	no	—
162	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
163	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×D₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₃₁	—	2	1	no	—
168	C₂²×C₄×C₃₁	—	2	1	no	—
169	C₂²×C₄×C₃₁	—	2	2	no	—
170	C₂²×C₄×C₃₁	—	2	8	no	—
171	C₂²×C₄×C₃₁	—	2	2	no	—
172	C₂²×C₄×C₃₁	—	2	1	no	—
173	C₂²×C₄×C₃₁	—	2	2	no	—
174	C₂²×C₄×C₃₁	—	2	2	no	—
175	C₂²×C₄×C₃₁	—	8	2	no	—
176	C₂²×C₄×C₃₁	—	8	2	no	—
177	C₂²×C₄×C₃₁	—	8	2	no	—
178	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
186	M₁₆×C₃₁	—	8	2	no	—
187	C₂×C₈×C₃₁	—	2	1	no	—
188	C₂×C₈×C₃₁	—	2	1	no	—
189	C₂×C₈×C₃₁	—	2	2	no	—
190	C₂×C₈×C₃₁	—	8	2	no	—
191	C₄⋊C₄×C₃₁	—	2	4	no	—
192	C₄⋊C₄×C₃₁	—	2	2	no	—
193	C₄⋊C₄×C₃₁	—	2	1	no	—
194	C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₄⋊C₄×C₃₁	—	2	1	no	—
196	C₄⋊C₄×C₃₁	—	2	2	no	—
197	C₄⋊C₄×C₃₁	—	2	1	no	—
198	C₄⋊C₄×C₃₁	—	2	1	no	—
199	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
202	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₃₁	—	2	8	no	—
206	C₂²⋊C₄×C₃₁	—	2	2	no	—
207	C₂²⋊C₄×C₃₁	—	2	2	no	—
208	C₂²⋊C₄×C₃₁	—	2	1	no	—
209	C₂²⋊C₄×C₃₁	—	2	1	no	—
210	C₂²⋊C₄×C₃₁	—	2	2	no	—
211	C₂²⋊C₄×C₃₁	—	2	2	no	—
212	C₂²⋊C₄×C₃₁	—	2	1	no	—
213	C₂²⋊C₄×C₃₁	—	2	2	no	—
214	C₂²⋊C₄×C₃₁	—	2	1	no	—
215	C₂²⋊C₄×C₃₁	—	2	2	no	—
216	C₂²⋊C₄×C₃₁	—	2	1	no	—
217	C₂²⋊C₄×C₃₁	—	2	2	no	—
218	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
219	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
220	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
221	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
222	C₄²×C₃₁	—	2	4	no	—
223	C₄²×C₃₁	—	2	2	no	—
224	C₄²×C₃₁	—	2	1	no	—
225	C₄²×C₃₁	—	8	1	no	—
226	C₄²×C₃₁	—	8	2	no	—
227	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
229	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
231	#17547	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂³×C₃₁	—	2	2	no	—
233	C₂³×C₃₁	—	2	2	no	—
234	C₂³×C₃₁	—	2	4	no	—
235	C₂³×C₃₁	—	2	1	no	—
236	C₂³×C₃₁	—	2	2	no	—
237	C₂³×C₃₁	—	4	2	no	—
238	C₂³×C₃₁	—	4	4	no	—
239	C₂³×C₃₁	—	8	2	no	—
240	C₂³×C₃₁	—	8	2	no	—
241	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₃₁	—	4	1	no	—
245	Q₈×C₃₁	—	8	1	no	—
246	D₄×C₃₁	—	2	4	no	—
247	D₄×C₃₁	—	2	2	no	—
248	D₄×C₃₁	—	4	1	no	—
249	D₄×C₃₁	—	4	2	no	—
250	D₄×C₃₁	—	4	1	no	—
251	D₄×C₃₁	—	4	2	no	—
252	D₄×C₃₁	—	4	1	no	—
253	D₄×C₃₁	—	4	2	no	—
254	D₄×C₃₁	—	4	4	no	—
255	D₄×C₃₁	—	4	2	no	—
256	D₄×C₃₁	—	8	2	no	—
257	D₄×C₃₁	—	8	1	no	—
258	D₄×C₃₁	—	8	2	no	—
259	D₄×C₃₁	—	8	2	no	—
260	D₄×C₃₁	—	8	2	no	—
261	D₄×C₃₁	#104	1	4	yes	—
262	C₂×C₄×C₃₁	—	2	1	no	—
263	C₂×C₄×C₃₁	—	2	1	no	—
264	C₂×C₄×C₃₁	—	2	2	no	—
265	C₂×C₄×C₃₁	—	2	2	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	4	no	—
268	C₂×C₄×C₃₁	—	2	1	no	—
269	C₂×C₄×C₃₁	—	2	1	no	—
270	C₂×C₄×C₃₁	—	2	2	no	—
271	C₂×C₄×C₃₁	—	2	1	no	—
272	C₂×C₄×C₃₁	—	4	2	no	—
273	C₂×C₄×C₃₁	—	4	2	no	—
274	C₂×C₄×C₃₁	—	4	2	no	—
275	C₂×C₄×C₃₁	—	4	1	no	—
276	C₂×C₄×C₃₁	—	4	2	no	—
277	C₂×C₄×C₃₁	—	4	2	no	—
278	C₂×C₄×C₃₁	—	4	1	no	—
279	C₂×C₄×C₃₁	—	4	2	no	—
280	C₂×C₄×C₃₁	—	4	1	no	—
281	C₂×C₄×C₃₁	—	4	2	no	—
282	C₂×C₄×C₃₁	—	4	1	no	—
283	C₂×C₄×C₃₁	—	4	1	no	—
284	C₂×C₄×C₃₁	—	4	2	no	—
285	C₂×C₄×C₃₁	—	8	2	no	—
286	C₂×C₄×C₃₁	—	8	2	no	—
287	C₂×C₄×C₃₁	—	8	2	no	—
288	C₂×C₄×C₃₁	—	8	8	no	—
289	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
297	C₈×C₃₁	—	4	1	no	—
298	C₈×C₃₁	—	4	2	no	—
299	C₈×C₃₁	—	4	1	no	—
300	#3519	C₂×C₃₁	1	1	yes	characteristic
301	#2974	C₂×C₃₁	1	1	yes	characteristic, complemented
302	#2275	C₂×C₃₁	1	1	yes	characteristic, complemented
303	#1509	C₂×C₃₁	1	1	yes	characteristic, complemented
304	#1507	C₂×C₃₁	1	2	yes	complemented
305	#1505	C₂×C₃₁	1	1	yes	characteristic, complemented
306	#1504	C₂×C₃₁	1	2	yes	complemented
307	#1502	C₂×C₃₁	1	1	yes	characteristic, complemented
308	#1501	C₂×C₃₁	1	2	yes	complemented
309	#1500	C₂×C₃₁	1	1	yes	characteristic, complemented
310	C₂×#327	C₂×C₃₁	1	2	yes	complemented
311	C₂²×C₃₁	—	2	1	no	—
312	C₂²×C₃₁	—	2	2	no	—
313	C₂²×C₃₁	—	2	2	no	—
314	C₂²×C₃₁	—	2	1	no	—
315	C₂²×C₃₁	—	2	2	no	—
316	C₂²×C₃₁	—	2	2	no	—
317	C₂²×C₃₁	—	2	2	no	—
318	C₂²×C₃₁	—	4	4	no	—
319	C₂²×C₃₁	—	4	4	no	—
320	C₂²×C₃₁	—	4	2	no	—
321	C₂²×C₃₁	—	4	1	no	—
322	C₂²×C₃₁	—	4	2	no	—
323	C₂²×C₃₁	—	4	1	no	—
324	C₂²×C₃₁	—	4	1	no	—
325	C₂²×C₃₁	—	4	2	no	—
326	C₂²×C₃₁	—	16	4	no	—
327	C₂²×C₃₁	C₂×#104	1	4	yes	—
328	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₃₁	#576	1	1	yes	characteristic
330	C₂²×C₃₁	#577	1	1	yes	characteristic
331	C₄×C₃₁	—	2	1	no	—
332	C₄×C₃₁	—	2	1	no	—
333	C₄×C₃₁	—	2	2	no	—
334	C₄×C₃₁	—	2	2	no	—
335	C₄×C₃₁	—	2	1	no	—
336	C₄×C₃₁	—	2	1	no	—
337	C₄×C₃₁	—	2	1	no	—
338	C₄×C₃₁	—	4	2	no	—
339	C₄×C₃₁	—	4	4	no	—
340	C₄×C₃₁	—	4	2	no	—
341	C₄×C₃₁	—	4	1	no	—
342	C₄×C₃₁	—	4	1	no	—
343	C₄×C₃₁	—	4	2	no	—
344	C₄×C₃₁	—	4	1	no	—
345	C₄×C₃₁	C₂×#104	1	2	yes	—
346	#555	C₄×C₃₁	1	1	yes	characteristic, complemented
347	#554	C₄×C₃₁	1	1	yes	characteristic, complemented
348	#553	—	2	1	no	—
349	#553	C₄×C₃₁	1	2	yes	complemented
350	#550	C₄×C₃₁	1	1	yes	characteristic, complemented
351	#546	—	2	2	no	—
352	#546	C₄×C₃₁	1	2	yes	complemented
353	D₄²	—	2	1	no	—
354	D₄²	C₄×C₃₁	1	1	yes	characteristic, complemented
355	#540	—	2	1	no	—
356	#538	—	2	2	no	—
357	#532	C₂²×C₃₁	1	1	yes	characteristic
358	#529	C₂²×C₃₁	1	1	yes	characteristic
359	#525	C₂²×C₃₁	1	2	yes	—
360	C₂×#121	C₂²×C₃₁	1	2	yes	—
361	#518	—	2	1	no	—
362	C₂×C₄×D₄	—	2	1	no	—
363	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
364	#436	—	2	1	no	—
365	#435	—	2	2	no	—
366	C₈×D₄	—	2	1	no	—
367	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
368	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
369	#407	C₂²×C₃₁	1	2	yes	complemented
370	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
371	C₄×C₄⋊C₄	—	2	1	no	—
372	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
373	C₄×C₂²⋊C₄	—	2	2	no	—
374	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
375	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
376	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
377	#328	C₂²×C₃₁	1	1	yes	characteristic, complemented
378	#328	C₂²×C₃₁	1	1	yes	characteristic, complemented
379	#328	C₂²×C₃₁	1	2	yes	complemented
380	#327	C₂²×C₃₁	1	1	yes	characteristic
381	#327	C₂²×C₃₁	1	2	yes	—
382	#327	C₂²×C₃₁	1	1	yes	characteristic
383	#327	C₂²×C₃₁	1	2	yes	complemented
384	#327	C₂²×C₃₁	1	2	yes	complemented
385	#327	C₂²×C₃₁	1	2	yes	complemented
386	#327	C₂²×C₃₁	1	2	yes	complemented
387	C₂×C₃₁	—	2	1	no	—
388	C₂×C₃₁	—	2	1	no	—
389	C₂×C₃₁	—	2	4	no	—
390	C₂×C₃₁	—	4	2	no	—
391	C₂×C₃₁	—	8	2	no	—
392	C₂×C₃₁	—	8	1	no	—
393	C₂×C₃₁	#2883	1	1	yes	characteristic
394	C₂×C₃₁	#2897	1	1	yes	characteristic
395	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
396	C₂×#41	—	2	1	no	—
397	C₂×#41	C₂×C₄×C₃₁	1	2	yes	complemented
398	C₂²×D₄	—	2	2	no	—
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	complemented
401	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
402	C₂³×C₄	—	2	2	no	—
403	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
404	C₂×M₁₆	—	2	2	no	—
405	C₂²×C₈	—	2	2	no	—
406	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
407	#127	—	2	1	no	—
408	#127	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
409	#126	—	2	2	no	—
410	#126	—	2	1	no	—
411	#125	—	2	1	no	—
412	#125	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
413	#124	—	2	2	no	—
414	#124	—	2	1	no	—
415	#124	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
416	#123	—	2	2	no	—
417	#123	—	2	1	no	—
418	#123	—	2	2	no	—
419	#123	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
422	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
423	#121	—	2	2	no	—
424	#121	—	2	1	no	—
425	#121	—	2	2	no	—
426	#121	—	2	2	no	—
427	#121	—	2	1	no	—
428	#121	—	2	1	no	—
429	#121	—	2	2	no	—
430	#121	—	2	2	no	—
431	#121	C₂×C₄×C₃₁	1	2	yes	complemented
432	#121	C₂×C₄×C₃₁	1	2	yes	complemented
433	#121	C₂×C₄×C₃₁	1	2	yes	complemented
434	#121	C₂³×C₃₁	1	1	yes	characteristic
435	#121	C₂³×C₃₁	1	2	yes	—
436	#120	—	2	2	no	—
437	#120	—	2	2	no	—
438	#120	—	2	2	no	—
439	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
440	C₄×D₄	—	2	8	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
449	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
450	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
451	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
452	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	complemented
453	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
454	C₄×D₄	D₄×C₃₁	1	2	yes	—
455	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
456	#117	—	2	1	no	—
457	#117	—	2	1	no	—
458	#117	C₂×C₄×C₃₁	1	2	yes	complemented
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	complemented
461	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	2	2	no	—
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	2	no	—
469	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
470	C₄⋊C₈	—	2	1	no	—
471	C₄⋊C₈	—	2	1	no	—
472	C₂²⋊C₈	—	2	2	no	—
473	C₂²⋊C₈	—	2	2	no	—
474	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
476	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
477	#97	—	2	1	no	—
478	C₄×C₈	—	2	1	no	—
479	#95	—	2	2	no	—
480	#95	—	2	1	no	—
481	#95	C₂³×C₃₁	1	1	yes	characteristic
482	#95	C₂³×C₃₁	1	2	yes	—
483	#95	C₂³×C₃₁	1	1	yes	characteristic
484	C₃₁	#17547	1	1	yes	characteristic, direct product factor, Sylow
485	C₂⁴	—	2	2	no	—
486	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
487	#41	—	8	1	no	—
488	#41	—	8	1	no	—
489	#41	—	8	2	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	8	2	no	—
504	C₂×D₄	—	8	2	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
507	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
508	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
509	C₂×D₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
510	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	8	2	no	—
520	C₂²×C₄	—	8	2	no	—
521	C₂²×C₄	—	8	2	no	—
522	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
523	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
524	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
527	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
528	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
530	M₁₆	—	8	2	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	8	2	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
544	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
545	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
546	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
563	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
564	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
565	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	8	1	no	—
570	C₄²	—	8	2	no	—
571	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
572	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
573	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
574	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	8	2	no	—
583	C₂³	—	8	2	no	—
584	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
585	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
586	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
587	Q₈	—	4	1	no	—
588	Q₈	—	8	1	no	—
589	D₄	—	2	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	8	2	no	—
600	D₄	—	8	1	no	—
601	D₄	—	8	2	no	—
602	D₄	—	8	2	no	—
603	D₄	—	8	2	no	—
604	D₄	C₃₁×#104	1	4	yes	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	8	2	no	—
629	C₂×C₄	—	8	2	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	8	no	—
632	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
633	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
634	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
635	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
636	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
637	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
640	C₈	—	4	1	no	—
641	C₈	—	4	2	no	—
642	C₈	—	4	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	16	4	no	—
659	C₂²	C₂×C₃₁×#104	1	4	yes	—
660	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
661	C₂²	C₃₁×#576	1	1	yes	characteristic
662	C₂²	C₃₁×#577	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	1	no	—
677	C₄	C₂×C₃₁×#104	1	2	yes	—
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	4	no	—
681	C₂	—	4	2	no	—
682	C₂	—	8	1	no	—
683	C₂	—	8	2	no	—
684	C₂	C₃₁×#2883	1	1	yes	characteristic
685	C₂	C₃₁×#2897	1	1	yes	characteristic
686	C₂	C₂²×C₃₁×#104	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×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2974	C₂	semidirect
3. C₃₁×#2275	C₂	semidirect
4. C₃₁×#1509	C₂	semidirect
5. C₃₁×#1507	C₂	semidirect
6. C₃₁×#1505	C₂	semidirect
7. C₃₁×#1504	C₂	semidirect
8. C₃₁×#1502	C₂	semidirect
9. C₃₁×#1501	C₂	semidirect
10. C₃₁×#1500	C₂	semidirect
11. C₂×C₃₁×#327	C₂	semidirect
12. C₃₁×#555	C₄	semidirect
13. C₃₁×#554	C₄	semidirect
15. C₃₁×#553	C₄	semidirect
16. C₃₁×#550	C₄	semidirect
18. C₃₁×#546	C₄	semidirect
20. D₄²×C₃₁	C₄	semidirect
33. C₃₁×#432	C₂²	semidirect
34. C₃₁×#431	C₂²	semidirect
35. C₃₁×#407	C₂²	semidirect
36. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
38. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
41. C₃₁×#376	C₂²	semidirect
42. C₂×C₃₁×#95	C₂²	semidirect
43. C₃₁×#328	C₂²	semidirect
44. C₃₁×#328	C₂²	semidirect
45. C₃₁×#328	C₂²	semidirect
49. C₃₁×#327	C₂²	semidirect
50. C₃₁×#327	C₂²	semidirect
51. C₃₁×#327	C₂²	semidirect
52. C₃₁×#327	C₂²	semidirect
54. C₂×#41×C₃₁	C₂×C₄	semidirect
57. C₂²×D₄×C₃₁	C₂×C₄	semidirect
63. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
65. C₃₁×#127	C₂×C₄	semidirect
69. C₃₁×#125	C₂×C₄	semidirect
72. C₃₁×#124	C₂×C₄	semidirect
78. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
88. C₃₁×#121	C₂×C₄	semidirect
89. C₃₁×#121	C₂×C₄	semidirect
90. C₃₁×#121	C₂×C₄	semidirect
96. C₄×Q₈×C₃₁	C₂×C₄	semidirect
108. C₄×D₄×C₃₁	C₂×C₄	semidirect
109. C₄×D₄×C₃₁	C₂×C₄	semidirect
115. C₃₁×#117	C₂×C₄	semidirect
117. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
231. #17547	C₃₁	direct (N × H)
301. #2974	C₂×C₃₁	semidirect
302. #2275	C₂×C₃₁	semidirect
303. #1509	C₂×C₃₁	semidirect
304. #1507	C₂×C₃₁	semidirect
305. #1505	C₂×C₃₁	semidirect
306. #1504	C₂×C₃₁	semidirect
307. #1502	C₂×C₃₁	semidirect
308. #1501	C₂×C₃₁	semidirect
309. #1500	C₂×C₃₁	semidirect
310. C₂×#327	C₂×C₃₁	semidirect
346. #555	C₄×C₃₁	semidirect
347. #554	C₄×C₃₁	semidirect
349. #553	C₄×C₃₁	semidirect
350. #550	C₄×C₃₁	semidirect
352. #546	C₄×C₃₁	semidirect
354. D₄²	C₄×C₃₁	semidirect
367. #432	C₂²×C₃₁	semidirect
368. #431	C₂²×C₃₁	semidirect
369. #407	C₂²×C₃₁	semidirect
370. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
372. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
374. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
375. #376	C₂²×C₃₁	semidirect
376. C₂×#95	C₂²×C₃₁	semidirect
377. #328	C₂²×C₃₁	semidirect
378. #328	C₂²×C₃₁	semidirect
379. #328	C₂²×C₃₁	semidirect
383. #327	C₂²×C₃₁	semidirect
384. #327	C₂²×C₃₁	semidirect
385. #327	C₂²×C₃₁	semidirect
386. #327	C₂²×C₃₁	semidirect
397. C₂×#41	C₂×C₄×C₃₁	semidirect
400. C₂²×D₄	C₂×C₄×C₃₁	semidirect
406. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
408. #127	C₂×C₄×C₃₁	semidirect
412. #125	C₂×C₄×C₃₁	semidirect
415. #124	C₂×C₄×C₃₁	semidirect
421. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
431. #121	C₂×C₄×C₃₁	semidirect
432. #121	C₂×C₄×C₃₁	semidirect
433. #121	C₂×C₄×C₃₁	semidirect
439. C₄×Q₈	C₂×C₄×C₃₁	semidirect
451. C₄×D₄	C₂×C₄×C₃₁	semidirect
452. C₄×D₄	C₂×C₄×C₃₁	semidirect
458. #117	C₂×C₄×C₃₁	semidirect
460. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
484. C₃₁	#17547	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×#3519	2
C₃₁×#2974	2
C₃₁×#2275	2
C₃₁×#1509	2
C₃₁×#1507	2
C₃₁×#1505	2
C₃₁×#1504	2
C₃₁×#1502	2
C₃₁×#1501	2
C₃₁×#1500	2
C₂×C₃₁×#327	2
#17547	31

Subgroups — C31×#17547 #21474306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17547 #21474306