Subgroups — C₃₁×#19942 #21476701

Order 7936.

590 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic
2	Q₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1706	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1698	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1668	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1630	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1623	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#559	C₂²	1	2	yes	—
13	Q₈²×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#500	—	2	1	no	—
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#495	—	2	1	no	—
17	C₃₁×#493	C₂²	1	1	yes	characteristic
18	C₃₁×#492	C₂²	1	2	yes	—
19	C₃₁×#489	—	2	2	no	—
20	C₃₁×#486	C₂²	1	2	yes	—
21	C₃₁×#477	—	2	2	no	—
22	C₃₁×#477	C₂²	1	2	yes	—
23	C₃₁×#477	C₂²	1	2	yes	—
24	C₃₁×#474	—	2	2	no	—
25	C₃₁×#464	—	2	2	no	—
26	C₃₁×#463	—	2	2	no	—
27	C₃₁×#460	C₂²	1	2	yes	—
28	C₃₁×#460	C₂²	1	2	yes	—
29	C₃₁×#446	C₂²	1	2	yes	—
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#440	—	2	2	no	—
33	C₄×Q₁₆×C₃₁	—	2	1	no	—
34	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₃₁	—	2	1	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#335	C₂²	1	1	yes	characteristic
39	C₃₁×#333	C₂²	1	2	yes	—
40	C₃₁×#331	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₃₁	—	4	2	no	—
50	C₂×D₈×C₃₁	—	2	1	no	—
51	C₂×D₈×C₃₁	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	—	2	2	no	—
54	C₃₁×C₄⋊Q₈	—	4	2	no	—
55	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₃₁×#127	C₂³	1	2	yes	—
57	C₃₁×#124	—	2	2	no	—
58	C₃₁×#124	—	2	2	no	—
59	C₃₁×#123	—	4	2	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	—	2	2	no	—
62	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
65	C₄×D₄×C₃₁	—	2	2	no	—
66	C₄×D₄×C₃₁	—	2	2	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	2	no	—
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#107	D₄	1	1	yes	characteristic
73	C₃₁×C₄⋊C₈	—	2	1	no	—
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	—	2	2	no	—
76	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	D₄	1	1	yes	characteristic
82	C₃₁×#103	D₄	1	2	yes	—
83	C₃₁×#103	D₄	1	1	yes	characteristic
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	—	2	2	no	—
87	C₃₁×#102	—	2	2	no	—
88	C₃₁×#97	—	2	2	no	—
89	C₄×C₈×C₃₁	—	2	1	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	4	2	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
98	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂×D₄×C₃₁	—	2	2	no	—
102	C₂²×C₄×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	2	2	no	—
104	Q₁₆×C₃₁	—	2	2	no	—
105	SD₁₆×C₃₁	—	4	4	no	—
106	SD₁₆×C₃₁	—	8	4	no	—
107	SD₁₆×C₃₁	—	8	2	no	—
108	D₈×C₃₁	—	4	2	no	—
109	D₈×C₃₁	—	8	1	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	1	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	1	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	4	2	no	—
124	C₄⋊C₄×C₃₁	—	4	2	no	—
125	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₃₁	—	4	2	no	—
129	C₂²⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₄²×C₃₁	—	2	1	no	—
132	C₄²×C₃₁	—	2	1	no	—
133	C₄²×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	#19942	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	4	2	no	—
138	Q₈×C₃₁	—	2	1	no	—
139	Q₈×C₃₁	—	2	1	no	—
140	Q₈×C₃₁	—	2	2	no	—
141	Q₈×C₃₁	—	2	2	no	—
142	Q₈×C₃₁	—	2	1	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	Q₈×C₃₁	—	16	2	no	—
145	Q₈×C₃₁	#135	1	2	yes	—
146	D₄×C₃₁	—	4	2	no	—
147	D₄×C₃₁	—	4	2	no	—
148	D₄×C₃₁	—	4	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	8	2	no	—
151	C₂×C₄×C₃₁	—	2	1	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	16	2	no	—
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₈×C₃₁	—	2	2	no	—
163	C₈×C₃₁	—	2	1	no	—
164	C₈×C₃₁	—	2	1	no	—
165	C₈×C₃₁	—	2	1	no	—
166	C₈×C₃₁	—	4	2	no	—
167	C₈×C₃₁	—	4	1	no	—
168	C₈×C₃₁	—	4	1	no	—
169	C₈×C₃₁	#137	1	2	yes	—
170	#3396	C₂×C₃₁	1	1	yes	characteristic
171	Q₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#3375	C₂×C₃₁	1	2	yes	complemented
173	#1706	C₂×C₃₁	1	1	yes	characteristic
174	#1698	C₂×C₃₁	1	2	yes	complemented
175	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1668	C₂×C₃₁	1	1	yes	characteristic
177	#1630	C₂×C₃₁	1	2	yes	complemented
178	#1623	C₂×C₃₁	1	2	yes	complemented
179	#1591	C₂×C₃₁	1	1	yes	characteristic, complemented
180	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	8	2	no	—
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	D₄²	1	1	yes	characteristic
185	C₄×C₃₁	—	2	2	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	4	2	no	—
188	C₄×C₃₁	—	4	1	no	—
189	C₄×C₃₁	—	4	1	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	8	2	no	—
193	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
194	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
195	C₄×C₃₁	#577	1	1	yes	characteristic
196	C₄×C₃₁	#578	1	1	yes	characteristic
197	#559	C₂²×C₃₁	1	2	yes	—
198	Q₈²	C₂²×C₃₁	1	2	yes	—
199	#500	—	2	1	no	—
200	#500	C₂²×C₃₁	1	1	yes	characteristic
201	#495	—	2	1	no	—
202	#493	C₂²×C₃₁	1	1	yes	characteristic
203	#492	C₂²×C₃₁	1	2	yes	—
204	#489	—	2	2	no	—
205	#486	C₂²×C₃₁	1	2	yes	—
206	#477	—	2	2	no	—
207	#477	C₂²×C₃₁	1	2	yes	—
208	#477	C₂²×C₃₁	1	2	yes	—
209	#474	—	2	2	no	—
210	#464	—	2	2	no	—
211	#463	—	2	2	no	—
212	#460	C₂²×C₃₁	1	2	yes	—
213	#460	C₂²×C₃₁	1	2	yes	—
214	#446	C₂²×C₃₁	1	2	yes	—
215	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
217	#440	—	2	2	no	—
218	C₄×Q₁₆	—	2	1	no	—
219	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
220	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
221	C₄×D₈	—	2	1	no	—
222	#335	C₂²×C₃₁	1	1	yes	characteristic
223	#335	C₂²×C₃₁	1	1	yes	characteristic
224	#333	C₂²×C₃₁	1	2	yes	—
225	#331	C₂²×C₃₁	1	2	yes	—
226	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
227	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
228	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
229	C₈²	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₃₁	—	16	2	no	—
231	C₂×C₃₁	#3278	1	1	yes	characteristic
232	C₂×C₃₁	#3285	1	1	yes	characteristic
233	C₂×C₃₁	#3292	1	1	yes	characteristic
234	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
235	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×D₈	—	2	1	no	—
240	C₂×D₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	4	2	no	—
244	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
245	#127	C₂³×C₃₁	1	2	yes	—
246	#124	—	2	2	no	—
247	#124	—	2	2	no	—
248	#123	—	4	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
252	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
253	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	#107	—	2	1	no	—
257	#107	—	2	1	no	—
258	#107	—	2	2	no	—
259	#107	—	2	2	no	—
260	#107	D₄×C₃₁	1	1	yes	characteristic
261	#107	D₄×C₃₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
267	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	D₄×C₃₁	1	1	yes	characteristic
271	#103	D₄×C₃₁	1	2	yes	—
272	#103	D₄×C₃₁	1	1	yes	characteristic
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#97	—	2	2	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
283	C₃₁	#19942	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
288	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	8	4	no	—
297	SD₁₆	—	8	2	no	—
298	D₈	—	4	2	no	—
299	D₈	—	8	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
317	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
326	C₂³	—	4	2	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	2	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	16	2	no	—
334	Q₈	C₃₁×#135	1	2	yes	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	16	2	no	—
348	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
351	C₈	—	2	2	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	1	no	—
358	C₈	C₃₁×#137	1	2	yes	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	D₄²×C₃₁	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
372	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
373	C₄	C₃₁×#577	1	1	yes	characteristic
374	C₄	C₃₁×#578	1	1	yes	characteristic
375	C₂	—	16	2	no	—
376	C₂	C₃₁×#3278	1	1	yes	characteristic
377	C₂	C₃₁×#3285	1	1	yes	characteristic
378	C₂	C₃₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#493	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×Q₁₆×C₃₁	C₂	semidirect
3. C₃₁×#3375	C₂	semidirect
5. C₃₁×#1698	C₂	semidirect
6. C₃₁×#1676	C₂	semidirect
8. C₃₁×#1630	C₂	semidirect
9. C₃₁×#1623	C₂	semidirect
10. C₃₁×#1591	C₂	semidirect
11. C₈×Q₁₆×C₃₁	C₂	semidirect
136. #19942	C₃₁	direct (N × H)
171. Q₈×Q₁₆	C₂×C₃₁	semidirect
172. #3375	C₂×C₃₁	semidirect
174. #1698	C₂×C₃₁	semidirect
175. #1676	C₂×C₃₁	semidirect
177. #1630	C₂×C₃₁	semidirect
178. #1623	C₂×C₃₁	semidirect
179. #1591	C₂×C₃₁	semidirect
180. C₈×Q₁₆	C₂×C₃₁	semidirect
283. C₃₁	#19942	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×#3396	2
Q₈×Q₁₆×C₃₁	2
C₃₁×#3375	2
C₃₁×#1706	2
C₃₁×#1698	2
C₃₁×#1676	2
C₃₁×#1668	2
C₃₁×#1630	2
C₃₁×#1623	2
C₃₁×#1591	2
C₈×Q₁₆×C₃₁	2
#19942	31

Subgroups — C31×#19942 #21476701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19942 #21476701