Subgroups — C₃₁×#19909 #21476668

Order 7936.

638 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3391	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1697	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, complemented
8	C₃₁×#1631	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1622	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#554	C₂²	1	2	yes	—
13	C₃₁×#550	C₂²	1	2	yes	—
14	C₃₁×#500	C₂²	1	1	yes	characteristic
15	C₃₁×#499	—	2	1	no	—
16	C₃₁×#493	—	2	1	no	—
17	C₃₁×#493	C₂²	1	1	yes	characteristic
18	C₃₁×#492	C₂²	1	2	yes	—
19	C₃₁×#486	C₂²	1	2	yes	—
20	C₃₁×#480	—	2	2	no	—
21	C₃₁×#478	—	2	2	no	—
22	C₃₁×#477	C₂²	1	2	yes	—
23	C₃₁×#476	C₂²	1	2	yes	—
24	C₃₁×#468	—	2	2	no	—
25	C₃₁×#460	C₂²	1	2	yes	—
26	C₃₁×#459	—	2	2	no	—
27	C₃₁×#459	C₂²	1	2	yes	—
28	C₃₁×#452	—	2	2	no	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₃₁	—	2	1	no	—
33	C₄×D₈×C₃₁	—	2	1	no	—
34	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#436	C₂²	1	2	yes	—
36	C₃₁×#417	—	2	2	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×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₃₁	—	4	2	no	—
49	C₂×D₈×C₃₁	—	2	2	no	—
50	C₂×D₈×C₃₁	—	2	1	no	—
51	C₂×D₈×C₃₁	—	2	1	no	—
52	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₃₁	—	2	2	no	—
54	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₃₁×#127	—	2	2	no	—
56	C₃₁×#127	C₂³	1	2	yes	—
57	C₃₁×#125	—	2	2	no	—
58	C₃₁×C₂²⋊Q₈	—	2	2	no	—
59	C₃₁×C₂²⋊Q₈	—	4	2	no	—
60	C₃₁×#121	—	2	2	no	—
61	C₃₁×#121	—	4	2	no	—
62	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₃₁	—	2	2	no	—
65	C₄×D₄×C₃₁	—	2	2	no	—
66	C₄×D₄×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	1	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×#106	—	2	2	no	—
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	—	2	1	no	—
76	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	D₄	1	1	yes	characteristic
81	C₃₁×#103	D₄	1	1	yes	characteristic
82	C₃₁×#102	—	2	2	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	—	2	2	no	—
87	C₃₁×#102	D₄	1	2	yes	—
88	C₃₁×C₂²⋊C₈	—	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	#41×C₃₁	—	4	4	no	—
95	#41×C₃₁	—	8	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄×C₃₁	—	4	2	no	—
103	C₂×D₄×C₃₁	—	4	2	no	—
104	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	4	2	no	—
107	C₂²×C₄×C₃₁	—	4	2	no	—
108	Q₁₆×C₃₁	—	2	2	no	—
109	SD₁₆×C₃₁	—	8	4	no	—
110	SD₁₆×C₃₁	—	8	2	no	—
111	D₈×C₃₁	—	2	2	no	—
112	D₈×C₃₁	—	4	2	no	—
113	D₈×C₃₁	—	8	1	no	—
114	D₈×C₃₁	—	8	2	no	—
115	M₁₆×C₃₁	—	8	2	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₃₁	—	2	1	no	—
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	—	4	2	no	—
130	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₂²⋊C₄×C₃₁	—	4	2	no	—
135	C₂²⋊C₄×C₃₁	—	4	2	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
139	#19909	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	2	2	no	—
141	C₂³×C₃₁	—	4	2	no	—
142	Q₈×C₃₁	—	2	1	no	—
143	Q₈×C₃₁	—	2	1	no	—
144	Q₈×C₃₁	—	2	1	no	—
145	Q₈×C₃₁	—	8	2	no	—
146	Q₈×C₃₁	#135	1	2	yes	—
147	D₄×C₃₁	—	2	2	no	—
148	D₄×C₃₁	—	2	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	4	2	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	8	4	no	—
154	D₄×C₃₁	—	8	2	no	—
155	D₄×C₃₁	—	16	2	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	8	4	no	—
165	C₂×C₄×C₃₁	—	16	2	no	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
169	C₈×C₃₁	—	2	2	no	—
170	C₈×C₃₁	—	2	1	no	—
171	C₈×C₃₁	—	2	1	no	—
172	C₈×C₃₁	—	2	1	no	—
173	C₈×C₃₁	—	4	2	no	—
174	C₈×C₃₁	—	4	1	no	—
175	C₈×C₃₁	—	4	1	no	—
176	C₈×C₃₁	#137	1	2	yes	—
177	#3391	C₂×C₃₁	1	1	yes	characteristic
178	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#3333	C₂×C₃₁	1	2	yes	complemented
180	#1706	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#1697	C₂×C₃₁	1	2	yes	complemented
182	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#1668	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#1631	C₂×C₃₁	1	2	yes	complemented
185	#1622	C₂×C₃₁	1	2	yes	complemented
186	#1589	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
188	C₂²×C₃₁	—	4	2	no	—
189	C₂²×C₃₁	—	4	2	no	—
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	—	8	2	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	D₄²	1	1	yes	characteristic
195	C₄×C₃₁	—	2	2	no	—
196	C₄×C₃₁	—	2	1	no	—
197	C₄×C₃₁	—	4	2	no	—
198	C₄×C₃₁	—	4	1	no	—
199	C₄×C₃₁	—	4	1	no	—
200	C₄×C₃₁	—	4	1	no	—
201	C₄×C₃₁	—	8	2	no	—
202	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
203	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
204	C₄×C₃₁	#576	1	1	yes	characteristic
205	C₄×C₃₁	#577	1	1	yes	characteristic
206	#554	C₂²×C₃₁	1	2	yes	—
207	#550	C₂²×C₃₁	1	2	yes	—
208	#500	C₂²×C₃₁	1	1	yes	characteristic
209	#499	—	2	1	no	—
210	#493	—	2	1	no	—
211	#493	C₂²×C₃₁	1	1	yes	characteristic
212	#492	C₂²×C₃₁	1	2	yes	—
213	#486	C₂²×C₃₁	1	2	yes	—
214	#480	—	2	2	no	—
215	#478	—	2	2	no	—
216	#477	C₂²×C₃₁	1	2	yes	—
217	#476	C₂²×C₃₁	1	2	yes	—
218	#468	—	2	2	no	—
219	#460	C₂²×C₃₁	1	2	yes	—
220	#459	—	2	2	no	—
221	#459	C₂²×C₃₁	1	2	yes	—
222	#452	—	2	2	no	—
223	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
224	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
225	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
226	C₄×D₈	—	2	1	no	—
227	C₄×D₈	—	2	1	no	—
228	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
229	#436	C₂²×C₃₁	1	2	yes	—
230	#417	—	2	2	no	—
231	#335	C₂²×C₃₁	1	1	yes	characteristic
232	#335	C₂²×C₃₁	1	1	yes	characteristic
233	#333	C₂²×C₃₁	1	2	yes	—
234	#331	C₂²×C₃₁	1	2	yes	—
235	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
236	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
237	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
238	C₈²	C₂²×C₃₁	1	1	yes	characteristic
239	C₂×C₃₁	—	8	2	no	—
240	C₂×C₃₁	—	16	2	no	—
241	C₂×C₃₁	#3278	1	1	yes	characteristic
242	C₂×C₃₁	#3280	1	1	yes	characteristic
243	C₂×C₃₁	#3292	1	1	yes	characteristic
244	C₂×#41	—	2	2	no	—
245	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	4	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
252	C₂×M₁₆	—	2	2	no	—
253	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
254	#127	—	2	2	no	—
255	#127	C₂³×C₃₁	1	2	yes	—
256	#125	—	2	2	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	#121	—	2	2	no	—
260	#121	—	4	2	no	—
261	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
262	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	C₂³×C₃₁	1	2	yes	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	#107	—	2	1	no	—
268	#107	—	2	1	no	—
269	#107	—	2	2	no	—
270	#107	D₄×C₃₁	1	1	yes	characteristic
271	#107	D₄×C₃₁	1	1	yes	characteristic
272	#106	—	2	2	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
278	#103	—	2	2	no	—
279	#103	D₄×C₃₁	1	1	yes	characteristic
280	#103	D₄×C₃₁	1	1	yes	characteristic
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	D₄×C₃₁	1	2	yes	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
293	C₃₁	#19909	1	1	yes	characteristic, direct product factor, Sylow
294	#41	—	4	4	no	—
295	#41	—	8	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	Q₁₆	—	2	2	no	—
309	SD₁₆	—	8	4	no	—
310	SD₁₆	—	8	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	2	no	—
313	D₈	—	8	1	no	—
314	D₈	—	8	2	no	—
315	M₁₆	—	8	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
331	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
332	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	4	2	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	8	2	no	—
345	Q₈	C₃₁×#135	1	2	yes	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	2	no	—
354	D₄	—	16	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	16	2	no	—
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
367	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	C₃₁×#137	1	2	yes	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	D₄²×C₃₁	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
391	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
392	C₄	C₃₁×#576	1	1	yes	characteristic
393	C₄	C₃₁×#577	1	1	yes	characteristic
394	C₂	—	8	2	no	—
395	C₂	—	16	2	no	—
396	C₂	C₃₁×#3278	1	1	yes	characteristic
397	C₂	C₃₁×#3280	1	1	yes	characteristic
398	C₂	C₃₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#3391	C₂
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. C₃₁×#3380	C₂	semidirect
3. C₃₁×#3333	C₂	semidirect
4. C₃₁×#1706	C₂	semidirect
5. C₃₁×#1697	C₂	semidirect
6. C₃₁×#1676	C₂	semidirect
7. C₃₁×#1668	C₂	semidirect
8. C₃₁×#1631	C₂	semidirect
9. C₃₁×#1622	C₂	semidirect
10. C₃₁×#1589	C₂	semidirect
11. C₈×Q₁₆×C₃₁	C₂	semidirect
139. #19909	C₃₁	direct (N × H)
178. #3380	C₂×C₃₁	semidirect
179. #3333	C₂×C₃₁	semidirect
180. #1706	C₂×C₃₁	semidirect
181. #1697	C₂×C₃₁	semidirect
182. #1676	C₂×C₃₁	semidirect
183. #1668	C₂×C₃₁	semidirect
184. #1631	C₂×C₃₁	semidirect
185. #1622	C₂×C₃₁	semidirect
186. #1589	C₂×C₃₁	semidirect
187. C₈×Q₁₆	C₂×C₃₁	semidirect
293. C₃₁	#19909	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×#3391	2
C₃₁×#3380	2
C₃₁×#3333	2
C₃₁×#1706	2
C₃₁×#1697	2
C₃₁×#1676	2
C₃₁×#1668	2
C₃₁×#1631	2
C₃₁×#1622	2
C₃₁×#1589	2
C₈×Q₁₆×C₃₁	2
#19909	31

Subgroups — C31×#19909 #21476668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19909 #21476668