Subgroups — C₃₁×#25589 #21482348

Order 7936.

1068 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2868	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2005	C₂	1	4	yes	maximal
6	C₃₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1886	C₂	1	4	yes	maximal, complemented
9	C₄×C₃₁×#104	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃₁×#137	C₂²	1	2	yes	—
11	C₃₁×#557	—	2	2	no	—
12	C₃₁×#556	—	2	2	no	—
13	C₃₁×#552	—	2	4	no	—
14	C₃₁×#541	—	2	2	no	—
15	C₃₁×#536	C₂²	1	2	yes	—
16	C₃₁×#533	—	2	2	no	—
17	C₃₁×#533	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃₁×#519	C₂²	1	2	yes	—
22	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#491	—	2	2	no	—
24	C₃₁×#487	—	2	2	no	—
25	C₃₁×#462	—	2	2	no	—
26	C₃₁×#461	—	2	2	no	—
27	C₃₁×#423	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#104	C₂²	1	2	yes	—
29	C₃₁×#419	C₂²	1	4	yes	—
30	C₃₁×#419	C₂²	1	2	yes	—
31	C₂×C₃₁×#101	C₂²	1	4	yes	—
32	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#384	—	2	4	no	—
34	C₄³×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#339	C₂²	1	2	yes	—
36	C₃₁×#339	C₂²	1	4	yes	—
37	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
39	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
40	C₃₁×#137	—	4	4	no	—
41	C₂×Q₁₆×C₃₁	—	2	2	no	—
42	C₂×SD₁₆×C₃₁	—	2	2	no	—
43	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
44	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₃₁×C₄⋊Q₈	—	2	1	no	—
47	C₃₁×C₄⋊Q₈	—	2	1	no	—
48	C₃₁×C₄⋊Q₈	—	2	2	no	—
49	C₃₁×C₄⋊Q₈	—	2	2	no	—
50	C₃₁×C₄⋊Q₈	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	8	no	—
53	C₃₁×C₄⋊Q₈	—	4	4	no	—
54	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
55	C₃₁×#126	—	2	8	no	—
56	C₃₁×#125	—	2	4	no	—
57	C₃₁×#125	—	2	8	no	—
58	C₃₁×#125	D₄	1	2	yes	—
59	C₃₁×#124	—	2	2	no	—
60	C₃₁×#123	—	2	4	no	—
61	C₃₁×C₂²⋊Q₈	—	2	4	no	—
62	C₃₁×C₂²⋊Q₈	—	2	2	no	—
63	C₃₁×C₂²⋊Q₈	—	2	4	no	—
64	C₄×Q₈×C₃₁	—	2	4	no	—
65	C₄×Q₈×C₃₁	—	2	4	no	—
66	C₄×Q₈×C₃₁	—	2	4	no	—
67	C₄×Q₈×C₃₁	—	2	2	no	—
68	C₄×Q₈×C₃₁	D₄	1	2	yes	—
69	C₄×D₄×C₃₁	—	2	2	no	—
70	C₄×D₄×C₃₁	D₄	1	2	yes	—
71	C₃₁×#117	—	2	4	no	—
72	C₃₁×#117	—	2	4	no	—
73	C₃₁×#117	—	2	1	no	—
74	C₃₁×#117	C₂³	1	1	yes	characteristic
75	C₃₁×#117	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
77	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	—
79	C₂×C₄²×C₃₁	—	2	2	no	—
80	C₂×C₄²×C₃₁	—	2	1	no	—
81	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
83	C₃₁×C₄⋊C₈	—	2	2	no	—
84	C₃₁×#104	—	2	4	no	—
85	C₃₁×#103	—	2	4	no	—
86	C₃₁×#103	—	2	8	no	—
87	C₃₁×#101	—	4	4	no	—
88	C₃₁×#97	—	2	1	no	—
89	C₄×C₈×C₃₁	—	2	1	no	—
90	#41×C₃₁	—	2	2	no	—
91	#41×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	4	no	—
96	C₂×Q₈×C₃₁	—	2	4	no	—
97	C₂×Q₈×C₃₁	—	2	2	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	2	4	no	—
100	C₂×Q₈×C₃₁	—	2	4	no	—
101	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₃₁	—	2	1	no	—
103	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	2	1	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₃₁	—	4	4	no	—
112	SD₁₆×C₃₁	—	4	4	no	—
113	M₁₆×C₃₁	—	2	2	no	—
114	M₁₆×C₃₁	—	2	2	no	—
115	M₁₆×C₃₁	—	2	4	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	2	8	no	—
119	C₄⋊C₄×C₃₁	—	2	8	no	—
120	C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₄⋊C₄×C₃₁	—	2	4	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	4	no	—
125	C₄⋊C₄×C₃₁	—	4	16	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
130	C₂²⋊C₄×C₃₁	—	2	8	no	—
131	C₂²⋊C₄×C₃₁	—	2	1	no	—
132	C₂²⋊C₄×C₃₁	—	2	2	no	—
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	2	8	no	—
135	C₄²×C₃₁	—	2	8	no	—
136	C₄²×C₃₁	—	2	2	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	—	2	2	no	—
139	C₄²×C₃₁	—	2	2	no	—
140	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₃₁	C₂×D₄	1	2	yes	—
143	C₄²×C₃₁	#41	1	4	yes	—
144	#25589	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₃₁	—	2	1	no	—
146	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₃₁	—	2	1	no	—
148	Q₈×C₃₁	—	2	1	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	—	4	2	no	—
151	Q₈×C₃₁	—	4	4	no	—
152	Q₈×C₃₁	—	4	4	no	—
153	Q₈×C₃₁	—	4	2	no	—
154	Q₈×C₃₁	—	4	2	no	—
155	Q₈×C₃₁	—	4	4	no	—
156	D₄×C₃₁	—	2	1	no	—
157	D₄×C₃₁	—	2	1	no	—
158	D₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	2	8	no	—
160	C₂×C₄×C₃₁	—	2	4	no	—
161	C₂×C₄×C₃₁	—	2	4	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	1	no	—
166	C₂×C₄×C₃₁	—	2	8	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	4	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	4	4	no	—
171	C₂×C₄×C₃₁	#120	1	2	yes	—
172	C₂×C₄×C₃₁	#120	1	2	yes	—
173	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
176	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
177	C₈×C₃₁	—	4	2	no	—
178	C₈×C₃₁	—	4	2	no	—
179	#3509	C₂×C₃₁	1	1	yes	characteristic
180	#3139	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#3039	C₂×C₃₁	1	1	yes	characteristic
182	#2868	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#2005	C₂×C₃₁	1	4	yes	—
184	#1994	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#1966	C₂×C₃₁	1	1	yes	characteristic, complemented
186	#1886	C₂×C₃₁	1	4	yes	complemented
187	C₄×#104	C₂×C₃₁	1	1	yes	characteristic
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	4	1	no	—
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
192	C₂²×C₃₁	#546	1	2	yes	—
193	C₄×C₃₁	—	2	8	no	—
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	4	4	no	—
196	C₄×C₃₁	—	4	1	no	—
197	C₄×C₃₁	—	4	2	no	—
198	C₄×C₃₁	—	4	4	no	—
199	C₄×C₃₁	—	8	2	no	—
200	C₄×C₃₁	#456	1	4	yes	—
201	C₄×C₃₁	#532	1	1	yes	characteristic
202	C₄×C₃₁	#535	1	1	yes	characteristic
203	C₄×C₃₁	#550	1	2	yes	—
204	C₂×#137	C₂²×C₃₁	1	2	yes	—
205	#557	—	2	2	no	—
206	#556	—	2	2	no	—
207	#552	—	2	4	no	—
208	#541	—	2	2	no	—
209	#536	C₂²×C₃₁	1	2	yes	—
210	#533	—	2	2	no	—
211	#533	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
214	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
215	#519	C₂²×C₃₁	1	2	yes	—
216	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
217	#491	—	2	2	no	—
218	#487	—	2	2	no	—
219	#462	—	2	2	no	—
220	#461	—	2	2	no	—
221	#423	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×#104	C₂²×C₃₁	1	2	yes	—
223	#419	C₂²×C₃₁	1	4	yes	—
224	#419	C₂²×C₃₁	1	2	yes	—
225	C₂×#101	C₂²×C₃₁	1	4	yes	—
226	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
227	#384	—	2	4	no	—
228	C₄³	C₂²×C₃₁	1	1	yes	characteristic
229	#339	C₂²×C₃₁	1	2	yes	—
230	#339	C₂²×C₃₁	1	4	yes	—
231	C₂×C₃₁	—	2	2	no	—
232	C₂×C₃₁	—	8	1	no	—
233	C₂×C₃₁	#2431	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#456	1	2	yes	—
235	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
237	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
238	#137	—	4	4	no	—
239	C₂×Q₁₆	—	2	2	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
242	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	8	no	—
251	C₄⋊Q₈	—	4	4	no	—
252	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
253	#126	—	2	8	no	—
254	#125	—	2	4	no	—
255	#125	—	2	8	no	—
256	#125	D₄×C₃₁	1	2	yes	—
257	#124	—	2	2	no	—
258	#123	—	2	4	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	D₄×C₃₁	1	2	yes	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	D₄×C₃₁	1	2	yes	—
269	#117	—	2	4	no	—
270	#117	—	2	4	no	—
271	#117	—	2	1	no	—
272	#117	C₂³×C₃₁	1	1	yes	characteristic
273	#117	C₂³×C₃₁	1	2	yes	—
274	C₂×C₄⋊C₄	—	2	8	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
281	C₄⋊C₈	—	2	2	no	—
282	#104	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	—	2	8	no	—
285	#101	—	4	4	no	—
286	#97	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₃₁	#25589	1	1	yes	characteristic, direct product factor, Sylow
289	#41	—	2	2	no	—
290	#41	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
308	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
310	Q₁₆	—	4	4	no	—
311	SD₁₆	—	4	4	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	4	16	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
328	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	—	2	8	no	—
334	C₄²	—	2	8	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₃₁	1	2	yes	—
342	C₄²	#41×C₃₁	1	4	yes	—
343	C₂³	—	2	1	no	—
344	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	4	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	4	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	C₃₁×#120	1	2	yes	—
370	C₂×C₄	C₃₁×#120	1	2	yes	—
371	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
374	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
381	C₂²	C₃₁×#546	1	2	yes	—
382	C₄	—	2	8	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	C₃₁×#456	1	4	yes	—
390	C₄	C₃₁×#532	1	1	yes	characteristic
391	C₄	C₃₁×#535	1	1	yes	characteristic
392	C₄	C₃₁×#550	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	8	1	no	—
395	C₂	C₃₁×#2431	1	1	yes	characteristic
396	C₂	C₂×C₃₁×#456	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×#41×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3139	C₂	semidirect
4. C₃₁×#2868	C₂	semidirect
6. C₃₁×#1994	C₂	semidirect
7. C₃₁×#1966	C₂	semidirect
8. C₃₁×#1886	C₂	semidirect
144. #25589	C₃₁	direct (N × H)
180. #3139	C₂×C₃₁	semidirect
182. #2868	C₂×C₃₁	semidirect
184. #1994	C₂×C₃₁	semidirect
185. #1966	C₂×C₃₁	semidirect
186. #1886	C₂×C₃₁	semidirect
288. C₃₁	#25589	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×#3509	2
C₃₁×#3139	2
C₃₁×#3039	2
C₃₁×#2868	2
C₃₁×#2005	2
C₃₁×#1994	2
C₃₁×#1966	2
C₃₁×#1886	2
C₄×C₃₁×#104	2
#25589	31

Subgroups — C31×#25589 #21482348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25589 #21482348