Subgroups — C₃₁×#3312 #16843245

Order 3968.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#552	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#435	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×C₄⋊Q₈	—	2	1	no	—
24	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃₁×#126	—	2	1	no	—
26	C₃₁×#125	—	2	1	no	—
27	C₃₁×#125	C₂²	1	1	yes	characteristic
28	C₃₁×#123	—	2	1	no	—
29	C₃₁×C₂²⋊Q₈	—	2	1	no	—
30	C₃₁×C₂²⋊Q₈	—	2	1	no	—
31	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₃₁	—	2	1	no	—
38	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×#117	—	2	1	no	—
40	C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#107	C₂²	1	1	yes	characteristic
43	C₃₁×#106	C₂²	1	1	yes	characteristic
44	C₃₁×#106	C₂²	1	1	yes	characteristic
45	C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₃₁×#103	C₂²	1	1	yes	characteristic
47	C₃₁×#103	C₂²	1	1	yes	characteristic
48	C₃₁×#103	C₂²	1	1	yes	characteristic
49	C₃₁×#103	C₂²	1	1	yes	characteristic
50	C₃₁×#103	C₂²	1	1	yes	characteristic
51	C₃₁×#103	C₂²	1	1	yes	characteristic
52	C₃₁×#103	C₂²	1	1	yes	characteristic
53	C₃₁×#103	C₂²	1	1	yes	characteristic
54	C₃₁×#103	C₂²	1	1	yes	characteristic
55	C₃₁×#103	C₂²	1	1	yes	characteristic
56	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃₁×#97	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₃₁	—	2	1	no	—
60	C₂×Q₈×C₃₁	—	2	1	no	—
61	C₂×Q₈×C₃₁	—	2	2	no	—
62	C₂×Q₈×C₃₁	—	2	2	no	—
63	C₂×Q₈×C₃₁	—	4	1	no	—
64	C₂×Q₈×C₃₁	—	4	1	no	—
65	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
69	C₂×D₄×C₃₁	D₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	—	2	1	no	—
71	C₂²×C₄×C₃₁	—	2	1	no	—
72	C₂²×C₄×C₃₁	—	2	1	no	—
73	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
75	Q₁₆×C₃₁	—	2	2	no	—
76	Q₁₆×C₃₁	—	4	1	no	—
77	Q₁₆×C₃₁	—	4	1	no	—
78	M₁₆×C₃₁	—	4	1	no	—
79	C₂×C₈×C₃₁	—	4	1	no	—
80	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₃₁	—	2	1	no	—
85	C₄⋊C₄×C₃₁	—	2	1	no	—
86	C₄⋊C₄×C₃₁	—	2	1	no	—
87	C₄⋊C₄×C₃₁	—	2	1	no	—
88	C₄⋊C₄×C₃₁	—	2	1	no	—
89	C₄⋊C₄×C₃₁	—	2	1	no	—
90	C₄⋊C₄×C₃₁	—	2	1	no	—
91	C₄⋊C₄×C₃₁	—	2	1	no	—
92	C₄⋊C₄×C₃₁	—	2	1	no	—
93	C₄⋊C₄×C₃₁	—	2	1	no	—
94	C₄⋊C₄×C₃₁	—	2	1	no	—
95	C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
96	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²⋊C₄×C₃₁	—	2	1	no	—
101	C₂²⋊C₄×C₃₁	—	2	1	no	—
102	C₂²⋊C₄×C₃₁	—	2	1	no	—
103	C₂²⋊C₄×C₃₁	—	2	1	no	—
104	C₂²⋊C₄×C₃₁	—	2	1	no	—
105	C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
106	C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
107	C₄²×C₃₁	—	2	1	no	—
108	C₄²×C₃₁	—	2	1	no	—
109	C₄²×C₃₁	—	2	1	no	—
110	C₄²×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
113	Q₈×C₃₁	—	2	1	no	—
114	Q₈×C₃₁	—	2	1	no	—
115	Q₈×C₃₁	—	2	1	no	—
116	Q₈×C₃₁	—	2	1	no	—
117	Q₈×C₃₁	—	2	1	no	—
118	Q₈×C₃₁	—	2	1	no	—
119	Q₈×C₃₁	—	2	1	no	—
120	Q₈×C₃₁	—	4	2	no	—
121	Q₈×C₃₁	—	4	2	no	—
122	Q₈×C₃₁	#41	1	2	yes	—
123	D₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	1	no	—
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	2	1	no	—
128	C₂×C₄×C₃₁	—	2	1	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	2	1	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	—	2	1	no	—
134	C₂×C₄×C₃₁	—	2	1	no	—
135	C₂×C₄×C₃₁	—	2	1	no	—
136	C₂×C₄×C₃₁	—	4	2	no	—
137	C₂×C₄×C₃₁	—	4	2	no	—
138	C₂×C₄×C₃₁	—	4	2	no	—
139	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
144	C₈×C₃₁	—	2	1	no	—
145	C₈×C₃₁	—	2	1	no	—
146	C₈×C₃₁	—	2	1	no	—
147	C₈×C₃₁	—	2	1	no	—
148	#3312	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂²×C₃₁	—	2	1	no	—
150	C₂²×C₃₁	—	2	1	no	—
151	C₂²×C₃₁	—	2	1	no	—
152	C₂²×C₃₁	—	2	1	no	—
153	C₂²×C₃₁	—	2	1	no	—
154	C₂²×C₃₁	#137	1	2	yes	—
155	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₄×C₃₁	—	2	1	no	—
157	C₄×C₃₁	—	2	1	no	—
158	C₄×C₃₁	—	2	2	no	—
159	C₄×C₃₁	—	2	1	no	—
160	C₄×C₃₁	—	2	1	no	—
161	C₄×C₃₁	—	4	1	no	—
162	C₄×C₃₁	—	4	1	no	—
163	C₄×C₃₁	—	4	1	no	—
164	C₄×C₃₁	—	4	1	no	—
165	C₄×C₃₁	—	4	1	no	—
166	C₄×C₃₁	—	4	1	no	—
167	C₄×C₃₁	—	4	1	no	—
168	C₄×C₃₁	C₂×#41	1	1	yes	characteristic
169	C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
170	#552	C₂×C₃₁	1	1	yes	characteristic
171	D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic
172	#491	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#485	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#483	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#479	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#470	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#467	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#462	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#451	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#451	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#441	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#435	C₂×C₃₁	1	1	yes	characteristic
183	#419	C₂×C₃₁	1	1	yes	characteristic, complemented
184	C₂×#103	C₂×C₃₁	1	1	yes	characteristic, complemented
185	C₂×C₃₁	—	2	2	no	—
186	C₂×C₃₁	—	4	1	no	—
187	C₂×C₃₁	#546	1	1	yes	characteristic
188	C₂×C₃₁	C₂×#137	1	1	yes	characteristic
189	C₂×C₃₁	#578	1	1	yes	characteristic
190	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic
191	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
196	C₂²×C₈	C₂²×C₃₁	1	1	yes	characteristic
197	C₄⋊Q₈	—	2	1	no	—
198	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
199	#126	—	2	1	no	—
200	#125	—	2	1	no	—
201	#125	C₂²×C₃₁	1	1	yes	characteristic
202	#123	—	2	1	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
206	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
210	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
211	C₄×D₄	—	2	1	no	—
212	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
213	#117	—	2	1	no	—
214	#117	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
216	#107	C₂²×C₃₁	1	1	yes	characteristic
217	#106	C₂²×C₃₁	1	1	yes	characteristic
218	#106	C₂²×C₃₁	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
220	#103	C₂²×C₃₁	1	1	yes	characteristic
221	#103	C₂²×C₃₁	1	1	yes	characteristic
222	#103	C₂²×C₃₁	1	1	yes	characteristic
223	#103	C₂²×C₃₁	1	1	yes	characteristic
224	#103	C₂²×C₃₁	1	1	yes	characteristic
225	#103	C₂²×C₃₁	1	1	yes	characteristic
226	#103	C₂²×C₃₁	1	1	yes	characteristic
227	#103	C₂²×C₃₁	1	1	yes	characteristic
228	#103	C₂²×C₃₁	1	1	yes	characteristic
229	#103	C₂²×C₃₁	1	1	yes	characteristic
230	C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
232	#97	C₂²×C₃₁	1	1	yes	characteristic
233	C₃₁	#3312	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×Q₈	—	2	1	no	—
235	C₂×Q₈	—	2	1	no	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	4	1	no	—
239	C₂×Q₈	—	4	1	no	—
240	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
241	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
242	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
243	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
244	C₂×D₄	D₄×C₃₁	1	1	yes	characteristic
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
250	Q₁₆	—	2	2	no	—
251	Q₁₆	—	4	1	no	—
252	Q₁₆	—	4	1	no	—
253	M₁₆	—	4	1	no	—
254	C₂×C₈	—	4	1	no	—
255	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
256	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
257	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₄⋊C₄	—	2	1	no	—
260	C₄⋊C₄	—	2	1	no	—
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	2	1	no	—
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	2	1	no	—
267	C₄⋊C₄	—	2	1	no	—
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
271	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
272	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
273	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
274	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
275	C₂²⋊C₄	—	2	1	no	—
276	C₂²⋊C₄	—	2	1	no	—
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
281	C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	C₂³×C₃₁	1	1	yes	characteristic
286	C₂³	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂³	C₂×D₄×C₃₁	1	1	yes	characteristic
288	Q₈	—	2	1	no	—
289	Q₈	—	2	1	no	—
290	Q₈	—	2	1	no	—
291	Q₈	—	2	1	no	—
292	Q₈	—	2	1	no	—
293	Q₈	—	2	1	no	—
294	Q₈	—	2	1	no	—
295	Q₈	—	4	2	no	—
296	Q₈	—	4	2	no	—
297	Q₈	#41×C₃₁	1	2	yes	—
298	D₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
319	C₈	—	2	1	no	—
320	C₈	—	2	1	no	—
321	C₈	—	2	1	no	—
322	C₈	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	C₃₁×#137	1	2	yes	—
329	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
330	C₄	—	2	1	no	—
331	C₄	—	2	1	no	—
332	C₄	—	2	2	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	1	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	4	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	1	no	—
342	C₄	C₂×#41×C₃₁	1	1	yes	characteristic
343	C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂	—	2	2	no	—
345	C₂	—	4	1	no	—
346	C₂	C₃₁×#546	1	1	yes	characteristic
347	C₂	C₂×C₃₁×#137	1	1	yes	characteristic
348	C₂	C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₁
prime radical	C₂×D₄×C₃₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#491	C₂	semidirect
4. C₃₁×#485	C₂	semidirect
5. C₃₁×#483	C₂	semidirect
6. C₃₁×#479	C₂	semidirect
7. C₃₁×#470	C₂	semidirect
8. C₃₁×#467	C₂	semidirect
9. C₃₁×#462	C₂	semidirect
10. C₃₁×#451	C₂	semidirect
11. C₃₁×#451	C₂	semidirect
12. C₃₁×#441	C₂	semidirect
14. C₃₁×#419	C₂	semidirect
15. C₂×C₃₁×#103	C₂	semidirect
148. #3312	C₃₁	direct (N × H)
172. #491	C₂×C₃₁	semidirect
173. #485	C₂×C₃₁	semidirect
174. #483	C₂×C₃₁	semidirect
175. #479	C₂×C₃₁	semidirect
176. #470	C₂×C₃₁	semidirect
177. #467	C₂×C₃₁	semidirect
178. #462	C₂×C₃₁	semidirect
179. #451	C₂×C₃₁	semidirect
180. #451	C₂×C₃₁	semidirect
181. #441	C₂×C₃₁	semidirect
183. #419	C₂×C₃₁	semidirect
184. C₂×#103	C₂×C₃₁	semidirect
233. C₃₁	#3312	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×#552	2
D₄×Q₈×C₃₁	2
C₃₁×#491	2
C₃₁×#485	2
C₃₁×#483	2
C₃₁×#479	2
C₃₁×#470	2
C₃₁×#467	2
C₃₁×#462	2
C₃₁×#451	2
C₃₁×#441	2
C₃₁×#435	2
C₃₁×#419	2
C₂×C₃₁×#103	2
#3312	31

Subgroups — C31×#3312 #16843245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3312 #16843245