Subgroups — C₃₁×#60626 #21517385

Order 7936.

2134 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3142	C₂	1	3	yes	maximal, complemented
4	C₃₁×#3138	C₂	1	3	yes	maximal, complemented
5	C₃₁×#3136	C₂	1	12	yes	maximal, complemented
6	C₃₁×#3135	C₂	1	3	yes	maximal, complemented
7	C₂×C₃₁×#490	C₂	1	3	yes	maximal, complemented
8	C₃₁×#2897	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
11	C₂×C₃₁×#131	C₂²	1	2	yes	—
12	C₃₁×#557	—	2	2	no	—
13	C₃₁×#554	—	2	6	no	—
14	C₃₁×#550	—	2	2	no	—
15	D₄²×C₃₁	—	2	6	no	—
16	C₃₁×#544	C₂²	1	6	yes	complemented
17	C₃₁×#535	C₂²	1	6	yes	—
18	C₃₁×#533	C₂²	1	3	yes	complemented
19	C₃₁×#532	C₂²	1	3	yes	—
20	C₂×C₃₁×#127	C₂²	1	3	yes	—
21	C₂×C₃₁×#125	C₂²	1	3	yes	complemented
22	C₃₁×#520	C₂²	1	2	yes	—
23	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#491	C₂²	1	3	yes	complemented
26	C₃₁×#490	C₂²	1	3	yes	complemented
27	C₃₁×#490	C₂²	1	12	yes	complemented
28	C₃₁×#490	C₂²	1	6	yes	complemented
29	C₃₁×#490	C₂²	1	3	yes	complemented
30	C₃₁×#489	C₂²	1	12	yes	complemented
31	C₃₁×#488	C₂²	1	12	yes	complemented
32	C₃₁×#486	C₂²	1	12	yes	complemented
33	C₃₁×#418	C₂²	1	12	yes	complemented
34	C₃₁×#417	C₂²	1	12	yes	complemented
35	C₃₁×#416	C₂²	1	12	yes	complemented
36	C₂×C₃₁×#102	C₂²	1	12	yes	complemented
37	C₃₁×#405	C₂²	1	6	yes	complemented
38	C₄×M₁₆×C₃₁	C₂²	1	3	yes	complemented
39	C₂×C₃₁×#97	C₂²	1	3	yes	complemented
40	C₃₁×H(5,𝔽₂)	—	2	16	no	—
41	C₂×#41×C₃₁	—	2	2	no	—
42	C₂×#41×C₃₁	C₂³	1	6	yes	—
43	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₁	—	2	6	no	—
45	C₂²×D₄×C₃₁	—	2	6	no	—
46	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
47	C₃₁×#131	—	2	8	no	—
48	C₂×M₁₆×C₃₁	C₂³	1	6	yes	—
49	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
50	C₃₁×C₄⋊Q₈	—	2	6	no	—
51	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
52	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
53	C₃₁×#127	—	2	6	no	—
54	C₃₁×#127	C₂³	1	6	yes	—
55	C₃₁×#127	C₂³	1	3	yes	—
56	C₃₁×#125	—	2	6	no	—
57	C₃₁×#125	—	2	6	no	—
58	C₃₁×#125	C₂³	1	6	yes	—
59	C₃₁×#125	C₂³	1	3	yes	—
60	C₃₁×#125	C₂³	1	1	yes	characteristic
61	C₃₁×#124	C₂³	1	6	yes	—
62	C₃₁×C₂²⋊Q₈	—	2	6	no	—
63	C₃₁×C₂²⋊Q₈	—	2	12	no	—
64	C₃₁×#121	—	2	6	no	—
65	C₃₁×#121	—	2	12	no	—
66	C₃₁×#120	—	2	12	no	—
67	C₄×Q₈×C₃₁	—	2	2	no	—
68	C₄×Q₈×C₃₁	—	2	6	no	—
69	C₄×Q₈×C₃₁	D₄	1	2	yes	—
70	C₄×D₄×C₃₁	—	2	6	no	—
71	C₄×D₄×C₃₁	—	2	6	no	—
72	C₄×D₄×C₃₁	D₄	1	6	yes	—
73	C₃₁×#117	C₂³	1	6	yes	—
74	C₃₁×#117	C₂³	1	3	yes	—
75	C₂×C₄⋊C₄×C₃₁	—	2	6	no	—
76	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
77	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
78	C₃₁×#103	C₂³	1	4	yes	—
79	C₃₁×#103	C₂³	1	12	yes	—
80	C₃₁×#102	C₂³	1	12	yes	—
81	C₃₁×#102	C₂³	1	24	yes	—
82	C₃₁×#102	C₂³	1	12	yes	—
83	C₃₁×#97	C₂³	1	1	yes	characteristic
84	C₃₁×#97	C₂³	1	3	yes	—
85	C₃₁×#97	C₂³	1	6	yes	—
86	C₄×C₈×C₃₁	C₂³	1	6	yes	—
87	C₂⁴×C₃₁	—	2	6	no	—
88	#41×C₃₁	—	2	24	no	—
89	#41×C₃₁	—	4	8	no	—
90	#41×C₃₁	#41	1	8	yes	—
91	C₂×Q₈×C₃₁	—	2	6	no	—
92	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
94	C₂×D₄×C₃₁	—	2	6	no	—
95	C₂×D₄×C₃₁	—	2	6	no	—
96	C₂×D₄×C₃₁	—	2	6	no	—
97	C₂×D₄×C₃₁	—	2	12	no	—
98	C₂×D₄×C₃₁	—	2	24	no	—
99	C₂×D₄×C₃₁	—	4	24	no	—
100	C₂×D₄×C₃₁	—	8	12	no	—
101	C₂×D₄×C₃₁	C₂×D₄	1	3	yes	—
102	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
103	C₂²×C₄×C₃₁	—	2	6	no	—
104	C₂²×C₄×C₃₁	—	2	6	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	6	yes	—
106	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
107	M₁₆×C₃₁	—	2	12	no	—
108	C₂×C₈×C₃₁	—	2	12	no	—
109	C₂×C₈×C₃₁	C₂⁴	1	6	yes	—
110	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₃₁	—	2	6	no	—
112	C₄⋊C₄×C₃₁	—	2	12	no	—
113	C₄⋊C₄×C₃₁	—	2	6	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	6	no	—
117	C₄⋊C₄×C₃₁	C₂×D₄	1	6	yes	—
118	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
119	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
120	C₂²⋊C₄×C₃₁	—	2	6	no	—
121	C₂²⋊C₄×C₃₁	—	2	12	no	—
122	C₂²⋊C₄×C₃₁	C₂×D₄	1	6	yes	—
123	C₄²×C₃₁	—	2	6	no	—
124	C₄²×C₃₁	C₂×D₄	1	6	yes	—
125	C₄²×C₃₁	C₂⁴	1	3	yes	—
126	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
127	#60626	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	6	no	—
129	C₂³×C₃₁	—	4	12	no	—
130	C₂³×C₃₁	—	8	12	no	—
131	C₂³×C₃₁	C₂²×D₄	1	3	yes	—
132	Q₈×C₃₁	—	2	4	no	—
133	Q₈×C₃₁	—	8	6	no	—
134	Q₈×C₃₁	#124	1	4	yes	—
135	D₄×C₃₁	—	2	12	no	—
136	D₄×C₃₁	—	4	12	no	—
137	D₄×C₃₁	—	4	12	no	—
138	D₄×C₃₁	—	4	12	no	—
139	D₄×C₃₁	—	8	12	no	—
140	D₄×C₃₁	#124	1	12	yes	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	6	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	4	6	no	—
145	C₂×C₄×C₃₁	—	4	12	no	—
146	C₂×C₄×C₃₁	—	8	6	no	—
147	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
149	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
150	C₂×C₄×C₃₁	C₂×#41	1	12	yes	—
151	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
152	C₈×C₃₁	—	2	2	no	—
153	C₈×C₃₁	—	2	6	no	—
154	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
155	#3498	C₂×C₃₁	1	1	yes	characteristic
156	#3142	C₂×C₃₁	1	3	yes	complemented
157	#3138	C₂×C₃₁	1	3	yes	complemented
158	#3136	C₂×C₃₁	1	12	yes	complemented
159	#3135	C₂×C₃₁	1	3	yes	complemented
160	C₂×#490	C₂×C₃₁	1	3	yes	complemented
161	#2897	C₂×C₃₁	1	4	yes	complemented
162	#2875	C₂×C₃₁	1	1	yes	characteristic, complemented
163	C₂²×C₃₁	—	2	6	no	—
164	C₂²×C₃₁	—	4	12	no	—
165	C₂²×C₃₁	—	4	6	no	—
166	C₂²×C₃₁	—	16	12	no	—
167	C₂²×C₃₁	C₂×#124	1	6	yes	—
168	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	2	6	no	—
171	C₄×C₃₁	—	4	6	no	—
172	C₄×C₃₁	—	4	2	no	—
173	C₄×C₃₁	—	4	2	no	—
174	C₄×C₃₁	C₂×#124	1	6	yes	—
175	C₄×C₃₁	C₂²×#41	1	2	yes	—
176	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
177	C₂×#131	C₂²×C₃₁	1	2	yes	—
178	#557	—	2	2	no	—
179	#554	—	2	6	no	—
180	#550	—	2	2	no	—
181	D₄²	—	2	6	no	—
182	#544	C₂²×C₃₁	1	6	yes	complemented
183	#535	C₂²×C₃₁	1	6	yes	—
184	#533	C₂²×C₃₁	1	3	yes	complemented
185	#532	C₂²×C₃₁	1	3	yes	—
186	C₂×#127	C₂²×C₃₁	1	3	yes	—
187	C₂×#125	C₂²×C₃₁	1	3	yes	complemented
188	#520	C₂²×C₃₁	1	2	yes	—
189	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
190	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
191	#491	C₂²×C₃₁	1	3	yes	complemented
192	#490	C₂²×C₃₁	1	3	yes	complemented
193	#490	C₂²×C₃₁	1	12	yes	complemented
194	#490	C₂²×C₃₁	1	6	yes	complemented
195	#490	C₂²×C₃₁	1	3	yes	complemented
196	#489	C₂²×C₃₁	1	12	yes	complemented
197	#488	C₂²×C₃₁	1	12	yes	complemented
198	#486	C₂²×C₃₁	1	12	yes	complemented
199	#418	C₂²×C₃₁	1	12	yes	complemented
200	#417	C₂²×C₃₁	1	12	yes	complemented
201	#416	C₂²×C₃₁	1	12	yes	complemented
202	C₂×#102	C₂²×C₃₁	1	12	yes	complemented
203	#405	C₂²×C₃₁	1	6	yes	complemented
204	C₄×M₁₆	C₂²×C₃₁	1	3	yes	complemented
205	C₂×#97	C₂²×C₃₁	1	3	yes	complemented
206	C₂×C₃₁	—	2	6	no	—
207	C₂×C₃₁	—	8	6	no	—
208	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
209	C₂×C₃₁	#3585	1	2	yes	—
210	H(5,𝔽₂)	—	2	16	no	—
211	C₂×#41	—	2	2	no	—
212	C₂×#41	C₂³×C₃₁	1	6	yes	—
213	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
214	C₂²×D₄	—	2	6	no	—
215	C₂²×D₄	—	2	6	no	—
216	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
217	#131	—	2	8	no	—
218	C₂×M₁₆	C₂³×C₃₁	1	6	yes	—
219	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
220	C₄⋊Q₈	—	2	6	no	—
221	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
222	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
223	#127	—	2	6	no	—
224	#127	C₂³×C₃₁	1	3	yes	—
225	#127	C₂³×C₃₁	1	6	yes	—
226	#125	—	2	6	no	—
227	#125	—	2	6	no	—
228	#125	C₂³×C₃₁	1	3	yes	—
229	#125	C₂³×C₃₁	1	6	yes	—
230	#125	C₂³×C₃₁	1	1	yes	characteristic
231	#124	C₂³×C₃₁	1	6	yes	—
232	C₂²⋊Q₈	—	2	6	no	—
233	C₂²⋊Q₈	—	2	12	no	—
234	#121	—	2	6	no	—
235	#121	—	2	12	no	—
236	#120	—	2	12	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×Q₈	—	2	6	no	—
239	C₄×Q₈	D₄×C₃₁	1	2	yes	—
240	C₄×D₄	—	2	6	no	—
241	C₄×D₄	—	2	6	no	—
242	C₄×D₄	D₄×C₃₁	1	6	yes	—
243	#117	C₂³×C₃₁	1	6	yes	—
244	#117	C₂³×C₃₁	1	3	yes	—
245	C₂×C₄⋊C₄	—	2	6	no	—
246	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
247	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
248	#103	C₂³×C₃₁	1	4	yes	—
249	#103	C₂³×C₃₁	1	12	yes	—
250	#102	C₂³×C₃₁	1	12	yes	—
251	#102	C₂³×C₃₁	1	24	yes	—
252	#102	C₂³×C₃₁	1	12	yes	—
253	#97	C₂³×C₃₁	1	1	yes	characteristic
254	#97	C₂³×C₃₁	1	3	yes	—
255	#97	C₂³×C₃₁	1	6	yes	—
256	C₄×C₈	C₂³×C₃₁	1	6	yes	—
257	C₃₁	#60626	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	—	2	6	no	—
259	#41	—	2	24	no	—
260	#41	—	4	8	no	—
261	#41	#41×C₃₁	1	8	yes	—
262	C₂×Q₈	—	2	6	no	—
263	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
264	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
265	C₂×D₄	—	2	6	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	—	2	24	no	—
270	C₂×D₄	—	4	24	no	—
271	C₂×D₄	—	8	12	no	—
272	C₂×D₄	C₂×D₄×C₃₁	1	3	yes	—
273	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
274	C₂²×C₄	—	2	6	no	—
275	C₂²×C₄	—	2	6	no	—
276	C₂²×C₄	C₂×D₄×C₃₁	1	6	yes	—
277	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
278	M₁₆	—	2	12	no	—
279	C₂×C₈	—	2	12	no	—
280	C₂×C₈	C₂⁴×C₃₁	1	6	yes	—
281	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
282	C₄⋊C₄	—	2	6	no	—
283	C₄⋊C₄	—	2	12	no	—
284	C₄⋊C₄	—	2	6	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	6	no	—
288	C₄⋊C₄	C₂×D₄×C₃₁	1	6	yes	—
289	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
290	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
291	C₂²⋊C₄	—	2	6	no	—
292	C₂²⋊C₄	—	2	12	no	—
293	C₂²⋊C₄	C₂×D₄×C₃₁	1	6	yes	—
294	C₄²	—	2	6	no	—
295	C₄²	C₂×D₄×C₃₁	1	6	yes	—
296	C₄²	C₂⁴×C₃₁	1	3	yes	—
297	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
298	C₂³	—	2	6	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	8	12	no	—
301	C₂³	C₂²×D₄×C₃₁	1	3	yes	—
302	Q₈	—	2	4	no	—
303	Q₈	—	8	6	no	—
304	Q₈	C₃₁×#124	1	4	yes	—
305	D₄	—	2	12	no	—
306	D₄	—	4	12	no	—
307	D₄	—	4	12	no	—
308	D₄	—	4	12	no	—
309	D₄	—	8	12	no	—
310	D₄	C₃₁×#124	1	12	yes	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	6	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	6	no	—
315	C₂×C₄	—	4	12	no	—
316	C₂×C₄	—	8	6	no	—
317	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
318	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
319	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
320	C₂×C₄	C₂×#41×C₃₁	1	12	yes	—
321	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	6	no	—
324	C₂²	—	2	6	no	—
325	C₂²	—	4	6	no	—
326	C₂²	—	4	12	no	—
327	C₂²	—	16	12	no	—
328	C₂²	C₂×C₃₁×#124	1	6	yes	—
329	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	6	no	—
332	C₄	—	4	2	no	—
333	C₄	—	4	6	no	—
334	C₄	—	4	2	no	—
335	C₄	C₂×C₃₁×#124	1	6	yes	—
336	C₄	C₂²×#41×C₃₁	1	2	yes	—
337	C₂	—	2	6	no	—
338	C₂	—	8	6	no	—
339	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
340	C₂	C₃₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3504	C₂	semidirect
3. C₃₁×#3142	C₂	semidirect
4. C₃₁×#3138	C₂	semidirect
5. C₃₁×#3136	C₂	semidirect
6. C₃₁×#3135	C₂	semidirect
7. C₂×C₃₁×#490	C₂	semidirect
8. C₃₁×#2897	C₂	semidirect
9. C₃₁×#2875	C₂	semidirect
16. C₃₁×#544	C₂²	semidirect
18. C₃₁×#533	C₂²	semidirect
21. C₂×C₃₁×#125	C₂²	semidirect
24. C₃₁×#491	C₂²	semidirect
25. C₃₁×#491	C₂²	semidirect
26. C₃₁×#490	C₂²	semidirect
27. C₃₁×#490	C₂²	semidirect
28. C₃₁×#490	C₂²	semidirect
29. C₃₁×#490	C₂²	semidirect
30. C₃₁×#489	C₂²	semidirect
31. C₃₁×#488	C₂²	semidirect
32. C₃₁×#486	C₂²	semidirect
33. C₃₁×#418	C₂²	semidirect
34. C₃₁×#417	C₂²	semidirect
35. C₃₁×#416	C₂²	semidirect
36. C₂×C₃₁×#102	C₂²	semidirect
37. C₃₁×#405	C₂²	semidirect
38. C₄×M₁₆×C₃₁	C₂²	semidirect
39. C₂×C₃₁×#97	C₂²	semidirect
127. #60626	C₃₁	direct (N × H)
154. #3504	C₂×C₃₁	semidirect
156. #3142	C₂×C₃₁	semidirect
157. #3138	C₂×C₃₁	semidirect
158. #3136	C₂×C₃₁	semidirect
159. #3135	C₂×C₃₁	semidirect
160. C₂×#490	C₂×C₃₁	semidirect
161. #2897	C₂×C₃₁	semidirect
162. #2875	C₂×C₃₁	semidirect
182. #544	C₂²×C₃₁	semidirect
184. #533	C₂²×C₃₁	semidirect
187. C₂×#125	C₂²×C₃₁	semidirect
190. #491	C₂²×C₃₁	semidirect
191. #491	C₂²×C₃₁	semidirect
192. #490	C₂²×C₃₁	semidirect
193. #490	C₂²×C₃₁	semidirect
194. #490	C₂²×C₃₁	semidirect
195. #490	C₂²×C₃₁	semidirect
196. #489	C₂²×C₃₁	semidirect
197. #488	C₂²×C₃₁	semidirect
198. #486	C₂²×C₃₁	semidirect
199. #418	C₂²×C₃₁	semidirect
200. #417	C₂²×C₃₁	semidirect
201. #416	C₂²×C₃₁	semidirect
202. C₂×#102	C₂²×C₃₁	semidirect
203. #405	C₂²×C₃₁	semidirect
204. C₄×M₁₆	C₂²×C₃₁	semidirect
205. C₂×#97	C₂²×C₃₁	semidirect
257. C₃₁	#60626	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×#3504	2
C₃₁×#3498	2
C₃₁×#3142	2
C₃₁×#3138	2
C₃₁×#3136	2
C₃₁×#3135	2
C₂×C₃₁×#490	2
C₃₁×#2897	2
C₃₁×#2875	2
#60626	31

Subgroups — C31×#60626 #21517385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60626 #21517385