Subgroups — C₃₁×#32831 #21489590

Order 7936.

654 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×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2641	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2067	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2065	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2059	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2041	C₂	1	2	yes	maximal
11	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#107	C₂²	1	2	yes	—
15	C₂×C₃₁×#106	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×#102	C₂²	1	2	yes	—
18	C₂×C₃₁×#102	C₂²	1	2	yes	—
19	C₂×C₃₁×#102	C₂²	1	2	yes	—
20	C₂×C₃₁×#102	C₂²	1	2	yes	—
21	C₃₁×#400	—	2	2	no	—
22	C₃₁×#398	—	2	2	no	—
23	C₃₁×#394	—	2	2	no	—
24	C₃₁×#394	—	2	2	no	—
25	C₃₁×#390	C₂²	1	1	yes	characteristic
26	C₃₁×#390	C₂²	1	1	yes	characteristic
27	C₃₁×#390	C₂²	1	1	yes	characteristic
28	C₃₁×#390	C₂²	1	1	yes	characteristic
29	C₃₁×#389	C₂²	1	2	yes	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#384	C₂²	1	1	yes	characteristic
32	C₃₁×#382	C₂²	1	1	yes	characteristic
33	C₃₁×#376	C₂²	1	1	yes	characteristic
34	C₃₁×#340	C₂²	1	2	yes	—
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	2	yes	—
37	C₃₁×#336	C₂²	1	1	yes	characteristic
38	C₃₁×#336	C₂²	1	1	yes	characteristic
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂²×D₄×C₃₁	—	2	1	no	—
41	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₃₁×#127	—	4	2	no	—
46	C₃₁×#125	—	4	2	no	—
47	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×#107	—	4	2	no	—
64	C₃₁×#106	—	4	2	no	—
65	C₃₁×C₄⋊C₈	—	4	2	no	—
66	C₃₁×#102	—	4	2	no	—
67	C₃₁×#102	—	4	2	no	—
68	C₃₁×#102	—	4	2	no	—
69	C₃₁×#102	—	4	2	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₃₁×#95	—	2	2	no	—
72	C₃₁×#95	—	2	2	no	—
73	C₃₁×#95	D₄	1	2	yes	—
74	C₃₁×#95	D₄	1	2	yes	—
75	C₂⁴×C₃₁	—	2	1	no	—
76	C₂⁴×C₃₁	—	2	1	no	—
77	C₂×D₄×C₃₁	—	2	1	no	—
78	C₂×D₄×C₃₁	—	2	1	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	2	2	no	—
82	C₂×D₄×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	1	no	—
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	—	4	2	no	—
86	C₂×D₄×C₃₁	—	4	2	no	—
87	C₂×D₄×C₃₁	—	8	2	no	—
88	C₂×D₄×C₃₁	—	8	2	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	1	no	—
92	C₂²×C₄×C₃₁	—	2	1	no	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	2	2	no	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	—	4	2	no	—
111	C₄⋊C₄×C₃₁	—	4	2	no	—
112	C₄⋊C₄×C₃₁	—	8	2	no	—
113	C₄⋊C₄×C₃₁	—	8	2	no	—
114	C₄⋊C₄×C₃₁	—	8	2	no	—
115	C₂²⋊C₄×C₃₁	—	8	2	no	—
116	C₂²⋊C₄×C₃₁	—	8	2	no	—
117	C₂²⋊C₄×C₃₁	—	8	2	no	—
118	C₂²⋊C₄×C₃₁	—	8	2	no	—
119	C₄²×C₃₁	—	2	1	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	C₄²×C₃₁	—	2	1	no	—
123	#32831	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₃₁	—	4	1	no	—
125	C₂³×C₃₁	—	4	1	no	—
126	C₂³×C₃₁	—	4	1	no	—
127	C₂³×C₃₁	—	4	1	no	—
128	C₂³×C₃₁	—	4	1	no	—
129	C₂³×C₃₁	—	4	1	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	2	no	—
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
135	D₄×C₃₁	—	4	2	no	—
136	D₄×C₃₁	—	4	2	no	—
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	4	2	no	—
139	D₄×C₃₁	—	8	4	no	—
140	D₄×C₃₁	—	8	4	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	2	1	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
163	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
164	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
165	C₈×C₃₁	—	4	2	no	—
166	C₈×C₃₁	—	4	2	no	—
167	#2647	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#2641	C₂×C₃₁	1	1	yes	characteristic
169	#2094	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#2093	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#2073	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2073	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#2067	C₂×C₃₁	1	2	yes	complemented
174	#2065	C₂×C₃₁	1	2	yes	complemented
175	#2059	C₂×C₃₁	1	2	yes	complemented
176	#2041	C₂×C₃₁	1	2	yes	—
177	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₂²×C₃₁	—	8	1	no	—
179	C₂²×C₃₁	—	8	1	no	—
180	C₂²×C₃₁	—	8	1	no	—
181	C₂²×C₃₁	—	8	1	no	—
182	C₂²×C₃₁	—	8	1	no	—
183	C₂²×C₃₁	—	8	1	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	—	8	2	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	#535	1	1	yes	characteristic
189	C₂²×C₃₁	#536	1	1	yes	characteristic
190	C₂²×C₃₁	#537	1	1	yes	characteristic
191	C₂²×C₃₁	#576	1	2	yes	—
192	C₂²×C₃₁	#577	1	2	yes	—
193	C₄×C₃₁	—	4	1	no	—
194	C₄×C₃₁	—	4	1	no	—
195	C₄×C₃₁	—	4	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	1	no	—
198	C₄×C₃₁	—	8	2	no	—
199	C₄×C₃₁	—	8	1	no	—
200	C₄×C₃₁	—	8	2	no	—
201	C₄×C₃₁	#562	1	2	yes	—
202	C₄×C₃₁	#563	1	2	yes	—
203	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×#107	C₂²×C₃₁	1	2	yes	—
206	C₂×#106	C₂²×C₃₁	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
208	C₂×#102	C₂²×C₃₁	1	2	yes	—
209	C₂×#102	C₂²×C₃₁	1	2	yes	—
210	C₂×#102	C₂²×C₃₁	1	2	yes	—
211	C₂×#102	C₂²×C₃₁	1	2	yes	—
212	#400	—	2	2	no	—
213	#398	—	2	2	no	—
214	#394	—	2	2	no	—
215	#394	—	2	2	no	—
216	#390	C₂²×C₃₁	1	1	yes	characteristic
217	#390	C₂²×C₃₁	1	1	yes	characteristic
218	#390	C₂²×C₃₁	1	1	yes	characteristic
219	#390	C₂²×C₃₁	1	1	yes	characteristic
220	#389	C₂²×C₃₁	1	2	yes	—
221	#389	C₂²×C₃₁	1	2	yes	—
222	#384	C₂²×C₃₁	1	1	yes	characteristic
223	#382	C₂²×C₃₁	1	1	yes	characteristic
224	#376	C₂²×C₃₁	1	1	yes	characteristic
225	#340	C₂²×C₃₁	1	2	yes	—
226	#340	C₂²×C₃₁	1	2	yes	—
227	#336	C₂²×C₃₁	1	2	yes	—
228	#336	C₂²×C₃₁	1	1	yes	characteristic
229	#336	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₃₁	—	16	1	no	—
231	C₂×C₃₁	—	16	1	no	—
232	C₂×C₃₁	#2820	1	1	yes	characteristic
233	C₂×C₃₁	#3220	1	1	yes	characteristic
234	C₂×C₃₁	#3222	1	1	yes	characteristic
235	C₂×C₃₁	#3241	1	2	yes	—
236	C₂×C₃₁	#3257	1	2	yes	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
240	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
243	#127	—	4	2	no	—
244	#125	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
261	#107	—	4	2	no	—
262	#106	—	4	2	no	—
263	C₄⋊C₈	—	4	2	no	—
264	#102	—	4	2	no	—
265	#102	—	4	2	no	—
266	#102	—	4	2	no	—
267	#102	—	4	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	D₄×C₃₁	1	2	yes	—
272	#95	D₄×C₃₁	1	2	yes	—
273	C₃₁	#32831	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	—	2	1	no	—
275	C₂⁴	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂×D₄	—	8	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	8	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₂²⋊C₄	—	8	2	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	4	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
362	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₃₁×#535	1	1	yes	characteristic
376	C₂²	C₃₁×#536	1	1	yes	characteristic
377	C₂²	C₃₁×#537	1	1	yes	characteristic
378	C₂²	C₃₁×#576	1	2	yes	—
379	C₂²	C₃₁×#577	1	2	yes	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	2	no	—
388	C₄	C₃₁×#562	1	2	yes	—
389	C₄	C₃₁×#563	1	2	yes	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	C₃₁×#2820	1	1	yes	characteristic
393	C₂	C₃₁×#3220	1	1	yes	characteristic
394	C₂	C₃₁×#3222	1	1	yes	characteristic
395	C₂	C₃₁×#3241	1	2	yes	—
396	C₂	C₃₁×#3257	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₃₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2647	C₂	semidirect
3. C₃₁×#2094	C₂	semidirect
4. C₃₁×#2093	C₂	semidirect
5. C₃₁×#2073	C₂	semidirect
6. C₃₁×#2073	C₂	semidirect
7. C₃₁×#2067	C₂	semidirect
8. C₃₁×#2065	C₂	semidirect
9. C₃₁×#2059	C₂	semidirect
11. C₃₁×#1832	C₂	semidirect
123. #32831	C₃₁	direct (N × H)
167. #2647	C₂×C₃₁	semidirect
169. #2094	C₂×C₃₁	semidirect
170. #2093	C₂×C₃₁	semidirect
171. #2073	C₂×C₃₁	semidirect
172. #2073	C₂×C₃₁	semidirect
173. #2067	C₂×C₃₁	semidirect
174. #2065	C₂×C₃₁	semidirect
175. #2059	C₂×C₃₁	semidirect
177. #1832	C₂×C₃₁	semidirect
273. C₃₁	#32831	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×#2647	2
C₃₁×#2641	2
C₃₁×#2094	2
C₃₁×#2093	2
C₃₁×#2073	2
C₃₁×#2067	2
C₃₁×#2065	2
C₃₁×#2059	2
C₃₁×#2041	2
C₃₁×#1832	2
#32831	31

Subgroups — C31×#32831 #21489590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#32831 #21489590