Subgroups — C₃₁×#33891 #21490650

Order 7936.

608 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2234	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2220	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2187	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2140	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
13	C₃₁×#556	—	2	1	no	—
14	D₄²×C₃₁	—	2	1	no	—
15	C₂×C₃₁×SD₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
17	C₂×C₃₁×M₃₂	C₂²	1	2	yes	complemented
18	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#493	C₂²	1	1	yes	characteristic
20	C₃₁×#485	—	2	2	no	—
21	C₃₁×#475	—	2	1	no	—
22	C₃₁×#467	C₂²	1	2	yes	complemented
23	C₃₁×#466	C₂²	1	2	yes	—
24	C₃₁×#459	—	2	1	no	—
25	C₃₁×#447	—	2	2	no	—
26	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#427	C₂²	1	2	yes	complemented
30	C₃₁×#367	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#366	C₂²	1	2	yes	complemented
32	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#358	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#357	C₂²	1	1	yes	characteristic
35	C₃₁×#357	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	2	yes	complemented
37	C₃₁×#357	C₂²	1	2	yes	complemented
38	C₃₁×#357	C₂²	1	2	yes	complemented
39	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₄×C₃₁	—	2	2	no	—
42	C₂²×D₄×C₃₁	—	4	1	no	—
43	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
44	C₂×D₈×C₃₁	—	2	4	no	—
45	C₂×D₈×C₃₁	—	2	2	no	—
46	C₂×D₈×C₃₁	—	2	1	no	—
47	C₂×D₈×C₃₁	—	4	2	no	—
48	C₂×D₈×C₃₁	C₂³	1	2	yes	—
49	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×#127	—	2	1	no	—
53	C₃₁×#126	—	4	2	no	—
54	C₃₁×#124	—	4	1	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#121	—	4	1	no	—
58	C₃₁×#120	—	4	2	no	—
59	C₄×Q₈×C₃₁	—	2	1	no	—
60	C₄×Q₈×C₃₁	—	4	1	no	—
61	C₄×D₄×C₃₁	—	2	1	no	—
62	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
63	C₃₁×#117	—	2	2	no	—
64	C₃₁×SD₃₂	—	2	2	no	—
65	C₃₁×SD₃₂	—	4	2	no	—
66	C₃₁×M₃₂	—	4	2	no	—
67	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
69	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×#107	—	2	1	no	—
71	C₃₁×#107	C₂³	1	1	yes	characteristic
72	C₃₁×#107	C₂³	1	2	yes	—
73	C₃₁×#107	C₂³	1	1	yes	characteristic
74	C₃₁×#106	—	2	2	no	—
75	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
76	C₃₁×#103	—	2	1	no	—
77	C₃₁×#103	—	2	2	no	—
78	C₃₁×#102	—	2	1	no	—
79	C₃₁×#102	—	2	2	no	—
80	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂⁴×C₃₁	—	4	2	no	—
83	C₂×Q₈×C₃₁	—	2	1	no	—
84	C₂×Q₈×C₃₁	—	4	1	no	—
85	C₂×D₄×C₃₁	—	2	1	no	—
86	C₂×D₄×C₃₁	—	2	2	no	—
87	C₂×D₄×C₃₁	—	4	4	no	—
88	C₂×D₄×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	—	4	2	no	—
90	C₂×D₄×C₃₁	—	4	1	no	—
91	C₂×D₄×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	8	2	no	—
93	C₂×D₄×C₃₁	—	8	4	no	—
94	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	—	4	1	no	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
97	Q₁₆×C₃₁	—	2	1	no	—
98	Q₁₆×C₃₁	—	2	1	no	—
99	D₈×C₃₁	—	2	2	no	—
100	D₈×C₃₁	—	2	1	no	—
101	D₈×C₃₁	—	2	2	no	—
102	D₈×C₃₁	—	4	4	no	—
103	D₈×C₃₁	—	8	1	no	—
104	D₈×C₃₁	#41	1	2	yes	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₃₁	—	2	1	no	—
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	4	1	no	—
114	C₄⋊C₄×C₃₁	—	4	2	no	—
115	C₄⋊C₄×C₃₁	—	4	1	no	—
116	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
117	C₂²⋊C₄×C₃₁	—	4	2	no	—
118	C₂²⋊C₄×C₃₁	—	4	2	no	—
119	C₂²⋊C₄×C₃₁	—	4	1	no	—
120	C₂²⋊C₄×C₃₁	—	4	2	no	—
121	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
122	C₄²×C₃₁	—	4	2	no	—
123	C₄²×C₃₁	—	4	1	no	—
124	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₃₁	—	2	1	no	—
126	C₁₆×C₃₁	—	2	1	no	—
127	C₁₆×C₃₁	—	2	2	no	—
128	#33891	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	4	1	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	—	8	4	no	—
132	C₂³×C₃₁	—	8	4	no	—
133	C₂³×C₃₁	—	16	2	no	—
134	C₂³×C₃₁	C₂×D₈	1	2	yes	—
135	Q₈×C₃₁	—	4	1	no	—
136	Q₈×C₃₁	—	4	1	no	—
137	Q₈×C₃₁	—	8	2	no	—
138	D₄×C₃₁	—	2	2	no	—
139	D₄×C₃₁	—	2	2	no	—
140	D₄×C₃₁	—	4	2	no	—
141	D₄×C₃₁	—	4	1	no	—
142	D₄×C₃₁	—	4	2	no	—
143	D₄×C₃₁	—	8	4	no	—
144	D₄×C₃₁	—	8	4	no	—
145	D₄×C₃₁	—	8	2	no	—
146	D₄×C₃₁	—	16	1	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	8	2	no	—
154	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
163	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic
164	#2240	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#2234	C₂×C₃₁	1	2	yes	complemented
166	#2224	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#2220	C₂×C₃₁	1	2	yes	complemented
168	#2207	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#2187	C₂×C₃₁	1	2	yes	complemented
170	C₄×SD₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#2169	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2140	C₂×C₃₁	1	2	yes	complemented
173	C₂²×C₃₁	—	2	2	no	—
174	C₂²×C₃₁	—	2	2	no	—
175	C₂²×C₃₁	—	2	2	no	—
176	C₂²×C₃₁	—	4	2	no	—
177	C₂²×C₃₁	—	8	1	no	—
178	C₂²×C₃₁	—	8	1	no	—
179	C₂²×C₃₁	—	8	2	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	16	8	no	—
183	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	2	no	—
186	C₄×C₃₁	—	8	1	no	—
187	C₄×C₃₁	—	8	2	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	—	8	1	no	—
190	C₄×C₃₁	#509	1	2	yes	—
191	C₄×C₃₁	#546	1	1	yes	characteristic
192	C₄×C₃₁	#577	1	1	yes	characteristic
193	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
194	#556	—	2	1	no	—
195	D₄²	—	2	1	no	—
196	C₂×SD₃₂	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
198	C₂×M₃₂	C₂²×C₃₁	1	2	yes	complemented
199	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
200	#493	C₂²×C₃₁	1	1	yes	characteristic
201	#485	—	2	2	no	—
202	#475	—	2	1	no	—
203	#467	C₂²×C₃₁	1	2	yes	complemented
204	#466	C₂²×C₃₁	1	2	yes	—
205	#459	—	2	1	no	—
206	#447	—	2	2	no	—
207	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
208	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
210	#427	C₂²×C₃₁	1	2	yes	complemented
211	#367	C₂²×C₃₁	1	1	yes	characteristic, complemented
212	#366	C₂²×C₃₁	1	2	yes	complemented
213	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
214	#358	C₂²×C₃₁	1	1	yes	characteristic, complemented
215	#357	C₂²×C₃₁	1	1	yes	characteristic
216	#357	C₂²×C₃₁	1	2	yes	—
217	#357	C₂²×C₃₁	1	2	yes	complemented
218	#357	C₂²×C₃₁	1	2	yes	complemented
219	#357	C₂²×C₃₁	1	2	yes	complemented
220	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
221	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
222	C₂×C₃₁	—	4	2	no	—
223	C₂×C₃₁	—	8	2	no	—
224	C₂×C₃₁	—	16	2	no	—
225	C₂×C₃₁	#3294	1	1	yes	characteristic
226	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
227	C₂×C₃₁	#3416	1	1	yes	characteristic
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	4	1	no	—
230	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
231	C₂×D₈	—	2	4	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	4	2	no	—
235	C₂×D₈	C₂³×C₃₁	1	2	yes	—
236	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
238	C₄⋊Q₈	—	2	1	no	—
239	#127	—	2	1	no	—
240	#126	—	4	2	no	—
241	#124	—	4	1	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	#121	—	2	2	no	—
244	#121	—	4	1	no	—
245	#120	—	4	2	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	—	4	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
250	#117	—	2	2	no	—
251	SD₃₂	—	2	2	no	—
252	SD₃₂	—	4	2	no	—
253	M₃₂	—	4	2	no	—
254	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
257	#107	—	2	1	no	—
258	#107	C₂³×C₃₁	1	2	yes	—
259	#107	C₂³×C₃₁	1	1	yes	characteristic
260	#107	C₂³×C₃₁	1	1	yes	characteristic
261	#106	—	2	2	no	—
262	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
263	#103	—	2	1	no	—
264	#103	—	2	2	no	—
265	#102	—	2	1	no	—
266	#102	—	2	2	no	—
267	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
268	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₃₁	#33891	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	—	4	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	8	2	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
285	Q₁₆	—	2	1	no	—
286	Q₁₆	—	2	1	no	—
287	D₈	—	2	2	no	—
288	D₈	—	2	1	no	—
289	D₈	—	2	2	no	—
290	D₈	—	4	4	no	—
291	D₈	—	8	1	no	—
292	D₈	#41×C₃₁	1	2	yes	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
297	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	1	no	—
312	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	4	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	16	2	no	—
321	C₂³	C₂×D₈×C₃₁	1	2	yes	—
322	Q₈	—	4	1	no	—
323	Q₈	—	4	1	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	2	no	—
333	D₄	—	16	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	—	2	1	no	—
347	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
348	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	8	1	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	16	8	no	—
359	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	C₃₁×#509	1	2	yes	—
367	C₄	C₃₁×#546	1	1	yes	characteristic
368	C₄	C₃₁×#577	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	8	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₃₁×#3294	1	1	yes	characteristic
373	C₂	C₂×C₃₁×#509	1	1	yes	characteristic
374	C₂	C₃₁×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	D₄×D₈×C₃₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×D₄×C₃₁ ◁ C₈×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3342	C₂	semidirect
3. C₃₁×#2240	C₂	semidirect
4. C₃₁×#2234	C₂	semidirect
5. C₃₁×#2224	C₂	semidirect
6. C₃₁×#2220	C₂	semidirect
7. C₃₁×#2207	C₂	semidirect
8. C₃₁×#2187	C₂	semidirect
9. C₄×C₃₁×SD₃₂	C₂	semidirect
10. C₃₁×#2169	C₂	semidirect
11. C₃₁×#2140	C₂	semidirect
16. C₂×C₃₁×SD₃₂	C₂²	semidirect
17. C₂×C₃₁×M₃₂	C₂²	semidirect
18. C₃₁×#500	C₂²	semidirect
22. C₃₁×#467	C₂²	semidirect
26. C₄×Q₁₆×C₃₁	C₂²	semidirect
29. C₃₁×#427	C₂²	semidirect
30. C₃₁×#367	C₂²	semidirect
31. C₃₁×#366	C₂²	semidirect
32. C₃₁×C₄⋊C₁₆	C₂²	semidirect
33. C₃₁×#358	C₂²	semidirect
36. C₃₁×#357	C₂²	semidirect
37. C₃₁×#357	C₂²	semidirect
38. C₃₁×#357	C₂²	semidirect
39. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₃₁	C₂²	semidirect
128. #33891	C₃₁	direct (N × H)
162. #3342	C₂×C₃₁	semidirect
164. #2240	C₂×C₃₁	semidirect
165. #2234	C₂×C₃₁	semidirect
166. #2224	C₂×C₃₁	semidirect
167. #2220	C₂×C₃₁	semidirect
168. #2207	C₂×C₃₁	semidirect
169. #2187	C₂×C₃₁	semidirect
170. C₄×SD₃₂	C₂×C₃₁	semidirect
171. #2169	C₂×C₃₁	semidirect
172. #2140	C₂×C₃₁	semidirect
197. C₂×SD₃₂	C₂²×C₃₁	semidirect
198. C₂×M₃₂	C₂²×C₃₁	semidirect
199. #500	C₂²×C₃₁	semidirect
203. #467	C₂²×C₃₁	semidirect
207. C₄×Q₁₆	C₂²×C₃₁	semidirect
210. #427	C₂²×C₃₁	semidirect
211. #367	C₂²×C₃₁	semidirect
212. #366	C₂²×C₃₁	semidirect
213. C₄⋊C₁₆	C₂²×C₃₁	semidirect
214. #358	C₂²×C₃₁	semidirect
217. #357	C₂²×C₃₁	semidirect
218. #357	C₂²×C₃₁	semidirect
219. #357	C₂²×C₃₁	semidirect
220. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
221. C₄×C₁₆	C₂²×C₃₁	semidirect
269. C₃₁	#33891	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×#3342	2
D₄×D₈×C₃₁	2
C₃₁×#2240	2
C₃₁×#2234	2
C₃₁×#2224	2
C₃₁×#2220	2
C₃₁×#2207	2
C₃₁×#2187	2
C₄×C₃₁×SD₃₂	2
C₃₁×#2169	2
C₃₁×#2140	2
#33891	31

Subgroups — C31×#33891 #21490650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33891 #21490650