Subgroups — C₃₁×#33865 #21490624

Order 7936.

580 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2241	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2235	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2217	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2185	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#358	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
13	D₄×Q₈×C₃₁	—	2	1	no	—
14	C₃₁×#547	—	2	1	no	—
15	C₂×C₃₁×SD₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
17	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	—
18	C₃₁×#500	C₂²	1	1	yes	characteristic
19	C₃₁×#494	C₂²	1	1	yes	characteristic
20	C₃₁×#480	—	2	2	no	—
21	C₃₁×#474	—	2	1	no	—
22	C₃₁×#467	C₂²	1	2	yes	—
23	C₃₁×#466	C₂²	1	2	yes	—
24	C₃₁×#462	—	2	1	no	—
25	C₃₁×#451	—	2	2	no	—
26	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#107	C₂²	1	2	yes	—
30	C₃₁×#367	C₂²	1	1	yes	characteristic
31	C₃₁×#367	C₂²	1	2	yes	—
32	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₃₁×#358	C₂²	1	1	yes	characteristic
34	C₃₁×#358	C₂²	1	2	yes	—
35	C₃₁×#358	C₂²	1	2	yes	—
36	C₃₁×#358	C₂²	1	2	yes	—
37	C₃₁×#358	C₂²	1	2	yes	—
38	C₃₁×#357	C₂²	1	1	yes	characteristic
39	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
40	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×#41×C₃₁	—	4	1	no	—
42	C₂²×Q₈×C₃₁	—	2	2	no	—
43	C₂×Q₁₆×C₃₁	—	2	4	no	—
44	C₂×Q₁₆×C₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	1	no	—
46	C₂×Q₁₆×C₃₁	—	4	2	no	—
47	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊Q₈	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	—	4	1	no	—
54	C₃₁×#123	—	4	2	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×C₂²⋊Q₈	—	4	1	no	—
57	C₃₁×C₂²⋊Q₈	—	4	2	no	—
58	C₃₁×#121	—	2	2	no	—
59	C₄×Q₈×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	—	2	1	no	—
61	C₄×D₄×C₃₁	—	4	1	no	—
62	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₃₁×SD₃₂	—	2	2	no	—
65	C₃₁×SD₃₂	—	4	2	no	—
66	C₂×C₁₆×C₃₁	—	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	2	no	—
71	C₃₁×#107	—	2	1	no	—
72	C₃₁×#107	C₂³	1	1	yes	characteristic
73	C₃₁×#107	C₂³	1	2	yes	—
74	C₃₁×#107	C₂³	1	1	yes	characteristic
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	#41×C₃₁	—	8	4	no	—
83	C₂×Q₈×C₃₁	—	2	1	no	—
84	C₂×Q₈×C₃₁	—	2	2	no	—
85	C₂×Q₈×C₃₁	—	4	4	no	—
86	C₂×Q₈×C₃₁	—	4	1	no	—
87	C₂×Q₈×C₃₁	—	4	2	no	—
88	C₂×Q₈×C₃₁	—	8	2	no	—
89	C₂×D₄×C₃₁	—	2	1	no	—
90	C₂×D₄×C₃₁	—	4	2	no	—
91	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	—	4	2	no	—
93	C₂²×C₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	—	4	1	no	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
96	Q₁₆×C₃₁	—	2	2	no	—
97	Q₁₆×C₃₁	—	2	1	no	—
98	Q₁₆×C₃₁	—	2	2	no	—
99	Q₁₆×C₃₁	—	4	4	no	—
100	Q₁₆×C₃₁	—	8	1	no	—
101	Q₁₆×C₃₁	#41	1	2	yes	complemented
102	D₈×C₃₁	—	2	1	no	—
103	D₈×C₃₁	—	2	1	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₃₁	—	2	1	no	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	4	2	no	—
113	C₄⋊C₄×C₃₁	—	4	1	no	—
114	C₄⋊C₄×C₃₁	—	4	1	no	—
115	C₄⋊C₄×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	—	4	1	no	—
117	C₄⋊C₄×C₃₁	—	4	1	no	—
118	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₃₁	—	4	1	no	—
121	C₂²⋊C₄×C₃₁	—	4	2	no	—
122	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
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	#33865	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	4	1	no	—
130	C₂³×C₃₁	C₂×D₈	1	2	yes	—
131	Q₈×C₃₁	—	2	2	no	—
132	Q₈×C₃₁	—	4	1	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	Q₈×C₃₁	—	4	2	no	—
135	Q₈×C₃₁	—	8	4	no	—
136	Q₈×C₃₁	—	8	2	no	—
137	D₄×C₃₁	—	4	1	no	—
138	D₄×C₃₁	—	4	1	no	—
139	D₄×C₃₁	—	8	4	no	—
140	D₄×C₃₁	SD₃₂	1	4	yes	complemented
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	4	1	no	—
144	C₂×C₄×C₃₁	—	4	1	no	—
145	C₂×C₄×C₃₁	—	4	1	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	8	4	no	—
149	C₂×C₄×C₃₁	—	8	4	no	—
150	C₂×C₄×C₃₁	—	8	2	no	—
151	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₃₁	—	2	2	no	—
156	C₈×C₃₁	—	2	1	no	—
157	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
159	#3334	C₂×C₃₁	1	1	yes	characteristic
160	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
161	#2241	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#2235	C₂×C₃₁	1	2	yes	complemented
163	#2225	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#2217	C₂×C₃₁	1	2	yes	complemented
165	#2208	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#2185	C₂×C₃₁	1	2	yes	complemented
167	C₄×SD₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
168	D₄×C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂×#358	C₂×C₃₁	1	2	yes	complemented
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	2	2	no	—
172	C₂²×C₃₁	—	8	1	no	—
173	C₂²×C₃₁	—	8	1	no	—
174	C₂²×C₃₁	—	8	1	no	—
175	C₂²×C₃₁	C₂×SD₃₂	1	4	yes	—
176	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	2	no	—
179	C₄×C₃₁	—	4	2	no	—
180	C₄×C₃₁	—	8	1	no	—
181	C₄×C₃₁	—	8	2	no	—
182	C₄×C₃₁	—	8	1	no	—
183	C₄×C₃₁	—	8	2	no	—
184	C₄×C₃₁	C₂×SD₃₂	1	2	yes	—
185	C₄×C₃₁	#546	1	1	yes	characteristic
186	C₄×C₃₁	#577	1	1	yes	characteristic
187	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
188	D₄×Q₈	—	2	1	no	—
189	#547	—	2	1	no	—
190	C₂×SD₃₂	C₂²×C₃₁	1	1	yes	characteristic
191	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
192	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	—
193	#500	C₂²×C₃₁	1	1	yes	characteristic
194	#494	C₂²×C₃₁	1	1	yes	characteristic
195	#480	—	2	2	no	—
196	#474	—	2	1	no	—
197	#467	C₂²×C₃₁	1	2	yes	—
198	#466	C₂²×C₃₁	1	2	yes	—
199	#462	—	2	1	no	—
200	#451	—	2	2	no	—
201	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
202	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
203	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#107	C₂²×C₃₁	1	2	yes	—
205	#367	C₂²×C₃₁	1	1	yes	characteristic
206	#367	C₂²×C₃₁	1	2	yes	—
207	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
208	#358	C₂²×C₃₁	1	1	yes	characteristic
209	#358	C₂²×C₃₁	1	2	yes	—
210	#358	C₂²×C₃₁	1	2	yes	—
211	#358	C₂²×C₃₁	1	2	yes	—
212	#358	C₂²×C₃₁	1	2	yes	—
213	#357	C₂²×C₃₁	1	1	yes	characteristic
214	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
215	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₃₁	—	2	4	no	—
217	C₂×C₃₁	—	16	1	no	—
218	C₂×C₃₁	#3294	1	1	yes	characteristic
219	C₂×C₃₁	C₂²×SD₃₂	1	1	yes	characteristic
220	C₂×C₃₁	#3417	1	1	yes	characteristic
221	C₂×#41	—	4	1	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂×Q₁₆	—	2	4	no	—
224	C₂×Q₁₆	—	2	2	no	—
225	C₂×Q₁₆	—	2	1	no	—
226	C₂×Q₁₆	—	4	2	no	—
227	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
228	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
229	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	4	1	no	—
234	#123	—	4	2	no	—
235	C₂²⋊Q₈	—	2	2	no	—
236	C₂²⋊Q₈	—	4	1	no	—
237	C₂²⋊Q₈	—	4	2	no	—
238	#121	—	2	2	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	4	1	no	—
242	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	2	2	no	—
244	SD₃₂	—	2	2	no	—
245	SD₃₂	—	4	2	no	—
246	C₂×C₁₆	—	4	2	no	—
247	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
248	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
249	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
250	#107	—	2	2	no	—
251	#107	—	2	1	no	—
252	#107	C₂³×C₃₁	1	1	yes	characteristic
253	#107	C₂³×C₃₁	1	1	yes	characteristic
254	#107	C₂³×C₃₁	1	2	yes	—
255	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
256	#103	—	2	1	no	—
257	#103	—	2	2	no	—
258	#102	—	2	1	no	—
259	#102	—	2	2	no	—
260	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
261	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
262	C₃₁	#33865	1	1	yes	characteristic, direct product factor, Sylow
263	#41	—	8	4	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	8	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	—	2	1	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	4	4	no	—
281	Q₁₆	—	8	1	no	—
282	Q₁₆	#41×C₃₁	1	2	yes	complemented
283	D₈	—	2	1	no	—
284	D₈	—	2	1	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
289	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
304	C₄²	—	4	1	no	—
305	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₁₆	—	2	1	no	—
307	C₁₆	—	2	1	no	—
308	C₁₆	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	C₂×D₈×C₃₁	1	2	yes	—
311	Q₈	—	2	2	no	—
312	Q₈	—	4	1	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	8	4	no	—
316	Q₈	—	8	2	no	—
317	D₄	—	4	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	8	4	no	—
320	D₄	C₃₁×SD₃₂	1	4	yes	complemented
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	4	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
333	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
335	C₈	—	2	2	no	—
336	C₈	—	2	1	no	—
337	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
338	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	8	1	no	—
342	C₂²	—	8	1	no	—
343	C₂²	—	8	1	no	—
344	C₂²	C₂×C₃₁×SD₃₂	1	4	yes	—
345	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	2	no	—
348	C₄	—	4	2	no	—
349	C₄	—	8	1	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	1	no	—
352	C₄	—	8	2	no	—
353	C₄	C₂×C₃₁×SD₃₂	1	2	yes	—
354	C₄	C₃₁×#546	1	1	yes	characteristic
355	C₄	C₃₁×#577	1	1	yes	characteristic
356	C₂	—	2	4	no	—
357	C₂	—	16	1	no	—
358	C₂	C₃₁×#3294	1	1	yes	characteristic
359	C₂	C₂²×C₃₁×SD₃₂	1	1	yes	characteristic
360	C₂	C₃₁×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3334	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
2. D₄×Q₁₆×C₃₁	C₂	semidirect
3. C₃₁×#2241	C₂	semidirect
4. C₃₁×#2235	C₂	semidirect
5. C₃₁×#2225	C₂	semidirect
6. C₃₁×#2217	C₂	semidirect
7. C₃₁×#2208	C₂	semidirect
8. C₃₁×#2185	C₂	semidirect
9. C₄×C₃₁×SD₃₂	C₂	semidirect
10. D₄×C₁₆×C₃₁	C₂	semidirect
11. C₂×C₃₁×#358	C₂	semidirect
101. Q₁₆×C₃₁	#41	semidirect
128. #33865	C₃₁	direct (N × H)
140. D₄×C₃₁	SD₃₂	semidirect
160. D₄×Q₁₆	C₂×C₃₁	semidirect
161. #2241	C₂×C₃₁	semidirect
162. #2235	C₂×C₃₁	semidirect
163. #2225	C₂×C₃₁	semidirect
164. #2217	C₂×C₃₁	semidirect
165. #2208	C₂×C₃₁	semidirect
166. #2185	C₂×C₃₁	semidirect
167. C₄×SD₃₂	C₂×C₃₁	semidirect
168. D₄×C₁₆	C₂×C₃₁	semidirect
169. C₂×#358	C₂×C₃₁	semidirect
262. C₃₁	#33865	direct (N × H)
282. Q₁₆	#41×C₃₁	semidirect
320. D₄	C₃₁×SD₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3334	2
D₄×Q₁₆×C₃₁	2
C₃₁×#2241	2
C₃₁×#2235	2
C₃₁×#2225	2
C₃₁×#2217	2
C₃₁×#2208	2
C₃₁×#2185	2
C₄×C₃₁×SD₃₂	2
D₄×C₁₆×C₃₁	2
C₂×C₃₁×#358	2
#33865	31

Subgroups — C31×#33865 #21490624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33865 #21490624