Subgroups — C₃₁×#29271 #21486030

Order 7936.

604 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2957	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2098	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2031	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1976	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1975	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1953	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1946	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1868	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1861	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
13	C₃₁×#568	C₂²	1	2	yes	—
14	C₃₁×#533	C₂²	1	1	yes	characteristic
15	C₃₁×#446	—	2	2	no	—
16	C₃₁×#446	—	2	2	no	—
17	C₃₁×#444	—	2	2	no	—
18	C₃₁×#443	—	2	2	no	—
19	C₃₁×#430	C₂²	1	2	yes	—
20	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
22	C₃₁×#427	C₂²	1	1	yes	characteristic
23	C₃₁×#424	C₂²	1	1	yes	characteristic
24	C₃₁×#424	C₂²	1	1	yes	characteristic
25	C₃₁×#424	C₂²	1	2	yes	—
26	C₃₁×#423	C₂²	1	1	yes	characteristic
27	C₃₁×#421	C₂²	1	2	yes	—
28	C₃₁×#421	C₂²	1	2	yes	—
29	C₂×C₃₁×#104	C₂²	1	2	yes	—
30	C₃₁×#410	C₂²	1	2	yes	—
31	C₃₁×#408	C₂²	1	2	yes	—
32	C₃₁×#405	C₂²	1	1	yes	characteristic
33	C₃₁×#405	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
35	C₃₁×#344	C₂²	1	2	yes	—
36	C₃₁×#344	C₂²	1	2	yes	—
37	C₃₁×#339	C₂²	1	2	yes	—
38	C₃₁×H(3,ℤ/4)	C₂²	1	2	yes	—
39	C₂×#41×C₃₁	C₂³	1	2	yes	—
40	C₃₁×#135	—	2	1	no	—
41	C₃₁×#135	—	2	1	no	—
42	C₃₁×#135	—	2	1	no	—
43	C₃₁×#135	—	2	1	no	—
44	C₂×Q₁₆×C₃₁	Q₈	1	1	yes	characteristic, complemented
45	C₂×SD₁₆×C₃₁	Q₈	1	2	yes	complemented
46	C₂×D₈×C₃₁	Q₈	1	1	yes	characteristic, complemented
47	C₃₁×#131	—	2	4	no	—
48	C₃₁×#131	—	4	2	no	—
49	C₂×M₁₆×C₃₁	—	4	2	no	—
50	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
52	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
53	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₃₁×C₄⋊Q₈	—	2	1	no	—
57	C₃₁×#125	—	2	1	no	—
58	C₃₁×C₂²⋊Q₈	—	2	2	no	—
59	C₄×Q₈×C₃₁	—	2	2	no	—
60	C₃₁×#117	C₂³	1	2	yes	—
61	C₃₁×#117	C₂³	1	1	yes	characteristic
62	C₃₁×#117	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×#108	—	2	1	no	—
65	C₃₁×#108	—	2	1	no	—
66	C₃₁×#108	—	2	1	no	—
67	C₃₁×#108	—	2	1	no	—
68	C₃₁×#108	—	4	2	no	—
69	C₃₁×#107	—	2	1	no	—
70	C₃₁×#106	—	2	1	no	—
71	C₃₁×C₄⋊C₈	—	2	2	no	—
72	C₃₁×C₄⋊C₈	—	2	2	no	—
73	C₃₁×C₄⋊C₈	—	2	2	no	—
74	C₃₁×C₄⋊C₈	—	4	2	no	—
75	C₃₁×#104	—	2	4	no	—
76	C₃₁×#104	—	2	2	no	—
77	C₃₁×#104	—	2	2	no	—
78	C₃₁×#104	—	4	2	no	—
79	C₃₁×#99	—	2	4	no	—
80	C₃₁×C₂²⋊C₈	—	4	2	no	—
81	C₃₁×#97	—	2	1	no	—
82	C₃₁×#97	—	2	1	no	—
83	C₃₁×#97	—	2	1	no	—
84	C₃₁×#97	D₄	1	2	yes	—
85	C₄×C₈×C₃₁	—	2	1	no	—
86	C₄×C₈×C₃₁	D₄	1	2	yes	—
87	#41×C₃₁	—	2	2	no	—
88	#41×C₃₁	—	2	2	no	—
89	#41×C₃₁	—	2	2	no	—
90	#41×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	C₂×Q₈	1	2	yes	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₃₁	—	2	1	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₃₁	—	2	1	no	—
99	Q₁₆×C₃₁	—	2	1	no	—
100	SD₁₆×C₃₁	—	2	2	no	—
101	SD₁₆×C₃₁	—	2	2	no	—
102	D₈×C₃₁	—	2	1	no	—
103	D₈×C₃₁	—	2	1	no	—
104	M₁₆×C₃₁	—	2	1	no	—
105	M₁₆×C₃₁	—	2	1	no	—
106	M₁₆×C₃₁	—	2	2	no	—
107	M₁₆×C₃₁	—	2	2	no	—
108	M₁₆×C₃₁	—	2	2	no	—
109	M₁₆×C₃₁	—	2	1	no	—
110	M₁₆×C₃₁	—	2	1	no	—
111	M₁₆×C₃₁	—	2	2	no	—
112	M₁₆×C₃₁	—	4	4	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	—	2	1	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	4	4	no	—
120	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
124	C₂×C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
126	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
127	C₄⋊C₄×C₃₁	—	2	4	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	1	no	—
130	C₄⋊C₄×C₃₁	—	2	1	no	—
131	C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₂²⋊C₄×C₃₁	—	2	1	no	—
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₂²⋊C₄×C₃₁	#41	1	2	yes	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	2	no	—
138	C₄²×C₃₁	C₂×D₄	1	2	yes	—
139	C₄²×C₃₁	#41	1	1	yes	characteristic
140	C₄²×C₃₁	#41	1	1	yes	characteristic
141	#29271	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	—	2	2	no	—
143	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
144	Q₈×C₃₁	—	2	2	no	—
145	Q₈×C₃₁	—	2	2	no	—
146	Q₈×C₃₁	—	8	2	no	—
147	D₄×C₃₁	—	2	2	no	—
148	D₄×C₃₁	—	2	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	2	1	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	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	—	8	1	no	—
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₈×C₃₁	—	2	2	no	—
167	C₈×C₃₁	—	4	1	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₈×C₃₁	—	4	1	no	—
170	C₈×C₃₁	—	4	2	no	—
171	C₈×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
172	C₈×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
173	C₈×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
174	C₈×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
175	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2957	C₂×C₃₁	1	1	yes	characteristic
177	#2098	C₂×C₃₁	1	2	yes	complemented
178	#2031	C₂×C₃₁	1	2	yes	complemented
179	#1976	C₂×C₃₁	1	1	yes	characteristic
180	#1975	C₂×C₃₁	1	1	yes	characteristic
181	#1953	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#1946	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#1868	C₂×C₃₁	1	2	yes	complemented
184	#1861	C₂×C₃₁	1	2	yes	complemented
185	#1833	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂²×C₃₁	—	4	1	no	—
187	C₂²×C₃₁	—	4	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	#525	1	1	yes	characteristic
190	C₂²×C₃₁	#554	1	1	yes	characteristic
191	C₂²×C₃₁	#559	1	1	yes	characteristic
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	4	1	no	—
194	C₄×C₃₁	—	4	2	no	—
195	C₄×C₃₁	—	4	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₄×C₃₁	#535	1	1	yes	characteristic
200	C₄×C₃₁	#554	1	1	yes	characteristic
201	C₄×C₃₁	#559	1	1	yes	characteristic
202	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
203	#568	C₂²×C₃₁	1	2	yes	—
204	#533	C₂²×C₃₁	1	1	yes	characteristic
205	#446	—	2	2	no	—
206	#446	—	2	2	no	—
207	#444	—	2	2	no	—
208	#443	—	2	2	no	—
209	#430	C₂²×C₃₁	1	2	yes	—
210	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
212	#427	C₂²×C₃₁	1	1	yes	characteristic
213	#424	C₂²×C₃₁	1	1	yes	characteristic
214	#424	C₂²×C₃₁	1	1	yes	characteristic
215	#424	C₂²×C₃₁	1	2	yes	—
216	#423	C₂²×C₃₁	1	1	yes	characteristic
217	#421	C₂²×C₃₁	1	2	yes	—
218	#421	C₂²×C₃₁	1	2	yes	—
219	C₂×#104	C₂²×C₃₁	1	2	yes	—
220	#410	C₂²×C₃₁	1	2	yes	—
221	#408	C₂²×C₃₁	1	2	yes	—
222	#405	C₂²×C₃₁	1	1	yes	characteristic
223	#405	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
225	#344	C₂²×C₃₁	1	2	yes	—
226	#344	C₂²×C₃₁	1	2	yes	—
227	#339	C₂²×C₃₁	1	2	yes	—
228	H(3,ℤ/4)	C₂²×C₃₁	1	2	yes	—
229	C₂×C₃₁	—	2	1	no	—
230	C₂×C₃₁	—	2	1	no	—
231	C₂×C₃₁	—	2	1	no	—
232	C₂×C₃₁	—	8	2	no	—
233	C₂×C₃₁	#2580	1	1	yes	characteristic
234	C₂×#41	C₂³×C₃₁	1	2	yes	—
235	#135	—	2	1	no	—
236	#135	—	2	1	no	—
237	#135	—	2	1	no	—
238	#135	—	2	1	no	—
239	C₂×Q₁₆	Q₈×C₃₁	1	1	yes	characteristic, complemented
240	C₂×SD₁₆	Q₈×C₃₁	1	2	yes	complemented
241	C₂×D₈	Q₈×C₃₁	1	1	yes	characteristic, complemented
242	#131	—	2	4	no	—
243	#131	—	4	2	no	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
246	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
247	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
248	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
251	C₄⋊Q₈	—	2	1	no	—
252	#125	—	2	1	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	#117	C₂³×C₃₁	1	2	yes	—
256	#117	C₂³×C₃₁	1	1	yes	characteristic
257	#117	C₂³×C₃₁	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
259	#108	—	2	1	no	—
260	#108	—	2	1	no	—
261	#108	—	2	1	no	—
262	#108	—	2	1	no	—
263	#108	—	4	2	no	—
264	#107	—	2	1	no	—
265	#106	—	2	1	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	4	2	no	—
270	#104	—	2	4	no	—
271	#104	—	2	2	no	—
272	#104	—	2	2	no	—
273	#104	—	4	2	no	—
274	#99	—	2	4	no	—
275	C₂²⋊C₈	—	4	2	no	—
276	#97	—	2	1	no	—
277	#97	—	2	1	no	—
278	#97	—	2	1	no	—
279	#97	D₄×C₃₁	1	2	yes	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	D₄×C₃₁	1	2	yes	—
282	C₃₁	#29271	1	1	yes	characteristic, direct product factor, Sylow
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	C₂×Q₈×C₃₁	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	C₂×Q₈×C₃₁	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
294	Q₁₆	—	2	1	no	—
295	Q₁₆	—	2	1	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	2	2	no	—
298	D₈	—	2	1	no	—
299	D₈	—	2	1	no	—
300	M₁₆	—	2	1	no	—
301	M₁₆	—	2	1	no	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	1	no	—
306	M₁₆	—	2	1	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	4	4	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₂×C₈	C₂×Q₈×C₃₁	1	1	yes	characteristic
320	C₂×C₈	C₂×Q₈×C₃₁	1	1	yes	characteristic
321	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
322	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	#41×C₃₁	1	2	yes	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	C₂×D₄×C₃₁	1	2	yes	—
335	C₄²	#41×C₃₁	1	1	yes	characteristic
336	C₄²	#41×C₃₁	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	8	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
356	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
367	C₈	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
368	C₈	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
369	C₈	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	C₃₁×#525	1	1	yes	characteristic
374	C₂²	C₃₁×#554	1	1	yes	characteristic
375	C₂²	C₃₁×#559	1	1	yes	characteristic
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	8	2	no	—
382	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
383	C₄	C₃₁×#535	1	1	yes	characteristic
384	C₄	C₃₁×#554	1	1	yes	characteristic
385	C₄	C₃₁×#559	1	1	yes	characteristic
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	8	2	no	—
390	C₂	C₃₁×#2580	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂×C₃₁	#2580
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2961	C₂	semidirect
3. C₃₁×#2098	C₂	semidirect
4. C₃₁×#2031	C₂	semidirect
7. C₃₁×#1953	C₂	semidirect
8. C₃₁×#1946	C₂	semidirect
9. C₃₁×#1868	C₂	semidirect
10. C₃₁×#1861	C₂	semidirect
11. C₃₁×#1833	C₂	semidirect
44. C₂×Q₁₆×C₃₁	Q₈	semidirect
45. C₂×SD₁₆×C₃₁	Q₈	semidirect
46. C₂×D₈×C₃₁	Q₈	semidirect
141. #29271	C₃₁	direct (N × H)
175. #2961	C₂×C₃₁	semidirect
177. #2098	C₂×C₃₁	semidirect
178. #2031	C₂×C₃₁	semidirect
181. #1953	C₂×C₃₁	semidirect
182. #1946	C₂×C₃₁	semidirect
183. #1868	C₂×C₃₁	semidirect
184. #1861	C₂×C₃₁	semidirect
185. #1833	C₂×C₃₁	semidirect
239. C₂×Q₁₆	Q₈×C₃₁	semidirect
240. C₂×SD₁₆	Q₈×C₃₁	semidirect
241. C₂×D₈	Q₈×C₃₁	semidirect
282. C₃₁	#29271	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×#2961	2
C₃₁×#2957	2
C₃₁×#2098	2
C₃₁×#2031	2
C₃₁×#1976	2
C₃₁×#1975	2
C₃₁×#1953	2
C₃₁×#1946	2
C₃₁×#1868	2
C₃₁×#1861	2
C₃₁×#1833	2
#29271	31

Subgroups — C31×#29271 #21486030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#29271 #21486030