Subgroups — C₃₁×#33702 #21490461

Order 7936.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3155	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2244	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2243	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2242	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2240	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2140	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#544	—	2	1	no	—
16	C₃₁×#535	—	2	1	no	—
17	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#501	—	2	2	no	—
20	C₃₁×#500	C₂²	1	2	yes	complemented
21	C₃₁×#499	C₂²	1	2	yes	complemented
22	C₃₁×#496	—	2	2	no	—
23	C₃₁×#495	C₂²	1	2	yes	—
24	C₃₁×#493	C₂²	1	2	yes	—
25	C₃₁×#428	—	2	1	no	—
26	C₃₁×#427	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
28	C₃₁×#405	C₂²	1	1	yes	characteristic
29	C₃₁×#358	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#358	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#358	C₂²	1	2	yes	complemented
32	C₃₁×#357	C₂²	1	2	yes	—
33	C₃₁×#357	C₂²	1	2	yes	—
34	C₃₁×#357	C₂²	1	2	yes	—
35	C₃₁×#357	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#357	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#357	C₂²	1	2	yes	complemented
39	C₃₁×#346	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₃₁	C₂²	1	2	yes	complemented
41	C₂×#41×C₃₁	—	2	1	no	—
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
44	C₃₁×#135	—	2	2	no	—
45	C₃₁×#135	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×SD₁₆×C₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₃₁	—	2	1	no	—
49	C₂×D₈×C₃₁	—	2	2	no	—
50	C₂×D₈×C₃₁	—	2	1	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	2	no	—
53	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₃₁	C₂³	1	2	yes	—
55	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₄⋊Q₈	—	2	2	no	—
58	C₃₁×C₄⋊Q₈	—	4	1	no	—
59	C₃₁×#127	—	2	2	no	—
60	C₃₁×#125	—	2	2	no	—
61	C₃₁×#125	—	4	1	no	—
62	C₃₁×#124	—	2	2	no	—
63	C₃₁×C₂²⋊Q₈	—	4	2	no	—
64	C₃₁×#121	—	4	1	no	—
65	C₃₁×#121	—	4	1	no	—
66	C₃₁×#120	—	4	2	no	—
67	C₃₁×#117	—	2	1	no	—
68	C₃₁×#117	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
70	C₃₁×M₃₂	—	2	2	no	—
71	C₂×C₁₆×C₃₁	—	2	2	no	—
72	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
75	C₃₁×#107	—	2	1	no	—
76	C₃₁×#107	—	2	2	no	—
77	C₃₁×#107	C₂³	1	2	yes	—
78	C₃₁×#107	C₂³	1	1	yes	characteristic
79	C₃₁×#107	C₂³	1	1	yes	characteristic
80	C₃₁×#106	—	2	1	no	—
81	C₃₁×#106	—	2	2	no	—
82	C₃₁×#97	D₄	1	2	yes	—
83	C₄×C₈×C₃₁	C₂³	1	2	yes	—
84	C₂⁴×C₃₁	—	4	1	no	—
85	#41×C₃₁	—	4	2	no	—
86	#41×C₃₁	—	4	2	no	—
87	C₂×Q₈×C₃₁	—	2	1	no	—
88	C₂×Q₈×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	—	2	1	no	—
91	C₂×D₄×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂×D₄×C₃₁	—	4	2	no	—
95	C₂×D₄×C₃₁	—	4	2	no	—
96	C₂×D₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	—	4	1	no	—
98	C₂²×C₄×C₃₁	—	4	1	no	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	Q₁₆×C₃₁	—	2	1	no	—
101	Q₁₆×C₃₁	—	2	1	no	—
102	SD₁₆×C₃₁	—	4	2	no	—
103	SD₁₆×C₃₁	—	4	4	no	—
104	D₈×C₃₁	—	2	2	no	—
105	D₈×C₃₁	—	2	2	no	—
106	D₈×C₃₁	—	2	1	no	—
107	D₈×C₃₁	—	2	1	no	—
108	D₈×C₃₁	—	4	2	no	—
109	D₈×C₃₁	—	4	4	no	—
110	M₁₆×C₃₁	SD₁₆	1	4	yes	—
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₃₁	#41	1	2	yes	—
114	C₂×C₈×C₃₁	#41	1	2	yes	—
115	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₄⋊C₄×C₃₁	—	4	1	no	—
120	C₄⋊C₄×C₃₁	—	4	2	no	—
121	C₄⋊C₄×C₃₁	—	4	2	no	—
122	C₄⋊C₄×C₃₁	—	4	2	no	—
123	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
124	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
125	C₂²⋊C₄×C₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₃₁	—	4	2	no	—
128	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
129	C₄²×C₃₁	—	4	1	no	—
130	C₄²×C₃₁	C₂×D₄	1	2	yes	—
131	C₁₆×C₃₁	—	2	1	no	—
132	C₁₆×C₃₁	—	2	1	no	—
133	C₁₆×C₃₁	—	2	2	no	—
134	#33702	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	—	4	1	no	—
137	C₂³×C₃₁	—	8	2	no	—
138	C₂³×C₃₁	—	16	1	no	—
139	C₂³×C₃₁	—	16	1	no	—
140	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
141	Q₈×C₃₁	—	4	1	no	—
142	Q₈×C₃₁	—	4	1	no	—
143	Q₈×C₃₁	—	16	2	no	—
144	D₄×C₃₁	—	4	2	no	—
145	D₄×C₃₁	—	4	1	no	—
146	D₄×C₃₁	—	4	1	no	—
147	D₄×C₃₁	—	4	2	no	—
148	D₄×C₃₁	—	8	2	no	—
149	D₄×C₃₁	—	8	2	no	—
150	D₄×C₃₁	—	16	2	no	—
151	D₄×C₃₁	—	16	2	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	4	1	no	—
154	C₂×C₄×C₃₁	—	4	1	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	8	2	no	—
157	C₂×C₄×C₃₁	—	16	1	no	—
158	C₂×C₄×C₃₁	#124	1	2	yes	—
159	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₃₁	#124	1	2	yes	—
165	C₈×C₃₁	C₂×SD₁₆	1	4	yes	—
166	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
167	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
168	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#3155	C₂×C₃₁	1	1	yes	characteristic
170	#2244	C₂×C₃₁	1	2	yes	complemented
171	#2243	C₂×C₃₁	1	2	yes	complemented
172	#2242	C₂×C₃₁	1	2	yes	complemented
173	#2240	C₂×C₃₁	1	2	yes	complemented
174	#2140	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#2139	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2138	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂×#357	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#2108	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	8	1	no	—
182	C₂²×C₃₁	—	8	2	no	—
183	C₂²×C₃₁	—	8	1	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	1	no	—
186	C₂²×C₃₁	—	8	2	no	—
187	C₂²×C₃₁	—	16	4	no	—
188	C₂²×C₃₁	#486	1	2	yes	—
189	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
190	C₄×C₃₁	—	2	2	no	—
191	C₄×C₃₁	—	2	2	no	—
192	C₄×C₃₁	—	8	1	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	—	8	1	no	—
195	C₄×C₃₁	—	8	1	no	—
196	C₄×C₃₁	#486	1	2	yes	—
197	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
198	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
199	C₂×AGL(1,ℤ/8)	—	2	1	no	—
200	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
201	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
202	#544	—	2	1	no	—
203	#535	—	2	1	no	—
204	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
205	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
206	#501	—	2	2	no	—
207	#500	C₂²×C₃₁	1	2	yes	complemented
208	#499	C₂²×C₃₁	1	2	yes	complemented
209	#496	—	2	2	no	—
210	#495	C₂²×C₃₁	1	2	yes	—
211	#493	C₂²×C₃₁	1	2	yes	—
212	#428	—	2	1	no	—
213	#427	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
215	#405	C₂²×C₃₁	1	1	yes	characteristic
216	#358	C₂²×C₃₁	1	1	yes	characteristic, complemented
217	#358	C₂²×C₃₁	1	1	yes	characteristic, complemented
218	#358	C₂²×C₃₁	1	2	yes	complemented
219	#357	C₂²×C₃₁	1	2	yes	—
220	#357	C₂²×C₃₁	1	2	yes	—
221	#357	C₂²×C₃₁	1	2	yes	—
222	#357	C₂²×C₃₁	1	2	yes	—
223	#357	C₂²×C₃₁	1	1	yes	characteristic, complemented
224	#357	C₂²×C₃₁	1	1	yes	characteristic, complemented
225	#357	C₂²×C₃₁	1	2	yes	complemented
226	#346	C₂²×C₃₁	1	2	yes	complemented
227	C₄×C₁₆	C₂²×C₃₁	1	2	yes	complemented
228	C₂×C₃₁	—	2	2	no	—
229	C₂×C₃₁	—	16	1	no	—
230	C₂×C₃₁	—	16	2	no	—
231	C₂×C₃₁	C₂×#486	1	1	yes	characteristic
232	C₂×C₃₁	#3415	1	1	yes	characteristic
233	C₂×C₃₁	#3416	1	1	yes	characteristic
234	C₂×#41	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	AGL(1,ℤ/8)	—	4	4	no	—
237	#135	—	2	2	no	—
238	#135	—	2	2	no	—
239	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
240	C₂×SD₁₆	—	2	1	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	—	2	1	no	—
243	C₂×D₈	—	2	2	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂×D₈	—	2	2	no	—
246	C₂×D₈	C₂³×C₃₁	1	2	yes	—
247	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
248	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	4	1	no	—
252	#127	—	2	2	no	—
253	#125	—	2	2	no	—
254	#125	—	4	1	no	—
255	#124	—	2	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	#121	—	4	1	no	—
258	#121	—	4	1	no	—
259	#120	—	4	2	no	—
260	#117	—	2	1	no	—
261	#117	D₄×C₃₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	2	1	no	—
263	M₃₂	—	2	2	no	—
264	C₂×C₁₆	—	2	2	no	—
265	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
266	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
267	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
268	#107	—	2	1	no	—
269	#107	—	2	2	no	—
270	#107	C₂³×C₃₁	1	2	yes	—
271	#107	C₂³×C₃₁	1	1	yes	characteristic
272	#107	C₂³×C₃₁	1	1	yes	characteristic
273	#106	—	2	1	no	—
274	#106	—	2	2	no	—
275	#97	D₄×C₃₁	1	2	yes	—
276	C₄×C₈	C₂³×C₃₁	1	2	yes	—
277	C₃₁	#33702	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	—	4	1	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
294	Q₁₆	—	2	1	no	—
295	Q₁₆	—	2	1	no	—
296	SD₁₆	—	4	2	no	—
297	SD₁₆	—	4	4	no	—
298	D₈	—	2	2	no	—
299	D₈	—	2	2	no	—
300	D₈	—	2	1	no	—
301	D₈	—	2	1	no	—
302	D₈	—	4	2	no	—
303	D₈	—	4	4	no	—
304	M₁₆	SD₁₆×C₃₁	1	4	yes	—
305	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
307	C₂×C₈	#41×C₃₁	1	2	yes	—
308	C₂×C₈	#41×C₃₁	1	2	yes	—
309	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
318	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
323	C₄²	—	4	1	no	—
324	C₄²	C₂×D₄×C₃₁	1	2	yes	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	2	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	8	2	no	—
331	C₂³	—	16	1	no	—
332	C₂³	—	16	1	no	—
333	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
334	Q₈	—	4	1	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	16	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	1	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	D₄	—	16	2	no	—
344	D₄	—	16	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	16	1	no	—
351	C₂×C₄	C₃₁×#124	1	2	yes	—
352	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
353	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
354	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
357	C₈	C₃₁×#124	1	2	yes	—
358	C₈	C₂×SD₁₆×C₃₁	1	4	yes	—
359	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
360	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	C₃₁×#486	1	2	yes	—
371	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	C₃₁×#486	1	2	yes	—
379	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
380	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	16	2	no	—
383	C₂	—	16	1	no	—
384	C₂	C₂×C₃₁×#486	1	1	yes	characteristic
385	C₂	C₃₁×#3415	1	1	yes	characteristic
386	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	C₃₁×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#117 ◁ C₃₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3164	C₂	semidirect
3. C₃₁×#2244	C₂	semidirect
4. C₃₁×#2243	C₂	semidirect
5. C₃₁×#2242	C₂	semidirect
6. C₃₁×#2240	C₂	semidirect
7. C₃₁×#2140	C₂	semidirect
8. C₃₁×#2139	C₂	semidirect
9. C₃₁×#2138	C₂	semidirect
10. C₂×C₃₁×#357	C₂	semidirect
11. C₃₁×#2108	C₂	semidirect
20. C₃₁×#500	C₂²	semidirect
21. C₃₁×#499	C₂²	semidirect
29. C₃₁×#358	C₂²	semidirect
30. C₃₁×#358	C₂²	semidirect
31. C₃₁×#358	C₂²	semidirect
36. C₃₁×#357	C₂²	semidirect
37. C₃₁×#357	C₂²	semidirect
38. C₃₁×#357	C₂²	semidirect
39. C₃₁×#346	C₂²	semidirect
40. C₄×C₁₆×C₃₁	C₂²	semidirect
134. #33702	C₃₁	direct (N × H)
168. #3164	C₂×C₃₁	semidirect
170. #2244	C₂×C₃₁	semidirect
171. #2243	C₂×C₃₁	semidirect
172. #2242	C₂×C₃₁	semidirect
173. #2240	C₂×C₃₁	semidirect
174. #2140	C₂×C₃₁	semidirect
175. #2139	C₂×C₃₁	semidirect
176. #2138	C₂×C₃₁	semidirect
177. C₂×#357	C₂×C₃₁	semidirect
178. #2108	C₂×C₃₁	semidirect
207. #500	C₂²×C₃₁	semidirect
208. #499	C₂²×C₃₁	semidirect
216. #358	C₂²×C₃₁	semidirect
217. #358	C₂²×C₃₁	semidirect
218. #358	C₂²×C₃₁	semidirect
223. #357	C₂²×C₃₁	semidirect
224. #357	C₂²×C₃₁	semidirect
225. #357	C₂²×C₃₁	semidirect
226. #346	C₂²×C₃₁	semidirect
227. C₄×C₁₆	C₂²×C₃₁	semidirect
277. C₃₁	#33702	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×#3164	2
C₃₁×#3155	2
C₃₁×#2244	2
C₃₁×#2243	2
C₃₁×#2242	2
C₃₁×#2240	2
C₃₁×#2140	2
C₃₁×#2139	2
C₃₁×#2138	2
C₂×C₃₁×#357	2
C₃₁×#2108	2
#33702	31

Subgroups — C31×#33702 #21490461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33702 #21490461