Subgroups — C₃₁×#19101 #21475860

Order 7936.

802 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3100	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1669	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1667	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1665	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#135	—	2	1	no	—
10	C₂×C₃₁×#135	—	2	1	no	—
11	C₂³×C₈×C₃₁	—	2	1	no	—
12	C₃₁×#532	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#495	—	2	1	no	—
15	C₃₁×#495	—	2	1	no	—
16	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
17	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
18	C₃₁×#492	C₂²	1	2	yes	complemented
19	C₃₁×#480	—	2	2	no	—
20	C₃₁×#474	C₂²	1	4	yes	—
21	C₃₁×#459	C₂²	1	4	yes	—
22	C₃₁×#447	—	2	2	no	—
23	C₄×D₈×C₃₁	—	2	4	no	—
24	C₈×D₄×C₃₁	—	2	1	no	—
25	C₈×D₄×C₃₁	—	2	1	no	—
26	C₈×D₄×C₃₁	C₂²	1	2	yes	—
27	C₈×D₄×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#431	C₂²	1	2	yes	—
29	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	2	yes	complemented
33	C₃₁×#334	C₂²	1	2	yes	complemented
34	C₃₁×#332	C₂²	1	4	yes	complemented
35	C₃₁×#331	C₂²	1	4	yes	complemented
36	C₂×#41×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	—	2	1	no	—
39	C₃₁×#135	—	4	4	no	—
40	C₃₁×#135	—	4	4	no	—
41	C₂×Q₁₆×C₃₁	—	2	1	no	—
42	C₂×Q₁₆×C₃₁	—	2	1	no	—
43	C₂×SD₁₆×C₃₁	—	2	2	no	—
44	C₂×SD₁₆×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	2	4	no	—
46	C₂×D₈×C₃₁	—	2	1	no	—
47	C₂×D₈×C₃₁	—	2	1	no	—
48	C₂²×C₈×C₃₁	—	2	1	no	—
49	C₂²×C₈×C₃₁	—	2	2	no	—
50	C₂²×C₈×C₃₁	—	2	2	no	—
51	C₂²×C₈×C₃₁	—	4	4	no	—
52	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
54	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₃₁×#127	C₂³	1	2	yes	—
56	C₃₁×#124	—	2	2	no	—
57	C₃₁×#121	—	2	2	no	—
58	C₃₁×#121	—	2	2	no	—
59	C₄×D₄×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	—	2	2	no	—
61	C₄×D₄×C₃₁	—	2	1	no	—
62	C₄×D₄×C₃₁	—	2	2	no	—
63	C₄×D₄×C₃₁	D₄	1	2	yes	—
64	C₄×D₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
68	C₃₁×#107	—	2	4	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
72	C₃₁×#102	—	2	4	no	—
73	C₃₁×#102	—	2	4	no	—
74	C₃₁×C₂²⋊C₈	—	2	2	no	—
75	C₃₁×C₂²⋊C₈	—	2	2	no	—
76	C₃₁×C₂²⋊C₈	—	2	2	no	—
77	C₄×C₈×C₃₁	—	2	2	no	—
78	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
79	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
80	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂⁴×C₃₁	—	2	1	no	—
83	#41×C₃₁	—	4	4	no	—
84	#41×C₃₁	—	4	4	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×D₄×C₃₁	—	2	4	no	—
87	C₂×D₄×C₃₁	—	2	1	no	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	4	2	no	—
92	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	—	2	1	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	—	4	2	no	—
98	C₂²×C₄×C₃₁	—	4	2	no	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
102	Q₁₆×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	4	2	no	—
104	SD₁₆×C₃₁	—	4	4	no	—
105	SD₁₆×C₃₁	—	4	4	no	—
106	D₈×C₃₁	—	4	2	no	—
107	D₈×C₃₁	—	4	8	no	—
108	D₈×C₃₁	—	4	2	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	4	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	4	2	no	—
113	C₂×C₈×C₃₁	—	4	4	no	—
114	C₂×C₈×C₃₁	—	4	4	no	—
115	C₂×C₈×C₃₁	D₈	1	4	yes	complemented
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₃₁	—	2	1	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₂²⋊C₄×C₃₁	—	2	2	no	—
126	C₂²⋊C₄×C₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₃₁	—	4	2	no	—
128	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₁	#41	1	1	yes	characteristic
131	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
132	#19101	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₃₁	—	2	4	no	—
134	C₂³×C₃₁	—	2	2	no	—
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	—	4	2	no	—
137	C₂³×C₃₁	—	4	2	no	—
138	C₂³×C₃₁	#121	1	1	yes	characteristic
139	Q₈×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	4	2	no	—
141	D₄×C₃₁	—	2	4	no	—
142	D₄×C₃₁	—	2	2	no	—
143	D₄×C₃₁	—	4	2	no	—
144	D₄×C₃₁	—	4	4	no	—
145	D₄×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	8	2	no	—
147	D₄×C₃₁	—	8	4	no	—
148	D₄×C₃₁	#135	1	4	yes	complemented
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	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	4	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	8	4	no	—
158	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
159	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
160	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	2	1	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₈×C₃₁	—	4	4	no	—
170	C₈×C₃₁	C₂×D₈	1	2	yes	—
171	C₈×C₃₁	C₂×D₈	1	2	yes	—
172	#3147	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#3100	C₂×C₃₁	1	2	yes	complemented
174	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1669	C₂×C₃₁	1	2	yes	complemented
176	#1667	C₂×C₃₁	1	2	yes	complemented
177	#1665	C₂×C₃₁	1	4	yes	complemented
178	#1564	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#1540	C₂×C₃₁	1	2	yes	complemented
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	2	1	no	—
182	C₂²×C₃₁	—	2	4	no	—
183	C₂²×C₃₁	—	4	8	no	—
184	C₂²×C₃₁	—	4	2	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	—	8	2	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	#459	1	2	yes	—
190	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	2	1	no	—
193	C₄×C₃₁	—	2	1	no	—
194	C₄×C₃₁	—	4	2	no	—
195	C₄×C₃₁	—	8	2	no	—
196	C₄×C₃₁	#459	1	2	yes	—
197	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
198	C₄×C₃₁	C₂×#135	1	2	yes	—
199	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂×#135	—	2	1	no	—
201	C₂×#135	—	2	1	no	—
202	C₂³×C₈	—	2	1	no	—
203	#532	C₂²×C₃₁	1	2	yes	—
204	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
205	#495	—	2	1	no	—
206	#495	—	2	1	no	—
207	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
208	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
209	#492	C₂²×C₃₁	1	2	yes	complemented
210	#480	—	2	2	no	—
211	#474	C₂²×C₃₁	1	4	yes	—
212	#459	C₂²×C₃₁	1	4	yes	—
213	#447	—	2	2	no	—
214	C₄×D₈	—	2	4	no	—
215	C₈×D₄	—	2	1	no	—
216	C₈×D₄	—	2	1	no	—
217	C₈×D₄	C₂²×C₃₁	1	2	yes	—
218	C₈×D₄	C₂²×C₃₁	1	2	yes	—
219	#431	C₂²×C₃₁	1	2	yes	—
220	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	—	2	1	no	—
222	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
223	#335	C₂²×C₃₁	1	2	yes	complemented
224	#334	C₂²×C₃₁	1	2	yes	complemented
225	#332	C₂²×C₃₁	1	4	yes	complemented
226	#331	C₂²×C₃₁	1	4	yes	complemented
227	C₂×C₃₁	—	2	2	no	—
228	C₂×C₃₁	—	4	4	no	—
229	C₂×C₃₁	—	16	2	no	—
230	C₂×C₃₁	C₂×#459	1	1	yes	characteristic
231	C₂×C₃₁	#3050	1	1	yes	characteristic
232	C₂×C₃₁	#3067	1	1	yes	characteristic
233	C₂×#41	—	2	2	no	—
234	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
235	C₂³×C₄	—	2	1	no	—
236	#135	—	4	4	no	—
237	#135	—	4	4	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	—	2	4	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	4	4	no	—
249	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
251	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
252	#127	C₂³×C₃₁	1	2	yes	—
253	#124	—	2	2	no	—
254	#121	—	2	2	no	—
255	#121	—	2	2	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	D₄×C₃₁	1	2	yes	—
261	C₄×D₄	C₂³×C₃₁	1	2	yes	—
262	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
265	#107	—	2	4	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
268	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
269	#102	—	2	4	no	—
270	#102	—	2	4	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
276	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₃₁	#19101	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	2	1	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
300	Q₁₆	—	4	2	no	—
301	Q₁₆	—	4	2	no	—
302	SD₁₆	—	4	4	no	—
303	SD₁₆	—	4	4	no	—
304	D₈	—	4	2	no	—
305	D₈	—	4	8	no	—
306	D₈	—	4	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	D₈×C₃₁	1	4	yes	complemented
314	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
328	C₄²	#41×C₃₁	1	1	yes	characteristic
329	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₃₁×#121	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	4	no	—
345	D₄	C₃₁×#135	1	4	yes	complemented
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
356	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
357	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
358	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
359	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	4	no	—
367	C₈	C₂×D₈×C₃₁	1	2	yes	—
368	C₈	C₂×D₈×C₃₁	1	2	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	C₃₁×#459	1	2	yes	—
379	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	C₃₁×#459	1	2	yes	—
386	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
387	C₄	C₂×C₃₁×#135	1	2	yes	—
388	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×C₃₁×#459	1	1	yes	characteristic
393	C₂	C₃₁×#3050	1	1	yes	characteristic
394	C₂	C₃₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3147	C₂	semidirect
2. C₃₁×#3100	C₂	semidirect
3. C₂×C₈×D₄×C₃₁	C₂	semidirect
4. C₃₁×#1669	C₂	semidirect
5. C₃₁×#1667	C₂	semidirect
6. C₃₁×#1665	C₂	semidirect
7. C₃₁×#1564	C₂	semidirect
8. C₃₁×#1540	C₂	semidirect
16. C₃₁×#494	C₂²	semidirect
17. C₃₁×#493	C₂²	semidirect
18. C₃₁×#492	C₂²	semidirect
32. C₃₁×#335	C₂²	semidirect
33. C₃₁×#334	C₂²	semidirect
34. C₃₁×#332	C₂²	semidirect
35. C₃₁×#331	C₂²	semidirect
115. C₂×C₈×C₃₁	D₈	semidirect
132. #19101	C₃₁	direct (N × H)
148. D₄×C₃₁	#135	semidirect
172. #3147	C₂×C₃₁	semidirect
173. #3100	C₂×C₃₁	semidirect
174. C₂×C₈×D₄	C₂×C₃₁	semidirect
175. #1669	C₂×C₃₁	semidirect
176. #1667	C₂×C₃₁	semidirect
177. #1665	C₂×C₃₁	semidirect
178. #1564	C₂×C₃₁	semidirect
179. #1540	C₂×C₃₁	semidirect
207. #494	C₂²×C₃₁	semidirect
208. #493	C₂²×C₃₁	semidirect
209. #492	C₂²×C₃₁	semidirect
223. #335	C₂²×C₃₁	semidirect
224. #334	C₂²×C₃₁	semidirect
225. #332	C₂²×C₃₁	semidirect
226. #331	C₂²×C₃₁	semidirect
279. C₃₁	#19101	direct (N × H)
313. C₂×C₈	D₈×C₃₁	semidirect
345. D₄	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3147	2
C₃₁×#3100	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1669	2
C₃₁×#1667	2
C₃₁×#1665	2
C₃₁×#1564	2
C₃₁×#1540	2
#19101	31

Subgroups — C31×#19101 #21475860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19101 #21475860