Subgroups — C₃₁×#61011 #21517770

Order 7936.

1896 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3259	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3228	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3205	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3199	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3184	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3169	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3122	C₂	1	8	yes	maximal, complemented
9	C₃₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#559	—	2	4	no	—
11	C₃₁×#550	—	2	4	no	—
12	C₃₁×#546	—	2	4	no	—
13	C₃₁×#546	—	2	4	no	—
14	C₃₁×#540	C₂²	1	4	yes	—
15	C₃₁×#540	C₂²	1	4	yes	complemented
16	C₃₁×#535	C₂²	1	4	yes	—
17	C₃₁×#533	C₂²	1	2	yes	complemented
18	C₃₁×#532	C₂²	1	4	yes	—
19	C₃₁×#532	C₂²	1	4	yes	complemented
20	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
21	C₃₁×#518	C₂²	1	4	yes	complemented
22	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#500	C₂²	1	2	yes	complemented
24	C₃₁×#498	C₂²	1	2	yes	complemented
25	C₃₁×#493	C₂²	1	2	yes	—
26	C₃₁×#493	C₂²	1	2	yes	—
27	C₃₁×#486	C₂²	1	4	yes	complemented
28	C₃₁×#486	C₂²	1	4	yes	complemented
29	C₃₁×#482	C₂²	1	16	yes	complemented
30	C₃₁×#478	C₂²	1	16	yes	complemented
31	C₃₁×#469	C₂²	1	8	yes	complemented
32	C₃₁×#466	C₂²	1	8	yes	complemented
33	C₃₁×#459	C₂²	1	16	yes	complemented
34	C₃₁×#447	C₂²	1	16	yes	complemented
35	C₃₁×#442	C₂²	1	8	yes	complemented
36	C₄×D₈×C₃₁	C₂²	1	8	yes	complemented
37	C₃₁×#433	C₂²	1	4	yes	complemented
38	C₃₁×#431	C₂²	1	4	yes	complemented
39	C₃₁×#424	C₂²	1	2	yes	complemented
40	C₃₁×#408	C₂²	1	2	yes	—
41	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₃₁	—	2	4	no	—
44	C₂×#41×C₃₁	—	2	4	no	—
45	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₁	—	2	4	no	—
47	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
48	C₂×D₈×C₃₁	C₂³	1	8	yes	—
49	C₂×D₈×C₃₁	C₂³	1	8	yes	—
50	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
52	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₃₁×#127	—	2	4	no	—
54	C₃₁×#127	—	2	4	no	—
55	C₃₁×#127	C₂³	1	4	yes	—
56	C₃₁×#127	C₂³	1	4	yes	—
57	C₃₁×#125	C₂³	1	4	yes	—
58	C₃₁×#124	—	2	4	no	—
59	C₃₁×#124	—	2	4	no	—
60	C₃₁×#124	—	2	4	no	—
61	C₃₁×#123	—	2	8	no	—
62	C₃₁×#123	—	2	8	no	—
63	C₃₁×C₂²⋊Q₈	—	2	4	no	—
64	C₃₁×#121	—	2	4	no	—
65	C₃₁×#121	—	2	4	no	—
66	C₃₁×#121	—	2	8	no	—
67	C₃₁×#121	—	2	8	no	—
68	C₃₁×#121	C₂³	1	8	yes	—
69	C₃₁×#121	C₂³	1	8	yes	—
70	C₃₁×#120	—	2	4	no	—
71	C₃₁×#120	—	2	4	no	—
72	C₄×Q₈×C₃₁	—	2	4	no	—
73	C₄×Q₈×C₃₁	D₄	1	2	yes	—
74	C₄×D₄×C₃₁	—	2	8	no	—
75	C₄×D₄×C₃₁	—	2	4	no	—
76	C₄×D₄×C₃₁	—	2	4	no	—
77	C₄×D₄×C₃₁	D₄	1	2	yes	—
78	C₄×D₄×C₃₁	D₄	1	4	yes	—
79	C₄×D₄×C₃₁	C₂³	1	8	yes	—
80	C₄×D₄×C₃₁	C₂³	1	8	yes	—
81	C₃₁×#117	C₂³	1	4	yes	—
82	C₃₁×#117	C₂³	1	1	yes	characteristic
83	C₃₁×#117	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
85	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
87	C₃₁×#107	C₂³	1	8	yes	—
88	C₃₁×#106	C₂³	1	8	yes	—
89	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
90	C₃₁×#102	C₂³	1	16	yes	—
91	C₃₁×#102	C₂³	1	16	yes	—
92	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
93	C₃₁×#97	C₂³	1	2	yes	—
94	C₄×C₈×C₃₁	C₂³	1	2	yes	—
95	C₄×C₈×C₃₁	C₂³	1	2	yes	—
96	C₄×C₈×C₃₁	C₂³	1	2	yes	—
97	C₂⁴×C₃₁	—	2	4	no	—
98	#41×C₃₁	—	4	2	no	—
99	#41×C₃₁	—	8	8	no	—
100	#41×C₃₁	—	8	8	no	—
101	C₂×Q₈×C₃₁	—	2	4	no	—
102	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₃₁	—	2	8	no	—
104	C₂×D₄×C₃₁	—	2	8	no	—
105	C₂×D₄×C₃₁	—	2	4	no	—
106	C₂×D₄×C₃₁	—	2	4	no	—
107	C₂×D₄×C₃₁	—	2	4	no	—
108	C₂×D₄×C₃₁	—	2	8	no	—
109	C₂×D₄×C₃₁	—	4	8	no	—
110	C₂×D₄×C₃₁	—	8	8	no	—
111	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₃₁	—	2	8	no	—
115	C₂²×C₄×C₃₁	—	2	8	no	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
120	D₈×C₃₁	—	4	8	no	—
121	D₈×C₃₁	—	4	8	no	—
122	M₁₆×C₃₁	—	4	2	no	—
123	C₂×C₈×C₃₁	—	4	2	no	—
124	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
125	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
126	C₄⋊C₄×C₃₁	—	2	4	no	—
127	C₄⋊C₄×C₃₁	—	2	8	no	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
131	C₂²⋊C₄×C₃₁	—	2	4	no	—
132	C₂²⋊C₄×C₃₁	—	2	8	no	—
133	C₂²⋊C₄×C₃₁	—	2	8	no	—
134	C₂²⋊C₄×C₃₁	—	2	8	no	—
135	C₂²⋊C₄×C₃₁	—	2	8	no	—
136	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
138	C₄²×C₃₁	—	2	4	no	—
139	C₄²×C₃₁	C₂×D₄	1	2	yes	—
140	C₄²×C₃₁	C₂×D₄	1	4	yes	—
141	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
142	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
143	C₄²×C₃₁	C₂⁴	1	2	yes	—
144	#61011	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₃₁	—	2	8	no	—
146	C₂³×C₃₁	—	4	8	no	—
147	C₂³×C₃₁	—	8	8	no	—
148	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
149	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₃₁	—	4	1	no	—
151	Q₈×C₃₁	—	4	8	no	—
152	D₄×C₃₁	—	2	16	no	—
153	D₄×C₃₁	—	4	2	no	—
154	D₄×C₃₁	—	4	1	no	—
155	D₄×C₃₁	—	4	8	no	—
156	D₄×C₃₁	—	4	8	no	—
157	D₄×C₃₁	—	4	8	no	—
158	D₄×C₃₁	—	8	8	no	—
159	D₄×C₃₁	—	8	8	no	—
160	D₄×C₃₁	—	8	8	no	—
161	C₂×C₄×C₃₁	—	2	8	no	—
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	8	no	—
166	C₂×C₄×C₃₁	—	8	8	no	—
167	C₂×C₄×C₃₁	—	8	8	no	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
174	C₈×C₃₁	—	2	4	no	—
175	C₈×C₃₁	—	2	4	no	—
176	#3508	C₂×C₃₁	1	2	yes	complemented
177	#3259	C₂×C₃₁	1	4	yes	complemented
178	#3228	C₂×C₃₁	1	4	yes	complemented
179	#3205	C₂×C₃₁	1	4	yes	complemented
180	#3199	C₂×C₃₁	1	4	yes	complemented
181	#3184	C₂×C₃₁	1	2	yes	complemented
182	#3169	C₂×C₃₁	1	2	yes	complemented
183	#3122	C₂×C₃₁	1	8	yes	complemented
184	#2922	C₂×C₃₁	1	1	yes	characteristic, complemented
185	C₂²×C₃₁	—	2	2	no	—
186	C₂²×C₃₁	—	2	1	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	4	no	—
189	C₂²×C₃₁	—	4	8	no	—
190	C₂²×C₃₁	—	4	8	no	—
191	C₂²×C₃₁	—	4	8	no	—
192	C₂²×C₃₁	—	16	8	no	—
193	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	2	1	no	—
196	C₄×C₃₁	—	2	2	no	—
197	C₄×C₃₁	—	2	4	no	—
198	C₄×C₃₁	—	4	8	no	—
199	C₄×C₃₁	#576	1	4	yes	—
200	C₄×C₃₁	#585	1	2	yes	—
201	#559	—	2	4	no	—
202	#550	—	2	4	no	—
203	#546	—	2	4	no	—
204	#546	—	2	4	no	—
205	#540	C₂²×C₃₁	1	4	yes	—
206	#540	C₂²×C₃₁	1	4	yes	complemented
207	#535	C₂²×C₃₁	1	4	yes	—
208	#533	C₂²×C₃₁	1	2	yes	complemented
209	#532	C₂²×C₃₁	1	4	yes	—
210	#532	C₂²×C₃₁	1	4	yes	complemented
211	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
212	#518	C₂²×C₃₁	1	4	yes	complemented
213	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
214	#500	C₂²×C₃₁	1	2	yes	complemented
215	#498	C₂²×C₃₁	1	2	yes	complemented
216	#493	C₂²×C₃₁	1	2	yes	—
217	#493	C₂²×C₃₁	1	2	yes	—
218	#486	C₂²×C₃₁	1	4	yes	complemented
219	#486	C₂²×C₃₁	1	4	yes	complemented
220	#482	C₂²×C₃₁	1	16	yes	complemented
221	#478	C₂²×C₃₁	1	16	yes	complemented
222	#469	C₂²×C₃₁	1	8	yes	complemented
223	#466	C₂²×C₃₁	1	8	yes	complemented
224	#459	C₂²×C₃₁	1	16	yes	complemented
225	#447	C₂²×C₃₁	1	16	yes	complemented
226	#442	C₂²×C₃₁	1	8	yes	complemented
227	C₄×D₈	C₂²×C₃₁	1	8	yes	complemented
228	#433	C₂²×C₃₁	1	4	yes	complemented
229	#431	C₂²×C₃₁	1	4	yes	complemented
230	#424	C₂²×C₃₁	1	2	yes	complemented
231	#408	C₂²×C₃₁	1	2	yes	—
232	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
233	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
234	C₂×C₃₁	—	4	1	no	—
235	C₂×C₃₁	—	4	2	no	—
236	C₂×C₃₁	—	8	8	no	—
237	C₂×C₃₁	#3449	1	1	yes	characteristic
238	C₂×C₃₁	C₂×#576	1	2	yes	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
244	C₂×D₈	C₂³×C₃₁	1	8	yes	—
245	C₂×D₈	C₂³×C₃₁	1	8	yes	—
246	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
247	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
248	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
249	#127	—	2	4	no	—
250	#127	—	2	4	no	—
251	#127	C₂³×C₃₁	1	4	yes	—
252	#127	C₂³×C₃₁	1	4	yes	—
253	#125	C₂³×C₃₁	1	4	yes	—
254	#124	—	2	4	no	—
255	#124	—	2	4	no	—
256	#124	—	2	4	no	—
257	#123	—	2	8	no	—
258	#123	—	2	8	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	#121	—	2	4	no	—
261	#121	—	2	4	no	—
262	#121	—	2	8	no	—
263	#121	—	2	8	no	—
264	#121	C₂³×C₃₁	1	8	yes	—
265	#121	C₂³×C₃₁	1	8	yes	—
266	#120	—	2	4	no	—
267	#120	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	D₄×C₃₁	1	2	yes	—
270	C₄×D₄	—	2	8	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	D₄×C₃₁	1	2	yes	—
274	C₄×D₄	D₄×C₃₁	1	4	yes	—
275	C₄×D₄	C₂³×C₃₁	1	8	yes	—
276	C₄×D₄	C₂³×C₃₁	1	8	yes	—
277	#117	C₂³×C₃₁	1	4	yes	—
278	#117	C₂³×C₃₁	1	2	yes	—
279	#117	C₂³×C₃₁	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
282	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
283	#107	C₂³×C₃₁	1	8	yes	—
284	#106	C₂³×C₃₁	1	8	yes	—
285	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
286	#102	C₂³×C₃₁	1	16	yes	—
287	#102	C₂³×C₃₁	1	16	yes	—
288	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
289	#97	C₂³×C₃₁	1	2	yes	—
290	C₄×C₈	C₂³×C₃₁	1	2	yes	—
291	C₄×C₈	C₂³×C₃₁	1	2	yes	—
292	C₄×C₈	C₂³×C₃₁	1	2	yes	—
293	C₃₁	#61011	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	—	2	4	no	—
295	#41	—	4	2	no	—
296	#41	—	8	8	no	—
297	#41	—	8	8	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	4	8	no	—
307	C₂×D₄	—	8	8	no	—
308	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
310	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
315	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
317	D₈	—	4	8	no	—
318	D₈	—	4	8	no	—
319	M₁₆	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
322	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
326	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
327	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
334	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂×D₄×C₃₁	1	2	yes	—
337	C₄²	C₂×D₄×C₃₁	1	4	yes	—
338	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
339	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
340	C₄²	C₂⁴×C₃₁	1	2	yes	—
341	C₂³	—	2	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	8	8	no	—
344	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
345	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
346	Q₈	—	4	1	no	—
347	Q₈	—	4	8	no	—
348	D₄	—	2	16	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	8	no	—
353	D₄	—	4	8	no	—
354	D₄	—	8	8	no	—
355	D₄	—	8	8	no	—
356	D₄	—	8	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	8	8	no	—
363	C₂×C₄	—	8	8	no	—
364	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
369	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	8	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	4	8	no	—
386	C₄	C₃₁×#576	1	4	yes	—
387	C₄	C₃₁×#585	1	2	yes	—
388	C₂	—	4	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	8	8	no	—
391	C₂	C₃₁×#3449	1	1	yes	characteristic
392	C₂	C₂×C₃₁×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3259	C₂	semidirect
3. C₃₁×#3228	C₂	semidirect
4. C₃₁×#3205	C₂	semidirect
5. C₃₁×#3199	C₂	semidirect
6. C₃₁×#3184	C₂	semidirect
7. C₃₁×#3169	C₂	semidirect
8. C₃₁×#3122	C₂	semidirect
9. C₃₁×#2922	C₂	semidirect
15. C₃₁×#540	C₂²	semidirect
17. C₃₁×#533	C₂²	semidirect
19. C₃₁×#532	C₂²	semidirect
20. C₂×C₃₁×#127	C₂²	semidirect
21. C₃₁×#518	C₂²	semidirect
23. C₃₁×#500	C₂²	semidirect
24. C₃₁×#498	C₂²	semidirect
27. C₃₁×#486	C₂²	semidirect
28. C₃₁×#486	C₂²	semidirect
29. C₃₁×#482	C₂²	semidirect
30. C₃₁×#478	C₂²	semidirect
31. C₃₁×#469	C₂²	semidirect
32. C₃₁×#466	C₂²	semidirect
33. C₃₁×#459	C₂²	semidirect
34. C₃₁×#447	C₂²	semidirect
35. C₃₁×#442	C₂²	semidirect
36. C₄×D₈×C₃₁	C₂²	semidirect
37. C₃₁×#433	C₂²	semidirect
38. C₃₁×#431	C₂²	semidirect
39. C₃₁×#424	C₂²	semidirect
41. C₄×M₁₆×C₃₁	C₂²	semidirect
42. C₂×C₄×C₈×C₃₁	C₂²	semidirect
144. #61011	C₃₁	direct (N × H)
176. #3508	C₂×C₃₁	semidirect
177. #3259	C₂×C₃₁	semidirect
178. #3228	C₂×C₃₁	semidirect
179. #3205	C₂×C₃₁	semidirect
180. #3199	C₂×C₃₁	semidirect
181. #3184	C₂×C₃₁	semidirect
182. #3169	C₂×C₃₁	semidirect
183. #3122	C₂×C₃₁	semidirect
184. #2922	C₂×C₃₁	semidirect
206. #540	C₂²×C₃₁	semidirect
208. #533	C₂²×C₃₁	semidirect
210. #532	C₂²×C₃₁	semidirect
211. C₂×#127	C₂²×C₃₁	semidirect
212. #518	C₂²×C₃₁	semidirect
214. #500	C₂²×C₃₁	semidirect
215. #498	C₂²×C₃₁	semidirect
218. #486	C₂²×C₃₁	semidirect
219. #486	C₂²×C₃₁	semidirect
220. #482	C₂²×C₃₁	semidirect
221. #478	C₂²×C₃₁	semidirect
222. #469	C₂²×C₃₁	semidirect
223. #466	C₂²×C₃₁	semidirect
224. #459	C₂²×C₃₁	semidirect
225. #447	C₂²×C₃₁	semidirect
226. #442	C₂²×C₃₁	semidirect
227. C₄×D₈	C₂²×C₃₁	semidirect
228. #433	C₂²×C₃₁	semidirect
229. #431	C₂²×C₃₁	semidirect
230. #424	C₂²×C₃₁	semidirect
232. C₄×M₁₆	C₂²×C₃₁	semidirect
233. C₂×C₄×C₈	C₂²×C₃₁	semidirect
293. C₃₁	#61011	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×#3508	2
C₃₁×#3259	2
C₃₁×#3228	2
C₃₁×#3205	2
C₃₁×#3199	2
C₃₁×#3184	2
C₃₁×#3169	2
C₃₁×#3122	2
C₃₁×#2922	2
#61011	31

Subgroups — C31×#61011 #21517770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61011 #21517770