Subgroups — C₃₁×#33766 #21490525

Order 7936.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3058	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2237	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2234	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2220	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2217	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2187	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2185	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
11	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
13	C₃₁×#536	—	2	1	no	—
14	C₃₁×#535	—	2	1	no	—
15	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
17	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#470	—	2	1	no	—
20	C₃₁×#470	—	2	1	no	—
21	C₃₁×#469	—	2	1	no	—
22	C₃₁×#469	—	2	1	no	—
23	C₃₁×#467	C₂²	1	2	yes	—
24	C₃₁×#467	C₂²	1	2	yes	complemented
25	C₃₁×#466	C₂²	1	2	yes	—
26	C₃₁×#466	C₂²	1	2	yes	—
27	C₃₁×#427	C₂²	1	1	yes	characteristic
28	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#419	—	2	1	no	—
30	C₃₁×#418	—	2	1	no	—
31	C₃₁×#367	C₂²	1	2	yes	complemented
32	C₃₁×#366	C₂²	1	2	yes	complemented
33	C₃₁×#358	C₂²	1	2	yes	complemented
34	C₃₁×#358	C₂²	1	2	yes	complemented
35	C₃₁×#357	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	2	yes	—
37	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
38	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
39	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₃₁	—	2	1	no	—
41	C₂²×D₄×C₃₁	—	2	1	no	—
42	C₂×Q₁₆×C₃₁	—	2	1	no	—
43	C₂×Q₁₆×C₃₁	—	4	1	no	—
44	C₂×Q₁₆×C₃₁	—	4	1	no	—
45	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
46	C₂×D₈×C₃₁	—	2	1	no	—
47	C₂×D₈×C₃₁	—	4	1	no	—
48	C₂×D₈×C₃₁	—	4	1	no	—
49	C₂×D₈×C₃₁	C₂³	1	2	yes	—
50	C₃₁×#131	—	4	1	no	—
51	C₃₁×#131	—	4	1	no	—
52	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
54	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×C₄⋊Q₈	—	4	1	no	—
59	C₃₁×#127	—	4	1	no	—
60	C₃₁×#124	—	4	1	no	—
61	C₃₁×#124	—	4	1	no	—
62	C₃₁×#123	—	4	1	no	—
63	C₃₁×#123	—	4	1	no	—
64	C₃₁×C₂²⋊Q₈	—	2	2	no	—
65	C₃₁×C₂²⋊Q₈	—	2	2	no	—
66	C₃₁×#121	—	2	2	no	—
67	C₃₁×#121	—	2	2	no	—
68	C₃₁×#120	—	4	1	no	—
69	C₃₁×#120	—	4	1	no	—
70	C₃₁×#117	—	2	1	no	—
71	C₃₁×#117	—	2	1	no	—
72	C₃₁×SD₃₂	—	4	2	no	—
73	C₃₁×SD₃₂	—	4	2	no	—
74	C₃₁×M₃₂	—	4	1	no	—
75	C₂×C₁₆×C₃₁	—	4	1	no	—
76	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
77	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
78	C₃₁×#107	C₂³	1	2	yes	—
79	C₃₁×#107	C₂³	1	2	yes	—
80	C₃₁×#106	—	2	1	no	—
81	C₃₁×#106	—	2	1	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₂⁴×C₃₁	—	4	1	no	—
87	#41×C₃₁	—	4	1	no	—
88	#41×C₃₁	—	4	1	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	4	2	no	—
91	C₂×Q₈×C₃₁	—	4	2	no	—
92	C₂×Q₈×C₃₁	—	4	1	no	—
93	C₂×Q₈×C₃₁	D₈	1	1	yes	characteristic
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	4	2	no	—
96	C₂×D₄×C₃₁	—	4	2	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
101	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
102	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	—	4	1	no	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	2	2	no	—
109	Q₁₆×C₃₁	—	4	2	no	—
110	D₈×C₃₁	—	2	2	no	—
111	D₈×C₃₁	—	2	2	no	—
112	D₈×C₃₁	—	4	2	no	—
113	M₁₆×C₃₁	—	4	1	no	—
114	M₁₆×C₃₁	—	4	1	no	—
115	M₁₆×C₃₁	—	4	1	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	2	1	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	1	no	—
131	C₂²⋊C₄×C₃₁	—	4	1	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₃₁	—	4	2	no	—
135	C₂²⋊C₄×C₃₁	—	4	2	no	—
136	C₄²×C₃₁	—	4	1	no	—
137	C₄²×C₃₁	—	4	1	no	—
138	C₁₆×C₃₁	—	2	2	no	—
139	C₁₆×C₃₁	—	2	2	no	—
140	#33766	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₃₁	—	4	2	no	—
142	C₂³×C₃₁	—	8	2	no	—
143	C₂³×C₃₁	—	16	2	no	—
144	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
145	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
146	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
147	Q₈×C₃₁	—	4	1	no	—
148	Q₈×C₃₁	—	4	2	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	—	8	2	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	4	1	no	—
153	D₄×C₃₁	—	4	1	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	8	2	no	—
157	D₄×C₃₁	—	16	2	no	—
158	D₄×C₃₁	—	16	2	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	1	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	1	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	8	2	no	—
169	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₃₁	—	2	1	no	—
174	C₈×C₃₁	—	2	1	no	—
175	C₈×C₃₁	—	2	1	no	—
176	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
177	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
178	#3059	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#3058	C₂×C₃₁	1	1	yes	characteristic
180	#2237	C₂×C₃₁	1	2	yes	complemented
181	#2234	C₂×C₃₁	1	2	yes	complemented
182	#2220	C₂×C₃₁	1	2	yes	complemented
183	#2217	C₂×C₃₁	1	2	yes	complemented
184	#2187	C₂×C₃₁	1	2	yes	complemented
185	#2185	C₂×C₃₁	1	2	yes	complemented
186	#2113	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	2	2	no	—
190	C₂²×C₃₁	—	2	1	no	—
191	C₂²×C₃₁	—	2	1	no	—
192	C₂²×C₃₁	—	2	1	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	—	8	2	no	—
196	C₂²×C₃₁	—	16	4	no	—
197	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
198	C₄×C₃₁	—	2	1	no	—
199	C₄×C₃₁	—	2	1	no	—
200	C₄×C₃₁	—	2	1	no	—
201	C₄×C₃₁	—	8	2	no	—
202	C₄×C₃₁	—	8	2	no	—
203	C₄×C₃₁	—	8	2	no	—
204	C₄×C₃₁	#534	1	1	yes	characteristic
205	C₄×C₃₁	#575	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
207	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
209	#536	—	2	1	no	—
210	#535	—	2	1	no	—
211	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
212	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
213	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic, complemented
214	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
215	#470	—	2	1	no	—
216	#470	—	2	1	no	—
217	#469	—	2	1	no	—
218	#469	—	2	1	no	—
219	#467	C₂²×C₃₁	1	2	yes	—
220	#467	C₂²×C₃₁	1	2	yes	complemented
221	#466	C₂²×C₃₁	1	2	yes	—
222	#466	C₂²×C₃₁	1	2	yes	—
223	#427	C₂²×C₃₁	1	1	yes	characteristic
224	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
225	#419	—	2	1	no	—
226	#418	—	2	1	no	—
227	#367	C₂²×C₃₁	1	2	yes	complemented
228	#366	C₂²×C₃₁	1	2	yes	complemented
229	#358	C₂²×C₃₁	1	2	yes	complemented
230	#358	C₂²×C₃₁	1	2	yes	complemented
231	#357	C₂²×C₃₁	1	2	yes	—
232	#357	C₂²×C₃₁	1	2	yes	—
233	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
234	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
235	C₂×C₃₁	—	4	1	no	—
236	C₂×C₃₁	—	4	1	no	—
237	C₂×C₃₁	—	4	1	no	—
238	C₂×C₃₁	—	16	2	no	—
239	C₂×C₃₁	#3186	1	1	yes	characteristic
240	C₂×C₃₁	#3416	1	2	yes	—
241	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂×Q₁₆	—	2	1	no	—
245	C₂×Q₁₆	—	4	1	no	—
246	C₂×Q₁₆	—	4	1	no	—
247	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	4	1	no	—
250	C₂×D₈	—	4	1	no	—
251	C₂×D₈	C₂³×C₃₁	1	2	yes	—
252	#131	—	4	1	no	—
253	#131	—	4	1	no	—
254	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
255	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
256	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
260	C₄⋊Q₈	—	4	1	no	—
261	#127	—	4	1	no	—
262	#124	—	4	1	no	—
263	#124	—	4	1	no	—
264	#123	—	4	1	no	—
265	#123	—	4	1	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	#121	—	2	2	no	—
269	#121	—	2	2	no	—
270	#120	—	4	1	no	—
271	#120	—	4	1	no	—
272	#117	—	2	1	no	—
273	#117	—	2	1	no	—
274	SD₃₂	—	4	2	no	—
275	SD₃₂	—	4	2	no	—
276	M₃₂	—	4	1	no	—
277	C₂×C₁₆	—	4	1	no	—
278	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
279	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
280	#107	C₂³×C₃₁	1	2	yes	—
281	#107	C₂³×C₃₁	1	2	yes	—
282	#106	—	2	1	no	—
283	#106	—	2	1	no	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	C₃₁	#33766	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	D₈×C₃₁	1	1	yes	characteristic
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
304	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
305	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	4	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	2	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
328	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	—	16	2	no	—
346	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
347	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
348	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	16	2	no	—
360	D₄	—	16	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
379	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₃₁×#534	1	1	yes	characteristic
398	C₄	C₃₁×#575	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	16	2	no	—
403	C₂	C₃₁×#3186	1	1	yes	characteristic
404	C₂	C₃₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×#41×C₃₁ ◁ C₂×C₃₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3059	C₂	semidirect
3. C₃₁×#2237	C₂	semidirect
4. C₃₁×#2234	C₂	semidirect
5. C₃₁×#2220	C₂	semidirect
6. C₃₁×#2217	C₂	semidirect
7. C₃₁×#2187	C₂	semidirect
8. C₃₁×#2185	C₂	semidirect
9. C₃₁×#2113	C₂	semidirect
10. C₂²×Q₁₆×C₃₁	C₂²	semidirect
17. C₂×C₃₁×M₃₂	C₂²	semidirect
18. C₂²×C₁₆×C₃₁	C₂²	semidirect
24. C₃₁×#467	C₂²	semidirect
28. C₃₁×#427	C₂²	semidirect
31. C₃₁×#367	C₂²	semidirect
32. C₃₁×#366	C₂²	semidirect
33. C₃₁×#358	C₂²	semidirect
34. C₃₁×#358	C₂²	semidirect
38. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
140. #33766	C₃₁	direct (N × H)
178. #3059	C₂×C₃₁	semidirect
180. #2237	C₂×C₃₁	semidirect
181. #2234	C₂×C₃₁	semidirect
182. #2220	C₂×C₃₁	semidirect
183. #2217	C₂×C₃₁	semidirect
184. #2187	C₂×C₃₁	semidirect
185. #2185	C₂×C₃₁	semidirect
186. #2113	C₂×C₃₁	semidirect
206. C₂²×Q₁₆	C₂²×C₃₁	semidirect
213. C₂×M₃₂	C₂²×C₃₁	semidirect
214. C₂²×C₁₆	C₂²×C₃₁	semidirect
220. #467	C₂²×C₃₁	semidirect
224. #427	C₂²×C₃₁	semidirect
227. #367	C₂²×C₃₁	semidirect
228. #366	C₂²×C₃₁	semidirect
229. #358	C₂²×C₃₁	semidirect
230. #358	C₂²×C₃₁	semidirect
234. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
288. C₃₁	#33766	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×#3059	2
C₃₁×#3058	2
C₃₁×#2237	2
C₃₁×#2234	2
C₃₁×#2220	2
C₃₁×#2217	2
C₃₁×#2187	2
C₃₁×#2185	2
C₃₁×#2113	2
#33766	31

Subgroups — C31×#33766 #21490525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33766 #21490525