Subgroups — C₃₁×#33786 #21490545

Order 7936.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2210	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2206	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2186	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2184	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2164	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×#540	—	2	1	no	—
16	C₃₁×#535	—	2	1	no	—
17	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₃₁×D₁₆	C₂²	1	2	yes	—
19	C₂×C₃₁×D₁₆	C₂²	1	2	yes	—
20	C₂×C₃₁×D₁₆	C₂²	1	2	yes	complemented
21	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#496	—	2	1	no	—
23	C₃₁×#496	—	2	1	no	—
24	C₃₁×#495	C₂²	1	1	yes	characteristic
25	C₃₁×#495	C₂²	1	1	yes	characteristic
26	C₃₁×#493	C₂²	1	1	yes	characteristic
27	C₃₁×#493	C₂²	1	1	yes	characteristic
28	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#490	—	2	1	no	—
30	C₃₁×#469	—	2	1	no	—
31	C₃₁×#466	C₂²	1	2	yes	—
32	C₃₁×#442	—	2	1	no	—
33	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#405	C₂²	1	1	yes	characteristic
35	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₃₁×#358	C₂²	1	2	yes	complemented
37	C₃₁×#357	C₂²	1	2	yes	—
38	C₃₁×#357	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	complemented
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₃₁×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₂²×D₄×C₃₁	—	2	1	no	—
45	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
46	C₃₁×#135	—	4	2	no	—
47	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₃₁	—	2	1	no	—
49	C₂×SD₁₆×C₃₁	—	2	1	no	—
50	C₂×SD₁₆×C₃₁	—	2	1	no	—
51	C₂×D₈×C₃₁	—	2	1	no	—
52	C₂×D₈×C₃₁	—	2	1	no	—
53	C₂×D₈×C₃₁	—	2	1	no	—
54	C₂×D₈×C₃₁	—	2	1	no	—
55	C₂×D₈×C₃₁	—	4	2	no	—
56	C₂×D₈×C₃₁	C₂³	1	2	yes	—
57	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#127	—	2	1	no	—
63	C₃₁×#127	—	2	1	no	—
64	C₃₁×#127	—	2	1	no	—
65	C₃₁×#125	—	2	1	no	—
66	C₃₁×#124	—	2	1	no	—
67	C₃₁×#124	—	2	1	no	—
68	C₃₁×#123	—	4	2	no	—
69	C₃₁×#121	—	2	2	no	—
70	C₃₁×#121	—	4	2	no	—
71	C₃₁×#121	—	4	2	no	—
72	C₃₁×#120	—	4	2	no	—
73	C₄×D₄×C₃₁	—	2	2	no	—
74	C₃₁×#117	D₄	1	1	yes	characteristic
75	C₃₁×SD₃₂	—	4	2	no	—
76	C₃₁×D₁₆	—	4	2	no	—
77	C₃₁×D₁₆	—	4	2	no	—
78	C₃₁×D₁₆	—	4	2	no	—
79	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
81	C₃₁×#107	C₂³	1	2	yes	—
82	C₃₁×#106	—	2	1	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#97	D₄	1	1	yes	characteristic
86	C₃₁×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂⁴×C₃₁	—	4	1	no	—
90	#41×C₃₁	—	4	2	no	—
91	#41×C₃₁	—	4	2	no	—
92	C₂×Q₈×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	1	no	—
95	C₂×D₄×C₃₁	—	2	1	no	—
96	C₂×D₄×C₃₁	—	2	1	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	—	4	2	no	—
101	C₂×D₄×C₃₁	—	4	1	no	—
102	C₂×D₄×C₃₁	—	4	2	no	—
103	C₂×D₄×C₃₁	—	4	2	no	—
104	C₂×D₄×C₃₁	—	4	2	no	—
105	C₂²×C₄×C₃₁	—	4	1	no	—
106	C₂²×C₄×C₃₁	—	4	2	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₃₁	—	2	2	no	—
109	SD₁₆×C₃₁	—	4	2	no	—
110	SD₁₆×C₃₁	—	4	2	no	—
111	SD₁₆×C₃₁	—	4	2	no	—
112	D₈×C₃₁	—	2	2	no	—
113	D₈×C₃₁	—	2	2	no	—
114	D₈×C₃₁	—	2	2	no	—
115	D₈×C₃₁	—	2	2	no	—
116	D₈×C₃₁	—	2	2	no	—
117	D₈×C₃₁	—	4	2	no	—
118	D₈×C₃₁	—	4	2	no	—
119	D₈×C₃₁	—	4	2	no	—
120	D₈×C₃₁	—	4	2	no	—
121	M₁₆×C₃₁	—	2	2	no	—
122	C₂×C₈×C₃₁	—	2	2	no	—
123	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	D₈	1	2	yes	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₃₁	—	2	2	no	—
138	C₁₆×C₃₁	—	2	2	no	—
139	#33786	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	4	2	no	—
141	C₂³×C₃₁	—	4	1	no	—
142	C₂³×C₃₁	—	4	1	no	—
143	C₂³×C₃₁	—	4	1	no	—
144	C₂³×C₃₁	—	8	2	no	—
145	C₂³×C₃₁	—	16	2	no	—
146	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
147	Q₈×C₃₁	—	4	1	no	—
148	Q₈×C₃₁	—	4	1	no	—
149	D₄×C₃₁	—	4	1	no	—
150	D₄×C₃₁	—	4	1	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	4	1	no	—
154	D₄×C₃₁	—	4	1	no	—
155	D₄×C₃₁	—	4	1	no	—
156	D₄×C₃₁	—	4	2	no	—
157	D₄×C₃₁	—	8	2	no	—
158	D₄×C₃₁	—	8	2	no	—
159	D₄×C₃₁	—	16	2	no	—
160	D₄×C₃₁	—	16	2	no	—
161	D₄×C₃₁	—	16	2	no	—
162	D₄×C₃₁	—	16	2	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	1	no	—
165	C₂×C₄×C₃₁	—	4	1	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	8	2	no	—
168	C₂×C₄×C₃₁	—	16	2	no	—
169	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
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	AGL(1,ℤ/8)	1	2	yes	—
176	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
177	#3176	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#3155	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#2250	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#2246	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#2244	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#2242	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#2210	C₂×C₃₁	1	2	yes	complemented
184	#2206	C₂×C₃₁	1	2	yes	complemented
185	#2186	C₂×C₃₁	1	2	yes	complemented
186	#2184	C₂×C₃₁	1	2	yes	complemented
187	#2164	C₂×C₃₁	1	1	yes	characteristic, complemented
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	2	1	no	—
190	C₂²×C₃₁	—	8	2	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	—	8	2	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	—	8	1	no	—
196	C₂²×C₃₁	—	8	1	no	—
197	C₂²×C₃₁	—	8	1	no	—
198	C₂²×C₃₁	—	8	2	no	—
199	C₂²×C₃₁	—	16	4	no	—
200	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
201	C₄×C₃₁	—	2	2	no	—
202	C₄×C₃₁	—	2	2	no	—
203	C₄×C₃₁	—	2	1	no	—
204	C₄×C₃₁	—	8	2	no	—
205	C₄×C₃₁	—	8	1	no	—
206	C₄×C₃₁	#535	1	1	yes	characteristic
207	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂×AGL(1,ℤ/8)	—	2	1	no	—
209	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
210	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
211	#540	—	2	1	no	—
212	#535	—	2	1	no	—
213	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
214	C₂×D₁₆	C₂²×C₃₁	1	2	yes	—
215	C₂×D₁₆	C₂²×C₃₁	1	2	yes	—
216	C₂×D₁₆	C₂²×C₃₁	1	2	yes	complemented
217	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
218	#496	—	2	1	no	—
219	#496	—	2	1	no	—
220	#495	C₂²×C₃₁	1	1	yes	characteristic
221	#495	C₂²×C₃₁	1	1	yes	characteristic
222	#493	C₂²×C₃₁	1	1	yes	characteristic
223	#493	C₂²×C₃₁	1	1	yes	characteristic
224	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
225	#490	—	2	1	no	—
226	#469	—	2	1	no	—
227	#466	C₂²×C₃₁	1	2	yes	—
228	#442	—	2	1	no	—
229	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
230	#405	C₂²×C₃₁	1	1	yes	characteristic
231	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
232	#358	C₂²×C₃₁	1	2	yes	complemented
233	#357	C₂²×C₃₁	1	2	yes	—
234	#357	C₂²×C₃₁	1	2	yes	—
235	#357	C₂²×C₃₁	1	2	yes	complemented
236	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
237	#346	C₂²×C₃₁	1	1	yes	characteristic, complemented
238	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
239	C₂×C₃₁	—	4	1	no	—
240	C₂×C₃₁	—	16	2	no	—
241	C₂×C₃₁	—	16	1	no	—
242	C₂×C₃₁	—	16	1	no	—
243	C₂×C₃₁	—	16	1	no	—
244	C₂×C₃₁	#3205	1	1	yes	characteristic
245	C₂×C₃₁	#3415	1	2	yes	—
246	C₂×#41	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	AGL(1,ℤ/8)	—	4	4	no	—
249	#135	—	4	2	no	—
250	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×SD₁₆	—	2	1	no	—
252	C₂×SD₁₆	—	2	1	no	—
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	4	2	no	—
259	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
262	C₂×D₈	C₂³×C₃₁	1	2	yes	—
263	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#125	—	2	1	no	—
269	#124	—	2	1	no	—
270	#124	—	2	1	no	—
271	#123	—	4	2	no	—
272	#121	—	2	2	no	—
273	#121	—	4	2	no	—
274	#121	—	4	2	no	—
275	#120	—	4	2	no	—
276	C₄×D₄	—	2	2	no	—
277	#117	D₄×C₃₁	1	1	yes	characteristic
278	SD₃₂	—	4	2	no	—
279	D₁₆	—	4	2	no	—
280	D₁₆	—	4	2	no	—
281	D₁₆	—	4	2	no	—
282	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
283	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
284	#107	C₂³×C₃₁	1	2	yes	—
285	#106	—	2	1	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#97	D₄×C₃₁	1	1	yes	characteristic
289	#97	D₄×C₃₁	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
292	C₃₁	#33786	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	—	4	1	no	—
294	#41	—	4	2	no	—
295	#41	—	4	2	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
312	Q₁₆	—	2	2	no	—
313	SD₁₆	—	4	2	no	—
314	SD₁₆	—	4	2	no	—
315	SD₁₆	—	4	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	2	no	—
322	D₈	—	4	2	no	—
323	D₈	—	4	2	no	—
324	D₈	—	4	2	no	—
325	M₁₆	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
330	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	D₈×C₃₁	1	2	yes	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
339	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	16	2	no	—
349	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	16	2	no	—
363	D₄	—	16	2	no	—
364	D₄	—	16	2	no	—
365	D₄	—	16	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	16	2	no	—
372	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
373	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
374	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
379	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	16	4	no	—
392	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₃₁×#535	1	1	yes	characteristic
399	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	—	16	1	no	—
403	C₂	—	16	2	no	—
404	C₂	—	16	1	no	—
405	C₂	C₃₁×#3205	1	1	yes	characteristic
406	C₂	C₃₁×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
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×#3176	C₂	semidirect
2. C₃₁×#3155	C₂	semidirect
3. C₃₁×#2250	C₂	semidirect
4. C₃₁×#2246	C₂	semidirect
5. C₃₁×#2244	C₂	semidirect
6. C₃₁×#2242	C₂	semidirect
7. C₃₁×#2210	C₂	semidirect
8. C₃₁×#2206	C₂	semidirect
9. C₃₁×#2186	C₂	semidirect
10. C₃₁×#2184	C₂	semidirect
11. C₃₁×#2164	C₂	semidirect
17. C₂×C₃₁×SD₃₂	C₂²	semidirect
20. C₂×C₃₁×D₁₆	C₂²	semidirect
21. C₃₁×#499	C₂²	semidirect
28. C₃₁×#493	C₂²	semidirect
33. C₄×D₈×C₃₁	C₂²	semidirect
35. C₃₁×C₄⋊C₁₆	C₂²	semidirect
36. C₃₁×#358	C₂²	semidirect
39. C₃₁×#357	C₂²	semidirect
41. C₃₁×#346	C₂²	semidirect
42. C₄×C₁₆×C₃₁	C₂²	semidirect
139. #33786	C₃₁	direct (N × H)
177. #3176	C₂×C₃₁	semidirect
178. #3155	C₂×C₃₁	semidirect
179. #2250	C₂×C₃₁	semidirect
180. #2246	C₂×C₃₁	semidirect
181. #2244	C₂×C₃₁	semidirect
182. #2242	C₂×C₃₁	semidirect
183. #2210	C₂×C₃₁	semidirect
184. #2206	C₂×C₃₁	semidirect
185. #2186	C₂×C₃₁	semidirect
186. #2184	C₂×C₃₁	semidirect
187. #2164	C₂×C₃₁	semidirect
213. C₂×SD₃₂	C₂²×C₃₁	semidirect
216. C₂×D₁₆	C₂²×C₃₁	semidirect
217. #499	C₂²×C₃₁	semidirect
224. #493	C₂²×C₃₁	semidirect
229. C₄×D₈	C₂²×C₃₁	semidirect
231. C₄⋊C₁₆	C₂²×C₃₁	semidirect
232. #358	C₂²×C₃₁	semidirect
235. #357	C₂²×C₃₁	semidirect
237. #346	C₂²×C₃₁	semidirect
238. C₄×C₁₆	C₂²×C₃₁	semidirect
292. C₃₁	#33786	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×#3176	2
C₃₁×#3155	2
C₃₁×#2250	2
C₃₁×#2246	2
C₃₁×#2244	2
C₃₁×#2242	2
C₃₁×#2210	2
C₃₁×#2206	2
C₃₁×#2186	2
C₃₁×#2184	2
C₃₁×#2164	2
#33786	31

Subgroups — C31×#33786 #21490545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33786 #21490545