Subgroups — C₃₁×#33753 #21490512

Order 7936.

642 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2235	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2233	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2217	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2187	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2185	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
10	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₃₁×#121	—	2	1	no	—
14	C₂×C₃₁×SD₃₂	C₂²	1	4	yes	complemented
15	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	complemented
16	C₃₁×#467	—	2	1	no	—
17	C₃₁×#467	—	2	1	no	—
18	C₃₁×#467	C₂²	1	2	yes	—
19	C₃₁×#467	C₂²	1	2	yes	complemented
20	C₃₁×#466	—	2	1	no	—
21	C₃₁×#466	—	2	1	no	—
22	C₃₁×#466	C₂²	1	2	yes	—
23	C₃₁×#466	C₂²	1	2	yes	—
24	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#103	—	2	1	no	—
27	C₂×C₃₁×#102	—	2	1	no	—
28	C₃₁×#367	C₂²	1	4	yes	complemented
29	C₃₁×#358	C₂²	1	4	yes	complemented
30	C₃₁×#357	C₂²	1	4	yes	complemented
31	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₂²×Q₈×C₃₁	—	2	1	no	—
34	C₂²×D₄×C₃₁	—	2	1	no	—
35	C₂²×D₄×C₃₁	—	4	1	no	—
36	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
37	C₂×Q₁₆×C₃₁	—	2	1	no	—
38	C₂×Q₁₆×C₃₁	—	4	2	no	—
39	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
40	C₂×D₈×C₃₁	—	2	1	no	—
41	C₂×D₈×C₃₁	—	4	2	no	—
42	C₂×D₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	—	4	2	no	—
44	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×C₂²⋊Q₈	—	2	2	no	—
51	C₃₁×C₂²⋊Q₈	—	2	2	no	—
52	C₃₁×C₂²⋊Q₈	—	4	1	no	—
53	C₃₁×C₂²⋊Q₈	—	4	1	no	—
54	C₃₁×#121	—	2	2	no	—
55	C₃₁×#121	—	2	2	no	—
56	C₃₁×#121	—	4	1	no	—
57	C₃₁×#121	—	4	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	4	1	no	—
61	C₂×C₂²⋊C₄×C₃₁	—	4	1	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	4	1	no	—
63	C₃₁×SD₃₂	—	4	4	no	—
64	C₂×C₁₆×C₃₁	—	4	2	no	—
65	C₂×C₁₆×C₃₁	C₂³	1	4	yes	—
66	C₃₁×#107	—	2	1	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	C₂³	1	2	yes	—
69	C₃₁×#107	C₂³	1	2	yes	—
70	C₃₁×#103	—	2	2	no	—
71	C₃₁×#103	—	2	2	no	—
72	C₃₁×#102	—	2	2	no	—
73	C₃₁×#102	—	2	2	no	—
74	C₂⁴×C₃₁	—	4	1	no	—
75	C₂⁴×C₃₁	D₈	1	1	yes	characteristic
76	C₂×Q₈×C₃₁	—	2	2	no	—
77	C₂×Q₈×C₃₁	—	4	2	no	—
78	C₂×Q₈×C₃₁	—	4	2	no	—
79	C₂×Q₈×C₃₁	—	4	1	no	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	4	2	no	—
82	C₂×D₄×C₃₁	—	4	2	no	—
83	C₂×D₄×C₃₁	—	4	2	no	—
84	C₂×D₄×C₃₁	—	4	2	no	—
85	C₂×D₄×C₃₁	—	4	1	no	—
86	C₂×D₄×C₃₁	—	8	4	no	—
87	C₂²×C₄×C₃₁	—	4	1	no	—
88	C₂²×C₄×C₃₁	—	4	1	no	—
89	C₂²×C₄×C₃₁	—	4	1	no	—
90	C₂²×C₄×C₃₁	—	4	1	no	—
91	C₂²×C₄×C₃₁	—	4	1	no	—
92	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	Q₁₆×C₃₁	—	2	4	no	—
99	Q₁₆×C₃₁	—	4	2	no	—
100	D₈×C₃₁	—	2	4	no	—
101	D₈×C₃₁	—	4	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	4	1	no	—
106	C₂×C₈×C₃₁	—	4	1	no	—
107	C₂×C₈×C₃₁	—	4	1	no	—
108	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	4	1	no	—
115	C₄⋊C₄×C₃₁	—	4	1	no	—
116	C₄⋊C₄×C₃₁	—	4	2	no	—
117	C₄⋊C₄×C₃₁	—	4	2	no	—
118	C₂²⋊C₄×C₃₁	—	4	2	no	—
119	C₂²⋊C₄×C₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₃₁	—	4	2	no	—
121	C₂²⋊C₄×C₃₁	—	4	2	no	—
122	C₁₆×C₃₁	—	2	4	no	—
123	#33753	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₃₁	—	4	1	no	—
125	C₂³×C₃₁	—	4	1	no	—
126	C₂³×C₃₁	—	4	2	no	—
127	C₂³×C₃₁	—	8	2	no	—
128	C₂³×C₃₁	—	8	2	no	—
129	C₂³×C₃₁	—	8	2	no	—
130	C₂³×C₃₁	SD₃₂	1	4	yes	complemented
131	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
132	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
133	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
134	Q₈×C₃₁	—	4	2	no	—
135	Q₈×C₃₁	—	4	2	no	—
136	Q₈×C₃₁	—	8	2	no	—
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	4	2	no	—
139	D₄×C₃₁	—	8	2	no	—
140	D₄×C₃₁	—	8	4	no	—
141	D₄×C₃₁	—	8	4	no	—
142	C₂×C₄×C₃₁	—	2	1	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	8	2	no	—
155	C₂×C₄×C₃₁	—	8	2	no	—
156	C₂×C₄×C₃₁	—	8	2	no	—
157	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	—	2	1	no	—
164	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
165	C₂×#467	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂×#466	C₂×C₃₁	1	1	yes	characteristic
167	#2235	C₂×C₃₁	1	2	yes	complemented
168	#2233	C₂×C₃₁	1	2	yes	complemented
169	#2217	C₂×C₃₁	1	4	yes	complemented
170	#2187	C₂×C₃₁	1	2	yes	complemented
171	#2185	C₂×C₃₁	1	2	yes	complemented
172	C₂×C₂²⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂²×C₃₁	—	2	1	no	—
174	C₂²×C₃₁	—	2	1	no	—
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	4	4	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	8	2	no	—
183	C₂²×C₃₁	—	16	4	no	—
184	C₂²×C₃₁	C₂×SD₃₂	1	2	yes	—
185	C₂²×C₃₁	C₂×SD₃₂	1	2	yes	—
186	C₂²×C₃₁	C₂×SD₃₂	1	2	yes	—
187	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	2	1	no	—
191	C₄×C₃₁	—	8	2	no	—
192	C₄×C₃₁	—	8	2	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	#534	1	1	yes	characteristic
195	C₄×C₃₁	#575	1	1	yes	characteristic
196	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
197	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
199	C₂×C₂²⋊Q₈	—	2	1	no	—
200	C₂×#121	—	2	1	no	—
201	C₂×SD₃₂	C₂²×C₃₁	1	4	yes	complemented
202	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	complemented
203	#467	—	2	1	no	—
204	#467	—	2	1	no	—
205	#467	C₂²×C₃₁	1	2	yes	—
206	#467	C₂²×C₃₁	1	2	yes	complemented
207	#466	—	2	1	no	—
208	#466	—	2	1	no	—
209	#466	C₂²×C₃₁	1	2	yes	—
210	#466	C₂²×C₃₁	1	2	yes	—
211	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
213	C₂×#103	—	2	1	no	—
214	C₂×#102	—	2	1	no	—
215	#367	C₂²×C₃₁	1	4	yes	complemented
216	#358	C₂²×C₃₁	1	4	yes	complemented
217	#357	C₂²×C₃₁	1	4	yes	complemented
218	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
219	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
220	C₂×C₃₁	—	2	2	no	—
221	C₂×C₃₁	—	2	2	no	—
222	C₂×C₃₁	—	2	2	no	—
223	C₂×C₃₁	—	16	2	no	—
224	C₂×C₃₁	#3186	1	1	yes	characteristic
225	C₂×C₃₁	C₂²×SD₃₂	1	1	yes	characteristic
226	C₂×C₃₁	#3414	1	1	yes	characteristic
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	—	4	1	no	—
230	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
231	C₂×Q₁₆	—	2	1	no	—
232	C₂×Q₁₆	—	4	2	no	—
233	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	4	2	no	—
236	C₂×D₈	C₂³×C₃₁	1	2	yes	—
237	C₂²×C₈	—	4	2	no	—
238	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	4	1	no	—
247	C₂²⋊Q₈	—	4	1	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	4	1	no	—
251	#121	—	4	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	4	1	no	—
255	C₂×C₂²⋊C₄	—	4	1	no	—
256	C₂×C₂²⋊C₄	—	4	1	no	—
257	SD₃₂	—	4	4	no	—
258	C₂×C₁₆	—	4	2	no	—
259	C₂×C₁₆	C₂³×C₃₁	1	4	yes	—
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	C₂³×C₃₁	1	2	yes	—
263	#107	C₂³×C₃₁	1	2	yes	—
264	#103	—	2	2	no	—
265	#103	—	2	2	no	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	C₃₁	#33753	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	—	4	1	no	—
270	C₂⁴	D₈×C₃₁	1	1	yes	characteristic
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	Q₁₆	—	2	4	no	—
294	Q₁₆	—	4	2	no	—
295	D₈	—	2	4	no	—
296	D₈	—	4	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₁₆	—	2	4	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	—	8	2	no	—
323	C₂³	—	8	2	no	—
324	C₂³	C₃₁×SD₃₂	1	4	yes	complemented
325	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
326	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
327	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	4	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	C₂×C₃₁×SD₃₂	1	2	yes	—
371	C₂²	C₂×C₃₁×SD₃₂	1	2	yes	—
372	C₂²	C₂×C₃₁×SD₃₂	1	2	yes	—
373	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₃₁×#534	1	1	yes	characteristic
381	C₄	C₃₁×#575	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	2	2	no	—
385	C₂	—	16	2	no	—
386	C₂	C₃₁×#3186	1	1	yes	characteristic
387	C₂	C₂²×C₃₁×SD₃₂	1	1	yes	characteristic
388	C₂	C₃₁×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#467	C₂	semidirect
3. C₃₁×#2235	C₂	semidirect
4. C₃₁×#2233	C₂	semidirect
5. C₃₁×#2217	C₂	semidirect
6. C₃₁×#2187	C₂	semidirect
7. C₃₁×#2185	C₂	semidirect
8. C₂×C₃₁×C₂²⋊C₁₆	C₂	semidirect
9. C₂²×Q₁₆×C₃₁	C₂²	semidirect
14. C₂×C₃₁×SD₃₂	C₂²	semidirect
15. C₂²×C₁₆×C₃₁	C₂²	semidirect
19. C₃₁×#467	C₂²	semidirect
25. C₂×C₃₁×#107	C₂²	semidirect
28. C₃₁×#367	C₂²	semidirect
29. C₃₁×#358	C₂²	semidirect
30. C₃₁×#357	C₂²	semidirect
32. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
123. #33753	C₃₁	direct (N × H)
130. C₂³×C₃₁	SD₃₂	semidirect
165. C₂×#467	C₂×C₃₁	semidirect
167. #2235	C₂×C₃₁	semidirect
168. #2233	C₂×C₃₁	semidirect
169. #2217	C₂×C₃₁	semidirect
170. #2187	C₂×C₃₁	semidirect
171. #2185	C₂×C₃₁	semidirect
172. C₂×C₂²⋊C₁₆	C₂×C₃₁	semidirect
196. C₂²×Q₁₆	C₂²×C₃₁	semidirect
201. C₂×SD₃₂	C₂²×C₃₁	semidirect
202. C₂²×C₁₆	C₂²×C₃₁	semidirect
206. #467	C₂²×C₃₁	semidirect
212. C₂×#107	C₂²×C₃₁	semidirect
215. #367	C₂²×C₃₁	semidirect
216. #358	C₂²×C₃₁	semidirect
217. #357	C₂²×C₃₁	semidirect
219. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
268. C₃₁	#33753	direct (N × H)
324. C₂³	C₃₁×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#467	2
C₂×C₃₁×#466	2
C₃₁×#2235	2
C₃₁×#2233	2
C₃₁×#2217	2
C₃₁×#2187	2
C₃₁×#2185	2
C₂×C₃₁×C₂²⋊C₁₆	2
#33753	31

Subgroups — C31×#33753 #21490512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33753 #21490512