Subgroups — C₃₁×#33275 #21490034

Order 7936.

690 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2644	C₂	1	2	yes	maximal, complemented
2	C₃₁×#1972	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1972	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1970	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1936	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1934	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1934	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#102	C₂²	1	2	yes	—
17	C₂×C₃₁×#102	C₂²	1	2	yes	—
18	C₂×C₃₁×#102	C₂²	1	2	yes	—
19	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#397	—	2	2	no	—
26	C₃₁×#397	—	2	2	no	—
27	C₃₁×#397	—	2	2	no	—
28	C₃₁×#396	—	2	2	no	—
29	C₃₁×#390	C₂²	1	2	yes	—
30	C₃₁×#390	C₂²	1	2	yes	—
31	C₃₁×#390	C₂²	1	2	yes	—
32	C₃₁×#389	C₂²	1	2	yes	—
33	C₃₁×#389	C₂²	1	2	yes	—
34	C₃₁×#389	C₂²	1	2	yes	—
35	C₃₁×#376	C₂²	1	1	yes	characteristic
36	C₃₁×#340	C₂²	1	2	yes	—
37	C₃₁×#340	C₂²	1	2	yes	—
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
40	C₂×D₈×C₃₁	—	2	2	no	—
41	C₂×D₈×C₃₁	—	2	2	no	—
42	C₂×D₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#107	—	2	2	no	—
63	C₃₁×#106	—	2	2	no	—
64	C₃₁×#106	—	2	2	no	—
65	C₃₁×#102	—	2	4	no	—
66	C₃₁×#102	—	2	4	no	—
67	C₃₁×#102	—	2	4	no	—
68	C₃₁×#97	—	2	2	no	—
69	C₃₁×#97	—	2	2	no	—
70	C₃₁×#97	—	2	2	no	—
71	C₄×C₈×C₃₁	—	2	2	no	—
72	C₄×C₈×C₃₁	—	2	2	no	—
73	C₄×C₈×C₃₁	—	2	2	no	—
74	C₃₁×#95	—	2	2	no	—
75	C₃₁×#95	—	2	2	no	—
76	C₃₁×#95	—	2	2	no	—
77	C₃₁×#95	D₄	1	2	yes	—
78	C₃₁×#95	D₄	1	2	yes	—
79	C₂⁴×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	2	2	no	—
82	C₂×D₄×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	—	2	2	no	—
85	C₂×D₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	2	2	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
94	D₈×C₃₁	—	4	4	no	—
95	C₂×C₈×C₃₁	—	2	1	no	—
96	C₂×C₈×C₃₁	—	2	1	no	—
97	C₂×C₈×C₃₁	—	2	1	no	—
98	C₂×C₈×C₃₁	—	2	1	no	—
99	C₂×C₈×C₃₁	—	2	1	no	—
100	C₂×C₈×C₃₁	—	2	1	no	—
101	C₂×C₈×C₃₁	#41	1	2	yes	—
102	C₂×C₈×C₃₁	#41	1	2	yes	—
103	C₂×C₈×C₃₁	#41	1	2	yes	—
104	C₂×C₈×C₃₁	#41	1	2	yes	—
105	C₂×C₈×C₃₁	#41	1	2	yes	—
106	C₂×C₈×C₃₁	#41	1	2	yes	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	8	2	no	—
114	C₄⋊C₄×C₃₁	—	8	2	no	—
115	C₄⋊C₄×C₃₁	—	8	2	no	—
116	C₂²⋊C₄×C₃₁	—	8	2	no	—
117	C₂²⋊C₄×C₃₁	—	8	2	no	—
118	C₂²⋊C₄×C₃₁	—	8	2	no	—
119	C₂²⋊C₄×C₃₁	—	8	2	no	—
120	C₂²⋊C₄×C₃₁	—	8	2	no	—
121	C₂²⋊C₄×C₃₁	—	8	2	no	—
122	C₄²×C₃₁	—	2	1	no	—
123	C₄²×C₃₁	—	2	1	no	—
124	C₄²×C₃₁	—	2	1	no	—
125	C₄²×C₃₁	—	2	1	no	—
126	C₄²×C₃₁	—	2	1	no	—
127	C₄²×C₃₁	—	2	1	no	—
128	#33275	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	4	2	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	2	no	—
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	—	4	2	no	—
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	4	2	no	—
139	D₄×C₃₁	—	4	2	no	—
140	D₄×C₃₁	—	4	2	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	2	1	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	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	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
166	C₈×C₃₁	—	2	2	no	—
167	C₈×C₃₁	—	2	2	no	—
168	C₈×C₃₁	—	2	2	no	—
169	C₈×C₃₁	#126	1	4	yes	—
170	#2644	C₂×C₃₁	1	2	yes	complemented
171	#1972	C₂×C₃₁	1	1	yes	characteristic
172	#1972	C₂×C₃₁	1	1	yes	characteristic
173	#1970	C₂×C₃₁	1	1	yes	characteristic
174	#1944	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1943	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1941	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1936	C₂×C₃₁	1	2	yes	complemented
178	#1934	C₂×C₃₁	1	2	yes	complemented
179	#1934	C₂×C₃₁	1	2	yes	complemented
180	#1726	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	8	2	no	—
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	—	8	2	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	#532	1	1	yes	characteristic
189	C₂²×C₃₁	#532	1	1	yes	characteristic
190	C₂²×C₃₁	#532	1	1	yes	characteristic
191	C₂²×C₃₁	#576	1	2	yes	—
192	C₂²×C₃₁	#577	1	2	yes	—
193	C₄×C₃₁	—	4	1	no	—
194	C₄×C₃₁	—	4	1	no	—
195	C₄×C₃₁	—	4	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	—	8	2	no	—
199	C₄×C₃₁	—	8	2	no	—
200	C₄×C₃₁	C₂×#126	1	1	yes	characteristic
201	C₄×C₃₁	#529	1	1	yes	characteristic
202	C₄×C₃₁	#529	1	1	yes	characteristic
203	C₄×C₃₁	#529	1	1	yes	characteristic
204	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#102	C₂²×C₃₁	1	2	yes	—
209	C₂×#102	C₂²×C₃₁	1	2	yes	—
210	C₂×#102	C₂²×C₃₁	1	2	yes	—
211	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
217	#397	—	2	2	no	—
218	#397	—	2	2	no	—
219	#397	—	2	2	no	—
220	#396	—	2	2	no	—
221	#390	C₂²×C₃₁	1	2	yes	—
222	#390	C₂²×C₃₁	1	2	yes	—
223	#390	C₂²×C₃₁	1	2	yes	—
224	#389	C₂²×C₃₁	1	2	yes	—
225	#389	C₂²×C₃₁	1	2	yes	—
226	#389	C₂²×C₃₁	1	2	yes	—
227	#376	C₂²×C₃₁	1	1	yes	characteristic
228	#340	C₂²×C₃₁	1	2	yes	—
229	#340	C₂²×C₃₁	1	2	yes	—
230	#340	C₂²×C₃₁	1	2	yes	—
231	C₂×C₃₁	—	16	2	no	—
232	C₂×C₃₁	#2860	1	1	yes	characteristic
233	C₂×C₃₁	#3173	1	1	yes	characteristic
234	C₂×C₃₁	#3176	1	1	yes	characteristic
235	C₂×C₃₁	#3179	1	2	yes	—
236	C₂×C₃₁	#3179	1	2	yes	—
237	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
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×C₈	C₂³×C₃₁	1	1	yes	characteristic
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
260	#107	—	2	2	no	—
261	#106	—	2	2	no	—
262	#106	—	2	2	no	—
263	#102	—	2	4	no	—
264	#102	—	2	4	no	—
265	#102	—	2	4	no	—
266	#97	—	2	2	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	D₄×C₃₁	1	2	yes	—
276	#95	D₄×C₃₁	1	2	yes	—
277	C₃₁	#33275	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
293	D₈	—	4	4	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	#41×C₃₁	1	2	yes	—
301	C₂×C₈	#41×C₃₁	1	2	yes	—
302	C₂×C₈	#41×C₃₁	1	2	yes	—
303	C₂×C₈	#41×C₃₁	1	2	yes	—
304	C₂×C₈	#41×C₃₁	1	2	yes	—
305	C₂×C₈	#41×C₃₁	1	2	yes	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₄⋊C₄	—	8	2	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	8	2	no	—
319	C₂²⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	2	no	—
367	C₈	C₃₁×#126	1	4	yes	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₃₁×#532	1	1	yes	characteristic
376	C₂²	C₃₁×#532	1	1	yes	characteristic
377	C₂²	C₃₁×#532	1	1	yes	characteristic
378	C₂²	C₃₁×#576	1	2	yes	—
379	C₂²	C₃₁×#577	1	2	yes	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₂×C₃₁×#126	1	1	yes	characteristic
388	C₄	C₃₁×#529	1	1	yes	characteristic
389	C₄	C₃₁×#529	1	1	yes	characteristic
390	C₄	C₃₁×#529	1	1	yes	characteristic
391	C₂	—	16	2	no	—
392	C₂	C₃₁×#2860	1	1	yes	characteristic
393	C₂	C₃₁×#3173	1	1	yes	characteristic
394	C₂	C₃₁×#3176	1	1	yes	characteristic
395	C₂	C₃₁×#3179	1	2	yes	—
396	C₂	C₃₁×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₈×C₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₃₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2644	C₂	semidirect
5. C₃₁×#1944	C₂	semidirect
6. C₃₁×#1943	C₂	semidirect
7. C₃₁×#1941	C₂	semidirect
8. C₃₁×#1936	C₂	semidirect
9. C₃₁×#1934	C₂	semidirect
10. C₃₁×#1934	C₂	semidirect
11. C₃₁×#1726	C₂	semidirect
128. #33275	C₃₁	direct (N × H)
170. #2644	C₂×C₃₁	semidirect
174. #1944	C₂×C₃₁	semidirect
175. #1943	C₂×C₃₁	semidirect
176. #1941	C₂×C₃₁	semidirect
177. #1936	C₂×C₃₁	semidirect
178. #1934	C₂×C₃₁	semidirect
179. #1934	C₂×C₃₁	semidirect
180. #1726	C₂×C₃₁	semidirect
277. C₃₁	#33275	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×#2644	2
C₃₁×#1972	2
C₃₁×#1970	2
C₃₁×#1944	2
C₃₁×#1943	2
C₃₁×#1941	2
C₃₁×#1936	2
C₃₁×#1934	2
C₃₁×#1726	2
#33275	31

Subgroups — C31×#33275 #21490034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33275 #21490034