Subgroups — C₃₁×#33284 #21490043

Order 7936.

718 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2641	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1992	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1961	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1957	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1936	C₂	1	2	yes	maximal, 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	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#102	C₂²	1	2	yes	—
15	C₂×C₃₁×#102	C₂²	1	2	yes	—
16	C₂×C₃₁×#102	C₂²	1	2	yes	—
17	C₂×C₃₁×#102	C₂²	1	2	yes	—
18	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₃₁	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	C₃₁×#400	—	2	2	no	—
25	C₃₁×#398	—	2	2	no	—
26	C₃₁×#394	—	2	2	no	—
27	C₃₁×#394	—	2	2	no	—
28	C₃₁×#390	C₂²	1	2	yes	—
29	C₃₁×#390	C₂²	1	2	yes	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#389	C₂²	1	2	yes	—
32	C₃₁×#384	C₂²	1	1	yes	characteristic
33	C₃₁×#382	C₂²	1	1	yes	characteristic
34	C₃₁×#376	C₂²	1	1	yes	characteristic
35	C₃₁×#340	C₂²	1	2	yes	—
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	—	2	2	no	—
40	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₃₁×#127	—	2	2	no	—
46	C₃₁×#127	—	2	2	no	—
47	C₃₁×#125	—	2	2	no	—
48	C₃₁×#125	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×#102	—	2	4	no	—
64	C₃₁×#102	—	2	4	no	—
65	C₃₁×#102	—	2	4	no	—
66	C₃₁×#102	—	2	4	no	—
67	C₃₁×#97	—	2	2	no	—
68	C₃₁×#97	—	2	2	no	—
69	C₃₁×#97	—	2	2	no	—
70	C₄×C₈×C₃₁	—	2	2	no	—
71	C₄×C₈×C₃₁	—	2	2	no	—
72	C₄×C₈×C₃₁	—	2	2	no	—
73	C₃₁×#95	—	2	2	no	—
74	C₃₁×#95	—	2	2	no	—
75	C₃₁×#95	—	2	2	no	—
76	C₃₁×#95	D₄	1	2	yes	—
77	C₃₁×#95	D₄	1	2	yes	—
78	C₂⁴×C₃₁	—	2	2	no	—
79	C₂×D₄×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	—	4	4	no	—
86	C₂×D₄×C₃₁	—	8	2	no	—
87	C₂×D₄×C₃₁	—	8	2	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
102	C₂×C₈×C₃₁	—	2	1	no	—
103	C₂×C₈×C₃₁	—	2	1	no	—
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	C₂×C₈×C₃₁	#41	1	2	yes	—
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	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	4	4	no	—
115	C₄⋊C₄×C₃₁	—	8	2	no	—
116	C₄⋊C₄×C₃₁	—	8	2	no	—
117	C₄⋊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	#41	1	2	yes	—
127	C₄²×C₃₁	#41	1	2	yes	—
128	#33284	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	D₄×C₃₁	—	8	8	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	1	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	#124	1	4	yes	—
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	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
167	C₈×C₃₁	—	2	2	no	—
168	C₈×C₃₁	—	2	2	no	—
169	C₈×C₃₁	—	2	2	no	—
170	C₈×C₃₁	—	2	2	no	—
171	#2647	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2641	C₂×C₃₁	1	1	yes	characteristic
173	#1992	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1991	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1961	C₂×C₃₁	1	1	yes	characteristic
176	#1957	C₂×C₃₁	1	1	yes	characteristic
177	#1936	C₂×C₃₁	1	2	yes	complemented
178	#1936	C₂×C₃₁	1	2	yes	complemented
179	#1934	C₂×C₃₁	1	2	yes	complemented
180	#1934	C₂×C₃₁	1	2	yes	complemented
181	#1726	C₂×C₃₁	1	1	yes	characteristic, complemented
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	—	8	2	no	—
189	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
190	C₂²×C₃₁	#532	1	1	yes	characteristic
191	C₂²×C₃₁	#532	1	1	yes	characteristic
192	C₂²×C₃₁	#576	1	2	yes	—
193	C₂²×C₃₁	#577	1	2	yes	—
194	C₄×C₃₁	—	2	4	no	—
195	C₄×C₃₁	—	4	1	no	—
196	C₄×C₃₁	—	4	1	no	—
197	C₄×C₃₁	—	4	2	no	—
198	C₄×C₃₁	—	8	2	no	—
199	C₄×C₃₁	—	8	2	no	—
200	C₄×C₃₁	—	8	2	no	—
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	C₄×C₃₁	#529	1	1	yes	characteristic
205	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#102	C₂²×C₃₁	1	2	yes	—
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	#400	—	2	2	no	—
218	#398	—	2	2	no	—
219	#394	—	2	2	no	—
220	#394	—	2	2	no	—
221	#390	C₂²×C₃₁	1	2	yes	—
222	#390	C₂²×C₃₁	1	2	yes	—
223	#389	C₂²×C₃₁	1	2	yes	—
224	#389	C₂²×C₃₁	1	2	yes	—
225	#384	C₂²×C₃₁	1	1	yes	characteristic
226	#382	C₂²×C₃₁	1	1	yes	characteristic
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	#340	C₂²×C₃₁	1	2	yes	—
232	C₂×C₃₁	—	16	2	no	—
233	C₂×C₃₁	#2861	1	1	yes	characteristic
234	C₂×C₃₁	#3136	1	2	yes	—
235	C₂×C₃₁	#3174	1	1	yes	characteristic
236	C₂×C₃₁	#3176	1	1	yes	characteristic
237	C₂×C₃₁	#3179	1	2	yes	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
240	C₂²×C₈	C₂³×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	#127	—	2	2	no	—
245	#127	—	2	2	no	—
246	#125	—	2	2	no	—
247	#125	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
262	#102	—	2	4	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	#33284	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	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂×D₄	—	8	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	#41×C₃₁	1	2	yes	—
305	C₂×C₈	#41×C₃₁	1	2	yes	—
306	C₂×C₈	#41×C₃₁	1	2	yes	—
307	C₂×C₈	#41×C₃₁	1	2	yes	—
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	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	8	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₄⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	8	2	no	—
319	C₂²⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	#41×C₃₁	1	2	yes	—
327	C₄²	#41×C₃₁	1	2	yes	—
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	—	4	2	no	—
335	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	8	8	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	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	—	2	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	—	4	2	no	—
359	C₂×C₄	C₃₁×#124	1	4	yes	—
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	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	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	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
378	C₂²	C₃₁×#532	1	1	yes	characteristic
379	C₂²	C₃₁×#532	1	1	yes	characteristic
380	C₂²	C₃₁×#576	1	2	yes	—
381	C₂²	C₃₁×#577	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₃₁×#529	1	1	yes	characteristic
390	C₄	C₃₁×#529	1	1	yes	characteristic
391	C₄	C₃₁×#529	1	1	yes	characteristic
392	C₄	C₃₁×#529	1	1	yes	characteristic
393	C₂	—	16	2	no	—
394	C₂	C₃₁×#2861	1	1	yes	characteristic
395	C₂	C₃₁×#3136	1	2	yes	—
396	C₂	C₃₁×#3174	1	1	yes	characteristic
397	C₂	C₃₁×#3176	1	1	yes	characteristic
398	C₂	C₃₁×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	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×#2647	C₂	semidirect
3. C₃₁×#1992	C₂	semidirect
4. C₃₁×#1991	C₂	semidirect
7. C₃₁×#1936	C₂	semidirect
8. C₃₁×#1936	C₂	semidirect
9. C₃₁×#1934	C₂	semidirect
10. C₃₁×#1934	C₂	semidirect
11. C₃₁×#1726	C₂	semidirect
128. #33284	C₃₁	direct (N × H)
171. #2647	C₂×C₃₁	semidirect
173. #1992	C₂×C₃₁	semidirect
174. #1991	C₂×C₃₁	semidirect
177. #1936	C₂×C₃₁	semidirect
178. #1936	C₂×C₃₁	semidirect
179. #1934	C₂×C₃₁	semidirect
180. #1934	C₂×C₃₁	semidirect
181. #1726	C₂×C₃₁	semidirect
277. C₃₁	#33284	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×#2647	2
C₃₁×#2641	2
C₃₁×#1992	2
C₃₁×#1991	2
C₃₁×#1961	2
C₃₁×#1957	2
C₃₁×#1936	2
C₃₁×#1934	2
C₃₁×#1726	2
#33284	31

Subgroups — C31×#33284 #21490043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33284 #21490043