Subgroups — C₂×C₃₁×#1531 #21474403

Order 7936.

1050 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃₁×#97	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1531	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#330	C₂	1	4	yes	maximal, complemented
6	C₂³×C₈×C₃₁	—	2	1	no	—
7	C₃₁×#533	—	2	2	no	—
8	C₃₁×#533	—	2	2	no	—
9	C₃₁×#533	C₄	1	4	yes	—
10	C₃₁×#533	C₂²	1	4	yes	—
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₃₁×#125	C₂²	1	2	yes	—
14	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
18	C₂×C₃₁×#117	C₄	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#432	—	2	2	no	—
21	C₃₁×#432	C₂²	1	4	yes	—
22	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
23	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
24	C₂×C₃₁×#97	—	2	1	no	—
25	C₂×C₃₁×#97	—	2	2	no	—
26	C₂×C₃₁×#97	C₂²	1	2	yes	—
27	C₂×C₃₁×#97	C₂²	1	4	yes	—
28	C₂×C₃₁×#97	C₂²	1	2	yes	—
29	C₃₁×#330	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₃₁	—	2	1	no	—
31	C₂²×Q₈×C₃₁	—	2	1	no	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	—	2	8	no	—
36	C₂²×C₈×C₃₁	—	2	4	no	—
37	C₂²×C₈×C₃₁	—	2	2	no	—
38	C₂²×C₈×C₃₁	—	2	2	no	—
39	C₃₁×C₄⋊Q₈	—	2	2	no	—
40	C₃₁×C₄⋊Q₈	—	2	2	no	—
41	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
42	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
43	C₃₁×#125	—	2	2	no	—
44	C₃₁×#125	—	2	2	no	—
45	C₃₁×#125	C₂×C₄	1	4	yes	—
46	C₃₁×#125	C₂³	1	4	yes	—
47	C₃₁×C₂²⋊Q₈	—	2	4	no	—
48	C₃₁×C₂²⋊Q₈	—	2	4	no	—
49	C₃₁×C₂²⋊Q₈	—	2	4	no	—
50	C₃₁×C₂²⋊Q₈	—	2	4	no	—
51	C₄×Q₈×C₃₁	—	2	4	no	—
52	C₄×Q₈×C₃₁	—	2	4	no	—
53	C₄×Q₈×C₃₁	—	2	4	no	—
54	C₄×Q₈×C₃₁	—	2	4	no	—
55	C₃₁×#117	—	2	4	no	—
56	C₃₁×#117	C₂×C₄	1	8	yes	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	D₄	1	2	yes	—
69	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	D₄	1	2	yes	—
71	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	—	2	4	no	—
74	C₃₁×C₂²⋊C₈	—	2	4	no	—
75	C₃₁×#97	—	2	4	no	—
76	C₃₁×#97	—	2	2	no	—
77	C₃₁×#97	—	2	2	no	—
78	C₃₁×#97	C₂³	1	4	yes	—
79	C₃₁×#97	C₂³	1	4	yes	—
80	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Q₈×C₃₁	—	2	4	no	—
82	C₂×Q₈×C₃₁	—	2	4	no	—
83	C₂×Q₈×C₃₁	—	4	4	no	—
84	C₂×Q₈×C₃₁	—	4	4	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	2	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	4	2	no	—
90	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₃₁	—	2	8	no	—
103	C₂×C₈×C₃₁	—	2	16	no	—
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	—	2	4	no	—
106	C₂×C₈×C₃₁	—	4	4	no	—
107	C₄⋊C₄×C₃₁	—	2	4	no	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	4	no	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₄⋊C₄×C₃₁	—	2	4	no	—
115	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
117	C₂²⋊C₄×C₃₁	—	2	8	no	—
118	C₄²×C₃₁	—	2	8	no	—
119	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
124	C₄²×C₃₁	C₂×D₄	1	2	yes	—
125	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₃₁	C₂×D₄	1	2	yes	—
128	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
129	C₂×#1531	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	2	no	—
132	C₂³×C₃₁	#101	1	4	yes	—
133	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	Q₈×C₃₁	—	4	8	no	—
136	Q₈×C₃₁	—	4	8	no	—
137	C₂×C₄×C₃₁	—	2	4	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	4	no	—
145	C₂×C₄×C₃₁	—	2	4	no	—
146	C₂×C₄×C₃₁	—	2	4	no	—
147	C₂×C₄×C₃₁	—	2	4	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	4	no	—
151	C₂×C₄×C₃₁	—	4	4	no	—
152	C₂×C₄×C₃₁	#104	1	4	yes	—
153	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₃₁	—	2	8	no	—
163	C₈×C₃₁	—	4	4	no	—
164	C₂×#533	C₂×C₃₁	1	1	yes	characteristic
165	C₂×#432	C₂×C₃₁	1	1	yes	characteristic
166	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic
167	#1531	C₂×C₃₁	1	8	yes	direct product factor
168	C₂×#330	C₂×C₃₁	1	4	yes	complemented
169	C₂²×C₃₁	—	2	2	no	—
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	2	8	no	—
172	C₂²×C₃₁	C₂×#101	1	4	yes	—
173	C₂²×C₃₁	C₂×#101	1	2	yes	—
174	C₂²×C₃₁	C₂×#104	1	2	yes	—
175	C₂²×C₃₁	#421	1	2	yes	—
176	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	2	1	no	—
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	4	4	no	—
186	C₄×C₃₁	—	4	4	no	—
187	C₄×C₃₁	C₂×#104	1	4	yes	—
188	C₂³×C₈	—	2	1	no	—
189	#533	—	2	2	no	—
190	#533	—	2	2	no	—
191	#533	C₄×C₃₁	1	4	yes	—
192	#533	C₂²×C₃₁	1	4	yes	—
193	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
195	C₂×#125	C₂²×C₃₁	1	2	yes	—
196	C₂×C₂²⋊Q₈	—	2	1	no	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₄×Q₈	—	2	1	no	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×#117	C₄×C₃₁	1	2	yes	—
201	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
202	#432	—	2	2	no	—
203	#432	C₂²×C₃₁	1	4	yes	—
204	C₂×C₄⋊C₈	—	2	1	no	—
205	C₂×C₂²⋊C₈	—	2	1	no	—
206	C₂×#97	—	2	1	no	—
207	C₂×#97	—	2	2	no	—
208	C₂×#97	C₂²×C₃₁	1	2	yes	—
209	C₂×#97	C₂²×C₃₁	1	4	yes	—
210	C₂×#97	C₂²×C₃₁	1	2	yes	—
211	#330	C₂²×C₃₁	1	16	yes	complemented
212	C₂×C₃₁	—	2	4	no	—
213	C₂×C₃₁	#1531	1	4	yes	direct product factor
214	C₂×C₃₁	C₂²×#101	1	1	yes	characteristic
215	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
216	C₂×C₃₁	C₂×#421	1	1	yes	characteristic
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	—	2	1	no	—
219	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
222	C₂²×C₈	—	2	8	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
229	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
230	#125	—	2	2	no	—
231	#125	—	2	2	no	—
232	#125	C₂×C₄×C₃₁	1	4	yes	—
233	#125	C₂³×C₃₁	1	4	yes	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	#117	—	2	4	no	—
243	#117	C₂×C₄×C₃₁	1	8	yes	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
254	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₃₁	1	2	yes	—
257	C₂×C₄²	D₄×C₃₁	1	2	yes	—
258	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
260	C₄⋊C₈	—	2	4	no	—
261	C₂²⋊C₈	—	2	4	no	—
262	#97	—	2	4	no	—
263	#97	—	2	2	no	—
264	#97	—	2	2	no	—
265	#97	C₂³×C₃₁	1	4	yes	—
266	#97	C₂³×C₃₁	1	4	yes	—
267	C₃₁	C₂×#1531	1	1	yes	characteristic, direct product factor, Sylow
268	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
281	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
283	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	4	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
304	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
305	C₂²⋊C₄	—	2	8	no	—
306	C₄²	—	2	8	no	—
307	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
308	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
309	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
310	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
311	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
312	C₄²	C₂×D₄×C₃₁	1	2	yes	—
313	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₃₁	1	2	yes	—
316	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	C₃₁×#101	1	4	yes	—
320	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
322	Q₈	—	4	8	no	—
323	Q₈	—	4	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	C₃₁×#104	1	4	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
346	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₈	—	2	8	no	—
350	C₈	—	4	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	8	no	—
354	C₂²	C₂×C₃₁×#101	1	4	yes	—
355	C₂²	C₂×C₃₁×#101	1	2	yes	—
356	C₂²	C₂×C₃₁×#104	1	2	yes	—
357	C₂²	C₃₁×#421	1	2	yes	—
358	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	4	no	—
369	C₄	C₂×C₃₁×#104	1	4	yes	—
370	C₂	—	2	4	no	—
371	C₂	C₃₁×#1531	1	4	yes	direct product factor
372	C₂	C₂²×C₃₁×#101	1	1	yes	characteristic
373	C₂	C₂²×C₃₁×#104	1	1	yes	characteristic
374	C₂	C₂×C₃₁×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1531	C₂	direct (N × H)
5. C₂×C₃₁×#330	C₂	semidirect
29. C₃₁×#330	C₂²	semidirect
129. C₂×#1531	C₃₁	direct (N × H)
167. #1531	C₂×C₃₁	direct (N × H)
168. C₂×#330	C₂×C₃₁	semidirect
211. #330	C₂²×C₃₁	semidirect
213. C₂×C₃₁	#1531	direct (N × H)
267. C₃₁	C₂×#1531	direct (N × H)
371. C₂	C₃₁×#1531	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#533	2
C₂×C₃₁×#432	2
C₂²×C₃₁×#97	2
C₃₁×#1531	2
C₂×C₃₁×#330	2
C₂×#1531	31

Subgroups — C2×C31×#1531 #21474403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1531 #21474403