Subgroups — C₃₁×#10851 #21467610

Order 7936.

978 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×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#339	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
6	C₂×C₃₁×#117	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
8	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
9	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₄×M₁₆×C₃₁	—	2	2	no	—
11	C₄×M₁₆×C₃₁	C₄	1	4	yes	complemented
12	C₂×C₃₁×#97	—	2	1	no	—
13	C₂×C₄×C₈×C₃₁	—	2	1	no	—
14	C₃₁×#384	C₄	1	2	yes	complemented
15	C₃₁×#382	C₄	1	2	yes	complemented
16	C₃₁×#380	—	2	1	no	—
17	C₃₁×#380	—	2	1	no	—
18	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
19	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
20	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
21	C₄×C₄⋊C₄×C₃₁	C₄	1	4	yes	complemented
22	C₂×C₃₁×#95	—	2	1	no	—
23	C₃₁×#339	—	2	8	no	—
24	C₂³×C₄×C₃₁	—	2	2	no	—
25	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₃₁	—	2	2	no	—
29	C₂×M₁₆×C₃₁	—	2	2	no	—
30	C₂×M₁₆×C₃₁	—	2	2	no	—
31	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
32	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
33	C₂×M₁₆×C₃₁	Q₈	1	4	yes	—
34	C₂²×C₈×C₃₁	—	2	2	no	—
35	C₃₁×#117	—	2	4	no	—
36	C₃₁×#117	—	2	4	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
42	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
43	C₂×C₄²×C₃₁	—	2	4	no	—
44	C₂×C₄²×C₃₁	—	2	4	no	—
45	C₂×C₄²×C₃₁	—	2	2	no	—
46	C₂×C₄²×C₃₁	—	2	2	no	—
47	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	D₄	1	2	yes	—
53	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	Q₈	1	2	yes	—
56	C₃₁×#97	—	2	4	no	—
57	C₄×C₈×C₃₁	—	2	4	no	—
58	C₃₁×#95	—	2	4	no	—
59	C₃₁×#95	—	2	2	no	—
60	C₃₁×#95	—	2	2	no	—
61	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₃₁	—	2	4	no	—
63	C₂²×C₄×C₃₁	—	2	8	no	—
64	C₂²×C₄×C₃₁	—	2	4	no	—
65	C₂²×C₄×C₃₁	—	2	4	no	—
66	C₂²×C₄×C₃₁	—	4	2	no	—
67	C₂²×C₄×C₃₁	—	4	4	no	—
68	C₂²×C₄×C₃₁	—	4	2	no	—
69	C₂²×C₄×C₃₁	—	4	2	no	—
70	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₃₁	#41	1	2	yes	—
87	C₂²×C₄×C₃₁	#41	1	2	yes	—
88	M₁₆×C₃₁	—	2	4	no	—
89	M₁₆×C₃₁	—	2	4	no	—
90	M₁₆×C₃₁	—	2	4	no	—
91	M₁₆×C₃₁	C₄⋊C₄	1	8	yes	complemented
92	C₂×C₈×C₃₁	—	2	4	no	—
93	C₂×C₈×C₃₁	—	2	4	no	—
94	C₂×C₈×C₃₁	—	2	4	no	—
95	C₄⋊C₄×C₃₁	—	2	16	no	—
96	C₄⋊C₄×C₃₁	—	2	8	no	—
97	C₄⋊C₄×C₃₁	—	4	4	no	—
98	C₄⋊C₄×C₃₁	—	4	4	no	—
99	C₂²⋊C₄×C₃₁	—	4	2	no	—
100	C₂²⋊C₄×C₃₁	—	4	2	no	—
101	C₄²×C₃₁	—	2	8	no	—
102	C₄²×C₃₁	—	4	4	no	—
103	C₄²×C₃₁	—	4	4	no	—
104	C₄²×C₃₁	C₄²	1	2	yes	—
105	C₄²×C₃₁	C₄²	1	2	yes	—
106	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
107	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
108	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
109	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
110	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
111	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
112	#10851	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₃₁	#124	1	1	yes	characteristic
119	C₂³×C₃₁	#124	1	1	yes	characteristic
120	C₂³×C₃₁	#127	1	1	yes	characteristic
121	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	4	no	—
126	C₂×C₄×C₃₁	—	2	4	no	—
127	C₂×C₄×C₃₁	—	2	8	no	—
128	C₂×C₄×C₃₁	—	4	2	no	—
129	C₂×C₄×C₃₁	—	4	2	no	—
130	C₂×C₄×C₃₁	—	4	8	no	—
131	C₂×C₄×C₃₁	—	4	8	no	—
132	C₂×C₄×C₃₁	—	4	4	no	—
133	C₂×C₄×C₃₁	—	4	4	no	—
134	C₂×C₄×C₃₁	—	4	4	no	—
135	C₂×C₄×C₃₁	—	4	4	no	—
136	C₂×C₄×C₃₁	—	4	4	no	—
137	C₂×C₄×C₃₁	#95	1	2	yes	—
138	C₂×C₄×C₃₁	#95	1	2	yes	—
139	C₂×C₄×C₃₁	#95	1	2	yes	—
140	C₂×C₄×C₃₁	#95	1	2	yes	—
141	C₂×C₄×C₃₁	#104	1	4	yes	—
142	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	#117	1	2	yes	—
148	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₃₁	#121	1	2	yes	—
153	C₂×C₄×C₃₁	#121	1	2	yes	—
154	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₃₁	#125	1	2	yes	—
157	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
158	C₈×C₃₁	—	2	8	no	—
159	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
160	#2285	C₂×C₃₁	1	1	yes	characteristic
161	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
162	C₂×#339	C₂×C₃₁	1	4	yes	—
163	C₂²×C₃₁	—	2	2	no	—
164	C₂²×C₃₁	—	2	2	no	—
165	C₂²×C₃₁	—	2	2	no	—
166	C₂²×C₃₁	—	2	2	no	—
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
172	C₂²×C₃₁	#382	1	1	yes	characteristic
173	C₂²×C₃₁	#384	1	1	yes	characteristic
174	C₂²×C₃₁	#390	1	1	yes	characteristic
175	C₂²×C₃₁	#390	1	1	yes	characteristic
176	C₂²×C₃₁	#391	1	1	yes	characteristic
177	C₂²×C₃₁	#391	1	1	yes	characteristic
178	C₂²×C₃₁	C₂×#104	1	2	yes	—
179	C₂²×C₃₁	#421	1	2	yes	—
180	C₄×C₃₁	—	2	2	no	—
181	C₄×C₃₁	—	2	2	no	—
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	4	8	no	—
184	C₄×C₃₁	—	8	4	no	—
185	C₄×C₃₁	#339	1	4	yes	complemented
186	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
187	C₄×C₃₁	#380	1	2	yes	—
188	C₄×C₃₁	#389	1	2	yes	—
189	C₄×C₃₁	#389	1	2	yes	—
190	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
191	C₂×#117	C₂²×C₃₁	1	2	yes	—
192	C₂²×C₄⋊C₄	—	2	1	no	—
193	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
194	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
195	C₄×M₁₆	—	2	2	no	—
196	C₄×M₁₆	C₄×C₃₁	1	4	yes	complemented
197	C₂×#97	—	2	1	no	—
198	C₂×C₄×C₈	—	2	1	no	—
199	#384	C₄×C₃₁	1	2	yes	complemented
200	#382	C₄×C₃₁	1	2	yes	complemented
201	#380	—	2	1	no	—
202	#380	—	2	1	no	—
203	C₄×C₄⋊C₄	—	2	2	no	—
204	C₄×C₄⋊C₄	—	2	1	no	—
205	C₄×C₄⋊C₄	—	2	1	no	—
206	C₄×C₄⋊C₄	C₄×C₃₁	1	4	yes	complemented
207	C₂×#95	—	2	1	no	—
208	#339	—	2	8	no	—
209	C₂×C₃₁	—	2	1	no	—
210	C₂×C₃₁	—	2	1	no	—
211	C₂×C₃₁	—	2	1	no	—
212	C₂×C₃₁	—	2	1	no	—
213	C₂×C₃₁	C₄⋊#95	1	1	yes	characteristic
214	C₂×C₃₁	C₂×#339	1	1	yes	characteristic
215	C₂×C₃₁	#1733	1	1	yes	characteristic
216	C₂×C₃₁	#1980	1	2	yes	—
217	C₂×C₃₁	#1986	1	2	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
226	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
227	C₂×M₁₆	Q₈×C₃₁	1	4	yes	—
228	C₂²×C₈	—	2	2	no	—
229	#117	—	2	4	no	—
230	#117	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	8	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
242	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
243	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
244	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₃₁	1	2	yes	—
249	C₂×C₄²	Q₈×C₃₁	1	2	yes	—
250	#97	—	2	4	no	—
251	C₄×C₈	—	2	4	no	—
252	#95	—	2	4	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	C₃₁	#10851	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
270	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
272	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
281	C₂²×C₄	#41×C₃₁	1	2	yes	—
282	C₂²×C₄	#41×C₃₁	1	2	yes	—
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	C₄⋊C₄×C₃₁	1	8	yes	complemented
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₄⋊C₄	—	2	16	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₄²	—	2	8	no	—
297	C₄²	—	4	4	no	—
298	C₄²	—	4	4	no	—
299	C₄²	C₄²×C₃₁	1	2	yes	—
300	C₄²	C₄²×C₃₁	1	2	yes	—
301	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
302	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
303	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
304	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
305	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
306	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
310	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
311	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
312	C₂³	C₃₁×#124	1	1	yes	characteristic
313	C₂³	C₃₁×#124	1	1	yes	characteristic
314	C₂³	C₃₁×#127	1	1	yes	characteristic
315	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	C₃₁×#95	1	2	yes	—
332	C₂×C₄	C₃₁×#95	1	2	yes	—
333	C₂×C₄	C₃₁×#95	1	2	yes	—
334	C₂×C₄	C₃₁×#95	1	2	yes	—
335	C₂×C₄	C₃₁×#104	1	4	yes	—
336	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
339	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₃₁×#117	1	2	yes	—
342	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
343	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
344	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
345	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
346	C₂×C₄	C₃₁×#121	1	2	yes	—
347	C₂×C₄	C₃₁×#121	1	2	yes	—
348	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
349	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
350	C₂×C₄	C₃₁×#125	1	2	yes	—
351	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
362	C₂²	C₃₁×#382	1	1	yes	characteristic
363	C₂²	C₃₁×#384	1	1	yes	characteristic
364	C₂²	C₃₁×#390	1	1	yes	characteristic
365	C₂²	C₃₁×#390	1	1	yes	characteristic
366	C₂²	C₃₁×#391	1	1	yes	characteristic
367	C₂²	C₃₁×#391	1	1	yes	characteristic
368	C₂²	C₂×C₃₁×#104	1	2	yes	—
369	C₂²	C₃₁×#421	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	8	no	—
374	C₄	—	8	4	no	—
375	C₄	C₃₁×#339	1	4	yes	complemented
376	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
377	C₄	C₃₁×#380	1	2	yes	—
378	C₄	C₃₁×#389	1	2	yes	—
379	C₄	C₃₁×#389	1	2	yes	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	C₃₁×C₄⋊#95	1	1	yes	characteristic
385	C₂	C₂×C₃₁×#339	1	1	yes	characteristic
386	C₂	C₃₁×#1733	1	1	yes	characteristic
387	C₂	C₃₁×#1980	1	2	yes	—
388	C₂	C₃₁×#1986	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂³×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₄×M₁₆×C₃₁	C₄	semidirect
14. C₃₁×#384	C₄	semidirect
15. C₃₁×#382	C₄	semidirect
21. C₄×C₄⋊C₄×C₃₁	C₄	semidirect
91. M₁₆×C₃₁	C₄⋊C₄	semidirect
112. #10851	C₃₁	direct (N × H)
185. C₄×C₃₁	#339	semidirect
196. C₄×M₁₆	C₄×C₃₁	semidirect
199. #384	C₄×C₃₁	semidirect
200. #382	C₄×C₃₁	semidirect
206. C₄×C₄⋊C₄	C₄×C₃₁	semidirect
255. C₃₁	#10851	direct (N × H)
286. M₁₆	C₄⋊C₄×C₃₁	semidirect
375. C₄	C₃₁×#339	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#2285	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₂×C₃₁×#339	2
#10851	31

Subgroups — C31×#10851 #21467610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10851 #21467610