Subgroups — C₃₁×#20510 #21477269

Order 7936.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#443	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2943	C₂	1	1	yes	maximal, characteristic
4	C₄×C₃₁×#131	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1773	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1765	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1764	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1759	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#131	C₂²	1	2	yes	—
14	C₂×C₃₁×#131	C₂²	1	2	yes	—
15	C₄×#41×C₃₁	C₂²	1	2	yes	—
16	C₃₁×#444	C₄	1	8	yes	complemented
17	C₃₁×#443	C₄	1	8	yes	complemented
18	C₃₁×#442	C₄	1	2	yes	complemented
19	C₃₁×#441	C₄	1	2	yes	complemented
20	C₃₁×#440	C₄	1	4	yes	complemented
21	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
23	C₃₁×#427	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#104	C₂²	1	2	yes	—
25	C₂×C₃₁×#104	C₂²	1	2	yes	—
26	C₃₁×#416	C₂²	1	2	yes	—
27	C₃₁×#405	—	2	2	no	—
28	C₃₁×#405	—	2	2	no	—
29	C₃₁×#405	C₂²	1	2	yes	—
30	C₃₁×#405	C₂²	1	2	yes	—
31	C₄×M₁₆×C₃₁	—	2	2	no	—
32	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
33	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₃₁	—	2	2	no	—
37	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#376	C₂²	1	1	yes	characteristic
41	C₃₁×#341	C₂²	1	2	yes	—
42	C₃₁×#339	C₂²	1	2	yes	—
43	C₃₁×#339	C₂²	1	2	yes	—
44	C₂×#41×C₃₁	C₂³	1	2	yes	—
45	C₃₁×#135	C₂×C₄	1	4	yes	—
46	C₃₁×#135	C₂×C₄	1	4	yes	—
47	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₃₁	C₂×C₄	1	2	yes	—
49	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
50	C₃₁×#131	—	2	4	no	—
51	C₃₁×#131	—	2	4	no	—
52	C₃₁×#131	C₂×C₄	1	8	yes	complemented
53	C₃₁×#131	C₂×C₄	1	8	yes	complemented
54	C₂×M₁₆×C₃₁	—	2	2	no	—
55	C₂×M₁₆×C₃₁	—	2	2	no	—
56	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₃₁	—	2	2	no	—
59	C₂²×C₈×C₃₁	—	2	2	no	—
60	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₃₁	C₂×C₄	1	4	yes	—
65	C₄×D₄×C₃₁	—	2	4	no	—
66	C₄×D₄×C₃₁	C₂×C₄	1	4	yes	—
67	C₃₁×#117	—	2	2	no	—
68	C₃₁×#117	C₂³	1	2	yes	—
69	C₂×C₄²×C₃₁	—	2	2	no	—
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
73	C₃₁×#108	C₂×C₄	1	4	yes	complemented
74	C₃₁×#108	C₂×C₄	1	4	yes	complemented
75	C₃₁×#107	C₂×C₄	1	2	yes	—
76	C₃₁×#106	C₂×C₄	1	2	yes	—
77	C₃₁×#104	C₂×C₄	1	8	yes	complemented
78	C₃₁×#104	C₂×C₄	1	8	yes	complemented
79	C₃₁×#103	C₂×C₄	1	4	yes	—
80	C₃₁×#102	C₂×C₄	1	4	yes	—
81	C₃₁×#97	—	2	2	no	—
82	C₃₁×#97	—	2	2	no	—
83	C₃₁×#97	—	2	2	no	—
84	C₃₁×#97	—	2	2	no	—
85	C₃₁×#97	C₂×C₄	1	2	yes	—
86	C₃₁×#97	C₂×C₄	1	2	yes	—
87	C₃₁×#97	C₂×C₄	1	4	yes	complemented
88	C₄×C₈×C₃₁	—	2	2	no	—
89	C₄×C₈×C₃₁	—	2	2	no	—
90	C₄×C₈×C₃₁	—	2	2	no	—
91	C₄×C₈×C₃₁	—	2	2	no	—
92	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	complemented
93	C₄×C₈×C₃₁	D₄	1	2	yes	—
94	C₄×C₈×C₃₁	D₄	1	2	yes	—
95	C₃₁×#95	—	2	2	no	—
96	#41×C₃₁	—	2	2	no	—
97	#41×C₃₁	—	2	2	no	—
98	#41×C₃₁	C₂²×C₄	1	4	yes	—
99	#41×C₃₁	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₃₁	—	2	2	no	—
102	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	1	no	—
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	2	4	no	—
107	C₂²×C₄×C₃₁	#41	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₃₁	C₄²	1	4	yes	—
110	SD₁₆×C₃₁	C₄²	1	8	yes	—
111	D₈×C₃₁	C₄²	1	4	yes	—
112	M₁₆×C₃₁	—	2	2	no	—
113	M₁₆×C₃₁	—	2	2	no	—
114	M₁₆×C₃₁	—	2	8	no	—
115	M₁₆×C₃₁	—	2	8	no	—
116	M₁₆×C₃₁	C₂²×C₄	1	4	yes	—
117	M₁₆×C₃₁	C₂²×C₄	1	4	yes	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	8	no	—
123	C₂×C₈×C₃₁	—	2	8	no	—
124	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₃₁	#41	1	2	yes	—
135	C₂×C₈×C₃₁	#41	1	2	yes	—
136	C₄⋊C₄×C₃₁	—	2	4	no	—
137	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
138	C₂²⋊C₄×C₃₁	—	2	2	no	—
139	C₂²⋊C₄×C₃₁	—	2	4	no	—
140	C₄²×C₃₁	—	2	4	no	—
141	C₄²×C₃₁	—	2	2	no	—
142	C₄²×C₃₁	—	2	1	no	—
143	C₄²×C₃₁	—	2	1	no	—
144	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
145	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
146	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
147	C₄²×C₃₁	C₂×D₄	1	2	yes	—
148	#20510	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₃₁	—	2	2	no	—
150	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
151	Q₈×C₃₁	—	2	2	no	—
152	Q₈×C₃₁	C₂×C₄²	1	4	yes	—
153	D₄×C₃₁	—	2	4	no	—
154	D₄×C₃₁	—	2	4	no	—
155	D₄×C₃₁	—	2	2	no	—
156	D₄×C₃₁	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	4	no	—
159	C₂×C₄×C₃₁	—	2	4	no	—
160	C₂×C₄×C₃₁	—	2	4	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	8	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
168	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₃₁	—	2	4	no	—
175	C₈×C₃₁	—	2	4	no	—
176	C₈×C₃₁	—	2	2	no	—
177	C₈×C₃₁	C₂×C₄²	1	2	yes	—
178	C₈×C₃₁	C₂×C₄²	1	2	yes	—
179	C₈×C₃₁	C₄×D₄	1	2	yes	—
180	C₈×C₃₁	C₄×D₄	1	4	yes	—
181	C₈×C₃₁	C₄×D₄	1	2	yes	—
182	C₂×#444	C₂×C₃₁	1	1	yes	characteristic
183	C₂×#443	C₂×C₃₁	1	1	yes	characteristic
184	#2943	C₂×C₃₁	1	1	yes	characteristic
185	C₄×#131	C₂×C₃₁	1	2	yes	complemented
186	#1778	C₂×C₃₁	1	1	yes	characteristic, complemented
187	#1773	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#1772	C₂×C₃₁	1	1	yes	characteristic, complemented
189	#1765	C₂×C₃₁	1	2	yes	complemented
190	#1764	C₂×C₃₁	1	2	yes	complemented
191	#1759	C₂×C₃₁	1	2	yes	complemented
192	#1726	C₂×C₃₁	1	1	yes	characteristic, complemented
193	C₂²×C₃₁	—	2	2	no	—
194	C₂²×C₃₁	—	2	4	no	—
195	C₂²×C₃₁	—	4	4	no	—
196	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
198	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
199	C₄×C₃₁	—	2	4	no	—
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	—	4	2	no	—
202	C₄×C₃₁	—	4	2	no	—
203	C₄×C₃₁	—	4	4	no	—
204	C₄×C₃₁	C₂²×C₄²	1	1	yes	characteristic
205	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₃₁	C₄×#41	1	1	yes	characteristic
208	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×#131	C₂²×C₃₁	1	2	yes	—
210	C₂×#131	C₂²×C₃₁	1	2	yes	—
211	C₄×#41	C₂²×C₃₁	1	2	yes	—
212	#444	C₄×C₃₁	1	8	yes	complemented
213	#443	C₄×C₃₁	1	8	yes	complemented
214	#442	C₄×C₃₁	1	2	yes	complemented
215	#441	C₄×C₃₁	1	2	yes	complemented
216	#440	C₄×C₃₁	1	4	yes	complemented
217	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
219	#427	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×#104	C₂²×C₃₁	1	2	yes	—
221	C₂×#104	C₂²×C₃₁	1	2	yes	—
222	#416	C₂²×C₃₁	1	2	yes	—
223	#405	—	2	2	no	—
224	#405	—	2	2	no	—
225	#405	C₂²×C₃₁	1	2	yes	—
226	#405	C₂²×C₃₁	1	2	yes	—
227	C₄×M₁₆	—	2	2	no	—
228	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
229	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₄×C₈	—	2	2	no	—
233	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
236	#376	C₂²×C₃₁	1	1	yes	characteristic
237	#341	C₂²×C₃₁	1	2	yes	—
238	#339	C₂²×C₃₁	1	2	yes	—
239	#339	C₂²×C₃₁	1	2	yes	—
240	C₂×C₃₁	—	2	1	no	—
241	C₂×C₃₁	—	2	1	no	—
242	C₂×C₃₁	—	4	4	no	—
243	C₂×C₃₁	C₄²×D₄	1	1	yes	characteristic
244	C₂×C₃₁	#2955	1	2	yes	—
245	C₂×#41	C₂³×C₃₁	1	2	yes	—
246	#135	C₂×C₄×C₃₁	1	4	yes	—
247	#135	C₂×C₄×C₃₁	1	4	yes	—
248	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
249	C₂×SD₁₆	C₂×C₄×C₃₁	1	2	yes	—
250	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
251	#131	—	2	4	no	—
252	#131	—	2	4	no	—
253	#131	C₂×C₄×C₃₁	1	8	yes	complemented
254	#131	C₂×C₄×C₃₁	1	8	yes	complemented
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
258	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₄×Q₈	C₂×C₄×C₃₁	1	4	yes	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	C₂×C₄×C₃₁	1	4	yes	—
268	#117	—	2	2	no	—
269	#117	C₂³×C₃₁	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
274	#108	C₂×C₄×C₃₁	1	4	yes	complemented
275	#108	C₂×C₄×C₃₁	1	4	yes	complemented
276	#107	C₂×C₄×C₃₁	1	2	yes	—
277	#106	C₂×C₄×C₃₁	1	2	yes	—
278	#104	C₂×C₄×C₃₁	1	8	yes	complemented
279	#104	C₂×C₄×C₃₁	1	8	yes	complemented
280	#103	C₂×C₄×C₃₁	1	4	yes	—
281	#102	C₂×C₄×C₃₁	1	4	yes	—
282	#97	—	2	2	no	—
283	#97	—	2	2	no	—
284	#97	—	2	2	no	—
285	#97	—	2	2	no	—
286	#97	C₂×C₄×C₃₁	1	2	yes	—
287	#97	C₂×C₄×C₃₁	1	2	yes	—
288	#97	C₂×C₄×C₃₁	1	4	yes	complemented
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	complemented
294	C₄×C₈	D₄×C₃₁	1	2	yes	—
295	C₄×C₈	D₄×C₃₁	1	2	yes	—
296	#95	—	2	2	no	—
297	C₃₁	#20510	1	1	yes	characteristic, direct product factor, Sylow
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	C₂²×C₄×C₃₁	1	4	yes	—
301	#41	C₂²×C₄×C₃₁	1	4	yes	—
302	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	#41×C₃₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
311	Q₁₆	C₄²×C₃₁	1	4	yes	—
312	SD₁₆	C₄²×C₃₁	1	8	yes	—
313	D₈	C₄²×C₃₁	1	4	yes	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	8	no	—
317	M₁₆	—	2	8	no	—
318	M₁₆	C₂²×C₄×C₃₁	1	4	yes	—
319	M₁₆	C₂²×C₄×C₃₁	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	8	no	—
326	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
327	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
329	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
330	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
331	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
334	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
336	C₂×C₈	#41×C₃₁	1	2	yes	—
337	C₂×C₈	#41×C₃₁	1	2	yes	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
347	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
348	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
349	C₄²	C₂×D₄×C₃₁	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	C₂×C₄²×C₃₁	1	4	yes	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	C₂×C₄²×C₃₁	1	4	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	C₂×C₄²×C₃₁	1	2	yes	—
379	C₈	C₂×C₄²×C₃₁	1	2	yes	—
380	C₈	C₄×D₄×C₃₁	1	2	yes	—
381	C₈	C₄×D₄×C₃₁	1	4	yes	—
382	C₈	C₄×D₄×C₃₁	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
387	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
388	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	C₂²×C₄²×C₃₁	1	1	yes	characteristic
395	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
396	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
397	C₄	C₄×#41×C₃₁	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	4	4	no	—
401	C₂	C₄²×D₄×C₃₁	1	1	yes	characteristic
402	C₂	C₃₁×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂×D₄
commutator	C₄	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄×C₃₁×#131	C₂	semidirect
5. C₃₁×#1778	C₂	semidirect
6. C₃₁×#1773	C₂	semidirect
7. C₃₁×#1772	C₂	semidirect
8. C₃₁×#1765	C₂	semidirect
9. C₃₁×#1764	C₂	semidirect
10. C₃₁×#1759	C₂	semidirect
11. C₃₁×#1726	C₂	semidirect
16. C₃₁×#444	C₄	semidirect
17. C₃₁×#443	C₄	semidirect
18. C₃₁×#442	C₄	semidirect
19. C₃₁×#441	C₄	semidirect
20. C₃₁×#440	C₄	semidirect
52. C₃₁×#131	C₂×C₄	semidirect
53. C₃₁×#131	C₂×C₄	semidirect
73. C₃₁×#108	C₂×C₄	semidirect
74. C₃₁×#108	C₂×C₄	semidirect
77. C₃₁×#104	C₂×C₄	semidirect
78. C₃₁×#104	C₂×C₄	semidirect
87. C₃₁×#97	C₂×C₄	semidirect
92. C₄×C₈×C₃₁	C₂×C₄	semidirect
148. #20510	C₃₁	direct (N × H)
185. C₄×#131	C₂×C₃₁	semidirect
186. #1778	C₂×C₃₁	semidirect
187. #1773	C₂×C₃₁	semidirect
188. #1772	C₂×C₃₁	semidirect
189. #1765	C₂×C₃₁	semidirect
190. #1764	C₂×C₃₁	semidirect
191. #1759	C₂×C₃₁	semidirect
192. #1726	C₂×C₃₁	semidirect
212. #444	C₄×C₃₁	semidirect
213. #443	C₄×C₃₁	semidirect
214. #442	C₄×C₃₁	semidirect
215. #441	C₄×C₃₁	semidirect
216. #440	C₄×C₃₁	semidirect
253. #131	C₂×C₄×C₃₁	semidirect
254. #131	C₂×C₄×C₃₁	semidirect
274. #108	C₂×C₄×C₃₁	semidirect
275. #108	C₂×C₄×C₃₁	semidirect
278. #104	C₂×C₄×C₃₁	semidirect
279. #104	C₂×C₄×C₃₁	semidirect
288. #97	C₂×C₄×C₃₁	semidirect
293. C₄×C₈	C₂×C₄×C₃₁	semidirect
297. C₃₁	#20510	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×#444	2
C₂×C₃₁×#443	2
C₃₁×#2943	2
C₄×C₃₁×#131	2
C₃₁×#1778	2
C₃₁×#1773	2
C₃₁×#1772	2
C₃₁×#1765	2
C₃₁×#1764	2
C₃₁×#1759	2
C₃₁×#1726	2
#20510	31

Subgroups — C31×#20510 #21477269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20510 #21477269