Subgroups — C₃₁×#26060 #21482819

Order 7936.

894 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#106	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2440	C₂	1	2	yes	maximal
4	C₃₁×#2084	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2058	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1853	C₂	1	2	yes	maximal
9	C₃₁×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1807	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₃₁×#498	—	2	4	no	—
17	C₂×C₃₁×#106	—	2	4	no	—
18	C₂×C₃₁×#106	C₂²	1	2	yes	—
19	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#106	C₂²	1	2	yes	—
22	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#106	C₂²	1	2	yes	—
24	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#398	—	2	2	no	—
29	C₃₁×#395	—	2	2	no	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#389	C₂²	1	2	yes	—
32	C₃₁×#385	—	2	2	no	—
33	C₃₁×#384	C₂²	1	2	yes	—
34	C₃₁×#380	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₃₁	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	C₃₁×#336	C₂²	1	1	yes	characteristic
40	C₃₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₁	—	2	2	no	—
42	C₂³×C₄×C₃₁	—	2	2	no	—
43	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×C₄⋊Q₈	—	2	4	no	—
52	C₃₁×C₄⋊Q₈	—	4	2	no	—
53	C₃₁×C₂²⋊Q₈	—	4	8	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
68	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×#106	—	2	2	no	—
71	C₃₁×#106	—	2	2	no	—
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	—	2	4	no	—
74	C₃₁×#106	—	2	4	no	—
75	C₃₁×#106	—	4	2	no	—
76	C₃₁×#106	D₄	1	4	yes	—
77	C₃₁×C₂²⋊C₈	Q₈	1	4	yes	complemented
78	C₄×C₈×C₃₁	—	2	2	no	—
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₃₁×#95	—	2	2	no	—
81	C₃₁×#95	—	2	2	no	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	D₄	1	2	yes	—
84	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₃₁	—	4	4	no	—
86	C₂×Q₈×C₃₁	—	4	4	no	—
87	C₂×Q₈×C₃₁	—	8	2	no	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	2	1	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	4	4	no	—
97	C₂²×C₄×C₃₁	—	4	4	no	—
98	C₂²×C₄×C₃₁	—	8	2	no	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₃₁	—	2	1	no	—
106	C₂×C₈×C₃₁	—	2	1	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	—	2	8	no	—
112	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₃₁	#41	1	2	yes	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	4	4	no	—
126	C₄⋊C₄×C₃₁	—	4	4	no	—
127	C₄⋊C₄×C₃₁	—	4	4	no	—
128	C₄⋊C₄×C₃₁	—	4	4	no	—
129	C₄⋊C₄×C₃₁	—	4	4	no	—
130	C₄⋊C₄×C₃₁	—	8	2	no	—
131	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₃₁	—	4	4	no	—
133	C₂²⋊C₄×C₃₁	SD₁₆	1	8	yes	—
134	C₄²×C₃₁	—	2	1	no	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	#26060	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	—	2	1	no	—
140	C₂³×C₃₁	—	2	1	no	—
141	C₂³×C₃₁	—	2	2	no	—
142	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
143	C₂³×C₃₁	C₂×SD₁₆	1	4	yes	—
144	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₃₁	—	8	8	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	1	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	4	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	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	8	8	no	—
169	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
170	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
171	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
178	C₈×C₃₁	—	2	2	no	—
179	C₈×C₃₁	—	2	2	no	—
180	C₈×C₃₁	—	2	2	no	—
181	C₈×C₃₁	C₂²⋊Q₈	1	4	yes	complemented
182	C₂×#498	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×#106	C₂×C₃₁	1	1	yes	characteristic
184	#2440	C₂×C₃₁	1	2	yes	—
185	#2084	C₂×C₃₁	1	2	yes	complemented
186	#2058	C₂×C₃₁	1	2	yes	complemented
187	#1941	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#1941	C₂×C₃₁	1	1	yes	characteristic, complemented
189	#1853	C₂×C₃₁	1	2	yes	—
190	#1844	C₂×C₃₁	1	1	yes	characteristic, complemented
191	#1807	C₂×C₃₁	1	1	yes	characteristic
192	C₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
193	C₂²×C₃₁	—	2	4	no	—
194	C₂²×C₃₁	—	2	2	no	—
195	C₂²×C₃₁	—	2	2	no	—
196	C₂²×C₃₁	—	2	4	no	—
197	C₂²×C₃₁	#498	1	4	yes	complemented
198	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
199	C₂²×C₃₁	D₄²	1	1	yes	characteristic
200	C₂²×C₃₁	#547	1	1	yes	characteristic
201	C₂²×C₃₁	C₂²×SD₁₆	1	2	yes	—
202	C₂²×C₃₁	#577	1	2	yes	—
203	C₄×C₃₁	—	2	4	no	—
204	C₄×C₃₁	—	2	2	no	—
205	C₄×C₃₁	—	2	4	no	—
206	C₄×C₃₁	—	4	4	no	—
207	C₄×C₃₁	—	8	2	no	—
208	C₄×C₃₁	—	8	2	no	—
209	C₄×C₃₁	—	8	2	no	—
210	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₄×C₃₁	#544	1	1	yes	characteristic
212	C₄×C₃₁	D₄×Q₈	1	1	yes	characteristic
213	C₄×C₃₁	#554	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
216	C₂×C₂²⋊Q₈	—	2	2	no	—
217	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
218	#498	—	2	4	no	—
219	C₂×#106	—	2	4	no	—
220	C₂×#106	C₂²×C₃₁	1	2	yes	—
221	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×#106	C₂²×C₃₁	1	2	yes	—
224	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
225	C₂×#106	C₂²×C₃₁	1	2	yes	—
226	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
230	#398	—	2	2	no	—
231	#395	—	2	2	no	—
232	#389	C₂²×C₃₁	1	2	yes	—
233	#389	C₂²×C₃₁	1	2	yes	—
234	#385	—	2	2	no	—
235	#384	C₂²×C₃₁	1	2	yes	—
236	#380	C₂²×C₃₁	1	2	yes	—
237	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
238	#340	C₂²×C₃₁	1	2	yes	—
239	#340	C₂²×C₃₁	1	2	yes	—
240	#340	C₂²×C₃₁	1	2	yes	—
241	#336	C₂²×C₃₁	1	1	yes	characteristic
242	#336	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×C₃₁	—	2	4	no	—
244	C₂×C₃₁	#2440	1	1	yes	characteristic
245	C₂×C₃₁	C₂×#498	1	1	yes	characteristic
246	C₂×C₃₁	#3163	1	1	yes	characteristic
247	C₂×C₃₁	D₄×SD₁₆	1	2	yes	—
248	C₂×C₃₁	#3335	1	2	yes	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	Q₈×C₃₁	1	4	yes	complemented
255	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₄⋊Q₈	—	2	4	no	—
260	C₄⋊Q₈	—	4	2	no	—
261	C₂²⋊Q₈	—	4	8	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	4	2	no	—
270	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
276	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
278	#106	—	2	2	no	—
279	#106	—	2	2	no	—
280	#106	—	2	2	no	—
281	#106	—	2	4	no	—
282	#106	—	2	4	no	—
283	#106	—	4	2	no	—
284	#106	D₄×C₃₁	1	4	yes	—
285	C₂²⋊C₈	Q₈×C₃₁	1	4	yes	complemented
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	D₄×C₃₁	1	2	yes	—
292	C₃₁	#26060	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
311	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
312	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
322	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
323	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
324	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
325	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
326	C₂×C₈	#41×C₃₁	1	2	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	SD₁₆×C₃₁	1	8	yes	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
351	C₂³	C₂×SD₁₆×C₃₁	1	4	yes	—
352	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	Q₈	—	8	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	8	no	—
377	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
378	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
379	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
382	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
384	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	C₃₁×C₂²⋊Q₈	1	4	yes	complemented
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	4	no	—
394	C₂²	C₃₁×#498	1	4	yes	complemented
395	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
396	C₂²	D₄²×C₃₁	1	1	yes	characteristic
397	C₂²	C₃₁×#547	1	1	yes	characteristic
398	C₂²	C₂²×SD₁₆×C₃₁	1	2	yes	—
399	C₂²	C₃₁×#577	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
408	C₄	C₃₁×#544	1	1	yes	characteristic
409	C₄	D₄×Q₈×C₃₁	1	1	yes	characteristic
410	C₄	C₃₁×#554	1	1	yes	characteristic
411	C₂	—	2	4	no	—
412	C₂	C₃₁×#2440	1	1	yes	characteristic
413	C₂	C₂×C₃₁×#498	1	1	yes	characteristic
414	C₂	C₃₁×#3163	1	1	yes	characteristic
415	C₂	D₄×SD₁₆×C₃₁	1	2	yes	—
416	C₂	C₃₁×#3335	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#498	C₂	semidirect
4. C₃₁×#2084	C₂	semidirect
5. C₃₁×#2058	C₂	semidirect
6. C₃₁×#1941	C₂	semidirect
7. C₃₁×#1941	C₂	semidirect
9. C₃₁×#1844	C₂	semidirect
46. C₂²×C₈×C₃₁	Q₈	semidirect
77. C₃₁×C₂²⋊C₈	Q₈	semidirect
138. #26060	C₃₁	direct (N × H)
181. C₈×C₃₁	C₂²⋊Q₈	semidirect
182. C₂×#498	C₂×C₃₁	semidirect
185. #2084	C₂×C₃₁	semidirect
186. #2058	C₂×C₃₁	semidirect
187. #1941	C₂×C₃₁	semidirect
188. #1941	C₂×C₃₁	semidirect
190. #1844	C₂×C₃₁	semidirect
197. C₂²×C₃₁	#498	semidirect
254. C₂²×C₈	Q₈×C₃₁	semidirect
285. C₂²⋊C₈	Q₈×C₃₁	semidirect
292. C₃₁	#26060	direct (N × H)
389. C₈	C₃₁×C₂²⋊Q₈	semidirect
394. C₂²	C₃₁×#498	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#498	2
C₂²×C₃₁×#106	2
C₃₁×#2440	2
C₃₁×#2084	2
C₃₁×#2058	2
C₃₁×#1941	2
C₃₁×#1853	2
C₃₁×#1844	2
C₃₁×#1807	2
C₈×C₂²⋊C₄×C₃₁	2
#26060	31

Subgroups — C31×#26060 #21482819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#26060 #21482819