Subgroups — C₂×C₃₁×#2820 #21493440

Order 7936.

2566 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2820	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#396	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#395	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#394	C₂	1	2	yes	maximal
9	C₂×C₃₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#125	—	2	8	no	—
13	C₂×C₃₁×#125	C₂²	1	8	yes	complemented
14	C₂×C₃₁×#124	—	2	8	no	—
15	C₂×C₃₁×#124	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
21	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
25	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
26	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#399	C₂²	1	16	yes	complemented
28	C₃₁×#397	C₂²	1	16	yes	complemented
29	C₃₁×#396	C₂²	1	32	yes	complemented
30	C₃₁×#395	C₂²	1	16	yes	complemented
31	C₃₁×#394	C₂²	1	16	yes	—
32	C₃₁×#382	C₂²	1	8	yes	complemented
33	C₂×C₃₁×#95	C₂²	1	2	yes	—
34	C₂×C₃₁×#95	C₂²	1	4	yes	—
35	C₂×C₃₁×#95	C₂²	1	2	yes	—
36	C₂⁵×C₃₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₃₁	—	2	4	no	—
38	C₂²×Q₈×C₃₁	—	4	4	no	—
39	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
40	C₂²×D₄×C₃₁	—	2	4	no	—
41	C₂²×D₄×C₃₁	—	4	4	no	—
42	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×#125	—	2	32	no	—
51	C₃₁×#124	—	2	32	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
56	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
64	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
71	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
72	C₂×C₄²×C₃₁	D₄	1	8	yes	—
73	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
74	C₃₁×#95	C₂³	1	16	yes	—
75	C₃₁×#95	C₂³	1	8	yes	—
76	C₃₁×#95	C₂³	1	8	yes	—
77	C₂⁴×C₃₁	—	2	4	no	—
78	C₂⁴×C₃₁	—	2	4	no	—
79	C₂⁴×C₃₁	—	2	8	no	—
80	C₂⁴×C₃₁	—	2	8	no	—
81	C₂⁴×C₃₁	—	2	4	no	—
82	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
83	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
84	C₂×Q₈×C₃₁	—	2	8	no	—
85	C₂×Q₈×C₃₁	—	4	8	no	—
86	C₂×Q₈×C₃₁	—	4	16	no	—
87	C₂×D₄×C₃₁	—	2	8	no	—
88	C₂×D₄×C₃₁	—	4	8	no	—
89	C₂×D₄×C₃₁	—	4	16	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	4	no	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	—	2	4	no	—
95	C₂²×C₄×C₃₁	—	2	4	no	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	—	2	4	no	—
98	C₂²×C₄×C₃₁	—	2	8	no	—
99	C₂²×C₄×C₃₁	—	2	8	no	—
100	C₂²×C₄×C₃₁	—	2	8	no	—
101	C₂²×C₄×C₃₁	—	2	8	no	—
102	C₂²×C₄×C₃₁	—	2	4	no	—
103	C₂²×C₄×C₃₁	—	2	8	no	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
114	C₄⋊C₄×C₃₁	—	2	16	no	—
115	C₄⋊C₄×C₃₁	—	2	8	no	—
116	C₄⋊C₄×C₃₁	—	2	8	no	—
117	C₄⋊C₄×C₃₁	—	2	16	no	—
118	C₄⋊C₄×C₃₁	—	4	8	no	—
119	C₄⋊C₄×C₃₁	—	4	16	no	—
120	C₂²⋊C₄×C₃₁	—	2	16	no	—
121	C₂²⋊C₄×C₃₁	—	2	16	no	—
122	C₂²⋊C₄×C₃₁	—	4	16	no	—
123	C₂²⋊C₄×C₃₁	—	4	16	no	—
124	C₄²×C₃₁	C₂×D₄	1	16	yes	—
125	C₂×#2820	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₃₁	—	2	4	no	—
127	C₂³×C₃₁	—	2	4	no	—
128	C₂³×C₃₁	—	2	8	no	—
129	C₂³×C₃₁	—	2	8	no	—
130	C₂³×C₃₁	—	2	4	no	—
131	C₂³×C₃₁	—	4	8	no	—
132	C₂³×C₃₁	—	4	8	no	—
133	C₂³×C₃₁	—	4	8	no	—
134	C₂³×C₃₁	—	4	16	no	—
135	C₂³×C₃₁	—	4	16	no	—
136	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
137	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
138	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
139	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
140	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
141	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
142	Q₈×C₃₁	—	4	16	no	—
143	D₄×C₃₁	—	4	16	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	2	8	no	—
146	C₂×C₄×C₃₁	—	2	8	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	4	no	—
149	C₂×C₄×C₃₁	—	2	4	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	4	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	4	no	—
155	C₂×C₄×C₃₁	—	2	8	no	—
156	C₂×C₄×C₃₁	—	2	8	no	—
157	C₂×C₄×C₃₁	—	2	8	no	—
158	C₂×C₄×C₃₁	—	2	8	no	—
159	C₂×C₄×C₃₁	—	2	4	no	—
160	C₂×C₄×C₃₁	—	2	8	no	—
161	C₂×C₄×C₃₁	—	4	8	no	—
162	C₂×C₄×C₃₁	—	4	8	no	—
163	C₂×C₄×C₃₁	—	4	8	no	—
164	C₂×C₄×C₃₁	—	4	16	no	—
165	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
167	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
168	C₂²×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂²×#124	C₂×C₃₁	1	1	yes	characteristic
170	#2820	C₂×C₃₁	1	16	yes	direct product factor
171	C₂×#399	C₂×C₃₁	1	2	yes	complemented
172	C₂×#397	C₂×C₃₁	1	2	yes	complemented
173	C₂×#396	C₂×C₃₁	1	4	yes	complemented
174	C₂×#395	C₂×C₃₁	1	2	yes	complemented
175	C₂×#394	C₂×C₃₁	1	2	yes	—
176	C₂×#382	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂²×C₃₁	—	4	4	no	—
178	C₂²×C₃₁	—	4	4	no	—
179	C₂²×C₃₁	—	4	4	no	—
180	C₂²×C₃₁	—	4	8	no	—
181	C₂²×C₃₁	—	4	8	no	—
182	C₂²×C₃₁	—	8	16	no	—
183	C₂²×C₃₁	#535	1	4	yes	—
184	C₂²×C₃₁	#536	1	4	yes	—
185	C₂²×C₃₁	#537	1	4	yes	—
186	C₂²×C₃₁	#562	1	8	yes	—
187	C₂²×C₃₁	#563	1	8	yes	—
188	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
189	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
190	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
191	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
192	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
193	C₄×C₃₁	—	2	4	no	—
194	C₄×C₃₁	—	2	4	no	—
195	C₄×C₃₁	—	2	4	no	—
196	C₄×C₃₁	—	4	4	no	—
197	C₄×C₃₁	—	4	4	no	—
198	C₄×C₃₁	—	4	4	no	—
199	C₄×C₃₁	—	4	8	no	—
200	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
201	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
202	C₂×#125	—	2	8	no	—
203	C₂×#125	C₂²×C₃₁	1	8	yes	complemented
204	C₂×#124	—	2	8	no	—
205	C₂×#124	C₂²×C₃₁	1	8	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
216	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
217	#399	C₂²×C₃₁	1	16	yes	complemented
218	#397	C₂²×C₃₁	1	16	yes	complemented
219	#396	C₂²×C₃₁	1	32	yes	complemented
220	#395	C₂²×C₃₁	1	16	yes	complemented
221	#394	C₂²×C₃₁	1	16	yes	—
222	#382	C₂²×C₃₁	1	8	yes	complemented
223	C₂×#95	C₂²×C₃₁	1	2	yes	—
224	C₂×#95	C₂²×C₃₁	1	4	yes	—
225	C₂×#95	C₂²×C₃₁	1	2	yes	—
226	C₂×C₃₁	—	8	4	no	—
227	C₂×C₃₁	#2820	1	8	yes	direct product factor
228	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
230	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
231	C₂×C₃₁	C₂×#562	1	2	yes	—
232	C₂×C₃₁	C₂×#563	1	2	yes	—
233	C₂⁵	C₂³×C₃₁	1	2	yes	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	—	4	4	no	—
236	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
237	C₂²×D₄	—	2	4	no	—
238	C₂²×D₄	—	4	4	no	—
239	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
240	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
241	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
242	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
243	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
244	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
247	#125	—	2	32	no	—
248	#124	—	2	32	no	—
249	C₂×C₄⋊C₄	—	2	8	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	4	4	no	—
254	C₂×C₄⋊C₄	—	4	8	no	—
255	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
257	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
260	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₂²⋊C₄	—	2	8	no	—
263	C₂×C₂²⋊C₄	—	4	8	no	—
264	C₂×C₂²⋊C₄	—	4	8	no	—
265	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
269	C₂×C₄²	D₄×C₃₁	1	8	yes	—
270	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
271	#95	C₂³×C₃₁	1	8	yes	—
272	#95	C₂³×C₃₁	1	8	yes	—
273	#95	C₂³×C₃₁	1	16	yes	—
274	C₃₁	C₂×#2820	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	8	no	—
278	C₂⁴	—	2	8	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
281	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	4	8	no	—
284	C₂×Q₈	—	4	16	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	4	16	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
303	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
304	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
312	C₄⋊C₄	—	2	16	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	16	no	—
316	C₄⋊C₄	—	4	8	no	—
317	C₄⋊C₄	—	4	16	no	—
318	C₂²⋊C₄	—	2	16	no	—
319	C₂²⋊C₄	—	2	16	no	—
320	C₂²⋊C₄	—	4	16	no	—
321	C₂²⋊C₄	—	4	16	no	—
322	C₄²	C₂×D₄×C₃₁	1	16	yes	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	8	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	8	no	—
329	C₂³	—	4	8	no	—
330	C₂³	—	4	8	no	—
331	C₂³	—	4	16	no	—
332	C₂³	—	4	16	no	—
333	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
334	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
335	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
336	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
337	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
338	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
339	Q₈	—	4	16	no	—
340	D₄	—	4	16	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	16	no	—
362	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
363	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
364	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	4	8	no	—
370	C₂²	—	8	16	no	—
371	C₂²	C₃₁×#535	1	4	yes	—
372	C₂²	C₃₁×#536	1	4	yes	—
373	C₂²	C₃₁×#537	1	4	yes	—
374	C₂²	C₃₁×#562	1	8	yes	—
375	C₂²	C₃₁×#563	1	8	yes	—
376	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
377	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
378	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
380	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	8	no	—
388	C₂	—	8	4	no	—
389	C₂	C₃₁×#2820	1	8	yes	direct product factor
390	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
391	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
392	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
393	C₂	C₂×C₃₁×#562	1	2	yes	—
394	C₂	C₂×C₃₁×#563	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂³×D₄×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#125	C₂	semidirect
3. C₃₁×#2820	C₂	direct (N × H)
4. C₂×C₃₁×#399	C₂	semidirect
5. C₂×C₃₁×#397	C₂	semidirect
6. C₂×C₃₁×#396	C₂	semidirect
7. C₂×C₃₁×#395	C₂	semidirect
9. C₂×C₃₁×#382	C₂	semidirect
13. C₂×C₃₁×#125	C₂²	semidirect
27. C₃₁×#399	C₂²	semidirect
28. C₃₁×#397	C₂²	semidirect
29. C₃₁×#396	C₂²	semidirect
30. C₃₁×#395	C₂²	semidirect
32. C₃₁×#382	C₂²	semidirect
125. C₂×#2820	C₃₁	direct (N × H)
168. C₂²×#125	C₂×C₃₁	semidirect
170. #2820	C₂×C₃₁	direct (N × H)
171. C₂×#399	C₂×C₃₁	semidirect
172. C₂×#397	C₂×C₃₁	semidirect
173. C₂×#396	C₂×C₃₁	semidirect
174. C₂×#395	C₂×C₃₁	semidirect
176. C₂×#382	C₂×C₃₁	semidirect
203. C₂×#125	C₂²×C₃₁	semidirect
217. #399	C₂²×C₃₁	semidirect
218. #397	C₂²×C₃₁	semidirect
219. #396	C₂²×C₃₁	semidirect
220. #395	C₂²×C₃₁	semidirect
222. #382	C₂²×C₃₁	semidirect
227. C₂×C₃₁	#2820	direct (N × H)
274. C₃₁	C₂×#2820	direct (N × H)
389. C₂	C₃₁×#2820	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#125	2
C₂²×C₃₁×#124	2
C₃₁×#2820	2
C₂×C₃₁×#399	2
C₂×C₃₁×#397	2
C₂×C₃₁×#396	2
C₂×C₃₁×#395	2
C₂×C₃₁×#394	2
C₂×C₃₁×#382	2
C₂×#2820	31

Subgroups — C2×C31×#2820 #21493440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2820 #21493440