Subgroups — C₂×C₃₁×#2592 #21491660

Order 7936.

2918 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2592	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#397	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#393	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#390	C₂	1	2	yes	maximal
8	C₂×C₃₁×#388	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#124	—	2	8	no	—
14	C₂×C₃₁×#124	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₃₁	—	2	8	no	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
24	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
26	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#397	C₂²	1	16	yes	complemented
28	C₃₁×#393	C₂²	1	16	yes	complemented
29	C₃₁×#391	C₂²	1	16	yes	complemented
30	C₃₁×#390	C₂²	1	16	yes	—
31	C₃₁×#388	C₂²	1	32	yes	complemented
32	C₄×C₄⋊C₄×C₃₁	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	4	yes	—
36	C₂⁵×C₃₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₃₁	—	2	4	no	—
38	C₂²×Q₈×C₃₁	—	2	4	no	—
39	C₂²×Q₈×C₃₁	—	2	8	no	—
40	C₂²×Q₈×C₃₁	—	2	8	no	—
41	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
42	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
43	C₂²×D₄×C₃₁	—	2	4	no	—
44	C₂²×D₄×C₃₁	—	2	8	no	—
45	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₃₁×#124	—	2	32	no	—
54	C₄×Q₈×C₃₁	—	2	32	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
65	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
69	C₂×C₄²×C₃₁	—	2	8	no	—
70	C₂×C₄²×C₃₁	—	4	4	no	—
71	C₂×C₄²×C₃₁	D₄	1	8	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
73	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
74	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
75	C₃₁×#95	C₂³	1	8	yes	—
76	C₃₁×#95	C₂³	1	16	yes	—
77	C₃₁×#95	C₂³	1	16	yes	—
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	—	2	4	no	—
83	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
84	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
85	C₂×Q₈×C₃₁	—	2	32	no	—
86	C₂×Q₈×C₃₁	—	2	8	no	—
87	C₂×Q₈×C₃₁	—	2	8	no	—
88	C₂×Q₈×C₃₁	—	2	16	no	—
89	C₂×Q₈×C₃₁	—	2	16	no	—
90	C₂×Q₈×C₃₁	—	4	16	no	—
91	C₂×D₄×C₃₁	—	2	8	no	—
92	C₂×D₄×C₃₁	—	2	16	no	—
93	C₂×D₄×C₃₁	—	4	16	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	2	no	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	—	2	4	no	—
100	C₂²×C₄×C₃₁	—	2	4	no	—
101	C₂²×C₄×C₃₁	—	2	8	no	—
102	C₂²×C₄×C₃₁	—	2	8	no	—
103	C₂²×C₄×C₃₁	—	2	8	no	—
104	C₂²×C₄×C₃₁	—	2	8	no	—
105	C₂²×C₄×C₃₁	—	2	4	no	—
106	C₂²×C₄×C₃₁	—	2	4	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₃₁	#41	1	8	yes	—
111	C₂²×C₄×C₃₁	#41	1	8	yes	—
112	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
119	C₄⋊C₄×C₃₁	—	2	16	no	—
120	C₄⋊C₄×C₃₁	—	2	8	no	—
121	C₄⋊C₄×C₃₁	—	2	16	no	—
122	C₂²⋊C₄×C₃₁	—	2	16	no	—
123	C₂²⋊C₄×C₃₁	—	2	16	no	—
124	C₂²⋊C₄×C₃₁	—	2	32	no	—
125	C₂²⋊C₄×C₃₁	—	4	16	no	—
126	C₄²×C₃₁	—	2	16	no	—
127	C₄²×C₃₁	—	4	8	no	—
128	C₄²×C₃₁	C₂×D₄	1	16	yes	—
129	C₂×#2592	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	4	no	—
131	C₂³×C₃₁	—	2	8	no	—
132	C₂³×C₃₁	—	2	8	no	—
133	C₂³×C₃₁	—	2	4	no	—
134	C₂³×C₃₁	—	2	4	no	—
135	C₂³×C₃₁	—	4	8	no	—
136	C₂³×C₃₁	—	4	8	no	—
137	C₂³×C₃₁	—	4	8	no	—
138	C₂³×C₃₁	—	4	16	no	—
139	C₂³×C₃₁	—	4	16	no	—
140	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
141	C₂³×C₃₁	C₂×#41	1	4	yes	—
142	C₂³×C₃₁	C₂×#41	1	4	yes	—
143	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
144	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
145	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
146	Q₈×C₃₁	—	2	32	no	—
147	Q₈×C₃₁	—	4	16	no	—
148	D₄×C₃₁	—	4	16	no	—
149	C₂×C₄×C₃₁	—	2	8	no	—
150	C₂×C₄×C₃₁	—	2	16	no	—
151	C₂×C₄×C₃₁	—	2	8	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	2	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	4	no	—
158	C₂×C₄×C₃₁	—	2	4	no	—
159	C₂×C₄×C₃₁	—	2	8	no	—
160	C₂×C₄×C₃₁	—	2	8	no	—
161	C₂×C₄×C₃₁	—	2	8	no	—
162	C₂×C₄×C₃₁	—	2	8	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	4	8	no	—
166	C₂×C₄×C₃₁	—	4	8	no	—
167	C₂×C₄×C₃₁	—	4	16	no	—
168	C₂×C₄×C₃₁	#124	1	16	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
173	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
174	C₂²×#124	C₂×C₃₁	1	1	yes	characteristic
175	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2592	C₂×C₃₁	1	16	yes	direct product factor
177	C₂×#397	C₂×C₃₁	1	2	yes	complemented
178	C₂×#393	C₂×C₃₁	1	2	yes	complemented
179	C₂×#391	C₂×C₃₁	1	2	yes	complemented
180	C₂×#390	C₂×C₃₁	1	2	yes	—
181	C₂×#388	C₂×C₃₁	1	4	yes	complemented
182	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×C₃₁	—	4	4	no	—
184	C₂²×C₃₁	—	4	4	no	—
185	C₂²×C₃₁	—	4	4	no	—
186	C₂²×C₃₁	—	4	8	no	—
187	C₂²×C₃₁	—	4	8	no	—
188	C₂²×C₃₁	—	8	16	no	—
189	C₂²×C₃₁	#525	1	4	yes	—
190	C₂²×C₃₁	C₂×#124	1	4	yes	—
191	C₂²×C₃₁	#537	1	4	yes	—
192	C₂²×C₃₁	#556	1	8	yes	—
193	C₂²×C₃₁	#559	1	8	yes	—
194	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
195	C₂²×C₃₁	C₂²×#41	1	2	yes	—
196	C₂²×C₃₁	C₂²×#41	1	2	yes	—
197	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
198	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
199	C₄×C₃₁	—	2	4	no	—
200	C₄×C₃₁	—	2	8	no	—
201	C₄×C₃₁	—	2	4	no	—
202	C₄×C₃₁	—	4	4	no	—
203	C₄×C₃₁	—	4	4	no	—
204	C₄×C₃₁	—	4	8	no	—
205	C₄×C₃₁	C₂×#124	1	8	yes	—
206	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×#124	—	2	8	no	—
210	C₂×#124	C₂²×C₃₁	1	8	yes	—
211	C₂×C₄×Q₈	—	2	8	no	—
212	C₂×C₄×Q₈	C₂²×C₃₁	1	8	yes	complemented
213	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
216	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
220	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
221	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
222	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
223	#397	C₂²×C₃₁	1	16	yes	complemented
224	#393	C₂²×C₃₁	1	16	yes	complemented
225	#391	C₂²×C₃₁	1	16	yes	complemented
226	#390	C₂²×C₃₁	1	16	yes	—
227	#388	C₂²×C₃₁	1	32	yes	complemented
228	C₄×C₄⋊C₄	C₂²×C₃₁	1	8	yes	complemented
229	C₂×#95	C₂²×C₃₁	1	2	yes	—
230	C₂×#95	C₂²×C₃₁	1	4	yes	—
231	C₂×#95	C₂²×C₃₁	1	4	yes	—
232	C₂×C₃₁	—	8	4	no	—
233	C₂×C₃₁	#2592	1	8	yes	direct product factor
234	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
235	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
236	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
237	C₂×C₃₁	C₂×#556	1	2	yes	—
238	C₂×C₃₁	C₂×#559	1	2	yes	—
239	C₂⁵	C₂³×C₃₁	1	2	yes	—
240	C₂²×Q₈	—	2	4	no	—
241	C₂²×Q₈	—	2	4	no	—
242	C₂²×Q₈	—	2	8	no	—
243	C₂²×Q₈	—	2	8	no	—
244	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
245	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
246	C₂²×D₄	—	2	4	no	—
247	C₂²×D₄	—	2	8	no	—
248	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
249	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
250	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
251	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
252	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
255	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
256	#124	—	2	32	no	—
257	C₄×Q₈	—	2	32	no	—
258	C₂×C₄⋊C₄	—	2	8	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	8	no	—
261	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
264	C₂×C₂²⋊C₄	—	2	8	no	—
265	C₂×C₂²⋊C₄	—	2	8	no	—
266	C₂×C₂²⋊C₄	—	2	16	no	—
267	C₂×C₂²⋊C₄	—	4	8	no	—
268	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
272	C₂×C₄²	—	2	8	no	—
273	C₂×C₄²	—	4	4	no	—
274	C₂×C₄²	D₄×C₃₁	1	8	yes	—
275	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
276	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
277	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
278	#95	C₂³×C₃₁	1	8	yes	—
279	#95	C₂³×C₃₁	1	16	yes	—
280	#95	C₂³×C₃₁	1	16	yes	—
281	C₃₁	C₂×#2592	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	8	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
288	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
289	C₂×Q₈	—	2	32	no	—
290	C₂×Q₈	—	2	8	no	—
291	C₂×Q₈	—	2	8	no	—
292	C₂×Q₈	—	2	16	no	—
293	C₂×Q₈	—	2	16	no	—
294	C₂×Q₈	—	4	16	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
314	C₂²×C₄	#41×C₃₁	1	8	yes	—
315	C₂²×C₄	#41×C₃₁	1	8	yes	—
316	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
317	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
318	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
323	C₄⋊C₄	—	2	16	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	16	no	—
326	C₂²⋊C₄	—	2	16	no	—
327	C₂²⋊C₄	—	2	16	no	—
328	C₂²⋊C₄	—	2	32	no	—
329	C₂²⋊C₄	—	4	16	no	—
330	C₄²	—	2	16	no	—
331	C₄²	—	4	8	no	—
332	C₄²	C₂×D₄×C₃₁	1	16	yes	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	8	no	—
340	C₂³	—	4	8	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	4	16	no	—
343	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
344	C₂³	C₂×#41×C₃₁	1	4	yes	—
345	C₂³	C₂×#41×C₃₁	1	4	yes	—
346	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
347	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
348	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
349	Q₈	—	2	32	no	—
350	Q₈	—	4	16	no	—
351	D₄	—	4	16	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	16	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	16	no	—
371	C₂×C₄	C₃₁×#124	1	16	yes	—
372	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
373	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
374	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
375	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
376	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	8	no	—
382	C₂²	—	8	16	no	—
383	C₂²	C₃₁×#525	1	4	yes	—
384	C₂²	C₂×C₃₁×#124	1	4	yes	—
385	C₂²	C₃₁×#537	1	4	yes	—
386	C₂²	C₃₁×#556	1	8	yes	—
387	C₂²	C₃₁×#559	1	8	yes	—
388	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
389	C₂²	C₂²×#41×C₃₁	1	2	yes	—
390	C₂²	C₂²×#41×C₃₁	1	2	yes	—
391	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
393	C₄	—	2	4	no	—
394	C₄	—	2	8	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	8	no	—
399	C₄	C₂×C₃₁×#124	1	8	yes	—
400	C₂	—	8	4	no	—
401	C₂	C₃₁×#2592	1	8	yes	direct product factor
402	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
403	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
404	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
405	C₂	C₂×C₃₁×#556	1	2	yes	—
406	C₂	C₂×C₃₁×#559	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
2. C₂²×C₄×Q₈×C₃₁	C₂	semidirect
3. C₃₁×#2592	C₂	direct (N × H)
4. C₂×C₃₁×#397	C₂	semidirect
5. C₂×C₃₁×#393	C₂	semidirect
6. C₂×C₃₁×#391	C₂	semidirect
8. C₂×C₃₁×#388	C₂	semidirect
9. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
16. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
27. C₃₁×#397	C₂²	semidirect
28. C₃₁×#393	C₂²	semidirect
29. C₃₁×#391	C₂²	semidirect
31. C₃₁×#388	C₂²	semidirect
32. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
129. C₂×#2592	C₃₁	direct (N × H)
175. C₂²×C₄×Q₈	C₂×C₃₁	semidirect
176. #2592	C₂×C₃₁	direct (N × H)
177. C₂×#397	C₂×C₃₁	semidirect
178. C₂×#393	C₂×C₃₁	semidirect
179. C₂×#391	C₂×C₃₁	semidirect
181. C₂×#388	C₂×C₃₁	semidirect
182. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
212. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
223. #397	C₂²×C₃₁	semidirect
224. #393	C₂²×C₃₁	semidirect
225. #391	C₂²×C₃₁	semidirect
227. #388	C₂²×C₃₁	semidirect
228. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
233. C₂×C₃₁	#2592	direct (N × H)
281. C₃₁	C₂×#2592	direct (N × H)
401. C₂	C₃₁×#2592	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×#124	2
C₂²×C₄×Q₈×C₃₁	2
C₃₁×#2592	2
C₂×C₃₁×#397	2
C₂×C₃₁×#393	2
C₂×C₃₁×#391	2
C₂×C₃₁×#390	2
C₂×C₃₁×#388	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₂×#2592	31

Subgroups — C2×C31×#2592 #21491660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2592 #21491660