Subgroups — C₂×C₃₁×#2665 #21491335

Order 7936.

2286 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2665	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃₁×#400	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#396	C₂	1	2	yes	maximal
4	C₂×C₃₁×#395	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#393	C₂	1	2	yes	maximal
6	C₂×C₃₁×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#381	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#400	C₂²	1	16	yes	complemented
23	C₃₁×#396	C₂²	1	16	yes	—
24	C₃₁×#395	C₂²	1	16	yes	complemented
25	C₃₁×#393	C₂²	1	16	yes	—
26	C₃₁×#391	C₂²	1	16	yes	complemented
27	C₃₁×#387	C₂²	1	16	yes	complemented
28	C₃₁×#381	C₂²	1	8	yes	—
29	C₃₁×#380	C₂²	1	8	yes	—
30	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
31	C₂×C₃₁×#95	C₂²	1	2	yes	—
32	C₂×C₃₁×#95	C₂²	1	2	yes	—
33	C₂×C₃₁×#95	C₂²	1	2	yes	—
34	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#95	C₂²	1	2	yes	—
36	C₂×C₃₁×#95	C₂²	1	2	yes	—
37	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#95	C₂²	1	2	yes	—
39	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
41	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₃₁	—	2	8	no	—
43	C₂²×Q₈×C₃₁	—	4	4	no	—
44	C₂²×Q₈×C₃₁	—	4	4	no	—
45	C₂²×Q₈×C₃₁	C₂³	1	8	yes	—
46	C₂³×C₄×C₃₁	—	4	4	no	—
47	C₂³×C₄×C₃₁	Q₈	1	8	yes	complemented
48	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
58	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
59	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
60	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
68	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
73	C₂×C₄²×C₃₁	—	4	4	no	—
74	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
75	C₃₁×#95	C₂³	1	4	yes	—
76	C₃₁×#95	C₂³	1	8	yes	—
77	C₃₁×#95	C₂³	1	8	yes	—
78	C₃₁×#95	C₂³	1	8	yes	—
79	C₃₁×#95	C₂³	1	4	yes	—
80	C₃₁×#95	C₂³	1	8	yes	—
81	C₃₁×#95	C₂³	1	8	yes	—
82	C₃₁×#95	C₂³	1	8	yes	—
83	C₃₁×#95	C₂³	1	4	yes	—
84	C₃₁×#95	C₂³	1	4	yes	—
85	C₂⁴×C₃₁	—	2	4	no	—
86	C₂⁴×C₃₁	—	2	2	no	—
87	C₂⁴×C₃₁	—	2	4	no	—
88	C₂⁴×C₃₁	—	2	2	no	—
89	C₂⁴×C₃₁	C₂×Q₈	1	4	yes	—
90	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
91	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
92	C₂×Q₈×C₃₁	—	2	16	no	—
93	C₂×Q₈×C₃₁	—	4	8	no	—
94	C₂×Q₈×C₃₁	—	4	8	no	—
95	C₂×Q₈×C₃₁	—	4	32	no	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	—	2	4	no	—
98	C₂²×C₄×C₃₁	—	2	4	no	—
99	C₂²×C₄×C₃₁	—	2	4	no	—
100	C₂²×C₄×C₃₁	—	2	4	no	—
101	C₂²×C₄×C₃₁	—	2	4	no	—
102	C₂²×C₄×C₃₁	—	2	4	no	—
103	C₂²×C₄×C₃₁	—	2	4	no	—
104	C₂²×C₄×C₃₁	—	2	4	no	—
105	C₂²×C₄×C₃₁	—	2	4	no	—
106	C₂²×C₄×C₃₁	—	2	4	no	—
107	C₂²×C₄×C₃₁	—	2	4	no	—
108	C₂²×C₄×C₃₁	—	2	4	no	—
109	C₂²×C₄×C₃₁	—	2	4	no	—
110	C₂²×C₄×C₃₁	—	2	4	no	—
111	C₂²×C₄×C₃₁	—	2	4	no	—
112	C₂²×C₄×C₃₁	—	2	4	no	—
113	C₂²×C₄×C₃₁	—	2	4	no	—
114	C₂²×C₄×C₃₁	—	2	4	no	—
115	C₂²×C₄×C₃₁	—	4	16	no	—
116	C₂²×C₄×C₃₁	—	4	8	no	—
117	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
118	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
119	C₂²×C₄×C₃₁	C₂×Q₈	1	16	yes	complemented
120	C₂²×C₄×C₃₁	#41	1	8	yes	—
121	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
129	C₄⋊C₄×C₃₁	—	2	16	no	—
130	C₄⋊C₄×C₃₁	—	4	8	no	—
131	C₄⋊C₄×C₃₁	—	4	8	no	—
132	C₄⋊C₄×C₃₁	—	4	8	no	—
133	C₂²⋊C₄×C₃₁	—	2	16	no	—
134	C₂²⋊C₄×C₃₁	—	4	4	no	—
135	C₂²⋊C₄×C₃₁	—	4	8	no	—
136	C₂²⋊C₄×C₃₁	—	4	4	no	—
137	C₄²×C₃₁	—	4	8	no	—
138	C₂×#2665	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	—	2	8	no	—
140	C₂³×C₃₁	—	2	8	no	—
141	C₂³×C₃₁	—	2	8	no	—
142	C₂³×C₃₁	—	2	4	no	—
143	C₂³×C₃₁	—	2	2	no	—
144	C₂³×C₃₁	—	2	4	no	—
145	C₂³×C₃₁	—	2	2	no	—
146	C₂³×C₃₁	—	4	8	no	—
147	C₂³×C₃₁	—	4	8	no	—
148	C₂³×C₃₁	C₂²×Q₈	1	4	yes	—
149	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
150	C₂³×C₃₁	C₂×#41	1	4	yes	—
151	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
152	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
153	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
154	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
155	Q₈×C₃₁	—	4	32	no	—
156	C₂×C₄×C₃₁	—	2	16	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	4	no	—
161	C₂×C₄×C₃₁	—	2	4	no	—
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	4	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	4	no	—
169	C₂×C₄×C₃₁	—	2	4	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	2	4	no	—
172	C₂×C₄×C₃₁	—	2	4	no	—
173	C₂×C₄×C₃₁	—	2	4	no	—
174	C₂×C₄×C₃₁	—	2	4	no	—
175	C₂×C₄×C₃₁	—	2	4	no	—
176	C₂×C₄×C₃₁	—	2	4	no	—
177	C₂×C₄×C₃₁	—	2	4	no	—
178	C₂×C₄×C₃₁	—	4	16	no	—
179	C₂×C₄×C₃₁	—	4	8	no	—
180	C₂×C₄×C₃₁	—	4	8	no	—
181	C₂×C₄×C₃₁	—	4	8	no	—
182	C₂×C₄×C₃₁	—	4	8	no	—
183	C₂×C₄×C₃₁	—	4	8	no	—
184	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
185	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
186	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
187	#2665	C₂×C₃₁	1	16	yes	direct product factor
188	C₂×#400	C₂×C₃₁	1	2	yes	complemented
189	C₂×#396	C₂×C₃₁	1	2	yes	—
190	C₂×#395	C₂×C₃₁	1	2	yes	complemented
191	C₂×#393	C₂×C₃₁	1	2	yes	—
192	C₂×#391	C₂×C₃₁	1	2	yes	complemented
193	C₂×#387	C₂×C₃₁	1	2	yes	complemented
194	C₂×#381	C₂×C₃₁	1	1	yes	characteristic
195	C₂×#380	C₂×C₃₁	1	1	yes	characteristic
196	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
197	C₂²×C₃₁	—	2	4	no	—
198	C₂²×C₃₁	—	2	4	no	—
199	C₂²×C₃₁	—	2	4	no	—
200	C₂²×C₃₁	—	4	16	no	—
201	C₂²×C₃₁	—	4	4	no	—
202	C₂²×C₃₁	—	4	4	no	—
203	C₂²×C₃₁	#533	1	4	yes	—
204	C₂²×C₃₁	#538	1	8	yes	—
205	C₂²×C₃₁	#542	1	8	yes	—
206	C₂²×C₃₁	#543	1	4	yes	—
207	C₂²×C₃₁	#544	1	4	yes	—
208	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
209	C₂²×C₃₁	C₂²×#41	1	2	yes	—
210	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
212	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
213	C₄×C₃₁	—	2	8	no	—
214	C₄×C₃₁	—	2	4	no	—
215	C₄×C₃₁	—	2	4	no	—
216	C₄×C₃₁	—	4	4	no	—
217	C₄×C₃₁	—	4	4	no	—
218	C₄×C₃₁	—	4	4	no	—
219	C₄×C₃₁	—	4	4	no	—
220	C₄×C₃₁	—	4	4	no	—
221	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
222	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
229	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
232	#400	C₂²×C₃₁	1	16	yes	complemented
233	#396	C₂²×C₃₁	1	16	yes	—
234	#395	C₂²×C₃₁	1	16	yes	complemented
235	#393	C₂²×C₃₁	1	16	yes	—
236	#391	C₂²×C₃₁	1	16	yes	complemented
237	#387	C₂²×C₃₁	1	16	yes	complemented
238	#381	C₂²×C₃₁	1	8	yes	—
239	#380	C₂²×C₃₁	1	8	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
241	C₂×#95	C₂²×C₃₁	1	2	yes	—
242	C₂×#95	C₂²×C₃₁	1	2	yes	—
243	C₂×#95	C₂²×C₃₁	1	2	yes	—
244	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×#95	C₂²×C₃₁	1	2	yes	—
246	C₂×#95	C₂²×C₃₁	1	2	yes	—
247	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
248	C₂×#95	C₂²×C₃₁	1	2	yes	—
249	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
250	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
251	C₂×C₃₁	—	4	4	no	—
252	C₂×C₃₁	#2665	1	8	yes	direct product factor
253	C₂×C₃₁	C₂×#533	1	1	yes	characteristic
254	C₂×C₃₁	C₂×#538	1	2	yes	—
255	C₂×C₃₁	C₂×#542	1	2	yes	—
256	C₂×C₃₁	C₂×#543	1	1	yes	characteristic
257	C₂×C₃₁	C₂×#544	1	1	yes	characteristic
258	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
259	C₂²×Q₈	—	2	8	no	—
260	C₂²×Q₈	—	4	4	no	—
261	C₂²×Q₈	—	4	4	no	—
262	C₂²×Q₈	C₂³×C₃₁	1	8	yes	—
263	C₂³×C₄	—	4	4	no	—
264	C₂³×C₄	Q₈×C₃₁	1	8	yes	complemented
265	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
266	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
267	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
268	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
269	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
270	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
273	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
274	C₂×C₄⋊C₄	—	2	8	no	—
275	C₂×C₄⋊C₄	—	4	4	no	—
276	C₂×C₄⋊C₄	—	4	4	no	—
277	C₂×C₄⋊C₄	—	4	4	no	—
278	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
279	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	—	4	2	no	—
284	C₂×C₂²⋊C₄	—	4	4	no	—
285	C₂×C₂²⋊C₄	—	4	2	no	—
286	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
290	C₂×C₄²	—	4	4	no	—
291	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
292	#95	C₂³×C₃₁	1	4	yes	—
293	#95	C₂³×C₃₁	1	4	yes	—
294	#95	C₂³×C₃₁	1	8	yes	—
295	#95	C₂³×C₃₁	1	4	yes	—
296	#95	C₂³×C₃₁	1	4	yes	—
297	#95	C₂³×C₃₁	1	8	yes	—
298	#95	C₂³×C₃₁	1	8	yes	—
299	#95	C₂³×C₃₁	1	8	yes	—
300	#95	C₂³×C₃₁	1	8	yes	—
301	#95	C₂³×C₃₁	1	8	yes	—
302	C₃₁	C₂×#2665	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	—	2	2	no	—
307	C₂⁴	C₂×Q₈×C₃₁	1	4	yes	—
308	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
309	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
310	C₂×Q₈	—	2	16	no	—
311	C₂×Q₈	—	4	8	no	—
312	C₂×Q₈	—	4	8	no	—
313	C₂×Q₈	—	4	32	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	4	16	no	—
334	C₂²×C₄	—	4	8	no	—
335	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
336	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
337	C₂²×C₄	C₂×Q₈×C₃₁	1	16	yes	complemented
338	C₂²×C₄	#41×C₃₁	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
343	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
344	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
347	C₄⋊C₄	—	2	16	no	—
348	C₄⋊C₄	—	4	8	no	—
349	C₄⋊C₄	—	4	8	no	—
350	C₄⋊C₄	—	4	8	no	—
351	C₂²⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₄²	—	4	8	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	8	no	—
365	C₂³	C₂²×Q₈×C₃₁	1	4	yes	—
366	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
367	C₂³	C₂×#41×C₃₁	1	4	yes	—
368	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
369	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
370	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
371	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
372	Q₈	—	4	32	no	—
373	C₂×C₄	—	2	16	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	16	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
402	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
403	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	16	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	C₃₁×#533	1	4	yes	—
411	C₂²	C₃₁×#538	1	8	yes	—
412	C₂²	C₃₁×#542	1	8	yes	—
413	C₂²	C₃₁×#543	1	4	yes	—
414	C₂²	C₃₁×#544	1	4	yes	—
415	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
416	C₂²	C₂²×#41×C₃₁	1	2	yes	—
417	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
419	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
420	C₄	—	2	8	no	—
421	C₄	—	2	4	no	—
422	C₄	—	2	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₂	—	4	4	no	—
429	C₂	C₃₁×#2665	1	8	yes	direct product factor
430	C₂	C₂×C₃₁×#533	1	1	yes	characteristic
431	C₂	C₂×C₃₁×#538	1	2	yes	—
432	C₂	C₂×C₃₁×#542	1	2	yes	—
433	C₂	C₂×C₃₁×#543	1	1	yes	characteristic
434	C₂	C₂×C₃₁×#544	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
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. C₃₁×#2665	C₂	direct (N × H)
2. C₂×C₃₁×#400	C₂	semidirect
4. C₂×C₃₁×#395	C₂	semidirect
6. C₂×C₃₁×#391	C₂	semidirect
7. C₂×C₃₁×#387	C₂	semidirect
22. C₃₁×#400	C₂²	semidirect
24. C₃₁×#395	C₂²	semidirect
26. C₃₁×#391	C₂²	semidirect
27. C₃₁×#387	C₂²	semidirect
47. C₂³×C₄×C₃₁	Q₈	semidirect
119. C₂²×C₄×C₃₁	C₂×Q₈	semidirect
138. C₂×#2665	C₃₁	direct (N × H)
187. #2665	C₂×C₃₁	direct (N × H)
188. C₂×#400	C₂×C₃₁	semidirect
190. C₂×#395	C₂×C₃₁	semidirect
192. C₂×#391	C₂×C₃₁	semidirect
193. C₂×#387	C₂×C₃₁	semidirect
232. #400	C₂²×C₃₁	semidirect
234. #395	C₂²×C₃₁	semidirect
236. #391	C₂²×C₃₁	semidirect
237. #387	C₂²×C₃₁	semidirect
252. C₂×C₃₁	#2665	direct (N × H)
264. C₂³×C₄	Q₈×C₃₁	semidirect
302. C₃₁	C₂×#2665	direct (N × H)
337. C₂²×C₄	C₂×Q₈×C₃₁	semidirect
429. C₂	C₃₁×#2665	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2665	2
C₂×C₃₁×#400	2
C₂×C₃₁×#396	2
C₂×C₃₁×#395	2
C₂×C₃₁×#393	2
C₂×C₃₁×#391	2
C₂×C₃₁×#387	2
C₂×C₃₁×#381	2
C₂×C₃₁×#380	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2665	31

Subgroups — C2×C31×#2665 #21491335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2665 #21491335