Subgroups — C₂×C₃₁×#3568 #21519495

Order 7936.

6726 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	C₃₁×#3568	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	C₂	1	3	yes	maximal, complemented
3	C₂×C₃₁×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#556	C₂	1	6	yes	maximal, complemented
5	C₂×C₃₁×#551	C₂	1	6	yes	maximal, complemented
6	C₂×C₃₁×#542	C₂	1	6	yes	maximal, complemented
7	C₂×C₃₁×#538	C₂	1	6	yes	maximal, complemented
8	C₂×C₃₁×#529	C₂	1	3	yes	maximal, complemented
9	C₃₁×#563	C₂²	1	48	yes	complemented
10	C₃₁×H(3,𝔽₄)	C₂²	1	16	yes	complemented
11	C₃₁×#556	C₂²	1	96	yes	complemented
12	C₃₁×#551	C₂²	1	96	yes	complemented
13	C₃₁×#542	C₂²	1	96	yes	complemented
14	C₃₁×#538	C₂²	1	96	yes	complemented
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	6	yes	complemented
16	C₃₁×#529	C₂²	1	48	yes	complemented
17	C₂×C₃₁×#126	C₂²	1	6	yes	complemented
18	C₂×C₃₁×#126	C₂²	1	6	yes	complemented
19	C₂×C₃₁×#126	C₂²	1	6	yes	complemented
20	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#126	C₂²	1	6	yes	complemented
22	C₂×C₃₁×#125	C₂²	1	3	yes	complemented
23	C₂×C₃₁×#124	C₂²	1	3	yes	—
24	C₂×C₃₁×#124	C₂²	1	6	yes	—
25	C₂×C₃₁×#124	C₂²	1	6	yes	—
26	C₂×C₃₁×#124	C₂²	1	6	yes	complemented
27	C₂×C₃₁×#123	C₂²	1	6	yes	—
28	C₂×C₃₁×#123	C₂²	1	6	yes	—
29	C₂×C₃₁×#123	C₂²	1	6	yes	complemented
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	3	yes	complemented
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
33	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
34	C₂×C₃₁×#121	C₂²	1	3	yes	—
35	C₂×C₃₁×#121	C₂²	1	6	yes	—
36	C₂×C₃₁×#120	C₂²	1	6	yes	—
37	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
38	C₂×C₄×Q₈×C₃₁	C₂²	1	3	yes	complemented
39	C₂×C₄×Q₈×C₃₁	C₂²	1	6	yes	complemented
40	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
41	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	—
42	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
43	C₂×C₃₁×#117	C₂²	1	6	yes	complemented
44	C₂×C₃₁×#117	C₂²	1	6	yes	complemented
45	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	complemented
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₃₁	C₂³	1	2	yes	—
48	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
49	C₂²×Q₈×C₃₁	C₂³	1	3	yes	—
50	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
51	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
52	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
53	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
54	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
55	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
56	C₃₁×C₄⋊Q₈	C₂³	1	48	yes	complemented
57	C₃₁×#126	C₂³	1	48	yes	complemented
58	C₃₁×#126	C₂³	1	48	yes	complemented
59	C₃₁×#126	C₂³	1	48	yes	complemented
60	C₃₁×#126	C₂³	1	16	yes	complemented
61	C₃₁×#126	C₂³	1	48	yes	complemented
62	C₃₁×#125	C₂³	1	24	yes	complemented
63	C₃₁×#124	C₂³	1	24	yes	—
64	C₃₁×#124	C₂³	1	48	yes	—
65	C₃₁×#124	C₂³	1	48	yes	—
66	C₃₁×#124	C₂³	1	48	yes	complemented
67	C₃₁×#123	C₂³	1	48	yes	—
68	C₃₁×#123	C₂³	1	48	yes	—
69	C₃₁×#123	C₂³	1	48	yes	complemented
70	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	complemented
71	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
72	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
73	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
74	C₃₁×#121	C₂³	1	24	yes	—
75	C₃₁×#121	C₂³	1	48	yes	—
76	C₃₁×#120	C₂³	1	48	yes	—
77	C₃₁×#120	C₂³	1	16	yes	complemented
78	C₄×Q₈×C₃₁	C₂³	1	24	yes	complemented
79	C₄×Q₈×C₃₁	C₂³	1	48	yes	complemented
80	C₄×D₄×C₃₁	C₂³	1	24	yes	—
81	C₄×D₄×C₃₁	C₂³	1	48	yes	—
82	C₄×D₄×C₃₁	C₂³	1	48	yes	complemented
83	C₃₁×#117	C₂³	1	48	yes	complemented
84	C₃₁×#117	C₂³	1	48	yes	complemented
85	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
87	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
89	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
90	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
91	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
92	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
93	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
95	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
96	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
97	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
98	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
99	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
100	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
101	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
102	C₂×C₂²⋊C₄×C₃₁	C₂³	1	48	yes	complemented
103	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
104	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
106	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
107	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
109	C₂⁴×C₃₁	—	4	12	no	—
110	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
111	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
112	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
113	C₂×Q₈×C₃₁	—	4	12	no	—
114	C₂×Q₈×C₃₁	—	4	6	no	—
115	C₂×Q₈×C₃₁	C₂⁴	1	24	yes	—
116	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
117	C₂×D₄×C₃₁	—	4	12	no	—
118	C₂×D₄×C₃₁	—	4	6	no	—
119	C₂×D₄×C₃₁	—	4	12	no	—
120	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
121	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
122	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
123	C₂²×C₄×C₃₁	—	4	12	no	—
124	C₂²×C₄×C₃₁	—	4	6	no	—
125	C₂²×C₄×C₃₁	—	4	12	no	—
126	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
131	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
132	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
133	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
134	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
135	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
136	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
137	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
138	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
139	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
140	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
141	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
142	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
143	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
144	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
145	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
146	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
147	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
148	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
149	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
150	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
151	C₄²×C₃₁	C₂⁴	1	12	yes	—
152	C₄²×C₃₁	C₂⁴	1	4	yes	—
153	C₄²×C₃₁	C₂⁴	1	24	yes	—
154	C₄²×C₃₁	C₂⁴	1	24	yes	—
155	C₄²×C₃₁	C₂⁴	1	8	yes	—
156	C₂×#3568	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₃₁	—	2	6	no	—
158	C₂³×C₃₁	—	2	12	no	—
159	C₂³×C₃₁	—	2	12	no	—
160	C₂³×C₃₁	—	2	12	no	—
161	C₂³×C₃₁	—	4	24	no	—
162	C₂³×C₃₁	—	8	16	no	—
163	C₂³×C₃₁	C₂⁵	1	12	yes	—
164	C₂³×C₃₁	C₂⁵	1	2	yes	—
165	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
166	Q₈×C₃₁	—	4	24	no	—
167	Q₈×C₃₁	—	4	12	no	—
168	D₄×C₃₁	—	4	24	no	—
169	D₄×C₃₁	—	4	12	no	—
170	D₄×C₃₁	—	4	24	no	—
171	C₂×C₄×C₃₁	—	2	6	no	—
172	C₂×C₄×C₃₁	—	2	12	no	—
173	C₂×C₄×C₃₁	—	2	6	no	—
174	C₂×C₄×C₃₁	—	2	12	no	—
175	C₂×C₄×C₃₁	—	2	12	no	—
176	C₂×C₄×C₃₁	—	4	24	no	—
177	C₂×C₄×C₃₁	—	4	12	no	—
178	C₂×C₄×C₃₁	—	4	24	no	—
179	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
180	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
181	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
182	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
183	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
184	#3568	C₂×C₃₁	1	32	yes	direct product factor
185	C₂×#563	C₂×C₃₁	1	3	yes	complemented
186	C₂×H(3,𝔽₄)	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂×#556	C₂×C₃₁	1	6	yes	complemented
188	C₂×#551	C₂×C₃₁	1	6	yes	complemented
189	C₂×#542	C₂×C₃₁	1	6	yes	complemented
190	C₂×#538	C₂×C₃₁	1	6	yes	complemented
191	C₂×#529	C₂×C₃₁	1	3	yes	complemented
192	C₂²×C₃₁	—	2	6	no	—
193	C₂²×C₃₁	—	2	12	no	—
194	C₂²×C₃₁	—	2	12	no	—
195	C₂²×C₃₁	—	2	12	no	—
196	C₂²×C₃₁	—	4	4	no	—
197	C₂²×C₃₁	—	4	24	no	—
198	C₂²×C₃₁	—	8	16	no	—
199	C₂²×C₃₁	#585	1	6	yes	—
200	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
201	C₄×C₃₁	—	2	6	no	—
202	C₄×C₃₁	—	2	12	no	—
203	C₄×C₃₁	—	2	6	no	—
204	C₄×C₃₁	—	2	12	no	—
205	C₄×C₃₁	—	2	12	no	—
206	#563	C₂²×C₃₁	1	48	yes	complemented
207	H(3,𝔽₄)	C₂²×C₃₁	1	16	yes	complemented
208	#556	C₂²×C₃₁	1	96	yes	complemented
209	#551	C₂²×C₃₁	1	96	yes	complemented
210	#542	C₂²×C₃₁	1	96	yes	complemented
211	#538	C₂²×C₃₁	1	96	yes	complemented
212	C₂×C₄⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
213	#529	C₂²×C₃₁	1	48	yes	complemented
214	C₂×#126	C₂²×C₃₁	1	6	yes	complemented
215	C₂×#126	C₂²×C₃₁	1	6	yes	complemented
216	C₂×#126	C₂²×C₃₁	1	6	yes	complemented
217	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
218	C₂×#126	C₂²×C₃₁	1	6	yes	complemented
219	C₂×#125	C₂²×C₃₁	1	3	yes	complemented
220	C₂×#124	C₂²×C₃₁	1	3	yes	—
221	C₂×#124	C₂²×C₃₁	1	6	yes	—
222	C₂×#124	C₂²×C₃₁	1	6	yes	—
223	C₂×#124	C₂²×C₃₁	1	6	yes	complemented
224	C₂×#123	C₂²×C₃₁	1	6	yes	—
225	C₂×#123	C₂²×C₃₁	1	6	yes	—
226	C₂×#123	C₂²×C₃₁	1	6	yes	complemented
227	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
228	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
229	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
230	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
231	C₂×#121	C₂²×C₃₁	1	3	yes	—
232	C₂×#121	C₂²×C₃₁	1	6	yes	—
233	C₂×#120	C₂²×C₃₁	1	6	yes	—
234	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
235	C₂×C₄×Q₈	C₂²×C₃₁	1	3	yes	complemented
236	C₂×C₄×Q₈	C₂²×C₃₁	1	6	yes	complemented
237	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
238	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	—
239	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
240	C₂×#117	C₂²×C₃₁	1	6	yes	complemented
241	C₂×#117	C₂²×C₃₁	1	6	yes	complemented
242	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	complemented
243	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
244	C₂×C₃₁	—	4	2	no	—
245	C₂×C₃₁	—	4	12	no	—
246	C₂×C₃₁	#3568	1	4	yes	direct product factor
247	C₂×C₃₁	C₂×#585	1	3	yes	—
248	C₂⁵	C₂³×C₃₁	1	2	yes	—
249	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
250	C₂²×Q₈	C₂³×C₃₁	1	3	yes	—
251	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
252	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
253	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
254	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
255	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
256	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
257	C₄⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
258	#126	C₂³×C₃₁	1	48	yes	complemented
259	#126	C₂³×C₃₁	1	48	yes	complemented
260	#126	C₂³×C₃₁	1	48	yes	complemented
261	#126	C₂³×C₃₁	1	16	yes	complemented
262	#126	C₂³×C₃₁	1	48	yes	complemented
263	#125	C₂³×C₃₁	1	24	yes	complemented
264	#124	C₂³×C₃₁	1	24	yes	—
265	#124	C₂³×C₃₁	1	48	yes	—
266	#124	C₂³×C₃₁	1	48	yes	—
267	#124	C₂³×C₃₁	1	48	yes	complemented
268	#123	C₂³×C₃₁	1	48	yes	—
269	#123	C₂³×C₃₁	1	48	yes	—
270	#123	C₂³×C₃₁	1	48	yes	complemented
271	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	complemented
272	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
273	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
274	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
275	#121	C₂³×C₃₁	1	24	yes	—
276	#121	C₂³×C₃₁	1	48	yes	—
277	#120	C₂³×C₃₁	1	48	yes	—
278	#120	C₂³×C₃₁	1	16	yes	complemented
279	C₄×Q₈	C₂³×C₃₁	1	24	yes	complemented
280	C₄×Q₈	C₂³×C₃₁	1	48	yes	complemented
281	C₄×D₄	C₂³×C₃₁	1	24	yes	—
282	C₄×D₄	C₂³×C₃₁	1	48	yes	—
283	C₄×D₄	C₂³×C₃₁	1	48	yes	complemented
284	#117	C₂³×C₃₁	1	48	yes	complemented
285	#117	C₂³×C₃₁	1	48	yes	complemented
286	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
287	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
288	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
289	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
291	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₃₁	1	48	yes	complemented
304	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
305	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
306	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
307	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
308	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
310	C₃₁	C₂×#3568	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	—	4	12	no	—
312	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
313	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
314	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
315	C₂×Q₈	—	4	12	no	—
316	C₂×Q₈	—	4	6	no	—
317	C₂×Q₈	C₂⁴×C₃₁	1	24	yes	—
318	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
319	C₂×D₄	—	4	12	no	—
320	C₂×D₄	—	4	6	no	—
321	C₂×D₄	—	4	12	no	—
322	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
323	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
324	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
325	C₂²×C₄	—	4	12	no	—
326	C₂²×C₄	—	4	6	no	—
327	C₂²×C₄	—	4	12	no	—
328	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
329	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
330	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
331	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
332	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
333	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
334	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
335	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
336	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
337	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
338	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
339	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
340	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
341	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
342	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
343	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
344	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
345	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
346	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
347	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
348	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
349	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
350	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
351	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
352	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
353	C₄²	C₂⁴×C₃₁	1	12	yes	—
354	C₄²	C₂⁴×C₃₁	1	4	yes	—
355	C₄²	C₂⁴×C₃₁	1	24	yes	—
356	C₄²	C₂⁴×C₃₁	1	24	yes	—
357	C₄²	C₂⁴×C₃₁	1	8	yes	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	2	12	no	—
362	C₂³	—	4	24	no	—
363	C₂³	—	8	16	no	—
364	C₂³	C₂⁵×C₃₁	1	12	yes	—
365	C₂³	C₂⁵×C₃₁	1	2	yes	—
366	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
367	Q₈	—	4	24	no	—
368	Q₈	—	4	12	no	—
369	D₄	—	4	24	no	—
370	D₄	—	4	12	no	—
371	D₄	—	4	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	12	no	—
376	C₂×C₄	—	2	12	no	—
377	C₂×C₄	—	4	24	no	—
378	C₂×C₄	—	4	12	no	—
379	C₂×C₄	—	4	24	no	—
380	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
381	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
382	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
383	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
384	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
385	C₂²	—	2	6	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	2	12	no	—
389	C₂²	—	4	24	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	16	no	—
392	C₂²	C₃₁×#585	1	6	yes	—
393	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	2	6	no	—
397	C₄	—	2	12	no	—
398	C₄	—	2	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	4	2	no	—
401	C₂	C₃₁×#3568	1	4	yes	direct product factor
402	C₂	C₂×C₃₁×#585	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3568	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×H(3,𝔽₄)	C₂	semidirect
4. C₂×C₃₁×#556	C₂	semidirect
5. C₂×C₃₁×#551	C₂	semidirect
6. C₂×C₃₁×#542	C₂	semidirect
7. C₂×C₃₁×#538	C₂	semidirect
8. C₂×C₃₁×#529	C₂	semidirect
9. C₃₁×#563	C₂²	semidirect
10. C₃₁×H(3,𝔽₄)	C₂²	semidirect
11. C₃₁×#556	C₂²	semidirect
12. C₃₁×#551	C₂²	semidirect
13. C₃₁×#542	C₂²	semidirect
14. C₃₁×#538	C₂²	semidirect
15. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
16. C₃₁×#529	C₂²	semidirect
17. C₂×C₃₁×#126	C₂²	semidirect
18. C₂×C₃₁×#126	C₂²	semidirect
19. C₂×C₃₁×#126	C₂²	semidirect
20. C₂×C₃₁×#126	C₂²	semidirect
21. C₂×C₃₁×#126	C₂²	semidirect
22. C₂×C₃₁×#125	C₂²	semidirect
26. C₂×C₃₁×#124	C₂²	semidirect
29. C₂×C₃₁×#123	C₂²	semidirect
30. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₃₁×#120	C₂²	semidirect
38. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
39. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
42. C₂×C₄×D₄×C₃₁	C₂²	semidirect
43. C₂×C₃₁×#117	C₂²	semidirect
44. C₂×C₃₁×#117	C₂²	semidirect
45. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
46. C₂²×C₄²×C₃₁	C₂²	semidirect
56. C₃₁×C₄⋊Q₈	C₂³	semidirect
57. C₃₁×#126	C₂³	semidirect
58. C₃₁×#126	C₂³	semidirect
59. C₃₁×#126	C₂³	semidirect
60. C₃₁×#126	C₂³	semidirect
61. C₃₁×#126	C₂³	semidirect
62. C₃₁×#125	C₂³	semidirect
66. C₃₁×#124	C₂³	semidirect
69. C₃₁×#123	C₂³	semidirect
70. C₃₁×C₂²⋊Q₈	C₂³	semidirect
71. C₃₁×C₂²⋊Q₈	C₂³	semidirect
72. C₃₁×C₂²⋊Q₈	C₂³	semidirect
73. C₃₁×C₂²⋊Q₈	C₂³	semidirect
77. C₃₁×#120	C₂³	semidirect
78. C₄×Q₈×C₃₁	C₂³	semidirect
79. C₄×Q₈×C₃₁	C₂³	semidirect
82. C₄×D₄×C₃₁	C₂³	semidirect
83. C₃₁×#117	C₂³	semidirect
84. C₃₁×#117	C₂³	semidirect
102. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
108. C₂×C₄²×C₃₁	C₂³	semidirect
156. C₂×#3568	C₃₁	direct (N × H)
184. #3568	C₂×C₃₁	direct (N × H)
185. C₂×#563	C₂×C₃₁	semidirect
186. C₂×H(3,𝔽₄)	C₂×C₃₁	semidirect
187. C₂×#556	C₂×C₃₁	semidirect
188. C₂×#551	C₂×C₃₁	semidirect
189. C₂×#542	C₂×C₃₁	semidirect
190. C₂×#538	C₂×C₃₁	semidirect
191. C₂×#529	C₂×C₃₁	semidirect
206. #563	C₂²×C₃₁	semidirect
207. H(3,𝔽₄)	C₂²×C₃₁	semidirect
208. #556	C₂²×C₃₁	semidirect
209. #551	C₂²×C₃₁	semidirect
210. #542	C₂²×C₃₁	semidirect
211. #538	C₂²×C₃₁	semidirect
212. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
213. #529	C₂²×C₃₁	semidirect
214. C₂×#126	C₂²×C₃₁	semidirect
215. C₂×#126	C₂²×C₃₁	semidirect
216. C₂×#126	C₂²×C₃₁	semidirect
217. C₂×#126	C₂²×C₃₁	semidirect
218. C₂×#126	C₂²×C₃₁	semidirect
219. C₂×#125	C₂²×C₃₁	semidirect
223. C₂×#124	C₂²×C₃₁	semidirect
226. C₂×#123	C₂²×C₃₁	semidirect
227. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
228. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
229. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
230. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
234. C₂×#120	C₂²×C₃₁	semidirect
235. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
236. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
239. C₂×C₄×D₄	C₂²×C₃₁	semidirect
240. C₂×#117	C₂²×C₃₁	semidirect
241. C₂×#117	C₂²×C₃₁	semidirect
242. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
243. C₂²×C₄²	C₂²×C₃₁	semidirect
246. C₂×C₃₁	#3568	direct (N × H)
257. C₄⋊Q₈	C₂³×C₃₁	semidirect
258. #126	C₂³×C₃₁	semidirect
259. #126	C₂³×C₃₁	semidirect
260. #126	C₂³×C₃₁	semidirect
261. #126	C₂³×C₃₁	semidirect
262. #126	C₂³×C₃₁	semidirect
263. #125	C₂³×C₃₁	semidirect
267. #124	C₂³×C₃₁	semidirect
270. #123	C₂³×C₃₁	semidirect
271. C₂²⋊Q₈	C₂³×C₃₁	semidirect
272. C₂²⋊Q₈	C₂³×C₃₁	semidirect
273. C₂²⋊Q₈	C₂³×C₃₁	semidirect
274. C₂²⋊Q₈	C₂³×C₃₁	semidirect
278. #120	C₂³×C₃₁	semidirect
279. C₄×Q₈	C₂³×C₃₁	semidirect
280. C₄×Q₈	C₂³×C₃₁	semidirect
283. C₄×D₄	C₂³×C₃₁	semidirect
284. #117	C₂³×C₃₁	semidirect
285. #117	C₂³×C₃₁	semidirect
303. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
309. C₂×C₄²	C₂³×C₃₁	semidirect
310. C₃₁	C₂×#3568	direct (N × H)
401. C₂	C₃₁×#3568	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×#3568	2
C₂×C₃₁×#563	2
C₂×C₃₁×H(3,𝔽₄)	2
C₂×C₃₁×#556	2
C₂×C₃₁×#551	2
C₂×C₃₁×#542	2
C₂×C₃₁×#538	2
C₂×C₃₁×#529	2
C₂×#3568	31

Subgroups — C2×C31×#3568 #21519495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3568 #21519495