Subgroups — C₂×C₃₁×#3506 #21519528

Order 7936.

7994 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#559	C₂	1	4	yes	maximal, complemented
3	C₂×C₃₁×#556	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#555	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#553	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#550	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#538	C₂	1	4	yes	maximal, complemented
9	C₂×C₃₁×#535	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#525	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₁×#520	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₃₁	C₂²	1	2	yes	—
16	C₂²×#41×C₃₁	C₂²	1	4	yes	complemented
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
19	C₃₁×#559	C₂²	1	64	yes	complemented
20	C₃₁×#556	C₂²	1	32	yes	complemented
21	C₃₁×#555	C₂²	1	32	yes	complemented
22	C₃₁×#553	C₂²	1	64	yes	complemented
23	C₃₁×#550	C₂²	1	32	yes	complemented
24	C₃₁×#547	C₂²	1	32	yes	complemented
25	C₃₁×#538	C₂²	1	64	yes	complemented
26	C₃₁×#535	C₂²	1	32	yes	complemented
27	C₃₁×#533	C₂²	1	16	yes	complemented
28	C₃₁×#532	C₂²	1	16	yes	complemented
29	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃₁×#127	C₂²	1	4	yes	—
33	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#126	C₂²	1	8	yes	complemented
35	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
36	C₂×C₃₁×#124	C₂²	1	4	yes	—
37	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#124	C₂²	1	8	yes	complemented
39	C₃₁×#525	C₂²	1	64	yes	complemented
40	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
41	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₂×C₃₁×#121	C₂²	1	2	yes	—
46	C₂×C₃₁×#121	C₂²	1	2	yes	—
47	C₂×C₃₁×#121	C₂²	1	4	yes	—
48	C₂×C₃₁×#121	C₂²	1	4	yes	—
49	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
50	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
51	C₂×C₃₁×#120	C₂²	1	8	yes	—
52	C₃₁×#520	C₂²	1	32	yes	complemented
53	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
54	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
55	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
57	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	—
61	C₂×C₄×D₄×C₃₁	C₂²	1	16	yes	complemented
62	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
63	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
64	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
65	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
66	C₂×C₃₁×#117	C₂²	1	2	yes	—
67	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
68	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
69	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
71	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
73	C₂⁵×C₃₁	C₂³	1	2	yes	—
74	C₂×#41×C₃₁	—	2	16	no	—
75	C₂×#41×C₃₁	—	4	16	no	—
76	C₂×#41×C₃₁	C₂³	1	16	yes	—
77	C₂×#41×C₃₁	C₂³	1	32	yes	complemented
78	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
79	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
80	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₃₁	—	2	8	no	—
82	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
83	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
84	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
91	C₂³×C₄×C₃₁	—	4	8	no	—
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
98	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	16	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
102	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
103	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
104	C₃₁×#127	C₂³	1	32	yes	—
105	C₃₁×#127	C₂³	1	8	yes	complemented
106	C₃₁×#126	C₂³	1	64	yes	complemented
107	C₃₁×#125	C₂³	1	16	yes	complemented
108	C₃₁×#124	C₂³	1	32	yes	—
109	C₃₁×#124	C₂³	1	16	yes	complemented
110	C₃₁×#124	C₂³	1	64	yes	complemented
111	C₃₁×#123	C₂³	1	64	yes	complemented
112	C₃₁×#123	C₂³	1	64	yes	complemented
113	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
114	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
115	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
116	C₃₁×#121	C₂³	1	16	yes	—
117	C₃₁×#121	C₂³	1	16	yes	—
118	C₃₁×#121	C₂³	1	32	yes	—
119	C₃₁×#121	C₂³	1	32	yes	—
120	C₃₁×#121	C₂³	1	32	yes	complemented
121	C₃₁×#121	C₂³	1	64	yes	complemented
122	C₃₁×#120	C₂³	1	64	yes	—
123	C₄×Q₈×C₃₁	C₂³	1	32	yes	complemented
124	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
125	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
126	C₄×D₄×C₃₁	C₂³	1	16	yes	—
127	C₄×D₄×C₃₁	C₂³	1	16	yes	—
128	C₄×D₄×C₃₁	C₂³	1	16	yes	—
129	C₄×D₄×C₃₁	C₂³	1	16	yes	—
130	C₄×D₄×C₃₁	C₂³	1	64	yes	—
131	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
132	C₄×D₄×C₃₁	C₂³	1	64	yes	complemented
133	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
134	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
135	C₃₁×#117	C₂³	1	16	yes	—
136	C₃₁×#117	C₂³	1	32	yes	complemented
137	C₃₁×#117	C₂³	1	32	yes	complemented
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	32	yes	complemented
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
160	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
165	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
166	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
167	C₂⁴×C₃₁	—	2	8	no	—
168	C₂⁴×C₃₁	—	4	4	no	—
169	C₂⁴×C₃₁	—	4	4	no	—
170	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
171	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
172	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
173	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
174	#41×C₃₁	—	2	64	no	—
175	#41×C₃₁	—	4	64	no	—
176	C₂×Q₈×C₃₁	—	2	8	no	—
177	C₂×Q₈×C₃₁	—	2	8	no	—
178	C₂×Q₈×C₃₁	—	4	4	no	—
179	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
180	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
181	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
182	C₂×D₄×C₃₁	—	2	16	no	—
183	C₂×D₄×C₃₁	—	2	8	no	—
184	C₂×D₄×C₃₁	—	2	8	no	—
185	C₂×D₄×C₃₁	—	2	8	no	—
186	C₂×D₄×C₃₁	—	2	32	no	—
187	C₂×D₄×C₃₁	—	2	8	no	—
188	C₂×D₄×C₃₁	—	4	4	no	—
189	C₂×D₄×C₃₁	—	4	16	no	—
190	C₂×D₄×C₃₁	—	4	16	no	—
191	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
192	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
193	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
194	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
195	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
196	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
197	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
198	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
199	C₂²×C₄×C₃₁	—	2	16	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	2	16	no	—
202	C₂²×C₄×C₃₁	—	4	32	no	—
203	C₂²×C₄×C₃₁	—	4	4	no	—
204	C₂²×C₄×C₃₁	—	4	8	no	—
205	C₂²×C₄×C₃₁	—	4	2	no	—
206	C₂²×C₄×C₃₁	—	4	16	no	—
207	C₂²×C₄×C₃₁	#41	1	8	yes	complemented
208	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
227	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
228	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
229	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
230	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
231	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
232	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
233	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
234	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
235	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
236	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
237	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
238	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
239	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
240	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
241	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
242	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
243	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
244	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
245	C₄²×C₃₁	C₂⁴	1	4	yes	—
246	C₄²×C₃₁	C₂⁴	1	4	yes	—
247	C₄²×C₃₁	C₂⁴	1	4	yes	—
248	C₄²×C₃₁	C₂⁴	1	4	yes	—
249	C₄²×C₃₁	C₂⁴	1	16	yes	—
250	C₄²×C₃₁	C₂⁴	1	32	yes	—
251	C₂×#3506	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	2	no	—
254	C₂³×C₃₁	—	2	8	no	—
255	C₂³×C₃₁	—	2	16	no	—
256	C₂³×C₃₁	—	2	8	no	—
257	C₂³×C₃₁	—	2	8	no	—
258	C₂³×C₃₁	—	2	8	no	—
259	C₂³×C₃₁	—	2	8	no	—
260	C₂³×C₃₁	—	2	8	no	—
261	C₂³×C₃₁	—	4	8	no	—
262	C₂³×C₃₁	—	4	8	no	—
263	C₂³×C₃₁	—	4	32	no	—
264	C₂³×C₃₁	C₂×#41	1	4	yes	—
265	C₂³×C₃₁	C₂⁵	1	8	yes	—
266	C₂³×C₃₁	C₂⁵	1	8	yes	—
267	C₂³×C₃₁	C₂⁵	1	2	yes	—
268	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
269	Q₈×C₃₁	—	2	16	no	—
270	Q₈×C₃₁	—	2	16	no	—
271	Q₈×C₃₁	—	4	8	no	—
272	D₄×C₃₁	—	2	32	no	—
273	D₄×C₃₁	—	2	16	no	—
274	D₄×C₃₁	—	2	16	no	—
275	D₄×C₃₁	—	2	16	no	—
276	D₄×C₃₁	—	2	16	no	—
277	D₄×C₃₁	—	4	8	no	—
278	D₄×C₃₁	—	4	32	no	—
279	D₄×C₃₁	—	4	32	no	—
280	C₂×C₄×C₃₁	—	2	8	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	8	no	—
283	C₂×C₄×C₃₁	—	2	8	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	8	no	—
287	C₂×C₄×C₃₁	—	2	32	no	—
288	C₂×C₄×C₃₁	—	2	8	no	—
289	C₂×C₄×C₃₁	—	2	32	no	—
290	C₂×C₄×C₃₁	—	4	8	no	—
291	C₂×C₄×C₃₁	—	4	16	no	—
292	C₂×C₄×C₃₁	—	4	4	no	—
293	C₂×C₄×C₃₁	—	4	32	no	—
294	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
295	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
296	C₂×C₄×C₃₁	C₂×#41	1	16	yes	complemented
297	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
298	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
299	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
300	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
301	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
302	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
303	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
304	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
305	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
306	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
307	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
308	#3506	C₂×C₃₁	1	32	yes	direct product factor
309	C₂×#559	C₂×C₃₁	1	4	yes	complemented
310	C₂×#556	C₂×C₃₁	1	2	yes	complemented
311	C₂×#555	C₂×C₃₁	1	2	yes	complemented
312	C₂×#553	C₂×C₃₁	1	4	yes	complemented
313	C₂×#550	C₂×C₃₁	1	2	yes	complemented
314	C₂×#547	C₂×C₃₁	1	2	yes	complemented
315	C₂×#538	C₂×C₃₁	1	4	yes	complemented
316	C₂×#535	C₂×C₃₁	1	2	yes	complemented
317	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
318	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
319	C₂×#525	C₂×C₃₁	1	4	yes	complemented
320	C₂×#520	C₂×C₃₁	1	2	yes	complemented
321	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
322	C₂²×C₃₁	—	2	2	no	—
323	C₂²×C₃₁	—	2	2	no	—
324	C₂²×C₃₁	—	2	8	no	—
325	C₂²×C₃₁	—	2	8	no	—
326	C₂²×C₃₁	—	2	8	no	—
327	C₂²×C₃₁	—	2	8	no	—
328	C₂²×C₃₁	—	2	8	no	—
329	C₂²×C₃₁	—	2	8	no	—
330	C₂²×C₃₁	—	2	8	no	—
331	C₂²×C₃₁	—	4	32	no	—
332	C₂²×C₃₁	—	4	16	no	—
333	C₂²×C₃₁	—	4	16	no	—
334	C₂²×C₃₁	C₂²×#41	1	4	yes	—
335	C₂²×C₃₁	C₂²×#41	1	2	yes	—
336	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₃₁	#585	1	2	yes	—
338	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
339	C₄×C₃₁	—	2	8	no	—
340	C₄×C₃₁	—	2	2	no	—
341	C₄×C₃₁	—	2	8	no	—
342	C₄×C₃₁	—	2	8	no	—
343	C₄×C₃₁	—	2	2	no	—
344	C₄×C₃₁	—	2	2	no	—
345	C₄×C₃₁	—	2	8	no	—
346	C₄×C₃₁	C₂²×#41	1	4	yes	—
347	C₄×C₃₁	C₂²×#41	1	4	yes	—
348	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
349	C₂²×#41	C₂²×C₃₁	1	2	yes	—
350	C₂²×#41	C₂²×C₃₁	1	4	yes	complemented
351	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
352	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
353	#559	C₂²×C₃₁	1	64	yes	complemented
354	#556	C₂²×C₃₁	1	32	yes	complemented
355	#555	C₂²×C₃₁	1	32	yes	complemented
356	#553	C₂²×C₃₁	1	64	yes	complemented
357	#550	C₂²×C₃₁	1	32	yes	complemented
358	#547	C₂²×C₃₁	1	32	yes	complemented
359	#538	C₂²×C₃₁	1	64	yes	complemented
360	#535	C₂²×C₃₁	1	32	yes	complemented
361	#533	C₂²×C₃₁	1	16	yes	complemented
362	#532	C₂²×C₃₁	1	16	yes	complemented
363	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
364	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
365	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#127	C₂²×C₃₁	1	4	yes	—
367	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
368	C₂×#126	C₂²×C₃₁	1	8	yes	complemented
369	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
370	C₂×#124	C₂²×C₃₁	1	4	yes	—
371	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
372	C₂×#124	C₂²×C₃₁	1	8	yes	complemented
373	#525	C₂²×C₃₁	1	64	yes	complemented
374	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
375	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
376	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
377	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
379	C₂×#121	C₂²×C₃₁	1	2	yes	—
380	C₂×#121	C₂²×C₃₁	1	2	yes	—
381	C₂×#121	C₂²×C₃₁	1	4	yes	—
382	C₂×#121	C₂²×C₃₁	1	4	yes	—
383	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
384	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
385	C₂×#120	C₂²×C₃₁	1	8	yes	—
386	#520	C₂²×C₃₁	1	32	yes	complemented
387	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
388	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
389	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
390	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
392	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
393	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
394	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	—
395	C₂×C₄×D₄	C₂²×C₃₁	1	16	yes	complemented
396	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
397	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
398	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
399	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
400	C₂×#117	C₂²×C₃₁	1	2	yes	—
401	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
402	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
403	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
405	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
406	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
407	C₂×C₃₁	—	2	4	no	—
408	C₂×C₃₁	—	4	8	no	—
409	C₂×C₃₁	—	4	8	no	—
410	C₂×C₃₁	#3506	1	4	yes	direct product factor
411	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
412	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
414	C₂⁵	C₂³×C₃₁	1	2	yes	—
415	C₂×#41	—	2	16	no	—
416	C₂×#41	—	4	16	no	—
417	C₂×#41	C₂³×C₃₁	1	16	yes	—
418	C₂×#41	C₂³×C₃₁	1	32	yes	complemented
419	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
420	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
421	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
422	C₂²×D₄	—	2	8	no	—
423	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
424	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
425	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
426	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
427	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
428	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
429	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
430	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
431	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
432	C₂³×C₄	—	4	8	no	—
433	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
434	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
435	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
438	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
439	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
440	C₂³×C₄	C₂³×C₃₁	1	16	yes	—
441	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
442	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
443	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
444	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
445	#127	C₂³×C₃₁	1	32	yes	—
446	#127	C₂³×C₃₁	1	8	yes	complemented
447	#126	C₂³×C₃₁	1	64	yes	complemented
448	#125	C₂³×C₃₁	1	16	yes	complemented
449	#124	C₂³×C₃₁	1	32	yes	—
450	#124	C₂³×C₃₁	1	16	yes	complemented
451	#124	C₂³×C₃₁	1	64	yes	complemented
452	#123	C₂³×C₃₁	1	64	yes	complemented
453	#123	C₂³×C₃₁	1	64	yes	complemented
454	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
455	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
456	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
457	#121	C₂³×C₃₁	1	16	yes	—
458	#121	C₂³×C₃₁	1	16	yes	—
459	#121	C₂³×C₃₁	1	32	yes	—
460	#121	C₂³×C₃₁	1	32	yes	—
461	#121	C₂³×C₃₁	1	32	yes	complemented
462	#121	C₂³×C₃₁	1	64	yes	complemented
463	#120	C₂³×C₃₁	1	64	yes	—
464	C₄×Q₈	C₂³×C₃₁	1	32	yes	complemented
465	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
466	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
467	C₄×D₄	C₂³×C₃₁	1	16	yes	—
468	C₄×D₄	C₂³×C₃₁	1	16	yes	—
469	C₄×D₄	C₂³×C₃₁	1	16	yes	—
470	C₄×D₄	C₂³×C₃₁	1	16	yes	—
471	C₄×D₄	C₂³×C₃₁	1	64	yes	—
472	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
473	C₄×D₄	C₂³×C₃₁	1	64	yes	complemented
474	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
475	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
476	#117	C₂³×C₃₁	1	16	yes	—
477	#117	C₂³×C₃₁	1	32	yes	complemented
478	#117	C₂³×C₃₁	1	32	yes	complemented
479	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃₁	1	32	yes	complemented
492	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
501	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
502	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
503	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
508	C₃₁	C₂×#3506	1	1	yes	characteristic, direct product factor, Sylow
509	C₂⁴	—	2	8	no	—
510	C₂⁴	—	4	4	no	—
511	C₂⁴	—	4	4	no	—
512	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
513	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
514	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
515	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
516	#41	—	2	64	no	—
517	#41	—	4	64	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	2	8	no	—
520	C₂×Q₈	—	4	4	no	—
521	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
522	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
523	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
524	C₂×D₄	—	2	16	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	8	no	—
528	C₂×D₄	—	2	32	no	—
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	16	no	—
532	C₂×D₄	—	4	16	no	—
533	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
534	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
535	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
536	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
537	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
538	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
539	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
540	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
541	C₂²×C₄	—	2	16	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	16	no	—
544	C₂²×C₄	—	4	32	no	—
545	C₂²×C₄	—	4	4	no	—
546	C₂²×C₄	—	4	8	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	16	no	—
549	C₂²×C₄	#41×C₃₁	1	8	yes	complemented
550	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
559	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
560	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
562	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	—
563	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
564	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
568	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
569	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
570	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
571	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
572	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
573	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
574	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
575	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
576	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
577	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
578	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
579	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
580	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
581	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
582	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
583	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
584	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
585	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
586	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
587	C₄²	C₂⁴×C₃₁	1	4	yes	—
588	C₄²	C₂⁴×C₃₁	1	4	yes	—
589	C₄²	C₂⁴×C₃₁	1	4	yes	—
590	C₄²	C₂⁴×C₃₁	1	4	yes	—
591	C₄²	C₂⁴×C₃₁	1	16	yes	—
592	C₄²	C₂⁴×C₃₁	1	32	yes	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	8	no	—
596	C₂³	—	2	16	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	32	no	—
605	C₂³	C₂×#41×C₃₁	1	4	yes	—
606	C₂³	C₂⁵×C₃₁	1	8	yes	—
607	C₂³	C₂⁵×C₃₁	1	8	yes	—
608	C₂³	C₂⁵×C₃₁	1	2	yes	—
609	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
610	Q₈	—	2	16	no	—
611	Q₈	—	2	16	no	—
612	Q₈	—	4	8	no	—
613	D₄	—	2	32	no	—
614	D₄	—	2	16	no	—
615	D₄	—	2	16	no	—
616	D₄	—	2	16	no	—
617	D₄	—	2	16	no	—
618	D₄	—	4	8	no	—
619	D₄	—	4	32	no	—
620	D₄	—	4	32	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	32	no	—
629	C₂×C₄	—	2	8	no	—
630	C₂×C₄	—	2	32	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	16	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	32	no	—
635	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
636	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
637	C₂×C₄	C₂×#41×C₃₁	1	16	yes	complemented
638	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
639	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
640	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
641	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
642	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
643	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
644	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
645	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
646	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
647	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
648	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	2	8	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	8	no	—
655	C₂²	—	2	8	no	—
656	C₂²	—	2	8	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	4	32	no	—
659	C₂²	—	4	16	no	—
660	C₂²	—	4	16	no	—
661	C₂²	C₂²×#41×C₃₁	1	4	yes	—
662	C₂²	C₂²×#41×C₃₁	1	2	yes	—
663	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
664	C₂²	C₃₁×#585	1	2	yes	—
665	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
666	C₄	—	2	8	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	8	no	—
669	C₄	—	2	8	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	8	no	—
673	C₄	C₂²×#41×C₃₁	1	4	yes	—
674	C₄	C₂²×#41×C₃₁	1	4	yes	—
675	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	4	8	no	—
678	C₂	—	4	8	no	—
679	C₂	C₃₁×#3506	1	4	yes	direct product factor
680	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
681	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	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×#3506	C₂	direct (N × H)
2. C₂×C₃₁×#559	C₂	semidirect
3. C₂×C₃₁×#556	C₂	semidirect
4. C₂×C₃₁×#555	C₂	semidirect
5. C₂×C₃₁×#553	C₂	semidirect
6. C₂×C₃₁×#550	C₂	semidirect
7. C₂×C₃₁×#547	C₂	semidirect
8. C₂×C₃₁×#538	C₂	semidirect
9. C₂×C₃₁×#535	C₂	semidirect
10. C₂×C₃₁×#533	C₂	semidirect
11. C₂×C₃₁×#532	C₂	semidirect
12. C₂×C₃₁×#525	C₂	semidirect
13. C₂×C₃₁×#520	C₂	semidirect
14. C₂²×C₄×D₄×C₃₁	C₂	semidirect
16. C₂²×#41×C₃₁	C₂²	semidirect
19. C₃₁×#559	C₂²	semidirect
20. C₃₁×#556	C₂²	semidirect
21. C₃₁×#555	C₂²	semidirect
22. C₃₁×#553	C₂²	semidirect
23. C₃₁×#550	C₂²	semidirect
24. C₃₁×#547	C₂²	semidirect
25. C₃₁×#538	C₂²	semidirect
26. C₃₁×#535	C₂²	semidirect
27. C₃₁×#533	C₂²	semidirect
28. C₃₁×#532	C₂²	semidirect
29. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₃₁×#127	C₂²	semidirect
34. C₂×C₃₁×#126	C₂²	semidirect
35. C₂×C₃₁×#125	C₂²	semidirect
37. C₂×C₃₁×#124	C₂²	semidirect
38. C₂×C₃₁×#124	C₂²	semidirect
39. C₃₁×#525	C₂²	semidirect
40. C₂×C₃₁×#123	C₂²	semidirect
41. C₂×C₃₁×#123	C₂²	semidirect
44. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₃₁×#121	C₂²	semidirect
50. C₂×C₃₁×#121	C₂²	semidirect
52. C₃₁×#520	C₂²	semidirect
53. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
54. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
55. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
61. C₂×C₄×D₄×C₃₁	C₂²	semidirect
62. C₂×C₄×D₄×C₃₁	C₂²	semidirect
63. C₂×C₄×D₄×C₃₁	C₂²	semidirect
64. C₂×C₄×D₄×C₃₁	C₂²	semidirect
65. C₂×C₄×D₄×C₃₁	C₂²	semidirect
67. C₂×C₃₁×#117	C₂²	semidirect
68. C₂×C₃₁×#117	C₂²	semidirect
70. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
77. C₂×#41×C₃₁	C₂³	semidirect
101. C₃₁×C₄⋊Q₈	C₂³	semidirect
102. C₃₁×C₄⋊Q₈	C₂³	semidirect
103. C₃₁×C₄⋊Q₈	C₂³	semidirect
105. C₃₁×#127	C₂³	semidirect
106. C₃₁×#126	C₂³	semidirect
107. C₃₁×#125	C₂³	semidirect
109. C₃₁×#124	C₂³	semidirect
110. C₃₁×#124	C₂³	semidirect
111. C₃₁×#123	C₂³	semidirect
112. C₃₁×#123	C₂³	semidirect
115. C₃₁×C₂²⋊Q₈	C₂³	semidirect
120. C₃₁×#121	C₂³	semidirect
121. C₃₁×#121	C₂³	semidirect
123. C₄×Q₈×C₃₁	C₂³	semidirect
124. C₄×Q₈×C₃₁	C₂³	semidirect
125. C₄×Q₈×C₃₁	C₂³	semidirect
131. C₄×D₄×C₃₁	C₂³	semidirect
132. C₄×D₄×C₃₁	C₂³	semidirect
133. C₄×D₄×C₃₁	C₂³	semidirect
134. C₄×D₄×C₃₁	C₂³	semidirect
136. C₃₁×#117	C₂³	semidirect
137. C₃₁×#117	C₂³	semidirect
150. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
207. C₂²×C₄×C₃₁	#41	semidirect
251. C₂×#3506	C₃₁	direct (N × H)
296. C₂×C₄×C₃₁	C₂×#41	semidirect
308. #3506	C₂×C₃₁	direct (N × H)
309. C₂×#559	C₂×C₃₁	semidirect
310. C₂×#556	C₂×C₃₁	semidirect
311. C₂×#555	C₂×C₃₁	semidirect
312. C₂×#553	C₂×C₃₁	semidirect
313. C₂×#550	C₂×C₃₁	semidirect
314. C₂×#547	C₂×C₃₁	semidirect
315. C₂×#538	C₂×C₃₁	semidirect
316. C₂×#535	C₂×C₃₁	semidirect
317. C₂×#533	C₂×C₃₁	semidirect
318. C₂×#532	C₂×C₃₁	semidirect
319. C₂×#525	C₂×C₃₁	semidirect
320. C₂×#520	C₂×C₃₁	semidirect
321. C₂²×C₄×D₄	C₂×C₃₁	semidirect
350. C₂²×#41	C₂²×C₃₁	semidirect
353. #559	C₂²×C₃₁	semidirect
354. #556	C₂²×C₃₁	semidirect
355. #555	C₂²×C₃₁	semidirect
356. #553	C₂²×C₃₁	semidirect
357. #550	C₂²×C₃₁	semidirect
358. #547	C₂²×C₃₁	semidirect
359. #538	C₂²×C₃₁	semidirect
360. #535	C₂²×C₃₁	semidirect
361. #533	C₂²×C₃₁	semidirect
362. #532	C₂²×C₃₁	semidirect
363. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
364. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
365. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
367. C₂×#127	C₂²×C₃₁	semidirect
368. C₂×#126	C₂²×C₃₁	semidirect
369. C₂×#125	C₂²×C₃₁	semidirect
371. C₂×#124	C₂²×C₃₁	semidirect
372. C₂×#124	C₂²×C₃₁	semidirect
373. #525	C₂²×C₃₁	semidirect
374. C₂×#123	C₂²×C₃₁	semidirect
375. C₂×#123	C₂²×C₃₁	semidirect
378. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
383. C₂×#121	C₂²×C₃₁	semidirect
384. C₂×#121	C₂²×C₃₁	semidirect
386. #520	C₂²×C₃₁	semidirect
387. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
388. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
389. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
395. C₂×C₄×D₄	C₂²×C₃₁	semidirect
396. C₂×C₄×D₄	C₂²×C₃₁	semidirect
397. C₂×C₄×D₄	C₂²×C₃₁	semidirect
398. C₂×C₄×D₄	C₂²×C₃₁	semidirect
399. C₂×C₄×D₄	C₂²×C₃₁	semidirect
401. C₂×#117	C₂²×C₃₁	semidirect
402. C₂×#117	C₂²×C₃₁	semidirect
404. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
410. C₂×C₃₁	#3506	direct (N × H)
418. C₂×#41	C₂³×C₃₁	semidirect
442. C₄⋊Q₈	C₂³×C₃₁	semidirect
443. C₄⋊Q₈	C₂³×C₃₁	semidirect
444. C₄⋊Q₈	C₂³×C₃₁	semidirect
446. #127	C₂³×C₃₁	semidirect
447. #126	C₂³×C₃₁	semidirect
448. #125	C₂³×C₃₁	semidirect
450. #124	C₂³×C₃₁	semidirect
451. #124	C₂³×C₃₁	semidirect
452. #123	C₂³×C₃₁	semidirect
453. #123	C₂³×C₃₁	semidirect
456. C₂²⋊Q₈	C₂³×C₃₁	semidirect
461. #121	C₂³×C₃₁	semidirect
462. #121	C₂³×C₃₁	semidirect
464. C₄×Q₈	C₂³×C₃₁	semidirect
465. C₄×Q₈	C₂³×C₃₁	semidirect
466. C₄×Q₈	C₂³×C₃₁	semidirect
472. C₄×D₄	C₂³×C₃₁	semidirect
473. C₄×D₄	C₂³×C₃₁	semidirect
474. C₄×D₄	C₂³×C₃₁	semidirect
475. C₄×D₄	C₂³×C₃₁	semidirect
477. #117	C₂³×C₃₁	semidirect
478. #117	C₂³×C₃₁	semidirect
491. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
508. C₃₁	C₂×#3506	direct (N × H)
549. C₂²×C₄	#41×C₃₁	semidirect
637. C₂×C₄	C₂×#41×C₃₁	semidirect
679. C₂	C₃₁×#3506	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×#3506	2
C₂×C₃₁×#559	2
C₂×C₃₁×#556	2
C₂×C₃₁×#555	2
C₂×C₃₁×#553	2
C₂×C₃₁×#550	2
C₂×C₃₁×#547	2
C₂×C₃₁×#538	2
C₂×C₃₁×#535	2
C₂×C₃₁×#533	2
C₂×C₃₁×#532	2
C₂×C₃₁×#525	2
C₂×C₃₁×#520	2
C₂²×C₄×D₄×C₃₁	2
C₂×#3506	31

Subgroups — C2×C31×#3506 #21519528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3506 #21519528