Subgroups — C₃₁×#3541 #16843474

Order 3968.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#563	C₂	1	2	yes	maximal, complemented
2	C₃₁×#562	C₂	1	2	yes	maximal, complemented
3	C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#554	C₂	1	2	yes	maximal, complemented
6	C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#553	C₂	1	2	yes	maximal, complemented
8	C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#542	C₂	1	2	yes	maximal, complemented
15	C₃₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#539	C₂	1	2	yes	maximal, complemented
17	C₃₁×#538	C₂	1	2	yes	maximal, complemented
18	C₃₁×#538	C₂	1	2	yes	maximal, complemented
19	C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
31	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#126	C₂²	1	2	yes	—
35	C₃₁×#126	C₂²	1	2	yes	—
36	C₃₁×#126	C₂²	1	2	yes	—
37	C₃₁×#126	C₂²	1	2	yes	—
38	C₃₁×#126	C₂²	1	2	yes	complemented
39	C₃₁×#126	C₂²	1	2	yes	complemented
40	C₃₁×#126	C₂²	1	2	yes	complemented
41	C₃₁×#125	C₂²	1	2	yes	complemented
42	C₃₁×#125	C₂²	1	2	yes	complemented
43	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#125	C₂²	1	2	yes	complemented
45	C₃₁×#125	C₂²	1	2	yes	complemented
46	C₃₁×#124	C₂²	1	2	yes	—
47	C₃₁×#124	C₂²	1	2	yes	—
48	C₃₁×#124	C₂²	1	2	yes	—
49	C₃₁×#124	C₂²	1	2	yes	—
50	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#124	C₂²	1	2	yes	complemented
52	C₃₁×#123	C₂²	1	1	yes	characteristic
53	C₃₁×#123	C₂²	1	1	yes	characteristic
54	C₃₁×#123	C₂²	1	2	yes	—
55	C₃₁×#123	C₂²	1	2	yes	—
56	C₃₁×#123	C₂²	1	2	yes	—
57	C₃₁×#123	C₂²	1	2	yes	—
58	C₃₁×#123	C₂²	1	2	yes	—
59	C₃₁×#123	C₂²	1	2	yes	complemented
60	C₃₁×#123	C₂²	1	2	yes	complemented
61	C₃₁×#123	C₂²	1	2	yes	complemented
62	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
63	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
65	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
66	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
67	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
68	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
69	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
72	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
73	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
74	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
79	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
80	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
81	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
82	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
83	C₃₁×#121	C₂²	1	1	yes	characteristic
84	C₃₁×#121	C₂²	1	1	yes	characteristic
85	C₃₁×#121	C₂²	1	1	yes	characteristic
86	C₃₁×#121	C₂²	1	1	yes	characteristic
87	C₃₁×#121	C₂²	1	2	yes	—
88	C₃₁×#121	C₂²	1	2	yes	—
89	C₃₁×#121	C₂²	1	2	yes	—
90	C₃₁×#121	C₂²	1	2	yes	—
91	C₃₁×#121	C₂²	1	2	yes	—
92	C₃₁×#121	C₂²	1	2	yes	—
93	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#121	C₂²	1	2	yes	complemented
95	C₃₁×#120	C₂²	1	1	yes	characteristic
96	C₃₁×#120	C₂²	1	2	yes	—
97	C₃₁×#120	C₂²	1	1	yes	characteristic
98	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₄×C₃₁	C₂²	1	2	yes	—
103	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×D₄×C₃₁	C₂²	1	2	yes	—
108	C₄×D₄×C₃₁	C₂²	1	2	yes	—
109	C₄×D₄×C₃₁	C₂²	1	2	yes	—
110	C₄×D₄×C₃₁	C₂²	1	2	yes	—
111	C₄×D₄×C₃₁	C₂²	1	2	yes	—
112	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
113	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#117	C₂²	1	1	yes	characteristic
115	C₃₁×#117	C₂²	1	1	yes	characteristic
116	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#117	C₂²	1	2	yes	complemented
118	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
123	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
124	#41×C₃₁	—	4	2	no	—
125	#41×C₃₁	—	4	2	no	—
126	#41×C₃₁	—	4	2	no	—
127	C₂×Q₈×C₃₁	—	4	2	no	—
128	C₂×Q₈×C₃₁	—	4	2	no	—
129	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
133	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
136	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₃₁	C₂³	1	2	yes	—
139	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₃₁	C₂³	1	2	yes	—
142	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₄×C₃₁	C₂³	1	2	yes	—
148	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×C₄×C₃₁	—	4	2	no	—
150	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
156	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
202	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
205	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
221	C₄²×C₃₁	C₂³	1	2	yes	—
222	C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₄²×C₃₁	C₂³	1	1	yes	characteristic
224	C₄²×C₃₁	C₂³	1	2	yes	—
225	C₄²×C₃₁	C₂³	1	2	yes	—
226	C₄²×C₃₁	C₂³	1	2	yes	—
227	C₄²×C₃₁	C₂³	1	2	yes	—
228	C₂³×C₃₁	—	2	2	no	—
229	C₂³×C₃₁	—	4	1	no	—
230	C₂³×C₃₁	—	4	1	no	—
231	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
233	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
234	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₃₁	C₂⁴	1	2	yes	—
236	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
237	Q₈×C₃₁	—	2	2	no	—
238	Q₈×C₃₁	—	2	2	no	—
239	Q₈×C₃₁	—	2	2	no	—
240	Q₈×C₃₁	—	4	2	no	—
241	Q₈×C₃₁	—	4	2	no	—
242	Q₈×C₃₁	—	4	2	no	—
243	Q₈×C₃₁	—	4	1	no	—
244	D₄×C₃₁	—	2	2	no	—
245	D₄×C₃₁	—	2	2	no	—
246	D₄×C₃₁	—	2	4	no	—
247	D₄×C₃₁	—	2	2	no	—
248	D₄×C₃₁	—	4	1	no	—
249	D₄×C₃₁	—	4	2	no	—
250	D₄×C₃₁	—	4	2	no	—
251	D₄×C₃₁	—	4	1	no	—
252	D₄×C₃₁	—	4	1	no	—
253	D₄×C₃₁	—	4	1	no	—
254	D₄×C₃₁	—	4	1	no	—
255	D₄×C₃₁	—	4	2	no	—
256	D₄×C₃₁	—	4	2	no	—
257	C₂×C₄×C₃₁	—	2	2	no	—
258	C₂×C₄×C₃₁	—	2	2	no	—
259	C₂×C₄×C₃₁	—	2	2	no	—
260	C₂×C₄×C₃₁	—	2	2	no	—
261	C₂×C₄×C₃₁	—	2	2	no	—
262	C₂×C₄×C₃₁	—	4	1	no	—
263	C₂×C₄×C₃₁	—	4	1	no	—
264	C₂×C₄×C₃₁	—	4	1	no	—
265	C₂×C₄×C₃₁	—	4	2	no	—
266	C₂×C₄×C₃₁	—	4	2	no	—
267	C₂×C₄×C₃₁	—	4	2	no	—
268	C₂×C₄×C₃₁	—	4	2	no	—
269	C₂×C₄×C₃₁	—	4	2	no	—
270	C₂×C₄×C₃₁	—	4	2	no	—
271	C₂×C₄×C₃₁	—	4	2	no	—
272	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	#3541	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂²×C₃₁	—	2	1	no	—
291	C₂²×C₃₁	—	2	1	no	—
292	C₂²×C₃₁	—	2	1	no	—
293	C₂²×C₃₁	—	2	1	no	—
294	C₂²×C₃₁	—	2	1	no	—
295	C₂²×C₃₁	—	2	1	no	—
296	C₂²×C₃₁	—	2	2	no	—
297	C₂²×C₃₁	—	2	1	no	—
298	C₂²×C₃₁	—	2	1	no	—
299	C₂²×C₃₁	—	2	2	no	—
300	C₂²×C₃₁	—	2	1	no	—
301	C₂²×C₃₁	—	2	1	no	—
302	C₂²×C₃₁	—	2	1	no	—
303	C₂²×C₃₁	—	2	2	no	—
304	C₂²×C₃₁	—	2	1	no	—
305	C₂²×C₃₁	—	2	1	no	—
306	C₂²×C₃₁	—	2	1	no	—
307	C₂²×C₃₁	—	4	4	no	—
308	C₂²×C₃₁	2₋¹⁺⁴	1	2	yes	—
309	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
310	C₄×C₃₁	—	2	1	no	—
311	C₄×C₃₁	—	2	1	no	—
312	C₄×C₃₁	—	2	1	no	—
313	C₄×C₃₁	—	2	1	no	—
314	C₄×C₃₁	—	2	1	no	—
315	C₄×C₃₁	—	2	2	no	—
316	C₄×C₃₁	—	2	2	no	—
317	C₄×C₃₁	—	2	2	no	—
318	C₄×C₃₁	—	2	2	no	—
319	C₄×C₃₁	—	2	1	no	—
320	C₄×C₃₁	—	2	1	no	—
321	C₄×C₃₁	—	2	2	no	—
322	C₄×C₃₁	—	2	1	no	—
323	C₄×C₃₁	—	2	2	no	—
324	C₄×C₃₁	—	2	2	no	—
325	C₄×C₃₁	—	2	1	no	—
326	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
327	#563	C₂×C₃₁	1	2	yes	complemented
328	#562	C₂×C₃₁	1	2	yes	complemented
329	#556	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#554	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#554	C₂×C₃₁	1	2	yes	complemented
332	#553	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#553	C₂×C₃₁	1	2	yes	complemented
334	#552	C₂×C₃₁	1	1	yes	characteristic, complemented
335	D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#548	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#548	C₂×C₃₁	1	1	yes	characteristic, complemented
338	#547	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#542	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#542	C₂×C₃₁	1	2	yes	complemented
341	#541	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#539	C₂×C₃₁	1	2	yes	complemented
343	#538	C₂×C₃₁	1	2	yes	complemented
344	#538	C₂×C₃₁	1	2	yes	complemented
345	#537	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#536	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#525	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#525	C₂×C₃₁	1	1	yes	characteristic, complemented
349	C₂×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
350	C₂×C₃₁	—	2	2	no	—
351	C₂×C₃₁	—	4	1	no	—
352	C₂×C₃₁	—	4	1	no	—
353	C₂×C₃₁	—	4	2	no	—
354	C₂×C₃₁	—	4	1	no	—
355	C₂×C₃₁	—	4	1	no	—
356	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
358	C₂×C₃₁	#585	1	1	yes	characteristic
359	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
360	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
361	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
362	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic
363	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
364	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
365	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
366	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
367	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
368	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
369	#126	C₂²×C₃₁	1	2	yes	—
370	#126	C₂²×C₃₁	1	2	yes	—
371	#126	C₂²×C₃₁	1	2	yes	—
372	#126	C₂²×C₃₁	1	2	yes	—
373	#126	C₂²×C₃₁	1	2	yes	complemented
374	#126	C₂²×C₃₁	1	2	yes	complemented
375	#126	C₂²×C₃₁	1	2	yes	complemented
376	#125	C₂²×C₃₁	1	2	yes	complemented
377	#125	C₂²×C₃₁	1	2	yes	complemented
378	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
379	#125	C₂²×C₃₁	1	2	yes	complemented
380	#125	C₂²×C₃₁	1	2	yes	complemented
381	#124	C₂²×C₃₁	1	2	yes	—
382	#124	C₂²×C₃₁	1	2	yes	—
383	#124	C₂²×C₃₁	1	2	yes	—
384	#124	C₂²×C₃₁	1	2	yes	—
385	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
386	#124	C₂²×C₃₁	1	2	yes	complemented
387	#123	C₂²×C₃₁	1	1	yes	characteristic
388	#123	C₂²×C₃₁	1	1	yes	characteristic
389	#123	C₂²×C₃₁	1	2	yes	—
390	#123	C₂²×C₃₁	1	2	yes	—
391	#123	C₂²×C₃₁	1	2	yes	—
392	#123	C₂²×C₃₁	1	2	yes	—
393	#123	C₂²×C₃₁	1	2	yes	—
394	#123	C₂²×C₃₁	1	2	yes	complemented
395	#123	C₂²×C₃₁	1	2	yes	complemented
396	#123	C₂²×C₃₁	1	2	yes	complemented
397	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
398	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
399	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
400	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
402	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
403	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
405	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
407	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
408	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
409	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
411	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
412	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
413	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
414	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
415	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
416	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
417	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
418	#121	C₂²×C₃₁	1	1	yes	characteristic
419	#121	C₂²×C₃₁	1	1	yes	characteristic
420	#121	C₂²×C₃₁	1	1	yes	characteristic
421	#121	C₂²×C₃₁	1	1	yes	characteristic
422	#121	C₂²×C₃₁	1	2	yes	—
423	#121	C₂²×C₃₁	1	2	yes	—
424	#121	C₂²×C₃₁	1	2	yes	—
425	#121	C₂²×C₃₁	1	2	yes	—
426	#121	C₂²×C₃₁	1	2	yes	—
427	#121	C₂²×C₃₁	1	2	yes	—
428	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
429	#121	C₂²×C₃₁	1	2	yes	complemented
430	#120	C₂²×C₃₁	1	1	yes	characteristic
431	#120	C₂²×C₃₁	1	2	yes	—
432	#120	C₂²×C₃₁	1	1	yes	characteristic
433	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
436	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
437	C₄×D₄	C₂²×C₃₁	1	2	yes	—
438	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
439	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
440	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
441	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
442	C₄×D₄	C₂²×C₃₁	1	2	yes	—
443	C₄×D₄	C₂²×C₃₁	1	2	yes	—
444	C₄×D₄	C₂²×C₃₁	1	2	yes	—
445	C₄×D₄	C₂²×C₃₁	1	2	yes	—
446	C₄×D₄	C₂²×C₃₁	1	2	yes	—
447	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
448	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	#117	C₂²×C₃₁	1	1	yes	characteristic
450	#117	C₂²×C₃₁	1	1	yes	characteristic
451	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	#117	C₂²×C₃₁	1	2	yes	complemented
453	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
456	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
457	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
458	C₃₁	#3541	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	4	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
466	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
468	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
469	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
470	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
471	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
472	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
474	C₂×D₄	C₂³×C₃₁	1	2	yes	—
475	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
476	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×D₄	C₂³×C₃₁	1	2	yes	—
478	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×D₄	C₂³×C₃₁	1	2	yes	—
480	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
481	C₂×D₄	C₂³×C₃₁	1	2	yes	—
482	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
483	C₂×D₄	C₂³×C₃₁	1	2	yes	—
484	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
487	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
488	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
491	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
492	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
493	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
495	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
496	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
497	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
498	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
499	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
500	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
501	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
502	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
503	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
504	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
509	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
512	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
514	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
517	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
521	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
522	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
525	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
526	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
527	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
534	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
535	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
538	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
540	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
547	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
551	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₄²	C₂³×C₃₁	1	2	yes	—
558	C₄²	C₂³×C₃₁	1	1	yes	characteristic
559	C₄²	C₂³×C₃₁	1	1	yes	characteristic
560	C₄²	C₂³×C₃₁	1	2	yes	—
561	C₄²	C₂³×C₃₁	1	2	yes	—
562	C₄²	C₂³×C₃₁	1	2	yes	—
563	C₄²	C₂³×C₃₁	1	2	yes	—
564	C₂³	—	2	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
568	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
569	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
570	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
571	C₂³	C₂⁴×C₃₁	1	2	yes	—
572	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	4	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	4	1	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
609	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
616	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
617	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
619	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
620	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
622	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
623	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
624	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	4	4	no	—
643	C₂²	C₃₁×2₋¹⁺⁴	1	2	yes	—
644	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
670	C₂	C₃₁×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#563	C₂	semidirect
2. C₃₁×#562	C₂	semidirect
3. C₃₁×#556	C₂	semidirect
4. C₃₁×#554	C₂	semidirect
5. C₃₁×#554	C₂	semidirect
6. C₃₁×#553	C₂	semidirect
7. C₃₁×#553	C₂	semidirect
8. C₃₁×#552	C₂	semidirect
9. D₄×Q₈×C₃₁	C₂	semidirect
10. C₃₁×#548	C₂	semidirect
11. C₃₁×#548	C₂	semidirect
12. C₃₁×#547	C₂	semidirect
13. C₃₁×#542	C₂	semidirect
14. C₃₁×#542	C₂	semidirect
15. C₃₁×#541	C₂	semidirect
16. C₃₁×#539	C₂	semidirect
17. C₃₁×#538	C₂	semidirect
18. C₃₁×#538	C₂	semidirect
19. C₃₁×#537	C₂	semidirect
20. C₃₁×#536	C₂	semidirect
21. C₃₁×#525	C₂	semidirect
22. C₃₁×#525	C₂	semidirect
23. C₂×C₃₁×C₂²⋊Q₈	C₂	semidirect
26. C₂×#41×C₃₁	C₂²	semidirect
28. C₂²×Q₈×C₃₁	C₂²	semidirect
30. C₃₁×C₄⋊Q₈	C₂²	semidirect
31. C₃₁×C₄⋊Q₈	C₂²	semidirect
32. C₃₁×C₄⋊Q₈	C₂²	semidirect
33. C₃₁×C₄⋊Q₈	C₂²	semidirect
38. C₃₁×#126	C₂²	semidirect
39. C₃₁×#126	C₂²	semidirect
40. C₃₁×#126	C₂²	semidirect
41. C₃₁×#125	C₂²	semidirect
42. C₃₁×#125	C₂²	semidirect
43. C₃₁×#125	C₂²	semidirect
44. C₃₁×#125	C₂²	semidirect
45. C₃₁×#125	C₂²	semidirect
50. C₃₁×#124	C₂²	semidirect
51. C₃₁×#124	C₂²	semidirect
59. C₃₁×#123	C₂²	semidirect
60. C₃₁×#123	C₂²	semidirect
61. C₃₁×#123	C₂²	semidirect
74. C₃₁×C₂²⋊Q₈	C₂²	semidirect
75. C₃₁×C₂²⋊Q₈	C₂²	semidirect
76. C₃₁×C₂²⋊Q₈	C₂²	semidirect
77. C₃₁×C₂²⋊Q₈	C₂²	semidirect
78. C₃₁×C₂²⋊Q₈	C₂²	semidirect
79. C₃₁×C₂²⋊Q₈	C₂²	semidirect
80. C₃₁×C₂²⋊Q₈	C₂²	semidirect
81. C₃₁×C₂²⋊Q₈	C₂²	semidirect
82. C₃₁×C₂²⋊Q₈	C₂²	semidirect
93. C₃₁×#121	C₂²	semidirect
94. C₃₁×#121	C₂²	semidirect
98. C₄×Q₈×C₃₁	C₂²	semidirect
99. C₄×Q₈×C₃₁	C₂²	semidirect
100. C₄×Q₈×C₃₁	C₂²	semidirect
101. C₄×Q₈×C₃₁	C₂²	semidirect
112. C₄×D₄×C₃₁	C₂²	semidirect
113. C₄×D₄×C₃₁	C₂²	semidirect
116. C₃₁×#117	C₂²	semidirect
117. C₃₁×#117	C₂²	semidirect
120. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
121. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
289. #3541	C₃₁	direct (N × H)
327. #563	C₂×C₃₁	semidirect
328. #562	C₂×C₃₁	semidirect
329. #556	C₂×C₃₁	semidirect
330. #554	C₂×C₃₁	semidirect
331. #554	C₂×C₃₁	semidirect
332. #553	C₂×C₃₁	semidirect
333. #553	C₂×C₃₁	semidirect
334. #552	C₂×C₃₁	semidirect
335. D₄×Q₈	C₂×C₃₁	semidirect
336. #548	C₂×C₃₁	semidirect
337. #548	C₂×C₃₁	semidirect
338. #547	C₂×C₃₁	semidirect
339. #542	C₂×C₃₁	semidirect
340. #542	C₂×C₃₁	semidirect
341. #541	C₂×C₃₁	semidirect
342. #539	C₂×C₃₁	semidirect
343. #538	C₂×C₃₁	semidirect
344. #538	C₂×C₃₁	semidirect
345. #537	C₂×C₃₁	semidirect
346. #536	C₂×C₃₁	semidirect
347. #525	C₂×C₃₁	semidirect
348. #525	C₂×C₃₁	semidirect
349. C₂×C₂²⋊Q₈	C₂×C₃₁	semidirect
361. C₂×#41	C₂²×C₃₁	semidirect
363. C₂²×Q₈	C₂²×C₃₁	semidirect
365. C₄⋊Q₈	C₂²×C₃₁	semidirect
366. C₄⋊Q₈	C₂²×C₃₁	semidirect
367. C₄⋊Q₈	C₂²×C₃₁	semidirect
368. C₄⋊Q₈	C₂²×C₃₁	semidirect
373. #126	C₂²×C₃₁	semidirect
374. #126	C₂²×C₃₁	semidirect
375. #126	C₂²×C₃₁	semidirect
376. #125	C₂²×C₃₁	semidirect
377. #125	C₂²×C₃₁	semidirect
378. #125	C₂²×C₃₁	semidirect
379. #125	C₂²×C₃₁	semidirect
380. #125	C₂²×C₃₁	semidirect
385. #124	C₂²×C₃₁	semidirect
386. #124	C₂²×C₃₁	semidirect
394. #123	C₂²×C₃₁	semidirect
395. #123	C₂²×C₃₁	semidirect
396. #123	C₂²×C₃₁	semidirect
409. C₂²⋊Q₈	C₂²×C₃₁	semidirect
410. C₂²⋊Q₈	C₂²×C₃₁	semidirect
411. C₂²⋊Q₈	C₂²×C₃₁	semidirect
412. C₂²⋊Q₈	C₂²×C₃₁	semidirect
413. C₂²⋊Q₈	C₂²×C₃₁	semidirect
414. C₂²⋊Q₈	C₂²×C₃₁	semidirect
415. C₂²⋊Q₈	C₂²×C₃₁	semidirect
416. C₂²⋊Q₈	C₂²×C₃₁	semidirect
417. C₂²⋊Q₈	C₂²×C₃₁	semidirect
428. #121	C₂²×C₃₁	semidirect
429. #121	C₂²×C₃₁	semidirect
433. C₄×Q₈	C₂²×C₃₁	semidirect
434. C₄×Q₈	C₂²×C₃₁	semidirect
435. C₄×Q₈	C₂²×C₃₁	semidirect
436. C₄×Q₈	C₂²×C₃₁	semidirect
447. C₄×D₄	C₂²×C₃₁	semidirect
448. C₄×D₄	C₂²×C₃₁	semidirect
451. #117	C₂²×C₃₁	semidirect
452. #117	C₂²×C₃₁	semidirect
455. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
456. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
458. C₃₁	#3541	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×#563	2
C₃₁×#562	2
C₃₁×#556	2
C₃₁×#554	2
C₃₁×#553	2
C₃₁×#552	2
D₄×Q₈×C₃₁	2
C₃₁×#548	2
C₃₁×#547	2
C₃₁×#542	2
C₃₁×#541	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#537	2
C₃₁×#536	2
C₃₁×#525	2
C₂×C₃₁×C₂²⋊Q₈	2
#3541	31

Subgroups — C31×#3541 #16843474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3541 #16843474