Subgroups — C₃₁×#3513 #16843446

Order 3968.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#553	C₂	1	2	yes	maximal, complemented
5	C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#551	C₂	1	2	yes	maximal, complemented
7	C₃₁×#551	C₂	1	2	yes	maximal, complemented
8	C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#546	C₂	1	2	yes	maximal, complemented
12	D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#539	C₂	1	2	yes	maximal, complemented
16	C₃₁×#538	C₂	1	2	yes	maximal, complemented
17	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#525	C₂	1	2	yes	maximal, complemented
20	C₂×C₃₁×#123	C₂	1	2	yes	maximal, complemented
21	C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
26	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
29	C₂³×C₄×C₃₁	C₂²	1	2	yes	complemented
30	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#127	C₂²	1	1	yes	characteristic
32	C₃₁×#126	C₂²	1	2	yes	complemented
33	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#126	C₂²	1	2	yes	complemented
36	C₃₁×#126	C₂²	1	2	yes	complemented
37	C₃₁×#126	C₂²	1	2	yes	complemented
38	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#125	C₂²	1	2	yes	complemented
41	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#124	C₂²	1	2	yes	complemented
45	C₃₁×#124	C₂²	1	2	yes	complemented
46	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#123	C₂²	1	1	yes	characteristic
48	C₃₁×#123	C₂²	1	2	yes	—
49	C₃₁×#123	C₂²	1	2	yes	complemented
50	C₃₁×#123	C₂²	1	2	yes	complemented
51	C₃₁×#123	C₂²	1	2	yes	complemented
52	C₃₁×#123	C₂²	1	2	yes	complemented
53	C₃₁×#123	C₂²	1	2	yes	complemented
54	C₃₁×#123	C₂²	1	2	yes	complemented
55	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#123	C₂²	1	2	yes	complemented
57	C₃₁×#123	C₂²	1	2	yes	complemented
58	C₃₁×#123	C₂²	1	2	yes	complemented
59	C₃₁×#123	C₂²	1	2	yes	complemented
60	C₃₁×#123	C₂²	1	2	yes	complemented
61	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#121	C₂²	1	1	yes	characteristic
70	C₃₁×#121	C₂²	1	1	yes	characteristic
71	C₃₁×#121	C₂²	1	2	yes	—
72	C₃₁×#121	C₂²	1	1	yes	characteristic
73	C₃₁×#121	C₂²	1	2	yes	complemented
74	C₃₁×#121	C₂²	1	2	yes	complemented
75	C₃₁×#121	C₂²	1	2	yes	complemented
76	C₃₁×#121	C₂²	1	2	yes	complemented
77	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#121	C₂²	1	2	yes	complemented
79	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#120	C₂²	1	2	yes	—
81	C₃₁×#120	C₂²	1	2	yes	—
82	C₃₁×#120	C₂²	1	2	yes	complemented
83	C₃₁×#120	C₂²	1	2	yes	complemented
84	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
85	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
86	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
88	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
89	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
90	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
91	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
92	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
93	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
95	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
97	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
100	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
101	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
103	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#117	C₂²	1	2	yes	complemented
111	C₃₁×#117	C₂²	1	2	yes	complemented
112	C₃₁×#117	C₂²	1	2	yes	complemented
113	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
115	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
118	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
119	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
120	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₃₁	C₂³	1	2	yes	—
124	C₂⁴×C₃₁	C₂³	1	2	yes	—
125	#41×C₃₁	—	2	4	no	—
126	#41×C₃₁	—	4	4	no	—
127	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₄×C₃₁	—	2	4	no	—
131	C₂×D₄×C₃₁	—	2	4	no	—
132	C₂×D₄×C₃₁	—	4	4	no	—
133	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₃₁	C₂³	1	2	yes	—
135	C₂×D₄×C₃₁	C₂³	1	2	yes	—
136	C₂×D₄×C₃₁	C₂³	1	2	yes	—
137	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
145	C₂×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×C₄×C₃₁	—	4	4	no	—
149	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
152	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
163	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
165	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
181	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
212	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
219	C₄²×C₃₁	C₂³	1	1	yes	characteristic
220	C₄²×C₃₁	C₂³	1	1	yes	characteristic
221	C₄²×C₃₁	C₂³	1	1	yes	characteristic
222	C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₄²×C₃₁	C₂³	1	2	yes	—
224	C₄²×C₃₁	C₂³	1	2	yes	—
225	C₄²×C₃₁	C₂³	1	2	yes	—
226	C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₄²×C₃₁	C₂³	1	1	yes	characteristic
228	C₂³×C₃₁	—	2	4	no	—
229	C₂³×C₃₁	—	2	4	no	—
230	C₂³×C₃₁	—	2	4	no	—
231	C₂³×C₃₁	—	4	2	no	—
232	C₂³×C₃₁	—	4	2	no	—
233	C₂³×C₃₁	—	4	2	no	—
234	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₃₁	C₂⁴	1	2	yes	—
236	C₂³×C₃₁	C₂⁴	1	2	yes	—
237	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂³×C₃₁	C₂⁴	1	2	yes	—
239	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
240	Q₈×C₃₁	—	2	2	no	—
241	Q₈×C₃₁	—	4	1	no	—
242	Q₈×C₃₁	—	4	2	no	—
243	D₄×C₃₁	—	2	4	no	—
244	D₄×C₃₁	—	2	4	no	—
245	D₄×C₃₁	—	2	4	no	—
246	D₄×C₃₁	—	2	2	no	—
247	D₄×C₃₁	—	2	4	no	—
248	D₄×C₃₁	—	2	2	no	—
249	D₄×C₃₁	—	2	2	no	—
250	D₄×C₃₁	—	2	2	no	—
251	D₄×C₃₁	—	4	2	no	—
252	D₄×C₃₁	—	4	2	no	—
253	D₄×C₃₁	—	4	2	no	—
254	D₄×C₃₁	—	4	1	no	—
255	D₄×C₃₁	—	4	2	no	—
256	D₄×C₃₁	—	4	2	no	—
257	D₄×C₃₁	#41	1	4	yes	complemented
258	C₂×C₄×C₃₁	—	2	4	no	—
259	C₂×C₄×C₃₁	—	2	2	no	—
260	C₂×C₄×C₃₁	—	2	4	no	—
261	C₂×C₄×C₃₁	—	2	2	no	—
262	C₂×C₄×C₃₁	—	2	2	no	—
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	4	2	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	1	no	—
270	C₂×C₄×C₃₁	—	4	2	no	—
271	C₂×C₄×C₃₁	—	4	2	no	—
272	C₂×C₄×C₃₁	—	4	2	no	—
273	C₂×C₄×C₃₁	—	4	2	no	—
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	1	yes	characteristic
280	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
290	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	#3513	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂²×C₃₁	—	2	1	no	—
293	C₂²×C₃₁	—	2	2	no	—
294	C₂²×C₃₁	—	2	1	no	—
295	C₂²×C₃₁	—	2	2	no	—
296	C₂²×C₃₁	—	2	1	no	—
297	C₂²×C₃₁	—	2	1	no	—
298	C₂²×C₃₁	—	2	2	no	—
299	C₂²×C₃₁	—	2	2	no	—
300	C₂²×C₃₁	—	2	1	no	—
301	C₂²×C₃₁	—	2	2	no	—
302	C₂²×C₃₁	—	2	2	no	—
303	C₂²×C₃₁	—	2	1	no	—
304	C₂²×C₃₁	—	2	2	no	—
305	C₂²×C₃₁	—	2	1	no	—
306	C₂²×C₃₁	—	2	2	no	—
307	C₂²×C₃₁	—	2	1	no	—
308	C₂²×C₃₁	—	4	8	no	—
309	C₂²×C₃₁	—	8	4	no	—
310	C₂²×C₃₁	C₂×#41	1	4	yes	—
311	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
313	C₄×C₃₁	—	2	1	no	—
314	C₄×C₃₁	—	2	1	no	—
315	C₄×C₃₁	—	2	1	no	—
316	C₄×C₃₁	—	2	2	no	—
317	C₄×C₃₁	—	2	1	no	—
318	C₄×C₃₁	—	2	1	no	—
319	C₄×C₃₁	—	2	2	no	—
320	C₄×C₃₁	—	2	2	no	—
321	C₄×C₃₁	—	2	1	no	—
322	C₄×C₃₁	—	2	2	no	—
323	C₄×C₃₁	—	2	1	no	—
324	C₄×C₃₁	—	2	1	no	—
325	C₄×C₃₁	—	2	2	no	—
326	C₄×C₃₁	—	2	1	no	—
327	C₄×C₃₁	—	2	1	no	—
328	C₄×C₃₁	—	2	1	no	—
329	C₄×C₃₁	C₂×#41	1	2	yes	—
330	#559	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#554	C₂×C₃₁	1	1	yes	characteristic, 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	#551	C₂×C₃₁	1	2	yes	complemented
336	#551	C₂×C₃₁	1	2	yes	complemented
337	#547	C₂×C₃₁	1	1	yes	characteristic, complemented
338	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#546	C₂×C₃₁	1	2	yes	complemented
341	D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#542	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#540	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#539	C₂×C₃₁	1	2	yes	complemented
345	#538	C₂×C₃₁	1	2	yes	complemented
346	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#525	C₂×C₃₁	1	2	yes	complemented
349	C₂×#123	C₂×C₃₁	1	2	yes	complemented
350	#520	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#518	C₂×C₃₁	1	1	yes	characteristic, complemented
352	C₂×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
353	C₂×C₃₁	—	2	2	no	—
354	C₂×C₃₁	—	2	4	no	—
355	C₂×C₃₁	—	4	1	no	—
356	C₂×C₃₁	—	4	2	no	—
357	C₂×C₃₁	—	4	2	no	—
358	C₂×C₃₁	—	4	1	no	—
359	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
360	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₃₁	#585	1	1	yes	characteristic
362	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
363	C₂×#41	C₂²×C₃₁	1	2	yes	complemented
364	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
365	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
366	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
367	C₂³×C₄	C₂²×C₃₁	1	2	yes	complemented
368	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
369	#127	C₂²×C₃₁	1	1	yes	characteristic
370	#126	C₂²×C₃₁	1	2	yes	complemented
371	#126	C₂²×C₃₁	1	1	yes	characteristic, complemented
372	#126	C₂²×C₃₁	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
377	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
378	#125	C₂²×C₃₁	1	2	yes	complemented
379	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
380	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
381	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
382	#124	C₂²×C₃₁	1	2	yes	complemented
383	#124	C₂²×C₃₁	1	2	yes	complemented
384	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
385	#123	C₂²×C₃₁	1	1	yes	characteristic
386	#123	C₂²×C₃₁	1	2	yes	—
387	#123	C₂²×C₃₁	1	2	yes	complemented
388	#123	C₂²×C₃₁	1	2	yes	complemented
389	#123	C₂²×C₃₁	1	2	yes	complemented
390	#123	C₂²×C₃₁	1	2	yes	complemented
391	#123	C₂²×C₃₁	1	2	yes	complemented
392	#123	C₂²×C₃₁	1	2	yes	complemented
393	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
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	#123	C₂²×C₃₁	1	2	yes	complemented
398	#123	C₂²×C₃₁	1	2	yes	complemented
399	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
400	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
401	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
403	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
404	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
405	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
406	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	#121	C₂²×C₃₁	1	1	yes	characteristic
408	#121	C₂²×C₃₁	1	1	yes	characteristic
409	#121	C₂²×C₃₁	1	2	yes	—
410	#121	C₂²×C₃₁	1	1	yes	characteristic
411	#121	C₂²×C₃₁	1	2	yes	complemented
412	#121	C₂²×C₃₁	1	2	yes	complemented
413	#121	C₂²×C₃₁	1	2	yes	complemented
414	#121	C₂²×C₃₁	1	2	yes	complemented
415	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	#121	C₂²×C₃₁	1	2	yes	complemented
417	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
418	#120	C₂²×C₃₁	1	2	yes	—
419	#120	C₂²×C₃₁	1	2	yes	—
420	#120	C₂²×C₃₁	1	2	yes	complemented
421	#120	C₂²×C₃₁	1	2	yes	complemented
422	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
425	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
426	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
427	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
428	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
429	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
430	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
431	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
433	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
435	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
436	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
438	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
439	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
440	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
441	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
442	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
444	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
446	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
447	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
448	#117	C₂²×C₃₁	1	2	yes	complemented
449	#117	C₂²×C₃₁	1	2	yes	complemented
450	#117	C₂²×C₃₁	1	2	yes	complemented
451	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
453	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
455	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
456	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
457	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
458	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
459	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
460	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	C₃₁	#3513	1	1	yes	characteristic, direct product factor, Sylow
462	C₂⁴	C₂³×C₃₁	1	2	yes	—
463	C₂⁴	C₂³×C₃₁	1	2	yes	—
464	#41	—	2	4	no	—
465	#41	—	4	4	no	—
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×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×D₄	C₂³×C₃₁	1	2	yes	—
474	C₂×D₄	C₂³×C₃₁	1	2	yes	—
475	C₂×D₄	C₂³×C₃₁	1	2	yes	—
476	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×D₄	C₂³×C₃₁	1	2	yes	—
479	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
480	C₂×D₄	C₂³×C₃₁	1	2	yes	—
481	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
482	C₂×D₄	C₂³×C₃₁	1	2	yes	—
483	C₂×D₄	C₂³×C₃₁	1	2	yes	—
484	C₂×D₄	C₂³×C₃₁	1	2	yes	—
485	C₂×D₄	C₂³×C₃₁	1	2	yes	—
486	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
491	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
492	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
493	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
499	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
500	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
501	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
502	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
503	C₂²×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	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
509	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
511	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
512	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
514	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
520	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
521	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
522	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
526	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
531	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
533	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
535	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
540	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
544	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
545	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
548	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
551	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
552	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
558	C₄²	C₂³×C₃₁	1	1	yes	characteristic
559	C₄²	C₂³×C₃₁	1	1	yes	characteristic
560	C₄²	C₂³×C₃₁	1	1	yes	characteristic
561	C₄²	C₂³×C₃₁	1	1	yes	characteristic
562	C₄²	C₂³×C₃₁	1	2	yes	—
563	C₄²	C₂³×C₃₁	1	2	yes	—
564	C₄²	C₂³×C₃₁	1	2	yes	—
565	C₄²	C₂³×C₃₁	1	1	yes	characteristic
566	C₄²	C₂³×C₃₁	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
574	C₂³	C₂⁴×C₃₁	1	2	yes	—
575	C₂³	C₂⁴×C₃₁	1	2	yes	—
576	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
577	C₂³	C₂⁴×C₃₁	1	2	yes	—
578	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	4	no	—
587	D₄	—	2	2	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	#41×C₃₁	1	4	yes	complemented
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	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	—	4	1	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
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	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
622	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
623	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
624	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
625	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
626	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
627	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
628	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
629	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	4	8	no	—
647	C₂²	—	8	4	no	—
648	C₂²	C₂×#41×C₃₁	1	4	yes	—
649	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
650	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	C₂×#41×C₃₁	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	4	1	no	—
674	C₂	C₂²×#41×C₃₁	1	1	yes	characteristic
675	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
676	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×#559	C₂	semidirect
2. C₃₁×#554	C₂	semidirect
3. C₃₁×#553	C₂	semidirect
4. C₃₁×#553	C₂	semidirect
5. C₃₁×#552	C₂	semidirect
6. C₃₁×#551	C₂	semidirect
7. C₃₁×#551	C₂	semidirect
8. C₃₁×#547	C₂	semidirect
9. C₃₁×#546	C₂	semidirect
10. C₃₁×#546	C₂	semidirect
11. C₃₁×#546	C₂	semidirect
12. D₄²×C₃₁	C₂	semidirect
13. C₃₁×#542	C₂	semidirect
14. C₃₁×#540	C₂	semidirect
15. C₃₁×#539	C₂	semidirect
16. C₃₁×#538	C₂	semidirect
17. C₃₁×#529	C₂	semidirect
18. C₃₁×#529	C₂	semidirect
19. C₃₁×#525	C₂	semidirect
20. C₂×C₃₁×#123	C₂	semidirect
21. C₃₁×#520	C₂	semidirect
22. C₃₁×#518	C₂	semidirect
23. C₂×C₄×D₄×C₃₁	C₂	semidirect
25. C₂×#41×C₃₁	C₂²	semidirect
29. C₂³×C₄×C₃₁	C₂²	semidirect
30. C₃₁×C₄⋊Q₈	C₂²	semidirect
32. C₃₁×#126	C₂²	semidirect
33. C₃₁×#126	C₂²	semidirect
34. C₃₁×#126	C₂²	semidirect
35. C₃₁×#126	C₂²	semidirect
36. C₃₁×#126	C₂²	semidirect
37. C₃₁×#126	C₂²	semidirect
38. C₃₁×#125	C₂²	semidirect
39. C₃₁×#125	C₂²	semidirect
40. C₃₁×#125	C₂²	semidirect
41. C₃₁×#125	C₂²	semidirect
42. C₃₁×#124	C₂²	semidirect
43. C₃₁×#124	C₂²	semidirect
44. C₃₁×#124	C₂²	semidirect
45. C₃₁×#124	C₂²	semidirect
46. C₃₁×#124	C₂²	semidirect
49. C₃₁×#123	C₂²	semidirect
50. C₃₁×#123	C₂²	semidirect
51. C₃₁×#123	C₂²	semidirect
52. C₃₁×#123	C₂²	semidirect
53. C₃₁×#123	C₂²	semidirect
54. C₃₁×#123	C₂²	semidirect
55. C₃₁×#123	C₂²	semidirect
56. C₃₁×#123	C₂²	semidirect
57. C₃₁×#123	C₂²	semidirect
58. C₃₁×#123	C₂²	semidirect
59. C₃₁×#123	C₂²	semidirect
60. C₃₁×#123	C₂²	semidirect
61. C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₃₁×C₂²⋊Q₈	C₂²	semidirect
63. C₃₁×C₂²⋊Q₈	C₂²	semidirect
64. C₃₁×C₂²⋊Q₈	C₂²	semidirect
65. C₃₁×C₂²⋊Q₈	C₂²	semidirect
66. C₃₁×C₂²⋊Q₈	C₂²	semidirect
67. C₃₁×C₂²⋊Q₈	C₂²	semidirect
68. C₃₁×C₂²⋊Q₈	C₂²	semidirect
73. C₃₁×#121	C₂²	semidirect
74. C₃₁×#121	C₂²	semidirect
75. C₃₁×#121	C₂²	semidirect
76. C₃₁×#121	C₂²	semidirect
77. C₃₁×#121	C₂²	semidirect
78. C₃₁×#121	C₂²	semidirect
79. C₃₁×#121	C₂²	semidirect
82. C₃₁×#120	C₂²	semidirect
83. C₃₁×#120	C₂²	semidirect
84. C₄×Q₈×C₃₁	C₂²	semidirect
85. C₄×Q₈×C₃₁	C₂²	semidirect
86. C₄×Q₈×C₃₁	C₂²	semidirect
92. C₄×D₄×C₃₁	C₂²	semidirect
93. C₄×D₄×C₃₁	C₂²	semidirect
94. C₄×D₄×C₃₁	C₂²	semidirect
95. C₄×D₄×C₃₁	C₂²	semidirect
96. C₄×D₄×C₃₁	C₂²	semidirect
97. C₄×D₄×C₃₁	C₂²	semidirect
98. C₄×D₄×C₃₁	C₂²	semidirect
99. C₄×D₄×C₃₁	C₂²	semidirect
100. C₄×D₄×C₃₁	C₂²	semidirect
101. C₄×D₄×C₃₁	C₂²	semidirect
102. C₄×D₄×C₃₁	C₂²	semidirect
103. C₄×D₄×C₃₁	C₂²	semidirect
104. C₄×D₄×C₃₁	C₂²	semidirect
105. C₄×D₄×C₃₁	C₂²	semidirect
106. C₄×D₄×C₃₁	C₂²	semidirect
107. C₃₁×#117	C₂²	semidirect
108. C₃₁×#117	C₂²	semidirect
109. C₃₁×#117	C₂²	semidirect
110. C₃₁×#117	C₂²	semidirect
111. C₃₁×#117	C₂²	semidirect
112. C₃₁×#117	C₂²	semidirect
113. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
114. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
115. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
116. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
117. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
118. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
119. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
120. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
122. C₂×C₄²×C₃₁	C₂²	semidirect
257. D₄×C₃₁	#41	semidirect
291. #3513	C₃₁	direct (N × H)
330. #559	C₂×C₃₁	semidirect
331. #554	C₂×C₃₁	semidirect
332. #553	C₂×C₃₁	semidirect
333. #553	C₂×C₃₁	semidirect
334. #552	C₂×C₃₁	semidirect
335. #551	C₂×C₃₁	semidirect
336. #551	C₂×C₃₁	semidirect
337. #547	C₂×C₃₁	semidirect
338. #546	C₂×C₃₁	semidirect
339. #546	C₂×C₃₁	semidirect
340. #546	C₂×C₃₁	semidirect
341. D₄²	C₂×C₃₁	semidirect
342. #542	C₂×C₃₁	semidirect
343. #540	C₂×C₃₁	semidirect
344. #539	C₂×C₃₁	semidirect
345. #538	C₂×C₃₁	semidirect
346. #529	C₂×C₃₁	semidirect
347. #529	C₂×C₃₁	semidirect
348. #525	C₂×C₃₁	semidirect
349. C₂×#123	C₂×C₃₁	semidirect
350. #520	C₂×C₃₁	semidirect
351. #518	C₂×C₃₁	semidirect
352. C₂×C₄×D₄	C₂×C₃₁	semidirect
363. C₂×#41	C₂²×C₃₁	semidirect
367. C₂³×C₄	C₂²×C₃₁	semidirect
368. C₄⋊Q₈	C₂²×C₃₁	semidirect
370. #126	C₂²×C₃₁	semidirect
371. #126	C₂²×C₃₁	semidirect
372. #126	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. #124	C₂²×C₃₁	semidirect
381. #124	C₂²×C₃₁	semidirect
382. #124	C₂²×C₃₁	semidirect
383. #124	C₂²×C₃₁	semidirect
384. #124	C₂²×C₃₁	semidirect
387. #123	C₂²×C₃₁	semidirect
388. #123	C₂²×C₃₁	semidirect
389. #123	C₂²×C₃₁	semidirect
390. #123	C₂²×C₃₁	semidirect
391. #123	C₂²×C₃₁	semidirect
392. #123	C₂²×C₃₁	semidirect
393. #123	C₂²×C₃₁	semidirect
394. #123	C₂²×C₃₁	semidirect
395. #123	C₂²×C₃₁	semidirect
396. #123	C₂²×C₃₁	semidirect
397. #123	C₂²×C₃₁	semidirect
398. #123	C₂²×C₃₁	semidirect
399. C₂²⋊Q₈	C₂²×C₃₁	semidirect
400. C₂²⋊Q₈	C₂²×C₃₁	semidirect
401. C₂²⋊Q₈	C₂²×C₃₁	semidirect
402. C₂²⋊Q₈	C₂²×C₃₁	semidirect
403. C₂²⋊Q₈	C₂²×C₃₁	semidirect
404. C₂²⋊Q₈	C₂²×C₃₁	semidirect
405. C₂²⋊Q₈	C₂²×C₃₁	semidirect
406. C₂²⋊Q₈	C₂²×C₃₁	semidirect
411. #121	C₂²×C₃₁	semidirect
412. #121	C₂²×C₃₁	semidirect
413. #121	C₂²×C₃₁	semidirect
414. #121	C₂²×C₃₁	semidirect
415. #121	C₂²×C₃₁	semidirect
416. #121	C₂²×C₃₁	semidirect
417. #121	C₂²×C₃₁	semidirect
420. #120	C₂²×C₃₁	semidirect
421. #120	C₂²×C₃₁	semidirect
422. C₄×Q₈	C₂²×C₃₁	semidirect
423. C₄×Q₈	C₂²×C₃₁	semidirect
424. C₄×Q₈	C₂²×C₃₁	semidirect
430. C₄×D₄	C₂²×C₃₁	semidirect
431. C₄×D₄	C₂²×C₃₁	semidirect
432. C₄×D₄	C₂²×C₃₁	semidirect
433. C₄×D₄	C₂²×C₃₁	semidirect
434. C₄×D₄	C₂²×C₃₁	semidirect
435. C₄×D₄	C₂²×C₃₁	semidirect
436. C₄×D₄	C₂²×C₃₁	semidirect
437. C₄×D₄	C₂²×C₃₁	semidirect
438. C₄×D₄	C₂²×C₃₁	semidirect
439. C₄×D₄	C₂²×C₃₁	semidirect
440. C₄×D₄	C₂²×C₃₁	semidirect
441. C₄×D₄	C₂²×C₃₁	semidirect
442. C₄×D₄	C₂²×C₃₁	semidirect
443. C₄×D₄	C₂²×C₃₁	semidirect
444. C₄×D₄	C₂²×C₃₁	semidirect
445. #117	C₂²×C₃₁	semidirect
446. #117	C₂²×C₃₁	semidirect
447. #117	C₂²×C₃₁	semidirect
448. #117	C₂²×C₃₁	semidirect
449. #117	C₂²×C₃₁	semidirect
450. #117	C₂²×C₃₁	semidirect
451. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
452. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
453. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
454. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
455. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
456. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
457. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
458. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
459. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
460. C₂×C₄²	C₂²×C₃₁	semidirect
461. C₃₁	#3513	direct (N × H)
596. D₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#559	2
C₃₁×#554	2
C₃₁×#553	2
C₃₁×#552	2
C₃₁×#551	2
C₃₁×#547	2
C₃₁×#546	2
D₄²×C₃₁	2
C₃₁×#542	2
C₃₁×#540	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#529	2
C₃₁×#525	2
C₂×C₃₁×#123	2
C₃₁×#520	2
C₃₁×#518	2
C₂×C₄×D₄×C₃₁	2
#3513	31

Subgroups — C31×#3513 #16843446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3513 #16843446