Subgroups — C₃₁×#34084 #21490843

Order 7936.

2302 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	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2335	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2334	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2330	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2326	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2324	C₂	1	2	yes	maximal
7	C₃₁×#2323	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2298	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2296	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2293	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#529	C₄	1	16	yes	complemented
19	C₂×C₃₁×#126	C₂²	1	2	yes	—
20	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₃₁×#117	C₂²	1	2	yes	—
31	C₂×C₃₁×#117	C₂²	1	2	yes	—
32	C₂×C₃₁×#117	C₂²	1	2	yes	—
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
35	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#391	C₂²	1	2	yes	—
37	C₃₁×#390	C₂²	1	2	yes	—
38	C₃₁×#390	C₂²	1	4	yes	—
39	C₃₁×#389	C₂²	1	2	yes	—
40	C₃₁×#389	C₂²	1	4	yes	—
41	C₃₁×#389	C₂²	1	2	yes	—
42	C₃₁×#389	C₂²	1	4	yes	—
43	C₃₁×#389	C₂²	1	4	yes	—
44	C₃₁×#388	C₂²	1	4	yes	—
45	C₃₁×#388	C₂²	1	4	yes	—
46	C₃₁×#388	C₂²	1	4	yes	—
47	C₃₁×#388	C₂²	1	4	yes	—
48	C₃₁×#388	C₂²	1	4	yes	—
49	C₃₁×#388	C₂²	1	4	yes	—
50	C₃₁×#387	C₂²	1	4	yes	—
51	C₃₁×#387	C₂²	1	4	yes	—
52	C₃₁×#387	C₂²	1	4	yes	—
53	C₃₁×#387	C₂²	1	4	yes	—
54	C₃₁×#386	C₂²	1	4	yes	—
55	C₃₁×#385	C₂²	1	4	yes	—
56	C₃₁×#385	C₂²	1	4	yes	—
57	C₃₁×#385	C₂²	1	4	yes	—
58	C₃₁×#384	C₂²	1	2	yes	—
59	C₃₁×#382	C₂²	1	2	yes	—
60	C₃₁×#380	C₂²	1	2	yes	—
61	C₃₁×#380	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
66	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
79	C₃₁×#376	C₂²	1	2	yes	—
80	C₃₁×#376	C₂²	1	2	yes	—
81	C₄³×C₃₁	C₂²	1	1	yes	characteristic
82	C₄³×C₃₁	C₂²	1	1	yes	characteristic
83	C₄³×C₃₁	C₂²	1	2	yes	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₃₁×#126	C₂×C₄	1	16	yes	complemented
93	C₃₁×#125	C₂×C₄	1	8	yes	complemented
94	C₃₁×#124	C₂×C₄	1	8	yes	—
95	C₃₁×#123	C₂×C₄	1	16	yes	complemented
96	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₃₁×#121	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₃₁	—	2	8	no	—
99	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₃₁	—	2	8	no	—
101	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
103	C₃₁×#117	—	2	8	no	—
104	C₃₁×#117	—	4	4	no	—
105	C₃₁×#117	—	4	4	no	—
106	C₃₁×#117	C₂×C₄	1	16	yes	complemented
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₃₁	—	4	4	no	—
134	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	complemented
135	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
153	C₃₁×#95	C₂³	1	2	yes	—
154	C₃₁×#95	C₂³	1	2	yes	—
155	C₃₁×#95	C₂³	1	2	yes	—
156	C₃₁×#95	C₂³	1	2	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	2	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₃₁×#95	C₂³	1	4	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
168	C₂×Q₈×C₃₁	—	2	4	no	—
169	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₃₁	—	2	4	no	—
171	C₂×D₄×C₃₁	—	4	4	no	—
172	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
174	C₂²×C₄×C₃₁	—	2	4	no	—
175	C₂²×C₄×C₃₁	—	2	4	no	—
176	C₂²×C₄×C₃₁	—	2	2	no	—
177	C₂²×C₄×C₃₁	—	2	4	no	—
178	C₂²×C₄×C₃₁	—	2	2	no	—
179	C₂²×C₄×C₃₁	—	2	8	no	—
180	C₂²×C₄×C₃₁	—	4	4	no	—
181	C₂²×C₄×C₃₁	—	4	2	no	—
182	C₂²×C₄×C₃₁	—	4	4	no	—
183	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
186	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
202	C₄⋊C₄×C₃₁	—	2	4	no	—
203	C₄⋊C₄×C₃₁	—	2	4	no	—
204	C₄⋊C₄×C₃₁	—	2	4	no	—
205	C₄⋊C₄×C₃₁	—	2	8	no	—
206	C₄⋊C₄×C₃₁	—	2	4	no	—
207	C₄⋊C₄×C₃₁	—	4	4	no	—
208	C₄⋊C₄×C₃₁	—	4	4	no	—
209	C₄⋊C₄×C₃₁	—	4	4	no	—
210	C₄⋊C₄×C₃₁	—	4	4	no	—
211	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
214	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
217	C₂²⋊C₄×C₃₁	—	2	4	no	—
218	C₂²⋊C₄×C₃₁	—	2	4	no	—
219	C₂²⋊C₄×C₃₁	—	2	8	no	—
220	C₂²⋊C₄×C₃₁	—	4	4	no	—
221	C₂²⋊C₄×C₃₁	—	4	4	no	—
222	C₂²⋊C₄×C₃₁	—	4	4	no	—
223	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
228	C₄²×C₃₁	—	2	4	no	—
229	C₄²×C₃₁	—	2	8	no	—
230	C₄²×C₃₁	—	2	2	no	—
231	C₄²×C₃₁	—	2	4	no	—
232	C₄²×C₃₁	—	2	4	no	—
233	C₄²×C₃₁	—	2	2	no	—
234	C₄²×C₃₁	—	2	2	no	—
235	C₄²×C₃₁	—	2	2	no	—
236	C₄²×C₃₁	—	4	4	no	—
237	C₄²×C₃₁	—	4	2	no	—
238	C₄²×C₃₁	—	4	4	no	—
239	C₄²×C₃₁	—	4	2	no	—
240	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
241	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
242	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
243	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
244	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
245	C₄²×C₃₁	#41	1	8	yes	—
246	#34084	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂³×C₃₁	—	2	2	no	—
248	C₂³×C₃₁	—	2	4	no	—
249	C₂³×C₃₁	—	2	1	no	—
250	C₂³×C₃₁	—	2	2	no	—
251	C₂³×C₃₁	—	2	1	no	—
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	4	no	—
254	C₂³×C₃₁	—	2	2	no	—
255	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
256	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
257	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
258	Q₈×C₃₁	—	2	8	no	—
259	D₄×C₃₁	—	2	8	no	—
260	D₄×C₃₁	—	4	8	no	—
261	C₂×C₄×C₃₁	—	2	4	no	—
262	C₂×C₄×C₃₁	—	2	2	no	—
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	2	2	no	—
265	C₂×C₄×C₃₁	—	2	1	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	2	no	—
268	C₂×C₄×C₃₁	—	2	1	no	—
269	C₂×C₄×C₃₁	—	2	2	no	—
270	C₂×C₄×C₃₁	—	2	2	no	—
271	C₂×C₄×C₃₁	—	2	4	no	—
272	C₂×C₄×C₃₁	—	2	2	no	—
273	C₂×C₄×C₃₁	—	2	2	no	—
274	C₂×C₄×C₃₁	—	2	8	no	—
275	C₂×C₄×C₃₁	—	2	16	no	—
276	C₂×C₄×C₃₁	—	2	8	no	—
277	C₂×C₄×C₃₁	—	2	2	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	4	no	—
280	C₂×C₄×C₃₁	—	2	4	no	—
281	C₂×C₄×C₃₁	—	2	4	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	4	no	—
287	C₂×C₄×C₃₁	—	2	2	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	4	4	no	—
290	C₂×C₄×C₃₁	—	4	16	no	—
291	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
298	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
301	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
302	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
303	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
304	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
305	C₂×#529	C₂×C₃₁	1	1	yes	characteristic
306	#2335	C₂×C₃₁	1	4	yes	complemented
307	#2334	C₂×C₃₁	1	4	yes	complemented
308	#2330	C₂×C₃₁	1	2	yes	complemented
309	#2326	C₂×C₃₁	1	2	yes	complemented
310	#2324	C₂×C₃₁	1	2	yes	—
311	#2323	C₂×C₃₁	1	2	yes	complemented
312	#2298	C₂×C₃₁	1	2	yes	complemented
313	#2296	C₂×C₃₁	1	2	yes	complemented
314	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
315	#2293	C₂×C₃₁	1	2	yes	complemented
316	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
317	#2290	C₂×C₃₁	1	2	yes	complemented
318	#2285	C₂×C₃₁	1	1	yes	characteristic, complemented
319	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
320	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
321	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
322	C₂²×C₃₁	—	2	2	no	—
323	C₂²×C₃₁	—	2	4	no	—
324	C₂²×C₃₁	—	2	2	no	—
325	C₂²×C₃₁	—	2	4	no	—
326	C₂²×C₃₁	—	2	2	no	—
327	C₂²×C₃₁	—	2	4	no	—
328	C₂²×C₃₁	—	4	4	no	—
329	C₂²×C₃₁	—	4	2	no	—
330	C₂²×C₃₁	—	4	2	no	—
331	C₂²×C₃₁	—	4	4	no	—
332	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
333	C₂²×C₃₁	C₂²×#41	1	2	yes	—
334	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
336	C₂²×C₃₁	#585	1	2	yes	—
337	C₄×C₃₁	—	2	2	no	—
338	C₄×C₃₁	—	2	4	no	—
339	C₄×C₃₁	—	2	4	no	—
340	C₄×C₃₁	—	2	2	no	—
341	C₄×C₃₁	—	2	2	no	—
342	C₄×C₃₁	—	2	2	no	—
343	C₄×C₃₁	—	2	4	no	—
344	C₄×C₃₁	—	2	4	no	—
345	C₄×C₃₁	—	2	4	no	—
346	C₄×C₃₁	—	4	2	no	—
347	C₄×C₃₁	—	4	4	no	—
348	C₄×C₃₁	—	4	4	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	C₄×#41	1	4	yes	—
351	C₄×C₃₁	#520	1	4	yes	—
352	#529	C₄×C₃₁	1	16	yes	complemented
353	C₂×#126	C₂²×C₃₁	1	2	yes	—
354	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
355	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
356	C₂×#123	C₂²×C₃₁	1	2	yes	—
357	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
358	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
360	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
362	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
364	C₂×#117	C₂²×C₃₁	1	2	yes	—
365	C₂×#117	C₂²×C₃₁	1	2	yes	—
366	C₂×#117	C₂²×C₃₁	1	2	yes	—
367	C₂×#117	C₂²×C₃₁	1	2	yes	—
368	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
369	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
370	#391	C₂²×C₃₁	1	2	yes	—
371	#390	C₂²×C₃₁	1	2	yes	—
372	#390	C₂²×C₃₁	1	4	yes	—
373	#389	C₂²×C₃₁	1	2	yes	—
374	#389	C₂²×C₃₁	1	4	yes	—
375	#389	C₂²×C₃₁	1	2	yes	—
376	#389	C₂²×C₃₁	1	4	yes	—
377	#389	C₂²×C₃₁	1	4	yes	—
378	#388	C₂²×C₃₁	1	4	yes	—
379	#388	C₂²×C₃₁	1	4	yes	—
380	#388	C₂²×C₃₁	1	4	yes	—
381	#388	C₂²×C₃₁	1	4	yes	—
382	#388	C₂²×C₃₁	1	4	yes	—
383	#388	C₂²×C₃₁	1	4	yes	—
384	#387	C₂²×C₃₁	1	4	yes	—
385	#387	C₂²×C₃₁	1	4	yes	—
386	#387	C₂²×C₃₁	1	4	yes	—
387	#387	C₂²×C₃₁	1	4	yes	—
388	#386	C₂²×C₃₁	1	4	yes	—
389	#385	C₂²×C₃₁	1	4	yes	—
390	#385	C₂²×C₃₁	1	4	yes	—
391	#385	C₂²×C₃₁	1	4	yes	—
392	#384	C₂²×C₃₁	1	2	yes	—
393	#382	C₂²×C₃₁	1	2	yes	—
394	#380	C₂²×C₃₁	1	2	yes	—
395	#380	C₂²×C₃₁	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
399	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
400	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
401	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
404	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
408	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
413	#376	C₂²×C₃₁	1	2	yes	—
414	#376	C₂²×C₃₁	1	2	yes	—
415	C₄³	C₂²×C₃₁	1	1	yes	characteristic
416	C₄³	C₂²×C₃₁	1	1	yes	characteristic
417	C₄³	C₂²×C₃₁	1	2	yes	—
418	C₂×C₃₁	—	4	2	no	—
419	C₂×C₃₁	—	4	4	no	—
420	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
421	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
422	C₂×C₃₁	#3428	1	1	yes	characteristic
423	C₂×C₃₁	#3460	1	2	yes	—
424	C₂×C₃₁	#3461	1	2	yes	—
425	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
426	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
428	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
429	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
432	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
433	#126	C₂×C₄×C₃₁	1	16	yes	complemented
434	#125	C₂×C₄×C₃₁	1	8	yes	complemented
435	#124	C₂×C₄×C₃₁	1	8	yes	—
436	#123	C₂×C₄×C₃₁	1	16	yes	complemented
437	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
438	#121	C₂×C₄×C₃₁	1	8	yes	—
439	C₄×Q₈	—	2	8	no	—
440	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
441	C₄×D₄	—	2	8	no	—
442	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
443	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
444	#117	—	2	8	no	—
445	#117	—	4	4	no	—
446	#117	—	4	4	no	—
447	#117	C₂×C₄×C₃₁	1	16	yes	complemented
448	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
474	C₂×C₄²	—	4	4	no	—
475	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	complemented
476	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
477	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
479	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
480	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
481	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
485	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
486	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
487	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
488	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
494	#95	C₂³×C₃₁	1	2	yes	—
495	#95	C₂³×C₃₁	1	2	yes	—
496	#95	C₂³×C₃₁	1	2	yes	—
497	#95	C₂³×C₃₁	1	2	yes	—
498	#95	C₂³×C₃₁	1	4	yes	—
499	#95	C₂³×C₃₁	1	4	yes	—
500	#95	C₂³×C₃₁	1	2	yes	—
501	#95	C₂³×C₃₁	1	4	yes	—
502	#95	C₂³×C₃₁	1	4	yes	—
503	#95	C₂³×C₃₁	1	2	yes	—
504	#95	C₂³×C₃₁	1	4	yes	—
505	#95	C₂³×C₃₁	1	4	yes	—
506	#95	C₂³×C₃₁	1	4	yes	—
507	C₃₁	#34084	1	1	yes	characteristic, direct product factor, Sylow
508	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
509	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	4	4	no	—
514	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
515	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	8	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	4	no	—
525	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
526	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
527	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
528	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	8	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
554	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
557	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
558	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	8	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	2	4	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	2	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	4	4	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	4	no	—
581	C₄²	—	4	2	no	—
582	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
583	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
584	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
585	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
586	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
587	C₄²	#41×C₃₁	1	8	yes	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	4	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	2	no	—
596	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
597	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
598	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
599	Q₈	—	2	8	no	—
600	D₄	—	2	8	no	—
601	D₄	—	4	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	16	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
635	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
636	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
638	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
639	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
640	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
641	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
642	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
643	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
644	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
645	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	4	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	4	no	—
656	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
657	C₂²	C₂²×#41×C₃₁	1	2	yes	—
658	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
660	C₂²	C₃₁×#585	1	2	yes	—
661	C₄	—	2	2	no	—
662	C₄	—	2	4	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	2	4	no	—
669	C₄	—	2	4	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	2	no	—
674	C₄	C₄×#41×C₃₁	1	4	yes	—
675	C₄	C₃₁×#520	1	4	yes	—
676	C₂	—	4	2	no	—
677	C₂	—	4	4	no	—
678	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
679	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
680	C₂	C₃₁×#3428	1	1	yes	characteristic
681	C₂	C₃₁×#3460	1	2	yes	—
682	C₂	C₃₁×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2335	C₂	semidirect
3. C₃₁×#2334	C₂	semidirect
4. C₃₁×#2330	C₂	semidirect
5. C₃₁×#2326	C₂	semidirect
7. C₃₁×#2323	C₂	semidirect
8. C₃₁×#2298	C₂	semidirect
9. C₃₁×#2296	C₂	semidirect
10. C₃₁×#2295	C₂	semidirect
11. C₃₁×#2293	C₂	semidirect
12. C₃₁×#2293	C₂	semidirect
13. C₃₁×#2290	C₂	semidirect
14. C₃₁×#2285	C₂	semidirect
15. C₄²×Q₈×C₃₁	C₂	semidirect
16. C₄²×D₄×C₃₁	C₂	semidirect
17. C₄×C₃₁×#117	C₂	semidirect
18. C₃₁×#529	C₄	semidirect
92. C₃₁×#126	C₂×C₄	semidirect
93. C₃₁×#125	C₂×C₄	semidirect
95. C₃₁×#123	C₂×C₄	semidirect
96. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₄×Q₈×C₃₁	C₂×C₄	semidirect
102. C₄×D₄×C₃₁	C₂×C₄	semidirect
106. C₃₁×#117	C₂×C₄	semidirect
134. C₂×C₄²×C₃₁	C₂×C₄	semidirect
246. #34084	C₃₁	direct (N × H)
306. #2335	C₂×C₃₁	semidirect
307. #2334	C₂×C₃₁	semidirect
308. #2330	C₂×C₃₁	semidirect
309. #2326	C₂×C₃₁	semidirect
311. #2323	C₂×C₃₁	semidirect
312. #2298	C₂×C₃₁	semidirect
313. #2296	C₂×C₃₁	semidirect
314. #2295	C₂×C₃₁	semidirect
315. #2293	C₂×C₃₁	semidirect
316. #2293	C₂×C₃₁	semidirect
317. #2290	C₂×C₃₁	semidirect
318. #2285	C₂×C₃₁	semidirect
319. C₄²×Q₈	C₂×C₃₁	semidirect
320. C₄²×D₄	C₂×C₃₁	semidirect
321. C₄×#117	C₂×C₃₁	semidirect
352. #529	C₄×C₃₁	semidirect
433. #126	C₂×C₄×C₃₁	semidirect
434. #125	C₂×C₄×C₃₁	semidirect
436. #123	C₂×C₄×C₃₁	semidirect
437. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
440. C₄×Q₈	C₂×C₄×C₃₁	semidirect
443. C₄×D₄	C₂×C₄×C₃₁	semidirect
447. #117	C₂×C₄×C₃₁	semidirect
475. C₂×C₄²	C₂×C₄×C₃₁	semidirect
507. C₃₁	#34084	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#529	2
C₃₁×#2335	2
C₃₁×#2334	2
C₃₁×#2330	2
C₃₁×#2326	2
C₃₁×#2324	2
C₃₁×#2323	2
C₃₁×#2298	2
C₃₁×#2296	2
C₃₁×#2295	2
C₃₁×#2293	2
C₃₁×#2290	2
C₃₁×#2285	2
C₄²×Q₈×C₃₁	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
#34084	31

Subgroups — C31×#34084 #21490843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34084 #21490843