Subgroups — C₂×C₃₁×#3188 #21517489

Order 7936.

2718 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3188	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₃₁	—	2	1	no	—
15	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
18	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
19	C₂³×C₈×C₃₁	C₂²	1	2	yes	complemented
20	C₃₁×#525	—	2	4	no	—
21	C₃₁×#525	C₂²	1	8	yes	complemented
22	C₂×C₃₁×#123	—	2	1	no	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃₁×#121	—	2	1	no	—
26	C₂×C₃₁×#121	—	2	1	no	—
27	C₂×C₃₁×#121	—	2	4	no	—
28	C₂×C₃₁×#121	C₂²	1	2	yes	—
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
32	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×#120	—	2	1	no	—
34	C₂×C₄×D₄×C₃₁	—	2	1	no	—
35	C₂×C₄×D₄×C₃₁	—	2	1	no	—
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
39	C₃₁×#484	C₂²	1	8	yes	complemented
40	C₃₁×#482	C₂²	1	16	yes	complemented
41	C₃₁×#481	C₂²	1	8	yes	complemented
42	C₃₁×#466	C₂²	1	16	yes	complemented
43	C₃₁×#465	C₂²	1	16	yes	complemented
44	C₃₁×#450	C₂²	1	8	yes	complemented
45	C₃₁×#449	C₂²	1	16	yes	complemented
46	C₃₁×#447	C₂²	1	8	yes	complemented
47	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
48	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
49	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
50	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
51	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
52	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
53	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×C₂²⋊C₈	C₂²	1	8	yes	complemented
56	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
57	C₂⁵×C₃₁	—	2	1	no	—
58	C₂⁵×C₃₁	D₄	1	1	yes	characteristic
59	C₂×#41×C₃₁	—	2	2	no	—
60	C₂×#41×C₃₁	—	4	4	no	—
61	C₂×#41×C₃₁	C₂³	1	4	yes	complemented
62	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₃₁	—	2	1	no	—
64	C₂²×D₄×C₃₁	—	2	1	no	—
65	C₂²×D₄×C₃₁	—	2	1	no	—
66	C₂²×D₄×C₃₁	—	2	2	no	—
67	C₂²×D₄×C₃₁	—	2	2	no	—
68	C₂²×D₄×C₃₁	—	2	8	no	—
69	C₂²×D₄×C₃₁	—	2	2	no	—
70	C₂²×D₄×C₃₁	—	2	1	no	—
71	C₂²×D₄×C₃₁	—	4	4	no	—
72	C₂²×D₄×C₃₁	—	4	8	no	—
73	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
74	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
76	C₂³×C₄×C₃₁	—	2	1	no	—
77	C₂³×C₄×C₃₁	—	2	1	no	—
78	C₂³×C₄×C₃₁	—	4	4	no	—
79	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
80	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	D₄	1	4	yes	—
83	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
87	C₂×SD₁₆×C₃₁	—	4	4	no	—
88	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	complemented
89	C₂×D₈×C₃₁	—	4	4	no	—
90	C₂×D₈×C₃₁	C₂³	1	8	yes	complemented
91	C₂²×C₈×C₃₁	—	4	4	no	—
92	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
94	C₂²×C₈×C₃₁	C₂³	1	8	yes	complemented
95	C₃₁×#123	—	2	8	no	—
96	C₃₁×C₂²⋊Q₈	—	2	2	no	—
97	C₃₁×C₂²⋊Q₈	—	2	2	no	—
98	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
99	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	complemented
100	C₃₁×#121	—	2	4	no	—
101	C₃₁×#121	—	2	4	no	—
102	C₃₁×#121	—	2	8	no	—
103	C₃₁×#121	—	2	8	no	—
104	C₃₁×#121	—	2	2	no	—
105	C₃₁×#121	—	2	2	no	—
106	C₃₁×#121	C₂³	1	4	yes	—
107	C₃₁×#121	C₂³	1	8	yes	—
108	C₃₁×#121	C₂³	1	8	yes	—
109	C₃₁×#121	C₂³	1	4	yes	complemented
110	C₃₁×#120	—	2	8	no	—
111	C₄×D₄×C₃₁	—	2	8	no	—
112	C₄×D₄×C₃₁	—	2	8	no	—
113	C₃₁×#117	—	2	2	no	—
114	C₃₁×#117	C₂³	1	4	yes	complemented
115	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
127	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
128	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
129	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
131	C₂×C₄²×C₃₁	—	2	1	no	—
132	C₃₁×#107	C₂³	1	8	yes	complemented
133	C₃₁×#106	C₂³	1	8	yes	complemented
134	C₃₁×#103	C₂³	1	8	yes	complemented
135	C₃₁×#102	C₂³	1	8	yes	complemented
136	C₃₁×#102	C₂³	1	8	yes	complemented
137	C₃₁×#102	C₂³	1	8	yes	complemented
138	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
139	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
140	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	complemented
141	C₂⁴×C₃₁	—	2	4	no	—
142	C₂⁴×C₃₁	—	2	4	no	—
143	C₂⁴×C₃₁	—	2	4	no	—
144	C₂⁴×C₃₁	—	2	1	no	—
145	C₂⁴×C₃₁	—	2	2	no	—
146	C₂⁴×C₃₁	—	4	2	no	—
147	C₂⁴×C₃₁	—	4	4	no	—
148	C₂⁴×C₃₁	—	4	4	no	—
149	C₂⁴×C₃₁	—	4	4	no	—
150	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
152	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
154	#41×C₃₁	—	4	8	no	—
155	#41×C₃₁	—	4	8	no	—
156	C₂×Q₈×C₃₁	—	2	1	no	—
157	C₂×Q₈×C₃₁	—	2	4	no	—
158	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
159	C₂×D₄×C₃₁	—	2	4	no	—
160	C₂×D₄×C₃₁	—	2	4	no	—
161	C₂×D₄×C₃₁	—	2	4	no	—
162	C₂×D₄×C₃₁	—	2	8	no	—
163	C₂×D₄×C₃₁	—	2	8	no	—
164	C₂×D₄×C₃₁	—	2	4	no	—
165	C₂×D₄×C₃₁	—	2	2	no	—
166	C₂×D₄×C₃₁	—	2	1	no	—
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	2	4	no	—
169	C₂×D₄×C₃₁	—	2	4	no	—
170	C₂×D₄×C₃₁	—	4	8	no	—
171	C₂×D₄×C₃₁	—	4	4	no	—
172	C₂×D₄×C₃₁	—	4	8	no	—
173	C₂×D₄×C₃₁	—	4	32	no	—
174	C₂×D₄×C₃₁	—	4	8	no	—
175	C₂×D₄×C₃₁	—	4	4	no	—
176	C₂×D₄×C₃₁	—	4	4	no	—
177	C₂×D₄×C₃₁	—	4	4	no	—
178	C₂×D₄×C₃₁	—	4	8	no	—
179	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
180	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₃₁	—	2	4	no	—
182	C₂²×C₄×C₃₁	—	2	4	no	—
183	C₂²×C₄×C₃₁	—	2	4	no	—
184	C₂²×C₄×C₃₁	—	2	4	no	—
185	C₂²×C₄×C₃₁	—	2	1	no	—
186	C₂²×C₄×C₃₁	—	2	1	no	—
187	C₂²×C₄×C₃₁	—	2	1	no	—
188	C₂²×C₄×C₃₁	—	2	2	no	—
189	C₂²×C₄×C₃₁	—	2	4	no	—
190	C₂²×C₄×C₃₁	—	4	8	no	—
191	C₂²×C₄×C₃₁	—	4	8	no	—
192	C₂²×C₄×C₃₁	—	4	2	no	—
193	C₂²×C₄×C₃₁	—	4	2	no	—
194	C₂²×C₄×C₃₁	—	4	2	no	—
195	C₂²×C₄×C₃₁	—	4	4	no	—
196	C₂²×C₄×C₃₁	—	4	4	no	—
197	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
210	SD₁₆×C₃₁	—	4	8	no	—
211	D₈×C₃₁	—	4	8	no	—
212	C₂×C₈×C₃₁	—	2	4	no	—
213	C₂×C₈×C₃₁	—	2	4	no	—
214	C₂×C₈×C₃₁	—	4	8	no	—
215	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
216	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₃₁	—	2	4	no	—
218	C₄⋊C₄×C₃₁	—	2	2	no	—
219	C₄⋊C₄×C₃₁	—	2	4	no	—
220	C₄⋊C₄×C₃₁	—	2	4	no	—
221	C₄⋊C₄×C₃₁	—	2	1	no	—
222	C₄⋊C₄×C₃₁	—	2	1	no	—
223	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
224	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
225	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
226	C₂²⋊C₄×C₃₁	—	2	4	no	—
227	C₂²⋊C₄×C₃₁	—	2	4	no	—
228	C₂²⋊C₄×C₃₁	—	2	4	no	—
229	C₂²⋊C₄×C₃₁	—	2	8	no	—
230	C₂²⋊C₄×C₃₁	—	2	8	no	—
231	C₂²⋊C₄×C₃₁	—	2	4	no	—
232	C₂²⋊C₄×C₃₁	—	2	4	no	—
233	C₄²×C₃₁	—	2	4	no	—
234	C₂×#3188	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂³×C₃₁	—	2	2	no	—
236	C₂³×C₃₁	—	2	2	no	—
237	C₂³×C₃₁	—	2	2	no	—
238	C₂³×C₃₁	—	2	2	no	—
239	C₂³×C₃₁	—	2	2	no	—
240	C₂³×C₃₁	—	2	8	no	—
241	C₂³×C₃₁	—	2	2	no	—
242	C₂³×C₃₁	—	2	8	no	—
243	C₂³×C₃₁	—	2	2	no	—
244	C₂³×C₃₁	—	2	2	no	—
245	C₂³×C₃₁	—	2	4	no	—
246	C₂³×C₃₁	—	4	4	no	—
247	C₂³×C₃₁	—	4	16	no	—
248	C₂³×C₃₁	—	4	8	no	—
249	C₂³×C₃₁	—	4	8	no	—
250	C₂³×C₃₁	—	4	2	no	—
251	C₂³×C₃₁	—	4	4	no	—
252	C₂³×C₃₁	—	4	2	no	—
253	C₂³×C₃₁	—	4	8	no	—
254	C₂³×C₃₁	—	4	4	no	—
255	C₂³×C₃₁	—	4	4	no	—
256	C₂³×C₃₁	—	4	2	no	—
257	C₂³×C₃₁	—	8	16	no	—
258	C₂³×C₃₁	#135	1	4	yes	—
259	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
260	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
261	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
262	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
263	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
264	Q₈×C₃₁	—	2	4	no	—
265	Q₈×C₃₁	—	4	2	no	—
266	D₄×C₃₁	—	2	4	no	—
267	D₄×C₃₁	—	2	4	no	—
268	D₄×C₃₁	—	2	4	no	—
269	D₄×C₃₁	—	4	8	no	—
270	D₄×C₃₁	—	4	16	no	—
271	D₄×C₃₁	—	4	8	no	—
272	D₄×C₃₁	—	4	8	no	—
273	D₄×C₃₁	—	4	8	no	—
274	D₄×C₃₁	—	4	16	no	—
275	D₄×C₃₁	—	4	4	no	—
276	D₄×C₃₁	—	4	2	no	—
277	C₂×C₄×C₃₁	—	2	2	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	4	no	—
281	C₂×C₄×C₃₁	—	2	4	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	4	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	2	2	no	—
287	C₂×C₄×C₃₁	—	2	2	no	—
288	C₂×C₄×C₃₁	—	2	2	no	—
289	C₂×C₄×C₃₁	—	2	4	no	—
290	C₂×C₄×C₃₁	—	4	4	no	—
291	C₂×C₄×C₃₁	—	4	4	no	—
292	C₂×C₄×C₃₁	—	4	4	no	—
293	C₂×C₄×C₃₁	—	4	8	no	—
294	C₂×C₄×C₃₁	—	4	8	no	—
295	C₂×C₄×C₃₁	—	4	2	no	—
296	C₂×C₄×C₃₁	—	4	2	no	—
297	C₂×C₄×C₃₁	—	4	4	no	—
298	C₂×C₄×C₃₁	—	4	2	no	—
299	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
304	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
305	C₈×C₃₁	—	2	4	no	—
306	C₈×C₃₁	—	2	4	no	—
307	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
308	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
309	#3188	C₂×C₃₁	1	16	yes	direct product factor
310	C₂×#484	C₂×C₃₁	1	1	yes	characteristic, complemented
311	C₂×#481	C₂×C₃₁	1	1	yes	characteristic, complemented
312	C₂×#482	C₂×C₃₁	1	2	yes	complemented
313	C₂×#466	C₂×C₃₁	1	2	yes	complemented
314	C₂×#465	C₂×C₃₁	1	2	yes	complemented
315	C₂×#449	C₂×C₃₁	1	2	yes	complemented
316	C₂×#450	C₂×C₃₁	1	1	yes	characteristic, complemented
317	C₂×#447	C₂×C₃₁	1	1	yes	characteristic, complemented
318	C₂²×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
319	C₂²×C₃₁	—	2	8	no	—
320	C₂²×C₃₁	—	2	8	no	—
321	C₂²×C₃₁	—	2	2	no	—
322	C₂²×C₃₁	—	2	2	no	—
323	C₂²×C₃₁	—	2	2	no	—
324	C₂²×C₃₁	—	2	2	no	—
325	C₂²×C₃₁	—	2	2	no	—
326	C₂²×C₃₁	—	2	2	no	—
327	C₂²×C₃₁	—	2	2	no	—
328	C₂²×C₃₁	—	4	16	no	—
329	C₂²×C₃₁	—	4	4	no	—
330	C₂²×C₃₁	—	4	2	no	—
331	C₂²×C₃₁	—	4	4	no	—
332	C₂²×C₃₁	—	4	2	no	—
333	C₂²×C₃₁	—	4	4	no	—
334	C₂²×C₃₁	—	4	4	no	—
335	C₂²×C₃₁	—	4	2	no	—
336	C₂²×C₃₁	—	8	16	no	—
337	C₂²×C₃₁	—	8	4	no	—
338	C₂²×C₃₁	—	8	8	no	—
339	C₂²×C₃₁	#534	1	2	yes	—
340	C₂²×C₃₁	C₂×#135	1	4	yes	—
341	C₂²×C₃₁	C₂×#135	1	2	yes	—
342	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
343	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
344	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	2	no	—
347	C₄×C₃₁	—	2	2	no	—
348	C₄×C₃₁	—	4	2	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	—	4	4	no	—
351	C₄×C₃₁	—	4	2	no	—
352	C₄×C₃₁	#534	1	2	yes	—
353	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
354	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
355	C₂³×D₄	—	2	1	no	—
356	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
358	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
359	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
360	C₂³×C₈	C₂²×C₃₁	1	2	yes	complemented
361	#525	—	2	4	no	—
362	#525	C₂²×C₃₁	1	8	yes	complemented
363	C₂×#123	—	2	1	no	—
364	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#121	—	2	1	no	—
367	C₂×#121	—	2	1	no	—
368	C₂×#121	—	2	4	no	—
369	C₂×#121	C₂²×C₃₁	1	2	yes	—
370	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
371	C₂×#121	C₂²×C₃₁	1	2	yes	—
372	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
373	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
374	C₂×#120	—	2	1	no	—
375	C₂×C₄×D₄	—	2	1	no	—
376	C₂×C₄×D₄	—	2	1	no	—
377	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
378	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	—	2	1	no	—
380	#484	C₂²×C₃₁	1	8	yes	complemented
381	#482	C₂²×C₃₁	1	16	yes	complemented
382	#481	C₂²×C₃₁	1	8	yes	complemented
383	#466	C₂²×C₃₁	1	16	yes	complemented
384	#465	C₂²×C₃₁	1	16	yes	complemented
385	#450	C₂²×C₃₁	1	8	yes	complemented
386	#449	C₂²×C₃₁	1	16	yes	complemented
387	#447	C₂²×C₃₁	1	8	yes	complemented
388	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
389	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
390	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
391	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
392	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
393	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
394	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₃₁	1	8	yes	complemented
397	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
398	C₂×C₃₁	—	2	4	no	—
399	C₂×C₃₁	—	2	4	no	—
400	C₂×C₃₁	—	4	2	no	—
401	C₂×C₃₁	—	8	2	no	—
402	C₂×C₃₁	—	8	4	no	—
403	C₂×C₃₁	#3188	1	4	yes	direct product factor
404	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
405	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
406	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂⁵	—	2	1	no	—
408	C₂⁵	D₄×C₃₁	1	1	yes	characteristic
409	C₂×#41	—	2	2	no	—
410	C₂×#41	—	4	4	no	—
411	C₂×#41	C₂³×C₃₁	1	4	yes	complemented
412	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	—	2	2	no	—
418	C₂²×D₄	—	2	8	no	—
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	—	2	2	no	—
421	C₂²×D₄	—	4	4	no	—
422	C₂²×D₄	—	4	8	no	—
423	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
424	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	—	4	4	no	—
429	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
430	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
431	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
432	C₂³×C₄	D₄×C₃₁	1	4	yes	—
433	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
437	C₂×SD₁₆	—	4	4	no	—
438	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	complemented
439	C₂×D₈	—	4	4	no	—
440	C₂×D₈	C₂³×C₃₁	1	8	yes	complemented
441	C₂²×C₈	—	4	4	no	—
442	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
443	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
444	C₂²×C₈	C₂³×C₃₁	1	8	yes	complemented
445	#123	—	2	8	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
449	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	complemented
450	#121	—	2	4	no	—
451	#121	—	2	4	no	—
452	#121	—	2	8	no	—
453	#121	—	2	8	no	—
454	#121	—	2	2	no	—
455	#121	—	2	2	no	—
456	#121	C₂³×C₃₁	1	8	yes	—
457	#121	C₂³×C₃₁	1	8	yes	—
458	#121	C₂³×C₃₁	1	4	yes	—
459	#121	C₂³×C₃₁	1	4	yes	complemented
460	#120	—	2	8	no	—
461	C₄×D₄	—	2	8	no	—
462	C₄×D₄	—	2	8	no	—
463	#117	—	2	2	no	—
464	#117	C₂³×C₃₁	1	4	yes	complemented
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	—	2	2	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	2	no	—
477	C₂×C₂²⋊C₄	—	2	2	no	—
478	C₂×C₂²⋊C₄	—	2	8	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₄²	—	2	1	no	—
482	#107	C₂³×C₃₁	1	8	yes	complemented
483	#106	C₂³×C₃₁	1	8	yes	complemented
484	#103	C₂³×C₃₁	1	8	yes	complemented
485	#102	C₂³×C₃₁	1	8	yes	complemented
486	#102	C₂³×C₃₁	1	8	yes	complemented
487	#102	C₂³×C₃₁	1	8	yes	complemented
488	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
489	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	complemented
491	C₃₁	C₂×#3188	1	1	yes	characteristic, direct product factor, Sylow
492	C₂⁴	—	2	4	no	—
493	C₂⁴	—	2	4	no	—
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	2	2	no	—
497	C₂⁴	—	4	2	no	—
498	C₂⁴	—	4	4	no	—
499	C₂⁴	—	4	4	no	—
500	C₂⁴	—	4	4	no	—
501	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
502	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
503	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
504	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
505	#41	—	4	8	no	—
506	#41	—	4	8	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	4	8	no	—
522	C₂×D₄	—	4	4	no	—
523	C₂×D₄	—	4	8	no	—
524	C₂×D₄	—	4	32	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	8	no	—
530	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
531	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	8	no	—
542	C₂²×C₄	—	4	8	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
553	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
554	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
555	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
556	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
561	SD₁₆	—	4	8	no	—
562	D₈	—	4	8	no	—
563	C₂×C₈	—	2	4	no	—
564	C₂×C₈	—	2	4	no	—
565	C₂×C₈	—	4	8	no	—
566	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
567	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
575	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
576	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₄²	—	2	4	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	8	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	8	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	4	16	no	—
598	C₂³	—	4	8	no	—
599	C₂³	—	4	8	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	8	16	no	—
608	C₂³	C₃₁×#135	1	4	yes	—
609	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
610	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
611	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
612	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
613	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
614	Q₈	—	2	4	no	—
615	Q₈	—	4	2	no	—
616	D₄	—	2	4	no	—
617	D₄	—	2	4	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	16	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	8	no	—
623	D₄	—	4	8	no	—
624	D₄	—	4	16	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
653	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
654	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
655	C₈	—	2	4	no	—
656	C₈	—	2	4	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	4	16	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	8	16	no	—
675	C₂²	—	8	8	no	—
676	C₂²	—	8	4	no	—
677	C₂²	C₃₁×#534	1	2	yes	—
678	C₂²	C₂×C₃₁×#135	1	4	yes	—
679	C₂²	C₂×C₃₁×#135	1	2	yes	—
680	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
681	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
682	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	4	no	—
689	C₄	—	4	2	no	—
690	C₄	C₃₁×#534	1	2	yes	—
691	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
692	C₂	—	2	4	no	—
693	C₂	—	2	4	no	—
694	C₂	—	4	2	no	—
695	C₂	—	8	4	no	—
696	C₂	—	8	2	no	—
697	C₂	C₃₁×#3188	1	4	yes	direct product factor
698	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
699	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
700	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂⁴×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#525	C₂	semidirect
2. C₂²×C₃₁×#121	C₂	semidirect
3. C₃₁×#3188	C₂	direct (N × H)
4. C₂×C₃₁×#484	C₂	semidirect
5. C₂×C₃₁×#481	C₂	semidirect
6. C₂×C₃₁×#482	C₂	semidirect
7. C₂×C₃₁×#466	C₂	semidirect
8. C₂×C₃₁×#465	C₂	semidirect
9. C₂×C₃₁×#449	C₂	semidirect
10. C₂×C₃₁×#450	C₂	semidirect
11. C₂×C₃₁×#447	C₂	semidirect
12. C₂²×C₃₁×C₂²⋊C₈	C₂	semidirect
13. C₂²×#41×C₃₁	C₂²	semidirect
17. C₂²×SD₁₆×C₃₁	C₂²	semidirect
18. C₂²×D₈×C₃₁	C₂²	semidirect
19. C₂³×C₈×C₃₁	C₂²	semidirect
21. C₃₁×#525	C₂²	semidirect
24. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃₁×#121	C₂²	semidirect
32. C₂×C₃₁×#121	C₂²	semidirect
36. C₂×C₃₁×#117	C₂²	semidirect
39. C₃₁×#484	C₂²	semidirect
40. C₃₁×#482	C₂²	semidirect
41. C₃₁×#481	C₂²	semidirect
42. C₃₁×#466	C₂²	semidirect
43. C₃₁×#465	C₂²	semidirect
44. C₃₁×#450	C₂²	semidirect
45. C₃₁×#449	C₂²	semidirect
46. C₃₁×#447	C₂²	semidirect
47. C₂×C₃₁×#107	C₂²	semidirect
48. C₂×C₃₁×#106	C₂²	semidirect
49. C₂×C₃₁×#103	C₂²	semidirect
50. C₂×C₃₁×#102	C₂²	semidirect
51. C₂×C₃₁×#102	C₂²	semidirect
52. C₂×C₃₁×#102	C₂²	semidirect
55. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
56. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
61. C₂×#41×C₃₁	C₂³	semidirect
88. C₂×SD₁₆×C₃₁	C₂³	semidirect
90. C₂×D₈×C₃₁	C₂³	semidirect
94. C₂²×C₈×C₃₁	C₂³	semidirect
99. C₃₁×C₂²⋊Q₈	C₂³	semidirect
109. C₃₁×#121	C₂³	semidirect
114. C₃₁×#117	C₂³	semidirect
132. C₃₁×#107	C₂³	semidirect
133. C₃₁×#106	C₂³	semidirect
134. C₃₁×#103	C₂³	semidirect
135. C₃₁×#102	C₂³	semidirect
136. C₃₁×#102	C₂³	semidirect
137. C₃₁×#102	C₂³	semidirect
140. C₃₁×C₂²⋊C₈	C₂³	semidirect
234. C₂×#3188	C₃₁	direct (N × H)
307. C₂×#525	C₂×C₃₁	semidirect
308. C₂²×#121	C₂×C₃₁	semidirect
309. #3188	C₂×C₃₁	direct (N × H)
310. C₂×#484	C₂×C₃₁	semidirect
311. C₂×#481	C₂×C₃₁	semidirect
312. C₂×#482	C₂×C₃₁	semidirect
313. C₂×#466	C₂×C₃₁	semidirect
314. C₂×#465	C₂×C₃₁	semidirect
315. C₂×#449	C₂×C₃₁	semidirect
316. C₂×#450	C₂×C₃₁	semidirect
317. C₂×#447	C₂×C₃₁	semidirect
318. C₂²×C₂²⋊C₈	C₂×C₃₁	semidirect
354. C₂²×#41	C₂²×C₃₁	semidirect
358. C₂²×SD₁₆	C₂²×C₃₁	semidirect
359. C₂²×D₈	C₂²×C₃₁	semidirect
360. C₂³×C₈	C₂²×C₃₁	semidirect
362. #525	C₂²×C₃₁	semidirect
365. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
372. C₂×#121	C₂²×C₃₁	semidirect
373. C₂×#121	C₂²×C₃₁	semidirect
377. C₂×#117	C₂²×C₃₁	semidirect
380. #484	C₂²×C₃₁	semidirect
381. #482	C₂²×C₃₁	semidirect
382. #481	C₂²×C₃₁	semidirect
383. #466	C₂²×C₃₁	semidirect
384. #465	C₂²×C₃₁	semidirect
385. #450	C₂²×C₃₁	semidirect
386. #449	C₂²×C₃₁	semidirect
387. #447	C₂²×C₃₁	semidirect
388. C₂×#107	C₂²×C₃₁	semidirect
389. C₂×#106	C₂²×C₃₁	semidirect
390. C₂×#103	C₂²×C₃₁	semidirect
391. C₂×#102	C₂²×C₃₁	semidirect
392. C₂×#102	C₂²×C₃₁	semidirect
393. C₂×#102	C₂²×C₃₁	semidirect
396. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
397. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
403. C₂×C₃₁	#3188	direct (N × H)
411. C₂×#41	C₂³×C₃₁	semidirect
438. C₂×SD₁₆	C₂³×C₃₁	semidirect
440. C₂×D₈	C₂³×C₃₁	semidirect
444. C₂²×C₈	C₂³×C₃₁	semidirect
449. C₂²⋊Q₈	C₂³×C₃₁	semidirect
459. #121	C₂³×C₃₁	semidirect
464. #117	C₂³×C₃₁	semidirect
482. #107	C₂³×C₃₁	semidirect
483. #106	C₂³×C₃₁	semidirect
484. #103	C₂³×C₃₁	semidirect
485. #102	C₂³×C₃₁	semidirect
486. #102	C₂³×C₃₁	semidirect
487. #102	C₂³×C₃₁	semidirect
490. C₂²⋊C₈	C₂³×C₃₁	semidirect
491. C₃₁	C₂×#3188	direct (N × H)
697. C₂	C₃₁×#3188	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×#525	2
C₂²×C₃₁×#121	2
C₃₁×#3188	2
C₂×C₃₁×#484	2
C₂×C₃₁×#481	2
C₂×C₃₁×#482	2
C₂×C₃₁×#466	2
C₂×C₃₁×#465	2
C₂×C₃₁×#449	2
C₂×C₃₁×#450	2
C₂×C₃₁×#447	2
C₂²×C₃₁×C₂²⋊C₈	2
C₂×#3188	31

Subgroups — C2×C31×#3188 #21517489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3188 #21517489