Subgroups — C₂×C₃₁×#3274 #21517792

Order 7936.

3278 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3274	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#447	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₃₁	—	2	1	no	—
15	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
16	C₂×C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
17	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
18	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
20	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
21	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
22	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
24	C₃₁×#550	—	2	4	no	—
25	C₃₁×#550	C₂²	1	8	yes	complemented
26	D₄²×C₃₁	—	2	4	no	—
27	D₄²×C₃₁	C₂²	1	8	yes	complemented
28	C₂×C₃₁×#127	—	2	1	no	—
29	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#121	—	2	1	no	—
32	C₂×C₃₁×#121	—	2	2	no	—
33	C₂×C₃₁×#121	C₂²	1	2	yes	—
34	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
35	C₂×C₃₁×#120	—	2	2	no	—
36	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₃₁	—	2	1	no	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#493	C₂²	1	8	yes	complemented
41	C₃₁×#469	C₂²	1	16	yes	complemented
42	C₃₁×#460	C₂²	1	8	yes	complemented
43	C₃₁×#459	C₂²	1	8	yes	complemented
44	C₃₁×#449	C₂²	1	16	yes	complemented
45	C₃₁×#447	C₂²	1	16	yes	complemented
46	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
47	C₃₁×#436	C₂²	1	8	yes	complemented
48	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
53	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
54	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₃₁	—	2	2	no	—
57	C₂×#41×C₃₁	—	2	4	no	—
58	C₂×#41×C₃₁	—	2	8	no	—
59	C₂×#41×C₃₁	—	4	4	no	—
60	C₂×#41×C₃₁	C₂³	1	8	yes	complemented
61	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₃₁	—	2	8	no	—
63	C₂²×D₄×C₃₁	—	2	2	no	—
64	C₂²×D₄×C₃₁	—	2	2	no	—
65	C₂²×D₄×C₃₁	—	2	2	no	—
66	C₂²×D₄×C₃₁	—	2	8	no	—
67	C₂²×D₄×C₃₁	—	2	1	no	—
68	C₂²×D₄×C₃₁	—	2	2	no	—
69	C₂²×D₄×C₃₁	—	2	1	no	—
70	C₂²×D₄×C₃₁	—	2	4	no	—
71	C₂²×D₄×C₃₁	—	2	1	no	—
72	C₂²×D₄×C₃₁	—	2	1	no	—
73	C₂²×D₄×C₃₁	—	4	4	no	—
74	C₂²×D₄×C₃₁	—	4	8	no	—
75	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
76	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
77	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
79	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₃₁	—	2	2	no	—
81	C₂³×C₄×C₃₁	—	2	1	no	—
82	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
83	C₃₁×AGL(1,ℤ/8)	—	2	64	no	—
84	C₂×SD₁₆×C₃₁	—	2	8	no	—
85	C₂×SD₁₆×C₃₁	D₄	1	8	yes	complemented
86	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
87	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	complemented
88	C₂×D₈×C₃₁	—	2	8	no	—
89	C₂×D₈×C₃₁	—	2	8	no	—
90	C₂×D₈×C₃₁	—	4	4	no	—
91	C₂×D₈×C₃₁	C₂³	1	8	yes	—
92	C₂×D₈×C₃₁	C₂³	1	8	yes	complemented
93	C₂×D₈×C₃₁	C₂³	1	8	yes	complemented
94	C₂×M₁₆×C₃₁	—	2	8	no	—
95	C₂×M₁₆×C₃₁	C₂³	1	8	yes	complemented
96	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
98	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
99	C₃₁×#127	—	2	8	no	—
100	C₃₁×#127	—	2	2	no	—
101	C₃₁×#127	—	2	2	no	—
102	C₃₁×#127	C₂³	1	4	yes	—
103	C₃₁×#127	C₂³	1	4	yes	complemented
104	C₃₁×#121	—	2	4	no	—
105	C₃₁×#121	—	2	4	no	—
106	C₃₁×#121	—	2	8	no	—
107	C₃₁×#121	—	2	16	no	—
108	C₃₁×#121	C₂³	1	8	yes	—
109	C₃₁×#121	C₂³	1	8	yes	complemented
110	C₃₁×#120	—	2	16	no	—
111	C₄×Q₈×C₃₁	—	2	2	no	—
112	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
113	C₄×D₄×C₃₁	—	2	8	no	—
114	C₄×D₄×C₃₁	—	2	2	no	—
115	C₄×D₄×C₃₁	D₄	1	4	yes	—
116	C₄×D₄×C₃₁	C₂³	1	4	yes	—
117	C₄×D₄×C₃₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
126	C₂×C₄²×C₃₁	—	2	1	no	—
127	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
128	C₃₁×#106	C₂³	1	4	yes	complemented
129	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
130	C₃₁×#103	C₂³	1	4	yes	complemented
131	C₃₁×#102	C₂³	1	4	yes	—
132	C₃₁×#102	C₂³	1	8	yes	complemented
133	C₃₁×#102	C₂³	1	8	yes	complemented
134	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	complemented
135	C₄×C₈×C₃₁	C₂³	1	4	yes	complemented
136	C₂⁴×C₃₁	—	2	1	no	—
137	C₂⁴×C₃₁	—	2	2	no	—
138	C₂⁴×C₃₁	—	2	2	no	—
139	C₂⁴×C₃₁	—	2	8	no	—
140	C₂⁴×C₃₁	—	4	8	no	—
141	C₂⁴×C₃₁	—	4	8	no	—
142	C₂⁴×C₃₁	—	8	4	no	—
143	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
144	#41×C₃₁	—	2	16	no	—
145	#41×C₃₁	—	4	8	no	—
146	#41×C₃₁	—	4	16	no	—
147	C₂×Q₈×C₃₁	—	2	1	no	—
148	C₂×Q₈×C₃₁	—	2	2	no	—
149	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	complemented
150	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
151	C₂×D₄×C₃₁	—	2	16	no	—
152	C₂×D₄×C₃₁	—	2	8	no	—
153	C₂×D₄×C₃₁	—	2	8	no	—
154	C₂×D₄×C₃₁	—	2	8	no	—
155	C₂×D₄×C₃₁	—	2	4	no	—
156	C₂×D₄×C₃₁	—	2	1	no	—
157	C₂×D₄×C₃₁	—	2	4	no	—
158	C₂×D₄×C₃₁	—	2	4	no	—
159	C₂×D₄×C₃₁	—	2	4	no	—
160	C₂×D₄×C₃₁	—	2	8	no	—
161	C₂×D₄×C₃₁	—	2	2	no	—
162	C₂×D₄×C₃₁	—	2	2	no	—
163	C₂×D₄×C₃₁	—	2	4	no	—
164	C₂×D₄×C₃₁	—	2	4	no	—
165	C₂×D₄×C₃₁	—	2	4	no	—
166	C₂×D₄×C₃₁	—	2	2	no	—
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	2	4	no	—
169	C₂×D₄×C₃₁	—	4	8	no	—
170	C₂×D₄×C₃₁	—	4	16	no	—
171	C₂×D₄×C₃₁	—	4	8	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	—	8	2	no	—
178	C₂×D₄×C₃₁	—	8	2	no	—
179	C₂×D₄×C₃₁	—	8	4	no	—
180	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
181	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
182	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
183	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
184	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₃₁	—	2	1	no	—
186	C₂²×C₄×C₃₁	—	2	4	no	—
187	C₂²×C₄×C₃₁	—	2	4	no	—
188	C₂²×C₄×C₃₁	—	2	1	no	—
189	C₂²×C₄×C₃₁	—	2	1	no	—
190	C₂²×C₄×C₃₁	—	2	8	no	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	4	8	no	—
193	C₂²×C₄×C₃₁	—	4	4	no	—
194	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
200	SD₁₆×C₃₁	—	2	16	no	—
201	SD₁₆×C₃₁	C₂×D₄	1	16	yes	complemented
202	D₈×C₃₁	—	2	16	no	—
203	D₈×C₃₁	—	2	16	no	—
204	D₈×C₃₁	—	4	8	no	—
205	M₁₆×C₃₁	—	2	16	no	—
206	C₂×C₈×C₃₁	—	2	4	no	—
207	C₂×C₈×C₃₁	—	2	2	no	—
208	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	complemented
209	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
210	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
211	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
212	C₄⋊C₄×C₃₁	—	2	4	no	—
213	C₄⋊C₄×C₃₁	—	2	1	no	—
214	C₄⋊C₄×C₃₁	—	2	1	no	—
215	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
216	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²⋊C₄×C₃₁	—	2	8	no	—
219	C₂²⋊C₄×C₃₁	—	2	4	no	—
220	C₂²⋊C₄×C₃₁	—	2	8	no	—
221	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
222	C₄²×C₃₁	—	2	4	no	—
223	C₄²×C₃₁	C₂×D₄	1	2	yes	—
224	C₄²×C₃₁	C₂⁴	1	2	yes	—
225	C₂×#3274	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₃₁	—	2	4	no	—
227	C₂³×C₃₁	—	2	4	no	—
228	C₂³×C₃₁	—	2	4	no	—
229	C₂³×C₃₁	—	2	4	no	—
230	C₂³×C₃₁	—	2	2	no	—
231	C₂³×C₃₁	—	2	4	no	—
232	C₂³×C₃₁	—	2	4	no	—
233	C₂³×C₃₁	—	4	16	no	—
234	C₂³×C₃₁	—	4	16	no	—
235	C₂³×C₃₁	—	4	2	no	—
236	C₂³×C₃₁	—	4	2	no	—
237	C₂³×C₃₁	—	4	4	no	—
238	C₂³×C₃₁	—	4	4	no	—
239	C₂³×C₃₁	—	4	4	no	—
240	C₂³×C₃₁	—	4	4	no	—
241	C₂³×C₃₁	—	4	4	no	—
242	C₂³×C₃₁	—	4	4	no	—
243	C₂³×C₃₁	—	8	8	no	—
244	C₂³×C₃₁	—	8	32	no	—
245	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
246	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₃₁	—	2	4	no	—
248	Q₈×C₃₁	—	2	2	no	—
249	Q₈×C₃₁	C₂²×D₄	1	4	yes	complemented
250	D₄×C₃₁	—	2	4	no	—
251	D₄×C₃₁	—	2	8	no	—
252	D₄×C₃₁	—	2	4	no	—
253	D₄×C₃₁	—	2	4	no	—
254	D₄×C₃₁	—	2	2	no	—
255	D₄×C₃₁	—	2	4	no	—
256	D₄×C₃₁	—	2	4	no	—
257	D₄×C₃₁	—	4	16	no	—
258	D₄×C₃₁	—	4	16	no	—
259	D₄×C₃₁	—	4	16	no	—
260	D₄×C₃₁	—	4	4	no	—
261	D₄×C₃₁	—	4	4	no	—
262	D₄×C₃₁	—	4	8	no	—
263	D₄×C₃₁	—	4	8	no	—
264	D₄×C₃₁	—	8	4	no	—
265	D₄×C₃₁	—	8	4	no	—
266	D₄×C₃₁	—	8	8	no	—
267	D₄×C₃₁	C₂²×D₄	1	4	yes	—
268	C₂×C₄×C₃₁	—	2	4	no	—
269	C₂×C₄×C₃₁	—	2	4	no	—
270	C₂×C₄×C₃₁	—	2	2	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	8	no	—
273	C₂×C₄×C₃₁	—	2	4	no	—
274	C₂×C₄×C₃₁	—	2	4	no	—
275	C₂×C₄×C₃₁	—	2	2	no	—
276	C₂×C₄×C₃₁	—	2	2	no	—
277	C₂×C₄×C₃₁	—	4	16	no	—
278	C₂×C₄×C₃₁	—	4	2	no	—
279	C₂×C₄×C₃₁	—	4	2	no	—
280	C₂×C₄×C₃₁	—	4	8	no	—
281	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
282	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
284	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
288	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
289	C₈×C₃₁	—	2	4	no	—
290	C₈×C₃₁	—	2	2	no	—
291	C₈×C₃₁	C₂²×D₄	1	4	yes	complemented
292	C₂²×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
293	C₂×#550	C₂×C₃₁	1	1	yes	characteristic, complemented
294	C₂×D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
295	#3274	C₂×C₃₁	1	16	yes	direct product factor
296	C₂×#493	C₂×C₃₁	1	1	yes	characteristic, complemented
297	C₂×#469	C₂×C₃₁	1	2	yes	complemented
298	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
299	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
300	C₂×#449	C₂×C₃₁	1	2	yes	complemented
301	C₂×#447	C₂×C₃₁	1	2	yes	complemented
302	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
303	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
304	C₂²×C₃₁	—	2	4	no	—
305	C₂²×C₃₁	—	2	4	no	—
306	C₂²×C₃₁	—	2	4	no	—
307	C₂²×C₃₁	—	2	4	no	—
308	C₂²×C₃₁	—	4	8	no	—
309	C₂²×C₃₁	—	4	8	no	—
310	C₂²×C₃₁	—	4	2	no	—
311	C₂²×C₃₁	—	4	2	no	—
312	C₂²×C₃₁	—	4	4	no	—
313	C₂²×C₃₁	—	4	4	no	—
314	C₂²×C₃₁	—	4	4	no	—
315	C₂²×C₃₁	—	4	4	no	—
316	C₂²×C₃₁	—	4	4	no	—
317	C₂²×C₃₁	—	4	4	no	—
318	C₂²×C₃₁	—	8	32	no	—
319	C₂²×C₃₁	—	8	8	no	—
320	C₂²×C₃₁	—	8	8	no	—
321	C₂²×C₃₁	D₄²	1	2	yes	—
322	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
323	C₂²×C₃₁	#576	1	2	yes	—
324	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
325	C₄×C₃₁	—	2	4	no	—
326	C₄×C₃₁	—	2	4	no	—
327	C₄×C₃₁	—	2	2	no	—
328	C₄×C₃₁	—	4	2	no	—
329	C₄×C₃₁	—	4	2	no	—
330	C₄×C₃₁	D₄²	1	2	yes	—
331	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
332	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
333	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
335	C₂³×D₄	—	2	1	no	—
336	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
337	C₂×AGL(1,ℤ/8)	—	2	16	no	—
338	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	16	yes	complemented
339	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
340	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
341	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
342	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
343	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
344	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
345	#550	—	2	4	no	—
346	#550	C₂²×C₃₁	1	8	yes	complemented
347	D₄²	—	2	4	no	—
348	D₄²	C₂²×C₃₁	1	8	yes	complemented
349	C₂×#127	—	2	1	no	—
350	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
351	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
352	C₂×#121	—	2	1	no	—
353	C₂×#121	—	2	2	no	—
354	C₂×#121	C₂²×C₃₁	1	2	yes	—
355	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
356	C₂×#120	—	2	2	no	—
357	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
361	#493	C₂²×C₃₁	1	8	yes	complemented
362	#469	C₂²×C₃₁	1	16	yes	complemented
363	#460	C₂²×C₃₁	1	8	yes	complemented
364	#459	C₂²×C₃₁	1	8	yes	complemented
365	#449	C₂²×C₃₁	1	16	yes	complemented
366	#447	C₂²×C₃₁	1	16	yes	complemented
367	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
368	#436	C₂²×C₃₁	1	8	yes	complemented
369	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
370	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
371	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
372	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
373	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
374	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
375	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
376	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
377	C₂×C₃₁	—	4	4	no	—
378	C₂×C₃₁	—	4	4	no	—
379	C₂×C₃₁	—	8	4	no	—
380	C₂×C₃₁	—	8	4	no	—
381	C₂×C₃₁	#3274	1	4	yes	direct product factor
382	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
383	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
385	C₂⁵	—	2	2	no	—
386	C₂×#41	—	2	4	no	—
387	C₂×#41	—	2	8	no	—
388	C₂×#41	—	4	4	no	—
389	C₂×#41	C₂³×C₃₁	1	8	yes	complemented
390	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
391	C₂²×D₄	—	2	8	no	—
392	C₂²×D₄	—	2	2	no	—
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	—	2	8	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	2	no	—
398	C₂²×D₄	—	2	1	no	—
399	C₂²×D₄	—	2	4	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	4	4	no	—
403	C₂²×D₄	—	4	8	no	—
404	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
405	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
406	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
407	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
408	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
409	C₂³×C₄	—	2	2	no	—
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
412	AGL(1,ℤ/8)	—	2	64	no	—
413	C₂×SD₁₆	—	2	8	no	—
414	C₂×SD₁₆	D₄×C₃₁	1	8	yes	complemented
415	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
416	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	complemented
417	C₂×D₈	—	2	8	no	—
418	C₂×D₈	—	2	8	no	—
419	C₂×D₈	—	4	4	no	—
420	C₂×D₈	C₂³×C₃₁	1	8	yes	—
421	C₂×D₈	C₂³×C₃₁	1	8	yes	complemented
422	C₂×D₈	C₂³×C₃₁	1	8	yes	complemented
423	C₂×M₁₆	—	2	8	no	—
424	C₂×M₁₆	C₂³×C₃₁	1	8	yes	complemented
425	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
426	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
428	#127	—	2	8	no	—
429	#127	—	2	2	no	—
430	#127	—	2	2	no	—
431	#127	C₂³×C₃₁	1	4	yes	—
432	#127	C₂³×C₃₁	1	4	yes	complemented
433	#121	—	2	4	no	—
434	#121	—	2	4	no	—
435	#121	—	2	8	no	—
436	#121	—	2	16	no	—
437	#121	C₂³×C₃₁	1	8	yes	—
438	#121	C₂³×C₃₁	1	8	yes	complemented
439	#120	—	2	16	no	—
440	C₄×Q₈	—	2	2	no	—
441	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
442	C₄×D₄	—	2	8	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	D₄×C₃₁	1	4	yes	—
445	C₄×D₄	C₂³×C₃₁	1	4	yes	—
446	C₄×D₄	C₂³×C₃₁	1	4	yes	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	2	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
457	#106	C₂³×C₃₁	1	4	yes	complemented
458	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
459	#103	C₂³×C₃₁	1	4	yes	complemented
460	#102	C₂³×C₃₁	1	4	yes	—
461	#102	C₂³×C₃₁	1	8	yes	complemented
462	#102	C₂³×C₃₁	1	8	yes	complemented
463	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	complemented
464	C₄×C₈	C₂³×C₃₁	1	4	yes	complemented
465	C₃₁	C₂×#3274	1	1	yes	characteristic, direct product factor, Sylow
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	2	2	no	—
469	C₂⁴	—	2	8	no	—
470	C₂⁴	—	4	8	no	—
471	C₂⁴	—	4	8	no	—
472	C₂⁴	—	8	4	no	—
473	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
474	#41	—	2	16	no	—
475	#41	—	4	8	no	—
476	#41	—	4	16	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	complemented
480	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
481	C₂×D₄	—	2	16	no	—
482	C₂×D₄	—	2	8	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	8	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	4	8	no	—
500	C₂×D₄	—	4	16	no	—
501	C₂×D₄	—	4	8	no	—
502	C₂×D₄	—	4	8	no	—
503	C₂×D₄	—	4	32	no	—
504	C₂×D₄	—	4	8	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	—	8	2	no	—
508	C₂×D₄	—	8	2	no	—
509	C₂×D₄	—	8	4	no	—
510	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
511	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
512	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
513	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
514	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	8	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
527	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
530	SD₁₆	—	2	16	no	—
531	SD₁₆	C₂×D₄×C₃₁	1	16	yes	complemented
532	D₈	—	2	16	no	—
533	D₈	—	2	16	no	—
534	D₈	—	4	8	no	—
535	M₁₆	—	2	16	no	—
536	C₂×C₈	—	2	4	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	complemented
539	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
540	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
541	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
546	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
547	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
552	C₄²	—	2	4	no	—
553	C₄²	C₂×D₄×C₃₁	1	2	yes	—
554	C₄²	C₂⁴×C₃₁	1	2	yes	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	4	16	no	—
563	C₂³	—	4	16	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	4	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	4	no	—
570	C₂³	—	4	4	no	—
571	C₂³	—	4	4	no	—
572	C₂³	—	8	8	no	—
573	C₂³	—	8	32	no	—
574	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
575	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
576	Q₈	—	2	4	no	—
577	Q₈	—	2	2	no	—
578	Q₈	C₂²×D₄×C₃₁	1	4	yes	complemented
579	D₄	—	2	4	no	—
580	D₄	—	2	8	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	4	16	no	—
587	D₄	—	4	16	no	—
588	D₄	—	4	16	no	—
589	D₄	—	4	4	no	—
590	D₄	—	4	4	no	—
591	D₄	—	4	8	no	—
592	D₄	—	4	8	no	—
593	D₄	—	8	4	no	—
594	D₄	—	8	4	no	—
595	D₄	—	8	8	no	—
596	D₄	C₂²×D₄×C₃₁	1	4	yes	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	16	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
611	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
612	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
613	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
616	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
617	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
618	C₈	—	2	4	no	—
619	C₈	—	2	2	no	—
620	C₈	C₂²×D₄×C₃₁	1	4	yes	complemented
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	8	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	8	32	no	—
636	C₂²	—	8	8	no	—
637	C₂²	—	8	8	no	—
638	C₂²	D₄²×C₃₁	1	2	yes	—
639	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
640	C₂²	C₃₁×#576	1	2	yes	—
641	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
642	C₄	—	2	4	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	D₄²×C₃₁	1	2	yes	—
648	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
649	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
650	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂	—	4	4	no	—
652	C₂	—	4	4	no	—
653	C₂	—	8	4	no	—
654	C₂	—	8	4	no	—
655	C₂	C₃₁×#3274	1	4	yes	direct product factor
656	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
657	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
658	C₂	C₂×C₃₁×#576	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 ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃₁×#550	C₂	semidirect
3. C₂×D₄²×C₃₁	C₂	semidirect
4. C₃₁×#3274	C₂	direct (N × H)
5. C₂×C₃₁×#493	C₂	semidirect
6. C₂×C₃₁×#469	C₂	semidirect
7. C₂×C₃₁×#460	C₂	semidirect
8. C₂×C₃₁×#459	C₂	semidirect
9. C₂×C₃₁×#449	C₂	semidirect
10. C₂×C₃₁×#447	C₂	semidirect
11. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
12. C₂×C₃₁×#436	C₂	semidirect
13. C₂²×#41×C₃₁	C₂²	semidirect
17. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂²×SD₁₆×C₃₁	C₂²	semidirect
21. C₂²×D₈×C₃₁	C₂²	semidirect
22. C₂²×D₈×C₃₁	C₂²	semidirect
23. C₂²×M₁₆×C₃₁	C₂²	semidirect
25. C₃₁×#550	C₂²	semidirect
27. D₄²×C₃₁	C₂²	semidirect
30. C₂×C₃₁×#127	C₂²	semidirect
34. C₂×C₃₁×#121	C₂²	semidirect
36. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
40. C₃₁×#493	C₂²	semidirect
41. C₃₁×#469	C₂²	semidirect
42. C₃₁×#460	C₂²	semidirect
43. C₃₁×#459	C₂²	semidirect
44. C₃₁×#449	C₂²	semidirect
45. C₃₁×#447	C₂²	semidirect
46. C₄×SD₁₆×C₃₁	C₂²	semidirect
47. C₃₁×#436	C₂²	semidirect
48. C₂×C₃₁×#106	C₂²	semidirect
49. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
50. C₂×C₃₁×#103	C₂²	semidirect
52. C₂×C₃₁×#102	C₂²	semidirect
53. C₂×C₃₁×#102	C₂²	semidirect
54. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
55. C₂×C₄×C₈×C₃₁	C₂²	semidirect
60. C₂×#41×C₃₁	C₂³	semidirect
85. C₂×SD₁₆×C₃₁	D₄	semidirect
87. C₂×SD₁₆×C₃₁	C₂³	semidirect
92. C₂×D₈×C₃₁	C₂³	semidirect
93. C₂×D₈×C₃₁	C₂³	semidirect
95. C₂×M₁₆×C₃₁	C₂³	semidirect
103. C₃₁×#127	C₂³	semidirect
109. C₃₁×#121	C₂³	semidirect
112. C₄×Q₈×C₃₁	C₂³	semidirect
128. C₃₁×#106	C₂³	semidirect
129. C₃₁×C₄⋊C₈	C₂³	semidirect
130. C₃₁×#103	C₂³	semidirect
132. C₃₁×#102	C₂³	semidirect
133. C₃₁×#102	C₂³	semidirect
134. C₃₁×C₂²⋊C₈	C₂³	semidirect
135. C₄×C₈×C₃₁	C₂³	semidirect
149. C₂×Q₈×C₃₁	C₂×D₄	semidirect
201. SD₁₆×C₃₁	C₂×D₄	semidirect
208. C₂×C₈×C₃₁	C₂×D₄	semidirect
225. C₂×#3274	C₃₁	direct (N × H)
249. Q₈×C₃₁	C₂²×D₄	semidirect
281. C₂×C₄×C₃₁	AGL(1,ℤ/8)	semidirect
291. C₈×C₃₁	C₂²×D₄	semidirect
292. C₂²×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
293. C₂×#550	C₂×C₃₁	semidirect
294. C₂×D₄²	C₂×C₃₁	semidirect
295. #3274	C₂×C₃₁	direct (N × H)
296. C₂×#493	C₂×C₃₁	semidirect
297. C₂×#469	C₂×C₃₁	semidirect
298. C₂×#460	C₂×C₃₁	semidirect
299. C₂×#459	C₂×C₃₁	semidirect
300. C₂×#449	C₂×C₃₁	semidirect
301. C₂×#447	C₂×C₃₁	semidirect
302. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
303. C₂×#436	C₂×C₃₁	semidirect
331. C₄×C₃₁	C₂×AGL(1,ℤ/8)	semidirect
334. C₂²×#41	C₂²×C₃₁	semidirect
338. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
340. C₂²×SD₁₆	C₂²×C₃₁	semidirect
342. C₂²×D₈	C₂²×C₃₁	semidirect
343. C₂²×D₈	C₂²×C₃₁	semidirect
344. C₂²×M₁₆	C₂²×C₃₁	semidirect
346. #550	C₂²×C₃₁	semidirect
348. D₄²	C₂²×C₃₁	semidirect
351. C₂×#127	C₂²×C₃₁	semidirect
355. C₂×#121	C₂²×C₃₁	semidirect
357. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
361. #493	C₂²×C₃₁	semidirect
362. #469	C₂²×C₃₁	semidirect
363. #460	C₂²×C₃₁	semidirect
364. #459	C₂²×C₃₁	semidirect
365. #449	C₂²×C₃₁	semidirect
366. #447	C₂²×C₃₁	semidirect
367. C₄×SD₁₆	C₂²×C₃₁	semidirect
368. #436	C₂²×C₃₁	semidirect
369. C₂×#106	C₂²×C₃₁	semidirect
370. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
371. C₂×#103	C₂²×C₃₁	semidirect
373. C₂×#102	C₂²×C₃₁	semidirect
374. C₂×#102	C₂²×C₃₁	semidirect
375. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
376. C₂×C₄×C₈	C₂²×C₃₁	semidirect
381. C₂×C₃₁	#3274	direct (N × H)
389. C₂×#41	C₂³×C₃₁	semidirect
414. C₂×SD₁₆	D₄×C₃₁	semidirect
416. C₂×SD₁₆	C₂³×C₃₁	semidirect
421. C₂×D₈	C₂³×C₃₁	semidirect
422. C₂×D₈	C₂³×C₃₁	semidirect
424. C₂×M₁₆	C₂³×C₃₁	semidirect
432. #127	C₂³×C₃₁	semidirect
438. #121	C₂³×C₃₁	semidirect
441. C₄×Q₈	C₂³×C₃₁	semidirect
457. #106	C₂³×C₃₁	semidirect
458. C₄⋊C₈	C₂³×C₃₁	semidirect
459. #103	C₂³×C₃₁	semidirect
461. #102	C₂³×C₃₁	semidirect
462. #102	C₂³×C₃₁	semidirect
463. C₂²⋊C₈	C₂³×C₃₁	semidirect
464. C₄×C₈	C₂³×C₃₁	semidirect
465. C₃₁	C₂×#3274	direct (N × H)
479. C₂×Q₈	C₂×D₄×C₃₁	semidirect
531. SD₁₆	C₂×D₄×C₃₁	semidirect
538. C₂×C₈	C₂×D₄×C₃₁	semidirect
578. Q₈	C₂²×D₄×C₃₁	semidirect
610. C₂×C₄	C₃₁×AGL(1,ℤ/8)	semidirect
620. C₈	C₂²×D₄×C₃₁	semidirect
648. C₄	C₂×C₃₁×AGL(1,ℤ/8)	semidirect
655. C₂	C₃₁×#3274	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×AGL(1,ℤ/8)	2
C₂×C₃₁×#550	2
C₂×D₄²×C₃₁	2
C₃₁×#3274	2
C₂×C₃₁×#493	2
C₂×C₃₁×#469	2
C₂×C₃₁×#460	2
C₂×C₃₁×#459	2
C₂×C₃₁×#449	2
C₂×C₃₁×#447	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₃₁×#436	2
C₂×#3274	31

Subgroups — C2×C31×#3274 #21517792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3274 #21517792