Subgroups — C₂×C₃₁×#3343 #21517994

Order 7936.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#547	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3343	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₃₁	—	2	1	no	—
18	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#552	—	2	4	no	—
22	C₃₁×#552	C₂²	1	8	yes	complemented
23	C₃₁×#547	—	2	4	no	—
24	C₃₁×#547	C₂²	1	8	yes	—
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#126	—	2	1	no	—
27	C₂×C₃₁×#125	—	2	1	no	—
28	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#123	—	2	1	no	—
30	C₂×C₃₁×#123	—	2	1	no	—
31	C₂×C₃₁×#123	—	2	1	no	—
32	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	—	2	1	no	—
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#501	C₂²	1	8	yes	complemented
46	C₃₁×#484	C₂²	1	8	yes	complemented
47	C₃₁×#483	C₂²	1	8	yes	complemented
48	C₃₁×#482	C₂²	1	8	yes	complemented
49	C₃₁×#480	C₂²	1	8	yes	complemented
50	C₃₁×#478	C₂²	1	8	yes	complemented
51	C₃₁×#477	C₂²	1	8	yes	complemented
52	C₃₁×#468	C₂²	1	8	yes	complemented
53	C₃₁×#465	C₂²	1	8	yes	complemented
54	C₃₁×#440	C₂²	1	8	yes	complemented
55	C₃₁×#435	C₂²	1	8	yes	complemented
56	C₃₁×#428	C₂²	1	8	yes	complemented
57	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
59	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
63	C₂×C₃₁×#107	C₂²	1	8	yes	complemented
64	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
66	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
77	C₂×#41×C₃₁	—	2	8	no	—
78	C₂×#41×C₃₁	—	4	8	no	—
79	C₂²×Q₈×C₃₁	—	2	1	no	—
80	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₃₁	—	2	1	no	—
82	C₂²×D₄×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₃₁	—	2	1	no	—
86	C₂³×C₄×C₃₁	—	2	1	no	—
87	C₂³×C₄×C₃₁	—	2	1	no	—
88	C₂³×C₄×C₃₁	—	2	1	no	—
89	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₃₁	—	2	4	no	—
92	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
93	C₂×M₁₆×C₃₁	—	2	4	no	—
94	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂²×C₈×C₃₁	—	2	4	no	—
96	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
100	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	—	2	2	no	—
102	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
103	C₃₁×#126	—	2	8	no	—
104	C₃₁×#125	—	2	8	no	—
105	C₃₁×#125	—	2	2	no	—
106	C₃₁×#125	C₂³	1	4	yes	—
107	C₃₁×#123	—	2	8	no	—
108	C₃₁×#123	—	2	8	no	—
109	C₃₁×#123	—	2	8	no	—
110	C₃₁×C₂²⋊Q₈	—	2	2	no	—
111	C₃₁×C₂²⋊Q₈	—	2	2	no	—
112	C₃₁×C₂²⋊Q₈	—	2	8	no	—
113	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₃₁×#121	—	2	2	no	—
116	C₃₁×#121	—	2	2	no	—
117	C₃₁×#121	C₂³	1	4	yes	—
118	C₃₁×#121	C₂³	1	4	yes	—
119	C₄×Q₈×C₃₁	—	2	2	no	—
120	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
121	C₄×D₄×C₃₁	—	2	2	no	—
122	C₄×D₄×C₃₁	D₄	1	4	yes	—
123	C₄×D₄×C₃₁	C₂³	1	4	yes	—
124	C₄×D₄×C₃₁	C₂³	1	4	yes	—
125	C₃₁×#117	—	2	2	no	—
126	C₃₁×#117	—	2	8	no	—
127	C₃₁×#117	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
130	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
131	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
133	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
135	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
136	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
137	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
138	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
139	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
140	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₃₁	—	2	1	no	—
159	C₂×C₄²×C₃₁	—	2	1	no	—
160	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
161	C₃₁×#107	C₂³	1	4	yes	—
162	C₃₁×#107	C₂³	1	4	yes	—
163	C₃₁×#107	C₂³	1	4	yes	—
164	C₃₁×#107	C₂³	1	4	yes	—
165	C₃₁×#107	C₂³	1	4	yes	—
166	C₃₁×#107	C₂³	1	4	yes	—
167	C₃₁×#106	C₂³	1	4	yes	—
168	C₃₁×#106	C₂³	1	4	yes	—
169	C₃₁×#106	C₂³	1	4	yes	—
170	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
171	C₃₁×#103	C₂³	1	4	yes	—
172	C₃₁×#103	C₂³	1	4	yes	—
173	C₃₁×#103	C₂³	1	4	yes	—
174	C₃₁×#102	C₂³	1	4	yes	—
175	C₃₁×#102	C₂³	1	4	yes	—
176	C₃₁×#102	C₂³	1	4	yes	—
177	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₃₁×#97	C₂³	1	4	yes	—
180	C₂⁴×C₃₁	—	2	1	no	—
181	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
183	#41×C₃₁	—	4	32	no	—
184	C₂×Q₈×C₃₁	—	2	1	no	—
185	C₂×Q₈×C₃₁	—	2	4	no	—
186	C₂×Q₈×C₃₁	—	2	2	no	—
187	C₂×Q₈×C₃₁	—	2	2	no	—
188	C₂×Q₈×C₃₁	—	4	4	no	—
189	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
190	C₂×D₄×C₃₁	—	2	4	no	—
191	C₂×D₄×C₃₁	—	2	4	no	—
192	C₂×D₄×C₃₁	—	2	4	no	—
193	C₂×D₄×C₃₁	—	2	1	no	—
194	C₂×D₄×C₃₁	—	2	2	no	—
195	C₂×D₄×C₃₁	—	2	2	no	—
196	C₂×D₄×C₃₁	—	4	4	no	—
197	C₂×D₄×C₃₁	—	4	4	no	—
198	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
199	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₃₁	—	2	2	no	—
201	C₂²×C₄×C₃₁	—	2	2	no	—
202	C₂²×C₄×C₃₁	—	2	2	no	—
203	C₂²×C₄×C₃₁	—	2	2	no	—
204	C₂²×C₄×C₃₁	—	2	4	no	—
205	C₂²×C₄×C₃₁	—	2	4	no	—
206	C₂²×C₄×C₃₁	—	2	4	no	—
207	C₂²×C₄×C₃₁	—	2	1	no	—
208	C₂²×C₄×C₃₁	—	2	1	no	—
209	C₂²×C₄×C₃₁	—	2	1	no	—
210	C₂²×C₄×C₃₁	—	2	1	no	—
211	C₂²×C₄×C₃₁	—	2	1	no	—
212	C₂²×C₄×C₃₁	—	2	1	no	—
213	C₂²×C₄×C₃₁	—	2	1	no	—
214	C₂²×C₄×C₃₁	—	2	4	no	—
215	C₂²×C₄×C₃₁	—	4	4	no	—
216	C₂²×C₄×C₃₁	—	4	4	no	—
217	C₂²×C₄×C₃₁	—	4	4	no	—
218	C₂²×C₄×C₃₁	—	4	4	no	—
219	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₃₁	—	2	8	no	—
229	M₁₆×C₃₁	—	2	8	no	—
230	C₂×C₈×C₃₁	—	2	2	no	—
231	C₂×C₈×C₃₁	—	2	2	no	—
232	C₂×C₈×C₃₁	—	2	2	no	—
233	C₂×C₈×C₃₁	—	2	8	no	—
234	C₂×C₈×C₃₁	#41	1	4	yes	complemented
235	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
237	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
238	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₃₁	—	2	1	no	—
240	C₄⋊C₄×C₃₁	—	2	1	no	—
241	C₄⋊C₄×C₃₁	—	2	1	no	—
242	C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
268	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
269	C₄²×C₃₁	—	2	4	no	—
270	C₄²×C₃₁	—	2	4	no	—
271	C₄²×C₃₁	C₂×D₄	1	2	yes	—
272	C₄²×C₃₁	C₂⁴	1	2	yes	—
273	C₂×#3343	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂³×C₃₁	—	2	2	no	—
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	2	no	—
280	C₂³×C₃₁	—	4	2	no	—
281	C₂³×C₃₁	—	4	2	no	—
282	C₂³×C₃₁	—	4	2	no	—
283	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
284	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
285	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
286	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₃₁	—	2	2	no	—
288	Q₈×C₃₁	—	2	2	no	—
289	Q₈×C₃₁	—	4	8	no	—
290	Q₈×C₃₁	—	4	2	no	—
291	D₄×C₃₁	—	2	8	no	—
292	D₄×C₃₁	—	2	2	no	—
293	D₄×C₃₁	—	2	2	no	—
294	D₄×C₃₁	—	4	8	no	—
295	D₄×C₃₁	—	4	8	no	—
296	D₄×C₃₁	—	4	2	no	—
297	C₂×C₄×C₃₁	—	2	2	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	2	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	4	no	—
302	C₂×C₄×C₃₁	—	2	4	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	4	8	no	—
315	C₂×C₄×C₃₁	—	4	8	no	—
316	C₂×C₄×C₃₁	—	4	2	no	—
317	C₂×C₄×C₃₁	—	4	8	no	—
318	C₂×C₄×C₃₁	—	4	2	no	—
319	C₂×C₄×C₃₁	—	4	2	no	—
320	C₂×C₄×C₃₁	—	4	2	no	—
321	C₂×C₄×C₃₁	—	4	2	no	—
322	C₂×C₄×C₃₁	—	4	2	no	—
323	C₂×C₄×C₃₁	—	4	8	no	—
324	C₂×C₄×C₃₁	—	4	2	no	—
325	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
331	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
332	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
333	C₈×C₃₁	—	2	2	no	—
334	C₈×C₃₁	—	2	2	no	—
335	C₈×C₃₁	—	2	2	no	—
336	C₈×C₃₁	C₂×#41	1	4	yes	complemented
337	C₂×#552	C₂×C₃₁	1	1	yes	characteristic, complemented
338	C₂×#547	C₂×C₃₁	1	1	yes	characteristic
339	#3343	C₂×C₃₁	1	16	yes	direct product factor
340	C₂×#501	C₂×C₃₁	1	1	yes	characteristic, complemented
341	C₂×#484	C₂×C₃₁	1	1	yes	characteristic, complemented
342	C₂×#482	C₂×C₃₁	1	1	yes	characteristic, complemented
343	C₂×#483	C₂×C₃₁	1	1	yes	characteristic, complemented
344	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
345	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂×#468	C₂×C₃₁	1	1	yes	characteristic, complemented
348	C₂×#465	C₂×C₃₁	1	1	yes	characteristic, complemented
349	C₂×#440	C₂×C₃₁	1	1	yes	characteristic, complemented
350	C₂×#435	C₂×C₃₁	1	1	yes	characteristic, complemented
351	C₂×#428	C₂×C₃₁	1	1	yes	characteristic, complemented
352	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic, complemented
353	C₂²×C₃₁	—	2	8	no	—
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	2	no	—
356	C₂²×C₃₁	—	2	2	no	—
357	C₂²×C₃₁	—	2	2	no	—
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	4	4	no	—
360	C₂²×C₃₁	—	4	2	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	2	no	—
363	C₂²×C₃₁	—	8	4	no	—
364	C₂²×C₃₁	#547	1	2	yes	—
365	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
366	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
367	C₂²×C₃₁	#578	1	2	yes	—
368	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₃₁	—	2	2	no	—
370	C₄×C₃₁	—	2	2	no	—
371	C₄×C₃₁	—	2	2	no	—
372	C₄×C₃₁	—	2	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	—	4	2	no	—
375	C₄×C₃₁	—	4	2	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	#547	1	2	yes	—
381	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
382	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂²×#41	—	2	1	no	—
384	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
386	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
387	#552	—	2	4	no	—
388	#552	C₂²×C₃₁	1	8	yes	complemented
389	#547	—	2	4	no	—
390	#547	C₂²×C₃₁	1	8	yes	—
391	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
392	C₂×#126	—	2	1	no	—
393	C₂×#125	—	2	1	no	—
394	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×#123	—	2	1	no	—
396	C₂×#123	—	2	1	no	—
397	C₂×#123	—	2	1	no	—
398	C₂×C₂²⋊Q₈	—	2	1	no	—
399	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
406	C₂×#117	—	2	1	no	—
407	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
411	#501	C₂²×C₃₁	1	8	yes	complemented
412	#484	C₂²×C₃₁	1	8	yes	complemented
413	#483	C₂²×C₃₁	1	8	yes	complemented
414	#482	C₂²×C₃₁	1	8	yes	complemented
415	#480	C₂²×C₃₁	1	8	yes	complemented
416	#478	C₂²×C₃₁	1	8	yes	complemented
417	#477	C₂²×C₃₁	1	8	yes	complemented
418	#468	C₂²×C₃₁	1	8	yes	complemented
419	#465	C₂²×C₃₁	1	8	yes	complemented
420	#440	C₂²×C₃₁	1	8	yes	complemented
421	#435	C₂²×C₃₁	1	8	yes	complemented
422	#428	C₂²×C₃₁	1	8	yes	complemented
423	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
424	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
425	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
427	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
428	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
429	C₂×#107	C₂²×C₃₁	1	8	yes	complemented
430	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
433	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
436	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
437	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
439	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
442	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×C₃₁	—	2	4	no	—
444	C₂×C₃₁	—	4	2	no	—
445	C₂×C₃₁	—	8	2	no	—
446	C₂×C₃₁	#3343	1	4	yes	direct product factor
447	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
448	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
449	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
450	C₂×#41	—	2	8	no	—
451	C₂×#41	—	4	8	no	—
452	C₂²×Q₈	—	2	1	no	—
453	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂×SD₁₆	—	2	4	no	—
465	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
466	C₂×M₁₆	—	2	4	no	—
467	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
468	C₂²×C₈	—	2	4	no	—
469	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
471	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
476	#126	—	2	8	no	—
477	#125	—	2	8	no	—
478	#125	—	2	2	no	—
479	#125	C₂³×C₃₁	1	4	yes	—
480	#123	—	2	8	no	—
481	#123	—	2	8	no	—
482	#123	—	2	8	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	8	no	—
486	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
487	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	C₂³×C₃₁	1	4	yes	—
491	#121	C₂³×C₃₁	1	4	yes	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	D₄×C₃₁	1	4	yes	—
496	C₄×D₄	C₂³×C₃₁	1	4	yes	—
497	C₄×D₄	C₂³×C₃₁	1	4	yes	—
498	#117	—	2	2	no	—
499	#117	—	2	8	no	—
500	#117	C₂³×C₃₁	1	4	yes	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
520	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
534	#107	C₂³×C₃₁	1	4	yes	—
535	#107	C₂³×C₃₁	1	4	yes	—
536	#107	C₂³×C₃₁	1	4	yes	—
537	#107	C₂³×C₃₁	1	4	yes	—
538	#107	C₂³×C₃₁	1	4	yes	—
539	#107	C₂³×C₃₁	1	4	yes	—
540	#106	C₂³×C₃₁	1	4	yes	—
541	#106	C₂³×C₃₁	1	4	yes	—
542	#106	C₂³×C₃₁	1	4	yes	—
543	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
544	#103	C₂³×C₃₁	1	4	yes	—
545	#103	C₂³×C₃₁	1	4	yes	—
546	#103	C₂³×C₃₁	1	4	yes	—
547	#102	C₂³×C₃₁	1	4	yes	—
548	#102	C₂³×C₃₁	1	4	yes	—
549	#102	C₂³×C₃₁	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
552	#97	C₂³×C₃₁	1	4	yes	—
553	C₃₁	C₂×#3343	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁴	—	2	1	no	—
555	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
556	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
557	#41	—	4	32	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	4	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	4	4	no	—
563	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
573	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
602	SD₁₆	—	2	8	no	—
603	M₁₆	—	2	8	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	8	no	—
608	C₂×C₈	#41×C₃₁	1	4	yes	complemented
609	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
610	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
611	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
612	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
642	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	C₂×D₄×C₃₁	1	2	yes	—
646	C₄²	C₂⁴×C₃₁	1	2	yes	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
657	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
658	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
659	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	4	8	no	—
663	Q₈	—	4	2	no	—
664	D₄	—	2	8	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	8	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
704	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
705	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	C₂×#41×C₃₁	1	4	yes	complemented
710	C₂²	—	2	8	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	8	4	no	—
721	C₂²	C₃₁×#547	1	2	yes	—
722	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
723	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
724	C₂²	C₃₁×#578	1	2	yes	—
725	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	C₃₁×#547	1	2	yes	—
738	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
739	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
740	C₂	—	2	4	no	—
741	C₂	—	4	2	no	—
742	C₂	—	8	2	no	—
743	C₂	C₃₁×#3343	1	4	yes	direct product factor
744	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
745	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
746	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#547	C₂
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. C₂×C₃₁×#552	C₂	semidirect
3. C₃₁×#3343	C₂	direct (N × H)
4. C₂×C₃₁×#501	C₂	semidirect
5. C₂×C₃₁×#484	C₂	semidirect
6. C₂×C₃₁×#482	C₂	semidirect
7. C₂×C₃₁×#483	C₂	semidirect
8. C₂×C₃₁×#480	C₂	semidirect
9. C₂×C₃₁×#477	C₂	semidirect
10. C₂×C₃₁×#478	C₂	semidirect
11. C₂×C₃₁×#468	C₂	semidirect
12. C₂×C₃₁×#465	C₂	semidirect
13. C₂×C₃₁×#440	C₂	semidirect
14. C₂×C₃₁×#435	C₂	semidirect
15. C₂×C₃₁×#428	C₂	semidirect
16. C₂²×C₃₁×#107	C₂	semidirect
22. C₃₁×#552	C₂²	semidirect
45. C₃₁×#501	C₂²	semidirect
46. C₃₁×#484	C₂²	semidirect
47. C₃₁×#483	C₂²	semidirect
48. C₃₁×#482	C₂²	semidirect
49. C₃₁×#480	C₂²	semidirect
50. C₃₁×#478	C₂²	semidirect
51. C₃₁×#477	C₂²	semidirect
52. C₃₁×#468	C₂²	semidirect
53. C₃₁×#465	C₂²	semidirect
54. C₃₁×#440	C₂²	semidirect
55. C₃₁×#435	C₂²	semidirect
56. C₃₁×#428	C₂²	semidirect
63. C₂×C₃₁×#107	C₂²	semidirect
234. C₂×C₈×C₃₁	#41	semidirect
273. C₂×#3343	C₃₁	direct (N × H)
336. C₈×C₃₁	C₂×#41	semidirect
337. C₂×#552	C₂×C₃₁	semidirect
339. #3343	C₂×C₃₁	direct (N × H)
340. C₂×#501	C₂×C₃₁	semidirect
341. C₂×#484	C₂×C₃₁	semidirect
342. C₂×#482	C₂×C₃₁	semidirect
343. C₂×#483	C₂×C₃₁	semidirect
344. C₂×#480	C₂×C₃₁	semidirect
345. C₂×#477	C₂×C₃₁	semidirect
346. C₂×#478	C₂×C₃₁	semidirect
347. C₂×#468	C₂×C₃₁	semidirect
348. C₂×#465	C₂×C₃₁	semidirect
349. C₂×#440	C₂×C₃₁	semidirect
350. C₂×#435	C₂×C₃₁	semidirect
351. C₂×#428	C₂×C₃₁	semidirect
352. C₂²×#107	C₂×C₃₁	semidirect
388. #552	C₂²×C₃₁	semidirect
411. #501	C₂²×C₃₁	semidirect
412. #484	C₂²×C₃₁	semidirect
413. #483	C₂²×C₃₁	semidirect
414. #482	C₂²×C₃₁	semidirect
415. #480	C₂²×C₃₁	semidirect
416. #478	C₂²×C₃₁	semidirect
417. #477	C₂²×C₃₁	semidirect
418. #468	C₂²×C₃₁	semidirect
419. #465	C₂²×C₃₁	semidirect
420. #440	C₂²×C₃₁	semidirect
421. #435	C₂²×C₃₁	semidirect
422. #428	C₂²×C₃₁	semidirect
429. C₂×#107	C₂²×C₃₁	semidirect
446. C₂×C₃₁	#3343	direct (N × H)
553. C₃₁	C₂×#3343	direct (N × H)
608. C₂×C₈	#41×C₃₁	semidirect
709. C₈	C₂×#41×C₃₁	semidirect
743. C₂	C₃₁×#3343	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×#552	2
C₂×C₃₁×#547	2
C₃₁×#3343	2
C₂×C₃₁×#501	2
C₂×C₃₁×#484	2
C₂×C₃₁×#482	2
C₂×C₃₁×#483	2
C₂×C₃₁×#480	2
C₂×C₃₁×#477	2
C₂×C₃₁×#478	2
C₂×C₃₁×#468	2
C₂×C₃₁×#465	2
C₂×C₃₁×#440	2
C₂×C₃₁×#435	2
C₂×C₃₁×#428	2
C₂²×C₃₁×#107	2
C₂×#3343	31

Subgroups — C2×C31×#3343 #21517994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3343 #21517994