Subgroups — C₂×C₃₁×#3125 #21517313

Order 7936.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3125	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#449	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#542	—	2	4	no	—
23	C₃₁×#542	C₂²	1	8	yes	complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#126	—	2	1	no	—
26	C₂×C₃₁×#124	—	2	1	no	—
27	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#123	—	2	1	no	—
29	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₃₁×#520	—	2	4	no	—
33	C₃₁×#520	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₃₁	—	2	1	no	—
38	C₂×C₄×D₄×C₃₁	—	2	1	no	—
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#117	—	2	1	no	—
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#483	C₂²	1	8	yes	complemented
47	C₃₁×#481	C₂²	1	8	yes	complemented
48	C₃₁×#476	C₂²	1	8	yes	complemented
49	C₃₁×#475	C₂²	1	8	yes	complemented
50	C₃₁×#464	C₂²	1	8	yes	complemented
51	C₃₁×#463	C₂²	1	8	yes	complemented
52	C₃₁×#452	C₂²	1	8	yes	complemented
53	C₃₁×#449	C₂²	1	8	yes	—
54	C₃₁×#442	C₂²	1	8	yes	complemented
55	C₃₁×#441	C₂²	1	8	yes	complemented
56	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
57	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
58	C₃₁×#433	C₂²	1	8	yes	complemented
59	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
63	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
66	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
68	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
77	C₂×#41×C₃₁	—	2	4	no	—
78	C₂×#41×C₃₁	—	2	4	no	—
79	C₂×#41×C₃₁	—	2	2	no	—
80	C₂×#41×C₃₁	C₂³	1	4	yes	—
81	C₂²×Q₈×C₃₁	—	2	1	no	—
82	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₃₁	—	2	1	no	—
85	C₂²×D₄×C₃₁	—	2	1	no	—
86	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	—	2	1	no	—
89	C₂³×C₄×C₃₁	—	2	1	no	—
90	C₂³×C₄×C₃₁	—	2	1	no	—
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₁₆×C₃₁	—	2	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₃₁	—	2	4	no	—
97	C₂×SD₁₆×C₃₁	—	2	4	no	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×D₈×C₃₁	—	2	4	no	—
101	C₂×D₈×C₃₁	C₂³	1	4	yes	—
102	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
107	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
108	C₃₁×#126	—	2	8	no	—
109	C₃₁×#124	—	2	8	no	—
110	C₃₁×#124	—	2	2	no	—
111	C₃₁×#124	C₂³	1	4	yes	—
112	C₃₁×#123	—	2	8	no	—
113	C₃₁×C₂²⋊Q₈	—	2	2	no	—
114	C₃₁×C₂²⋊Q₈	—	2	8	no	—
115	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×#121	—	2	2	no	—
117	C₃₁×#121	C₂³	1	4	yes	—
118	C₄×Q₈×C₃₁	—	2	2	no	—
119	C₄×Q₈×C₃₁	—	2	2	no	—
120	C₄×Q₈×C₃₁	—	2	2	no	—
121	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
122	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
123	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
124	C₄×D₄×C₃₁	—	2	8	no	—
125	C₄×D₄×C₃₁	—	2	8	no	—
126	C₄×D₄×C₃₁	—	2	2	no	—
127	C₄×D₄×C₃₁	—	2	2	no	—
128	C₄×D₄×C₃₁	—	2	2	no	—
129	C₄×D₄×C₃₁	C₂³	1	4	yes	—
130	C₄×D₄×C₃₁	C₂³	1	4	yes	—
131	C₄×D₄×C₃₁	C₂³	1	4	yes	—
132	C₃₁×#117	—	2	8	no	—
133	C₃₁×#117	D₄	1	4	yes	—
134	C₃₁×#117	C₂³	1	4	yes	—
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	2	no	—
139	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
140	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
141	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
142	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
143	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	D₄	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	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₃₁	—	2	1	no	—
160	C₂×C₄²×C₃₁	—	2	1	no	—
161	C₂×C₄²×C₃₁	—	2	1	no	—
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₃₁×#106	C₂³	1	4	yes	—
165	C₃₁×#106	C₂³	1	4	yes	—
166	C₃₁×#106	C₂³	1	4	yes	—
167	C₃₁×#106	C₂³	1	4	yes	—
168	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
169	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
170	C₃₁×#103	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×#102	C₂³	1	4	yes	—
178	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₃₁×#97	C₂³	1	4	yes	—
181	C₄×C₈×C₃₁	C₂³	1	4	yes	—
182	C₂⁴×C₃₁	—	2	1	no	—
183	C₂⁴×C₃₁	—	2	1	no	—
184	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
185	#41×C₃₁	—	2	16	no	—
186	#41×C₃₁	—	2	8	no	—
187	#41×C₃₁	—	2	8	no	—
188	C₂×Q₈×C₃₁	—	2	1	no	—
189	C₂×Q₈×C₃₁	—	2	1	no	—
190	C₂×Q₈×C₃₁	—	2	4	no	—
191	C₂×Q₈×C₃₁	—	2	2	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	8	2	no	—
195	C₂×Q₈×C₃₁	#41	1	4	yes	—
196	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
198	C₂×D₄×C₃₁	—	2	8	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	1	no	—
202	C₂×D₄×C₃₁	—	2	1	no	—
203	C₂×D₄×C₃₁	—	2	2	no	—
204	C₂×D₄×C₃₁	—	2	2	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	8	2	no	—
207	C₂×D₄×C₃₁	#41	1	4	yes	—
208	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₁	—	2	8	no	—
211	C₂²×C₄×C₃₁	—	2	1	no	—
212	C₂²×C₄×C₃₁	—	2	4	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	1	no	—
216	C₂²×C₄×C₃₁	—	2	1	no	—
217	C₂²×C₄×C₃₁	—	2	1	no	—
218	C₂²×C₄×C₃₁	—	2	1	no	—
219	C₂²×C₄×C₃₁	—	2	1	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	4	no	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	—	8	2	no	—
225	C₂²×C₄×C₃₁	—	8	2	no	—
226	C₂²×C₄×C₃₁	—	8	2	no	—
227	C₂²×C₄×C₃₁	—	8	2	no	—
228	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₃₁	—	2	8	no	—
237	SD₁₆×C₃₁	—	2	8	no	—
238	SD₁₆×C₃₁	—	2	8	no	—
239	D₈×C₃₁	—	2	8	no	—
240	C₂×C₈×C₃₁	—	2	2	no	—
241	C₂×C₈×C₃₁	—	2	2	no	—
242	C₂×C₈×C₃₁	—	2	2	no	—
243	C₂×C₈×C₃₁	—	2	2	no	—
244	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
252	C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
273	C₄²×C₃₁	—	2	4	no	—
274	C₄²×C₃₁	—	2	4	no	—
275	C₄²×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	C₂×D₄	1	2	yes	—
277	C₄²×C₃₁	C₂×D₄	1	2	yes	—
278	C₄²×C₃₁	C₂⁴	1	2	yes	—
279	C₄²×C₃₁	C₂⁴	1	2	yes	—
280	C₂×#3125	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂³×C₃₁	—	2	2	no	—
282	C₂³×C₃₁	—	2	4	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	2	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	4	2	no	—
288	C₂³×C₃₁	—	4	2	no	—
289	C₂³×C₃₁	—	4	2	no	—
290	C₂³×C₃₁	—	4	2	no	—
291	C₂³×C₃₁	—	4	2	no	—
292	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
293	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₃₁	—	2	4	no	—
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	2	2	no	—
297	Q₈×C₃₁	—	2	2	no	—
298	Q₈×C₃₁	—	4	2	no	—
299	Q₈×C₃₁	—	8	4	no	—
300	Q₈×C₃₁	C₂×#41	1	4	yes	—
301	D₄×C₃₁	—	2	16	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	2	2	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	8	4	no	—
308	D₄×C₃₁	C₂×#41	1	4	yes	—
309	C₂×C₄×C₃₁	—	2	16	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	4	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	4	2	no	—
326	C₂×C₄×C₃₁	—	4	2	no	—
327	C₂×C₄×C₃₁	—	4	2	no	—
328	C₂×C₄×C₃₁	—	4	2	no	—
329	C₂×C₄×C₃₁	—	4	2	no	—
330	C₂×C₄×C₃₁	—	8	4	no	—
331	C₂×C₄×C₃₁	—	8	4	no	—
332	C₂×C₄×C₃₁	—	8	4	no	—
333	C₂×C₄×C₃₁	—	8	4	no	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
341	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
342	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
343	C₈×C₃₁	—	2	2	no	—
344	C₈×C₃₁	—	2	2	no	—
345	C₈×C₃₁	—	2	2	no	—
346	C₈×C₃₁	—	2	2	no	—
347	C₂×#542	C₂×C₃₁	1	1	yes	characteristic, complemented
348	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#3125	C₂×C₃₁	1	16	yes	direct product factor
350	C₂×#481	C₂×C₃₁	1	1	yes	characteristic, complemented
351	C₂×#483	C₂×C₃₁	1	1	yes	characteristic, complemented
352	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
353	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
354	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
355	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂×#452	C₂×C₃₁	1	1	yes	characteristic, complemented
357	C₂×#449	C₂×C₃₁	1	1	yes	characteristic
358	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂×#441	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂×#433	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	2	2	no	—
367	C₂²×C₃₁	—	4	4	no	—
368	C₂²×C₃₁	—	4	8	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	8	4	no	—
375	C₂²×C₃₁	#525	1	2	yes	—
376	C₂²×C₃₁	#577	1	2	yes	—
377	C₂²×C₃₁	#577	1	2	yes	—
378	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₃₁	—	2	2	no	—
380	C₄×C₃₁	—	2	4	no	—
381	C₄×C₃₁	—	2	2	no	—
382	C₄×C₃₁	—	2	2	no	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	2	no	—
385	C₄×C₃₁	—	4	2	no	—
386	C₄×C₃₁	—	4	2	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	#525	1	2	yes	—
391	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
392	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
393	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
394	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
395	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
396	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
397	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
398	#542	—	2	4	no	—
399	#542	C₂²×C₃₁	1	8	yes	complemented
400	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×#126	—	2	1	no	—
402	C₂×#124	—	2	1	no	—
403	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×#123	—	2	1	no	—
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
407	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
408	#520	—	2	4	no	—
409	#520	C₂²×C₃₁	1	8	yes	complemented
410	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
413	C₂×C₄×D₄	—	2	1	no	—
414	C₂×C₄×D₄	—	2	1	no	—
415	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
418	C₂×#117	—	2	1	no	—
419	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	—	2	1	no	—
421	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
422	#483	C₂²×C₃₁	1	8	yes	complemented
423	#481	C₂²×C₃₁	1	8	yes	complemented
424	#476	C₂²×C₃₁	1	8	yes	complemented
425	#475	C₂²×C₃₁	1	8	yes	complemented
426	#464	C₂²×C₃₁	1	8	yes	complemented
427	#463	C₂²×C₃₁	1	8	yes	complemented
428	#452	C₂²×C₃₁	1	8	yes	complemented
429	#449	C₂²×C₃₁	1	8	yes	—
430	#442	C₂²×C₃₁	1	8	yes	complemented
431	#441	C₂²×C₃₁	1	8	yes	complemented
432	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
433	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
434	#433	C₂²×C₃₁	1	8	yes	complemented
435	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
436	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
437	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
439	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
440	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
442	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
444	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
445	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
446	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×C₃₁	—	4	2	no	—
454	C₂×C₃₁	—	4	4	no	—
455	C₂×C₃₁	—	8	2	no	—
456	C₂×C₃₁	#3125	1	4	yes	direct product factor
457	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
458	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
459	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
460	C₂×#41	—	2	4	no	—
461	C₂×#41	—	2	4	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	C₂³×C₃₁	1	4	yes	—
464	C₂²×Q₈	—	2	1	no	—
465	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×Q₁₆	—	2	4	no	—
478	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
479	C₂×SD₁₆	—	2	4	no	—
480	C₂×SD₁₆	—	2	4	no	—
481	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
482	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
483	C₂×D₈	—	2	4	no	—
484	C₂×D₈	C₂³×C₃₁	1	4	yes	—
485	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
491	#126	—	2	8	no	—
492	#124	—	2	8	no	—
493	#124	—	2	2	no	—
494	#124	C₂³×C₃₁	1	4	yes	—
495	#123	—	2	8	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	8	no	—
498	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	#121	—	2	2	no	—
500	#121	C₂³×C₃₁	1	4	yes	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
505	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
506	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	C₂³×C₃₁	1	4	yes	—
513	C₄×D₄	C₂³×C₃₁	1	4	yes	—
514	C₄×D₄	C₂³×C₃₁	1	4	yes	—
515	#117	—	2	8	no	—
516	#117	D₄×C₃₁	1	4	yes	—
517	#117	C₂³×C₃₁	1	4	yes	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	8	no	—
526	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
542	C₂×C₄²	—	2	1	no	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
547	#106	C₂³×C₃₁	1	4	yes	—
548	#106	C₂³×C₃₁	1	4	yes	—
549	#106	C₂³×C₃₁	1	4	yes	—
550	#106	C₂³×C₃₁	1	4	yes	—
551	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
552	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
553	#103	C₂³×C₃₁	1	4	yes	—
554	#103	C₂³×C₃₁	1	4	yes	—
555	#103	C₂³×C₃₁	1	4	yes	—
556	#103	C₂³×C₃₁	1	4	yes	—
557	#102	C₂³×C₃₁	1	4	yes	—
558	#102	C₂³×C₃₁	1	4	yes	—
559	#102	C₂³×C₃₁	1	4	yes	—
560	#102	C₂³×C₃₁	1	4	yes	—
561	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
563	#97	C₂³×C₃₁	1	4	yes	—
564	C₄×C₈	C₂³×C₃₁	1	4	yes	—
565	C₃₁	C₂×#3125	1	1	yes	characteristic, direct product factor, Sylow
566	C₂⁴	—	2	1	no	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
569	#41	—	2	16	no	—
570	#41	—	2	8	no	—
571	#41	—	2	8	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	8	2	no	—
579	C₂×Q₈	#41×C₃₁	1	4	yes	—
580	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
581	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	8	2	no	—
591	C₂×D₄	#41×C₃₁	1	4	yes	—
592	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
593	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	8	2	no	—
609	C₂²×C₄	—	8	2	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	—	8	2	no	—
612	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
620	Q₁₆	—	2	8	no	—
621	SD₁₆	—	2	8	no	—
622	SD₁₆	—	2	8	no	—
623	D₈	—	2	8	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
629	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
630	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
631	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
643	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
644	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
656	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₃₁	1	2	yes	—
661	C₄²	C₂×D₄×C₃₁	1	2	yes	—
662	C₄²	C₂⁴×C₃₁	1	2	yes	—
663	C₄²	C₂⁴×C₃₁	1	2	yes	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
676	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
677	Q₈	—	2	4	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	2	no	—
682	Q₈	—	8	4	no	—
683	Q₈	C₂×#41×C₃₁	1	4	yes	—
684	D₄	—	2	16	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	8	4	no	—
691	D₄	C₂×#41×C₃₁	1	4	yes	—
692	C₂×C₄	—	2	16	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
723	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
724	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
725	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₈	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	8	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	4	no	—
742	C₂²	C₃₁×#525	1	2	yes	—
743	C₂²	C₃₁×#577	1	2	yes	—
744	C₂²	C₃₁×#577	1	2	yes	—
745	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	C₃₁×#525	1	2	yes	—
758	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
759	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
760	C₂	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₃₁×#3125	1	4	yes	direct product factor
764	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
765	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
766	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#542	C₂	semidirect
2. C₂×C₃₁×#520	C₂	semidirect
3. C₃₁×#3125	C₂	direct (N × H)
4. C₂×C₃₁×#481	C₂	semidirect
5. C₂×C₃₁×#483	C₂	semidirect
6. C₂×C₃₁×#475	C₂	semidirect
7. C₂×C₃₁×#476	C₂	semidirect
8. C₂×C₃₁×#464	C₂	semidirect
9. C₂×C₃₁×#463	C₂	semidirect
10. C₂×C₃₁×#452	C₂	semidirect
12. C₂×C₃₁×#442	C₂	semidirect
13. C₂×C₃₁×#441	C₂	semidirect
14. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
15. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
16. C₂×C₃₁×#433	C₂	semidirect
23. C₃₁×#542	C₂²	semidirect
33. C₃₁×#520	C₂²	semidirect
46. C₃₁×#483	C₂²	semidirect
47. C₃₁×#481	C₂²	semidirect
48. C₃₁×#476	C₂²	semidirect
49. C₃₁×#475	C₂²	semidirect
50. C₃₁×#464	C₂²	semidirect
51. C₃₁×#463	C₂²	semidirect
52. C₃₁×#452	C₂²	semidirect
54. C₃₁×#442	C₂²	semidirect
55. C₃₁×#441	C₂²	semidirect
56. C₄×SD₁₆×C₃₁	C₂²	semidirect
57. C₄×SD₁₆×C₃₁	C₂²	semidirect
58. C₃₁×#433	C₂²	semidirect
280. C₂×#3125	C₃₁	direct (N × H)
347. C₂×#542	C₂×C₃₁	semidirect
348. C₂×#520	C₂×C₃₁	semidirect
349. #3125	C₂×C₃₁	direct (N × H)
350. C₂×#481	C₂×C₃₁	semidirect
351. C₂×#483	C₂×C₃₁	semidirect
352. C₂×#475	C₂×C₃₁	semidirect
353. C₂×#476	C₂×C₃₁	semidirect
354. C₂×#464	C₂×C₃₁	semidirect
355. C₂×#463	C₂×C₃₁	semidirect
356. C₂×#452	C₂×C₃₁	semidirect
358. C₂×#442	C₂×C₃₁	semidirect
359. C₂×#441	C₂×C₃₁	semidirect
360. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
361. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
362. C₂×#433	C₂×C₃₁	semidirect
399. #542	C₂²×C₃₁	semidirect
409. #520	C₂²×C₃₁	semidirect
422. #483	C₂²×C₃₁	semidirect
423. #481	C₂²×C₃₁	semidirect
424. #476	C₂²×C₃₁	semidirect
425. #475	C₂²×C₃₁	semidirect
426. #464	C₂²×C₃₁	semidirect
427. #463	C₂²×C₃₁	semidirect
428. #452	C₂²×C₃₁	semidirect
430. #442	C₂²×C₃₁	semidirect
431. #441	C₂²×C₃₁	semidirect
432. C₄×SD₁₆	C₂²×C₃₁	semidirect
433. C₄×SD₁₆	C₂²×C₃₁	semidirect
434. #433	C₂²×C₃₁	semidirect
456. C₂×C₃₁	#3125	direct (N × H)
565. C₃₁	C₂×#3125	direct (N × H)
763. C₂	C₃₁×#3125	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×#542	2
C₂×C₃₁×#520	2
C₃₁×#3125	2
C₂×C₃₁×#481	2
C₂×C₃₁×#483	2
C₂×C₃₁×#475	2
C₂×C₃₁×#476	2
C₂×C₃₁×#464	2
C₂×C₃₁×#463	2
C₂×C₃₁×#452	2
C₂×C₃₁×#449	2
C₂×C₃₁×#442	2
C₂×C₃₁×#441	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₃₁×#433	2
C₂×#3125	31

Subgroups — C2×C31×#3125 #21517313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3125 #21517313