Subgroups — C₂×C₃₁×#3564 #21519493

Order 7936.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3564	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#541	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#539	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#538	C₂	1	1	yes	maximal, characteristic
18	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#563	C₂²	1	32	yes	complemented
22	C₃₁×#563	C₂²	1	32	yes	complemented
23	C₃₁×#556	C₂²	1	32	yes	complemented
24	C₃₁×#554	C₂²	1	32	yes	complemented
25	C₃₁×#552	C₂²	1	32	yes	complemented
26	C₃₁×#552	C₂²	1	32	yes	complemented
27	C₃₁×#551	C₂²	1	32	yes	complemented
28	C₃₁×#551	C₂²	1	32	yes	complemented
29	C₃₁×#544	C₂²	1	16	yes	complemented
30	C₃₁×#543	C₂²	1	16	yes	complemented
31	C₃₁×#542	C₂²	1	32	yes	complemented
32	C₃₁×#541	C₂²	1	32	yes	complemented
33	C₃₁×#541	C₂²	1	32	yes	complemented
34	C₃₁×#539	C₂²	1	16	yes	complemented
35	C₃₁×#539	C₂²	1	32	yes	complemented
36	C₃₁×#538	C₂²	1	16	yes	—
37	C₃₁×#533	C₂²	1	16	yes	complemented
38	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
43	C₃₁×#529	C₂²	1	16	yes	complemented
44	C₂×C₃₁×#126	C₂²	1	2	yes	—
45	C₂×C₃₁×#126	C₂²	1	2	yes	—
46	C₂×C₃₁×#126	C₂²	1	2	yes	—
47	C₂×C₃₁×#126	C₂²	1	2	yes	—
48	C₂×C₃₁×#126	C₂²	1	2	yes	—
49	C₂×C₃₁×#126	C₂²	1	2	yes	—
50	C₂×C₃₁×#126	C₂²	1	2	yes	—
51	C₂×C₃₁×#126	C₂²	1	2	yes	—
52	C₂×C₃₁×#126	C₂²	1	2	yes	—
53	C₂×C₃₁×#126	C₂²	1	16	yes	complemented
54	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
55	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
58	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
60	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
61	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
62	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
63	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
64	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
65	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
66	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
67	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
68	C₂×C₃₁×#124	C₂²	1	2	yes	—
69	C₂×C₃₁×#124	C₂²	1	2	yes	—
70	C₂×C₃₁×#124	C₂²	1	2	yes	—
71	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃₁×#123	C₂²	1	2	yes	—
73	C₂×C₃₁×#123	C₂²	1	2	yes	—
74	C₂×C₃₁×#123	C₂²	1	2	yes	—
75	C₂×C₃₁×#123	C₂²	1	2	yes	—
76	C₂×C₃₁×#123	C₂²	1	2	yes	—
77	C₂×C₃₁×#123	C₂²	1	2	yes	—
78	C₂×C₃₁×#123	C₂²	1	2	yes	—
79	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
80	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
81	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
83	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
84	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
85	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
86	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
87	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
88	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
89	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
90	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
91	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
92	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
94	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
95	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
96	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
97	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
98	C₂×C₃₁×#121	C₂²	1	2	yes	—
99	C₂×C₃₁×#120	C₂²	1	2	yes	—
100	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
102	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
105	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
107	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
108	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
109	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
110	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
111	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₃₁×#117	C₂²	1	2	yes	—
113	C₂×C₃₁×#117	C₂²	1	2	yes	—
114	C₂×C₃₁×#117	C₂²	1	2	yes	—
115	C₂×C₃₁×#117	C₂²	1	2	yes	—
116	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
117	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
118	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
120	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
121	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
126	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
127	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
130	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
132	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
148	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
150	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
151	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
152	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
153	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
154	C₃₁×#126	C₂³	1	16	yes	—
155	C₃₁×#126	C₂³	1	16	yes	—
156	C₃₁×#126	C₂³	1	16	yes	—
157	C₃₁×#126	C₂³	1	16	yes	—
158	C₃₁×#126	C₂³	1	16	yes	—
159	C₃₁×#126	C₂³	1	16	yes	—
160	C₃₁×#126	C₂³	1	16	yes	—
161	C₃₁×#126	C₂³	1	16	yes	—
162	C₃₁×#126	C₂³	1	16	yes	—
163	C₃₁×#126	C₂³	1	16	yes	complemented
164	C₃₁×#126	C₂³	1	16	yes	complemented
165	C₃₁×#126	C₂³	1	16	yes	complemented
166	C₃₁×#126	C₂³	1	16	yes	complemented
167	C₃₁×#125	C₂³	1	8	yes	complemented
168	C₃₁×#125	C₂³	1	16	yes	complemented
169	C₃₁×#125	C₂³	1	16	yes	complemented
170	C₃₁×#125	C₂³	1	16	yes	complemented
171	C₃₁×#125	C₂³	1	16	yes	complemented
172	C₃₁×#125	C₂³	1	16	yes	complemented
173	C₃₁×#125	C₂³	1	16	yes	complemented
174	C₃₁×#125	C₂³	1	16	yes	complemented
175	C₃₁×#125	C₂³	1	16	yes	complemented
176	C₃₁×#125	C₂³	1	16	yes	complemented
177	C₃₁×#124	C₂³	1	16	yes	—
178	C₃₁×#124	C₂³	1	16	yes	—
179	C₃₁×#124	C₂³	1	16	yes	—
180	C₃₁×#124	C₂³	1	8	yes	complemented
181	C₃₁×#123	C₂³	1	16	yes	—
182	C₃₁×#123	C₂³	1	16	yes	—
183	C₃₁×#123	C₂³	1	16	yes	—
184	C₃₁×#123	C₂³	1	16	yes	—
185	C₃₁×#123	C₂³	1	16	yes	—
186	C₃₁×#123	C₂³	1	16	yes	—
187	C₃₁×#123	C₂³	1	16	yes	—
188	C₃₁×#123	C₂³	1	16	yes	complemented
189	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
202	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
203	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
204	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
206	C₃₁×#121	C₂³	1	8	yes	—
207	C₃₁×#121	C₂³	1	16	yes	—
208	C₃₁×#120	C₂³	1	16	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
210	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
211	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
212	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
213	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
214	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
215	C₄×D₄×C₃₁	C₂³	1	16	yes	—
216	C₄×D₄×C₃₁	C₂³	1	16	yes	—
217	C₄×D₄×C₃₁	C₂³	1	16	yes	—
218	C₄×D₄×C₃₁	C₂³	1	16	yes	—
219	C₄×D₄×C₃₁	C₂³	1	16	yes	—
220	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
221	C₃₁×#117	C₂³	1	16	yes	—
222	C₃₁×#117	C₂³	1	16	yes	—
223	C₃₁×#117	C₂³	1	16	yes	—
224	C₃₁×#117	C₂³	1	16	yes	—
225	C₃₁×#117	C₂³	1	16	yes	complemented
226	C₃₁×#117	C₂³	1	16	yes	complemented
227	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
241	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
264	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
265	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
266	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
276	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
277	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
278	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
289	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
294	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
295	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
296	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
297	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
298	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
299	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
300	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
301	C₂⁴×C₃₁	—	2	4	no	—
302	C₂⁴×C₃₁	—	4	2	no	—
303	C₂⁴×C₃₁	—	4	2	no	—
304	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
305	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
306	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
308	C₂×Q₈×C₃₁	—	4	2	no	—
309	C₂×Q₈×C₃₁	—	4	4	no	—
310	C₂×Q₈×C₃₁	—	4	4	no	—
311	C₂×Q₈×C₃₁	—	4	2	no	—
312	C₂×Q₈×C₃₁	—	4	4	no	—
313	C₂×Q₈×C₃₁	—	4	2	no	—
314	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
315	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
316	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
318	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
319	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
320	C₂×D₄×C₃₁	—	2	8	no	—
321	C₂×D₄×C₃₁	—	4	4	no	—
322	C₂×D₄×C₃₁	—	4	2	no	—
323	C₂×D₄×C₃₁	—	4	4	no	—
324	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
325	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
326	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
327	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₃₁	—	2	4	no	—
329	C₂²×C₄×C₃₁	—	2	4	no	—
330	C₂²×C₄×C₃₁	—	4	4	no	—
331	C₂²×C₄×C₃₁	—	4	2	no	—
332	C₂²×C₄×C₃₁	—	4	2	no	—
333	C₂²×C₄×C₃₁	—	4	2	no	—
334	C₂²×C₄×C₃₁	—	4	4	no	—
335	C₂²×C₄×C₃₁	—	4	4	no	—
336	C₂²×C₄×C₃₁	—	4	4	no	—
337	C₂²×C₄×C₃₁	—	4	4	no	—
338	C₂²×C₄×C₃₁	—	4	2	no	—
339	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
341	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
365	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
372	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
373	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
379	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
381	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
382	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
384	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
385	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
389	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
390	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
391	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
393	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
394	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
395	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
397	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
399	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
403	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
404	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
409	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
411	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
412	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
418	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
419	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
420	C₄²×C₃₁	C₂⁴	1	4	yes	—
421	C₄²×C₃₁	C₂⁴	1	4	yes	—
422	C₄²×C₃₁	C₂⁴	1	4	yes	—
423	C₄²×C₃₁	C₂⁴	1	4	yes	—
424	C₄²×C₃₁	C₂⁴	1	8	yes	—
425	C₄²×C₃₁	C₂⁴	1	8	yes	—
426	C₄²×C₃₁	C₂⁴	1	8	yes	—
427	C₄²×C₃₁	C₂⁴	1	8	yes	—
428	C₄²×C₃₁	C₂⁴	1	8	yes	—
429	C₄²×C₃₁	C₂⁴	1	8	yes	—
430	C₄²×C₃₁	C₂⁴	1	8	yes	—
431	C₂×#3564	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂³×C₃₁	—	2	2	no	—
433	C₂³×C₃₁	—	2	2	no	—
434	C₂³×C₃₁	—	2	4	no	—
435	C₂³×C₃₁	—	2	4	no	—
436	C₂³×C₃₁	—	2	4	no	—
437	C₂³×C₃₁	—	2	4	no	—
438	C₂³×C₃₁	—	2	4	no	—
439	C₂³×C₃₁	—	2	4	no	—
440	C₂³×C₃₁	—	2	8	no	—
441	C₂³×C₃₁	—	4	4	no	—
442	C₂³×C₃₁	—	4	4	no	—
443	C₂³×C₃₁	—	8	8	no	—
444	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
445	C₂³×C₃₁	C₂⁵	1	4	yes	—
446	C₂³×C₃₁	C₂⁵	1	4	yes	—
447	C₂³×C₃₁	C₂⁵	1	2	yes	—
448	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
449	Q₈×C₃₁	—	4	4	no	—
450	Q₈×C₃₁	—	4	8	no	—
451	Q₈×C₃₁	—	4	8	no	—
452	Q₈×C₃₁	—	4	4	no	—
453	Q₈×C₃₁	—	4	8	no	—
454	Q₈×C₃₁	—	4	4	no	—
455	D₄×C₃₁	—	2	16	no	—
456	D₄×C₃₁	—	4	8	no	—
457	D₄×C₃₁	—	4	4	no	—
458	D₄×C₃₁	—	4	8	no	—
459	C₂×C₄×C₃₁	—	2	8	no	—
460	C₂×C₄×C₃₁	—	2	8	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	4	no	—
464	C₂×C₄×C₃₁	—	2	4	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	4	no	—
467	C₂×C₄×C₃₁	—	2	4	no	—
468	C₂×C₄×C₃₁	—	2	4	no	—
469	C₂×C₄×C₃₁	—	2	4	no	—
470	C₂×C₄×C₃₁	—	2	4	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	4	no	—
474	C₂×C₄×C₃₁	—	2	4	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	4	no	—
477	C₂×C₄×C₃₁	—	4	8	no	—
478	C₂×C₄×C₃₁	—	4	4	no	—
479	C₂×C₄×C₃₁	—	4	4	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	4	8	no	—
482	C₂×C₄×C₃₁	—	4	8	no	—
483	C₂×C₄×C₃₁	—	4	8	no	—
484	C₂×C₄×C₃₁	—	4	8	no	—
485	C₂×C₄×C₃₁	—	4	4	no	—
486	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
487	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
488	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
489	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
490	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
491	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
492	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
493	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
494	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
495	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
496	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
497	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
498	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
499	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
500	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
501	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
502	#3564	C₂×C₃₁	1	32	yes	direct product factor
503	C₂×#563	C₂×C₃₁	1	2	yes	complemented
504	C₂×#563	C₂×C₃₁	1	2	yes	complemented
505	C₂×#556	C₂×C₃₁	1	2	yes	complemented
506	C₂×#554	C₂×C₃₁	1	2	yes	complemented
507	C₂×#552	C₂×C₃₁	1	2	yes	complemented
508	C₂×#552	C₂×C₃₁	1	2	yes	complemented
509	C₂×#551	C₂×C₃₁	1	2	yes	complemented
510	C₂×#551	C₂×C₃₁	1	2	yes	complemented
511	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
512	C₂×#543	C₂×C₃₁	1	1	yes	characteristic, complemented
513	C₂×#542	C₂×C₃₁	1	2	yes	complemented
514	C₂×#541	C₂×C₃₁	1	2	yes	complemented
515	C₂×#541	C₂×C₃₁	1	2	yes	complemented
516	C₂×#539	C₂×C₃₁	1	1	yes	characteristic, complemented
517	C₂×#539	C₂×C₃₁	1	2	yes	complemented
518	C₂×#538	C₂×C₃₁	1	1	yes	characteristic
519	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
520	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
521	C₂²×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
522	C₂²×C₃₁	—	2	2	no	—
523	C₂²×C₃₁	—	2	2	no	—
524	C₂²×C₃₁	—	2	8	no	—
525	C₂²×C₃₁	—	2	4	no	—
526	C₂²×C₃₁	—	2	4	no	—
527	C₂²×C₃₁	—	2	4	no	—
528	C₂²×C₃₁	—	2	4	no	—
529	C₂²×C₃₁	—	2	4	no	—
530	C₂²×C₃₁	—	2	4	no	—
531	C₂²×C₃₁	—	4	8	no	—
532	C₂²×C₃₁	—	4	8	no	—
533	C₂²×C₃₁	—	8	8	no	—
534	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	—
535	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
536	C₂²×C₃₁	#585	1	2	yes	—
537	C₂²×C₃₁	#585	1	2	yes	—
538	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
539	C₄×C₃₁	—	2	2	no	—
540	C₄×C₃₁	—	2	2	no	—
541	C₄×C₃₁	—	2	4	no	—
542	C₄×C₃₁	—	2	4	no	—
543	C₄×C₃₁	—	2	2	no	—
544	C₄×C₃₁	—	2	4	no	—
545	C₄×C₃₁	—	2	4	no	—
546	C₄×C₃₁	—	2	4	no	—
547	C₄×C₃₁	—	2	4	no	—
548	C₄×C₃₁	—	2	4	no	—
549	C₄×C₃₁	—	2	2	no	—
550	C₄×C₃₁	—	2	2	no	—
551	C₄×C₃₁	—	2	4	no	—
552	C₄×C₃₁	—	2	4	no	—
553	C₄×C₃₁	—	2	2	no	—
554	C₄×C₃₁	—	2	4	no	—
555	#563	C₂²×C₃₁	1	32	yes	complemented
556	#563	C₂²×C₃₁	1	32	yes	complemented
557	#556	C₂²×C₃₁	1	32	yes	complemented
558	#554	C₂²×C₃₁	1	32	yes	complemented
559	#552	C₂²×C₃₁	1	32	yes	complemented
560	#552	C₂²×C₃₁	1	32	yes	complemented
561	#551	C₂²×C₃₁	1	32	yes	complemented
562	#551	C₂²×C₃₁	1	32	yes	complemented
563	#544	C₂²×C₃₁	1	16	yes	complemented
564	#543	C₂²×C₃₁	1	16	yes	complemented
565	#542	C₂²×C₃₁	1	32	yes	complemented
566	#541	C₂²×C₃₁	1	32	yes	complemented
567	#541	C₂²×C₃₁	1	32	yes	complemented
568	#539	C₂²×C₃₁	1	16	yes	complemented
569	#539	C₂²×C₃₁	1	32	yes	complemented
570	#538	C₂²×C₃₁	1	16	yes	—
571	#533	C₂²×C₃₁	1	16	yes	complemented
572	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
575	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
576	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
577	#529	C₂²×C₃₁	1	16	yes	complemented
578	C₂×#126	C₂²×C₃₁	1	2	yes	—
579	C₂×#126	C₂²×C₃₁	1	2	yes	—
580	C₂×#126	C₂²×C₃₁	1	2	yes	—
581	C₂×#126	C₂²×C₃₁	1	2	yes	—
582	C₂×#126	C₂²×C₃₁	1	2	yes	—
583	C₂×#126	C₂²×C₃₁	1	2	yes	—
584	C₂×#126	C₂²×C₃₁	1	2	yes	—
585	C₂×#126	C₂²×C₃₁	1	2	yes	—
586	C₂×#126	C₂²×C₃₁	1	2	yes	—
587	C₂×#126	C₂²×C₃₁	1	16	yes	complemented
588	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
589	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
590	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
591	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
592	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
594	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
595	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
596	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
597	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
598	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
599	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
600	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
601	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
602	C₂×#124	C₂²×C₃₁	1	2	yes	—
603	C₂×#124	C₂²×C₃₁	1	2	yes	—
604	C₂×#124	C₂²×C₃₁	1	2	yes	—
605	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	C₂×#123	C₂²×C₃₁	1	2	yes	—
607	C₂×#123	C₂²×C₃₁	1	2	yes	—
608	C₂×#123	C₂²×C₃₁	1	2	yes	—
609	C₂×#123	C₂²×C₃₁	1	2	yes	—
610	C₂×#123	C₂²×C₃₁	1	2	yes	—
611	C₂×#123	C₂²×C₃₁	1	2	yes	—
612	C₂×#123	C₂²×C₃₁	1	2	yes	—
613	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
614	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
615	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
617	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
618	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
619	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
620	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
621	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
622	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
623	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
624	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
625	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
626	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
627	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
628	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
629	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
630	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
631	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
632	C₂×#121	C₂²×C₃₁	1	2	yes	—
633	C₂×#120	C₂²×C₃₁	1	2	yes	—
634	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
636	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
639	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
640	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
641	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
642	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
643	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
644	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
645	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	C₂×#117	C₂²×C₃₁	1	2	yes	—
647	C₂×#117	C₂²×C₃₁	1	2	yes	—
648	C₂×#117	C₂²×C₃₁	1	2	yes	—
649	C₂×#117	C₂²×C₃₁	1	2	yes	—
650	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
651	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
652	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
653	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
654	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
655	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
656	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
657	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
658	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
659	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
660	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×C₃₁	—	2	4	no	—
662	C₂×C₃₁	—	4	4	no	—
663	C₂×C₃₁	—	4	4	no	—
664	C₂×C₃₁	#3564	1	4	yes	direct product factor
665	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
666	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
667	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
668	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
669	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
670	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
671	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
672	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
673	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
674	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
676	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
677	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
678	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
686	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
687	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
688	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
689	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
690	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
691	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
692	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
693	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
694	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
695	#126	C₂³×C₃₁	1	16	yes	—
696	#126	C₂³×C₃₁	1	16	yes	—
697	#126	C₂³×C₃₁	1	16	yes	—
698	#126	C₂³×C₃₁	1	16	yes	—
699	#126	C₂³×C₃₁	1	16	yes	—
700	#126	C₂³×C₃₁	1	16	yes	—
701	#126	C₂³×C₃₁	1	16	yes	—
702	#126	C₂³×C₃₁	1	16	yes	—
703	#126	C₂³×C₃₁	1	16	yes	—
704	#126	C₂³×C₃₁	1	16	yes	complemented
705	#126	C₂³×C₃₁	1	16	yes	complemented
706	#126	C₂³×C₃₁	1	16	yes	complemented
707	#126	C₂³×C₃₁	1	16	yes	complemented
708	#125	C₂³×C₃₁	1	8	yes	complemented
709	#125	C₂³×C₃₁	1	16	yes	complemented
710	#125	C₂³×C₃₁	1	16	yes	complemented
711	#125	C₂³×C₃₁	1	16	yes	complemented
712	#125	C₂³×C₃₁	1	16	yes	complemented
713	#125	C₂³×C₃₁	1	16	yes	complemented
714	#125	C₂³×C₃₁	1	16	yes	complemented
715	#125	C₂³×C₃₁	1	16	yes	complemented
716	#125	C₂³×C₃₁	1	16	yes	complemented
717	#125	C₂³×C₃₁	1	16	yes	complemented
718	#124	C₂³×C₃₁	1	16	yes	—
719	#124	C₂³×C₃₁	1	16	yes	—
720	#124	C₂³×C₃₁	1	16	yes	—
721	#124	C₂³×C₃₁	1	8	yes	complemented
722	#123	C₂³×C₃₁	1	16	yes	—
723	#123	C₂³×C₃₁	1	16	yes	—
724	#123	C₂³×C₃₁	1	16	yes	—
725	#123	C₂³×C₃₁	1	16	yes	—
726	#123	C₂³×C₃₁	1	16	yes	—
727	#123	C₂³×C₃₁	1	16	yes	—
728	#123	C₂³×C₃₁	1	16	yes	—
729	#123	C₂³×C₃₁	1	16	yes	complemented
730	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
731	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
732	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
733	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
734	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
735	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
736	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
737	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
738	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
739	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
740	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
741	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
742	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
743	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
744	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
745	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
746	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
747	#121	C₂³×C₃₁	1	8	yes	—
748	#121	C₂³×C₃₁	1	16	yes	—
749	#120	C₂³×C₃₁	1	16	yes	—
750	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
751	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
752	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
753	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
754	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
755	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
756	C₄×D₄	C₂³×C₃₁	1	16	yes	—
757	C₄×D₄	C₂³×C₃₁	1	16	yes	—
758	C₄×D₄	C₂³×C₃₁	1	16	yes	—
759	C₄×D₄	C₂³×C₃₁	1	16	yes	—
760	C₄×D₄	C₂³×C₃₁	1	16	yes	—
761	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
762	#117	C₂³×C₃₁	1	16	yes	—
763	#117	C₂³×C₃₁	1	16	yes	—
764	#117	C₂³×C₃₁	1	16	yes	—
765	#117	C₂³×C₃₁	1	16	yes	—
766	#117	C₂³×C₃₁	1	16	yes	complemented
767	#117	C₂³×C₃₁	1	16	yes	complemented
768	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
775	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
776	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
777	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
784	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
785	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
787	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
790	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
799	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
805	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
830	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
831	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
832	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
833	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
834	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
835	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
836	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
837	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
838	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
842	C₃₁	C₂×#3564	1	1	yes	characteristic, direct product factor, Sylow
843	C₂⁴	—	2	4	no	—
844	C₂⁴	—	4	2	no	—
845	C₂⁴	—	4	2	no	—
846	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
847	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
848	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
849	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
850	C₂×Q₈	—	4	2	no	—
851	C₂×Q₈	—	4	4	no	—
852	C₂×Q₈	—	4	4	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	4	no	—
855	C₂×Q₈	—	4	2	no	—
856	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
857	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
858	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
859	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
860	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
861	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
862	C₂×D₄	—	2	8	no	—
863	C₂×D₄	—	4	4	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	4	no	—
866	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
867	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
868	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
869	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	2	4	no	—
872	C₂²×C₄	—	4	4	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	4	no	—
877	C₂²×C₄	—	4	4	no	—
878	C₂²×C₄	—	4	4	no	—
879	C₂²×C₄	—	4	4	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
894	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
899	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
900	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
901	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
902	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
903	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
904	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
905	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
906	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
907	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
908	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
909	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
910	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
911	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
912	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
913	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
914	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
915	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
916	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
917	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
918	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
919	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
920	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
921	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
922	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
923	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
924	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
925	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
926	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
927	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
928	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
929	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
930	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
931	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
932	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
933	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
934	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
935	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
936	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
937	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
938	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
939	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
943	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
944	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
945	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
950	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
951	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
954	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
955	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
956	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
957	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
958	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
962	C₄²	C₂⁴×C₃₁	1	4	yes	—
963	C₄²	C₂⁴×C₃₁	1	4	yes	—
964	C₄²	C₂⁴×C₃₁	1	4	yes	—
965	C₄²	C₂⁴×C₃₁	1	4	yes	—
966	C₄²	C₂⁴×C₃₁	1	8	yes	—
967	C₄²	C₂⁴×C₃₁	1	8	yes	—
968	C₄²	C₂⁴×C₃₁	1	8	yes	—
969	C₄²	C₂⁴×C₃₁	1	8	yes	—
970	C₄²	C₂⁴×C₃₁	1	8	yes	—
971	C₄²	C₂⁴×C₃₁	1	8	yes	—
972	C₄²	C₂⁴×C₃₁	1	8	yes	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	4	no	—
976	C₂³	—	2	4	no	—
977	C₂³	—	2	4	no	—
978	C₂³	—	2	4	no	—
979	C₂³	—	2	4	no	—
980	C₂³	—	2	4	no	—
981	C₂³	—	2	8	no	—
982	C₂³	—	4	4	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	8	8	no	—
985	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
986	C₂³	C₂⁵×C₃₁	1	4	yes	—
987	C₂³	C₂⁵×C₃₁	1	4	yes	—
988	C₂³	C₂⁵×C₃₁	1	2	yes	—
989	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
990	Q₈	—	4	4	no	—
991	Q₈	—	4	8	no	—
992	Q₈	—	4	8	no	—
993	Q₈	—	4	4	no	—
994	Q₈	—	4	8	no	—
995	Q₈	—	4	4	no	—
996	D₄	—	2	16	no	—
997	D₄	—	4	8	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	8	no	—
1000	C₂×C₄	—	2	8	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	4	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	4	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	4	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	4	no	—
1011	C₂×C₄	—	2	4	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	4	no	—
1015	C₂×C₄	—	2	4	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	4	no	—
1018	C₂×C₄	—	4	8	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	8	no	—
1023	C₂×C₄	—	4	8	no	—
1024	C₂×C₄	—	4	8	no	—
1025	C₂×C₄	—	4	8	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1028	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1029	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1030	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1031	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1032	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1033	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1034	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1035	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1036	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1037	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1038	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1039	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1040	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1041	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1042	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	8	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	4	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	4	8	no	—
1053	C₂²	—	4	8	no	—
1054	C₂²	—	8	8	no	—
1055	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	—
1056	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
1057	C₂²	C₃₁×#585	1	2	yes	—
1058	C₂²	C₃₁×#585	1	2	yes	—
1059	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	4	no	—
1066	C₄	—	2	4	no	—
1067	C₄	—	2	4	no	—
1068	C₄	—	2	4	no	—
1069	C₄	—	2	4	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	4	no	—
1073	C₄	—	2	4	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	4	no	—
1076	C₂	—	2	4	no	—
1077	C₂	—	4	4	no	—
1078	C₂	—	4	4	no	—
1079	C₂	C₃₁×#3564	1	4	yes	direct product factor
1080	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₂	C₂×C₃₁×#585	1	1	yes	characteristic
1082	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
prime radical	C₂×C₃₁×#538	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3564	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×#563	C₂	semidirect
4. C₂×C₃₁×#556	C₂	semidirect
5. C₂×C₃₁×#554	C₂	semidirect
6. C₂×C₃₁×#552	C₂	semidirect
7. C₂×C₃₁×#552	C₂	semidirect
8. C₂×C₃₁×#551	C₂	semidirect
9. C₂×C₃₁×#551	C₂	semidirect
10. C₂×C₃₁×#544	C₂	semidirect
11. C₂×C₃₁×#543	C₂	semidirect
12. C₂×C₃₁×#542	C₂	semidirect
13. C₂×C₃₁×#541	C₂	semidirect
14. C₂×C₃₁×#541	C₂	semidirect
15. C₂×C₃₁×#539	C₂	semidirect
16. C₂×C₃₁×#539	C₂	semidirect
18. C₂×C₃₁×#533	C₂	semidirect
19. C₂×C₃₁×#529	C₂	semidirect
20. C₂²×C₃₁×#126	C₂	semidirect
21. C₃₁×#563	C₂²	semidirect
22. C₃₁×#563	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
25. C₃₁×#552	C₂²	semidirect
26. C₃₁×#552	C₂²	semidirect
27. C₃₁×#551	C₂²	semidirect
28. C₃₁×#551	C₂²	semidirect
29. C₃₁×#544	C₂²	semidirect
30. C₃₁×#543	C₂²	semidirect
31. C₃₁×#542	C₂²	semidirect
32. C₃₁×#541	C₂²	semidirect
33. C₃₁×#541	C₂²	semidirect
34. C₃₁×#539	C₂²	semidirect
35. C₃₁×#539	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
38. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
40. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
43. C₃₁×#529	C₂²	semidirect
53. C₂×C₃₁×#126	C₂²	semidirect
54. C₂×C₃₁×#126	C₂²	semidirect
55. C₂×C₃₁×#126	C₂²	semidirect
56. C₂×C₃₁×#126	C₂²	semidirect
57. C₂×C₃₁×#126	C₂²	semidirect
58. C₂×C₃₁×#125	C₂²	semidirect
59. C₂×C₃₁×#125	C₂²	semidirect
60. C₂×C₃₁×#125	C₂²	semidirect
61. C₂×C₃₁×#125	C₂²	semidirect
62. C₂×C₃₁×#125	C₂²	semidirect
63. C₂×C₃₁×#125	C₂²	semidirect
64. C₂×C₃₁×#125	C₂²	semidirect
65. C₂×C₃₁×#125	C₂²	semidirect
66. C₂×C₃₁×#125	C₂²	semidirect
67. C₂×C₃₁×#125	C₂²	semidirect
71. C₂×C₃₁×#124	C₂²	semidirect
79. C₂×C₃₁×#123	C₂²	semidirect
92. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
100. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
101. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
102. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
103. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
104. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
105. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
111. C₂×C₄×D₄×C₃₁	C₂²	semidirect
116. C₂×C₃₁×#117	C₂²	semidirect
117. C₂×C₃₁×#117	C₂²	semidirect
121. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
149. C₃₁×C₄⋊Q₈	C₂³	semidirect
150. C₃₁×C₄⋊Q₈	C₂³	semidirect
151. C₃₁×C₄⋊Q₈	C₂³	semidirect
152. C₃₁×C₄⋊Q₈	C₂³	semidirect
153. C₃₁×C₄⋊Q₈	C₂³	semidirect
163. C₃₁×#126	C₂³	semidirect
164. C₃₁×#126	C₂³	semidirect
165. C₃₁×#126	C₂³	semidirect
166. C₃₁×#126	C₂³	semidirect
167. C₃₁×#125	C₂³	semidirect
168. C₃₁×#125	C₂³	semidirect
169. C₃₁×#125	C₂³	semidirect
170. C₃₁×#125	C₂³	semidirect
171. C₃₁×#125	C₂³	semidirect
172. C₃₁×#125	C₂³	semidirect
173. C₃₁×#125	C₂³	semidirect
174. C₃₁×#125	C₂³	semidirect
175. C₃₁×#125	C₂³	semidirect
176. C₃₁×#125	C₂³	semidirect
180. C₃₁×#124	C₂³	semidirect
188. C₃₁×#123	C₂³	semidirect
201. C₃₁×C₂²⋊Q₈	C₂³	semidirect
202. C₃₁×C₂²⋊Q₈	C₂³	semidirect
203. C₃₁×C₂²⋊Q₈	C₂³	semidirect
204. C₃₁×C₂²⋊Q₈	C₂³	semidirect
205. C₃₁×C₂²⋊Q₈	C₂³	semidirect
209. C₄×Q₈×C₃₁	C₂³	semidirect
210. C₄×Q₈×C₃₁	C₂³	semidirect
211. C₄×Q₈×C₃₁	C₂³	semidirect
212. C₄×Q₈×C₃₁	C₂³	semidirect
213. C₄×Q₈×C₃₁	C₂³	semidirect
214. C₄×Q₈×C₃₁	C₂³	semidirect
220. C₄×D₄×C₃₁	C₂³	semidirect
225. C₃₁×#117	C₂³	semidirect
226. C₃₁×#117	C₂³	semidirect
263. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
431. C₂×#3564	C₃₁	direct (N × H)
502. #3564	C₂×C₃₁	direct (N × H)
503. C₂×#563	C₂×C₃₁	semidirect
504. C₂×#563	C₂×C₃₁	semidirect
505. C₂×#556	C₂×C₃₁	semidirect
506. C₂×#554	C₂×C₃₁	semidirect
507. C₂×#552	C₂×C₃₁	semidirect
508. C₂×#552	C₂×C₃₁	semidirect
509. C₂×#551	C₂×C₃₁	semidirect
510. C₂×#551	C₂×C₃₁	semidirect
511. C₂×#544	C₂×C₃₁	semidirect
512. C₂×#543	C₂×C₃₁	semidirect
513. C₂×#542	C₂×C₃₁	semidirect
514. C₂×#541	C₂×C₃₁	semidirect
515. C₂×#541	C₂×C₃₁	semidirect
516. C₂×#539	C₂×C₃₁	semidirect
517. C₂×#539	C₂×C₃₁	semidirect
519. C₂×#533	C₂×C₃₁	semidirect
520. C₂×#529	C₂×C₃₁	semidirect
521. C₂²×#126	C₂×C₃₁	semidirect
555. #563	C₂²×C₃₁	semidirect
556. #563	C₂²×C₃₁	semidirect
557. #556	C₂²×C₃₁	semidirect
558. #554	C₂²×C₃₁	semidirect
559. #552	C₂²×C₃₁	semidirect
560. #552	C₂²×C₃₁	semidirect
561. #551	C₂²×C₃₁	semidirect
562. #551	C₂²×C₃₁	semidirect
563. #544	C₂²×C₃₁	semidirect
564. #543	C₂²×C₃₁	semidirect
565. #542	C₂²×C₃₁	semidirect
566. #541	C₂²×C₃₁	semidirect
567. #541	C₂²×C₃₁	semidirect
568. #539	C₂²×C₃₁	semidirect
569. #539	C₂²×C₃₁	semidirect
571. #533	C₂²×C₃₁	semidirect
572. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
573. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
574. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
575. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
576. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
577. #529	C₂²×C₃₁	semidirect
587. C₂×#126	C₂²×C₃₁	semidirect
588. C₂×#126	C₂²×C₃₁	semidirect
589. C₂×#126	C₂²×C₃₁	semidirect
590. C₂×#126	C₂²×C₃₁	semidirect
591. C₂×#126	C₂²×C₃₁	semidirect
592. C₂×#125	C₂²×C₃₁	semidirect
593. C₂×#125	C₂²×C₃₁	semidirect
594. C₂×#125	C₂²×C₃₁	semidirect
595. C₂×#125	C₂²×C₃₁	semidirect
596. C₂×#125	C₂²×C₃₁	semidirect
597. C₂×#125	C₂²×C₃₁	semidirect
598. C₂×#125	C₂²×C₃₁	semidirect
599. C₂×#125	C₂²×C₃₁	semidirect
600. C₂×#125	C₂²×C₃₁	semidirect
601. C₂×#125	C₂²×C₃₁	semidirect
605. C₂×#124	C₂²×C₃₁	semidirect
613. C₂×#123	C₂²×C₃₁	semidirect
626. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
627. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
628. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
629. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
630. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
634. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
635. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
636. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
637. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
638. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
639. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
645. C₂×C₄×D₄	C₂²×C₃₁	semidirect
650. C₂×#117	C₂²×C₃₁	semidirect
651. C₂×#117	C₂²×C₃₁	semidirect
655. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
664. C₂×C₃₁	#3564	direct (N × H)
690. C₄⋊Q₈	C₂³×C₃₁	semidirect
691. C₄⋊Q₈	C₂³×C₃₁	semidirect
692. C₄⋊Q₈	C₂³×C₃₁	semidirect
693. C₄⋊Q₈	C₂³×C₃₁	semidirect
694. C₄⋊Q₈	C₂³×C₃₁	semidirect
704. #126	C₂³×C₃₁	semidirect
705. #126	C₂³×C₃₁	semidirect
706. #126	C₂³×C₃₁	semidirect
707. #126	C₂³×C₃₁	semidirect
708. #125	C₂³×C₃₁	semidirect
709. #125	C₂³×C₃₁	semidirect
710. #125	C₂³×C₃₁	semidirect
711. #125	C₂³×C₃₁	semidirect
712. #125	C₂³×C₃₁	semidirect
713. #125	C₂³×C₃₁	semidirect
714. #125	C₂³×C₃₁	semidirect
715. #125	C₂³×C₃₁	semidirect
716. #125	C₂³×C₃₁	semidirect
717. #125	C₂³×C₃₁	semidirect
721. #124	C₂³×C₃₁	semidirect
729. #123	C₂³×C₃₁	semidirect
742. C₂²⋊Q₈	C₂³×C₃₁	semidirect
743. C₂²⋊Q₈	C₂³×C₃₁	semidirect
744. C₂²⋊Q₈	C₂³×C₃₁	semidirect
745. C₂²⋊Q₈	C₂³×C₃₁	semidirect
746. C₂²⋊Q₈	C₂³×C₃₁	semidirect
750. C₄×Q₈	C₂³×C₃₁	semidirect
751. C₄×Q₈	C₂³×C₃₁	semidirect
752. C₄×Q₈	C₂³×C₃₁	semidirect
753. C₄×Q₈	C₂³×C₃₁	semidirect
754. C₄×Q₈	C₂³×C₃₁	semidirect
755. C₄×Q₈	C₂³×C₃₁	semidirect
761. C₄×D₄	C₂³×C₃₁	semidirect
766. #117	C₂³×C₃₁	semidirect
767. #117	C₂³×C₃₁	semidirect
804. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
842. C₃₁	C₂×#3564	direct (N × H)
1079. C₂	C₃₁×#3564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3564	2
C₂×C₃₁×#563	2
C₂×C₃₁×#556	2
C₂×C₃₁×#554	2
C₂×C₃₁×#552	2
C₂×C₃₁×#551	2
C₂×C₃₁×#544	2
C₂×C₃₁×#543	2
C₂×C₃₁×#542	2
C₂×C₃₁×#541	2
C₂×C₃₁×#539	2
C₂×C₃₁×#538	2
C₂×C₃₁×#533	2
C₂×C₃₁×#529	2
C₂²×C₃₁×#126	2
C₂×#3564	31

Subgroups — C2×C31×#3564 #21519493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3564 #21519493