Subgroups — C₂×C₃₁×#3565 #21519500

Order 7936.

6554 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3565	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#556	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
20	C₂×C₃₁×#541	C₂	1	2	yes	maximal, complemented
21	C₂×C₃₁×#539	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#563	C₂²	1	32	yes	complemented
26	C₃₁×#562	C₂²	1	32	yes	complemented
27	C₃₁×#557	C₂²	1	16	yes	complemented
28	C₃₁×#556	C₂²	1	32	yes	complemented
29	C₃₁×#556	C₂²	1	16	yes	complemented
30	C₃₁×#555	C₂²	1	16	yes	complemented
31	C₃₁×#554	C₂²	1	16	yes	complemented
32	C₃₁×#553	C₂²	1	16	yes	complemented
33	C₃₁×#553	C₂²	1	16	yes	complemented
34	C₃₁×#552	C₂²	1	32	yes	complemented
35	C₃₁×#552	C₂²	1	16	yes	complemented
36	C₃₁×#552	C₂²	1	16	yes	complemented
37	C₃₁×#544	C₂²	1	16	yes	complemented
38	C₃₁×#544	C₂²	1	16	yes	complemented
39	C₃₁×#542	C₂²	1	16	yes	complemented
40	C₃₁×#542	C₂²	1	16	yes	complemented
41	C₃₁×#542	C₂²	1	32	yes	complemented
42	C₃₁×#542	C₂²	1	32	yes	complemented
43	C₃₁×#541	C₂²	1	32	yes	complemented
44	C₃₁×#539	C₂²	1	32	yes	complemented
45	C₃₁×#533	C₂²	1	16	yes	complemented
46	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
49	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
53	C₃₁×#529	C₂²	1	16	yes	complemented
54	C₃₁×#529	C₂²	1	16	yes	complemented
55	C₂×C₃₁×#126	C₂²	1	2	yes	—
56	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
57	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#126	C₂²	1	2	yes	—
59	C₂×C₃₁×#126	C₂²	1	2	yes	—
60	C₂×C₃₁×#126	C₂²	1	2	yes	—
61	C₂×C₃₁×#126	C₂²	1	2	yes	—
62	C₂×C₃₁×#126	C₂²	1	2	yes	—
63	C₂×C₃₁×#126	C₂²	1	2	yes	—
64	C₂×C₃₁×#126	C₂²	1	2	yes	—
65	C₂×C₃₁×#126	C₂²	1	2	yes	—
66	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
68	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#125	C₂²	1	2	yes	—
71	C₂×C₃₁×#125	C₂²	1	2	yes	—
72	C₂×C₃₁×#125	C₂²	1	2	yes	—
73	C₂×C₃₁×#125	C₂²	1	2	yes	—
74	C₂×C₃₁×#125	C₂²	1	2	yes	—
75	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#125	C₂²	1	2	yes	—
77	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
78	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
79	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
80	C₂×C₃₁×#124	C₂²	1	2	yes	—
81	C₂×C₃₁×#124	C₂²	1	2	yes	—
82	C₂×C₃₁×#124	C₂²	1	2	yes	—
83	C₂×C₃₁×#124	C₂²	1	2	yes	—
84	C₂×C₃₁×#124	C₂²	1	2	yes	—
85	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
86	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
87	C₂×C₃₁×#123	C₂²	1	2	yes	—
88	C₂×C₃₁×#123	C₂²	1	2	yes	—
89	C₂×C₃₁×#123	C₂²	1	2	yes	—
90	C₂×C₃₁×#123	C₂²	1	2	yes	—
91	C₂×C₃₁×#123	C₂²	1	2	yes	—
92	C₂×C₃₁×#123	C₂²	1	2	yes	—
93	C₂×C₃₁×#123	C₂²	1	2	yes	—
94	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
95	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
96	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
97	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
98	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
99	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
100	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
101	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
102	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
103	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
104	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
105	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
106	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
107	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
108	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
109	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
110	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
111	C₂×C₃₁×#121	C₂²	1	2	yes	—
112	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
113	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
114	C₂×C₃₁×#121	C₂²	1	2	yes	—
115	C₂×C₃₁×#121	C₂²	1	2	yes	—
116	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
118	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
119	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
120	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
121	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
123	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
124	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
125	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
126	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
127	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
128	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
129	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
130	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
131	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
132	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
133	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
135	C₂×C₃₁×#117	C₂²	1	2	yes	—
136	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
137	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
138	C₂×C₃₁×#117	C₂²	1	2	yes	—
139	C₂×C₃₁×#117	C₂²	1	2	yes	—
140	C₂×C₃₁×#117	C₂²	1	2	yes	—
141	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
142	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
143	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
144	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
145	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
146	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
147	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
153	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
156	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
158	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
160	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
166	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
167	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
168	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
169	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
170	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
171	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
172	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	—
173	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	—
174	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
175	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
176	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	—
177	C₃₁×#126	C₂³	1	16	yes	—
178	C₃₁×#126	C₂³	1	8	yes	—
179	C₃₁×#126	C₂³	1	8	yes	—
180	C₃₁×#126	C₂³	1	16	yes	—
181	C₃₁×#126	C₂³	1	16	yes	—
182	C₃₁×#126	C₂³	1	16	yes	—
183	C₃₁×#126	C₂³	1	16	yes	—
184	C₃₁×#126	C₂³	1	16	yes	—
185	C₃₁×#126	C₂³	1	16	yes	—
186	C₃₁×#126	C₂³	1	16	yes	—
187	C₃₁×#126	C₂³	1	16	yes	—
188	C₃₁×#125	C₂³	1	8	yes	—
189	C₃₁×#125	C₂³	1	8	yes	—
190	C₃₁×#125	C₂³	1	8	yes	—
191	C₃₁×#125	C₂³	1	8	yes	—
192	C₃₁×#125	C₂³	1	16	yes	—
193	C₃₁×#125	C₂³	1	16	yes	—
194	C₃₁×#125	C₂³	1	16	yes	—
195	C₃₁×#125	C₂³	1	16	yes	—
196	C₃₁×#125	C₂³	1	16	yes	—
197	C₃₁×#125	C₂³	1	8	yes	—
198	C₃₁×#125	C₂³	1	16	yes	—
199	C₃₁×#125	C₂³	1	8	yes	—
200	C₃₁×#124	C₂³	1	8	yes	—
201	C₃₁×#124	C₂³	1	8	yes	—
202	C₃₁×#124	C₂³	1	16	yes	—
203	C₃₁×#124	C₂³	1	16	yes	—
204	C₃₁×#124	C₂³	1	16	yes	—
205	C₃₁×#124	C₂³	1	16	yes	—
206	C₃₁×#124	C₂³	1	16	yes	—
207	C₃₁×#123	C₂³	1	8	yes	—
208	C₃₁×#123	C₂³	1	8	yes	—
209	C₃₁×#123	C₂³	1	16	yes	—
210	C₃₁×#123	C₂³	1	16	yes	—
211	C₃₁×#123	C₂³	1	16	yes	—
212	C₃₁×#123	C₂³	1	16	yes	—
213	C₃₁×#123	C₂³	1	16	yes	—
214	C₃₁×#123	C₂³	1	16	yes	—
215	C₃₁×#123	C₂³	1	16	yes	—
216	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
217	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
221	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
222	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
225	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
226	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
227	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
228	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
229	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
230	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
231	C₃₁×#121	C₂³	1	8	yes	—
232	C₃₁×#121	C₂³	1	8	yes	—
233	C₃₁×#121	C₂³	1	16	yes	—
234	C₃₁×#121	C₂³	1	8	yes	—
235	C₃₁×#121	C₂³	1	8	yes	—
236	C₃₁×#121	C₂³	1	16	yes	—
237	C₃₁×#121	C₂³	1	16	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
241	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
242	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
243	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
244	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
245	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
246	C₄×D₄×C₃₁	C₂³	1	16	yes	—
247	C₄×D₄×C₃₁	C₂³	1	8	yes	—
248	C₄×D₄×C₃₁	C₂³	1	8	yes	—
249	C₄×D₄×C₃₁	C₂³	1	8	yes	—
250	C₄×D₄×C₃₁	C₂³	1	8	yes	—
251	C₄×D₄×C₃₁	C₂³	1	16	yes	—
252	C₄×D₄×C₃₁	C₂³	1	16	yes	—
253	C₄×D₄×C₃₁	C₂³	1	8	yes	—
254	C₄×D₄×C₃₁	C₂³	1	8	yes	—
255	C₃₁×#117	C₂³	1	8	yes	—
256	C₃₁×#117	C₂³	1	8	yes	—
257	C₃₁×#117	C₂³	1	16	yes	—
258	C₃₁×#117	C₂³	1	8	yes	—
259	C₃₁×#117	C₂³	1	8	yes	—
260	C₃₁×#117	C₂³	1	16	yes	—
261	C₃₁×#117	C₂³	1	16	yes	—
262	C₃₁×#117	C₂³	1	16	yes	—
263	C₃₁×#117	C₂³	1	8	yes	—
264	C₃₁×#117	C₂³	1	8	yes	—
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
273	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
276	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
277	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
278	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
294	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
298	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
299	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
300	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
301	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
302	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
303	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
304	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
307	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
311	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
312	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
313	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
315	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
320	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
321	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
325	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
326	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
327	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
329	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
330	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
332	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
335	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
336	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
337	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
338	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
339	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
340	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
343	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
344	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
345	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
349	C₂×Q₈×C₃₁	—	2	4	no	—
350	C₂×Q₈×C₃₁	—	4	2	no	—
351	C₂×Q₈×C₃₁	—	4	4	no	—
352	C₂×Q₈×C₃₁	—	4	4	no	—
353	C₂×Q₈×C₃₁	—	4	4	no	—
354	C₂×Q₈×C₃₁	—	4	4	no	—
355	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
356	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
357	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
358	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
359	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
360	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
361	C₂×D₄×C₃₁	—	2	4	no	—
362	C₂×D₄×C₃₁	—	4	2	no	—
363	C₂×D₄×C₃₁	—	4	2	no	—
364	C₂×D₄×C₃₁	—	4	4	no	—
365	C₂×D₄×C₃₁	—	4	4	no	—
366	C₂×D₄×C₃₁	—	4	2	no	—
367	C₂×D₄×C₃₁	—	4	4	no	—
368	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
369	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
370	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
371	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
372	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
373	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
374	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
375	C₂²×C₄×C₃₁	—	2	4	no	—
376	C₂²×C₄×C₃₁	—	2	4	no	—
377	C₂²×C₄×C₃₁	—	2	4	no	—
378	C₂²×C₄×C₃₁	—	4	4	no	—
379	C₂²×C₄×C₃₁	—	4	2	no	—
380	C₂²×C₄×C₃₁	—	4	4	no	—
381	C₂²×C₄×C₃₁	—	4	4	no	—
382	C₂²×C₄×C₃₁	—	4	4	no	—
383	C₂²×C₄×C₃₁	—	4	4	no	—
384	C₂²×C₄×C₃₁	—	4	2	no	—
385	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
386	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
387	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
407	C₂²×C₄×C₃₁	C₂⁴	1	4	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	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
419	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
421	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
422	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
423	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
424	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
425	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
426	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
427	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
430	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
431	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
432	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
433	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
434	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
436	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
438	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
439	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
441	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
442	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
443	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
444	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
445	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
446	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
447	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
448	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
449	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
450	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
451	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
453	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
454	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
455	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
456	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
457	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
458	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
459	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
460	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
461	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
463	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
464	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
465	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
466	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
467	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
468	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
469	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
470	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
471	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
472	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
473	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
474	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
475	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
476	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
477	C₄²×C₃₁	C₂⁴	1	4	yes	—
478	C₄²×C₃₁	C₂⁴	1	4	yes	—
479	C₄²×C₃₁	C₂⁴	1	4	yes	—
480	C₄²×C₃₁	C₂⁴	1	4	yes	—
481	C₄²×C₃₁	C₂⁴	1	8	yes	—
482	C₄²×C₃₁	C₂⁴	1	8	yes	—
483	C₄²×C₃₁	C₂⁴	1	8	yes	—
484	C₄²×C₃₁	C₂⁴	1	8	yes	—
485	C₄²×C₃₁	C₂⁴	1	4	yes	—
486	C₄²×C₃₁	C₂⁴	1	4	yes	—
487	C₄²×C₃₁	C₂⁴	1	8	yes	—
488	C₄²×C₃₁	C₂⁴	1	8	yes	—
489	C₄²×C₃₁	C₂⁴	1	8	yes	—
490	C₂×#3565	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂³×C₃₁	—	2	2	no	—
492	C₂³×C₃₁	—	2	2	no	—
493	C₂³×C₃₁	—	2	2	no	—
494	C₂³×C₃₁	—	2	4	no	—
495	C₂³×C₃₁	—	2	2	no	—
496	C₂³×C₃₁	—	2	2	no	—
497	C₂³×C₃₁	—	2	4	no	—
498	C₂³×C₃₁	—	2	2	no	—
499	C₂³×C₃₁	—	2	2	no	—
500	C₂³×C₃₁	—	2	4	no	—
501	C₂³×C₃₁	—	2	2	no	—
502	C₂³×C₃₁	—	2	2	no	—
503	C₂³×C₃₁	C₂⁵	1	2	yes	—
504	C₂³×C₃₁	C₂⁵	1	2	yes	—
505	C₂³×C₃₁	C₂⁵	1	2	yes	—
506	C₂³×C₃₁	C₂⁵	1	4	yes	—
507	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
508	Q₈×C₃₁	—	2	8	no	—
509	Q₈×C₃₁	—	4	4	no	—
510	Q₈×C₃₁	—	4	8	no	—
511	Q₈×C₃₁	—	4	8	no	—
512	Q₈×C₃₁	—	4	8	no	—
513	Q₈×C₃₁	—	4	8	no	—
514	D₄×C₃₁	—	2	8	no	—
515	D₄×C₃₁	—	4	4	no	—
516	D₄×C₃₁	—	4	4	no	—
517	D₄×C₃₁	—	4	8	no	—
518	D₄×C₃₁	—	4	8	no	—
519	D₄×C₃₁	—	4	4	no	—
520	D₄×C₃₁	—	4	8	no	—
521	C₂×C₄×C₃₁	—	2	2	no	—
522	C₂×C₄×C₃₁	—	2	2	no	—
523	C₂×C₄×C₃₁	—	2	2	no	—
524	C₂×C₄×C₃₁	—	2	4	no	—
525	C₂×C₄×C₃₁	—	2	2	no	—
526	C₂×C₄×C₃₁	—	2	2	no	—
527	C₂×C₄×C₃₁	—	2	4	no	—
528	C₂×C₄×C₃₁	—	2	2	no	—
529	C₂×C₄×C₃₁	—	2	4	no	—
530	C₂×C₄×C₃₁	—	2	4	no	—
531	C₂×C₄×C₃₁	—	2	4	no	—
532	C₂×C₄×C₃₁	—	2	2	no	—
533	C₂×C₄×C₃₁	—	2	2	no	—
534	C₂×C₄×C₃₁	—	2	4	no	—
535	C₂×C₄×C₃₁	—	2	2	no	—
536	C₂×C₄×C₃₁	—	2	2	no	—
537	C₂×C₄×C₃₁	—	2	4	no	—
538	C₂×C₄×C₃₁	—	2	2	no	—
539	C₂×C₄×C₃₁	—	2	8	no	—
540	C₂×C₄×C₃₁	—	2	8	no	—
541	C₂×C₄×C₃₁	—	2	8	no	—
542	C₂×C₄×C₃₁	—	4	8	no	—
543	C₂×C₄×C₃₁	—	4	4	no	—
544	C₂×C₄×C₃₁	—	4	8	no	—
545	C₂×C₄×C₃₁	—	4	8	no	—
546	C₂×C₄×C₃₁	—	4	8	no	—
547	C₂×C₄×C₃₁	—	4	8	no	—
548	C₂×C₄×C₃₁	—	4	4	no	—
549	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
550	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
551	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
552	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
553	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
554	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
555	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
556	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
557	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
558	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
559	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
560	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
561	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
562	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
563	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
564	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
565	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
566	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
567	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
568	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
569	#3565	C₂×C₃₁	1	32	yes	direct product factor
570	C₂×#563	C₂×C₃₁	1	2	yes	complemented
571	C₂×#562	C₂×C₃₁	1	2	yes	complemented
572	C₂×#557	C₂×C₃₁	1	1	yes	characteristic, complemented
573	C₂×#556	C₂×C₃₁	1	2	yes	complemented
574	C₂×#556	C₂×C₃₁	1	1	yes	characteristic, complemented
575	C₂×#555	C₂×C₃₁	1	1	yes	characteristic, complemented
576	C₂×#554	C₂×C₃₁	1	1	yes	characteristic, complemented
577	C₂×#553	C₂×C₃₁	1	1	yes	characteristic, complemented
578	C₂×#553	C₂×C₃₁	1	1	yes	characteristic, complemented
579	C₂×#552	C₂×C₃₁	1	2	yes	complemented
580	C₂×#552	C₂×C₃₁	1	1	yes	characteristic, complemented
581	C₂×#552	C₂×C₃₁	1	1	yes	characteristic, complemented
582	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
583	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
584	C₂×#542	C₂×C₃₁	1	1	yes	characteristic, complemented
585	C₂×#542	C₂×C₃₁	1	1	yes	characteristic, complemented
586	C₂×#542	C₂×C₃₁	1	2	yes	complemented
587	C₂×#542	C₂×C₃₁	1	2	yes	complemented
588	C₂×#541	C₂×C₃₁	1	2	yes	complemented
589	C₂×#539	C₂×C₃₁	1	2	yes	complemented
590	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
591	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
592	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
593	C₂²×C₃₁	—	2	2	no	—
594	C₂²×C₃₁	—	2	2	no	—
595	C₂²×C₃₁	—	2	2	no	—
596	C₂²×C₃₁	—	2	4	no	—
597	C₂²×C₃₁	—	2	2	no	—
598	C₂²×C₃₁	—	2	2	no	—
599	C₂²×C₃₁	—	2	4	no	—
600	C₂²×C₃₁	—	2	2	no	—
601	C₂²×C₃₁	—	2	2	no	—
602	C₂²×C₃₁	—	2	4	no	—
603	C₂²×C₃₁	—	2	2	no	—
604	C₂²×C₃₁	—	2	2	no	—
605	C₂²×C₃₁	—	4	4	no	—
606	C₂²×C₃₁	—	4	4	no	—
607	C₂²×C₃₁	—	4	4	no	—
608	C₂²×C₃₁	—	4	8	no	—
609	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
610	C₂²×C₃₁	#585	1	2	yes	—
611	C₂²×C₃₁	#585	1	2	yes	—
612	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
613	C₄×C₃₁	—	2	2	no	—
614	C₄×C₃₁	—	2	2	no	—
615	C₄×C₃₁	—	2	2	no	—
616	C₄×C₃₁	—	2	4	no	—
617	C₄×C₃₁	—	2	2	no	—
618	C₄×C₃₁	—	2	2	no	—
619	C₄×C₃₁	—	2	4	no	—
620	C₄×C₃₁	—	2	2	no	—
621	C₄×C₃₁	—	2	4	no	—
622	C₄×C₃₁	—	2	4	no	—
623	C₄×C₃₁	—	2	4	no	—
624	C₄×C₃₁	—	2	2	no	—
625	C₄×C₃₁	—	2	2	no	—
626	C₄×C₃₁	—	2	4	no	—
627	C₄×C₃₁	—	2	2	no	—
628	C₄×C₃₁	—	2	2	no	—
629	C₄×C₃₁	—	2	4	no	—
630	C₄×C₃₁	—	2	2	no	—
631	C₄×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	—
632	#563	C₂²×C₃₁	1	32	yes	complemented
633	#562	C₂²×C₃₁	1	32	yes	complemented
634	#557	C₂²×C₃₁	1	16	yes	complemented
635	#556	C₂²×C₃₁	1	32	yes	complemented
636	#556	C₂²×C₃₁	1	16	yes	complemented
637	#555	C₂²×C₃₁	1	16	yes	complemented
638	#554	C₂²×C₃₁	1	16	yes	complemented
639	#553	C₂²×C₃₁	1	16	yes	complemented
640	#553	C₂²×C₃₁	1	16	yes	complemented
641	#552	C₂²×C₃₁	1	32	yes	complemented
642	#552	C₂²×C₃₁	1	16	yes	complemented
643	#552	C₂²×C₃₁	1	16	yes	complemented
644	#544	C₂²×C₃₁	1	16	yes	complemented
645	#544	C₂²×C₃₁	1	16	yes	complemented
646	#542	C₂²×C₃₁	1	16	yes	complemented
647	#542	C₂²×C₃₁	1	16	yes	complemented
648	#542	C₂²×C₃₁	1	32	yes	complemented
649	#542	C₂²×C₃₁	1	32	yes	complemented
650	#541	C₂²×C₃₁	1	32	yes	complemented
651	#539	C₂²×C₃₁	1	32	yes	complemented
652	#533	C₂²×C₃₁	1	16	yes	complemented
653	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
655	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
656	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
657	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
659	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
660	#529	C₂²×C₃₁	1	16	yes	complemented
661	#529	C₂²×C₃₁	1	16	yes	complemented
662	C₂×#126	C₂²×C₃₁	1	2	yes	—
663	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
665	C₂×#126	C₂²×C₃₁	1	2	yes	—
666	C₂×#126	C₂²×C₃₁	1	2	yes	—
667	C₂×#126	C₂²×C₃₁	1	2	yes	—
668	C₂×#126	C₂²×C₃₁	1	2	yes	—
669	C₂×#126	C₂²×C₃₁	1	2	yes	—
670	C₂×#126	C₂²×C₃₁	1	2	yes	—
671	C₂×#126	C₂²×C₃₁	1	2	yes	—
672	C₂×#126	C₂²×C₃₁	1	2	yes	—
673	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
674	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
675	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
676	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
677	C₂×#125	C₂²×C₃₁	1	2	yes	—
678	C₂×#125	C₂²×C₃₁	1	2	yes	—
679	C₂×#125	C₂²×C₃₁	1	2	yes	—
680	C₂×#125	C₂²×C₃₁	1	2	yes	—
681	C₂×#125	C₂²×C₃₁	1	2	yes	—
682	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×#125	C₂²×C₃₁	1	2	yes	—
684	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
685	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
686	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×#124	C₂²×C₃₁	1	2	yes	—
688	C₂×#124	C₂²×C₃₁	1	2	yes	—
689	C₂×#124	C₂²×C₃₁	1	2	yes	—
690	C₂×#124	C₂²×C₃₁	1	2	yes	—
691	C₂×#124	C₂²×C₃₁	1	2	yes	—
692	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
693	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
694	C₂×#123	C₂²×C₃₁	1	2	yes	—
695	C₂×#123	C₂²×C₃₁	1	2	yes	—
696	C₂×#123	C₂²×C₃₁	1	2	yes	—
697	C₂×#123	C₂²×C₃₁	1	2	yes	—
698	C₂×#123	C₂²×C₃₁	1	2	yes	—
699	C₂×#123	C₂²×C₃₁	1	2	yes	—
700	C₂×#123	C₂²×C₃₁	1	2	yes	—
701	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
702	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
703	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
704	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
705	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
706	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
707	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
708	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
709	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
710	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
711	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
712	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
713	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
714	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
715	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
716	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
717	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
718	C₂×#121	C₂²×C₃₁	1	2	yes	—
719	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
720	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
721	C₂×#121	C₂²×C₃₁	1	2	yes	—
722	C₂×#121	C₂²×C₃₁	1	2	yes	—
723	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
724	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
725	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
726	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
727	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
728	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
729	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
730	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
731	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
732	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
733	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
734	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
735	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
736	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
737	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
738	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
739	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
740	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
741	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
742	C₂×#117	C₂²×C₃₁	1	2	yes	—
743	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
744	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
745	C₂×#117	C₂²×C₃₁	1	2	yes	—
746	C₂×#117	C₂²×C₃₁	1	2	yes	—
747	C₂×#117	C₂²×C₃₁	1	2	yes	—
748	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
749	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
750	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
751	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
752	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
753	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
754	C₂×C₃₁	—	4	2	no	—
755	C₂×C₃₁	—	4	2	no	—
756	C₂×C₃₁	—	4	2	no	—
757	C₂×C₃₁	—	4	4	no	—
758	C₂×C₃₁	#3565	1	4	yes	direct product factor
759	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
760	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
761	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
762	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
765	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
766	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
767	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
768	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
769	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
770	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
771	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
772	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
773	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
774	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
775	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
776	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
777	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
778	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
779	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
780	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
781	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
782	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
783	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
785	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
786	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
787	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	—
788	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	—
789	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
790	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
791	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	—
792	#126	C₂³×C₃₁	1	16	yes	—
793	#126	C₂³×C₃₁	1	8	yes	—
794	#126	C₂³×C₃₁	1	8	yes	—
795	#126	C₂³×C₃₁	1	16	yes	—
796	#126	C₂³×C₃₁	1	16	yes	—
797	#126	C₂³×C₃₁	1	16	yes	—
798	#126	C₂³×C₃₁	1	16	yes	—
799	#126	C₂³×C₃₁	1	16	yes	—
800	#126	C₂³×C₃₁	1	16	yes	—
801	#126	C₂³×C₃₁	1	16	yes	—
802	#126	C₂³×C₃₁	1	16	yes	—
803	#125	C₂³×C₃₁	1	8	yes	—
804	#125	C₂³×C₃₁	1	8	yes	—
805	#125	C₂³×C₃₁	1	8	yes	—
806	#125	C₂³×C₃₁	1	8	yes	—
807	#125	C₂³×C₃₁	1	16	yes	—
808	#125	C₂³×C₃₁	1	16	yes	—
809	#125	C₂³×C₃₁	1	16	yes	—
810	#125	C₂³×C₃₁	1	16	yes	—
811	#125	C₂³×C₃₁	1	16	yes	—
812	#125	C₂³×C₃₁	1	8	yes	—
813	#125	C₂³×C₃₁	1	16	yes	—
814	#125	C₂³×C₃₁	1	8	yes	—
815	#124	C₂³×C₃₁	1	8	yes	—
816	#124	C₂³×C₃₁	1	8	yes	—
817	#124	C₂³×C₃₁	1	16	yes	—
818	#124	C₂³×C₃₁	1	16	yes	—
819	#124	C₂³×C₃₁	1	16	yes	—
820	#124	C₂³×C₃₁	1	16	yes	—
821	#124	C₂³×C₃₁	1	16	yes	—
822	#123	C₂³×C₃₁	1	8	yes	—
823	#123	C₂³×C₃₁	1	8	yes	—
824	#123	C₂³×C₃₁	1	16	yes	—
825	#123	C₂³×C₃₁	1	16	yes	—
826	#123	C₂³×C₃₁	1	16	yes	—
827	#123	C₂³×C₃₁	1	16	yes	—
828	#123	C₂³×C₃₁	1	16	yes	—
829	#123	C₂³×C₃₁	1	16	yes	—
830	#123	C₂³×C₃₁	1	16	yes	—
831	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
832	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
833	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
834	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
835	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
836	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
837	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
838	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
839	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
840	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
841	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
842	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
843	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
844	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
845	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
846	#121	C₂³×C₃₁	1	8	yes	—
847	#121	C₂³×C₃₁	1	8	yes	—
848	#121	C₂³×C₃₁	1	16	yes	—
849	#121	C₂³×C₃₁	1	8	yes	—
850	#121	C₂³×C₃₁	1	8	yes	—
851	#121	C₂³×C₃₁	1	16	yes	—
852	#121	C₂³×C₃₁	1	16	yes	—
853	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
854	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
855	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
856	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
857	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
858	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
859	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
860	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
861	C₄×D₄	C₂³×C₃₁	1	16	yes	—
862	C₄×D₄	C₂³×C₃₁	1	8	yes	—
863	C₄×D₄	C₂³×C₃₁	1	8	yes	—
864	C₄×D₄	C₂³×C₃₁	1	8	yes	—
865	C₄×D₄	C₂³×C₃₁	1	8	yes	—
866	C₄×D₄	C₂³×C₃₁	1	16	yes	—
867	C₄×D₄	C₂³×C₃₁	1	16	yes	—
868	C₄×D₄	C₂³×C₃₁	1	8	yes	—
869	C₄×D₄	C₂³×C₃₁	1	8	yes	—
870	#117	C₂³×C₃₁	1	8	yes	—
871	#117	C₂³×C₃₁	1	8	yes	—
872	#117	C₂³×C₃₁	1	16	yes	—
873	#117	C₂³×C₃₁	1	8	yes	—
874	#117	C₂³×C₃₁	1	8	yes	—
875	#117	C₂³×C₃₁	1	16	yes	—
876	#117	C₂³×C₃₁	1	16	yes	—
877	#117	C₂³×C₃₁	1	16	yes	—
878	#117	C₂³×C₃₁	1	8	yes	—
879	#117	C₂³×C₃₁	1	8	yes	—
880	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
886	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
887	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
888	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
889	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
890	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
891	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
892	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
893	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
897	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
898	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
900	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
902	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
903	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
906	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
908	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
909	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
913	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
914	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
915	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
916	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
917	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
918	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
919	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
920	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
921	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
922	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
923	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
926	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
928	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
929	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
930	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
931	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
932	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
934	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
935	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
936	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
938	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
939	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
940	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
941	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
942	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
944	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
945	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
946	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
947	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
948	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
949	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
950	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
951	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
952	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
953	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
954	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
955	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
956	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
957	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
958	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
959	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
960	C₃₁	C₂×#3565	1	1	yes	characteristic, direct product factor, Sylow
961	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
965	C₂×Q₈	—	2	4	no	—
966	C₂×Q₈	—	4	2	no	—
967	C₂×Q₈	—	4	4	no	—
968	C₂×Q₈	—	4	4	no	—
969	C₂×Q₈	—	4	4	no	—
970	C₂×Q₈	—	4	4	no	—
971	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
972	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
973	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
974	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
975	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
976	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
977	C₂×D₄	—	2	4	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	2	no	—
980	C₂×D₄	—	4	4	no	—
981	C₂×D₄	—	4	4	no	—
982	C₂×D₄	—	4	2	no	—
983	C₂×D₄	—	4	4	no	—
984	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
985	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
986	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
987	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
988	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
989	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
990	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
991	C₂²×C₄	—	2	4	no	—
992	C₂²×C₄	—	2	4	no	—
993	C₂²×C₄	—	2	4	no	—
994	C₂²×C₄	—	4	4	no	—
995	C₂²×C₄	—	4	2	no	—
996	C₂²×C₄	—	4	4	no	—
997	C₂²×C₄	—	4	4	no	—
998	C₂²×C₄	—	4	4	no	—
999	C₂²×C₄	—	4	4	no	—
1000	C₂²×C₄	—	4	2	no	—
1001	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1010	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1013	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1016	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1019	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1021	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1022	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1023	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1024	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1025	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1026	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1027	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1028	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1029	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1031	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1032	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1033	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1034	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1035	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1036	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1037	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1038	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1039	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1040	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1041	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1042	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1043	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1044	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1045	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1046	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1047	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1048	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1049	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1050	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1051	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1052	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1053	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1054	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1055	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1056	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1057	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1058	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1059	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1060	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1061	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1062	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1063	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1064	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1065	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1066	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1067	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1068	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1069	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1070	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1071	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1072	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1073	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1074	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1075	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1076	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1077	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1078	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1079	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1080	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1081	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1082	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1083	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1084	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1085	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1086	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1087	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1088	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1089	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1090	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1091	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1092	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1093	C₄²	C₂⁴×C₃₁	1	4	yes	—
1094	C₄²	C₂⁴×C₃₁	1	4	yes	—
1095	C₄²	C₂⁴×C₃₁	1	4	yes	—
1096	C₄²	C₂⁴×C₃₁	1	4	yes	—
1097	C₄²	C₂⁴×C₃₁	1	8	yes	—
1098	C₄²	C₂⁴×C₃₁	1	8	yes	—
1099	C₄²	C₂⁴×C₃₁	1	8	yes	—
1100	C₄²	C₂⁴×C₃₁	1	8	yes	—
1101	C₄²	C₂⁴×C₃₁	1	4	yes	—
1102	C₄²	C₂⁴×C₃₁	1	4	yes	—
1103	C₄²	C₂⁴×C₃₁	1	8	yes	—
1104	C₄²	C₂⁴×C₃₁	1	8	yes	—
1105	C₄²	C₂⁴×C₃₁	1	8	yes	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	4	no	—
1110	C₂³	—	2	2	no	—
1111	C₂³	—	2	2	no	—
1112	C₂³	—	2	4	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	4	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	2	no	—
1118	C₂³	C₂⁵×C₃₁	1	2	yes	—
1119	C₂³	C₂⁵×C₃₁	1	2	yes	—
1120	C₂³	C₂⁵×C₃₁	1	2	yes	—
1121	C₂³	C₂⁵×C₃₁	1	4	yes	—
1122	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1123	Q₈	—	2	8	no	—
1124	Q₈	—	4	4	no	—
1125	Q₈	—	4	8	no	—
1126	Q₈	—	4	8	no	—
1127	Q₈	—	4	8	no	—
1128	Q₈	—	4	8	no	—
1129	D₄	—	2	8	no	—
1130	D₄	—	4	4	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	8	no	—
1133	D₄	—	4	8	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	8	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	4	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	4	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	4	no	—
1146	C₂×C₄	—	2	4	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	4	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	4	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	8	no	—
1155	C₂×C₄	—	2	8	no	—
1156	C₂×C₄	—	2	8	no	—
1157	C₂×C₄	—	4	8	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	8	no	—
1160	C₂×C₄	—	4	8	no	—
1161	C₂×C₄	—	4	8	no	—
1162	C₂×C₄	—	4	8	no	—
1163	C₂×C₄	—	4	4	no	—
1164	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
1165	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1166	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1167	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1168	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1169	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1170	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1171	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1172	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1173	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1174	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1175	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1176	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1177	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1178	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1179	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1180	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1181	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1182	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1183	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	4	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	4	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	4	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	4	4	no	—
1197	C₂²	—	4	4	no	—
1198	C₂²	—	4	4	no	—
1199	C₂²	—	4	8	no	—
1200	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
1201	C₂²	C₃₁×#585	1	2	yes	—
1202	C₂²	C₃₁×#585	1	2	yes	—
1203	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	4	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	4	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	4	no	—
1213	C₄	—	2	4	no	—
1214	C₄	—	2	4	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	4	no	—
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	4	no	—
1221	C₄	—	2	2	no	—
1222	C₄	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	—
1223	C₂	—	4	2	no	—
1224	C₂	—	4	2	no	—
1225	C₂	—	4	2	no	—
1226	C₂	—	4	4	no	—
1227	C₂	C₃₁×#3565	1	4	yes	direct product factor
1228	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1229	C₂	C₂×C₃₁×#585	1	1	yes	characteristic
1230	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
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×#3565	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×#562	C₂	semidirect
4. C₂×C₃₁×#557	C₂	semidirect
5. C₂×C₃₁×#556	C₂	semidirect
6. C₂×C₃₁×#556	C₂	semidirect
7. C₂×C₃₁×#555	C₂	semidirect
8. C₂×C₃₁×#554	C₂	semidirect
9. C₂×C₃₁×#553	C₂	semidirect
10. C₂×C₃₁×#553	C₂	semidirect
11. C₂×C₃₁×#552	C₂	semidirect
12. C₂×C₃₁×#552	C₂	semidirect
13. C₂×C₃₁×#552	C₂	semidirect
14. C₂×C₃₁×#544	C₂	semidirect
15. C₂×C₃₁×#544	C₂	semidirect
16. C₂×C₃₁×#542	C₂	semidirect
17. C₂×C₃₁×#542	C₂	semidirect
18. C₂×C₃₁×#542	C₂	semidirect
19. C₂×C₃₁×#542	C₂	semidirect
20. C₂×C₃₁×#541	C₂	semidirect
21. C₂×C₃₁×#539	C₂	semidirect
22. C₂×C₃₁×#533	C₂	semidirect
23. C₂×C₃₁×#529	C₂	semidirect
24. C₂×C₃₁×#529	C₂	semidirect
25. C₃₁×#563	C₂²	semidirect
26. C₃₁×#562	C₂²	semidirect
27. C₃₁×#557	C₂²	semidirect
28. C₃₁×#556	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
30. C₃₁×#555	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
33. C₃₁×#553	C₂²	semidirect
34. C₃₁×#552	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
37. C₃₁×#544	C₂²	semidirect
38. C₃₁×#544	C₂²	semidirect
39. C₃₁×#542	C₂²	semidirect
40. C₃₁×#542	C₂²	semidirect
41. C₃₁×#542	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
43. C₃₁×#541	C₂²	semidirect
44. C₃₁×#539	C₂²	semidirect
45. C₃₁×#533	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
54. C₃₁×#529	C₂²	semidirect
490. C₂×#3565	C₃₁	direct (N × H)
569. #3565	C₂×C₃₁	direct (N × H)
570. C₂×#563	C₂×C₃₁	semidirect
571. C₂×#562	C₂×C₃₁	semidirect
572. C₂×#557	C₂×C₃₁	semidirect
573. C₂×#556	C₂×C₃₁	semidirect
574. C₂×#556	C₂×C₃₁	semidirect
575. C₂×#555	C₂×C₃₁	semidirect
576. C₂×#554	C₂×C₃₁	semidirect
577. C₂×#553	C₂×C₃₁	semidirect
578. C₂×#553	C₂×C₃₁	semidirect
579. C₂×#552	C₂×C₃₁	semidirect
580. C₂×#552	C₂×C₃₁	semidirect
581. C₂×#552	C₂×C₃₁	semidirect
582. C₂×#544	C₂×C₃₁	semidirect
583. C₂×#544	C₂×C₃₁	semidirect
584. C₂×#542	C₂×C₃₁	semidirect
585. C₂×#542	C₂×C₃₁	semidirect
586. C₂×#542	C₂×C₃₁	semidirect
587. C₂×#542	C₂×C₃₁	semidirect
588. C₂×#541	C₂×C₃₁	semidirect
589. C₂×#539	C₂×C₃₁	semidirect
590. C₂×#533	C₂×C₃₁	semidirect
591. C₂×#529	C₂×C₃₁	semidirect
592. C₂×#529	C₂×C₃₁	semidirect
632. #563	C₂²×C₃₁	semidirect
633. #562	C₂²×C₃₁	semidirect
634. #557	C₂²×C₃₁	semidirect
635. #556	C₂²×C₃₁	semidirect
636. #556	C₂²×C₃₁	semidirect
637. #555	C₂²×C₃₁	semidirect
638. #554	C₂²×C₃₁	semidirect
639. #553	C₂²×C₃₁	semidirect
640. #553	C₂²×C₃₁	semidirect
641. #552	C₂²×C₃₁	semidirect
642. #552	C₂²×C₃₁	semidirect
643. #552	C₂²×C₃₁	semidirect
644. #544	C₂²×C₃₁	semidirect
645. #544	C₂²×C₃₁	semidirect
646. #542	C₂²×C₃₁	semidirect
647. #542	C₂²×C₃₁	semidirect
648. #542	C₂²×C₃₁	semidirect
649. #542	C₂²×C₃₁	semidirect
650. #541	C₂²×C₃₁	semidirect
651. #539	C₂²×C₃₁	semidirect
652. #533	C₂²×C₃₁	semidirect
660. #529	C₂²×C₃₁	semidirect
661. #529	C₂²×C₃₁	semidirect
758. C₂×C₃₁	#3565	direct (N × H)
960. C₃₁	C₂×#3565	direct (N × H)
1227. C₂	C₃₁×#3565	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×#3565	2
C₂×C₃₁×#563	2
C₂×C₃₁×#562	2
C₂×C₃₁×#557	2
C₂×C₃₁×#556	2
C₂×C₃₁×#555	2
C₂×C₃₁×#554	2
C₂×C₃₁×#553	2
C₂×C₃₁×#552	2
C₂×C₃₁×#544	2
C₂×C₃₁×#542	2
C₂×C₃₁×#541	2
C₂×C₃₁×#539	2
C₂×C₃₁×#533	2
C₂×C₃₁×#529	2
C₂×#3565	31

Subgroups — C2×C31×#3565 #21519500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3565 #21519500