Subgroups — C₂×C₃₁×#3563 #21519492

Order 7936.

6458 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3563	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#564	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#557	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#552	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#544	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#544	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#541	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#541	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₁×#539	C₂	1	2	yes	maximal
14	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#564	C₂²	1	32	yes	complemented
18	C₃₁×#563	C₂²	1	32	yes	complemented
19	C₃₁×#557	C₂²	1	32	yes	complemented
20	C₃₁×#554	C₂²	1	32	yes	complemented
21	C₃₁×#552	C₂²	1	64	yes	complemented
22	C₃₁×#552	C₂²	1	32	yes	complemented
23	C₃₁×#552	C₂²	1	32	yes	complemented
24	C₃₁×#544	C₂²	1	32	yes	complemented
25	C₃₁×#544	C₂²	1	32	yes	complemented
26	C₃₁×#541	C₂²	1	32	yes	complemented
27	C₃₁×#541	C₂²	1	64	yes	complemented
28	C₃₁×#539	C₂²	1	32	yes	—
29	C₃₁×#533	C₂²	1	16	yes	complemented
30	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
33	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
35	C₃₁×#529	C₂²	1	16	yes	—
36	C₂×C₃₁×#126	C₂²	1	2	yes	—
37	C₂×C₃₁×#126	C₂²	1	4	yes	—
38	C₂×C₃₁×#126	C₂²	1	4	yes	—
39	C₂×C₃₁×#126	C₂²	1	4	yes	—
40	C₂×C₃₁×#126	C₂²	1	4	yes	—
41	C₂×C₃₁×#125	C₂²	1	2	yes	—
42	C₂×C₃₁×#125	C₂²	1	2	yes	—
43	C₂×C₃₁×#125	C₂²	1	2	yes	—
44	C₂×C₃₁×#125	C₂²	1	2	yes	—
45	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#125	C₂²	1	2	yes	—
47	C₂×C₃₁×#125	C₂²	1	4	yes	—
48	C₂×C₃₁×#125	C₂²	1	4	yes	—
49	C₂×C₃₁×#125	C₂²	1	4	yes	—
50	C₂×C₃₁×#125	C₂²	1	4	yes	—
51	C₂×C₃₁×#125	C₂²	1	4	yes	—
52	C₂×C₃₁×#125	C₂²	1	4	yes	—
53	C₂×C₃₁×#125	C₂²	1	2	yes	—
54	C₂×C₃₁×#125	C₂²	1	4	yes	—
55	C₂×C₃₁×#125	C₂²	1	4	yes	—
56	C₂×C₃₁×#125	C₂²	1	16	yes	complemented
57	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#123	C₂²	1	2	yes	—
59	C₂×C₃₁×#123	C₂²	1	4	yes	—
60	C₂×C₃₁×#123	C₂²	1	4	yes	—
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
63	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
64	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
65	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
67	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
68	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
69	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
70	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
71	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
72	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
73	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
74	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	—
75	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
76	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
80	C₂×C₃₁×#117	C₂²	1	2	yes	—
81	C₂×C₃₁×#117	C₂²	1	2	yes	—
82	C₂×C₃₁×#117	C₂²	1	4	yes	—
83	C₂×C₃₁×#117	C₂²	1	2	yes	—
84	C₂×C₃₁×#117	C₂²	1	4	yes	—
85	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
86	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
87	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
88	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
89	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
91	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
92	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
93	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
94	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
104	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
105	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	32	yes	—
107	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	—
108	C₃₁×C₄⋊Q₈	C₂³	1	32	yes	—
109	C₃₁×#126	C₂³	1	16	yes	—
110	C₃₁×#126	C₂³	1	32	yes	—
111	C₃₁×#126	C₂³	1	32	yes	—
112	C₃₁×#126	C₂³	1	32	yes	—
113	C₃₁×#126	C₂³	1	32	yes	—
114	C₃₁×#125	C₂³	1	16	yes	—
115	C₃₁×#125	C₂³	1	16	yes	—
116	C₃₁×#125	C₂³	1	16	yes	—
117	C₃₁×#125	C₂³	1	16	yes	—
118	C₃₁×#125	C₂³	1	8	yes	—
119	C₃₁×#125	C₂³	1	16	yes	—
120	C₃₁×#125	C₂³	1	32	yes	—
121	C₃₁×#125	C₂³	1	32	yes	—
122	C₃₁×#125	C₂³	1	32	yes	—
123	C₃₁×#125	C₂³	1	32	yes	—
124	C₃₁×#125	C₂³	1	32	yes	—
125	C₃₁×#125	C₂³	1	32	yes	—
126	C₃₁×#125	C₂³	1	16	yes	—
127	C₃₁×#125	C₂³	1	32	yes	—
128	C₃₁×#125	C₂³	1	32	yes	—
129	C₃₁×#124	C₂³	1	8	yes	—
130	C₃₁×#123	C₂³	1	16	yes	—
131	C₃₁×#123	C₂³	1	32	yes	—
132	C₃₁×#123	C₂³	1	32	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
142	C₃₁×#121	C₂³	1	8	yes	—
143	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
144	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
145	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	32	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
149	C₄×D₄×C₃₁	C₂³	1	8	yes	—
150	C₄×D₄×C₃₁	C₂³	1	16	yes	—
151	C₄×D₄×C₃₁	C₂³	1	32	yes	—
152	C₃₁×#117	C₂³	1	16	yes	—
153	C₃₁×#117	C₂³	1	16	yes	—
154	C₃₁×#117	C₂³	1	32	yes	—
155	C₃₁×#117	C₂³	1	16	yes	—
156	C₃₁×#117	C₂³	1	32	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
204	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
208	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
209	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
210	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
211	C₂×Q₈×C₃₁	—	2	8	no	—
212	C₂×Q₈×C₃₁	—	4	8	no	—
213	C₂×Q₈×C₃₁	—	4	2	no	—
214	C₂×Q₈×C₃₁	—	4	4	no	—
215	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
216	C₂×Q₈×C₃₁	C₂⁴	1	16	yes	—
217	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
218	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
219	C₂×D₄×C₃₁	—	2	8	no	—
220	C₂×D₄×C₃₁	—	4	2	no	—
221	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
222	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	—	2	8	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	8	no	—
227	C₂²×C₄×C₃₁	—	4	4	no	—
228	C₂²×C₄×C₃₁	—	4	8	no	—
229	C₂²×C₄×C₃₁	—	4	2	no	—
230	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
231	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
251	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
252	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
253	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
254	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
255	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
256	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
269	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
270	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
271	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
273	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
274	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
275	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
276	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
277	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
278	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
279	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
280	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
281	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
283	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
284	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
285	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
286	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
287	C₄²×C₃₁	C₂⁴	1	4	yes	—
288	C₄²×C₃₁	C₂⁴	1	4	yes	—
289	C₄²×C₃₁	C₂⁴	1	4	yes	—
290	C₄²×C₃₁	C₂⁴	1	4	yes	—
291	C₄²×C₃₁	C₂⁴	1	16	yes	—
292	C₄²×C₃₁	C₂⁴	1	16	yes	—
293	C₄²×C₃₁	C₂⁴	1	8	yes	—
294	C₄²×C₃₁	C₂⁴	1	16	yes	—
295	C₄²×C₃₁	C₂⁴	1	16	yes	—
296	C₂×#3563	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	2	4	no	—
300	C₂³×C₃₁	—	2	4	no	—
301	C₂³×C₃₁	—	2	4	no	—
302	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
303	C₂³×C₃₁	C₂⁵	1	4	yes	—
304	C₂³×C₃₁	C₂⁵	1	2	yes	—
305	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
306	Q₈×C₃₁	—	2	16	no	—
307	Q₈×C₃₁	—	4	16	no	—
308	Q₈×C₃₁	—	4	4	no	—
309	Q₈×C₃₁	—	4	8	no	—
310	D₄×C₃₁	—	2	16	no	—
311	D₄×C₃₁	—	4	4	no	—
312	C₂×C₄×C₃₁	—	2	8	no	—
313	C₂×C₄×C₃₁	—	2	16	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	8	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	4	no	—
320	C₂×C₄×C₃₁	—	2	8	no	—
321	C₂×C₄×C₃₁	—	2	8	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	8	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	8	no	—
327	C₂×C₄×C₃₁	—	2	16	no	—
328	C₂×C₄×C₃₁	—	4	8	no	—
329	C₂×C₄×C₃₁	—	4	16	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
332	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
333	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
334	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
335	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
336	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
337	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
338	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
339	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
340	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
341	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
342	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
343	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
344	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
345	#3563	C₂×C₃₁	1	32	yes	direct product factor
346	C₂×#564	C₂×C₃₁	1	2	yes	complemented
347	C₂×#563	C₂×C₃₁	1	2	yes	complemented
348	C₂×#557	C₂×C₃₁	1	2	yes	complemented
349	C₂×#554	C₂×C₃₁	1	2	yes	complemented
350	C₂×#552	C₂×C₃₁	1	4	yes	complemented
351	C₂×#552	C₂×C₃₁	1	2	yes	complemented
352	C₂×#552	C₂×C₃₁	1	2	yes	complemented
353	C₂×#544	C₂×C₃₁	1	2	yes	complemented
354	C₂×#544	C₂×C₃₁	1	2	yes	complemented
355	C₂×#541	C₂×C₃₁	1	2	yes	complemented
356	C₂×#541	C₂×C₃₁	1	4	yes	complemented
357	C₂×#539	C₂×C₃₁	1	2	yes	—
358	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂×#529	C₂×C₃₁	1	1	yes	characteristic
360	C₂²×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	2	no	—
363	C₂²×C₃₁	—	2	8	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	2	4	no	—
366	C₂²×C₃₁	—	2	4	no	—
367	C₂²×C₃₁	—	4	8	no	—
368	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	—
369	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
370	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
371	C₂²×C₃₁	#585	1	2	yes	—
372	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
373	C₄×C₃₁	—	2	2	no	—
374	C₄×C₃₁	—	2	2	no	—
375	C₄×C₃₁	—	2	8	no	—
376	C₄×C₃₁	—	2	2	no	—
377	C₄×C₃₁	—	2	4	no	—
378	C₄×C₃₁	—	2	4	no	—
379	C₄×C₃₁	—	2	8	no	—
380	C₄×C₃₁	—	2	8	no	—
381	C₄×C₃₁	—	2	2	no	—
382	C₄×C₃₁	—	2	8	no	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	4	no	—
385	C₄×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	—
386	#564	C₂²×C₃₁	1	32	yes	complemented
387	#563	C₂²×C₃₁	1	32	yes	complemented
388	#557	C₂²×C₃₁	1	32	yes	complemented
389	#554	C₂²×C₃₁	1	32	yes	complemented
390	#552	C₂²×C₃₁	1	64	yes	complemented
391	#552	C₂²×C₃₁	1	32	yes	complemented
392	#552	C₂²×C₃₁	1	32	yes	complemented
393	#544	C₂²×C₃₁	1	32	yes	complemented
394	#544	C₂²×C₃₁	1	32	yes	complemented
395	#541	C₂²×C₃₁	1	32	yes	complemented
396	#541	C₂²×C₃₁	1	64	yes	complemented
397	#539	C₂²×C₃₁	1	32	yes	—
398	#533	C₂²×C₃₁	1	16	yes	complemented
399	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
400	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
402	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
403	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
404	#529	C₂²×C₃₁	1	16	yes	—
405	C₂×#126	C₂²×C₃₁	1	2	yes	—
406	C₂×#126	C₂²×C₃₁	1	4	yes	—
407	C₂×#126	C₂²×C₃₁	1	4	yes	—
408	C₂×#126	C₂²×C₃₁	1	4	yes	—
409	C₂×#126	C₂²×C₃₁	1	4	yes	—
410	C₂×#125	C₂²×C₃₁	1	2	yes	—
411	C₂×#125	C₂²×C₃₁	1	2	yes	—
412	C₂×#125	C₂²×C₃₁	1	2	yes	—
413	C₂×#125	C₂²×C₃₁	1	2	yes	—
414	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
415	C₂×#125	C₂²×C₃₁	1	2	yes	—
416	C₂×#125	C₂²×C₃₁	1	4	yes	—
417	C₂×#125	C₂²×C₃₁	1	4	yes	—
418	C₂×#125	C₂²×C₃₁	1	4	yes	—
419	C₂×#125	C₂²×C₃₁	1	4	yes	—
420	C₂×#125	C₂²×C₃₁	1	4	yes	—
421	C₂×#125	C₂²×C₃₁	1	4	yes	—
422	C₂×#125	C₂²×C₃₁	1	2	yes	—
423	C₂×#125	C₂²×C₃₁	1	4	yes	—
424	C₂×#125	C₂²×C₃₁	1	4	yes	—
425	C₂×#125	C₂²×C₃₁	1	16	yes	complemented
426	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
427	C₂×#123	C₂²×C₃₁	1	2	yes	—
428	C₂×#123	C₂²×C₃₁	1	4	yes	—
429	C₂×#123	C₂²×C₃₁	1	4	yes	—
430	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
432	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
433	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
434	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
435	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
436	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
437	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
438	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
439	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
440	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
442	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
443	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	—
444	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
446	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
449	C₂×#117	C₂²×C₃₁	1	2	yes	—
450	C₂×#117	C₂²×C₃₁	1	2	yes	—
451	C₂×#117	C₂²×C₃₁	1	4	yes	—
452	C₂×#117	C₂²×C₃₁	1	2	yes	—
453	C₂×#117	C₂²×C₃₁	1	4	yes	—
454	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
455	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
457	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
458	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
459	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×C₃₁	—	2	4	no	—
461	C₂×C₃₁	—	4	4	no	—
462	C₂×C₃₁	#3563	1	4	yes	direct product factor
463	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
465	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
467	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
468	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
469	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
471	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
473	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
476	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
477	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
479	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
480	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
481	C₄⋊Q₈	C₂³×C₃₁	1	32	yes	—
482	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	—
483	C₄⋊Q₈	C₂³×C₃₁	1	32	yes	—
484	#126	C₂³×C₃₁	1	16	yes	—
485	#126	C₂³×C₃₁	1	32	yes	—
486	#126	C₂³×C₃₁	1	32	yes	—
487	#126	C₂³×C₃₁	1	32	yes	—
488	#126	C₂³×C₃₁	1	32	yes	—
489	#125	C₂³×C₃₁	1	16	yes	—
490	#125	C₂³×C₃₁	1	16	yes	—
491	#125	C₂³×C₃₁	1	16	yes	—
492	#125	C₂³×C₃₁	1	16	yes	—
493	#125	C₂³×C₃₁	1	8	yes	—
494	#125	C₂³×C₃₁	1	16	yes	—
495	#125	C₂³×C₃₁	1	32	yes	—
496	#125	C₂³×C₃₁	1	32	yes	—
497	#125	C₂³×C₃₁	1	32	yes	—
498	#125	C₂³×C₃₁	1	32	yes	—
499	#125	C₂³×C₃₁	1	32	yes	—
500	#125	C₂³×C₃₁	1	32	yes	—
501	#125	C₂³×C₃₁	1	16	yes	—
502	#125	C₂³×C₃₁	1	32	yes	—
503	#125	C₂³×C₃₁	1	32	yes	—
504	#124	C₂³×C₃₁	1	8	yes	—
505	#123	C₂³×C₃₁	1	16	yes	—
506	#123	C₂³×C₃₁	1	32	yes	—
507	#123	C₂³×C₃₁	1	32	yes	—
508	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
509	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
510	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
511	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
513	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
514	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
515	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
516	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
517	#121	C₂³×C₃₁	1	8	yes	—
518	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
519	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
520	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
521	C₄×Q₈	C₂³×C₃₁	1	32	yes	—
522	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
524	C₄×D₄	C₂³×C₃₁	1	8	yes	—
525	C₄×D₄	C₂³×C₃₁	1	16	yes	—
526	C₄×D₄	C₂³×C₃₁	1	32	yes	—
527	#117	C₂³×C₃₁	1	16	yes	—
528	#117	C₂³×C₃₁	1	16	yes	—
529	#117	C₂³×C₃₁	1	32	yes	—
530	#117	C₂³×C₃₁	1	16	yes	—
531	#117	C₂³×C₃₁	1	32	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
575	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
576	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
579	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
581	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
584	C₃₁	C₂×#3563	1	1	yes	characteristic, direct product factor, Sylow
585	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
586	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
587	C₂×Q₈	—	2	8	no	—
588	C₂×Q₈	—	4	8	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×Q₈	—	4	4	no	—
591	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
592	C₂×Q₈	C₂⁴×C₃₁	1	16	yes	—
593	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
594	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
598	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
599	C₂²×C₄	—	2	8	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	8	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
618	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
621	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
622	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
623	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
624	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
625	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
626	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
627	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
628	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
629	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
630	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
631	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
632	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
633	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
634	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
635	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
636	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
637	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
640	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
642	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
643	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
644	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
645	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
646	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
647	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
648	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
649	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
650	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
651	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
652	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
653	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
656	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
657	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
658	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
659	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
660	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
661	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
662	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
663	C₄²	C₂⁴×C₃₁	1	4	yes	—
664	C₄²	C₂⁴×C₃₁	1	4	yes	—
665	C₄²	C₂⁴×C₃₁	1	4	yes	—
666	C₄²	C₂⁴×C₃₁	1	4	yes	—
667	C₄²	C₂⁴×C₃₁	1	16	yes	—
668	C₄²	C₂⁴×C₃₁	1	16	yes	—
669	C₄²	C₂⁴×C₃₁	1	8	yes	—
670	C₄²	C₂⁴×C₃₁	1	16	yes	—
671	C₄²	C₂⁴×C₃₁	1	16	yes	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
678	C₂³	C₂⁵×C₃₁	1	4	yes	—
679	C₂³	C₂⁵×C₃₁	1	2	yes	—
680	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
681	Q₈	—	2	16	no	—
682	Q₈	—	4	16	no	—
683	Q₈	—	4	4	no	—
684	Q₈	—	4	8	no	—
685	D₄	—	2	16	no	—
686	D₄	—	4	4	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	16	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	16	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
707	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
708	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
709	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
710	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
711	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
712	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
713	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
714	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
715	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
716	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
717	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
718	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
719	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	8	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	4	8	no	—
727	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	—
728	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
729	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
730	C₂²	C₃₁×#585	1	2	yes	—
731	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	8	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	8	no	—
739	C₄	—	2	8	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	8	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	4	no	—
744	C₄	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	—
745	C₂	—	2	4	no	—
746	C₂	—	4	4	no	—
747	C₂	C₃₁×#3563	1	4	yes	direct product factor
748	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
749	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
750	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×#121	C₂²
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×#3563	C₂	direct (N × H)
2. C₂×C₃₁×#564	C₂	semidirect
3. C₂×C₃₁×#563	C₂	semidirect
4. C₂×C₃₁×#557	C₂	semidirect
5. C₂×C₃₁×#554	C₂	semidirect
6. C₂×C₃₁×#552	C₂	semidirect
7. C₂×C₃₁×#552	C₂	semidirect
8. C₂×C₃₁×#552	C₂	semidirect
9. C₂×C₃₁×#544	C₂	semidirect
10. C₂×C₃₁×#544	C₂	semidirect
11. C₂×C₃₁×#541	C₂	semidirect
12. C₂×C₃₁×#541	C₂	semidirect
14. C₂×C₃₁×#533	C₂	semidirect
16. C₂²×C₃₁×#125	C₂	semidirect
17. C₃₁×#564	C₂²	semidirect
18. C₃₁×#563	C₂²	semidirect
19. C₃₁×#557	C₂²	semidirect
20. C₃₁×#554	C₂²	semidirect
21. C₃₁×#552	C₂²	semidirect
22. C₃₁×#552	C₂²	semidirect
23. C₃₁×#552	C₂²	semidirect
24. C₃₁×#544	C₂²	semidirect
25. C₃₁×#544	C₂²	semidirect
26. C₃₁×#541	C₂²	semidirect
27. C₃₁×#541	C₂²	semidirect
29. C₃₁×#533	C₂²	semidirect
56. C₂×C₃₁×#125	C₂²	semidirect
296. C₂×#3563	C₃₁	direct (N × H)
345. #3563	C₂×C₃₁	direct (N × H)
346. C₂×#564	C₂×C₃₁	semidirect
347. C₂×#563	C₂×C₃₁	semidirect
348. C₂×#557	C₂×C₃₁	semidirect
349. C₂×#554	C₂×C₃₁	semidirect
350. C₂×#552	C₂×C₃₁	semidirect
351. C₂×#552	C₂×C₃₁	semidirect
352. C₂×#552	C₂×C₃₁	semidirect
353. C₂×#544	C₂×C₃₁	semidirect
354. C₂×#544	C₂×C₃₁	semidirect
355. C₂×#541	C₂×C₃₁	semidirect
356. C₂×#541	C₂×C₃₁	semidirect
358. C₂×#533	C₂×C₃₁	semidirect
360. C₂²×#125	C₂×C₃₁	semidirect
386. #564	C₂²×C₃₁	semidirect
387. #563	C₂²×C₃₁	semidirect
388. #557	C₂²×C₃₁	semidirect
389. #554	C₂²×C₃₁	semidirect
390. #552	C₂²×C₃₁	semidirect
391. #552	C₂²×C₃₁	semidirect
392. #552	C₂²×C₃₁	semidirect
393. #544	C₂²×C₃₁	semidirect
394. #544	C₂²×C₃₁	semidirect
395. #541	C₂²×C₃₁	semidirect
396. #541	C₂²×C₃₁	semidirect
398. #533	C₂²×C₃₁	semidirect
425. C₂×#125	C₂²×C₃₁	semidirect
462. C₂×C₃₁	#3563	direct (N × H)
584. C₃₁	C₂×#3563	direct (N × H)
747. C₂	C₃₁×#3563	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×#3563	2
C₂×C₃₁×#564	2
C₂×C₃₁×#563	2
C₂×C₃₁×#557	2
C₂×C₃₁×#554	2
C₂×C₃₁×#552	2
C₂×C₃₁×#544	2
C₂×C₃₁×#541	2
C₂×C₃₁×#539	2
C₂×C₃₁×#533	2
C₂×C₃₁×#529	2
C₂²×C₃₁×#125	2
C₂×#3563	31

Subgroups — C2×C31×#3563 #21519492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3563 #21519492