Subgroups — C₃₁×#34700 #21491459

Order 7936.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2480	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2468	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2457	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2454	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2447	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2435	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2427	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2420	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2418	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2417	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2408	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2395	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×#120	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2280	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#529	—	2	8	no	—
27	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
28	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#120	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₃₁	—	2	8	no	—
39	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
50	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
51	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
52	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
54	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#400	C₂²	1	2	yes	complemented
57	C₃₁×#399	C₂²	1	2	yes	complemented
58	C₃₁×#398	C₂²	1	2	yes	complemented
59	C₃₁×#398	C₂²	1	2	yes	complemented
60	C₃₁×#397	C₂²	1	2	yes	complemented
61	C₃₁×#397	C₂²	1	2	yes	complemented
62	C₃₁×#397	C₂²	1	2	yes	complemented
63	C₃₁×#397	C₂²	1	2	yes	complemented
64	C₃₁×#396	C₂²	1	2	yes	complemented
65	C₃₁×#396	C₂²	1	2	yes	complemented
66	C₃₁×#394	C₂²	1	2	yes	—
67	C₃₁×#394	C₂²	1	2	yes	—
68	C₃₁×#394	C₂²	1	2	yes	—
69	C₃₁×#394	C₂²	1	2	yes	complemented
70	C₃₁×#394	C₂²	1	2	yes	complemented
71	C₃₁×#392	C₂²	1	2	yes	—
72	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#390	C₂²	1	1	yes	characteristic
75	C₃₁×#390	C₂²	1	1	yes	characteristic
76	C₃₁×#390	C₂²	1	1	yes	characteristic
77	C₃₁×#390	C₂²	1	1	yes	characteristic
78	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#388	C₂²	1	2	yes	complemented
83	C₃₁×#388	C₂²	1	2	yes	complemented
84	C₃₁×#388	C₂²	1	2	yes	complemented
85	C₃₁×#388	C₂²	1	2	yes	complemented
86	C₃₁×#388	C₂²	1	2	yes	complemented
87	C₃₁×#387	C₂²	1	2	yes	complemented
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	2	yes	complemented
90	C₃₁×#386	C₂²	1	2	yes	complemented
91	C₃₁×#386	C₂²	1	2	yes	complemented
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	complemented
95	C₃₁×#385	C₂²	1	2	yes	complemented
96	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#381	C₂²	1	2	yes	complemented
98	C₃₁×#381	C₂²	1	2	yes	complemented
99	C₃₁×#380	C₂²	1	1	yes	characteristic
100	C₃₁×#380	C₂²	1	2	yes	—
101	C₃₁×#380	C₂²	1	2	yes	—
102	C₃₁×#380	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#380	C₂²	1	2	yes	complemented
104	C₃₁×#380	C₂²	1	2	yes	complemented
105	C₃₁×#379	C₂²	1	2	yes	—
106	C₃₁×#379	C₂²	1	2	yes	—
107	C₃₁×#379	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₄³×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₃₁	C₂³	1	2	yes	—
126	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	—	2	4	no	—
128	C₂²×D₄×C₃₁	—	2	4	no	—
129	C₂²×D₄×C₃₁	—	2	4	no	—
130	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
132	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₃₁	—	2	8	no	—
137	C₂³×C₄×C₃₁	—	2	8	no	—
138	C₂³×C₄×C₃₁	—	4	4	no	—
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
149	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₃₁×#126	—	2	8	no	—
151	C₃₁×#125	—	2	4	no	—
152	C₃₁×#124	—	2	4	no	—
153	C₃₁×#124	—	2	4	no	—
154	C₃₁×#123	—	2	8	no	—
155	C₃₁×C₂²⋊Q₈	—	2	4	no	—
156	C₃₁×C₂²⋊Q₈	—	2	4	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#120	—	2	8	no	—
160	C₄×Q₈×C₃₁	—	2	4	no	—
161	C₄×D₄×C₃₁	—	2	4	no	—
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₄×D₄×C₃₁	—	2	8	no	—
164	C₄×D₄×C₃₁	—	2	8	no	—
165	C₄×D₄×C₃₁	—	2	4	no	—
166	C₄×D₄×C₃₁	—	2	4	no	—
167	C₄×D₄×C₃₁	—	2	4	no	—
168	C₄×D₄×C₃₁	—	2	8	no	—
169	C₄×D₄×C₃₁	—	2	4	no	—
170	C₄×D₄×C₃₁	—	4	4	no	—
171	C₄×D₄×C₃₁	D₄	1	8	yes	complemented
172	C₃₁×#117	—	2	8	no	—
173	C₃₁×#117	—	4	4	no	—
174	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
222	C₂×C₄²×C₃₁	—	2	4	no	—
223	C₂×C₄²×C₃₁	—	2	4	no	—
224	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
236	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	1	yes	characteristic
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	1	yes	characteristic
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₃₁×#95	C₂³	1	2	yes	—
244	C₃₁×#95	C₂³	1	2	yes	—
245	C₃₁×#95	C₂³	1	2	yes	—
246	C₃₁×#95	C₂³	1	2	yes	—
247	C₃₁×#95	C₂³	1	2	yes	—
248	C₃₁×#95	C₂³	1	1	yes	characteristic
249	C₃₁×#95	C₂³	1	2	yes	—
250	C₃₁×#95	C₂³	1	2	yes	—
251	C₃₁×#95	C₂³	1	2	yes	—
252	C₃₁×#95	C₂³	1	1	yes	characteristic
253	C₃₁×#95	C₂³	1	1	yes	characteristic
254	C₃₁×#95	C₂³	1	1	yes	characteristic
255	C₃₁×#95	C₂³	1	2	yes	—
256	C₃₁×#95	C₂³	1	2	yes	—
257	C₃₁×#95	C₂³	1	2	yes	—
258	C₂⁴×C₃₁	—	2	4	no	—
259	C₂⁴×C₃₁	—	2	4	no	—
260	C₂⁴×C₃₁	—	2	4	no	—
261	C₂⁴×C₃₁	—	2	4	no	—
262	C₂⁴×C₃₁	—	2	4	no	—
263	C₂⁴×C₃₁	—	4	2	no	—
264	C₂⁴×C₃₁	—	4	2	no	—
265	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
266	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
267	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂×Q₈×C₃₁	—	2	2	no	—
270	C₂×Q₈×C₃₁	—	2	2	no	—
271	C₂×Q₈×C₃₁	—	2	2	no	—
272	C₂×D₄×C₃₁	—	2	32	no	—
273	C₂×D₄×C₃₁	—	2	4	no	—
274	C₂×D₄×C₃₁	—	2	2	no	—
275	C₂×D₄×C₃₁	—	2	2	no	—
276	C₂×D₄×C₃₁	—	2	4	no	—
277	C₂×D₄×C₃₁	—	2	4	no	—
278	C₂×D₄×C₃₁	—	2	4	no	—
279	C₂×D₄×C₃₁	—	2	4	no	—
280	C₂×D₄×C₃₁	—	2	4	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	4	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	—	2	2	no	—
286	C₂×D₄×C₃₁	—	4	2	no	—
287	C₂×D₄×C₃₁	—	4	2	no	—
288	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
289	C₂×D₄×C₃₁	#41	1	4	yes	—
290	C₂×D₄×C₃₁	#41	1	4	yes	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	4	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	4	no	—
296	C₂²×C₄×C₃₁	—	2	2	no	—
297	C₂²×C₄×C₃₁	—	2	4	no	—
298	C₂²×C₄×C₃₁	—	2	2	no	—
299	C₂²×C₄×C₃₁	—	2	2	no	—
300	C₂²×C₄×C₃₁	—	2	4	no	—
301	C₂²×C₄×C₃₁	—	2	2	no	—
302	C₂²×C₄×C₃₁	—	2	2	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	2	2	no	—
305	C₂²×C₄×C₃₁	—	2	4	no	—
306	C₂²×C₄×C₃₁	—	2	4	no	—
307	C₂²×C₄×C₃₁	—	2	4	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	2	no	—
311	C₂²×C₄×C₃₁	—	2	4	no	—
312	C₂²×C₄×C₃₁	—	2	4	no	—
313	C₂²×C₄×C₃₁	—	2	4	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	4	no	—
316	C₂²×C₄×C₃₁	—	4	2	no	—
317	C₂²×C₄×C₃₁	—	4	2	no	—
318	C₂²×C₄×C₃₁	—	4	2	no	—
319	C₂²×C₄×C₃₁	—	4	1	no	—
320	C₂²×C₄×C₃₁	—	4	1	no	—
321	C₂²×C₄×C₃₁	—	4	32	no	—
322	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
323	C₂²×C₄×C₃₁	#41	1	4	yes	—
324	C₂²×C₄×C₃₁	#41	1	4	yes	—
325	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₄⋊C₄×C₃₁	—	2	4	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	4	no	—
347	C₄⋊C₄×C₃₁	—	2	4	no	—
348	C₄⋊C₄×C₃₁	—	2	4	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	4	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	4	no	—
357	C₄⋊C₄×C₃₁	—	4	2	no	—
358	C₄⋊C₄×C₃₁	—	4	2	no	—
359	C₄⋊C₄×C₃₁	—	4	2	no	—
360	C₄⋊C₄×C₃₁	—	4	2	no	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
362	C₂²⋊C₄×C₃₁	—	2	4	no	—
363	C₂²⋊C₄×C₃₁	—	2	4	no	—
364	C₂²⋊C₄×C₃₁	—	2	4	no	—
365	C₂²⋊C₄×C₃₁	—	2	4	no	—
366	C₂²⋊C₄×C₃₁	—	2	2	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	4	no	—
371	C₂²⋊C₄×C₃₁	—	2	4	no	—
372	C₂²⋊C₄×C₃₁	—	2	4	no	—
373	C₂²⋊C₄×C₃₁	—	2	4	no	—
374	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	4	no	—
381	C₂²⋊C₄×C₃₁	—	2	4	no	—
382	C₂²⋊C₄×C₃₁	—	4	2	no	—
383	C₂²⋊C₄×C₃₁	—	4	2	no	—
384	C₂²⋊C₄×C₃₁	—	4	2	no	—
385	C₂²⋊C₄×C₃₁	—	4	2	no	—
386	C₂²⋊C₄×C₃₁	—	4	2	no	—
387	C₂²⋊C₄×C₃₁	—	4	2	no	—
388	C₂²⋊C₄×C₃₁	—	4	2	no	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	2	no	—
392	C₄²×C₃₁	—	2	2	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	4	no	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	—	2	2	no	—
400	C₄²×C₃₁	—	2	2	no	—
401	C₄²×C₃₁	—	2	2	no	—
402	C₄²×C₃₁	—	2	4	no	—
403	C₄²×C₃₁	—	4	1	no	—
404	C₄²×C₃₁	C₂×D₄	1	4	yes	—
405	#34700	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂³×C₃₁	—	2	1	no	—
407	C₂³×C₃₁	—	2	1	no	—
408	C₂³×C₃₁	—	2	1	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	16	no	—
411	C₂³×C₃₁	—	2	1	no	—
412	C₂³×C₃₁	—	2	2	no	—
413	C₂³×C₃₁	—	2	1	no	—
414	C₂³×C₃₁	—	2	1	no	—
415	C₂³×C₃₁	—	2	2	no	—
416	C₂³×C₃₁	—	2	2	no	—
417	C₂³×C₃₁	—	2	2	no	—
418	C₂³×C₃₁	—	2	2	no	—
419	C₂³×C₃₁	—	2	1	no	—
420	C₂³×C₃₁	—	2	2	no	—
421	C₂³×C₃₁	—	2	2	no	—
422	C₂³×C₃₁	—	2	2	no	—
423	C₂³×C₃₁	—	2	2	no	—
424	C₂³×C₃₁	—	2	1	no	—
425	C₂³×C₃₁	—	2	2	no	—
426	C₂³×C₃₁	—	2	2	no	—
427	C₂³×C₃₁	—	2	2	no	—
428	C₂³×C₃₁	—	2	1	no	—
429	C₂³×C₃₁	—	4	8	no	—
430	C₂³×C₃₁	—	4	8	no	—
431	C₂³×C₃₁	—	4	8	no	—
432	C₂³×C₃₁	—	4	8	no	—
433	C₂³×C₃₁	—	4	8	no	—
434	C₂³×C₃₁	—	4	8	no	—
435	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
436	C₂³×C₃₁	C₂×#41	1	4	yes	—
437	C₂³×C₃₁	C₂×#41	1	2	yes	—
438	C₂³×C₃₁	C₂×#41	1	2	yes	—
439	C₂³×C₃₁	C₂×#41	1	2	yes	—
440	C₂³×C₃₁	C₂×#41	1	2	yes	—
441	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
442	Q₈×C₃₁	—	4	4	no	—
443	D₄×C₃₁	—	2	16	no	—
444	D₄×C₃₁	—	2	8	no	—
445	D₄×C₃₁	—	2	8	no	—
446	D₄×C₃₁	—	2	8	no	—
447	D₄×C₃₁	—	4	8	no	—
448	D₄×C₃₁	—	4	8	no	—
449	C₂×C₄×C₃₁	—	2	1	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	2	1	no	—
452	C₂×C₄×C₃₁	—	2	1	no	—
453	C₂×C₄×C₃₁	—	2	1	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	1	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	1	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	8	no	—
460	C₂×C₄×C₃₁	—	2	8	no	—
461	C₂×C₄×C₃₁	—	2	16	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	4	8	no	—
499	C₂×C₄×C₃₁	—	4	4	no	—
500	C₂×C₄×C₃₁	—	4	4	no	—
501	C₂×C₄×C₃₁	—	4	8	no	—
502	C₂×C₄×C₃₁	—	4	8	no	—
503	C₂×C₄×C₃₁	—	4	4	no	—
504	C₂×C₄×C₃₁	—	4	4	no	—
505	C₂×C₄×C₃₁	—	4	8	no	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
511	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
512	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
513	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
514	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
515	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
516	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
517	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
518	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#2480	C₂×C₃₁	1	2	yes	complemented
520	#2468	C₂×C₃₁	1	2	yes	complemented
521	#2457	C₂×C₃₁	1	2	yes	complemented
522	#2454	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#2447	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#2442	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#2435	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#2427	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#2420	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#2418	C₂×C₃₁	1	2	yes	complemented
529	#2417	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#2408	C₂×C₃₁	1	1	yes	characteristic
531	#2395	C₂×C₃₁	1	2	yes	complemented
532	#2392	C₂×C₃₁	1	2	yes	complemented
533	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
534	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
535	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
536	C₄×#120	C₂×C₃₁	1	2	yes	complemented
537	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#2280	C₂×C₃₁	1	2	yes	complemented
539	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
540	C₂²×C₃₁	—	2	2	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	4	no	—
547	C₂²×C₃₁	—	2	4	no	—
548	C₂²×C₃₁	—	2	2	no	—
549	C₂²×C₃₁	—	2	4	no	—
550	C₂²×C₃₁	—	2	2	no	—
551	C₂²×C₃₁	—	2	4	no	—
552	C₂²×C₃₁	—	2	4	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	4	no	—
555	C₂²×C₃₁	—	4	32	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	2	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	2	no	—
567	C₂²×C₃₁	—	4	2	no	—
568	C₂²×C₃₁	#529	1	4	yes	complemented
569	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
570	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
571	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
572	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
573	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
574	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂²×C₃₁	#585	1	1	yes	characteristic
576	C₄×C₃₁	—	2	2	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	2	4	no	—
580	C₄×C₃₁	—	2	2	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	2	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	2	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	2	no	—
593	C₄×C₃₁	#525	1	4	yes	—
594	C₄×C₃₁	#546	1	4	yes	—
595	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
596	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
597	#529	—	2	8	no	—
598	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
599	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
601	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
602	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
603	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
607	C₂×#120	C₂²×C₃₁	1	2	yes	—
608	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	C₂×C₄×D₄	—	2	8	no	—
610	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
611	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
614	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
620	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
621	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
622	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
623	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
624	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
625	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
626	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#400	C₂²×C₃₁	1	2	yes	complemented
628	#399	C₂²×C₃₁	1	2	yes	complemented
629	#398	C₂²×C₃₁	1	2	yes	complemented
630	#398	C₂²×C₃₁	1	2	yes	complemented
631	#397	C₂²×C₃₁	1	2	yes	complemented
632	#397	C₂²×C₃₁	1	2	yes	complemented
633	#397	C₂²×C₃₁	1	2	yes	complemented
634	#397	C₂²×C₃₁	1	2	yes	complemented
635	#396	C₂²×C₃₁	1	2	yes	complemented
636	#396	C₂²×C₃₁	1	2	yes	complemented
637	#394	C₂²×C₃₁	1	2	yes	—
638	#394	C₂²×C₃₁	1	2	yes	—
639	#394	C₂²×C₃₁	1	2	yes	—
640	#394	C₂²×C₃₁	1	2	yes	complemented
641	#394	C₂²×C₃₁	1	2	yes	complemented
642	#392	C₂²×C₃₁	1	2	yes	—
643	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#390	C₂²×C₃₁	1	1	yes	characteristic
646	#390	C₂²×C₃₁	1	1	yes	characteristic
647	#390	C₂²×C₃₁	1	1	yes	characteristic
648	#390	C₂²×C₃₁	1	1	yes	characteristic
649	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#388	C₂²×C₃₁	1	2	yes	complemented
654	#388	C₂²×C₃₁	1	2	yes	complemented
655	#388	C₂²×C₃₁	1	2	yes	complemented
656	#388	C₂²×C₃₁	1	2	yes	complemented
657	#388	C₂²×C₃₁	1	2	yes	complemented
658	#387	C₂²×C₃₁	1	2	yes	complemented
659	#386	C₂²×C₃₁	1	2	yes	—
660	#386	C₂²×C₃₁	1	2	yes	complemented
661	#386	C₂²×C₃₁	1	2	yes	complemented
662	#386	C₂²×C₃₁	1	2	yes	complemented
663	#385	C₂²×C₃₁	1	2	yes	—
664	#385	C₂²×C₃₁	1	2	yes	—
665	#385	C₂²×C₃₁	1	2	yes	complemented
666	#385	C₂²×C₃₁	1	2	yes	complemented
667	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#381	C₂²×C₃₁	1	2	yes	complemented
669	#381	C₂²×C₃₁	1	2	yes	complemented
670	#380	C₂²×C₃₁	1	1	yes	characteristic
671	#380	C₂²×C₃₁	1	2	yes	—
672	#380	C₂²×C₃₁	1	2	yes	—
673	#380	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#380	C₂²×C₃₁	1	2	yes	complemented
675	#380	C₂²×C₃₁	1	2	yes	complemented
676	#379	C₂²×C₃₁	1	2	yes	—
677	#379	C₂²×C₃₁	1	2	yes	—
678	#379	C₂²×C₃₁	1	2	yes	—
679	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
680	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
685	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
687	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
688	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
690	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
691	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
692	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
693	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	C₄³	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	C₂×C₃₁	—	2	4	no	—
697	C₂×C₃₁	—	4	2	no	—
698	C₂×C₃₁	—	4	4	no	—
699	C₂×C₃₁	—	4	4	no	—
700	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
701	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
702	C₂×C₃₁	#3460	1	1	yes	characteristic
703	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
704	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
705	C₂×C₃₁	#3475	1	1	yes	characteristic
706	C₂×C₃₁	#3481	1	1	yes	characteristic
707	C₂⁵	C₂³×C₃₁	1	2	yes	—
708	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂²×D₄	—	2	4	no	—
710	C₂²×D₄	—	2	4	no	—
711	C₂²×D₄	—	2	4	no	—
712	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
713	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
714	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
715	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
716	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
717	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
718	C₂³×C₄	—	2	8	no	—
719	C₂³×C₄	—	2	8	no	—
720	C₂³×C₄	—	4	4	no	—
721	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
722	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
726	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
727	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
728	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
729	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
730	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
732	#126	—	2	8	no	—
733	#125	—	2	4	no	—
734	#124	—	2	4	no	—
735	#124	—	2	4	no	—
736	#123	—	2	8	no	—
737	C₂²⋊Q₈	—	2	4	no	—
738	C₂²⋊Q₈	—	2	4	no	—
739	#121	—	2	4	no	—
740	#121	—	2	4	no	—
741	#120	—	2	8	no	—
742	C₄×Q₈	—	2	4	no	—
743	C₄×D₄	—	2	4	no	—
744	C₄×D₄	—	2	4	no	—
745	C₄×D₄	—	2	8	no	—
746	C₄×D₄	—	2	8	no	—
747	C₄×D₄	—	2	4	no	—
748	C₄×D₄	—	2	4	no	—
749	C₄×D₄	—	2	4	no	—
750	C₄×D₄	—	2	8	no	—
751	C₄×D₄	—	2	4	no	—
752	C₄×D₄	—	4	4	no	—
753	C₄×D₄	D₄×C₃₁	1	8	yes	complemented
754	#117	—	2	8	no	—
755	#117	—	4	4	no	—
756	C₂×C₄⋊C₄	—	2	4	no	—
757	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
766	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
775	C₂×C₂²⋊C₄	—	2	8	no	—
776	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
782	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
804	C₂×C₄²	—	2	4	no	—
805	C₂×C₄²	—	2	4	no	—
806	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
807	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
809	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
810	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
812	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
816	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
817	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
821	#95	C₂³×C₃₁	1	1	yes	characteristic
822	#95	C₂³×C₃₁	1	1	yes	characteristic
823	#95	C₂³×C₃₁	1	1	yes	characteristic
824	#95	C₂³×C₃₁	1	1	yes	characteristic
825	#95	C₂³×C₃₁	1	1	yes	characteristic
826	#95	C₂³×C₃₁	1	1	yes	characteristic
827	#95	C₂³×C₃₁	1	2	yes	—
828	#95	C₂³×C₃₁	1	2	yes	—
829	#95	C₂³×C₃₁	1	2	yes	—
830	#95	C₂³×C₃₁	1	2	yes	—
831	#95	C₂³×C₃₁	1	2	yes	—
832	#95	C₂³×C₃₁	1	2	yes	—
833	#95	C₂³×C₃₁	1	2	yes	—
834	#95	C₂³×C₃₁	1	2	yes	—
835	#95	C₂³×C₃₁	1	2	yes	—
836	#95	C₂³×C₃₁	1	2	yes	—
837	#95	C₂³×C₃₁	1	2	yes	—
838	#95	C₂³×C₃₁	1	2	yes	—
839	#95	C₂³×C₃₁	1	2	yes	—
840	C₃₁	#34700	1	1	yes	characteristic, direct product factor, Sylow
841	C₂⁴	—	2	4	no	—
842	C₂⁴	—	2	4	no	—
843	C₂⁴	—	2	4	no	—
844	C₂⁴	—	2	4	no	—
845	C₂⁴	—	2	4	no	—
846	C₂⁴	—	4	2	no	—
847	C₂⁴	—	4	2	no	—
848	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
849	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
850	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
851	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×D₄	—	2	32	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	2	4	no	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	4	no	—
863	C₂×D₄	—	2	4	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	4	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
872	C₂×D₄	#41×C₃₁	1	4	yes	—
873	C₂×D₄	#41×C₃₁	1	4	yes	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	4	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	4	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	4	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	4	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	4	no	—
889	C₂²×C₄	—	2	4	no	—
890	C₂²×C₄	—	2	4	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	4	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	1	no	—
903	C₂²×C₄	—	4	1	no	—
904	C₂²×C₄	—	4	32	no	—
905	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
906	C₂²×C₄	#41×C₃₁	1	4	yes	—
907	C₂²×C₄	#41×C₃₁	1	4	yes	—
908	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	4	no	—
930	C₄⋊C₄	—	2	4	no	—
931	C₄⋊C₄	—	2	4	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	4	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	4	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	4	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	4	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	4	no	—
986	C₄²	—	4	1	no	—
987	C₄²	C₂×D₄×C₃₁	1	4	yes	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	16	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	4	8	no	—
1012	C₂³	—	4	8	no	—
1013	C₂³	—	4	8	no	—
1014	C₂³	—	4	8	no	—
1015	C₂³	—	4	8	no	—
1016	C₂³	—	4	8	no	—
1017	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
1018	C₂³	C₂×#41×C₃₁	1	4	yes	—
1019	C₂³	C₂×#41×C₃₁	1	2	yes	—
1020	C₂³	C₂×#41×C₃₁	1	2	yes	—
1021	C₂³	C₂×#41×C₃₁	1	2	yes	—
1022	C₂³	C₂×#41×C₃₁	1	2	yes	—
1023	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1024	Q₈	—	4	4	no	—
1025	D₄	—	2	16	no	—
1026	D₄	—	2	8	no	—
1027	D₄	—	2	8	no	—
1028	D₄	—	2	8	no	—
1029	D₄	—	4	8	no	—
1030	D₄	—	4	8	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	8	no	—
1042	C₂×C₄	—	2	8	no	—
1043	C₂×C₄	—	2	16	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	4	8	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	4	no	—
1083	C₂×C₄	—	4	8	no	—
1084	C₂×C₄	—	4	8	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	8	no	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
1090	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1092	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1093	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1094	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1095	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1096	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1097	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1098	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	4	no	—
1106	C₂²	—	2	4	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	4	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	4	no	—
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	4	no	—
1114	C₂²	—	4	32	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	C₃₁×#529	1	4	yes	complemented
1128	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1129	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1130	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1131	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1132	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1133	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1134	C₂²	C₃₁×#585	1	1	yes	characteristic
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	4	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	C₃₁×#525	1	4	yes	—
1153	C₄	C₃₁×#546	1	4	yes	—
1154	C₂	—	2	4	no	—
1155	C₂	—	4	4	no	—
1156	C₂	—	4	4	no	—
1157	C₂	—	4	2	no	—
1158	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1159	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
1160	C₂	C₃₁×#3460	1	1	yes	characteristic
1161	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
1162	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1163	C₂	C₃₁×#3475	1	1	yes	characteristic
1164	C₂	C₃₁×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₃₁×#2408	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#529	C₂	semidirect
2. C₂²×C₄×D₄×C₃₁	C₂	semidirect
3. C₃₁×#2480	C₂	semidirect
4. C₃₁×#2468	C₂	semidirect
5. C₃₁×#2457	C₂	semidirect
6. C₃₁×#2454	C₂	semidirect
7. C₃₁×#2447	C₂	semidirect
8. C₃₁×#2442	C₂	semidirect
9. C₃₁×#2435	C₂	semidirect
10. C₃₁×#2427	C₂	semidirect
11. C₃₁×#2420	C₂	semidirect
12. C₃₁×#2418	C₂	semidirect
13. C₃₁×#2417	C₂	semidirect
15. C₃₁×#2395	C₂	semidirect
16. C₃₁×#2392	C₂	semidirect
17. C₄×C₃₁×#124	C₂	semidirect
18. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₃₁×#121	C₂	semidirect
20. C₄×C₃₁×#120	C₂	semidirect
21. C₃₁×#2293	C₂	semidirect
22. C₃₁×#2280	C₂	semidirect
23. C₄²×D₄×C₃₁	C₂	semidirect
27. C₂×C₃₁×#126	C₂²	semidirect
28. C₂×C₃₁×#125	C₂²	semidirect
31. C₂×C₃₁×#123	C₂²	semidirect
33. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
48. C₂×C₄×D₄×C₃₁	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₂×C₃₁×#117	C₂²	semidirect
51. C₂×C₃₁×#117	C₂²	semidirect
55. C₂²×C₄²×C₃₁	C₂²	semidirect
56. C₃₁×#400	C₂²	semidirect
57. C₃₁×#399	C₂²	semidirect
58. C₃₁×#398	C₂²	semidirect
59. C₃₁×#398	C₂²	semidirect
60. C₃₁×#397	C₂²	semidirect
61. C₃₁×#397	C₂²	semidirect
62. C₃₁×#397	C₂²	semidirect
63. C₃₁×#397	C₂²	semidirect
64. C₃₁×#396	C₂²	semidirect
65. C₃₁×#396	C₂²	semidirect
69. C₃₁×#394	C₂²	semidirect
70. C₃₁×#394	C₂²	semidirect
72. C₃₁×#391	C₂²	semidirect
73. C₃₁×#391	C₂²	semidirect
78. C₃₁×#389	C₂²	semidirect
79. C₃₁×#389	C₂²	semidirect
80. C₃₁×#389	C₂²	semidirect
81. C₃₁×#389	C₂²	semidirect
82. C₃₁×#388	C₂²	semidirect
83. C₃₁×#388	C₂²	semidirect
84. C₃₁×#388	C₂²	semidirect
85. C₃₁×#388	C₂²	semidirect
86. C₃₁×#388	C₂²	semidirect
87. C₃₁×#387	C₂²	semidirect
89. C₃₁×#386	C₂²	semidirect
90. C₃₁×#386	C₂²	semidirect
91. C₃₁×#386	C₂²	semidirect
94. C₃₁×#385	C₂²	semidirect
95. C₃₁×#385	C₂²	semidirect
96. C₃₁×#382	C₂²	semidirect
97. C₃₁×#381	C₂²	semidirect
98. C₃₁×#381	C₂²	semidirect
102. C₃₁×#380	C₂²	semidirect
103. C₃₁×#380	C₂²	semidirect
104. C₃₁×#380	C₂²	semidirect
108. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
109. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
110. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
111. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
112. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
124. C₄³×C₃₁	C₂²	semidirect
171. C₄×D₄×C₃₁	D₄	semidirect
405. #34700	C₃₁	direct (N × H)
517. C₂×#529	C₂×C₃₁	semidirect
518. C₂²×C₄×D₄	C₂×C₃₁	semidirect
519. #2480	C₂×C₃₁	semidirect
520. #2468	C₂×C₃₁	semidirect
521. #2457	C₂×C₃₁	semidirect
522. #2454	C₂×C₃₁	semidirect
523. #2447	C₂×C₃₁	semidirect
524. #2442	C₂×C₃₁	semidirect
525. #2435	C₂×C₃₁	semidirect
526. #2427	C₂×C₃₁	semidirect
527. #2420	C₂×C₃₁	semidirect
528. #2418	C₂×C₃₁	semidirect
529. #2417	C₂×C₃₁	semidirect
531. #2395	C₂×C₃₁	semidirect
532. #2392	C₂×C₃₁	semidirect
533. C₄×#124	C₂×C₃₁	semidirect
534. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
535. C₄×#121	C₂×C₃₁	semidirect
536. C₄×#120	C₂×C₃₁	semidirect
537. #2293	C₂×C₃₁	semidirect
538. #2280	C₂×C₃₁	semidirect
539. C₄²×D₄	C₂×C₃₁	semidirect
568. C₂²×C₃₁	#529	semidirect
598. C₂×#126	C₂²×C₃₁	semidirect
599. C₂×#125	C₂²×C₃₁	semidirect
602. C₂×#123	C₂²×C₃₁	semidirect
604. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
608. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
619. C₂×C₄×D₄	C₂²×C₃₁	semidirect
620. C₂×C₄×D₄	C₂²×C₃₁	semidirect
621. C₂×#117	C₂²×C₃₁	semidirect
622. C₂×#117	C₂²×C₃₁	semidirect
626. C₂²×C₄²	C₂²×C₃₁	semidirect
627. #400	C₂²×C₃₁	semidirect
628. #399	C₂²×C₃₁	semidirect
629. #398	C₂²×C₃₁	semidirect
630. #398	C₂²×C₃₁	semidirect
631. #397	C₂²×C₃₁	semidirect
632. #397	C₂²×C₃₁	semidirect
633. #397	C₂²×C₃₁	semidirect
634. #397	C₂²×C₃₁	semidirect
635. #396	C₂²×C₃₁	semidirect
636. #396	C₂²×C₃₁	semidirect
640. #394	C₂²×C₃₁	semidirect
641. #394	C₂²×C₃₁	semidirect
643. #391	C₂²×C₃₁	semidirect
644. #391	C₂²×C₃₁	semidirect
649. #389	C₂²×C₃₁	semidirect
650. #389	C₂²×C₃₁	semidirect
651. #389	C₂²×C₃₁	semidirect
652. #389	C₂²×C₃₁	semidirect
653. #388	C₂²×C₃₁	semidirect
654. #388	C₂²×C₃₁	semidirect
655. #388	C₂²×C₃₁	semidirect
656. #388	C₂²×C₃₁	semidirect
657. #388	C₂²×C₃₁	semidirect
658. #387	C₂²×C₃₁	semidirect
660. #386	C₂²×C₃₁	semidirect
661. #386	C₂²×C₃₁	semidirect
662. #386	C₂²×C₃₁	semidirect
665. #385	C₂²×C₃₁	semidirect
666. #385	C₂²×C₃₁	semidirect
667. #382	C₂²×C₃₁	semidirect
668. #381	C₂²×C₃₁	semidirect
669. #381	C₂²×C₃₁	semidirect
673. #380	C₂²×C₃₁	semidirect
674. #380	C₂²×C₃₁	semidirect
675. #380	C₂²×C₃₁	semidirect
679. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
680. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
681. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
682. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
683. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
688. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
690. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
691. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
692. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
693. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
694. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
695. C₄³	C₂²×C₃₁	semidirect
753. C₄×D₄	D₄×C₃₁	semidirect
840. C₃₁	#34700	direct (N × H)
1127. C₂²	C₃₁×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#529	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2480	2
C₃₁×#2468	2
C₃₁×#2457	2
C₃₁×#2454	2
C₃₁×#2447	2
C₃₁×#2442	2
C₃₁×#2435	2
C₃₁×#2427	2
C₃₁×#2420	2
C₃₁×#2418	2
C₃₁×#2417	2
C₃₁×#2408	2
C₃₁×#2395	2
C₃₁×#2392	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₄×C₃₁×#120	2
C₃₁×#2293	2
C₃₁×#2280	2
C₄²×D₄×C₃₁	2
#34700	31

Subgroups — C31×#34700 #21491459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34700 #21491459