Subgroups — C₃₁×#34477 #21491236

Order 7936.

2568 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2380	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2364	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2333	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2328	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#550	C₄	1	16	yes	complemented
27	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#127	C₂²	1	2	yes	—
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	2	yes	—
32	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#391	C₂²	1	1	yes	characteristic
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#391	C₂²	1	1	yes	characteristic
50	C₃₁×#391	C₂²	1	1	yes	characteristic
51	C₃₁×#390	C₂²	1	1	yes	characteristic
52	C₃₁×#390	C₂²	1	1	yes	characteristic
53	C₃₁×#390	C₂²	1	2	yes	—
54	C₃₁×#390	C₂²	1	1	yes	characteristic
55	C₃₁×#390	C₂²	1	2	yes	—
56	C₃₁×#390	C₂²	1	2	yes	—
57	C₃₁×#390	C₂²	1	1	yes	characteristic
58	C₃₁×#389	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#388	C₂²	1	2	yes	—
61	C₃₁×#388	C₂²	1	2	yes	—
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	2	yes	—
64	C₃₁×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	1	yes	characteristic
66	C₃₁×#388	C₂²	1	1	yes	characteristic
67	C₃₁×#387	C₂²	1	1	yes	characteristic
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	1	yes	characteristic
74	C₃₁×#386	C₂²	1	2	yes	—
75	C₃₁×#386	C₂²	1	2	yes	—
76	C₃₁×#386	C₂²	1	2	yes	—
77	C₃₁×#386	C₂²	1	2	yes	—
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#386	C₂²	1	2	yes	—
82	C₃₁×#386	C₂²	1	2	yes	—
83	C₃₁×#386	C₂²	1	1	yes	characteristic
84	C₃₁×#386	C₂²	1	2	yes	—
85	C₃₁×#386	C₂²	1	2	yes	—
86	C₃₁×#386	C₂²	1	2	yes	—
87	C₃₁×#386	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	2	yes	—
90	C₃₁×#386	C₂²	1	2	yes	—
91	C₃₁×#386	C₂²	1	2	yes	—
92	C₃₁×#386	C₂²	1	2	yes	—
93	C₃₁×#386	C₂²	1	2	yes	—
94	C₃₁×#386	C₂²	1	1	yes	characteristic
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#385	C₂²	1	1	yes	characteristic
98	C₃₁×#385	C₂²	1	1	yes	characteristic
99	C₃₁×#383	C₂²	1	2	yes	—
100	C₃₁×#383	C₂²	1	2	yes	—
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₃₁×#382	C₂²	1	1	yes	characteristic
103	C₃₁×#381	C₂²	1	2	yes	—
104	C₃₁×#381	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	2	yes	—
106	C₃₁×#380	C₂²	1	2	yes	—
107	C₃₁×#380	C₂²	1	1	yes	characteristic
108	C₃₁×#380	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₃₁×#376	C₂²	1	1	yes	characteristic
121	C₃₁×#376	C₂²	1	2	yes	—
122	C₂×C₃₁×#95	C₂²	1	2	yes	—
123	C₂×C₃₁×#95	C₂²	1	2	yes	—
124	C₂×#41×C₃₁	—	4	2	no	—
125	C₂×#41×C₃₁	—	4	2	no	—
126	C₂×#41×C₃₁	—	4	2	no	—
127	C₂×#41×C₃₁	—	4	2	no	—
128	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
129	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
134	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
140	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
148	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
149	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
150	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
151	C₃₁×#127	C₂×C₄	1	8	yes	complemented
152	C₃₁×#127	C₂×C₄	1	16	yes	complemented
153	C₃₁×#121	C₂×C₄	1	8	yes	complemented
154	C₃₁×#121	C₂×C₄	1	8	yes	complemented
155	C₃₁×#121	C₂×C₄	1	16	yes	complemented
156	C₃₁×#121	C₂×C₄	1	16	yes	complemented
157	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
158	C₄×D₄×C₃₁	—	4	4	no	—
159	C₄×D₄×C₃₁	—	4	2	no	—
160	C₄×D₄×C₃₁	—	4	2	no	—
161	C₄×D₄×C₃₁	—	4	2	no	—
162	C₄×D₄×C₃₁	—	4	2	no	—
163	C₄×D₄×C₃₁	—	4	4	no	—
164	C₄×D₄×C₃₁	—	4	4	no	—
165	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
166	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
167	C₃₁×#117	—	4	2	no	—
168	C₃₁×#117	—	4	2	no	—
169	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₃₁	—	4	2	no	—
210	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
219	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
220	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	1	yes	characteristic
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	1	yes	characteristic
235	C₃₁×#95	C₂³	1	1	yes	characteristic
236	C₃₁×#95	C₂³	1	1	yes	characteristic
237	C₃₁×#95	C₂³	1	1	yes	characteristic
238	C₃₁×#95	C₂³	1	2	yes	—
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	1	yes	characteristic
241	C₃₁×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
247	C₃₁×#95	C₂³	1	2	yes	—
248	C₃₁×#95	C₂³	1	2	yes	—
249	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
251	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
253	#41×C₃₁	—	4	16	no	—
254	#41×C₃₁	—	4	16	no	—
255	C₂×Q₈×C₃₁	—	2	2	no	—
256	C₂×Q₈×C₃₁	—	2	2	no	—
257	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	4	2	no	—
263	C₂×D₄×C₃₁	—	4	2	no	—
264	C₂×D₄×C₃₁	—	4	2	no	—
265	C₂×D₄×C₃₁	—	4	2	no	—
266	C₂×D₄×C₃₁	—	4	2	no	—
267	C₂×D₄×C₃₁	—	4	2	no	—
268	C₂×D₄×C₃₁	—	4	2	no	—
269	C₂×D₄×C₃₁	—	4	1	no	—
270	C₂×D₄×C₃₁	—	4	1	no	—
271	C₂×D₄×C₃₁	—	4	2	no	—
272	C₂×D₄×C₃₁	—	4	2	no	—
273	C₂×D₄×C₃₁	—	4	2	no	—
274	C₂×D₄×C₃₁	—	4	2	no	—
275	C₂×D₄×C₃₁	—	4	2	no	—
276	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
277	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
278	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
279	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
280	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
281	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
282	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
283	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
284	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	4	no	—
291	C₂²×C₄×C₃₁	—	4	1	no	—
292	C₂²×C₄×C₃₁	—	4	1	no	—
293	C₂²×C₄×C₃₁	—	4	1	no	—
294	C₂²×C₄×C₃₁	—	4	1	no	—
295	C₂²×C₄×C₃₁	—	4	1	no	—
296	C₂²×C₄×C₃₁	—	4	2	no	—
297	C₂²×C₄×C₃₁	—	4	2	no	—
298	C₂²×C₄×C₃₁	—	4	2	no	—
299	C₂²×C₄×C₃₁	—	4	2	no	—
300	C₂²×C₄×C₃₁	—	4	2	no	—
301	C₂²×C₄×C₃₁	—	4	2	no	—
302	C₂²×C₄×C₃₁	—	4	2	no	—
303	C₂²×C₄×C₃₁	—	4	2	no	—
304	C₂²×C₄×C₃₁	—	4	2	no	—
305	C₂²×C₄×C₃₁	—	4	2	no	—
306	C₂²×C₄×C₃₁	—	4	2	no	—
307	C₂²×C₄×C₃₁	—	4	2	no	—
308	C₂²×C₄×C₃₁	—	4	2	no	—
309	C₂²×C₄×C₃₁	—	4	2	no	—
310	C₂²×C₄×C₃₁	—	4	2	no	—
311	C₂²×C₄×C₃₁	—	4	2	no	—
312	C₂²×C₄×C₃₁	—	4	2	no	—
313	C₂²×C₄×C₃₁	—	4	2	no	—
314	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
315	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
316	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
317	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
318	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	4	2	no	—
343	C₄⋊C₄×C₃₁	—	4	1	no	—
344	C₄⋊C₄×C₃₁	—	4	1	no	—
345	C₄⋊C₄×C₃₁	—	4	1	no	—
346	C₄⋊C₄×C₃₁	—	4	2	no	—
347	C₄⋊C₄×C₃₁	—	4	2	no	—
348	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
349	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
350	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄×C₃₁	—	2	4	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	4	2	no	—
354	C₂²⋊C₄×C₃₁	—	4	2	no	—
355	C₂²⋊C₄×C₃₁	—	4	1	no	—
356	C₂²⋊C₄×C₃₁	—	4	2	no	—
357	C₂²⋊C₄×C₃₁	—	4	2	no	—
358	C₂²⋊C₄×C₃₁	—	4	2	no	—
359	C₂²⋊C₄×C₃₁	—	4	2	no	—
360	C₂²⋊C₄×C₃₁	—	4	1	no	—
361	C₂²⋊C₄×C₃₁	—	4	1	no	—
362	C₂²⋊C₄×C₃₁	—	4	1	no	—
363	C₂²⋊C₄×C₃₁	—	4	1	no	—
364	C₂²⋊C₄×C₃₁	—	4	2	no	—
365	C₂²⋊C₄×C₃₁	—	4	2	no	—
366	C₂²⋊C₄×C₃₁	—	4	2	no	—
367	C₂²⋊C₄×C₃₁	—	4	2	no	—
368	C₂²⋊C₄×C₃₁	—	4	2	no	—
369	C₂²⋊C₄×C₃₁	—	4	2	no	—
370	C₂²⋊C₄×C₃₁	—	4	2	no	—
371	C₂²⋊C₄×C₃₁	—	4	2	no	—
372	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
373	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
374	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
375	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
376	C₄²×C₃₁	—	2	2	no	—
377	C₄²×C₃₁	—	2	2	no	—
378	C₄²×C₃₁	—	2	2	no	—
379	C₄²×C₃₁	—	2	4	no	—
380	C₄²×C₃₁	—	2	2	no	—
381	C₄²×C₃₁	—	4	1	no	—
382	C₄²×C₃₁	—	4	1	no	—
383	C₄²×C₃₁	—	4	2	no	—
384	C₄²×C₃₁	—	4	2	no	—
385	C₄²×C₃₁	—	4	2	no	—
386	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
387	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
388	#34477	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂³×C₃₁	—	2	2	no	—
390	C₂³×C₃₁	—	2	1	no	—
391	C₂³×C₃₁	—	2	1	no	—
392	C₂³×C₃₁	—	2	1	no	—
393	C₂³×C₃₁	—	2	1	no	—
394	C₂³×C₃₁	—	2	2	no	—
395	C₂³×C₃₁	—	2	2	no	—
396	C₂³×C₃₁	—	2	2	no	—
397	C₂³×C₃₁	—	2	2	no	—
398	C₂³×C₃₁	—	2	2	no	—
399	C₂³×C₃₁	—	2	1	no	—
400	C₂³×C₃₁	—	2	1	no	—
401	C₂³×C₃₁	—	2	2	no	—
402	C₂³×C₃₁	—	2	1	no	—
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	2	1	no	—
406	C₂³×C₃₁	—	2	2	no	—
407	C₂³×C₃₁	—	2	1	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	2	no	—
411	C₂³×C₃₁	—	2	1	no	—
412	C₂³×C₃₁	—	2	2	no	—
413	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
414	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
415	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
416	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
417	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
418	Q₈×C₃₁	—	2	8	no	—
419	D₄×C₃₁	—	2	8	no	—
420	D₄×C₃₁	—	2	8	no	—
421	D₄×C₃₁	—	4	4	no	—
422	D₄×C₃₁	—	4	8	no	—
423	D₄×C₃₁	—	4	8	no	—
424	D₄×C₃₁	—	4	8	no	—
425	D₄×C₃₁	—	4	8	no	—
426	D₄×C₃₁	—	4	8	no	—
427	D₄×C₃₁	—	4	8	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	1	no	—
432	C₂×C₄×C₃₁	—	2	1	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	1	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	2	1	no	—
440	C₂×C₄×C₃₁	—	2	1	no	—
441	C₂×C₄×C₃₁	—	2	1	no	—
442	C₂×C₄×C₃₁	—	2	8	no	—
443	C₂×C₄×C₃₁	—	2	8	no	—
444	C₂×C₄×C₃₁	—	2	1	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	1	no	—
447	C₂×C₄×C₃₁	—	2	1	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	2	1	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	2	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	1	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	4	8	no	—
478	C₂×C₄×C₃₁	—	4	8	no	—
479	C₂×C₄×C₃₁	—	4	4	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	8	4	no	—
482	C₂×C₄×C₃₁	—	8	4	no	—
483	C₂×C₄×C₃₁	—	8	4	no	—
484	C₂×C₄×C₃₁	—	8	4	no	—
485	C₂×C₄×C₃₁	—	8	4	no	—
486	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
487	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
488	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
490	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
492	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
493	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
496	C₂×#550	C₂×C₃₁	1	1	yes	characteristic
497	#2380	C₂×C₃₁	1	2	yes	complemented
498	#2377	C₂×C₃₁	1	2	yes	complemented
499	#2366	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#2364	C₂×C₃₁	1	2	yes	complemented
501	#2363	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#2361	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#2356	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#2353	C₂×C₃₁	1	2	yes	complemented
505	#2352	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#2339	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#2339	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#2333	C₂×C₃₁	1	2	yes	complemented
509	#2328	C₂×C₃₁	1	2	yes	complemented
510	#2328	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#2325	C₂×C₃₁	1	2	yes	complemented
512	#2324	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#2320	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#2318	C₂×C₃₁	1	2	yes	complemented
515	#2311	C₂×C₃₁	1	1	yes	characteristic, complemented
516	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#2290	C₂×C₃₁	1	1	yes	characteristic, complemented
519	C₂²×C₃₁	—	2	2	no	—
520	C₂²×C₃₁	—	2	2	no	—
521	C₂²×C₃₁	—	2	4	no	—
522	C₂²×C₃₁	—	2	4	no	—
523	C₂²×C₃₁	—	2	2	no	—
524	C₂²×C₃₁	—	2	4	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	2	4	no	—
527	C₂²×C₃₁	—	2	2	no	—
528	C₂²×C₃₁	—	2	4	no	—
529	C₂²×C₃₁	—	2	2	no	—
530	C₂²×C₃₁	—	2	4	no	—
531	C₂²×C₃₁	—	4	1	no	—
532	C₂²×C₃₁	—	4	1	no	—
533	C₂²×C₃₁	—	4	2	no	—
534	C₂²×C₃₁	—	4	2	no	—
535	C₂²×C₃₁	—	4	1	no	—
536	C₂²×C₃₁	—	4	2	no	—
537	C₂²×C₃₁	—	4	2	no	—
538	C₂²×C₃₁	—	4	1	no	—
539	C₂²×C₃₁	—	4	1	no	—
540	C₂²×C₃₁	—	4	2	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	2	no	—
543	C₂²×C₃₁	—	4	2	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	2	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
548	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂²×C₃₁	#585	1	1	yes	characteristic
552	C₂²×C₃₁	#585	1	1	yes	characteristic
553	C₂²×C₃₁	#585	1	1	yes	characteristic
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	2	4	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	4	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	2	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	1	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	#518	1	4	yes	—
573	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
574	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
575	#550	C₄×C₃₁	1	16	yes	complemented
576	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
577	C₂×#127	C₂²×C₃₁	1	2	yes	—
578	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
579	C₂×#121	C₂²×C₃₁	1	2	yes	—
580	C₂×#121	C₂²×C₃₁	1	2	yes	—
581	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
582	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
583	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
584	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
585	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
586	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
589	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
591	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
592	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
593	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
594	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
595	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
596	#391	C₂²×C₃₁	1	1	yes	characteristic
597	#391	C₂²×C₃₁	1	1	yes	characteristic
598	#391	C₂²×C₃₁	1	1	yes	characteristic
599	#391	C₂²×C₃₁	1	1	yes	characteristic
600	#390	C₂²×C₃₁	1	1	yes	characteristic
601	#390	C₂²×C₃₁	1	1	yes	characteristic
602	#390	C₂²×C₃₁	1	2	yes	—
603	#390	C₂²×C₃₁	1	1	yes	characteristic
604	#390	C₂²×C₃₁	1	2	yes	—
605	#390	C₂²×C₃₁	1	2	yes	—
606	#390	C₂²×C₃₁	1	1	yes	characteristic
607	#389	C₂²×C₃₁	1	1	yes	characteristic
608	#389	C₂²×C₃₁	1	1	yes	characteristic
609	#388	C₂²×C₃₁	1	2	yes	—
610	#388	C₂²×C₃₁	1	2	yes	—
611	#388	C₂²×C₃₁	1	2	yes	—
612	#388	C₂²×C₃₁	1	2	yes	—
613	#388	C₂²×C₃₁	1	2	yes	—
614	#388	C₂²×C₃₁	1	1	yes	characteristic
615	#388	C₂²×C₃₁	1	1	yes	characteristic
616	#387	C₂²×C₃₁	1	1	yes	characteristic
617	#387	C₂²×C₃₁	1	2	yes	—
618	#387	C₂²×C₃₁	1	2	yes	—
619	#387	C₂²×C₃₁	1	2	yes	—
620	#387	C₂²×C₃₁	1	2	yes	—
621	#387	C₂²×C₃₁	1	2	yes	—
622	#387	C₂²×C₃₁	1	1	yes	characteristic
623	#386	C₂²×C₃₁	1	2	yes	—
624	#386	C₂²×C₃₁	1	2	yes	—
625	#386	C₂²×C₃₁	1	2	yes	—
626	#386	C₂²×C₃₁	1	2	yes	—
627	#386	C₂²×C₃₁	1	2	yes	—
628	#386	C₂²×C₃₁	1	2	yes	—
629	#386	C₂²×C₃₁	1	2	yes	—
630	#386	C₂²×C₃₁	1	2	yes	—
631	#386	C₂²×C₃₁	1	2	yes	—
632	#386	C₂²×C₃₁	1	1	yes	characteristic
633	#386	C₂²×C₃₁	1	2	yes	—
634	#386	C₂²×C₃₁	1	2	yes	—
635	#386	C₂²×C₃₁	1	2	yes	—
636	#386	C₂²×C₃₁	1	2	yes	—
637	#386	C₂²×C₃₁	1	2	yes	—
638	#386	C₂²×C₃₁	1	2	yes	—
639	#386	C₂²×C₃₁	1	2	yes	—
640	#386	C₂²×C₃₁	1	2	yes	—
641	#386	C₂²×C₃₁	1	2	yes	—
642	#386	C₂²×C₃₁	1	2	yes	—
643	#386	C₂²×C₃₁	1	1	yes	characteristic
644	#385	C₂²×C₃₁	1	2	yes	—
645	#385	C₂²×C₃₁	1	2	yes	—
646	#385	C₂²×C₃₁	1	1	yes	characteristic
647	#385	C₂²×C₃₁	1	1	yes	characteristic
648	#383	C₂²×C₃₁	1	2	yes	—
649	#383	C₂²×C₃₁	1	2	yes	—
650	#382	C₂²×C₃₁	1	2	yes	—
651	#382	C₂²×C₃₁	1	1	yes	characteristic
652	#381	C₂²×C₃₁	1	2	yes	—
653	#381	C₂²×C₃₁	1	2	yes	—
654	#380	C₂²×C₃₁	1	2	yes	—
655	#380	C₂²×C₃₁	1	2	yes	—
656	#380	C₂²×C₃₁	1	1	yes	characteristic
657	#380	C₂²×C₃₁	1	1	yes	characteristic
658	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
659	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
660	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
661	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
662	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
663	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
664	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
665	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
666	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
668	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
669	#376	C₂²×C₃₁	1	1	yes	characteristic
670	#376	C₂²×C₃₁	1	2	yes	—
671	C₂×#95	C₂²×C₃₁	1	2	yes	—
672	C₂×#95	C₂²×C₃₁	1	2	yes	—
673	C₂×C₃₁	—	4	2	no	—
674	C₂×C₃₁	—	4	2	no	—
675	C₂×C₃₁	—	4	4	no	—
676	C₂×C₃₁	—	4	4	no	—
677	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
678	C₂×C₃₁	#3428	1	1	yes	characteristic
679	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂×C₃₁	#3539	1	1	yes	characteristic
681	C₂×C₃₁	#3542	1	1	yes	characteristic
682	C₂×C₃₁	#3546	1	1	yes	characteristic
683	C₂×C₃₁	#3562	1	1	yes	characteristic
684	C₂×#41	—	4	2	no	—
685	C₂×#41	—	4	2	no	—
686	C₂×#41	—	4	2	no	—
687	C₂×#41	—	4	2	no	—
688	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
689	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
690	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
692	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
694	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
695	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
696	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
697	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
699	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
700	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
703	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
705	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
706	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
707	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
708	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
709	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
710	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
711	#127	C₂×C₄×C₃₁	1	8	yes	complemented
712	#127	C₂×C₄×C₃₁	1	16	yes	complemented
713	#121	C₂×C₄×C₃₁	1	8	yes	complemented
714	#121	C₂×C₄×C₃₁	1	8	yes	complemented
715	#121	C₂×C₄×C₃₁	1	16	yes	complemented
716	#121	C₂×C₄×C₃₁	1	16	yes	complemented
717	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
718	C₄×D₄	—	4	4	no	—
719	C₄×D₄	—	4	2	no	—
720	C₄×D₄	—	4	2	no	—
721	C₄×D₄	—	4	2	no	—
722	C₄×D₄	—	4	2	no	—
723	C₄×D₄	—	4	4	no	—
724	C₄×D₄	—	4	4	no	—
725	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
726	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
727	#117	—	4	2	no	—
728	#117	—	4	2	no	—
729	C₂×C₄⋊C₄	—	4	2	no	—
730	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
769	C₂×C₄²	—	4	2	no	—
770	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
774	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
776	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
777	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
778	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
782	#95	C₂³×C₃₁	1	1	yes	characteristic
783	#95	C₂³×C₃₁	1	1	yes	characteristic
784	#95	C₂³×C₃₁	1	2	yes	—
785	#95	C₂³×C₃₁	1	2	yes	—
786	#95	C₂³×C₃₁	1	2	yes	—
787	#95	C₂³×C₃₁	1	2	yes	—
788	#95	C₂³×C₃₁	1	2	yes	—
789	#95	C₂³×C₃₁	1	2	yes	—
790	#95	C₂³×C₃₁	1	1	yes	characteristic
791	#95	C₂³×C₃₁	1	2	yes	—
792	#95	C₂³×C₃₁	1	1	yes	characteristic
793	#95	C₂³×C₃₁	1	2	yes	—
794	#95	C₂³×C₃₁	1	1	yes	characteristic
795	#95	C₂³×C₃₁	1	1	yes	characteristic
796	#95	C₂³×C₃₁	1	1	yes	characteristic
797	#95	C₂³×C₃₁	1	1	yes	characteristic
798	#95	C₂³×C₃₁	1	2	yes	—
799	#95	C₂³×C₃₁	1	2	yes	—
800	#95	C₂³×C₃₁	1	1	yes	characteristic
801	#95	C₂³×C₃₁	1	2	yes	—
802	#95	C₂³×C₃₁	1	2	yes	—
803	#95	C₂³×C₃₁	1	2	yes	—
804	#95	C₂³×C₃₁	1	2	yes	—
805	#95	C₂³×C₃₁	1	2	yes	—
806	#95	C₂³×C₃₁	1	1	yes	characteristic
807	#95	C₂³×C₃₁	1	2	yes	—
808	#95	C₂³×C₃₁	1	2	yes	—
809	C₃₁	#34477	1	1	yes	characteristic, direct product factor, Sylow
810	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
811	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
812	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
813	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
814	#41	—	4	16	no	—
815	#41	—	4	16	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	—	4	1	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
838	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
839	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
840	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
841	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
842	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
843	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
844	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
845	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
876	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
877	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
878	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
879	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	4	1	no	—
905	C₄⋊C₄	—	4	1	no	—
906	C₄⋊C₄	—	4	1	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
910	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
911	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	1	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	1	no	—
922	C₂²⋊C₄	—	4	1	no	—
923	C₂²⋊C₄	—	4	1	no	—
924	C₂²⋊C₄	—	4	1	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	2	no	—
929	C₂²⋊C₄	—	4	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
934	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
935	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
936	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	2	4	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	4	1	no	—
943	C₄²	—	4	1	no	—
944	C₄²	—	4	2	no	—
945	C₄²	—	4	2	no	—
946	C₄²	—	4	2	no	—
947	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
948	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	2	no	—
973	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
974	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
975	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
976	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
977	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
978	Q₈	—	2	8	no	—
979	D₄	—	2	8	no	—
980	D₄	—	2	8	no	—
981	D₄	—	4	4	no	—
982	D₄	—	4	8	no	—
983	D₄	—	4	8	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	8	no	—
986	D₄	—	4	8	no	—
987	D₄	—	4	8	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	8	no	—
1003	C₂×C₄	—	2	8	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	4	8	no	—
1038	C₂×C₄	—	4	8	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	4	no	—
1041	C₂×C₄	—	8	4	no	—
1042	C₂×C₄	—	8	4	no	—
1043	C₂×C₄	—	8	4	no	—
1044	C₂×C₄	—	8	4	no	—
1045	C₂×C₄	—	8	4	no	—
1046	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1047	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1048	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1049	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1050	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1051	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1052	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1053	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1054	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1055	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	4	no	—
1059	C₂²	—	2	4	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1085	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1086	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1087	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1088	C₂²	C₃₁×#585	1	1	yes	characteristic
1089	C₂²	C₃₁×#585	1	1	yes	characteristic
1090	C₂²	C₃₁×#585	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	4	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	4	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	C₃₁×#518	1	4	yes	—
1110	C₂	—	4	2	no	—
1111	C₂	—	4	2	no	—
1112	C₂	—	4	4	no	—
1113	C₂	—	4	4	no	—
1114	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1115	C₂	C₃₁×#3428	1	1	yes	characteristic
1116	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1117	C₂	C₃₁×#3539	1	1	yes	characteristic
1118	C₂	C₃₁×#3542	1	1	yes	characteristic
1119	C₂	C₃₁×#3546	1	1	yes	characteristic
1120	C₂	C₃₁×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#550	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2380	C₂	semidirect
3. C₃₁×#2377	C₂	semidirect
4. C₃₁×#2366	C₂	semidirect
5. C₃₁×#2364	C₂	semidirect
6. C₃₁×#2363	C₂	semidirect
7. C₃₁×#2361	C₂	semidirect
8. C₃₁×#2356	C₂	semidirect
9. C₃₁×#2353	C₂	semidirect
10. C₃₁×#2352	C₂	semidirect
11. C₃₁×#2339	C₂	semidirect
12. C₃₁×#2339	C₂	semidirect
13. C₃₁×#2333	C₂	semidirect
14. C₃₁×#2328	C₂	semidirect
15. C₃₁×#2328	C₂	semidirect
16. C₃₁×#2325	C₂	semidirect
17. C₃₁×#2324	C₂	semidirect
18. C₃₁×#2320	C₂	semidirect
19. C₃₁×#2318	C₂	semidirect
20. C₃₁×#2311	C₂	semidirect
21. C₄×C₃₁×#121	C₂	semidirect
22. C₃₁×#2297	C₂	semidirect
23. C₃₁×#2290	C₂	semidirect
26. C₃₁×#550	C₄	semidirect
128. C₂×#41×C₃₁	C₂×C₄	semidirect
129. C₂×#41×C₃₁	C₂×C₄	semidirect
151. C₃₁×#127	C₂×C₄	semidirect
152. C₃₁×#127	C₂×C₄	semidirect
153. C₃₁×#121	C₂×C₄	semidirect
154. C₃₁×#121	C₂×C₄	semidirect
155. C₃₁×#121	C₂×C₄	semidirect
156. C₃₁×#121	C₂×C₄	semidirect
157. C₄×Q₈×C₃₁	C₂×C₄	semidirect
165. C₄×D₄×C₃₁	C₂×C₄	semidirect
166. C₄×D₄×C₃₁	C₂×C₄	semidirect
388. #34477	C₃₁	direct (N × H)
497. #2380	C₂×C₃₁	semidirect
498. #2377	C₂×C₃₁	semidirect
499. #2366	C₂×C₃₁	semidirect
500. #2364	C₂×C₃₁	semidirect
501. #2363	C₂×C₃₁	semidirect
502. #2361	C₂×C₃₁	semidirect
503. #2356	C₂×C₃₁	semidirect
504. #2353	C₂×C₃₁	semidirect
505. #2352	C₂×C₃₁	semidirect
506. #2339	C₂×C₃₁	semidirect
507. #2339	C₂×C₃₁	semidirect
508. #2333	C₂×C₃₁	semidirect
509. #2328	C₂×C₃₁	semidirect
510. #2328	C₂×C₃₁	semidirect
511. #2325	C₂×C₃₁	semidirect
512. #2324	C₂×C₃₁	semidirect
513. #2320	C₂×C₃₁	semidirect
514. #2318	C₂×C₃₁	semidirect
515. #2311	C₂×C₃₁	semidirect
516. C₄×#121	C₂×C₃₁	semidirect
517. #2297	C₂×C₃₁	semidirect
518. #2290	C₂×C₃₁	semidirect
575. #550	C₄×C₃₁	semidirect
688. C₂×#41	C₂×C₄×C₃₁	semidirect
689. C₂×#41	C₂×C₄×C₃₁	semidirect
711. #127	C₂×C₄×C₃₁	semidirect
712. #127	C₂×C₄×C₃₁	semidirect
713. #121	C₂×C₄×C₃₁	semidirect
714. #121	C₂×C₄×C₃₁	semidirect
715. #121	C₂×C₄×C₃₁	semidirect
716. #121	C₂×C₄×C₃₁	semidirect
717. C₄×Q₈	C₂×C₄×C₃₁	semidirect
725. C₄×D₄	C₂×C₄×C₃₁	semidirect
726. C₄×D₄	C₂×C₄×C₃₁	semidirect
809. C₃₁	#34477	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#550	2
C₃₁×#2380	2
C₃₁×#2377	2
C₃₁×#2366	2
C₃₁×#2364	2
C₃₁×#2363	2
C₃₁×#2361	2
C₃₁×#2356	2
C₃₁×#2353	2
C₃₁×#2352	2
C₃₁×#2339	2
C₃₁×#2333	2
C₃₁×#2328	2
C₃₁×#2325	2
C₃₁×#2324	2
C₃₁×#2320	2
C₃₁×#2318	2
C₃₁×#2311	2
C₄×C₃₁×#121	2
C₃₁×#2297	2
C₃₁×#2290	2
#34477	31

Subgroups — C31×#34477 #21491236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34477 #21491236