Subgroups — C₃₁×#61617 #21518376

Order 7936.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
7	D₄×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3274	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3192	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3008	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
28	C₃₁×#560	—	2	2	no	—
29	C₃₁×#553	C₂²	1	2	yes	complemented
30	C₃₁×#553	C₂²	1	2	yes	complemented
31	C₃₁×#550	C₂²	1	2	yes	complemented
32	C₃₁×#548	C₂²	1	2	yes	complemented
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	C₂²	1	2	yes	complemented
35	D₄²×C₃₁	—	2	2	no	—
36	D₄²×C₃₁	—	2	2	no	—
37	D₄²×C₃₁	C₂²	1	2	yes	complemented
38	D₄²×C₃₁	C₂²	1	2	yes	complemented
39	D₄²×C₃₁	C₂²	1	2	yes	complemented
40	C₃₁×#540	C₂²	1	2	yes	complemented
41	C₃₁×#538	—	2	1	no	—
42	C₃₁×#538	—	2	1	no	—
43	C₃₁×#537	—	2	1	no	—
44	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#535	—	2	1	no	—
46	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#535	C₂²	1	2	yes	complemented
48	C₃₁×#534	—	2	1	no	—
49	C₃₁×#534	—	2	1	no	—
50	C₃₁×#525	—	2	1	no	—
51	C₃₁×#525	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#121	—	2	1	no	—
53	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#496	C₂²	1	2	yes	complemented
58	C₃₁×#493	C₂²	1	2	yes	complemented
59	C₃₁×#490	C₂²	1	2	yes	complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	complemented
64	C₃₁×#481	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	2	yes	complemented
66	C₃₁×#480	C₂²	1	2	yes	complemented
67	C₃₁×#479	C₂²	1	2	yes	complemented
68	C₃₁×#478	C₂²	1	2	yes	complemented
69	C₃₁×#469	C₂²	1	2	yes	complemented
70	C₃₁×#469	C₂²	1	2	yes	complemented
71	C₃₁×#469	C₂²	1	2	yes	complemented
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#466	C₂²	1	2	yes	complemented
74	C₃₁×#466	C₂²	1	2	yes	complemented
75	C₃₁×#466	C₂²	1	2	yes	complemented
76	C₃₁×#465	C₂²	1	2	yes	complemented
77	C₃₁×#463	C₂²	1	2	yes	complemented
78	C₃₁×#463	C₂²	1	2	yes	complemented
79	C₃₁×#460	C₂²	1	2	yes	complemented
80	C₃₁×#459	C₂²	1	2	yes	complemented
81	C₃₁×#459	C₂²	1	2	yes	complemented
82	C₃₁×#459	C₂²	1	2	yes	complemented
83	C₃₁×#450	C₂²	1	2	yes	complemented
84	C₃₁×#449	C₂²	1	2	yes	complemented
85	C₃₁×#449	C₂²	1	2	yes	complemented
86	C₃₁×#449	C₂²	1	2	yes	complemented
87	C₃₁×#449	C₂²	1	2	yes	complemented
88	C₃₁×#449	C₂²	1	2	yes	complemented
89	C₃₁×#449	C₂²	1	2	yes	complemented
90	C₃₁×#449	C₂²	1	2	yes	complemented
91	C₃₁×#449	C₂²	1	2	yes	complemented
92	C₃₁×#448	C₂²	1	2	yes	complemented
93	C₃₁×#447	C₂²	1	2	yes	complemented
94	C₃₁×#447	C₂²	1	2	yes	complemented
95	C₃₁×#447	C₂²	1	2	yes	complemented
96	C₃₁×#447	C₂²	1	2	yes	complemented
97	C₃₁×#447	C₂²	1	2	yes	complemented
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₃₁×#442	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
105	C₃₁×#436	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#418	C₂²	1	2	yes	complemented
111	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#416	C₂²	1	2	yes	complemented
114	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×H(5,𝔽₂)	—	4	2	no	—
120	C₃₁×H(5,𝔽₂)	—	4	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	1	no	—
123	C₂×#41×C₃₁	—	2	1	no	—
124	C₂×#41×C₃₁	—	4	2	no	—
125	C₂×#41×C₃₁	—	4	2	no	—
126	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×#41×C₃₁	C₂³	1	2	yes	—
128	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₃₁	—	2	1	no	—
134	C₂²×D₄×C₃₁	—	2	1	no	—
135	C₂²×D₄×C₃₁	—	2	1	no	—
136	C₂²×D₄×C₃₁	—	2	1	no	—
137	C₂²×D₄×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	—	2	2	no	—
139	C₂²×D₄×C₃₁	—	2	2	no	—
140	C₂²×D₄×C₃₁	—	2	2	no	—
141	C₂²×D₄×C₃₁	—	2	2	no	—
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
148	C₂³×C₄×C₃₁	—	2	1	no	—
149	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
151	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
152	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
153	C₂×SD₁₆×C₃₁	—	4	2	no	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	—	4	2	no	—
159	C₂×D₈×C₃₁	—	4	4	no	—
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×D₈×C₃₁	C₂³	1	2	yes	—
166	C₂×D₈×C₃₁	C₂³	1	2	yes	—
167	C₂×D₈×C₃₁	C₂³	1	2	yes	—
168	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
171	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
174	C₃₁×#127	—	2	2	no	—
175	C₃₁×#127	—	2	2	no	—
176	C₃₁×#127	C₂³	1	2	yes	—
177	C₃₁×#127	C₂³	1	2	yes	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#126	—	2	2	no	—
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	D₄	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×#121	—	2	1	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	D₄	1	1	yes	characteristic
217	C₃₁×#121	D₄	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	2	yes	—
225	C₃₁×#121	C₂³	1	2	yes	—
226	C₃₁×#121	C₂³	1	2	yes	—
227	C₃₁×#120	—	2	2	no	—
228	C₃₁×#120	—	2	2	no	—
229	C₃₁×#120	—	2	2	no	—
230	C₃₁×#120	—	2	2	no	—
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	—	2	2	no	—
234	C₃₁×#120	—	2	2	no	—
235	C₃₁×#120	—	2	2	no	—
236	C₃₁×#120	—	2	2	no	—
237	C₃₁×#120	D₄	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	C₂³	1	2	yes	—
251	C₃₁×#117	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₃₁×#107	C₂³	1	2	yes	—
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#106	C₂³	1	2	yes	—
263	C₃₁×#106	C₂³	1	2	yes	—
264	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
265	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×#102	C₂³	1	2	yes	—
279	C₃₁×#102	C₂³	1	2	yes	—
280	C₃₁×#102	C₂³	1	2	yes	—
281	C₃₁×#102	C₂³	1	2	yes	—
282	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₃₁	C₂³	1	2	yes	—
290	C₂⁴×C₃₁	—	2	1	no	—
291	C₂⁴×C₃₁	—	2	2	no	—
292	C₂⁴×C₃₁	—	2	1	no	—
293	C₂⁴×C₃₁	—	2	1	no	—
294	C₂⁴×C₃₁	—	2	1	no	—
295	C₂⁴×C₃₁	—	2	2	no	—
296	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
297	#41×C₃₁	—	2	2	no	—
298	#41×C₃₁	—	2	2	no	—
299	#41×C₃₁	—	2	2	no	—
300	#41×C₃₁	—	2	4	no	—
301	#41×C₃₁	—	2	2	no	—
302	#41×C₃₁	—	4	1	no	—
303	#41×C₃₁	—	4	1	no	—
304	#41×C₃₁	—	4	1	no	—
305	#41×C₃₁	—	4	1	no	—
306	#41×C₃₁	—	4	1	no	—
307	#41×C₃₁	—	4	1	no	—
308	#41×C₃₁	—	4	2	no	—
309	#41×C₃₁	—	4	4	no	—
310	#41×C₃₁	—	4	4	no	—
311	#41×C₃₁	—	4	4	no	—
312	C₂×Q₈×C₃₁	—	2	1	no	—
313	C₂×Q₈×C₃₁	—	2	2	no	—
314	C₂×Q₈×C₃₁	—	4	1	no	—
315	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
317	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₃₁	—	2	1	no	—
319	C₂×D₄×C₃₁	—	2	2	no	—
320	C₂×D₄×C₃₁	—	2	4	no	—
321	C₂×D₄×C₃₁	—	2	2	no	—
322	C₂×D₄×C₃₁	—	2	2	no	—
323	C₂×D₄×C₃₁	—	2	2	no	—
324	C₂×D₄×C₃₁	—	2	1	no	—
325	C₂×D₄×C₃₁	—	2	1	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	1	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	4	1	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	4	1	no	—
347	C₂×D₄×C₃₁	—	4	1	no	—
348	C₂×D₄×C₃₁	—	4	1	no	—
349	C₂×D₄×C₃₁	—	4	2	no	—
350	C₂×D₄×C₃₁	—	4	1	no	—
351	C₂×D₄×C₃₁	—	4	1	no	—
352	C₂×D₄×C₃₁	—	4	1	no	—
353	C₂×D₄×C₃₁	—	4	2	no	—
354	C₂×D₄×C₃₁	—	4	4	no	—
355	C₂×D₄×C₃₁	—	4	4	no	—
356	C₂×D₄×C₃₁	—	4	8	no	—
357	C₂×D₄×C₃₁	—	8	4	no	—
358	C₂×D₄×C₃₁	—	8	4	no	—
359	C₂×D₄×C₃₁	—	8	2	no	—
360	C₂×D₄×C₃₁	—	8	2	no	—
361	C₂×D₄×C₃₁	—	8	4	no	—
362	C₂×D₄×C₃₁	—	8	2	no	—
363	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
370	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
371	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	1	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	1	no	—
377	C₂²×C₄×C₃₁	—	2	1	no	—
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	1	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	2	2	no	—
383	C₂²×C₄×C₃₁	—	2	2	no	—
384	C₂²×C₄×C₃₁	—	4	1	no	—
385	C₂²×C₄×C₃₁	—	4	1	no	—
386	C₂²×C₄×C₃₁	—	4	4	no	—
387	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
394	SD₁₆×C₃₁	—	2	4	no	—
395	SD₁₆×C₃₁	—	2	4	no	—
396	SD₁₆×C₃₁	—	4	2	no	—
397	SD₁₆×C₃₁	—	4	2	no	—
398	D₈×C₃₁	—	2	4	no	—
399	D₈×C₃₁	—	2	4	no	—
400	D₈×C₃₁	—	4	2	no	—
401	D₈×C₃₁	—	4	2	no	—
402	D₈×C₃₁	—	4	2	no	—
403	D₈×C₃₁	—	4	2	no	—
404	D₈×C₃₁	—	4	2	no	—
405	D₈×C₃₁	—	4	2	no	—
406	M₁₆×C₃₁	—	4	1	no	—
407	M₁₆×C₃₁	—	4	2	no	—
408	M₁₆×C₃₁	—	4	1	no	—
409	C₂×C₈×C₃₁	—	4	1	no	—
410	C₂×C₈×C₃₁	—	4	2	no	—
411	C₂×C₈×C₃₁	—	4	1	no	—
412	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
413	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
414	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
415	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
428	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₄²×C₃₁	—	2	2	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	C₂⁴	1	2	yes	—
454	#61617	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	2	no	—
457	C₂³×C₃₁	—	2	2	no	—
458	C₂³×C₃₁	—	2	2	no	—
459	C₂³×C₃₁	—	2	2	no	—
460	C₂³×C₃₁	—	2	1	no	—
461	C₂³×C₃₁	—	4	1	no	—
462	C₂³×C₃₁	—	4	1	no	—
463	C₂³×C₃₁	—	4	2	no	—
464	C₂³×C₃₁	—	4	4	no	—
465	C₂³×C₃₁	—	4	2	no	—
466	C₂³×C₃₁	—	4	2	no	—
467	C₂³×C₃₁	—	4	2	no	—
468	C₂³×C₃₁	—	4	2	no	—
469	C₂³×C₃₁	—	8	1	no	—
470	C₂³×C₃₁	—	8	1	no	—
471	C₂³×C₃₁	—	8	1	no	—
472	C₂³×C₃₁	—	8	2	no	—
473	C₂³×C₃₁	—	8	1	no	—
474	C₂³×C₃₁	—	8	2	no	—
475	C₂³×C₃₁	—	8	1	no	—
476	C₂³×C₃₁	—	8	1	no	—
477	C₂³×C₃₁	—	8	2	no	—
478	C₂³×C₃₁	—	8	2	no	—
479	C₂³×C₃₁	—	8	2	no	—
480	C₂³×C₃₁	—	8	1	no	—
481	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
482	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	Q₈×C₃₁	—	2	1	no	—
486	Q₈×C₃₁	—	2	1	no	—
487	Q₈×C₃₁	—	2	1	no	—
488	Q₈×C₃₁	—	4	1	no	—
489	Q₈×C₃₁	—	4	2	no	—
490	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
491	D₄×C₃₁	—	2	4	no	—
492	D₄×C₃₁	—	2	4	no	—
493	D₄×C₃₁	—	2	1	no	—
494	D₄×C₃₁	—	2	2	no	—
495	D₄×C₃₁	—	2	2	no	—
496	D₄×C₃₁	—	2	2	no	—
497	D₄×C₃₁	—	2	2	no	—
498	D₄×C₃₁	—	2	1	no	—
499	D₄×C₃₁	—	2	2	no	—
500	D₄×C₃₁	—	2	1	no	—
501	D₄×C₃₁	—	2	2	no	—
502	D₄×C₃₁	—	4	1	no	—
503	D₄×C₃₁	—	4	2	no	—
504	D₄×C₃₁	—	4	2	no	—
505	D₄×C₃₁	—	4	4	no	—
506	D₄×C₃₁	—	4	2	no	—
507	D₄×C₃₁	—	4	4	no	—
508	D₄×C₃₁	—	4	2	no	—
509	D₄×C₃₁	—	4	2	no	—
510	D₄×C₃₁	—	4	2	no	—
511	D₄×C₃₁	—	4	2	no	—
512	D₄×C₃₁	—	4	4	no	—
513	D₄×C₃₁	—	4	4	no	—
514	D₄×C₃₁	—	4	4	no	—
515	D₄×C₃₁	—	8	2	no	—
516	D₄×C₃₁	—	8	1	no	—
517	D₄×C₃₁	—	8	2	no	—
518	D₄×C₃₁	—	8	1	no	—
519	D₄×C₃₁	—	8	2	no	—
520	D₄×C₃₁	—	8	2	no	—
521	D₄×C₃₁	—	8	2	no	—
522	D₄×C₃₁	—	8	2	no	—
523	D₄×C₃₁	—	8	2	no	—
524	D₄×C₃₁	—	8	2	no	—
525	D₄×C₃₁	—	8	2	no	—
526	D₄×C₃₁	—	8	2	no	—
527	D₄×C₃₁	—	8	2	no	—
528	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
529	C₂×C₄×C₃₁	—	2	4	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	2	1	no	—
532	C₂×C₄×C₃₁	—	2	1	no	—
533	C₂×C₄×C₃₁	—	2	2	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	2	no	—
537	C₂×C₄×C₃₁	—	2	1	no	—
538	C₂×C₄×C₃₁	—	2	1	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	2	no	—
541	C₂×C₄×C₃₁	—	2	2	no	—
542	C₂×C₄×C₃₁	—	2	1	no	—
543	C₂×C₄×C₃₁	—	4	1	no	—
544	C₂×C₄×C₃₁	—	4	1	no	—
545	C₂×C₄×C₃₁	—	4	1	no	—
546	C₂×C₄×C₃₁	—	4	2	no	—
547	C₂×C₄×C₃₁	—	4	4	no	—
548	C₂×C₄×C₃₁	—	4	2	no	—
549	C₂×C₄×C₃₁	—	4	2	no	—
550	C₂×C₄×C₃₁	—	4	2	no	—
551	C₂×C₄×C₃₁	—	8	2	no	—
552	C₂×C₄×C₃₁	—	8	2	no	—
553	C₂×C₄×C₃₁	—	8	2	no	—
554	C₂×C₄×C₃₁	—	8	1	no	—
555	C₂×C₄×C₃₁	—	8	1	no	—
556	C₂×C₄×C₃₁	—	8	1	no	—
557	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
564	C₈×C₃₁	—	2	2	no	—
565	C₈×C₃₁	—	2	2	no	—
566	C₈×C₃₁	—	2	2	no	—
567	C₈×C₃₁	—	2	2	no	—
568	#3537	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3488	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#3322	C₂×C₃₁	1	2	yes	complemented
571	#3318	C₂×C₃₁	1	2	yes	complemented
572	#3309	C₂×C₃₁	1	2	yes	complemented
573	#3301	C₂×C₃₁	1	2	yes	complemented
574	D₄×D₈	C₂×C₃₁	1	2	yes	complemented
575	#3274	C₂×C₃₁	1	2	yes	complemented
576	#3265	C₂×C₃₁	1	2	yes	complemented
577	#3264	C₂×C₃₁	1	2	yes	complemented
578	#3220	C₂×C₃₁	1	2	yes	complemented
579	#3198	C₂×C₃₁	1	2	yes	complemented
580	#3192	C₂×C₃₁	1	1	yes	characteristic, complemented
581	#3186	C₂×C₃₁	1	1	yes	characteristic, complemented
582	#3119	C₂×C₃₁	1	2	yes	complemented
583	#3008	C₂×C₃₁	1	2	yes	complemented
584	#3006	C₂×C₃₁	1	1	yes	characteristic, complemented
585	C₂×#449	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#2976	C₂×C₃₁	1	1	yes	characteristic, complemented
587	C₂²×C₃₁	—	2	1	no	—
588	C₂²×C₃₁	—	2	1	no	—
589	C₂²×C₃₁	—	2	1	no	—
590	C₂²×C₃₁	—	2	2	no	—
591	C₂²×C₃₁	—	2	1	no	—
592	C₂²×C₃₁	—	2	1	no	—
593	C₂²×C₃₁	—	2	2	no	—
594	C₂²×C₃₁	—	2	1	no	—
595	C₂²×C₃₁	—	2	2	no	—
596	C₂²×C₃₁	—	2	1	no	—
597	C₂²×C₃₁	—	2	1	no	—
598	C₂²×C₃₁	—	2	2	no	—
599	C₂²×C₃₁	—	4	1	no	—
600	C₂²×C₃₁	—	4	1	no	—
601	C₂²×C₃₁	—	4	2	no	—
602	C₂²×C₃₁	—	4	2	no	—
603	C₂²×C₃₁	—	4	1	no	—
604	C₂²×C₃₁	—	4	2	no	—
605	C₂²×C₃₁	—	4	1	no	—
606	C₂²×C₃₁	—	4	2	no	—
607	C₂²×C₃₁	—	4	2	no	—
608	C₂²×C₃₁	—	4	2	no	—
609	C₂²×C₃₁	—	4	2	no	—
610	C₂²×C₃₁	—	4	2	no	—
611	C₂²×C₃₁	—	4	2	no	—
612	C₂²×C₃₁	—	4	1	no	—
613	C₂²×C₃₁	—	8	2	no	—
614	C₂²×C₃₁	—	8	4	no	—
615	C₂²×C₃₁	—	16	2	no	—
616	C₂²×C₃₁	—	16	4	no	—
617	C₂²×C₃₁	—	16	2	no	—
618	C₂²×C₃₁	—	16	2	no	—
619	C₂²×C₃₁	—	16	4	no	—
620	C₂²×C₃₁	#576	1	2	yes	—
621	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
622	C₄×C₃₁	—	2	2	no	—
623	C₄×C₃₁	—	2	1	no	—
624	C₄×C₃₁	—	2	2	no	—
625	C₄×C₃₁	—	2	1	no	—
626	C₄×C₃₁	—	2	2	no	—
627	C₄×C₃₁	—	2	1	no	—
628	C₄×C₃₁	—	2	2	no	—
629	C₄×C₃₁	—	4	2	no	—
630	C₄×C₃₁	—	4	1	no	—
631	C₄×C₃₁	—	4	2	no	—
632	C₄×C₃₁	—	4	2	no	—
633	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
634	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
640	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
643	#560	—	2	2	no	—
644	#553	C₂²×C₃₁	1	2	yes	complemented
645	#553	C₂²×C₃₁	1	2	yes	complemented
646	#550	C₂²×C₃₁	1	2	yes	complemented
647	#548	C₂²×C₃₁	1	2	yes	complemented
648	#546	—	2	2	no	—
649	#546	C₂²×C₃₁	1	2	yes	complemented
650	D₄²	—	2	2	no	—
651	D₄²	—	2	2	no	—
652	D₄²	C₂²×C₃₁	1	2	yes	complemented
653	D₄²	C₂²×C₃₁	1	2	yes	complemented
654	D₄²	C₂²×C₃₁	1	2	yes	complemented
655	#540	C₂²×C₃₁	1	2	yes	complemented
656	#538	—	2	1	no	—
657	#538	—	2	1	no	—
658	#537	—	2	1	no	—
659	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#535	—	2	1	no	—
661	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#535	C₂²×C₃₁	1	2	yes	complemented
663	#534	—	2	1	no	—
664	#534	—	2	1	no	—
665	#525	—	2	1	no	—
666	#525	C₂²×C₃₁	1	1	yes	characteristic
667	C₂×#121	—	2	1	no	—
668	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#496	C₂²×C₃₁	1	2	yes	complemented
673	#493	C₂²×C₃₁	1	2	yes	complemented
674	#490	C₂²×C₃₁	1	2	yes	complemented
675	#488	C₂²×C₃₁	1	2	yes	complemented
676	#485	C₂²×C₃₁	1	2	yes	complemented
677	#482	C₂²×C₃₁	1	2	yes	complemented
678	#481	C₂²×C₃₁	1	2	yes	complemented
679	#481	C₂²×C₃₁	1	2	yes	complemented
680	#480	C₂²×C₃₁	1	2	yes	complemented
681	#480	C₂²×C₃₁	1	2	yes	complemented
682	#479	C₂²×C₃₁	1	2	yes	complemented
683	#478	C₂²×C₃₁	1	2	yes	complemented
684	#469	C₂²×C₃₁	1	2	yes	complemented
685	#469	C₂²×C₃₁	1	2	yes	complemented
686	#469	C₂²×C₃₁	1	2	yes	complemented
687	#468	C₂²×C₃₁	1	2	yes	complemented
688	#466	C₂²×C₃₁	1	2	yes	complemented
689	#466	C₂²×C₃₁	1	2	yes	complemented
690	#466	C₂²×C₃₁	1	2	yes	complemented
691	#465	C₂²×C₃₁	1	2	yes	complemented
692	#463	C₂²×C₃₁	1	2	yes	complemented
693	#463	C₂²×C₃₁	1	2	yes	complemented
694	#460	C₂²×C₃₁	1	2	yes	complemented
695	#459	C₂²×C₃₁	1	2	yes	complemented
696	#459	C₂²×C₃₁	1	2	yes	complemented
697	#459	C₂²×C₃₁	1	2	yes	complemented
698	#450	C₂²×C₃₁	1	2	yes	complemented
699	#449	C₂²×C₃₁	1	2	yes	complemented
700	#449	C₂²×C₃₁	1	2	yes	complemented
701	#449	C₂²×C₃₁	1	2	yes	complemented
702	#449	C₂²×C₃₁	1	2	yes	complemented
703	#449	C₂²×C₃₁	1	2	yes	complemented
704	#449	C₂²×C₃₁	1	2	yes	complemented
705	#449	C₂²×C₃₁	1	2	yes	complemented
706	#449	C₂²×C₃₁	1	2	yes	complemented
707	#448	C₂²×C₃₁	1	2	yes	complemented
708	#447	C₂²×C₃₁	1	2	yes	complemented
709	#447	C₂²×C₃₁	1	2	yes	complemented
710	#447	C₂²×C₃₁	1	2	yes	complemented
711	#447	C₂²×C₃₁	1	2	yes	complemented
712	#447	C₂²×C₃₁	1	2	yes	complemented
713	#447	C₂²×C₃₁	1	2	yes	complemented
714	#447	C₂²×C₃₁	1	2	yes	complemented
715	#447	C₂²×C₃₁	1	2	yes	complemented
716	#442	C₂²×C₃₁	1	2	yes	complemented
717	#440	C₂²×C₃₁	1	2	yes	complemented
718	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
719	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
720	#436	C₂²×C₃₁	1	2	yes	complemented
721	#435	C₂²×C₃₁	1	2	yes	complemented
722	#435	C₂²×C₃₁	1	2	yes	complemented
723	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
724	#433	C₂²×C₃₁	1	2	yes	complemented
725	#418	C₂²×C₃₁	1	2	yes	complemented
726	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#416	C₂²×C₃₁	1	2	yes	complemented
729	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	#408	C₂²×C₃₁	1	2	yes	complemented
732	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
733	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
734	C₂×C₃₁	—	2	2	no	—
735	C₂×C₃₁	—	4	1	no	—
736	C₂×C₃₁	—	4	1	no	—
737	C₂×C₃₁	—	4	2	no	—
738	C₂×C₃₁	—	4	2	no	—
739	C₂×C₃₁	—	8	1	no	—
740	C₂×C₃₁	—	8	2	no	—
741	C₂×C₃₁	—	8	2	no	—
742	C₂×C₃₁	—	8	2	no	—
743	C₂×C₃₁	#3484	1	1	yes	characteristic
744	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
745	C₂×C₃₁	#3585	1	1	yes	characteristic
746	H(5,𝔽₂)	—	4	2	no	—
747	H(5,𝔽₂)	—	4	2	no	—
748	C₂×#41	—	2	1	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	4	2	no	—
752	C₂×#41	—	4	2	no	—
753	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
754	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
755	C₂×#41	C₂³×C₃₁	1	2	yes	—
756	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
757	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
759	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	—	2	2	no	—
766	C₂²×D₄	—	2	2	no	—
767	C₂²×D₄	—	2	2	no	—
768	C₂²×D₄	—	2	2	no	—
769	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
770	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
771	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
772	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
773	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
774	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
775	C₂³×C₄	—	2	1	no	—
776	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
777	AGL(1,ℤ/8)	—	4	2	no	—
778	AGL(1,ℤ/8)	—	4	4	no	—
779	AGL(1,ℤ/8)	—	4	2	no	—
780	C₂×SD₁₆	—	4	2	no	—
781	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
785	C₂×D₈	—	4	2	no	—
786	C₂×D₈	—	4	4	no	—
787	C₂×D₈	C₂³×C₃₁	1	2	yes	—
788	C₂×D₈	C₂³×C₃₁	1	2	yes	—
789	C₂×D₈	C₂³×C₃₁	1	2	yes	—
790	C₂×D₈	C₂³×C₃₁	1	2	yes	—
791	C₂×D₈	C₂³×C₃₁	1	2	yes	—
792	C₂×D₈	C₂³×C₃₁	1	2	yes	—
793	C₂×D₈	C₂³×C₃₁	1	2	yes	—
794	C₂×D₈	C₂³×C₃₁	1	2	yes	—
795	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
796	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
797	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
798	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
800	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
801	#127	—	2	2	no	—
802	#127	—	2	2	no	—
803	#127	C₂³×C₃₁	1	2	yes	—
804	#127	C₂³×C₃₁	1	2	yes	—
805	#126	—	2	2	no	—
806	#126	—	2	2	no	—
807	#125	C₂³×C₃₁	1	2	yes	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	C₂³×C₃₁	1	2	yes	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	D₄×C₃₁	1	2	yes	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
820	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
821	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
822	#121	—	2	1	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	D₄×C₃₁	1	1	yes	characteristic
844	#121	D₄×C₃₁	1	1	yes	characteristic
845	#121	C₂³×C₃₁	1	2	yes	—
846	#121	C₂³×C₃₁	1	2	yes	—
847	#121	C₂³×C₃₁	1	2	yes	—
848	#121	C₂³×C₃₁	1	2	yes	—
849	#121	C₂³×C₃₁	1	2	yes	—
850	#121	C₂³×C₃₁	1	2	yes	—
851	#121	C₂³×C₃₁	1	2	yes	—
852	#121	C₂³×C₃₁	1	2	yes	—
853	#121	C₂³×C₃₁	1	2	yes	—
854	#120	—	2	2	no	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	#120	—	2	2	no	—
863	#120	—	2	2	no	—
864	#120	D₄×C₃₁	1	2	yes	—
865	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	C₂³×C₃₁	1	2	yes	—
872	C₄×D₄	C₂³×C₃₁	1	2	yes	—
873	C₄×D₄	C₂³×C₃₁	1	2	yes	—
874	C₄×D₄	C₂³×C₃₁	1	2	yes	—
875	C₄×D₄	C₂³×C₃₁	1	2	yes	—
876	#117	—	2	1	no	—
877	#117	C₂³×C₃₁	1	2	yes	—
878	#117	C₂³×C₃₁	1	1	yes	characteristic
879	C₂×C₄⋊C₄	—	2	1	no	—
880	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₂×C₂²⋊C₄	—	2	1	no	—
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	#107	C₂³×C₃₁	1	2	yes	—
888	#107	C₂³×C₃₁	1	2	yes	—
889	#106	C₂³×C₃₁	1	2	yes	—
890	#106	C₂³×C₃₁	1	2	yes	—
891	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
892	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
893	#103	C₂³×C₃₁	1	2	yes	—
894	#103	C₂³×C₃₁	1	2	yes	—
895	#103	C₂³×C₃₁	1	2	yes	—
896	#103	C₂³×C₃₁	1	2	yes	—
897	#102	C₂³×C₃₁	1	2	yes	—
898	#102	C₂³×C₃₁	1	2	yes	—
899	#102	C₂³×C₃₁	1	2	yes	—
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	2	yes	—
903	#102	C₂³×C₃₁	1	2	yes	—
904	#102	C₂³×C₃₁	1	2	yes	—
905	#102	C₂³×C₃₁	1	2	yes	—
906	#102	C₂³×C₃₁	1	2	yes	—
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
915	#97	C₂³×C₃₁	1	2	yes	—
916	C₄×C₈	C₂³×C₃₁	1	2	yes	—
917	C₃₁	#61617	1	1	yes	characteristic, direct product factor, Sylow
918	C₂⁴	—	2	1	no	—
919	C₂⁴	—	2	2	no	—
920	C₂⁴	—	2	1	no	—
921	C₂⁴	—	2	1	no	—
922	C₂⁴	—	2	1	no	—
923	C₂⁴	—	2	2	no	—
924	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	2	4	no	—
929	#41	—	2	2	no	—
930	#41	—	4	1	no	—
931	#41	—	4	1	no	—
932	#41	—	4	1	no	—
933	#41	—	4	1	no	—
934	#41	—	4	1	no	—
935	#41	—	4	1	no	—
936	#41	—	4	2	no	—
937	#41	—	4	4	no	—
938	#41	—	4	4	no	—
939	#41	—	4	4	no	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	4	1	no	—
943	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	4	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	4	1	no	—
973	C₂×D₄	—	4	2	no	—
974	C₂×D₄	—	4	1	no	—
975	C₂×D₄	—	4	1	no	—
976	C₂×D₄	—	4	1	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	1	no	—
979	C₂×D₄	—	4	1	no	—
980	C₂×D₄	—	4	1	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	4	4	no	—
983	C₂×D₄	—	4	4	no	—
984	C₂×D₄	—	4	8	no	—
985	C₂×D₄	—	8	4	no	—
986	C₂×D₄	—	8	4	no	—
987	C₂×D₄	—	8	2	no	—
988	C₂×D₄	—	8	2	no	—
989	C₂×D₄	—	8	4	no	—
990	C₂×D₄	—	8	2	no	—
991	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
996	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
998	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
999	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	1	no	—
1013	C₂²×C₄	—	4	1	no	—
1014	C₂²×C₄	—	4	4	no	—
1015	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1016	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1017	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1022	SD₁₆	—	2	4	no	—
1023	SD₁₆	—	2	4	no	—
1024	SD₁₆	—	4	2	no	—
1025	SD₁₆	—	4	2	no	—
1026	D₈	—	2	4	no	—
1027	D₈	—	2	4	no	—
1028	D₈	—	4	2	no	—
1029	D₈	—	4	2	no	—
1030	D₈	—	4	2	no	—
1031	D₈	—	4	2	no	—
1032	D₈	—	4	2	no	—
1033	D₈	—	4	2	no	—
1034	M₁₆	—	4	1	no	—
1035	M₁₆	—	4	2	no	—
1036	M₁₆	—	4	1	no	—
1037	C₂×C₈	—	4	1	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	1	no	—
1040	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1052	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1054	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1057	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	C₂⁴×C₃₁	1	2	yes	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	2	2	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	4	1	no	—
1089	C₂³	—	4	1	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	4	no	—
1092	C₂³	—	4	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	4	2	no	—
1096	C₂³	—	8	1	no	—
1097	C₂³	—	8	1	no	—
1098	C₂³	—	8	1	no	—
1099	C₂³	—	8	2	no	—
1100	C₂³	—	8	1	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	—	8	1	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	—	8	2	no	—
1106	C₂³	—	8	2	no	—
1107	C₂³	—	8	1	no	—
1108	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1111	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	Q₈	—	2	1	no	—
1113	Q₈	—	2	1	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	4	1	no	—
1116	Q₈	—	4	2	no	—
1117	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1118	D₄	—	2	4	no	—
1119	D₄	—	2	4	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	2	no	—
1127	D₄	—	2	1	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	4	1	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	1	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	1	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1156	C₂×C₄	—	2	4	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	4	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	4	2	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	2	no	—
1180	C₂×C₄	—	8	2	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1186	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1187	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1190	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	2	2	no	—
1194	C₈	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	8	2	no	—
1222	C₂²	—	8	4	no	—
1223	C₂²	—	16	2	no	—
1224	C₂²	—	16	4	no	—
1225	C₂²	—	16	2	no	—
1226	C₂²	—	16	2	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₃₁×#576	1	2	yes	—
1229	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1230	C₄	—	2	1	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	2	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	2	no	—
1241	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1242	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1243	C₂	—	2	2	no	—
1244	C₂	—	4	1	no	—
1245	C₂	—	4	1	no	—
1246	C₂	—	4	2	no	—
1247	C₂	—	4	2	no	—
1248	C₂	—	8	1	no	—
1249	C₂	—	8	2	no	—
1250	C₂	—	8	2	no	—
1251	C₂	—	8	2	no	—
1252	C₂	C₃₁×#3484	1	1	yes	characteristic
1253	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1254	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3537	C₂	semidirect
2. C₃₁×#3488	C₂	semidirect
3. C₃₁×#3322	C₂	semidirect
4. C₃₁×#3318	C₂	semidirect
5. C₃₁×#3309	C₂	semidirect
6. C₃₁×#3301	C₂	semidirect
7. D₄×D₈×C₃₁	C₂	semidirect
8. C₃₁×#3274	C₂	semidirect
9. C₃₁×#3265	C₂	semidirect
10. C₃₁×#3264	C₂	semidirect
11. C₃₁×#3220	C₂	semidirect
12. C₃₁×#3198	C₂	semidirect
13. C₃₁×#3192	C₂	semidirect
14. C₃₁×#3186	C₂	semidirect
15. C₃₁×#3119	C₂	semidirect
16. C₃₁×#3008	C₂	semidirect
17. C₃₁×#3006	C₂	semidirect
18. C₂×C₃₁×#449	C₂	semidirect
19. C₃₁×#2976	C₂	semidirect
20. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×SD₁₆×C₃₁	C₂²	semidirect
26. C₂²×D₈×C₃₁	C₂²	semidirect
27. C₂²×D₈×C₃₁	C₂²	semidirect
29. C₃₁×#553	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
31. C₃₁×#550	C₂²	semidirect
32. C₃₁×#548	C₂²	semidirect
34. C₃₁×#546	C₂²	semidirect
37. D₄²×C₃₁	C₂²	semidirect
38. D₄²×C₃₁	C₂²	semidirect
39. D₄²×C₃₁	C₂²	semidirect
40. C₃₁×#540	C₂²	semidirect
44. C₃₁×#537	C₂²	semidirect
46. C₃₁×#535	C₂²	semidirect
47. C₃₁×#535	C₂²	semidirect
53. C₂×C₃₁×#121	C₂²	semidirect
54. C₂×C₃₁×#121	C₂²	semidirect
55. C₂×C₃₁×#121	C₂²	semidirect
56. C₃₁×#520	C₂²	semidirect
57. C₃₁×#496	C₂²	semidirect
58. C₃₁×#493	C₂²	semidirect
59. C₃₁×#490	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
66. C₃₁×#480	C₂²	semidirect
67. C₃₁×#479	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#469	C₂²	semidirect
70. C₃₁×#469	C₂²	semidirect
71. C₃₁×#469	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#466	C₂²	semidirect
74. C₃₁×#466	C₂²	semidirect
75. C₃₁×#466	C₂²	semidirect
76. C₃₁×#465	C₂²	semidirect
77. C₃₁×#463	C₂²	semidirect
78. C₃₁×#463	C₂²	semidirect
79. C₃₁×#460	C₂²	semidirect
80. C₃₁×#459	C₂²	semidirect
81. C₃₁×#459	C₂²	semidirect
82. C₃₁×#459	C₂²	semidirect
83. C₃₁×#450	C₂²	semidirect
84. C₃₁×#449	C₂²	semidirect
85. C₃₁×#449	C₂²	semidirect
86. C₃₁×#449	C₂²	semidirect
87. C₃₁×#449	C₂²	semidirect
88. C₃₁×#449	C₂²	semidirect
89. C₃₁×#449	C₂²	semidirect
90. C₃₁×#449	C₂²	semidirect
91. C₃₁×#449	C₂²	semidirect
92. C₃₁×#448	C₂²	semidirect
93. C₃₁×#447	C₂²	semidirect
94. C₃₁×#447	C₂²	semidirect
95. C₃₁×#447	C₂²	semidirect
96. C₃₁×#447	C₂²	semidirect
97. C₃₁×#447	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#447	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#442	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₄×SD₁₆×C₃₁	C₂²	semidirect
104. C₄×D₈×C₃₁	C₂²	semidirect
105. C₃₁×#436	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
108. C₈×D₄×C₃₁	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#418	C₂²	semidirect
111. C₃₁×#417	C₂²	semidirect
112. C₃₁×#417	C₂²	semidirect
113. C₃₁×#416	C₂²	semidirect
114. C₂×C₃₁×#103	C₂²	semidirect
115. C₂×C₃₁×#102	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
117. C₃₁×#407	C₂²	semidirect
118. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
454. #61617	C₃₁	direct (N × H)
568. #3537	C₂×C₃₁	semidirect
569. #3488	C₂×C₃₁	semidirect
570. #3322	C₂×C₃₁	semidirect
571. #3318	C₂×C₃₁	semidirect
572. #3309	C₂×C₃₁	semidirect
573. #3301	C₂×C₃₁	semidirect
574. D₄×D₈	C₂×C₃₁	semidirect
575. #3274	C₂×C₃₁	semidirect
576. #3265	C₂×C₃₁	semidirect
577. #3264	C₂×C₃₁	semidirect
578. #3220	C₂×C₃₁	semidirect
579. #3198	C₂×C₃₁	semidirect
580. #3192	C₂×C₃₁	semidirect
581. #3186	C₂×C₃₁	semidirect
582. #3119	C₂×C₃₁	semidirect
583. #3008	C₂×C₃₁	semidirect
584. #3006	C₂×C₃₁	semidirect
585. C₂×#449	C₂×C₃₁	semidirect
586. #2976	C₂×C₃₁	semidirect
635. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
636. C₂²×#41	C₂²×C₃₁	semidirect
637. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
638. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
639. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
640. C₂²×SD₁₆	C₂²×C₃₁	semidirect
641. C₂²×D₈	C₂²×C₃₁	semidirect
642. C₂²×D₈	C₂²×C₃₁	semidirect
644. #553	C₂²×C₃₁	semidirect
645. #553	C₂²×C₃₁	semidirect
646. #550	C₂²×C₃₁	semidirect
647. #548	C₂²×C₃₁	semidirect
649. #546	C₂²×C₃₁	semidirect
652. D₄²	C₂²×C₃₁	semidirect
653. D₄²	C₂²×C₃₁	semidirect
654. D₄²	C₂²×C₃₁	semidirect
655. #540	C₂²×C₃₁	semidirect
659. #537	C₂²×C₃₁	semidirect
661. #535	C₂²×C₃₁	semidirect
662. #535	C₂²×C₃₁	semidirect
668. C₂×#121	C₂²×C₃₁	semidirect
669. C₂×#121	C₂²×C₃₁	semidirect
670. C₂×#121	C₂²×C₃₁	semidirect
671. #520	C₂²×C₃₁	semidirect
672. #496	C₂²×C₃₁	semidirect
673. #493	C₂²×C₃₁	semidirect
674. #490	C₂²×C₃₁	semidirect
675. #488	C₂²×C₃₁	semidirect
676. #485	C₂²×C₃₁	semidirect
677. #482	C₂²×C₃₁	semidirect
678. #481	C₂²×C₃₁	semidirect
679. #481	C₂²×C₃₁	semidirect
680. #480	C₂²×C₃₁	semidirect
681. #480	C₂²×C₃₁	semidirect
682. #479	C₂²×C₃₁	semidirect
683. #478	C₂²×C₃₁	semidirect
684. #469	C₂²×C₃₁	semidirect
685. #469	C₂²×C₃₁	semidirect
686. #469	C₂²×C₃₁	semidirect
687. #468	C₂²×C₃₁	semidirect
688. #466	C₂²×C₃₁	semidirect
689. #466	C₂²×C₃₁	semidirect
690. #466	C₂²×C₃₁	semidirect
691. #465	C₂²×C₃₁	semidirect
692. #463	C₂²×C₃₁	semidirect
693. #463	C₂²×C₃₁	semidirect
694. #460	C₂²×C₃₁	semidirect
695. #459	C₂²×C₃₁	semidirect
696. #459	C₂²×C₃₁	semidirect
697. #459	C₂²×C₃₁	semidirect
698. #450	C₂²×C₃₁	semidirect
699. #449	C₂²×C₃₁	semidirect
700. #449	C₂²×C₃₁	semidirect
701. #449	C₂²×C₃₁	semidirect
702. #449	C₂²×C₃₁	semidirect
703. #449	C₂²×C₃₁	semidirect
704. #449	C₂²×C₃₁	semidirect
705. #449	C₂²×C₃₁	semidirect
706. #449	C₂²×C₃₁	semidirect
707. #448	C₂²×C₃₁	semidirect
708. #447	C₂²×C₃₁	semidirect
709. #447	C₂²×C₃₁	semidirect
710. #447	C₂²×C₃₁	semidirect
711. #447	C₂²×C₃₁	semidirect
712. #447	C₂²×C₃₁	semidirect
713. #447	C₂²×C₃₁	semidirect
714. #447	C₂²×C₃₁	semidirect
715. #447	C₂²×C₃₁	semidirect
716. #442	C₂²×C₃₁	semidirect
717. #440	C₂²×C₃₁	semidirect
718. C₄×SD₁₆	C₂²×C₃₁	semidirect
719. C₄×D₈	C₂²×C₃₁	semidirect
720. #436	C₂²×C₃₁	semidirect
721. #435	C₂²×C₃₁	semidirect
722. #435	C₂²×C₃₁	semidirect
723. C₈×D₄	C₂²×C₃₁	semidirect
724. #433	C₂²×C₃₁	semidirect
725. #418	C₂²×C₃₁	semidirect
726. #417	C₂²×C₃₁	semidirect
727. #417	C₂²×C₃₁	semidirect
728. #416	C₂²×C₃₁	semidirect
729. C₂×#103	C₂²×C₃₁	semidirect
730. C₂×#102	C₂²×C₃₁	semidirect
731. #408	C₂²×C₃₁	semidirect
732. #407	C₂²×C₃₁	semidirect
733. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
917. C₃₁	#61617	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×#3537	2
C₃₁×#3488	2
C₃₁×#3322	2
C₃₁×#3318	2
C₃₁×#3309	2
C₃₁×#3301	2
D₄×D₈×C₃₁	2
C₃₁×#3274	2
C₃₁×#3265	2
C₃₁×#3264	2
C₃₁×#3220	2
C₃₁×#3198	2
C₃₁×#3192	2
C₃₁×#3186	2
C₃₁×#3119	2
C₃₁×#3008	2
C₃₁×#3006	2
C₂×C₃₁×#449	2
C₃₁×#2976	2
#61617	31

Subgroups — C31×#61617 #21518376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61617 #21518376