Subgroups — C₃₁×#60575 #21517334

Order 7936.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₃₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3116	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3110	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2943	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#542	—	2	1	no	—
31	C₃₁×#542	C₂²	1	2	yes	complemented
32	C₃₁×#541	—	2	1	no	—
33	C₃₁×#541	C₂²	1	2	yes	complemented
34	C₃₁×#539	—	2	2	no	—
35	C₃₁×#537	C₂²	1	1	yes	characteristic
36	C₃₁×#536	C₂²	1	1	yes	characteristic
37	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#533	—	2	1	no	—
39	C₃₁×#533	C₂²	1	2	yes	complemented
40	C₃₁×#529	—	2	2	no	—
41	C₃₁×#529	—	2	1	no	—
42	C₃₁×#529	C₂²	1	2	yes	complemented
43	C₃₁×#520	—	2	1	no	—
44	C₃₁×#520	C₂²	1	1	yes	characteristic
45	C₃₁×#520	C₂²	1	2	yes	—
46	C₃₁×#520	C₂²	1	1	yes	characteristic
47	C₃₁×#518	—	2	2	no	—
48	C₃₁×#518	—	2	1	no	—
49	C₃₁×#518	C₂²	1	1	yes	characteristic
50	C₃₁×#518	C₂²	1	2	yes	—
51	C₄×#41×C₃₁	—	2	1	no	—
52	C₄×#41×C₃₁	C₂²	1	2	yes	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₃₁	—	2	2	no	—
58	C₂×C₄×D₄×C₃₁	—	2	1	no	—
59	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#485	C₂²	1	2	yes	complemented
63	C₃₁×#485	C₂²	1	2	yes	complemented
64	C₃₁×#484	C₂²	1	2	yes	complemented
65	C₃₁×#484	C₂²	1	2	yes	complemented
66	C₃₁×#483	C₂²	1	2	yes	complemented
67	C₃₁×#482	C₂²	1	2	yes	complemented
68	C₃₁×#480	C₂²	1	2	yes	complemented
69	C₃₁×#479	C₂²	1	2	yes	complemented
70	C₃₁×#478	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#477	C₂²	1	2	yes	complemented
74	C₃₁×#476	C₂²	1	2	yes	complemented
75	C₃₁×#474	C₂²	1	2	yes	complemented
76	C₃₁×#474	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#463	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#462	C₂²	1	2	yes	complemented
82	C₃₁×#461	C₂²	1	2	yes	complemented
83	C₃₁×#461	C₂²	1	2	yes	complemented
84	C₃₁×#461	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	—
86	C₃₁×#452	C₂²	1	2	yes	—
87	C₃₁×#452	C₂²	1	2	yes	—
88	C₃₁×#450	C₂²	1	2	yes	—
89	C₃₁×#450	C₂²	1	2	yes	—
90	C₃₁×#450	C₂²	1	2	yes	—
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#447	C₂²	1	2	yes	—
93	C₃₁×#442	C₂²	1	2	yes	complemented
94	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#441	C₂²	1	2	yes	complemented
97	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
109	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
113	C₃₁×#433	C₂²	1	2	yes	complemented
114	C₃₁×#433	C₂²	1	2	yes	complemented
115	C₃₁×#432	C₂²	1	2	yes	complemented
116	C₃₁×#432	C₂²	1	2	yes	complemented
117	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#418	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₃₁×#408	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×H(5,𝔽₂)	—	2	4	no	—
136	C₃₁×H(5,𝔽₂)	—	2	4	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	—	2	2	no	—
144	C₂²×D₄×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₃₁	—	2	1	no	—
148	C₂³×C₄×C₃₁	—	2	2	no	—
149	C₃₁×#137	—	2	4	no	—
150	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
151	C₃₁×#135	—	2	4	no	—
152	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₃₁	—	2	4	no	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	—	2	1	no	—
168	C₃₁×C₄⋊Q₈	—	2	1	no	—
169	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	C₂³	1	2	yes	—
199	C₄×Q₈×C₃₁	—	2	1	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	—	2	2	no	—
203	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
205	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	1	no	—
214	C₄×D₄×C₃₁	—	2	1	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	D₄	1	2	yes	—
233	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
234	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
235	C₄×D₄×C₃₁	D₄	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	—	2	1	no	—
270	C₂×C₄²×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	—	2	1	no	—
272	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	1	yes	characteristic
278	C₃₁×#107	C₂³	1	2	yes	—
279	C₃₁×#107	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	1	yes	characteristic
281	C₃₁×#106	C₂³	1	1	yes	characteristic
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×#97	C₂³	1	1	yes	characteristic
313	C₃₁×#97	C₂³	1	1	yes	characteristic
314	C₃₁×#97	C₂³	1	1	yes	characteristic
315	C₃₁×#97	C₂³	1	1	yes	characteristic
316	C₃₁×#97	C₂³	1	2	yes	—
317	C₄×C₈×C₃₁	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	2	no	—
319	C₂⁴×C₃₁	—	2	1	no	—
320	#41×C₃₁	—	2	8	no	—
321	#41×C₃₁	—	2	4	no	—
322	#41×C₃₁	—	2	4	no	—
323	#41×C₃₁	—	2	2	no	—
324	#41×C₃₁	—	2	2	no	—
325	#41×C₃₁	—	2	2	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	#41	1	4	yes	—
329	C₂×Q₈×C₃₁	—	2	1	no	—
330	C₂×Q₈×C₃₁	—	2	2	no	—
331	C₂×Q₈×C₃₁	—	2	2	no	—
332	C₂×Q₈×C₃₁	—	2	2	no	—
333	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₃₁	—	2	16	no	—
338	C₂×D₄×C₃₁	—	2	8	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	4	no	—
342	C₂×D₄×C₃₁	—	2	4	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₃₁	#41	1	4	yes	—
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	1	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	—	8	2	no	—
371	C₂²×C₄×C₃₁	—	8	4	no	—
372	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₃₁	—	2	2	no	—
379	Q₁₆×C₃₁	—	2	4	no	—
380	SD₁₆×C₃₁	—	2	2	no	—
381	SD₁₆×C₃₁	—	2	4	no	—
382	SD₁₆×C₃₁	—	2	4	no	—
383	SD₁₆×C₃₁	—	2	2	no	—
384	SD₁₆×C₃₁	—	2	4	no	—
385	SD₁₆×C₃₁	—	2	4	no	—
386	D₈×C₃₁	—	2	2	no	—
387	D₈×C₃₁	—	2	4	no	—
388	M₁₆×C₃₁	—	2	2	no	—
389	M₁₆×C₃₁	—	2	2	no	—
390	C₂×C₈×C₃₁	—	2	2	no	—
391	C₂×C₈×C₃₁	—	2	2	no	—
392	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
393	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
394	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	1	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	2	no	—
451	C₄²×C₃₁	—	2	1	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	—	2	1	no	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	—	2	1	no	—
456	C₄²×C₃₁	—	2	2	no	—
457	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₃₁	C₂×D₄	1	2	yes	—
460	C₄²×C₃₁	C₂×D₄	1	2	yes	—
461	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
462	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
463	C₄²×C₃₁	C₂⁴	1	2	yes	—
464	#60575	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂³×C₃₁	—	2	8	no	—
466	C₂³×C₃₁	—	2	2	no	—
467	C₂³×C₃₁	—	2	1	no	—
468	C₂³×C₃₁	—	2	4	no	—
469	C₂³×C₃₁	—	2	1	no	—
470	C₂³×C₃₁	—	8	1	no	—
471	C₂³×C₃₁	—	8	2	no	—
472	C₂³×C₃₁	—	8	1	no	—
473	C₂³×C₃₁	—	8	2	no	—
474	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
476	Q₈×C₃₁	—	2	2	no	—
477	Q₈×C₃₁	—	2	1	no	—
478	Q₈×C₃₁	—	2	2	no	—
479	Q₈×C₃₁	—	2	1	no	—
480	Q₈×C₃₁	—	2	2	no	—
481	Q₈×C₃₁	—	2	1	no	—
482	Q₈×C₃₁	—	4	2	no	—
483	Q₈×C₃₁	—	8	2	no	—
484	Q₈×C₃₁	C₂×#41	1	2	yes	—
485	D₄×C₃₁	—	2	8	no	—
486	D₄×C₃₁	—	2	8	no	—
487	D₄×C₃₁	—	2	4	no	—
488	D₄×C₃₁	—	2	4	no	—
489	D₄×C₃₁	—	2	2	no	—
490	D₄×C₃₁	—	2	4	no	—
491	D₄×C₃₁	—	2	2	no	—
492	D₄×C₃₁	—	2	1	no	—
493	D₄×C₃₁	—	2	1	no	—
494	D₄×C₃₁	—	2	1	no	—
495	D₄×C₃₁	—	4	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	C₂×#41	1	2	yes	—
498	D₄×C₃₁	C₂×#41	1	4	yes	—
499	C₂×C₄×C₃₁	—	2	8	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	4	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	4	1	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	1	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	8	1	no	—
522	C₂×C₄×C₃₁	—	8	1	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	—	8	2	no	—
525	C₂×C₄×C₃₁	—	8	2	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	1	no	—
528	C₂×C₄×C₃₁	—	8	1	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
539	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
540	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
541	C₈×C₃₁	—	2	1	no	—
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	1	no	—
544	C₈×C₃₁	—	2	1	no	—
545	C₈×C₃₁	—	2	2	no	—
546	C₈×C₃₁	—	2	2	no	—
547	#3461	C₂×C₃₁	1	1	yes	characteristic, complemented
548	C₄×H(5,𝔽₂)	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3124	C₂×C₃₁	1	2	yes	complemented
550	#3123	C₂×C₃₁	1	2	yes	complemented
551	#3120	C₂×C₃₁	1	2	yes	complemented
552	#3118	C₂×C₃₁	1	2	yes	complemented
553	#3116	C₂×C₃₁	1	2	yes	complemented
554	#3114	C₂×C₃₁	1	2	yes	complemented
555	#3111	C₂×C₃₁	1	2	yes	complemented
556	#3110	C₂×C₃₁	1	2	yes	complemented
557	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3042	C₂×C₃₁	1	1	yes	characteristic, complemented
563	#3012	C₂×C₃₁	1	1	yes	characteristic
564	#3009	C₂×C₃₁	1	1	yes	characteristic, complemented
565	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
566	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#2943	C₂×C₃₁	1	1	yes	characteristic, complemented
568	C₂×#440	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#2923	C₂×C₃₁	1	1	yes	characteristic, complemented
570	C₂²×C₃₁	—	2	1	no	—
571	C₂²×C₃₁	—	2	1	no	—
572	C₂²×C₃₁	—	2	2	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	2	no	—
575	C₂²×C₃₁	—	2	4	no	—
576	C₂²×C₃₁	—	2	2	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	2	no	—
580	C₂²×C₃₁	—	4	1	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	1	no	—
583	C₂²×C₃₁	—	4	1	no	—
584	C₂²×C₃₁	—	8	4	no	—
585	C₂²×C₃₁	—	8	8	no	—
586	C₂²×C₃₁	#525	1	2	yes	—
587	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₃₁	—	2	1	no	—
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	2	1	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	2	no	—
594	C₄×C₃₁	—	2	2	no	—
595	C₄×C₃₁	—	2	2	no	—
596	C₄×C₃₁	—	4	2	no	—
597	C₄×C₃₁	—	4	1	no	—
598	C₄×C₃₁	—	4	2	no	—
599	C₄×C₃₁	—	4	1	no	—
600	C₄×C₃₁	—	4	1	no	—
601	C₄×C₃₁	—	4	1	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	2	no	—
604	C₄×C₃₁	#525	1	2	yes	—
605	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
606	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
607	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
608	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
609	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
610	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
611	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
612	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#542	—	2	1	no	—
614	#542	C₂²×C₃₁	1	2	yes	complemented
615	#541	—	2	1	no	—
616	#541	C₂²×C₃₁	1	2	yes	complemented
617	#539	—	2	2	no	—
618	#537	C₂²×C₃₁	1	1	yes	characteristic
619	#536	C₂²×C₃₁	1	1	yes	characteristic
620	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#533	—	2	1	no	—
622	#533	C₂²×C₃₁	1	2	yes	complemented
623	#529	—	2	2	no	—
624	#529	—	2	1	no	—
625	#529	C₂²×C₃₁	1	2	yes	complemented
626	#520	—	2	1	no	—
627	#520	C₂²×C₃₁	1	1	yes	characteristic
628	#520	C₂²×C₃₁	1	2	yes	—
629	#520	C₂²×C₃₁	1	1	yes	characteristic
630	#518	—	2	2	no	—
631	#518	—	2	1	no	—
632	#518	C₂²×C₃₁	1	1	yes	characteristic
633	#518	C₂²×C₃₁	1	2	yes	—
634	C₄×#41	—	2	1	no	—
635	C₄×#41	C₂²×C₃₁	1	2	yes	—
636	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
637	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
638	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	C₂×C₄×D₄	—	2	2	no	—
641	C₂×C₄×D₄	—	2	1	no	—
642	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
643	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
644	#485	C₂²×C₃₁	1	2	yes	complemented
645	#485	C₂²×C₃₁	1	2	yes	complemented
646	#485	C₂²×C₃₁	1	2	yes	complemented
647	#484	C₂²×C₃₁	1	2	yes	complemented
648	#484	C₂²×C₃₁	1	2	yes	complemented
649	#483	C₂²×C₃₁	1	2	yes	complemented
650	#482	C₂²×C₃₁	1	2	yes	complemented
651	#480	C₂²×C₃₁	1	2	yes	complemented
652	#479	C₂²×C₃₁	1	2	yes	complemented
653	#478	C₂²×C₃₁	1	2	yes	complemented
654	#478	C₂²×C₃₁	1	2	yes	complemented
655	#478	C₂²×C₃₁	1	2	yes	complemented
656	#477	C₂²×C₃₁	1	2	yes	complemented
657	#476	C₂²×C₃₁	1	2	yes	complemented
658	#474	C₂²×C₃₁	1	2	yes	complemented
659	#474	C₂²×C₃₁	1	2	yes	complemented
660	#464	C₂²×C₃₁	1	2	yes	complemented
661	#463	C₂²×C₃₁	1	2	yes	complemented
662	#463	C₂²×C₃₁	1	2	yes	complemented
663	#463	C₂²×C₃₁	1	2	yes	complemented
664	#462	C₂²×C₃₁	1	2	yes	complemented
665	#461	C₂²×C₃₁	1	2	yes	complemented
666	#461	C₂²×C₃₁	1	2	yes	complemented
667	#461	C₂²×C₃₁	1	2	yes	complemented
668	#452	C₂²×C₃₁	1	2	yes	—
669	#452	C₂²×C₃₁	1	2	yes	—
670	#452	C₂²×C₃₁	1	2	yes	—
671	#450	C₂²×C₃₁	1	2	yes	—
672	#450	C₂²×C₃₁	1	2	yes	—
673	#450	C₂²×C₃₁	1	2	yes	—
674	#449	C₂²×C₃₁	1	2	yes	—
675	#447	C₂²×C₃₁	1	2	yes	—
676	#442	C₂²×C₃₁	1	2	yes	complemented
677	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#441	C₂²×C₃₁	1	2	yes	complemented
680	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#440	C₂²×C₃₁	1	2	yes	complemented
684	#440	C₂²×C₃₁	1	2	yes	complemented
685	#440	C₂²×C₃₁	1	2	yes	complemented
686	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#440	C₂²×C₃₁	1	2	yes	complemented
688	#440	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	#440	C₂²×C₃₁	1	2	yes	complemented
691	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
694	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
695	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
696	#433	C₂²×C₃₁	1	2	yes	complemented
697	#433	C₂²×C₃₁	1	2	yes	complemented
698	#432	C₂²×C₃₁	1	2	yes	complemented
699	#432	C₂²×C₃₁	1	2	yes	complemented
700	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	#418	C₂²×C₃₁	1	1	yes	characteristic
708	#417	C₂²×C₃₁	1	1	yes	characteristic
709	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	#416	C₂²×C₃₁	1	1	yes	characteristic
711	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
714	#408	C₂²×C₃₁	1	1	yes	characteristic
715	#408	C₂²×C₃₁	1	1	yes	characteristic
716	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	C₂×C₃₁	—	2	2	no	—
719	C₂×C₃₁	—	4	2	no	—
720	C₂×C₃₁	—	4	4	no	—
721	C₂×C₃₁	—	4	2	no	—
722	C₂×C₃₁	—	8	1	no	—
723	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
724	C₂×C₃₁	#3585	1	1	yes	characteristic
725	C₂×C₃₁	#3586	1	1	yes	characteristic
726	H(5,𝔽₂)	—	2	4	no	—
727	H(5,𝔽₂)	—	2	4	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₃₁	1	2	yes	—
730	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
733	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
734	C₂²×D₄	—	2	2	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
737	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
738	C₂³×C₄	—	2	1	no	—
739	C₂³×C₄	—	2	2	no	—
740	#137	—	2	4	no	—
741	AGL(1,ℤ/8)	—	2	4	no	—
742	#135	—	2	4	no	—
743	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×SD₁₆	—	2	4	no	—
746	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
752	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₂×D₈	C₂³×C₃₁	1	2	yes	—
754	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	—	2	1	no	—
768	#125	—	2	2	no	—
769	#125	—	2	2	no	—
770	#125	C₂³×C₃₁	1	2	yes	—
771	#124	—	2	1	no	—
772	#124	—	2	2	no	—
773	#124	C₂³×C₃₁	1	2	yes	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	C₂³×C₃₁	1	2	yes	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	D₄×C₃₁	1	2	yes	—
824	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
825	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
826	C₄×D₄	D₄×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₃₁	1	2	yes	—
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	C₄×D₄	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	C₂³×C₃₁	1	2	yes	—
832	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	C₂³×C₃₁	1	1	yes	characteristic
844	#117	C₂³×C₃₁	1	2	yes	—
845	#117	C₂³×C₃₁	1	1	yes	characteristic
846	#117	C₂³×C₃₁	1	1	yes	characteristic
847	#117	C₂³×C₃₁	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
853	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	2	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₄²	—	2	1	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	2	2	no	—
862	C₂×C₄²	—	2	1	no	—
863	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
864	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
865	#107	C₂³×C₃₁	1	2	yes	—
866	#107	C₂³×C₃₁	1	2	yes	—
867	#107	C₂³×C₃₁	1	1	yes	characteristic
868	#107	C₂³×C₃₁	1	1	yes	characteristic
869	#107	C₂³×C₃₁	1	2	yes	—
870	#107	C₂³×C₃₁	1	2	yes	—
871	#106	C₂³×C₃₁	1	1	yes	characteristic
872	#106	C₂³×C₃₁	1	1	yes	characteristic
873	#106	C₂³×C₃₁	1	2	yes	—
874	#106	C₂³×C₃₁	1	2	yes	—
875	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
876	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
877	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
879	#103	C₂³×C₃₁	1	2	yes	—
880	#103	C₂³×C₃₁	1	2	yes	—
881	#103	C₂³×C₃₁	1	1	yes	characteristic
882	#103	C₂³×C₃₁	1	1	yes	characteristic
883	#103	C₂³×C₃₁	1	1	yes	characteristic
884	#103	C₂³×C₃₁	1	1	yes	characteristic
885	#103	C₂³×C₃₁	1	2	yes	—
886	#103	C₂³×C₃₁	1	2	yes	—
887	#103	C₂³×C₃₁	1	2	yes	—
888	#103	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	2	yes	—
890	#102	C₂³×C₃₁	1	2	yes	—
891	#102	C₂³×C₃₁	1	1	yes	characteristic
892	#102	C₂³×C₃₁	1	1	yes	characteristic
893	#102	C₂³×C₃₁	1	1	yes	characteristic
894	#102	C₂³×C₃₁	1	1	yes	characteristic
895	#102	C₂³×C₃₁	1	2	yes	—
896	#102	C₂³×C₃₁	1	2	yes	—
897	#102	C₂³×C₃₁	1	2	yes	—
898	#102	C₂³×C₃₁	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
903	#97	C₂³×C₃₁	1	1	yes	characteristic
904	#97	C₂³×C₃₁	1	1	yes	characteristic
905	#97	C₂³×C₃₁	1	1	yes	characteristic
906	#97	C₂³×C₃₁	1	1	yes	characteristic
907	#97	C₂³×C₃₁	1	2	yes	—
908	C₄×C₈	C₂³×C₃₁	1	2	yes	—
909	C₃₁	#60575	1	1	yes	characteristic, direct product factor, Sylow
910	C₂⁴	—	2	2	no	—
911	C₂⁴	—	2	1	no	—
912	#41	—	2	8	no	—
913	#41	—	2	4	no	—
914	#41	—	2	4	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	#41×C₃₁	1	4	yes	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×D₄	—	2	16	no	—
930	C₂×D₄	—	2	8	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₂×D₄	#41×C₃₁	1	4	yes	—
943	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	8	2	no	—
963	C₂²×C₄	—	8	4	no	—
964	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	Q₁₆	—	2	2	no	—
971	Q₁₆	—	2	4	no	—
972	SD₁₆	—	2	2	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	SD₁₆	—	2	2	no	—
976	SD₁₆	—	2	4	no	—
977	SD₁₆	—	2	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	2	4	no	—
980	M₁₆	—	2	2	no	—
981	M₁₆	—	2	2	no	—
982	C₂×C₈	—	2	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
985	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
986	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1038	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1051	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1052	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1053	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₃₁	1	2	yes	—
1056	C₂³	—	2	8	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	8	1	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	2	no	—
1065	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	C₂×#41×C₃₁	1	2	yes	—
1076	D₄	—	2	8	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	4	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	C₂×#41×C₃₁	1	2	yes	—
1089	D₄	C₂×#41×C₃₁	1	4	yes	—
1090	C₂×C₄	—	2	8	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	4	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	1	no	—
1113	C₂×C₄	—	8	1	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	1	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1129	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1130	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1131	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	4	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	8	4	no	—
1153	C₂²	—	8	8	no	—
1154	C₂²	C₃₁×#525	1	2	yes	—
1155	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	C₃₁×#525	1	2	yes	—
1173	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1174	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1181	C₂	C₃₁×#3585	1	1	yes	characteristic
1182	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3012	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3461	C₂	semidirect
2. C₄×C₃₁×H(5,𝔽₂)	C₂	semidirect
3. C₃₁×#3124	C₂	semidirect
4. C₃₁×#3123	C₂	semidirect
5. C₃₁×#3120	C₂	semidirect
6. C₃₁×#3118	C₂	semidirect
7. C₃₁×#3116	C₂	semidirect
8. C₃₁×#3114	C₂	semidirect
9. C₃₁×#3111	C₂	semidirect
10. C₃₁×#3110	C₂	semidirect
11. C₃₁×#3098	C₂	semidirect
12. C₃₁×#3097	C₂	semidirect
13. C₃₁×#3083	C₂	semidirect
14. C₃₁×#3081	C₂	semidirect
15. C₃₁×#3046	C₂	semidirect
16. C₃₁×#3042	C₂	semidirect
18. C₃₁×#3009	C₂	semidirect
19. C₄×C₃₁×#137	C₂	semidirect
20. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
21. C₃₁×#2943	C₂	semidirect
22. C₂×C₃₁×#440	C₂	semidirect
23. C₃₁×#2923	C₂	semidirect
29. C₃₁×#544	C₂²	semidirect
31. C₃₁×#542	C₂²	semidirect
33. C₃₁×#541	C₂²	semidirect
37. C₃₁×#536	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
42. C₃₁×#529	C₂²	semidirect
55. C₄×#41×C₃₁	C₂²	semidirect
56. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#484	C₂²	semidirect
65. C₃₁×#484	C₂²	semidirect
66. C₃₁×#483	C₂²	semidirect
67. C₃₁×#482	C₂²	semidirect
68. C₃₁×#480	C₂²	semidirect
69. C₃₁×#479	C₂²	semidirect
70. C₃₁×#478	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#477	C₂²	semidirect
74. C₃₁×#476	C₂²	semidirect
75. C₃₁×#474	C₂²	semidirect
76. C₃₁×#474	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#463	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#462	C₂²	semidirect
82. C₃₁×#461	C₂²	semidirect
83. C₃₁×#461	C₂²	semidirect
84. C₃₁×#461	C₂²	semidirect
93. C₃₁×#442	C₂²	semidirect
94. C₃₁×#442	C₂²	semidirect
95. C₃₁×#442	C₂²	semidirect
96. C₃₁×#441	C₂²	semidirect
97. C₃₁×#441	C₂²	semidirect
98. C₃₁×#441	C₂²	semidirect
99. C₃₁×#440	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₃₁×#440	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₄×Q₁₆×C₃₁	C₂²	semidirect
110. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
112. C₄×D₈×C₃₁	C₂²	semidirect
113. C₃₁×#433	C₂²	semidirect
114. C₃₁×#433	C₂²	semidirect
115. C₃₁×#432	C₂²	semidirect
116. C₃₁×#432	C₂²	semidirect
117. C₃₁×#428	C₂²	semidirect
118. C₃₁×#428	C₂²	semidirect
119. C₃₁×#427	C₂²	semidirect
120. C₂×C₃₁×#107	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
123. C₃₁×#419	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
128. C₃₁×#416	C₂²	semidirect
129. C₂×C₃₁×#103	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₂×C₃₁×#97	C₂²	semidirect
464. #60575	C₃₁	direct (N × H)
547. #3461	C₂×C₃₁	semidirect
548. C₄×H(5,𝔽₂)	C₂×C₃₁	semidirect
549. #3124	C₂×C₃₁	semidirect
550. #3123	C₂×C₃₁	semidirect
551. #3120	C₂×C₃₁	semidirect
552. #3118	C₂×C₃₁	semidirect
553. #3116	C₂×C₃₁	semidirect
554. #3114	C₂×C₃₁	semidirect
555. #3111	C₂×C₃₁	semidirect
556. #3110	C₂×C₃₁	semidirect
557. #3098	C₂×C₃₁	semidirect
558. #3097	C₂×C₃₁	semidirect
559. #3083	C₂×C₃₁	semidirect
560. #3081	C₂×C₃₁	semidirect
561. #3046	C₂×C₃₁	semidirect
562. #3042	C₂×C₃₁	semidirect
564. #3009	C₂×C₃₁	semidirect
565. C₄×#137	C₂×C₃₁	semidirect
566. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
567. #2943	C₂×C₃₁	semidirect
568. C₂×#440	C₂×C₃₁	semidirect
569. #2923	C₂×C₃₁	semidirect
612. #544	C₂²×C₃₁	semidirect
614. #542	C₂²×C₃₁	semidirect
616. #541	C₂²×C₃₁	semidirect
620. #536	C₂²×C₃₁	semidirect
622. #533	C₂²×C₃₁	semidirect
625. #529	C₂²×C₃₁	semidirect
638. C₄×#41	C₂²×C₃₁	semidirect
639. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
644. #485	C₂²×C₃₁	semidirect
645. #485	C₂²×C₃₁	semidirect
646. #485	C₂²×C₃₁	semidirect
647. #484	C₂²×C₃₁	semidirect
648. #484	C₂²×C₃₁	semidirect
649. #483	C₂²×C₃₁	semidirect
650. #482	C₂²×C₃₁	semidirect
651. #480	C₂²×C₃₁	semidirect
652. #479	C₂²×C₃₁	semidirect
653. #478	C₂²×C₃₁	semidirect
654. #478	C₂²×C₃₁	semidirect
655. #478	C₂²×C₃₁	semidirect
656. #477	C₂²×C₃₁	semidirect
657. #476	C₂²×C₃₁	semidirect
658. #474	C₂²×C₃₁	semidirect
659. #474	C₂²×C₃₁	semidirect
660. #464	C₂²×C₃₁	semidirect
661. #463	C₂²×C₃₁	semidirect
662. #463	C₂²×C₃₁	semidirect
663. #463	C₂²×C₃₁	semidirect
664. #462	C₂²×C₃₁	semidirect
665. #461	C₂²×C₃₁	semidirect
666. #461	C₂²×C₃₁	semidirect
667. #461	C₂²×C₃₁	semidirect
676. #442	C₂²×C₃₁	semidirect
677. #442	C₂²×C₃₁	semidirect
678. #442	C₂²×C₃₁	semidirect
679. #441	C₂²×C₃₁	semidirect
680. #441	C₂²×C₃₁	semidirect
681. #441	C₂²×C₃₁	semidirect
682. #440	C₂²×C₃₁	semidirect
683. #440	C₂²×C₃₁	semidirect
684. #440	C₂²×C₃₁	semidirect
685. #440	C₂²×C₃₁	semidirect
686. #440	C₂²×C₃₁	semidirect
687. #440	C₂²×C₃₁	semidirect
688. #440	C₂²×C₃₁	semidirect
689. #440	C₂²×C₃₁	semidirect
690. #440	C₂²×C₃₁	semidirect
691. #440	C₂²×C₃₁	semidirect
692. C₄×Q₁₆	C₂²×C₃₁	semidirect
693. C₄×SD₁₆	C₂²×C₃₁	semidirect
694. C₄×SD₁₆	C₂²×C₃₁	semidirect
695. C₄×D₈	C₂²×C₃₁	semidirect
696. #433	C₂²×C₃₁	semidirect
697. #433	C₂²×C₃₁	semidirect
698. #432	C₂²×C₃₁	semidirect
699. #432	C₂²×C₃₁	semidirect
700. #428	C₂²×C₃₁	semidirect
701. #428	C₂²×C₃₁	semidirect
702. #427	C₂²×C₃₁	semidirect
703. C₂×#107	C₂²×C₃₁	semidirect
704. #424	C₂²×C₃₁	semidirect
705. #424	C₂²×C₃₁	semidirect
706. #419	C₂²×C₃₁	semidirect
709. #417	C₂²×C₃₁	semidirect
711. #416	C₂²×C₃₁	semidirect
712. C₂×#103	C₂²×C₃₁	semidirect
716. C₄×M₁₆	C₂²×C₃₁	semidirect
717. C₂×#97	C₂²×C₃₁	semidirect
909. C₃₁	#60575	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×#3461	2
C₄×C₃₁×H(5,𝔽₂)	2
C₃₁×#3124	2
C₃₁×#3123	2
C₃₁×#3120	2
C₃₁×#3118	2
C₃₁×#3116	2
C₃₁×#3114	2
C₃₁×#3111	2
C₃₁×#3110	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3083	2
C₃₁×#3081	2
C₃₁×#3046	2
C₃₁×#3042	2
C₃₁×#3012	2
C₃₁×#3009	2
C₄×C₃₁×#137	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₃₁×#2943	2
C₂×C₃₁×#440	2
C₃₁×#2923	2
#60575	31

Subgroups — C31×#60575 #21517334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60575 #21517334