Subgroups — C₃₁×#60991 #21517750

Order 7936.

1726 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3460	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3174	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3126	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	—	2	1	no	—
25	C₃₁×#557	—	2	1	no	—
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	—	2	1	no	—
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#552	—	2	1	no	—
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	C₂²	1	1	yes	characteristic
35	C₃₁×#542	C₂²	1	1	yes	characteristic
36	C₃₁×#541	C₂²	1	2	yes	—
37	C₃₁×#541	C₂²	1	2	yes	complemented
38	C₃₁×#540	—	2	1	no	—
39	C₃₁×#540	C₂²	1	1	yes	characteristic
40	C₃₁×#540	C₂²	1	1	yes	characteristic
41	C₃₁×#538	—	2	1	no	—
42	C₃₁×#538	—	2	1	no	—
43	C₃₁×#537	C₂²	1	1	yes	characteristic
44	C₃₁×#536	C₂²	1	2	yes	—
45	C₃₁×#535	C₂²	1	1	yes	characteristic
46	C₃₁×#535	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#532	—	2	1	no	—
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#529	—	2	1	no	—
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#529	C₂²	1	1	yes	characteristic
59	C₃₁×#525	—	2	1	no	—
60	C₃₁×#525	—	2	1	no	—
61	C₃₁×#519	C₂²	1	2	yes	complemented
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
65	C₃₁×#501	C₂²	1	2	yes	complemented
66	C₃₁×#499	C₂²	1	2	yes	complemented
67	C₃₁×#497	C₂²	1	2	yes	—
68	C₃₁×#492	C₂²	1	2	yes	—
69	C₃₁×#491	C₂²	1	2	yes	complemented
70	C₃₁×#490	C₂²	1	2	yes	—
71	C₃₁×#488	C₂²	1	2	yes	—
72	C₃₁×#487	C₂²	1	2	yes	complemented
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#484	C₂²	1	2	yes	—
77	C₃₁×#483	C₂²	1	2	yes	—
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#482	C₂²	1	2	yes	—
80	C₃₁×#482	C₂²	1	2	yes	complemented
81	C₃₁×#479	C₂²	1	2	yes	complemented
82	C₃₁×#479	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#477	C₂²	1	2	yes	complemented
85	C₃₁×#476	C₂²	1	1	yes	characteristic
86	C₃₁×#476	C₂²	1	1	yes	characteristic
87	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#475	C₂²	1	2	yes	complemented
90	C₃₁×#474	C₂²	1	1	yes	characteristic
91	C₃₁×#474	C₂²	1	1	yes	characteristic
92	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#470	C₂²	1	2	yes	complemented
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	complemented
97	C₃₁×#467	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#465	C₂²	1	2	yes	complemented
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#464	C₂²	1	2	yes	—
103	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#461	C₂²	1	1	yes	characteristic
106	C₃₁×#461	C₂²	1	1	yes	characteristic
107	C₃₁×#461	C₂²	1	1	yes	characteristic
108	C₃₁×#461	C₂²	1	1	yes	characteristic
109	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#460	C₂²	1	2	yes	—
112	C₃₁×#460	C₂²	1	2	yes	—
113	C₃₁×#452	C₂²	1	2	yes	—
114	C₃₁×#452	C₂²	1	2	yes	—
115	C₃₁×#451	C₂²	1	2	yes	complemented
116	C₃₁×#450	C₂²	1	2	yes	—
117	C₃₁×#450	C₂²	1	2	yes	—
118	C₃₁×#448	C₂²	1	2	yes	—
119	C₃₁×#448	C₂²	1	2	yes	—
120	C₃₁×#448	C₂²	1	2	yes	complemented
121	C₃₁×#441	C₂²	1	2	yes	complemented
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₃₁×#440	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
129	C₃₁×#433	C₂²	1	2	yes	—
130	C₃₁×#433	C₂²	1	2	yes	complemented
131	C₃₁×#432	C₂²	1	1	yes	characteristic
132	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#408	C₂²	1	2	yes	—
138	C₃₁×#405	C₂²	1	2	yes	complemented
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₃₁	—	2	1	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	2	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	C₂³	1	1	yes	characteristic
188	C₃₁×#125	C₂³	1	2	yes	—
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	C₂³	1	1	yes	characteristic
197	C₃₁×#124	C₂³	1	1	yes	characteristic
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	1	no	—
203	C₃₁×#123	—	2	1	no	—
204	C₃₁×#123	—	2	1	no	—
205	C₃₁×#123	—	2	1	no	—
206	C₃₁×#123	—	2	1	no	—
207	C₃₁×#123	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	1	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	1	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	1	no	—
217	C₃₁×C₂²⋊Q₈	—	2	1	no	—
218	C₃₁×C₂²⋊Q₈	—	2	1	no	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	1	no	—
227	C₃₁×#121	—	2	1	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	—	2	1	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	1	no	—
236	C₃₁×#121	C₂³	1	1	yes	characteristic
237	C₃₁×#121	C₂³	1	1	yes	characteristic
238	C₃₁×#121	C₂³	1	1	yes	characteristic
239	C₃₁×#121	C₂³	1	1	yes	characteristic
240	C₃₁×#121	C₂³	1	1	yes	characteristic
241	C₃₁×#121	C₂³	1	1	yes	characteristic
242	C₃₁×#120	—	2	1	no	—
243	C₃₁×#120	—	2	1	no	—
244	C₃₁×#120	—	2	1	no	—
245	C₃₁×#120	—	2	1	no	—
246	C₄×Q₈×C₃₁	—	2	2	no	—
247	C₄×Q₈×C₃₁	—	2	2	no	—
248	C₄×Q₈×C₃₁	—	2	1	no	—
249	C₄×Q₈×C₃₁	—	2	1	no	—
250	C₄×Q₈×C₃₁	—	2	1	no	—
251	C₄×Q₈×C₃₁	—	2	1	no	—
252	C₄×Q₈×C₃₁	—	2	1	no	—
253	C₄×Q₈×C₃₁	—	2	1	no	—
254	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
255	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
257	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
258	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
260	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
261	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	1	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	1	no	—
268	C₄×D₄×C₃₁	—	2	1	no	—
269	C₄×D₄×C₃₁	—	2	1	no	—
270	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
271	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
272	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
273	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
274	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
275	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
276	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₃₁×#117	—	2	1	no	—
283	C₃₁×#117	—	2	1	no	—
284	C₃₁×#117	—	2	1	no	—
285	C₃₁×#117	—	2	1	no	—
286	C₃₁×#117	—	2	2	no	—
287	C₃₁×#117	—	2	2	no	—
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	—	2	1	no	—
291	C₃₁×#117	C₂³	1	2	yes	—
292	C₃₁×#117	C₂³	1	1	yes	characteristic
293	C₃₁×#117	C₂³	1	1	yes	characteristic
294	C₃₁×#117	C₂³	1	1	yes	characteristic
295	C₃₁×#117	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
300	C₂×C₄²×C₃₁	—	2	1	no	—
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
304	C₃₁×#107	C₂³	1	2	yes	—
305	C₃₁×#107	C₂³	1	2	yes	—
306	C₃₁×#107	C₂³	1	2	yes	—
307	C₃₁×#107	C₂³	1	2	yes	—
308	C₃₁×#106	C₂³	1	2	yes	—
309	C₃₁×#106	C₂³	1	2	yes	—
310	C₃₁×#106	C₂³	1	2	yes	—
311	C₃₁×#106	C₂³	1	2	yes	—
312	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
313	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
315	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
318	C₃₁×#103	C₂³	1	2	yes	—
319	C₃₁×#103	C₂³	1	2	yes	—
320	C₃₁×#103	C₂³	1	2	yes	—
321	C₃₁×#103	C₂³	1	2	yes	—
322	C₃₁×#103	C₂³	1	2	yes	—
323	C₃₁×#103	C₂³	1	2	yes	—
324	C₃₁×#103	C₂³	1	2	yes	—
325	C₃₁×#103	C₂³	1	2	yes	—
326	C₃₁×#103	C₂³	1	2	yes	—
327	C₃₁×#103	C₂³	1	2	yes	—
328	C₃₁×#102	C₂³	1	2	yes	—
329	C₃₁×#102	C₂³	1	2	yes	—
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×#102	C₂³	1	2	yes	—
334	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×#97	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₃₁	C₂³	1	2	yes	—
341	C₄×C₈×C₃₁	C₂³	1	2	yes	—
342	C₂⁴×C₃₁	—	2	1	no	—
343	#41×C₃₁	—	4	1	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	1	no	—
346	#41×C₃₁	—	4	1	no	—
347	#41×C₃₁	—	8	2	no	—
348	#41×C₃₁	—	8	2	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	1	no	—
351	C₂×Q₈×C₃₁	—	2	2	no	—
352	C₂×Q₈×C₃₁	—	2	1	no	—
353	C₂×Q₈×C₃₁	—	2	1	no	—
354	C₂×Q₈×C₃₁	—	4	2	no	—
355	C₂×Q₈×C₃₁	—	4	2	no	—
356	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	—	2	1	no	—
362	C₂×D₄×C₃₁	—	2	1	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	1	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	1	no	—
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	2	1	no	—
372	C₂×D₄×C₃₁	—	4	1	no	—
373	C₂×D₄×C₃₁	—	4	1	no	—
374	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	1	no	—
382	C₂²×C₄×C₃₁	—	2	1	no	—
383	C₂²×C₄×C₃₁	—	2	1	no	—
384	C₂²×C₄×C₃₁	—	2	1	no	—
385	C₂²×C₄×C₃₁	—	2	1	no	—
386	C₂²×C₄×C₃₁	—	2	1	no	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
388	C₂²×C₄×C₃₁	—	2	1	no	—
389	C₂²×C₄×C₃₁	—	8	2	no	—
390	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₃₁	—	4	2	no	—
400	Q₁₆×C₃₁	—	4	2	no	—
401	SD₁₆×C₃₁	—	4	2	no	—
402	SD₁₆×C₃₁	—	4	2	no	—
403	SD₁₆×C₃₁	—	4	2	no	—
404	SD₁₆×C₃₁	—	4	2	no	—
405	SD₁₆×C₃₁	—	4	2	no	—
406	SD₁₆×C₃₁	—	4	2	no	—
407	M₁₆×C₃₁	—	4	2	no	—
408	C₂×C₈×C₃₁	—	4	2	no	—
409	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
410	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
411	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
412	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	—	2	1	no	—
424	C₄⋊C₄×C₃₁	—	2	2	no	—
425	C₄⋊C₄×C₃₁	—	2	2	no	—
426	C₄⋊C₄×C₃₁	—	2	2	no	—
427	C₄⋊C₄×C₃₁	—	2	2	no	—
428	C₄⋊C₄×C₃₁	—	2	1	no	—
429	C₄⋊C₄×C₃₁	—	2	1	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	1	no	—
435	C₄⋊C₄×C₃₁	—	2	1	no	—
436	C₄⋊C₄×C₃₁	—	2	2	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	no	—
439	C₄⋊C₄×C₃₁	—	2	2	no	—
440	C₄⋊C₄×C₃₁	—	2	2	no	—
441	C₄⋊C₄×C₃₁	—	2	2	no	—
442	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₂²⋊C₄×C₃₁	—	2	2	no	—
455	C₂²⋊C₄×C₃₁	—	2	2	no	—
456	C₂²⋊C₄×C₃₁	—	2	2	no	—
457	C₂²⋊C₄×C₃₁	—	2	2	no	—
458	C₂²⋊C₄×C₃₁	—	2	2	no	—
459	C₂²⋊C₄×C₃₁	—	2	1	no	—
460	C₂²⋊C₄×C₃₁	—	2	1	no	—
461	C₂²⋊C₄×C₃₁	—	2	1	no	—
462	C₂²⋊C₄×C₃₁	—	2	1	no	—
463	C₂²⋊C₄×C₃₁	—	2	1	no	—
464	C₂²⋊C₄×C₃₁	—	2	1	no	—
465	C₂²⋊C₄×C₃₁	—	2	1	no	—
466	C₂²⋊C₄×C₃₁	—	2	1	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	1	no	—
475	C₂²⋊C₄×C₃₁	—	2	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	1	no	—
477	C₂²⋊C₄×C₃₁	—	2	1	no	—
478	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
484	C₄²×C₃₁	—	2	1	no	—
485	C₄²×C₃₁	—	2	1	no	—
486	C₄²×C₃₁	—	2	1	no	—
487	C₄²×C₃₁	—	2	2	no	—
488	C₄²×C₃₁	—	2	2	no	—
489	C₄²×C₃₁	—	2	2	no	—
490	C₄²×C₃₁	—	2	2	no	—
491	C₄²×C₃₁	—	2	2	no	—
492	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
500	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
501	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
502	#60991	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
503	C₂³×C₃₁	—	2	1	no	—
504	C₂³×C₃₁	—	2	1	no	—
505	C₂³×C₃₁	—	2	1	no	—
506	C₂³×C₃₁	—	4	2	no	—
507	C₂³×C₃₁	—	8	1	no	—
508	C₂³×C₃₁	—	8	1	no	—
509	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₃₁	—	2	2	no	—
513	Q₈×C₃₁	—	2	2	no	—
514	Q₈×C₃₁	—	2	2	no	—
515	Q₈×C₃₁	—	2	2	no	—
516	Q₈×C₃₁	—	2	1	no	—
517	Q₈×C₃₁	—	2	1	no	—
518	Q₈×C₃₁	—	4	1	no	—
519	Q₈×C₃₁	—	4	2	no	—
520	Q₈×C₃₁	—	4	4	no	—
521	Q₈×C₃₁	—	4	2	no	—
522	Q₈×C₃₁	—	8	1	no	—
523	Q₈×C₃₁	—	8	1	no	—
524	D₄×C₃₁	—	2	1	no	—
525	D₄×C₃₁	—	2	1	no	—
526	D₄×C₃₁	—	2	1	no	—
527	D₄×C₃₁	—	2	1	no	—
528	D₄×C₃₁	—	2	1	no	—
529	D₄×C₃₁	—	2	1	no	—
530	D₄×C₃₁	—	4	1	no	—
531	D₄×C₃₁	—	4	1	no	—
532	D₄×C₃₁	—	4	1	no	—
533	D₄×C₃₁	—	4	2	no	—
534	D₄×C₃₁	—	4	2	no	—
535	D₄×C₃₁	—	8	1	no	—
536	D₄×C₃₁	—	8	1	no	—
537	D₄×C₃₁	—	8	1	no	—
538	D₄×C₃₁	—	8	1	no	—
539	D₄×C₃₁	—	8	1	no	—
540	D₄×C₃₁	—	8	1	no	—
541	D₄×C₃₁	—	8	1	no	—
542	D₄×C₃₁	—	8	1	no	—
543	D₄×C₃₁	—	8	1	no	—
544	D₄×C₃₁	—	8	1	no	—
545	C₂×C₄×C₃₁	—	2	2	no	—
546	C₂×C₄×C₃₁	—	2	2	no	—
547	C₂×C₄×C₃₁	—	2	2	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	2	1	no	—
550	C₂×C₄×C₃₁	—	2	1	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	2	2	no	—
555	C₂×C₄×C₃₁	—	2	2	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	2	no	—
560	C₂×C₄×C₃₁	—	2	2	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	4	1	no	—
564	C₂×C₄×C₃₁	—	4	1	no	—
565	C₂×C₄×C₃₁	—	4	1	no	—
566	C₂×C₄×C₃₁	—	4	2	no	—
567	C₂×C₄×C₃₁	—	4	4	no	—
568	C₂×C₄×C₃₁	—	4	2	no	—
569	C₂×C₄×C₃₁	—	4	2	no	—
570	C₂×C₄×C₃₁	—	4	2	no	—
571	C₂×C₄×C₃₁	—	8	1	no	—
572	C₂×C₄×C₃₁	—	8	1	no	—
573	C₂×C₄×C₃₁	—	8	1	no	—
574	C₂×C₄×C₃₁	—	8	1	no	—
575	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
587	C₈×C₃₁	—	2	2	no	—
588	C₈×C₃₁	—	2	2	no	—
589	C₈×C₃₁	—	2	2	no	—
590	C₈×C₃₁	—	2	2	no	—
591	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3460	C₂×C₃₁	1	1	yes	characteristic
593	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3242	C₂×C₃₁	1	2	yes	complemented
598	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#3222	C₂×C₃₁	1	2	yes	complemented
601	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3201	C₂×C₃₁	1	2	yes	complemented
604	#3200	C₂×C₃₁	1	2	yes	complemented
605	#3178	C₂×C₃₁	1	2	yes	complemented
606	#3174	C₂×C₃₁	1	2	yes	complemented
607	#3126	C₂×C₃₁	1	2	yes	complemented
608	#3121	C₂×C₃₁	1	2	yes	complemented
609	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
613	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
614	C₂²×C₃₁	—	2	1	no	—
615	C₂²×C₃₁	—	2	1	no	—
616	C₂²×C₃₁	—	2	1	no	—
617	C₂²×C₃₁	—	2	1	no	—
618	C₂²×C₃₁	—	2	1	no	—
619	C₂²×C₃₁	—	2	1	no	—
620	C₂²×C₃₁	—	2	1	no	—
621	C₂²×C₃₁	—	2	1	no	—
622	C₂²×C₃₁	—	2	1	no	—
623	C₂²×C₃₁	—	4	1	no	—
624	C₂²×C₃₁	—	4	1	no	—
625	C₂²×C₃₁	—	4	1	no	—
626	C₂²×C₃₁	—	4	1	no	—
627	C₂²×C₃₁	—	4	1	no	—
628	C₂²×C₃₁	—	4	1	no	—
629	C₂²×C₃₁	—	4	1	no	—
630	C₂²×C₃₁	—	4	1	no	—
631	C₂²×C₃₁	—	4	1	no	—
632	C₂²×C₃₁	—	8	4	no	—
633	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
634	C₄×C₃₁	—	2	1	no	—
635	C₄×C₃₁	—	2	1	no	—
636	C₄×C₃₁	—	2	1	no	—
637	C₄×C₃₁	—	2	1	no	—
638	C₄×C₃₁	—	2	1	no	—
639	C₄×C₃₁	—	2	1	no	—
640	C₄×C₃₁	—	2	1	no	—
641	C₄×C₃₁	—	2	1	no	—
642	C₄×C₃₁	—	2	1	no	—
643	C₄×C₃₁	—	2	1	no	—
644	C₄×C₃₁	—	4	1	no	—
645	C₄×C₃₁	—	4	2	no	—
646	C₄×C₃₁	—	4	1	no	—
647	C₄×C₃₁	—	4	2	no	—
648	C₄×C₃₁	—	4	2	no	—
649	C₄×C₃₁	—	4	1	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	1	no	—
652	C₄×C₃₁	—	4	2	no	—
653	C₄×C₃₁	#577	1	2	yes	—
654	C₄×C₃₁	#585	1	1	yes	characteristic
655	C₄×C₃₁	#585	1	1	yes	characteristic
656	#557	—	2	1	no	—
657	#557	—	2	1	no	—
658	#556	—	2	1	no	—
659	#556	—	2	1	no	—
660	#552	—	2	1	no	—
661	#552	—	2	1	no	—
662	#552	—	2	1	no	—
663	#552	—	2	1	no	—
664	#544	C₂²×C₃₁	1	1	yes	characteristic
665	#542	—	2	1	no	—
666	#542	C₂²×C₃₁	1	1	yes	characteristic
667	#542	C₂²×C₃₁	1	1	yes	characteristic
668	#541	C₂²×C₃₁	1	2	yes	—
669	#541	C₂²×C₃₁	1	2	yes	complemented
670	#540	—	2	1	no	—
671	#540	C₂²×C₃₁	1	1	yes	characteristic
672	#540	C₂²×C₃₁	1	1	yes	characteristic
673	#538	—	2	1	no	—
674	#538	—	2	1	no	—
675	#537	C₂²×C₃₁	1	1	yes	characteristic
676	#536	C₂²×C₃₁	1	2	yes	—
677	#535	C₂²×C₃₁	1	1	yes	characteristic
678	#535	C₂²×C₃₁	1	1	yes	characteristic
679	#533	C₂²×C₃₁	1	1	yes	characteristic
680	#533	C₂²×C₃₁	1	1	yes	characteristic
681	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#532	—	2	1	no	—
685	#532	C₂²×C₃₁	1	1	yes	characteristic
686	#532	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#529	—	2	1	no	—
689	#529	C₂²×C₃₁	1	1	yes	characteristic
690	#529	C₂²×C₃₁	1	1	yes	characteristic
691	#525	—	2	1	no	—
692	#525	—	2	1	no	—
693	#519	C₂²×C₃₁	1	2	yes	complemented
694	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
697	#501	C₂²×C₃₁	1	2	yes	complemented
698	#499	C₂²×C₃₁	1	2	yes	complemented
699	#497	C₂²×C₃₁	1	2	yes	—
700	#492	C₂²×C₃₁	1	2	yes	—
701	#491	C₂²×C₃₁	1	2	yes	complemented
702	#490	C₂²×C₃₁	1	2	yes	—
703	#488	C₂²×C₃₁	1	2	yes	—
704	#487	C₂²×C₃₁	1	2	yes	complemented
705	#485	C₂²×C₃₁	1	2	yes	—
706	#485	C₂²×C₃₁	1	2	yes	—
707	#485	C₂²×C₃₁	1	2	yes	complemented
708	#484	C₂²×C₃₁	1	2	yes	—
709	#483	C₂²×C₃₁	1	2	yes	—
710	#482	C₂²×C₃₁	1	2	yes	—
711	#482	C₂²×C₃₁	1	2	yes	—
712	#482	C₂²×C₃₁	1	2	yes	complemented
713	#479	C₂²×C₃₁	1	2	yes	complemented
714	#479	C₂²×C₃₁	1	2	yes	complemented
715	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#477	C₂²×C₃₁	1	2	yes	complemented
717	#476	C₂²×C₃₁	1	1	yes	characteristic
718	#476	C₂²×C₃₁	1	1	yes	characteristic
719	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	#475	C₂²×C₃₁	1	2	yes	complemented
722	#474	C₂²×C₃₁	1	1	yes	characteristic
723	#474	C₂²×C₃₁	1	1	yes	characteristic
724	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	#470	C₂²×C₃₁	1	2	yes	complemented
726	#468	C₂²×C₃₁	1	2	yes	—
727	#468	C₂²×C₃₁	1	2	yes	—
728	#468	C₂²×C₃₁	1	2	yes	complemented
729	#467	C₂²×C₃₁	1	2	yes	complemented
730	#465	C₂²×C₃₁	1	2	yes	—
731	#465	C₂²×C₃₁	1	2	yes	—
732	#465	C₂²×C₃₁	1	2	yes	complemented
733	#464	C₂²×C₃₁	1	2	yes	—
734	#464	C₂²×C₃₁	1	2	yes	—
735	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
736	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
737	#461	C₂²×C₃₁	1	1	yes	characteristic
738	#461	C₂²×C₃₁	1	1	yes	characteristic
739	#461	C₂²×C₃₁	1	1	yes	characteristic
740	#461	C₂²×C₃₁	1	1	yes	characteristic
741	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
743	#460	C₂²×C₃₁	1	2	yes	—
744	#460	C₂²×C₃₁	1	2	yes	—
745	#452	C₂²×C₃₁	1	2	yes	—
746	#452	C₂²×C₃₁	1	2	yes	—
747	#451	C₂²×C₃₁	1	2	yes	complemented
748	#450	C₂²×C₃₁	1	2	yes	—
749	#450	C₂²×C₃₁	1	2	yes	—
750	#448	C₂²×C₃₁	1	2	yes	—
751	#448	C₂²×C₃₁	1	2	yes	—
752	#448	C₂²×C₃₁	1	2	yes	complemented
753	#441	C₂²×C₃₁	1	2	yes	complemented
754	#440	C₂²×C₃₁	1	2	yes	—
755	#440	C₂²×C₃₁	1	2	yes	—
756	#440	C₂²×C₃₁	1	2	yes	complemented
757	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
758	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
759	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
760	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
761	#433	C₂²×C₃₁	1	2	yes	—
762	#433	C₂²×C₃₁	1	2	yes	complemented
763	#432	C₂²×C₃₁	1	1	yes	characteristic
764	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	#431	C₂²×C₃₁	1	1	yes	characteristic
766	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
767	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
768	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
769	#408	C₂²×C₃₁	1	2	yes	—
770	#405	C₂²×C₃₁	1	2	yes	complemented
771	C₂×C₃₁	—	4	1	no	—
772	C₂×C₃₁	—	4	1	no	—
773	C₂×C₃₁	—	4	1	no	—
774	C₂×C₃₁	—	8	1	no	—
775	C₂×C₃₁	—	8	1	no	—
776	C₂×C₃₁	—	8	1	no	—
777	C₂×C₃₁	#3449	1	1	yes	characteristic
778	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
779	C₂×C₃₁	#3586	1	1	yes	characteristic
780	C₂×#41	—	2	1	no	—
781	C₂×#41	—	2	1	no	—
782	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
784	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₂³×C₄	—	2	1	no	—
787	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
788	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
789	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
793	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
794	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
795	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
796	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
797	C₄⋊Q₈	—	2	2	no	—
798	C₄⋊Q₈	—	2	1	no	—
799	C₄⋊Q₈	—	2	1	no	—
800	C₄⋊Q₈	—	2	1	no	—
801	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
804	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
805	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	#127	—	2	1	no	—
809	#127	C₂³×C₃₁	1	1	yes	characteristic
810	#127	C₂³×C₃₁	1	1	yes	characteristic
811	#126	—	2	1	no	—
812	#126	—	2	1	no	—
813	#126	—	2	2	no	—
814	#126	—	2	2	no	—
815	#126	—	2	2	no	—
816	#126	—	2	2	no	—
817	#126	—	2	1	no	—
818	#126	—	2	1	no	—
819	#125	—	2	1	no	—
820	#125	—	2	2	no	—
821	#125	—	2	2	no	—
822	#125	—	2	2	no	—
823	#125	—	2	2	no	—
824	#125	—	2	1	no	—
825	#125	—	2	1	no	—
826	#125	—	2	1	no	—
827	#125	—	2	1	no	—
828	#125	C₂³×C₃₁	1	1	yes	characteristic
829	#125	C₂³×C₃₁	1	1	yes	characteristic
830	#125	C₂³×C₃₁	1	2	yes	—
831	#124	—	2	1	no	—
832	#124	—	2	2	no	—
833	#124	—	2	1	no	—
834	#124	—	2	1	no	—
835	#124	—	2	1	no	—
836	#124	—	2	1	no	—
837	#124	C₂³×C₃₁	1	1	yes	characteristic
838	#124	C₂³×C₃₁	1	1	yes	characteristic
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	#123	—	2	1	no	—
842	#123	—	2	1	no	—
843	#123	—	2	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
863	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
864	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
865	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	C₂³×C₃₁	1	1	yes	characteristic
878	#121	C₂³×C₃₁	1	1	yes	characteristic
879	#121	C₂³×C₃₁	1	1	yes	characteristic
880	#121	C₂³×C₃₁	1	1	yes	characteristic
881	#121	C₂³×C₃₁	1	1	yes	characteristic
882	#121	C₂³×C₃₁	1	1	yes	characteristic
883	#120	—	2	1	no	—
884	#120	—	2	1	no	—
885	#120	—	2	1	no	—
886	#120	—	2	1	no	—
887	C₄×Q₈	—	2	2	no	—
888	C₄×Q₈	—	2	2	no	—
889	C₄×Q₈	—	2	1	no	—
890	C₄×Q₈	—	2	1	no	—
891	C₄×Q₈	—	2	1	no	—
892	C₄×Q₈	—	2	1	no	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	—	2	1	no	—
895	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
896	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
897	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
900	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
901	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
902	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	—	2	1	no	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
912	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
913	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
914	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
915	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
916	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
918	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
919	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
920	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
921	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
922	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
923	#117	—	2	1	no	—
924	#117	—	2	1	no	—
925	#117	—	2	1	no	—
926	#117	—	2	1	no	—
927	#117	—	2	2	no	—
928	#117	—	2	2	no	—
929	#117	—	2	1	no	—
930	#117	—	2	1	no	—
931	#117	—	2	1	no	—
932	#117	C₂³×C₃₁	1	1	yes	characteristic
933	#117	C₂³×C₃₁	1	2	yes	—
934	#117	C₂³×C₃₁	1	1	yes	characteristic
935	#117	C₂³×C₃₁	1	1	yes	characteristic
936	#117	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×C₄⋊C₄	—	2	1	no	—
938	C₂×C₄⋊C₄	—	2	1	no	—
939	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	—	2	1	no	—
941	C₂×C₄²	—	2	1	no	—
942	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
944	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
945	#107	C₂³×C₃₁	1	2	yes	—
946	#107	C₂³×C₃₁	1	2	yes	—
947	#107	C₂³×C₃₁	1	2	yes	—
948	#107	C₂³×C₃₁	1	2	yes	—
949	#106	C₂³×C₃₁	1	2	yes	—
950	#106	C₂³×C₃₁	1	2	yes	—
951	#106	C₂³×C₃₁	1	2	yes	—
952	#106	C₂³×C₃₁	1	2	yes	—
953	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
954	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
955	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
956	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
957	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
958	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
959	#103	C₂³×C₃₁	1	2	yes	—
960	#103	C₂³×C₃₁	1	2	yes	—
961	#103	C₂³×C₃₁	1	2	yes	—
962	#103	C₂³×C₃₁	1	2	yes	—
963	#103	C₂³×C₃₁	1	2	yes	—
964	#103	C₂³×C₃₁	1	2	yes	—
965	#103	C₂³×C₃₁	1	2	yes	—
966	#103	C₂³×C₃₁	1	2	yes	—
967	#103	C₂³×C₃₁	1	2	yes	—
968	#103	C₂³×C₃₁	1	2	yes	—
969	#102	C₂³×C₃₁	1	2	yes	—
970	#102	C₂³×C₃₁	1	2	yes	—
971	#102	C₂³×C₃₁	1	2	yes	—
972	#102	C₂³×C₃₁	1	2	yes	—
973	#102	C₂³×C₃₁	1	2	yes	—
974	#102	C₂³×C₃₁	1	2	yes	—
975	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
976	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
979	#97	C₂³×C₃₁	1	2	yes	—
980	#97	C₂³×C₃₁	1	2	yes	—
981	C₄×C₈	C₂³×C₃₁	1	2	yes	—
982	C₄×C₈	C₂³×C₃₁	1	2	yes	—
983	C₃₁	#60991	1	1	yes	characteristic, direct product factor, Sylow
984	C₂⁴	—	2	1	no	—
985	#41	—	4	1	no	—
986	#41	—	4	1	no	—
987	#41	—	4	1	no	—
988	#41	—	4	1	no	—
989	#41	—	8	2	no	—
990	#41	—	8	2	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	2	1	no	—
996	C₂×Q₈	—	4	2	no	—
997	C₂×Q₈	—	4	2	no	—
998	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1001	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	4	1	no	—
1015	C₂×D₄	—	4	1	no	—
1016	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1017	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1019	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	8	2	no	—
1032	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1037	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1041	Q₁₆	—	4	2	no	—
1042	Q₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	SD₁₆	—	4	2	no	—
1047	SD₁₆	—	4	2	no	—
1048	SD₁₆	—	4	2	no	—
1049	M₁₆	—	4	2	no	—
1050	C₂×C₈	—	4	2	no	—
1051	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1053	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1054	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1087	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1088	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1089	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1090	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1091	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1092	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1093	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1094	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1095	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1125	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	1	no	—
1129	C₄²	—	2	2	no	—
1130	C₄²	—	2	2	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	—	2	2	no	—
1133	C₄²	—	2	2	no	—
1134	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1135	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1136	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1137	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1138	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1139	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1140	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1141	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1142	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1143	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1144	C₂³	—	2	1	no	—
1145	C₂³	—	2	1	no	—
1146	C₂³	—	2	1	no	—
1147	C₂³	—	4	2	no	—
1148	C₂³	—	8	1	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1151	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1152	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	2	no	—
1155	Q₈	—	2	2	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	4	1	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	4	4	no	—
1162	Q₈	—	4	2	no	—
1163	Q₈	—	8	1	no	—
1164	Q₈	—	8	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	1	no	—
1172	D₄	—	4	1	no	—
1173	D₄	—	4	1	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	8	1	no	—
1177	D₄	—	8	1	no	—
1178	D₄	—	8	1	no	—
1179	D₄	—	8	1	no	—
1180	D₄	—	8	1	no	—
1181	D₄	—	8	1	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	1	no	—
1184	D₄	—	8	1	no	—
1185	D₄	—	8	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	4	1	no	—
1205	C₂×C₄	—	4	1	no	—
1206	C₂×C₄	—	4	1	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	4	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1223	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1227	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1228	C₈	—	2	2	no	—
1229	C₈	—	2	2	no	—
1230	C₈	—	2	2	no	—
1231	C₈	—	2	2	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	8	4	no	—
1251	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1252	C₄	—	2	1	no	—
1253	C₄	—	2	1	no	—
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	2	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	C₃₁×#577	1	2	yes	—
1272	C₄	C₃₁×#585	1	1	yes	characteristic
1273	C₄	C₃₁×#585	1	1	yes	characteristic
1274	C₂	—	4	1	no	—
1275	C₂	—	4	1	no	—
1276	C₂	—	4	1	no	—
1277	C₂	—	8	1	no	—
1278	C₂	—	8	1	no	—
1279	C₂	—	8	1	no	—
1280	C₂	C₃₁×#3449	1	1	yes	characteristic
1281	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1282	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×#3460	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×#3509	C₂	semidirect
3. C₃₁×#3254	C₂	semidirect
4. C₃₁×#3252	C₂	semidirect
5. C₃₁×#3248	C₂	semidirect
6. C₃₁×#3246	C₂	semidirect
7. C₃₁×#3242	C₂	semidirect
8. C₃₁×#3235	C₂	semidirect
9. C₃₁×#3233	C₂	semidirect
10. C₃₁×#3222	C₂	semidirect
11. C₃₁×#3218	C₂	semidirect
12. C₃₁×#3206	C₂	semidirect
13. C₃₁×#3201	C₂	semidirect
14. C₃₁×#3200	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3174	C₂	semidirect
17. C₃₁×#3126	C₂	semidirect
18. C₃₁×#3121	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
20. C₃₁×#3110	C₂	semidirect
21. C₃₁×#3107	C₂	semidirect
22. C₃₁×#3101	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
37. C₃₁×#541	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
55. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
61. C₃₁×#519	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#499	C₂²	semidirect
69. C₃₁×#491	C₂²	semidirect
72. C₃₁×#487	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
80. C₃₁×#482	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
82. C₃₁×#479	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#477	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#475	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#470	C₂²	semidirect
96. C₃₁×#468	C₂²	semidirect
97. C₃₁×#467	C₂²	semidirect
100. C₃₁×#465	C₂²	semidirect
103. C₃₁×#462	C₂²	semidirect
104. C₃₁×#462	C₂²	semidirect
109. C₃₁×#461	C₂²	semidirect
110. C₃₁×#461	C₂²	semidirect
115. C₃₁×#451	C₂²	semidirect
120. C₃₁×#448	C₂²	semidirect
121. C₃₁×#441	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×Q₁₆×C₃₁	C₂²	semidirect
128. C₄×SD₁₆×C₃₁	C₂²	semidirect
130. C₃₁×#433	C₂²	semidirect
132. C₃₁×#432	C₂²	semidirect
134. C₃₁×#431	C₂²	semidirect
135. C₃₁×#423	C₂²	semidirect
136. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
138. C₃₁×#405	C₂²	semidirect
502. #60991	C₃₁	direct (N × H)
591. #3509	C₂×C₃₁	semidirect
593. #3254	C₂×C₃₁	semidirect
594. #3252	C₂×C₃₁	semidirect
595. #3248	C₂×C₃₁	semidirect
596. #3246	C₂×C₃₁	semidirect
597. #3242	C₂×C₃₁	semidirect
598. #3235	C₂×C₃₁	semidirect
599. #3233	C₂×C₃₁	semidirect
600. #3222	C₂×C₃₁	semidirect
601. #3218	C₂×C₃₁	semidirect
602. #3206	C₂×C₃₁	semidirect
603. #3201	C₂×C₃₁	semidirect
604. #3200	C₂×C₃₁	semidirect
605. #3178	C₂×C₃₁	semidirect
606. #3174	C₂×C₃₁	semidirect
607. #3126	C₂×C₃₁	semidirect
608. #3121	C₂×C₃₁	semidirect
609. #3116	C₂×C₃₁	semidirect
610. #3110	C₂×C₃₁	semidirect
611. #3107	C₂×C₃₁	semidirect
612. #3101	C₂×C₃₁	semidirect
613. #2925	C₂×C₃₁	semidirect
669. #541	C₂²×C₃₁	semidirect
681. #533	C₂²×C₃₁	semidirect
682. #533	C₂²×C₃₁	semidirect
683. #533	C₂²×C₃₁	semidirect
687. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
693. #519	C₂²×C₃₁	semidirect
697. #501	C₂²×C₃₁	semidirect
698. #499	C₂²×C₃₁	semidirect
701. #491	C₂²×C₃₁	semidirect
704. #487	C₂²×C₃₁	semidirect
707. #485	C₂²×C₃₁	semidirect
712. #482	C₂²×C₃₁	semidirect
713. #479	C₂²×C₃₁	semidirect
714. #479	C₂²×C₃₁	semidirect
715. #477	C₂²×C₃₁	semidirect
716. #477	C₂²×C₃₁	semidirect
719. #476	C₂²×C₃₁	semidirect
720. #475	C₂²×C₃₁	semidirect
721. #475	C₂²×C₃₁	semidirect
724. #474	C₂²×C₃₁	semidirect
725. #470	C₂²×C₃₁	semidirect
728. #468	C₂²×C₃₁	semidirect
729. #467	C₂²×C₃₁	semidirect
732. #465	C₂²×C₃₁	semidirect
735. #462	C₂²×C₃₁	semidirect
736. #462	C₂²×C₃₁	semidirect
741. #461	C₂²×C₃₁	semidirect
742. #461	C₂²×C₃₁	semidirect
747. #451	C₂²×C₃₁	semidirect
752. #448	C₂²×C₃₁	semidirect
753. #441	C₂²×C₃₁	semidirect
756. #440	C₂²×C₃₁	semidirect
757. C₄×Q₁₆	C₂²×C₃₁	semidirect
760. C₄×SD₁₆	C₂²×C₃₁	semidirect
762. #433	C₂²×C₃₁	semidirect
764. #432	C₂²×C₃₁	semidirect
766. #431	C₂²×C₃₁	semidirect
767. #423	C₂²×C₃₁	semidirect
768. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
770. #405	C₂²×C₃₁	semidirect
983. C₃₁	#60991	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×#3509	2
C₃₁×#3460	2
C₃₁×#3254	2
C₃₁×#3252	2
C₃₁×#3248	2
C₃₁×#3246	2
C₃₁×#3242	2
C₃₁×#3235	2
C₃₁×#3233	2
C₃₁×#3222	2
C₃₁×#3218	2
C₃₁×#3206	2
C₃₁×#3201	2
C₃₁×#3200	2
C₃₁×#3178	2
C₃₁×#3174	2
C₃₁×#3126	2
C₃₁×#3121	2
C₃₁×#3116	2
C₃₁×#3110	2
C₃₁×#3107	2
C₃₁×#3101	2
C₃₁×#2925	2
#60991	31

Subgroups — C31×#60991 #21517750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60991 #21517750