Subgroups — C₃₁×#60977 #21517736

Order 7936.

1732 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3195	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3194	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3173	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#554	—	2	1	no	—
26	C₃₁×#552	—	2	1	no	—
27	C₃₁×#552	—	2	1	no	—
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#551	—	2	1	no	—
31	C₃₁×#551	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	—	2	1	no	—
35	C₃₁×#542	—	2	1	no	—
36	C₃₁×#542	—	2	1	no	—
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#542	C₂²	1	2	yes	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#542	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#542	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#541	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#541	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×#126	—	2	1	no	—
52	C₂×C₃₁×#124	—	2	1	no	—
53	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
54	C₃₁×#525	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×#123	—	2	1	no	—
56	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
60	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
64	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
65	C₃₁×#501	C₂²	1	2	yes	complemented
66	C₃₁×#498	C₂²	1	2	yes	complemented
67	C₃₁×#497	C₂²	1	2	yes	complemented
68	C₃₁×#495	C₂²	1	2	yes	complemented
69	C₃₁×#489	C₂²	1	2	yes	complemented
70	C₃₁×#489	C₂²	1	2	yes	complemented
71	C₃₁×#488	C₂²	1	2	yes	complemented
72	C₃₁×#487	C₂²	1	2	yes	complemented
73	C₃₁×#485	C₂²	1	2	yes	complemented
74	C₃₁×#483	C₂²	1	1	yes	characteristic
75	C₃₁×#483	C₂²	1	1	yes	characteristic
76	C₃₁×#483	C₂²	1	1	yes	characteristic
77	C₃₁×#483	C₂²	1	1	yes	characteristic
78	C₃₁×#483	C₂²	1	1	yes	characteristic
79	C₃₁×#483	C₂²	1	1	yes	characteristic
80	C₃₁×#483	C₂²	1	2	yes	complemented
81	C₃₁×#482	C₂²	1	2	yes	—
82	C₃₁×#481	C₂²	1	2	yes	—
83	C₃₁×#480	C₂²	1	1	yes	characteristic
84	C₃₁×#480	C₂²	1	1	yes	characteristic
85	C₃₁×#479	C₂²	1	2	yes	complemented
86	C₃₁×#478	C₂²	1	2	yes	complemented
87	C₃₁×#477	C₂²	1	2	yes	complemented
88	C₃₁×#476	C₂²	1	2	yes	complemented
89	C₃₁×#476	C₂²	1	2	yes	complemented
90	C₃₁×#475	C₂²	1	2	yes	complemented
91	C₃₁×#475	C₂²	1	2	yes	complemented
92	C₃₁×#475	C₂²	1	2	yes	complemented
93	C₃₁×#470	C₂²	1	2	yes	complemented
94	C₃₁×#470	C₂²	1	2	yes	complemented
95	C₃₁×#469	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	—
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	complemented
102	C₃₁×#464	C₂²	1	2	yes	complemented
103	C₃₁×#464	C₂²	1	2	yes	complemented
104	C₃₁×#464	C₂²	1	2	yes	complemented
105	C₃₁×#463	C₂²	1	2	yes	complemented
106	C₃₁×#463	C₂²	1	2	yes	complemented
107	C₃₁×#462	C₂²	1	2	yes	complemented
108	C₃₁×#461	C₂²	1	2	yes	complemented
109	C₃₁×#452	C₂²	1	2	yes	complemented
110	C₃₁×#451	C₂²	1	1	yes	characteristic
111	C₃₁×#451	C₂²	1	1	yes	characteristic
112	C₃₁×#451	C₂²	1	1	yes	characteristic
113	C₃₁×#451	C₂²	1	2	yes	complemented
114	C₃₁×#450	C₂²	1	1	yes	characteristic
115	C₃₁×#450	C₂²	1	1	yes	characteristic
116	C₃₁×#450	C₂²	1	1	yes	characteristic
117	C₃₁×#449	C₂²	1	2	yes	—
118	C₃₁×#448	C₂²	1	1	yes	characteristic
119	C₃₁×#448	C₂²	1	2	yes	—
120	C₃₁×#447	C₂²	1	1	yes	characteristic
121	C₃₁×#442	C₂²	1	2	yes	complemented
122	C₃₁×#441	C₂²	1	2	yes	complemented
123	C₃₁×#441	C₂²	1	2	yes	complemented
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	complemented
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
129	C₃₁×#433	C₂²	1	2	yes	complemented
130	C₃₁×#433	C₂²	1	2	yes	complemented
131	C₃₁×#432	C₂²	1	1	yes	characteristic
132	C₃₁×#432	C₂²	1	1	yes	characteristic
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₃₁×#424	C₂²	1	2	yes	complemented
136	C₃₁×#407	C₂²	1	1	yes	characteristic
137	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₃₁×#405	C₂²	1	2	yes	complemented
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₃₁	—	2	1	no	—
146	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×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×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#126	—	2	1	no	—
173	C₃₁×#126	—	2	1	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	C₂³	1	1	yes	characteristic
186	C₃₁×#125	C₂³	1	1	yes	characteristic
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	C₂³	1	1	yes	characteristic
196	C₃₁×#124	C₂³	1	2	yes	—
197	C₃₁×#124	C₂³	1	2	yes	—
198	C₃₁×#124	C₂³	1	1	yes	characteristic
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	1	no	—
207	C₃₁×#123	—	2	1	no	—
208	C₃₁×#123	—	2	1	no	—
209	C₃₁×#123	—	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	2	no	—
217	C₃₁×C₂²⋊Q₈	—	2	2	no	—
218	C₃₁×C₂²⋊Q₈	—	2	2	no	—
219	C₃₁×C₂²⋊Q₈	—	2	2	no	—
220	C₃₁×C₂²⋊Q₈	—	2	1	no	—
221	C₃₁×C₂²⋊Q₈	—	2	1	no	—
222	C₃₁×C₂²⋊Q₈	—	2	1	no	—
223	C₃₁×C₂²⋊Q₈	—	2	1	no	—
224	C₃₁×C₂²⋊Q₈	—	2	1	no	—
225	C₃₁×C₂²⋊Q₈	—	2	1	no	—
226	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
233	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	2	yes	—
238	C₃₁×#121	C₂³	1	2	yes	—
239	C₃₁×#121	C₂³	1	1	yes	characteristic
240	C₃₁×#120	—	2	1	no	—
241	C₄×Q₈×C₃₁	—	2	1	no	—
242	C₄×Q₈×C₃₁	—	2	1	no	—
243	C₄×Q₈×C₃₁	—	2	1	no	—
244	C₄×Q₈×C₃₁	—	2	1	no	—
245	C₄×Q₈×C₃₁	—	2	1	no	—
246	C₄×Q₈×C₃₁	—	2	1	no	—
247	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
252	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	1	no	—
257	C₄×D₄×C₃₁	—	2	1	no	—
258	C₄×D₄×C₃₁	—	2	1	no	—
259	C₄×D₄×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	1	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	C₂³	1	2	yes	—
264	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₃₁	C₂³	1	2	yes	—
266	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₃₁×#117	—	2	1	no	—
268	C₃₁×#117	—	2	1	no	—
269	C₃₁×#117	—	2	1	no	—
270	C₃₁×#117	—	2	1	no	—
271	C₃₁×#117	—	2	1	no	—
272	C₃₁×#117	—	2	1	no	—
273	C₃₁×#117	—	2	1	no	—
274	C₃₁×#117	D₄	1	1	yes	characteristic
275	C₃₁×#117	D₄	1	1	yes	characteristic
276	C₃₁×#117	D₄	1	1	yes	characteristic
277	C₃₁×#117	D₄	1	1	yes	characteristic
278	C₃₁×#117	C₂³	1	1	yes	characteristic
279	C₃₁×#117	C₂³	1	1	yes	characteristic
280	C₃₁×#117	C₂³	1	1	yes	characteristic
281	C₃₁×#117	C₂³	1	1	yes	characteristic
282	C₃₁×#117	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
301	C₂×C₄²×C₃₁	—	2	1	no	—
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×#106	C₂³	1	2	yes	—
307	C₃₁×#106	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	2	yes	—
313	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
314	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
315	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
316	C₃₁×#103	C₂³	1	2	yes	—
317	C₃₁×#103	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×#102	C₂³	1	2	yes	—
327	C₃₁×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
344	#41×C₃₁	—	4	2	no	—
345	C₂×Q₈×C₃₁	—	2	1	no	—
346	C₂×Q₈×C₃₁	—	2	1	no	—
347	C₂×Q₈×C₃₁	—	2	1	no	—
348	C₂×Q₈×C₃₁	—	2	1	no	—
349	C₂×Q₈×C₃₁	—	2	2	no	—
350	C₂×Q₈×C₃₁	—	2	2	no	—
351	C₂×Q₈×C₃₁	—	4	2	no	—
352	C₂×Q₈×C₃₁	—	4	2	no	—
353	C₂×Q₈×C₃₁	—	8	2	no	—
354	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₃₁	—	2	1	no	—
359	C₂×D₄×C₃₁	—	2	1	no	—
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	—	2	2	no	—
362	C₂×D₄×C₃₁	—	2	2	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	4	2	no	—
365	C₂×D₄×C₃₁	—	8	2	no	—
366	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	—	4	2	no	—
379	C₂²×C₄×C₃₁	—	8	2	no	—
380	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₃₁	—	4	2	no	—
391	Q₁₆×C₃₁	—	4	2	no	—
392	Q₁₆×C₃₁	—	4	2	no	—
393	SD₁₆×C₃₁	—	4	2	no	—
394	SD₁₆×C₃₁	—	4	2	no	—
395	SD₁₆×C₃₁	—	4	2	no	—
396	SD₁₆×C₃₁	—	4	2	no	—
397	D₈×C₃₁	—	4	2	no	—
398	M₁₆×C₃₁	—	4	2	no	—
399	C₂×C₈×C₃₁	—	4	2	no	—
400	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
401	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
402	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
403	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	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	1	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	—	2	1	no	—
427	C₄⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
449	C₂²⋊C₄×C₃₁	—	2	1	no	—
450	C₂²⋊C₄×C₃₁	—	2	1	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	no	—
452	C₂²⋊C₄×C₃₁	—	2	2	no	—
453	C₂²⋊C₄×C₃₁	—	2	1	no	—
454	C₂²⋊C₄×C₃₁	—	2	1	no	—
455	C₂²⋊C₄×C₃₁	—	2	1	no	—
456	C₂²⋊C₄×C₃₁	—	2	1	no	—
457	C₂²⋊C₄×C₃₁	—	2	1	no	—
458	C₂²⋊C₄×C₃₁	—	2	2	no	—
459	C₂²⋊C₄×C₃₁	—	2	2	no	—
460	C₂²⋊C₄×C₃₁	—	2	2	no	—
461	C₂²⋊C₄×C₃₁	—	2	2	no	—
462	C₂²⋊C₄×C₃₁	—	2	2	no	—
463	C₂²⋊C₄×C₃₁	—	2	2	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₃₁	—	2	2	no	—
483	C₄²×C₃₁	—	2	2	no	—
484	C₄²×C₃₁	—	2	1	no	—
485	C₄²×C₃₁	—	2	1	no	—
486	C₄²×C₃₁	—	2	1	no	—
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	1	no	—
489	C₄²×C₃₁	—	2	1	no	—
490	C₄²×C₃₁	—	2	1	no	—
491	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
496	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
497	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
498	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
499	#60977	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂³×C₃₁	—	2	2	no	—
501	C₂³×C₃₁	—	2	1	no	—
502	C₂³×C₃₁	—	2	2	no	—
503	C₂³×C₃₁	—	4	1	no	—
504	C₂³×C₃₁	—	4	1	no	—
505	C₂³×C₃₁	—	4	2	no	—
506	C₂³×C₃₁	—	4	2	no	—
507	C₂³×C₃₁	—	4	2	no	—
508	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	Q₈×C₃₁	—	2	2	no	—
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	—	4	2	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	8	1	no	—
519	Q₈×C₃₁	—	8	1	no	—
520	Q₈×C₃₁	—	8	2	no	—
521	Q₈×C₃₁	—	8	2	no	—
522	D₄×C₃₁	—	2	2	no	—
523	D₄×C₃₁	—	2	2	no	—
524	D₄×C₃₁	—	2	2	no	—
525	D₄×C₃₁	—	4	2	no	—
526	D₄×C₃₁	—	4	2	no	—
527	D₄×C₃₁	—	4	2	no	—
528	D₄×C₃₁	—	8	1	no	—
529	D₄×C₃₁	—	8	2	no	—
530	D₄×C₃₁	—	8	2	no	—
531	C₂×C₄×C₃₁	—	2	2	no	—
532	C₂×C₄×C₃₁	—	2	2	no	—
533	C₂×C₄×C₃₁	—	2	2	no	—
534	C₂×C₄×C₃₁	—	2	2	no	—
535	C₂×C₄×C₃₁	—	2	2	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	1	no	—
538	C₂×C₄×C₃₁	—	2	2	no	—
539	C₂×C₄×C₃₁	—	2	1	no	—
540	C₂×C₄×C₃₁	—	2	1	no	—
541	C₂×C₄×C₃₁	—	2	1	no	—
542	C₂×C₄×C₃₁	—	2	2	no	—
543	C₂×C₄×C₃₁	—	2	1	no	—
544	C₂×C₄×C₃₁	—	2	1	no	—
545	C₂×C₄×C₃₁	—	2	2	no	—
546	C₂×C₄×C₃₁	—	4	1	no	—
547	C₂×C₄×C₃₁	—	4	1	no	—
548	C₂×C₄×C₃₁	—	4	1	no	—
549	C₂×C₄×C₃₁	—	4	1	no	—
550	C₂×C₄×C₃₁	—	4	1	no	—
551	C₂×C₄×C₃₁	—	4	2	no	—
552	C₂×C₄×C₃₁	—	4	2	no	—
553	C₂×C₄×C₃₁	—	4	2	no	—
554	C₂×C₄×C₃₁	—	4	2	no	—
555	C₂×C₄×C₃₁	—	4	2	no	—
556	C₂×C₄×C₃₁	—	8	1	no	—
557	C₂×C₄×C₃₁	—	8	1	no	—
558	C₂×C₄×C₃₁	—	8	2	no	—
559	C₂×C₄×C₃₁	—	8	2	no	—
560	C₂×C₄×C₃₁	—	8	1	no	—
561	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
573	C₈×C₃₁	—	2	2	no	—
574	C₈×C₃₁	—	2	2	no	—
575	C₈×C₃₁	—	2	2	no	—
576	C₈×C₃₁	—	2	2	no	—
577	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
578	C₂×#542	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#3263	C₂×C₃₁	1	2	yes	complemented
580	#3258	C₂×C₃₁	1	2	yes	complemented
581	#3244	C₂×C₃₁	1	2	yes	complemented
582	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
583	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
584	#3225	C₂×C₃₁	1	2	yes	complemented
585	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#3211	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#3195	C₂×C₃₁	1	1	yes	characteristic, complemented
588	#3194	C₂×C₃₁	1	1	yes	characteristic
589	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#3187	C₂×C₃₁	1	1	yes	characteristic, complemented
591	#3178	C₂×C₃₁	1	2	yes	complemented
592	#3173	C₂×C₃₁	1	2	yes	complemented
593	#3125	C₂×C₃₁	1	2	yes	complemented
594	#3121	C₂×C₃₁	1	2	yes	complemented
595	#3114	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
598	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
600	C₂²×C₃₁	—	2	1	no	—
601	C₂²×C₃₁	—	2	1	no	—
602	C₂²×C₃₁	—	2	1	no	—
603	C₂²×C₃₁	—	2	1	no	—
604	C₂²×C₃₁	—	2	1	no	—
605	C₂²×C₃₁	—	2	1	no	—
606	C₂²×C₃₁	—	2	1	no	—
607	C₂²×C₃₁	—	2	1	no	—
608	C₂²×C₃₁	—	4	1	no	—
609	C₂²×C₃₁	—	4	2	no	—
610	C₂²×C₃₁	—	4	1	no	—
611	C₂²×C₃₁	—	4	2	no	—
612	C₂²×C₃₁	—	4	2	no	—
613	C₂²×C₃₁	—	4	1	no	—
614	C₂²×C₃₁	—	8	2	no	—
615	C₂²×C₃₁	—	8	4	no	—
616	C₂²×C₃₁	#577	1	2	yes	—
617	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₃₁	—	2	1	no	—
619	C₄×C₃₁	—	2	1	no	—
620	C₄×C₃₁	—	2	1	no	—
621	C₄×C₃₁	—	2	1	no	—
622	C₄×C₃₁	—	2	1	no	—
623	C₄×C₃₁	—	2	1	no	—
624	C₄×C₃₁	—	2	1	no	—
625	C₄×C₃₁	—	2	1	no	—
626	C₄×C₃₁	—	2	1	no	—
627	C₄×C₃₁	—	2	1	no	—
628	C₄×C₃₁	—	2	1	no	—
629	C₄×C₃₁	—	4	1	no	—
630	C₄×C₃₁	—	4	1	no	—
631	C₄×C₃₁	—	4	1	no	—
632	C₄×C₃₁	—	4	1	no	—
633	C₄×C₃₁	—	4	2	no	—
634	C₄×C₃₁	—	4	1	no	—
635	C₄×C₃₁	—	4	1	no	—
636	C₄×C₃₁	—	4	2	no	—
637	C₄×C₃₁	—	4	2	no	—
638	C₄×C₃₁	—	4	1	no	—
639	C₄×C₃₁	#585	1	2	yes	—
640	#556	—	2	1	no	—
641	#554	—	2	1	no	—
642	#552	—	2	1	no	—
643	#552	—	2	1	no	—
644	#552	—	2	1	no	—
645	#552	—	2	1	no	—
646	#551	—	2	1	no	—
647	#551	—	2	1	no	—
648	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#542	—	2	1	no	—
650	#542	—	2	1	no	—
651	#542	—	2	1	no	—
652	#542	—	2	1	no	—
653	#542	C₂²×C₃₁	1	2	yes	—
654	#542	C₂²×C₃₁	1	2	yes	—
655	#542	C₂²×C₃₁	1	2	yes	—
656	#542	C₂²×C₃₁	1	2	yes	—
657	#542	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#542	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#541	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#541	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#533	C₂²×C₃₁	1	1	yes	characteristic
663	#533	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
665	#529	C₂²×C₃₁	1	1	yes	characteristic
666	#529	C₂²×C₃₁	1	1	yes	characteristic
667	C₂×#126	—	2	1	no	—
668	C₂×#124	—	2	1	no	—
669	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
670	#525	C₂²×C₃₁	1	1	yes	characteristic
671	C₂×#123	—	2	1	no	—
672	C₂×C₂²⋊Q₈	—	2	1	no	—
673	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
674	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
675	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
676	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
679	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
680	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
681	#501	C₂²×C₃₁	1	2	yes	complemented
682	#498	C₂²×C₃₁	1	2	yes	complemented
683	#497	C₂²×C₃₁	1	2	yes	complemented
684	#495	C₂²×C₃₁	1	2	yes	complemented
685	#489	C₂²×C₃₁	1	2	yes	complemented
686	#489	C₂²×C₃₁	1	2	yes	complemented
687	#488	C₂²×C₃₁	1	2	yes	complemented
688	#487	C₂²×C₃₁	1	2	yes	complemented
689	#485	C₂²×C₃₁	1	2	yes	complemented
690	#483	C₂²×C₃₁	1	1	yes	characteristic
691	#483	C₂²×C₃₁	1	1	yes	characteristic
692	#483	C₂²×C₃₁	1	1	yes	characteristic
693	#483	C₂²×C₃₁	1	1	yes	characteristic
694	#483	C₂²×C₃₁	1	1	yes	characteristic
695	#483	C₂²×C₃₁	1	1	yes	characteristic
696	#483	C₂²×C₃₁	1	2	yes	complemented
697	#482	C₂²×C₃₁	1	2	yes	—
698	#481	C₂²×C₃₁	1	2	yes	—
699	#480	C₂²×C₃₁	1	1	yes	characteristic
700	#480	C₂²×C₃₁	1	1	yes	characteristic
701	#479	C₂²×C₃₁	1	2	yes	complemented
702	#478	C₂²×C₃₁	1	2	yes	complemented
703	#477	C₂²×C₃₁	1	2	yes	complemented
704	#476	C₂²×C₃₁	1	2	yes	complemented
705	#476	C₂²×C₃₁	1	2	yes	complemented
706	#475	C₂²×C₃₁	1	2	yes	complemented
707	#475	C₂²×C₃₁	1	2	yes	complemented
708	#475	C₂²×C₃₁	1	2	yes	complemented
709	#470	C₂²×C₃₁	1	2	yes	complemented
710	#470	C₂²×C₃₁	1	2	yes	complemented
711	#469	C₂²×C₃₁	1	2	yes	—
712	#468	C₂²×C₃₁	1	2	yes	—
713	#467	C₂²×C₃₁	1	2	yes	complemented
714	#465	C₂²×C₃₁	1	2	yes	—
715	#465	C₂²×C₃₁	1	2	yes	—
716	#465	C₂²×C₃₁	1	2	yes	complemented
717	#464	C₂²×C₃₁	1	2	yes	complemented
718	#464	C₂²×C₃₁	1	2	yes	complemented
719	#464	C₂²×C₃₁	1	2	yes	complemented
720	#464	C₂²×C₃₁	1	2	yes	complemented
721	#463	C₂²×C₃₁	1	2	yes	complemented
722	#463	C₂²×C₃₁	1	2	yes	complemented
723	#462	C₂²×C₃₁	1	2	yes	complemented
724	#461	C₂²×C₃₁	1	2	yes	complemented
725	#452	C₂²×C₃₁	1	2	yes	complemented
726	#451	C₂²×C₃₁	1	1	yes	characteristic
727	#451	C₂²×C₃₁	1	1	yes	characteristic
728	#451	C₂²×C₃₁	1	1	yes	characteristic
729	#451	C₂²×C₃₁	1	2	yes	complemented
730	#450	C₂²×C₃₁	1	1	yes	characteristic
731	#450	C₂²×C₃₁	1	1	yes	characteristic
732	#450	C₂²×C₃₁	1	1	yes	characteristic
733	#449	C₂²×C₃₁	1	2	yes	—
734	#448	C₂²×C₃₁	1	1	yes	characteristic
735	#448	C₂²×C₃₁	1	2	yes	—
736	#447	C₂²×C₃₁	1	1	yes	characteristic
737	#442	C₂²×C₃₁	1	2	yes	complemented
738	#441	C₂²×C₃₁	1	2	yes	complemented
739	#441	C₂²×C₃₁	1	2	yes	complemented
740	#440	C₂²×C₃₁	1	2	yes	complemented
741	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
742	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
743	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
744	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
745	#433	C₂²×C₃₁	1	2	yes	complemented
746	#433	C₂²×C₃₁	1	2	yes	complemented
747	#432	C₂²×C₃₁	1	1	yes	characteristic
748	#432	C₂²×C₃₁	1	1	yes	characteristic
749	#431	C₂²×C₃₁	1	1	yes	characteristic
750	#431	C₂²×C₃₁	1	1	yes	characteristic
751	#424	C₂²×C₃₁	1	2	yes	complemented
752	#407	C₂²×C₃₁	1	1	yes	characteristic
753	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
754	#405	C₂²×C₃₁	1	2	yes	complemented
755	C₂×C₃₁	—	2	2	no	—
756	C₂×C₃₁	—	4	1	no	—
757	C₂×C₃₁	—	4	1	no	—
758	C₂×C₃₁	—	8	1	no	—
759	C₂×C₃₁	—	8	2	no	—
760	C₂×C₃₁	#3449	1	1	yes	characteristic
761	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
762	C₂×C₃₁	#3586	1	1	yes	characteristic
763	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
764	C₂²×Q₈	—	2	1	no	—
765	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₂²×D₄	—	2	1	no	—
768	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
769	C₂³×C₄	—	2	1	no	—
770	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
773	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
778	C₂×D₈	C₂³×C₃₁	1	2	yes	—
779	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
780	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
781	C₄⋊Q₈	—	2	1	no	—
782	C₄⋊Q₈	—	2	1	no	—
783	C₄⋊Q₈	—	2	1	no	—
784	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	#126	—	2	2	no	—
791	#126	—	2	2	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	1	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#125	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	C₂³×C₃₁	1	1	yes	characteristic
810	#125	C₂³×C₃₁	1	1	yes	characteristic
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	—	2	1	no	—
816	#124	—	2	1	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	C₂³×C₃₁	1	2	yes	—
820	#124	C₂³×C₃₁	1	2	yes	—
821	#124	C₂³×C₃₁	1	1	yes	characteristic
822	#124	C₂³×C₃₁	1	1	yes	characteristic
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	1	no	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	2	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	C₂³×C₃₁	1	2	yes	—
861	#121	C₂³×C₃₁	1	2	yes	—
862	#121	C₂³×C₃₁	1	1	yes	characteristic
863	#121	C₂³×C₃₁	1	1	yes	characteristic
864	#120	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
872	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
873	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	C₂³×C₃₁	1	2	yes	—
888	C₄×D₄	C₂³×C₃₁	1	2	yes	—
889	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
891	#117	—	2	1	no	—
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	D₄×C₃₁	1	1	yes	characteristic
899	#117	D₄×C₃₁	1	1	yes	characteristic
900	#117	D₄×C₃₁	1	1	yes	characteristic
901	#117	D₄×C₃₁	1	1	yes	characteristic
902	#117	C₂³×C₃₁	1	1	yes	characteristic
903	#117	C₂³×C₃₁	1	1	yes	characteristic
904	#117	C₂³×C₃₁	1	1	yes	characteristic
905	#117	C₂³×C₃₁	1	1	yes	characteristic
906	#117	C₂³×C₃₁	1	1	yes	characteristic
907	C₂×C₄⋊C₄	—	2	1	no	—
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	—	2	1	no	—
911	C₂×C₄⋊C₄	—	2	1	no	—
912	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
913	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	—	2	1	no	—
918	C₂×C₂²⋊C₄	—	2	1	no	—
919	C₂×C₂²⋊C₄	—	2	1	no	—
920	C₂×C₂²⋊C₄	—	2	1	no	—
921	C₂×C₂²⋊C₄	—	2	1	no	—
922	C₂×C₂²⋊C₄	—	2	1	no	—
923	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
925	C₂×C₄²	—	2	1	no	—
926	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
927	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
928	#107	C₂³×C₃₁	1	2	yes	—
929	#107	C₂³×C₃₁	1	2	yes	—
930	#106	C₂³×C₃₁	1	2	yes	—
931	#106	C₂³×C₃₁	1	2	yes	—
932	#106	C₂³×C₃₁	1	2	yes	—
933	#106	C₂³×C₃₁	1	2	yes	—
934	#106	C₂³×C₃₁	1	2	yes	—
935	#106	C₂³×C₃₁	1	2	yes	—
936	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
937	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
938	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
939	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
940	#103	C₂³×C₃₁	1	2	yes	—
941	#103	C₂³×C₃₁	1	2	yes	—
942	#103	C₂³×C₃₁	1	2	yes	—
943	#103	C₂³×C₃₁	1	2	yes	—
944	#103	C₂³×C₃₁	1	2	yes	—
945	#103	C₂³×C₃₁	1	2	yes	—
946	#103	C₂³×C₃₁	1	2	yes	—
947	#103	C₂³×C₃₁	1	2	yes	—
948	#103	C₂³×C₃₁	1	2	yes	—
949	#103	C₂³×C₃₁	1	2	yes	—
950	#102	C₂³×C₃₁	1	2	yes	—
951	#102	C₂³×C₃₁	1	2	yes	—
952	#102	C₂³×C₃₁	1	2	yes	—
953	#102	C₂³×C₃₁	1	2	yes	—
954	#102	C₂³×C₃₁	1	2	yes	—
955	#102	C₂³×C₃₁	1	2	yes	—
956	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
957	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
958	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
962	#97	C₂³×C₃₁	1	2	yes	—
963	#97	C₂³×C₃₁	1	2	yes	—
964	C₄×C₈	C₂³×C₃₁	1	2	yes	—
965	C₄×C₈	C₂³×C₃₁	1	2	yes	—
966	C₃₁	#60977	1	1	yes	characteristic, direct product factor, Sylow
967	C₂⁴	—	2	1	no	—
968	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
969	#41	—	4	2	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	1	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	4	2	no	—
977	C₂×Q₈	—	4	2	no	—
978	C₂×Q₈	—	8	2	no	—
979	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
980	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	8	2	no	—
991	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	8	2	no	—
1005	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	Q₁₆	—	4	2	no	—
1016	Q₁₆	—	4	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	4	2	no	—
1019	SD₁₆	—	4	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	D₈	—	4	2	no	—
1023	M₁₆	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1026	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
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	1	no	—
1060	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1073	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1102	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1103	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1104	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1107	C₄²	—	2	2	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1117	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1118	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1119	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1120	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1121	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1123	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1124	C₂³	—	2	2	no	—
1125	C₂³	—	2	1	no	—
1126	C₂³	—	2	2	no	—
1127	C₂³	—	4	1	no	—
1128	C₂³	—	4	1	no	—
1129	C₂³	—	4	2	no	—
1130	C₂³	—	4	2	no	—
1131	C₂³	—	4	2	no	—
1132	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1133	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1134	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	1	no	—
1143	Q₈	—	8	1	no	—
1144	Q₈	—	8	2	no	—
1145	Q₈	—	8	2	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	2	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	8	1	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	4	2	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	8	1	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1196	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1197	C₈	—	2	2	no	—
1198	C₈	—	2	2	no	—
1199	C₈	—	2	2	no	—
1200	C₈	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	8	2	no	—
1216	C₂²	—	8	4	no	—
1217	C₂²	C₃₁×#577	1	2	yes	—
1218	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1219	C₄	—	2	1	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	C₃₁×#585	1	2	yes	—
1241	C₂	—	2	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	8	2	no	—
1245	C₂	—	8	1	no	—
1246	C₂	C₃₁×#3449	1	1	yes	characteristic
1247	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1248	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×#3194	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₂×C₃₁×#542	C₂	semidirect
3. C₃₁×#3263	C₂	semidirect
4. C₃₁×#3258	C₂	semidirect
5. C₃₁×#3244	C₂	semidirect
6. C₃₁×#3238	C₂	semidirect
7. C₃₁×#3229	C₂	semidirect
8. C₃₁×#3225	C₂	semidirect
9. C₃₁×#3215	C₂	semidirect
10. C₃₁×#3211	C₂	semidirect
11. C₃₁×#3195	C₂	semidirect
13. C₃₁×#3190	C₂	semidirect
14. C₃₁×#3187	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3173	C₂	semidirect
17. C₃₁×#3125	C₂	semidirect
18. C₃₁×#3121	C₂	semidirect
19. C₃₁×#3114	C₂	semidirect
20. C₃₁×#3113	C₂	semidirect
21. C₃₁×#3108	C₂	semidirect
22. C₃₁×#3101	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
32. C₃₁×#544	C₂²	semidirect
41. C₃₁×#542	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
43. C₃₁×#541	C₂²	semidirect
44. C₃₁×#541	C₂²	semidirect
45. C₃₁×#536	C₂²	semidirect
60. C₃₁×#520	C₂²	semidirect
61. C₃₁×#519	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#498	C₂²	semidirect
67. C₃₁×#497	C₂²	semidirect
68. C₃₁×#495	C₂²	semidirect
69. C₃₁×#489	C₂²	semidirect
70. C₃₁×#489	C₂²	semidirect
71. C₃₁×#488	C₂²	semidirect
72. C₃₁×#487	C₂²	semidirect
73. C₃₁×#485	C₂²	semidirect
80. C₃₁×#483	C₂²	semidirect
85. C₃₁×#479	C₂²	semidirect
86. C₃₁×#478	C₂²	semidirect
87. C₃₁×#477	C₂²	semidirect
88. C₃₁×#476	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#475	C₂²	semidirect
92. C₃₁×#475	C₂²	semidirect
93. C₃₁×#470	C₂²	semidirect
94. C₃₁×#470	C₂²	semidirect
97. C₃₁×#467	C₂²	semidirect
100. C₃₁×#465	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
102. C₃₁×#464	C₂²	semidirect
103. C₃₁×#464	C₂²	semidirect
104. C₃₁×#464	C₂²	semidirect
105. C₃₁×#463	C₂²	semidirect
106. C₃₁×#463	C₂²	semidirect
107. C₃₁×#462	C₂²	semidirect
108. C₃₁×#461	C₂²	semidirect
109. C₃₁×#452	C₂²	semidirect
113. C₃₁×#451	C₂²	semidirect
121. C₃₁×#442	C₂²	semidirect
122. C₃₁×#441	C₂²	semidirect
123. C₃₁×#441	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×Q₁₆×C₃₁	C₂²	semidirect
126. C₄×SD₁₆×C₃₁	C₂²	semidirect
127. C₄×SD₁₆×C₃₁	C₂²	semidirect
128. C₄×SD₁₆×C₃₁	C₂²	semidirect
129. C₃₁×#433	C₂²	semidirect
130. C₃₁×#433	C₂²	semidirect
135. C₃₁×#424	C₂²	semidirect
138. C₃₁×#405	C₂²	semidirect
499. #60977	C₃₁	direct (N × H)
577. #3495	C₂×C₃₁	semidirect
578. C₂×#542	C₂×C₃₁	semidirect
579. #3263	C₂×C₃₁	semidirect
580. #3258	C₂×C₃₁	semidirect
581. #3244	C₂×C₃₁	semidirect
582. #3238	C₂×C₃₁	semidirect
583. #3229	C₂×C₃₁	semidirect
584. #3225	C₂×C₃₁	semidirect
585. #3215	C₂×C₃₁	semidirect
586. #3211	C₂×C₃₁	semidirect
587. #3195	C₂×C₃₁	semidirect
589. #3190	C₂×C₃₁	semidirect
590. #3187	C₂×C₃₁	semidirect
591. #3178	C₂×C₃₁	semidirect
592. #3173	C₂×C₃₁	semidirect
593. #3125	C₂×C₃₁	semidirect
594. #3121	C₂×C₃₁	semidirect
595. #3114	C₂×C₃₁	semidirect
596. #3113	C₂×C₃₁	semidirect
597. #3108	C₂×C₃₁	semidirect
598. #3101	C₂×C₃₁	semidirect
599. #2924	C₂×C₃₁	semidirect
648. #544	C₂²×C₃₁	semidirect
657. #542	C₂²×C₃₁	semidirect
658. #542	C₂²×C₃₁	semidirect
659. #541	C₂²×C₃₁	semidirect
660. #541	C₂²×C₃₁	semidirect
661. #536	C₂²×C₃₁	semidirect
676. #520	C₂²×C₃₁	semidirect
677. #519	C₂²×C₃₁	semidirect
681. #501	C₂²×C₃₁	semidirect
682. #498	C₂²×C₃₁	semidirect
683. #497	C₂²×C₃₁	semidirect
684. #495	C₂²×C₃₁	semidirect
685. #489	C₂²×C₃₁	semidirect
686. #489	C₂²×C₃₁	semidirect
687. #488	C₂²×C₃₁	semidirect
688. #487	C₂²×C₃₁	semidirect
689. #485	C₂²×C₃₁	semidirect
696. #483	C₂²×C₃₁	semidirect
701. #479	C₂²×C₃₁	semidirect
702. #478	C₂²×C₃₁	semidirect
703. #477	C₂²×C₃₁	semidirect
704. #476	C₂²×C₃₁	semidirect
705. #476	C₂²×C₃₁	semidirect
706. #475	C₂²×C₃₁	semidirect
707. #475	C₂²×C₃₁	semidirect
708. #475	C₂²×C₃₁	semidirect
709. #470	C₂²×C₃₁	semidirect
710. #470	C₂²×C₃₁	semidirect
713. #467	C₂²×C₃₁	semidirect
716. #465	C₂²×C₃₁	semidirect
717. #464	C₂²×C₃₁	semidirect
718. #464	C₂²×C₃₁	semidirect
719. #464	C₂²×C₃₁	semidirect
720. #464	C₂²×C₃₁	semidirect
721. #463	C₂²×C₃₁	semidirect
722. #463	C₂²×C₃₁	semidirect
723. #462	C₂²×C₃₁	semidirect
724. #461	C₂²×C₃₁	semidirect
725. #452	C₂²×C₃₁	semidirect
729. #451	C₂²×C₃₁	semidirect
737. #442	C₂²×C₃₁	semidirect
738. #441	C₂²×C₃₁	semidirect
739. #441	C₂²×C₃₁	semidirect
740. #440	C₂²×C₃₁	semidirect
741. C₄×Q₁₆	C₂²×C₃₁	semidirect
742. C₄×SD₁₆	C₂²×C₃₁	semidirect
743. C₄×SD₁₆	C₂²×C₃₁	semidirect
744. C₄×SD₁₆	C₂²×C₃₁	semidirect
745. #433	C₂²×C₃₁	semidirect
746. #433	C₂²×C₃₁	semidirect
751. #424	C₂²×C₃₁	semidirect
754. #405	C₂²×C₃₁	semidirect
966. C₃₁	#60977	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×#3495	2
C₂×C₃₁×#542	2
C₃₁×#3263	2
C₃₁×#3258	2
C₃₁×#3244	2
C₃₁×#3238	2
C₃₁×#3229	2
C₃₁×#3225	2
C₃₁×#3215	2
C₃₁×#3211	2
C₃₁×#3195	2
C₃₁×#3194	2
C₃₁×#3190	2
C₃₁×#3187	2
C₃₁×#3178	2
C₃₁×#3173	2
C₃₁×#3125	2
C₃₁×#3121	2
C₃₁×#3114	2
C₃₁×#3113	2
C₃₁×#3108	2
C₃₁×#3101	2
C₃₁×#2924	2
#60977	31

Subgroups — C31×#60977 #21517736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60977 #21517736