Subgroups — C₃₁×#60982 #21517741

Order 7936.

1728 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3260	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3193	C₂	1	1	yes	maximal, characteristic, complemented
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×#3174	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#555	—	2	1	no	—
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#553	—	2	1	no	—
27	C₃₁×#551	—	2	1	no	—
28	C₃₁×#551	—	2	1	no	—
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic
33	C₃₁×#542	C₂²	1	1	yes	characteristic
34	C₃₁×#542	C₂²	1	1	yes	characteristic
35	C₃₁×#541	—	2	1	no	—
36	C₃₁×#541	—	2	1	no	—
37	C₃₁×#541	—	2	1	no	—
38	C₃₁×#541	—	2	1	no	—
39	C₃₁×#541	C₂²	1	2	yes	—
40	C₃₁×#541	C₂²	1	2	yes	—
41	C₃₁×#541	C₂²	1	2	yes	complemented
42	C₃₁×#541	C₂²	1	2	yes	complemented
43	C₃₁×#540	C₂²	1	1	yes	characteristic
44	C₃₁×#540	C₂²	1	1	yes	characteristic
45	C₃₁×#535	C₂²	1	1	yes	characteristic
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
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×#126	—	2	1	no	—
53	C₂×C₃₁×#125	—	2	1	no	—
54	C₂×C₃₁×#125	—	2	1	no	—
55	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#525	C₂²	1	1	yes	characteristic
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
61	C₃₁×#518	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₃₁×#117	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	complemented
68	C₃₁×#492	C₂²	1	2	yes	complemented
69	C₃₁×#491	C₂²	1	2	yes	complemented
70	C₃₁×#490	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	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#484	C₂²	1	2	yes	—
76	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#483	C₂²	1	2	yes	—
78	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#481	C₂²	1	1	yes	characteristic
80	C₃₁×#481	C₂²	1	1	yes	characteristic
81	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#480	C₂²	1	1	yes	characteristic
83	C₃₁×#480	C₂²	1	1	yes	characteristic
84	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#479	C₂²	1	2	yes	complemented
86	C₃₁×#479	C₂²	1	2	yes	complemented
87	C₃₁×#479	C₂²	1	2	yes	complemented
88	C₃₁×#478	C₂²	1	2	yes	complemented
89	C₃₁×#478	C₂²	1	2	yes	complemented
90	C₃₁×#478	C₂²	1	2	yes	complemented
91	C₃₁×#477	C₂²	1	2	yes	complemented
92	C₃₁×#475	C₂²	1	2	yes	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	complemented
102	C₃₁×#464	C₂²	1	2	yes	complemented
103	C₃₁×#462	C₂²	1	2	yes	complemented
104	C₃₁×#461	C₂²	1	2	yes	complemented
105	C₃₁×#461	C₂²	1	2	yes	complemented
106	C₃₁×#461	C₂²	1	2	yes	complemented
107	C₃₁×#460	C₂²	1	2	yes	complemented
108	C₃₁×#460	C₂²	1	2	yes	complemented
109	C₃₁×#452	C₂²	1	2	yes	—
110	C₃₁×#452	C₂²	1	2	yes	—
111	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#450	C₂²	1	2	yes	—
114	C₃₁×#450	C₂²	1	2	yes	—
115	C₃₁×#448	C₂²	1	1	yes	characteristic
116	C₃₁×#448	C₂²	1	1	yes	characteristic
117	C₃₁×#448	C₂²	1	1	yes	characteristic
118	C₃₁×#448	C₂²	1	1	yes	characteristic
119	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#441	C₂²	1	2	yes	complemented
122	C₃₁×#440	C₂²	1	2	yes	complemented
123	C₃₁×#440	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	—
130	C₃₁×#433	C₂²	1	2	yes	—
131	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
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	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
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×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×SD₁₆×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	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#126	—	2	1	no	—
167	C₃₁×#126	—	2	1	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
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×#126	—	2	2	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#125	—	2	2	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	2	no	—
184	C₃₁×#125	—	2	2	no	—
185	C₃₁×#125	—	2	2	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	—	2	1	no	—
189	C₃₁×#125	C₂³	1	2	yes	—
190	C₃₁×#125	C₂³	1	1	yes	characteristic
191	C₃₁×#125	C₂³	1	2	yes	—
192	C₃₁×#125	C₂³	1	1	yes	characteristic
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	—	2	1	no	—
197	C₃₁×#124	C₂³	1	1	yes	characteristic
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	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	C₂³	1	2	yes	—
217	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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×#121	—	2	1	no	—
223	C₃₁×#121	—	2	1	no	—
224	C₃₁×#121	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
233	C₃₁×#121	C₂³	1	1	yes	characteristic
234	C₃₁×#121	C₂³	1	1	yes	characteristic
235	C₃₁×#121	C₂³	1	1	yes	characteristic
236	C₃₁×#121	C₂³	1	1	yes	characteristic
237	C₃₁×#121	C₂³	1	1	yes	characteristic
238	C₃₁×#120	—	2	1	no	—
239	C₃₁×#120	—	2	1	no	—
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	C₂³	1	2	yes	—
246	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
247	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
249	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	—	2	1	no	—
252	C₄×D₄×C₃₁	—	2	1	no	—
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
271	C₃₁×#117	D₄	1	1	yes	characteristic
272	C₃₁×#117	D₄	1	1	yes	characteristic
273	C₃₁×#117	D₄	1	1	yes	characteristic
274	C₃₁×#117	C₂³	1	1	yes	characteristic
275	C₃₁×#117	C₂³	1	1	yes	characteristic
276	C₃₁×#117	C₂³	1	1	yes	characteristic
277	C₃₁×#117	C₂³	1	1	yes	characteristic
278	C₃₁×#117	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
280	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	—	2	1	no	—
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×#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	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	#41×C₃₁	—	8	2	no	—
346	#41×C₃₁	—	8	2	no	—
347	C₂×Q₈×C₃₁	—	2	1	no	—
348	C₂×Q₈×C₃₁	—	2	1	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	1	no	—
351	C₂×Q₈×C₃₁	—	4	2	no	—
352	C₂×Q₈×C₃₁	—	4	2	no	—
353	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
356	C₂×D₄×C₃₁	—	2	1	no	—
357	C₂×D₄×C₃₁	—	2	1	no	—
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	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	—	4	2	no	—
369	C₂×D₄×C₃₁	—	8	2	no	—
370	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	1	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	1	no	—
377	C₂²×C₄×C₃₁	—	2	1	no	—
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	1	no	—
380	C₂²×C₄×C₃₁	—	2	1	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	—	4	2	no	—
386	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	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	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	Q₁₆×C₃₁	—	4	2	no	—
397	Q₁₆×C₃₁	—	4	2	no	—
398	SD₁₆×C₃₁	—	4	2	no	—
399	SD₁₆×C₃₁	—	4	2	no	—
400	SD₁₆×C₃₁	—	4	2	no	—
401	SD₁₆×C₃₁	—	4	2	no	—
402	SD₁₆×C₃₁	—	4	2	no	—
403	SD₁₆×C₃₁	—	4	2	no	—
404	M₁₆×C₃₁	—	4	2	no	—
405	C₂×C₈×C₃₁	—	4	2	no	—
406	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
407	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
409	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	2	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	2	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	1	no	—
437	C₄⋊C₄×C₃₁	—	2	1	no	—
438	C₄⋊C₄×C₃₁	—	2	1	no	—
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	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	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	1	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	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
484	C₄²×C₃₁	—	2	2	no	—
485	C₄²×C₃₁	—	2	2	no	—
486	C₄²×C₃₁	—	2	2	no	—
487	C₄²×C₃₁	—	2	2	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	#60982	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	1	no	—
503	C₂³×C₃₁	—	2	1	no	—
504	C₂³×C₃₁	—	4	1	no	—
505	C₂³×C₃₁	—	4	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	2	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	4	2	no	—
519	Q₈×C₃₁	—	8	1	no	—
520	Q₈×C₃₁	—	8	1	no	—
521	D₄×C₃₁	—	2	2	no	—
522	D₄×C₃₁	—	2	2	no	—
523	D₄×C₃₁	—	2	2	no	—
524	D₄×C₃₁	—	4	2	no	—
525	D₄×C₃₁	—	4	2	no	—
526	D₄×C₃₁	—	4	2	no	—
527	D₄×C₃₁	—	4	2	no	—
528	D₄×C₃₁	—	4	2	no	—
529	D₄×C₃₁	—	8	1	no	—
530	D₄×C₃₁	—	8	1	no	—
531	D₄×C₃₁	—	8	1	no	—
532	D₄×C₃₁	—	8	1	no	—
533	D₄×C₃₁	—	8	1	no	—
534	D₄×C₃₁	—	8	1	no	—
535	D₄×C₃₁	—	8	1	no	—
536	C₂×C₄×C₃₁	—	2	2	no	—
537	C₂×C₄×C₃₁	—	2	2	no	—
538	C₂×C₄×C₃₁	—	2	2	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	2	no	—
541	C₂×C₄×C₃₁	—	2	1	no	—
542	C₂×C₄×C₃₁	—	2	2	no	—
543	C₂×C₄×C₃₁	—	2	2	no	—
544	C₂×C₄×C₃₁	—	2	2	no	—
545	C₂×C₄×C₃₁	—	2	2	no	—
546	C₂×C₄×C₃₁	—	2	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	2	1	no	—
550	C₂×C₄×C₃₁	—	4	1	no	—
551	C₂×C₄×C₃₁	—	4	1	no	—
552	C₂×C₄×C₃₁	—	4	1	no	—
553	C₂×C₄×C₃₁	—	4	1	no	—
554	C₂×C₄×C₃₁	—	4	1	no	—
555	C₂×C₄×C₃₁	—	4	2	no	—
556	C₂×C₄×C₃₁	—	4	2	no	—
557	C₂×C₄×C₃₁	—	4	2	no	—
558	C₂×C₄×C₃₁	—	4	2	no	—
559	C₂×C₄×C₃₁	—	4	2	no	—
560	C₂×C₄×C₃₁	—	8	1	no	—
561	C₂×C₄×C₃₁	—	8	1	no	—
562	C₂×C₄×C₃₁	—	8	1	no	—
563	C₂×C₄×C₃₁	—	8	1	no	—
564	C₂×C₄×C₃₁	—	8	1	no	—
565	C₂×C₄×C₃₁	—	8	1	no	—
566	C₂×C₄×C₃₁	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
579	C₈×C₃₁	—	2	2	no	—
580	C₈×C₃₁	—	2	2	no	—
581	C₈×C₃₁	—	2	2	no	—
582	C₈×C₃₁	—	2	2	no	—
583	#3494	C₂×C₃₁	1	1	yes	characteristic
584	C₂×#541	C₂×C₃₁	1	1	yes	characteristic, complemented
585	#3260	C₂×C₃₁	1	2	yes	complemented
586	#3258	C₂×C₃₁	1	2	yes	complemented
587	#3242	C₂×C₃₁	1	2	yes	complemented
588	#3234	C₂×C₃₁	1	1	yes	characteristic, complemented
589	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
590	#3222	C₂×C₃₁	1	2	yes	complemented
591	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3196	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3193	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3187	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3178	C₂×C₃₁	1	2	yes	complemented
598	#3174	C₂×C₃₁	1	2	yes	complemented
599	#3123	C₂×C₃₁	1	2	yes	complemented
600	#3120	C₂×C₃₁	1	2	yes	complemented
601	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
606	C₂²×C₃₁	—	2	1	no	—
607	C₂²×C₃₁	—	2	1	no	—
608	C₂²×C₃₁	—	2	1	no	—
609	C₂²×C₃₁	—	2	1	no	—
610	C₂²×C₃₁	—	2	1	no	—
611	C₂²×C₃₁	—	2	1	no	—
612	C₂²×C₃₁	—	2	1	no	—
613	C₂²×C₃₁	—	2	1	no	—
614	C₂²×C₃₁	—	4	1	no	—
615	C₂²×C₃₁	—	4	1	no	—
616	C₂²×C₃₁	—	4	1	no	—
617	C₂²×C₃₁	—	4	1	no	—
618	C₂²×C₃₁	—	4	1	no	—
619	C₂²×C₃₁	—	4	1	no	—
620	C₂²×C₃₁	—	4	1	no	—
621	C₂²×C₃₁	—	4	1	no	—
622	C₂²×C₃₁	—	4	1	no	—
623	C₂²×C₃₁	—	8	2	no	—
624	C₂²×C₃₁	—	16	2	no	—
625	C₂²×C₃₁	#577	1	2	yes	—
626	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
627	C₄×C₃₁	—	2	1	no	—
628	C₄×C₃₁	—	2	1	no	—
629	C₄×C₃₁	—	2	1	no	—
630	C₄×C₃₁	—	2	1	no	—
631	C₄×C₃₁	—	2	1	no	—
632	C₄×C₃₁	—	2	1	no	—
633	C₄×C₃₁	—	2	1	no	—
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	—	4	2	no	—
639	C₄×C₃₁	—	4	1	no	—
640	C₄×C₃₁	—	4	1	no	—
641	C₄×C₃₁	—	4	2	no	—
642	C₄×C₃₁	—	4	2	no	—
643	C₄×C₃₁	—	4	2	no	—
644	C₄×C₃₁	—	4	1	no	—
645	C₄×C₃₁	—	4	1	no	—
646	C₄×C₃₁	—	4	1	no	—
647	C₄×C₃₁	#585	1	2	yes	—
648	#555	—	2	1	no	—
649	#553	—	2	1	no	—
650	#553	—	2	1	no	—
651	#551	—	2	1	no	—
652	#551	—	2	1	no	—
653	#547	—	2	1	no	—
654	#546	—	2	1	no	—
655	#546	—	2	1	no	—
656	#544	C₂²×C₃₁	1	1	yes	characteristic
657	#542	C₂²×C₃₁	1	1	yes	characteristic
658	#542	C₂²×C₃₁	1	1	yes	characteristic
659	#541	—	2	1	no	—
660	#541	—	2	1	no	—
661	#541	—	2	1	no	—
662	#541	—	2	1	no	—
663	#541	C₂²×C₃₁	1	2	yes	—
664	#541	C₂²×C₃₁	1	2	yes	—
665	#541	C₂²×C₃₁	1	2	yes	complemented
666	#541	C₂²×C₃₁	1	2	yes	complemented
667	#540	C₂²×C₃₁	1	1	yes	characteristic
668	#540	C₂²×C₃₁	1	1	yes	characteristic
669	#535	C₂²×C₃₁	1	1	yes	characteristic
670	#532	C₂²×C₃₁	1	1	yes	characteristic
671	#532	C₂²×C₃₁	1	1	yes	characteristic
672	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#529	C₂²×C₃₁	1	1	yes	characteristic
674	#529	C₂²×C₃₁	1	1	yes	characteristic
675	C₂×#126	—	2	1	no	—
676	C₂×#126	—	2	1	no	—
677	C₂×#125	—	2	1	no	—
678	C₂×#125	—	2	1	no	—
679	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#525	C₂²×C₃₁	1	1	yes	characteristic
681	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
682	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
684	#520	C₂²×C₃₁	1	1	yes	characteristic
685	#518	C₂²×C₃₁	1	1	yes	characteristic
686	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
689	#501	C₂²×C₃₁	1	2	yes	complemented
690	#499	C₂²×C₃₁	1	2	yes	complemented
691	#497	C₂²×C₃₁	1	2	yes	complemented
692	#492	C₂²×C₃₁	1	2	yes	complemented
693	#491	C₂²×C₃₁	1	2	yes	complemented
694	#490	C₂²×C₃₁	1	2	yes	complemented
695	#488	C₂²×C₃₁	1	2	yes	complemented
696	#487	C₂²×C₃₁	1	2	yes	complemented
697	#485	C₂²×C₃₁	1	2	yes	—
698	#485	C₂²×C₃₁	1	2	yes	—
699	#484	C₂²×C₃₁	1	2	yes	—
700	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#483	C₂²×C₃₁	1	2	yes	—
702	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#481	C₂²×C₃₁	1	1	yes	characteristic
704	#481	C₂²×C₃₁	1	1	yes	characteristic
705	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#480	C₂²×C₃₁	1	1	yes	characteristic
707	#480	C₂²×C₃₁	1	1	yes	characteristic
708	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#479	C₂²×C₃₁	1	2	yes	complemented
710	#479	C₂²×C₃₁	1	2	yes	complemented
711	#479	C₂²×C₃₁	1	2	yes	complemented
712	#478	C₂²×C₃₁	1	2	yes	complemented
713	#478	C₂²×C₃₁	1	2	yes	complemented
714	#478	C₂²×C₃₁	1	2	yes	complemented
715	#477	C₂²×C₃₁	1	2	yes	complemented
716	#475	C₂²×C₃₁	1	2	yes	complemented
717	#470	C₂²×C₃₁	1	2	yes	complemented
718	#468	C₂²×C₃₁	1	2	yes	—
719	#468	C₂²×C₃₁	1	2	yes	—
720	#468	C₂²×C₃₁	1	2	yes	complemented
721	#467	C₂²×C₃₁	1	2	yes	complemented
722	#465	C₂²×C₃₁	1	2	yes	—
723	#465	C₂²×C₃₁	1	2	yes	—
724	#465	C₂²×C₃₁	1	2	yes	complemented
725	#464	C₂²×C₃₁	1	2	yes	complemented
726	#464	C₂²×C₃₁	1	2	yes	complemented
727	#462	C₂²×C₃₁	1	2	yes	complemented
728	#461	C₂²×C₃₁	1	2	yes	complemented
729	#461	C₂²×C₃₁	1	2	yes	complemented
730	#461	C₂²×C₃₁	1	2	yes	complemented
731	#460	C₂²×C₃₁	1	2	yes	complemented
732	#460	C₂²×C₃₁	1	2	yes	complemented
733	#452	C₂²×C₃₁	1	2	yes	—
734	#452	C₂²×C₃₁	1	2	yes	—
735	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
736	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
737	#450	C₂²×C₃₁	1	2	yes	—
738	#450	C₂²×C₃₁	1	2	yes	—
739	#448	C₂²×C₃₁	1	1	yes	characteristic
740	#448	C₂²×C₃₁	1	1	yes	characteristic
741	#448	C₂²×C₃₁	1	1	yes	characteristic
742	#448	C₂²×C₃₁	1	1	yes	characteristic
743	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
744	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
745	#441	C₂²×C₃₁	1	2	yes	complemented
746	#440	C₂²×C₃₁	1	2	yes	complemented
747	#440	C₂²×C₃₁	1	2	yes	complemented
748	#440	C₂²×C₃₁	1	2	yes	complemented
749	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
750	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
751	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
752	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
753	#433	C₂²×C₃₁	1	2	yes	—
754	#433	C₂²×C₃₁	1	2	yes	—
755	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
756	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
757	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
758	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#424	C₂²×C₃₁	1	2	yes	complemented
760	#407	C₂²×C₃₁	1	1	yes	characteristic
761	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
762	#405	C₂²×C₃₁	1	2	yes	complemented
763	C₂×C₃₁	—	2	2	no	—
764	C₂×C₃₁	—	4	1	no	—
765	C₂×C₃₁	—	4	1	no	—
766	C₂×C₃₁	—	8	1	no	—
767	C₂×C₃₁	—	8	1	no	—
768	C₂×C₃₁	—	8	1	no	—
769	C₂×C₃₁	#3449	1	1	yes	characteristic
770	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
771	C₂×C₃₁	#3586	1	1	yes	characteristic
772	C₂×#41	—	2	1	no	—
773	C₂×#41	—	2	1	no	—
774	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₂²×D₄	—	2	1	no	—
778	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
779	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
780	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
781	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
788	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
789	C₂²×C₈	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	C₂³×C₃₁	1	2	yes	—
794	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
795	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	#127	C₂³×C₃₁	1	1	yes	characteristic
798	#127	C₂³×C₃₁	1	1	yes	characteristic
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	2	no	—
802	#126	—	2	2	no	—
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#126	—	2	2	no	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#126	—	2	1	no	—
810	#126	—	2	1	no	—
811	#125	—	2	2	no	—
812	#125	—	2	2	no	—
813	#125	—	2	2	no	—
814	#125	—	2	2	no	—
815	#125	—	2	2	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	2	no	—
819	#125	—	2	1	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	C₂³×C₃₁	1	2	yes	—
823	#125	C₂³×C₃₁	1	2	yes	—
824	#125	C₂³×C₃₁	1	1	yes	characteristic
825	#125	C₂³×C₃₁	1	1	yes	characteristic
826	#124	—	2	1	no	—
827	#124	—	2	1	no	—
828	#124	—	2	1	no	—
829	#124	—	2	1	no	—
830	#124	C₂³×C₃₁	1	1	yes	characteristic
831	#124	C₂³×C₃₁	1	1	yes	characteristic
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	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	C₂³×C₃₁	1	2	yes	—
850	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
851	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
852	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
853	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	C₂³×C₃₁	1	1	yes	characteristic
866	#121	C₂³×C₃₁	1	1	yes	characteristic
867	#121	C₂³×C₃₁	1	1	yes	characteristic
868	#121	C₂³×C₃₁	1	1	yes	characteristic
869	#121	C₂³×C₃₁	1	1	yes	characteristic
870	#121	C₂³×C₃₁	1	1	yes	characteristic
871	#120	—	2	1	no	—
872	#120	—	2	1	no	—
873	#120	—	2	1	no	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
879	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
880	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
881	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
882	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
895	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
896	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
900	#117	—	2	1	no	—
901	#117	—	2	1	no	—
902	#117	—	2	1	no	—
903	#117	D₄×C₃₁	1	1	yes	characteristic
904	#117	D₄×C₃₁	1	1	yes	characteristic
905	#117	D₄×C₃₁	1	1	yes	characteristic
906	#117	D₄×C₃₁	1	1	yes	characteristic
907	#117	C₂³×C₃₁	1	1	yes	characteristic
908	#117	C₂³×C₃₁	1	1	yes	characteristic
909	#117	C₂³×C₃₁	1	1	yes	characteristic
910	#117	C₂³×C₃₁	1	1	yes	characteristic
911	#117	C₂³×C₃₁	1	1	yes	characteristic
912	C₂×C₄⋊C₄	—	2	1	no	—
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	—	2	1	no	—
918	C₂×C₄⋊C₄	—	2	1	no	—
919	C₂×C₄⋊C₄	—	2	1	no	—
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
922	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
925	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	—	2	1	no	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	1	no	—
929	C₂×C₂²⋊C₄	—	2	1	no	—
930	C₂×C₂²⋊C₄	—	2	1	no	—
931	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
932	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
933	C₂×C₄²	—	2	1	no	—
934	C₂×C₄²	—	2	1	no	—
935	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
936	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
937	#107	C₂³×C₃₁	1	2	yes	—
938	#107	C₂³×C₃₁	1	2	yes	—
939	#107	C₂³×C₃₁	1	2	yes	—
940	#107	C₂³×C₃₁	1	2	yes	—
941	#106	C₂³×C₃₁	1	2	yes	—
942	#106	C₂³×C₃₁	1	2	yes	—
943	#106	C₂³×C₃₁	1	2	yes	—
944	#106	C₂³×C₃₁	1	2	yes	—
945	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
946	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
947	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
948	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
949	#103	C₂³×C₃₁	1	2	yes	—
950	#103	C₂³×C₃₁	1	2	yes	—
951	#103	C₂³×C₃₁	1	2	yes	—
952	#103	C₂³×C₃₁	1	2	yes	—
953	#103	C₂³×C₃₁	1	2	yes	—
954	#103	C₂³×C₃₁	1	2	yes	—
955	#103	C₂³×C₃₁	1	2	yes	—
956	#103	C₂³×C₃₁	1	2	yes	—
957	#103	C₂³×C₃₁	1	2	yes	—
958	#103	C₂³×C₃₁	1	2	yes	—
959	#102	C₂³×C₃₁	1	2	yes	—
960	#102	C₂³×C₃₁	1	2	yes	—
961	#102	C₂³×C₃₁	1	2	yes	—
962	#102	C₂³×C₃₁	1	2	yes	—
963	#102	C₂³×C₃₁	1	2	yes	—
964	#102	C₂³×C₃₁	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
966	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
967	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
969	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
970	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
971	#97	C₂³×C₃₁	1	2	yes	—
972	#97	C₂³×C₃₁	1	2	yes	—
973	C₄×C₈	C₂³×C₃₁	1	2	yes	—
974	C₄×C₈	C₂³×C₃₁	1	2	yes	—
975	C₃₁	#60982	1	1	yes	characteristic, direct product factor, Sylow
976	C₂⁴	—	2	1	no	—
977	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
978	#41	—	4	2	no	—
979	#41	—	8	2	no	—
980	#41	—	8	2	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	4	2	no	—
986	C₂×Q₈	—	4	2	no	—
987	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
989	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	4	2	no	—
1003	C₂×D₄	—	8	2	no	—
1004	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	4	2	no	—
1020	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1025	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1026	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	Q₁₆	—	4	2	no	—
1031	Q₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	SD₁₆	—	4	2	no	—
1036	SD₁₆	—	4	2	no	—
1037	SD₁₆	—	4	2	no	—
1038	M₁₆	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	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	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1112	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1113	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1114	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1115	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1118	C₄²	—	2	2	no	—
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	—	2	2	no	—
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1126	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1127	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1131	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1132	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	4	1	no	—
1138	C₂³	—	4	1	no	—
1139	C₂³	—	4	2	no	—
1140	C₂³	—	8	1	no	—
1141	C₂³	—	8	1	no	—
1142	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1143	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1144	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	2	no	—
1147	Q₈	—	2	2	no	—
1148	Q₈	—	2	2	no	—
1149	Q₈	—	2	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	4	2	no	—
1152	Q₈	—	8	1	no	—
1153	Q₈	—	8	1	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	2	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	1	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	1	no	—
1166	D₄	—	8	1	no	—
1167	D₄	—	8	1	no	—
1168	D₄	—	8	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	2	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	8	1	no	—
1194	C₂×C₄	—	8	1	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1209	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1210	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1211	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₈	—	2	2	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	8	2	no	—
1234	C₂²	—	16	2	no	—
1235	C₂²	C₃₁×#577	1	2	yes	—
1236	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	1	no	—
1245	C₄	—	2	1	no	—
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	2	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	C₃₁×#585	1	2	yes	—
1258	C₂	—	2	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	1	no	—
1261	C₂	—	8	1	no	—
1262	C₂	—	8	1	no	—
1263	C₂	—	8	1	no	—
1264	C₂	C₃₁×#3449	1	1	yes	characteristic
1265	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1266	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×#3494	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
2. C₂×C₃₁×#541	C₂	semidirect
3. C₃₁×#3260	C₂	semidirect
4. C₃₁×#3258	C₂	semidirect
5. C₃₁×#3242	C₂	semidirect
6. C₃₁×#3234	C₂	semidirect
7. C₃₁×#3232	C₂	semidirect
8. C₃₁×#3222	C₂	semidirect
9. C₃₁×#3218	C₂	semidirect
10. C₃₁×#3206	C₂	semidirect
11. C₃₁×#3196	C₂	semidirect
12. C₃₁×#3193	C₂	semidirect
13. C₃₁×#3190	C₂	semidirect
14. C₃₁×#3187	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3174	C₂	semidirect
17. C₃₁×#3123	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₃₁×#3117	C₂	semidirect
20. C₃₁×#3112	C₂	semidirect
21. C₃₁×#3108	C₂	semidirect
22. C₃₁×#3103	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
41. C₃₁×#541	C₂²	semidirect
42. C₃₁×#541	C₂²	semidirect
48. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
55. C₂×C₃₁×#125	C₂²	semidirect
62. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
63. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#499	C₂²	semidirect
67. C₃₁×#497	C₂²	semidirect
68. C₃₁×#492	C₂²	semidirect
69. C₃₁×#491	C₂²	semidirect
70. C₃₁×#490	C₂²	semidirect
71. C₃₁×#488	C₂²	semidirect
72. C₃₁×#487	C₂²	semidirect
76. C₃₁×#484	C₂²	semidirect
78. C₃₁×#483	C₂²	semidirect
81. C₃₁×#481	C₂²	semidirect
84. C₃₁×#480	C₂²	semidirect
85. C₃₁×#479	C₂²	semidirect
86. C₃₁×#479	C₂²	semidirect
87. C₃₁×#479	C₂²	semidirect
88. C₃₁×#478	C₂²	semidirect
89. C₃₁×#478	C₂²	semidirect
90. C₃₁×#478	C₂²	semidirect
91. C₃₁×#477	C₂²	semidirect
92. C₃₁×#475	C₂²	semidirect
93. C₃₁×#470	C₂²	semidirect
96. C₃₁×#468	C₂²	semidirect
97. C₃₁×#467	C₂²	semidirect
100. C₃₁×#465	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
102. C₃₁×#464	C₂²	semidirect
103. C₃₁×#462	C₂²	semidirect
104. C₃₁×#461	C₂²	semidirect
105. C₃₁×#461	C₂²	semidirect
106. C₃₁×#461	C₂²	semidirect
107. C₃₁×#460	C₂²	semidirect
108. C₃₁×#460	C₂²	semidirect
111. C₃₁×#451	C₂²	semidirect
112. C₃₁×#451	C₂²	semidirect
119. C₃₁×#448	C₂²	semidirect
120. C₃₁×#448	C₂²	semidirect
121. C₃₁×#441	C₂²	semidirect
122. C₃₁×#440	C₂²	semidirect
123. C₃₁×#440	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
131. C₃₁×#432	C₂²	semidirect
132. C₃₁×#432	C₂²	semidirect
133. C₃₁×#431	C₂²	semidirect
134. C₃₁×#431	C₂²	semidirect
135. C₃₁×#424	C₂²	semidirect
138. C₃₁×#405	C₂²	semidirect
499. #60982	C₃₁	direct (N × H)
584. C₂×#541	C₂×C₃₁	semidirect
585. #3260	C₂×C₃₁	semidirect
586. #3258	C₂×C₃₁	semidirect
587. #3242	C₂×C₃₁	semidirect
588. #3234	C₂×C₃₁	semidirect
589. #3232	C₂×C₃₁	semidirect
590. #3222	C₂×C₃₁	semidirect
591. #3218	C₂×C₃₁	semidirect
592. #3206	C₂×C₃₁	semidirect
593. #3196	C₂×C₃₁	semidirect
594. #3193	C₂×C₃₁	semidirect
595. #3190	C₂×C₃₁	semidirect
596. #3187	C₂×C₃₁	semidirect
597. #3178	C₂×C₃₁	semidirect
598. #3174	C₂×C₃₁	semidirect
599. #3123	C₂×C₃₁	semidirect
600. #3120	C₂×C₃₁	semidirect
601. #3117	C₂×C₃₁	semidirect
602. #3112	C₂×C₃₁	semidirect
603. #3108	C₂×C₃₁	semidirect
604. #3103	C₂×C₃₁	semidirect
605. #2924	C₂×C₃₁	semidirect
665. #541	C₂²×C₃₁	semidirect
666. #541	C₂²×C₃₁	semidirect
672. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
679. C₂×#125	C₂²×C₃₁	semidirect
686. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
687. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
689. #501	C₂²×C₃₁	semidirect
690. #499	C₂²×C₃₁	semidirect
691. #497	C₂²×C₃₁	semidirect
692. #492	C₂²×C₃₁	semidirect
693. #491	C₂²×C₃₁	semidirect
694. #490	C₂²×C₃₁	semidirect
695. #488	C₂²×C₃₁	semidirect
696. #487	C₂²×C₃₁	semidirect
700. #484	C₂²×C₃₁	semidirect
702. #483	C₂²×C₃₁	semidirect
705. #481	C₂²×C₃₁	semidirect
708. #480	C₂²×C₃₁	semidirect
709. #479	C₂²×C₃₁	semidirect
710. #479	C₂²×C₃₁	semidirect
711. #479	C₂²×C₃₁	semidirect
712. #478	C₂²×C₃₁	semidirect
713. #478	C₂²×C₃₁	semidirect
714. #478	C₂²×C₃₁	semidirect
715. #477	C₂²×C₃₁	semidirect
716. #475	C₂²×C₃₁	semidirect
717. #470	C₂²×C₃₁	semidirect
720. #468	C₂²×C₃₁	semidirect
721. #467	C₂²×C₃₁	semidirect
724. #465	C₂²×C₃₁	semidirect
725. #464	C₂²×C₃₁	semidirect
726. #464	C₂²×C₃₁	semidirect
727. #462	C₂²×C₃₁	semidirect
728. #461	C₂²×C₃₁	semidirect
729. #461	C₂²×C₃₁	semidirect
730. #461	C₂²×C₃₁	semidirect
731. #460	C₂²×C₃₁	semidirect
732. #460	C₂²×C₃₁	semidirect
735. #451	C₂²×C₃₁	semidirect
736. #451	C₂²×C₃₁	semidirect
743. #448	C₂²×C₃₁	semidirect
744. #448	C₂²×C₃₁	semidirect
745. #441	C₂²×C₃₁	semidirect
746. #440	C₂²×C₃₁	semidirect
747. #440	C₂²×C₃₁	semidirect
748. #440	C₂²×C₃₁	semidirect
749. C₄×Q₁₆	C₂²×C₃₁	semidirect
750. C₄×SD₁₆	C₂²×C₃₁	semidirect
751. C₄×SD₁₆	C₂²×C₃₁	semidirect
752. C₄×SD₁₆	C₂²×C₃₁	semidirect
755. #432	C₂²×C₃₁	semidirect
756. #432	C₂²×C₃₁	semidirect
757. #431	C₂²×C₃₁	semidirect
758. #431	C₂²×C₃₁	semidirect
759. #424	C₂²×C₃₁	semidirect
762. #405	C₂²×C₃₁	semidirect
975. C₃₁	#60982	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×#3494	2
C₂×C₃₁×#541	2
C₃₁×#3260	2
C₃₁×#3258	2
C₃₁×#3242	2
C₃₁×#3234	2
C₃₁×#3232	2
C₃₁×#3222	2
C₃₁×#3218	2
C₃₁×#3206	2
C₃₁×#3196	2
C₃₁×#3193	2
C₃₁×#3190	2
C₃₁×#3187	2
C₃₁×#3178	2
C₃₁×#3174	2
C₃₁×#3123	2
C₃₁×#3120	2
C₃₁×#3117	2
C₃₁×#3112	2
C₃₁×#3108	2
C₃₁×#3103	2
C₃₁×#2924	2
#60982	31

Subgroups — C31×#60982 #21517741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60982 #21517741