Subgroups — C₃₁×#61453 #21518212

Order 7936.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3110	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#440	C₂	1	2	yes	maximal, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#557	—	2	1	no	—
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#554	—	2	2	no	—
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#554	C₂²	1	1	yes	characteristic
34	C₃₁×#554	C₂²	1	1	yes	characteristic
35	C₃₁×#554	C₂²	1	2	yes	complemented
36	C₃₁×#553	—	2	1	no	—
37	C₃₁×#553	C₂²	1	2	yes	—
38	C₃₁×#551	—	2	2	no	—
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#533	—	2	2	no	—
45	C₃₁×#533	—	2	1	no	—
46	C₃₁×#533	C₂²	1	2	yes	complemented
47	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#529	—	2	1	no	—
50	C₃₁×#529	C₂²	1	2	yes	—
51	C₃₁×#525	—	2	2	no	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₃₁	—	2	1	no	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#497	C₂²	1	2	yes	complemented
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#491	C₂²	1	2	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#484	C₂²	1	2	yes	complemented
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	2	yes	—
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic
79	C₃₁×#474	C₂²	1	2	yes	—
80	C₃₁×#474	C₂²	1	2	yes	complemented
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#467	C₂²	1	2	yes	complemented
84	C₃₁×#467	C₂²	1	2	yes	complemented
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#461	C₂²	1	2	yes	—
91	C₃₁×#461	C₂²	1	1	yes	characteristic
92	C₃₁×#461	C₂²	1	2	yes	complemented
93	C₃₁×#460	C₂²	1	1	yes	characteristic
94	C₃₁×#460	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#451	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	2	yes	—
98	C₃₁×#450	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#440	C₂²	1	1	yes	characteristic
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₃₁×#440	C₂²	1	2	yes	—
110	C₃₁×#440	C₂²	1	1	yes	characteristic
111	C₃₁×#440	C₂²	1	2	yes	complemented
112	C₃₁×#440	C₂²	1	2	yes	complemented
113	C₃₁×#440	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₃₁×#440	C₂²	1	2	yes	complemented
116	C₃₁×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#435	C₂²	1	2	yes	complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#432	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
129	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#417	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₃₁	—	2	2	no	—
143	C₃₁×#137	—	2	4	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	—	2	8	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	—	2	2	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	—	2	2	no	—
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#125	—	2	1	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#120	—	2	2	no	—
208	C₃₁×#120	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	2	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	2	no	—
217	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
242	C₄×D₄×C₃₁	D₄	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	D₄	1	2	yes	—
255	C₃₁×#117	D₄	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₂⁴×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	4	1	no	—
318	#41×C₃₁	—	8	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	4	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	—	4	1	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₃₁	—	2	4	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	4	2	no	—
341	C₂×D₄×C₃₁	—	4	4	no	—
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	8	4	no	—
358	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	Q₁₆×C₃₁	—	2	2	no	—
365	Q₁₆×C₃₁	—	2	2	no	—
366	Q₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	2	4	no	—
368	SD₁₆×C₃₁	—	2	4	no	—
369	SD₁₆×C₃₁	—	2	2	no	—
370	SD₁₆×C₃₁	—	2	4	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	#41	1	4	yes	complemented
374	M₁₆×C₃₁	—	2	2	no	—
375	M₁₆×C₃₁	—	4	1	no	—
376	C₂×C₈×C₃₁	—	2	4	no	—
377	C₂×C₈×C₃₁	—	4	2	no	—
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
382	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂×D₄	1	2	yes	—
449	C₄²×C₃₁	C₂×D₄	1	2	yes	—
450	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	2	yes	—
453	#61453	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂³×C₃₁	—	2	1	no	—
455	C₂³×C₃₁	—	2	2	no	—
456	C₂³×C₃₁	—	4	4	no	—
457	C₂³×C₃₁	—	4	4	no	—
458	C₂³×C₃₁	—	8	2	no	—
459	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	4	2	no	—
470	Q₈×C₃₁	—	4	4	no	—
471	Q₈×C₃₁	—	8	2	no	—
472	Q₈×C₃₁	—	8	1	no	—
473	Q₈×C₃₁	—	8	1	no	—
474	Q₈×C₃₁	C₂×#41	1	2	yes	—
475	D₄×C₃₁	—	2	4	no	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	4	4	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	4	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	8	1	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	#137	1	4	yes	complemented
486	D₄×C₃₁	C₂×#41	1	2	yes	—
487	C₂×C₄×C₃₁	—	2	4	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	1	no	—
505	C₂×C₄×C₃₁	—	4	4	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	4	4	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	8	2	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	—	8	1	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
525	C₈×C₃₁	—	2	2	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	2	no	—
529	C₈×C₃₁	—	2	1	no	—
530	C₈×C₃₁	C₂×#41	1	2	yes	—
531	#3481	C₂×C₃₁	1	1	yes	characteristic
532	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3346	C₂×C₃₁	1	2	yes	complemented
538	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3320	C₂×C₃₁	1	2	yes	complemented
540	#3314	C₂×C₃₁	1	2	yes	complemented
541	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
543	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3266	C₂×C₃₁	1	2	yes	complemented
545	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3181	C₂×C₃₁	1	2	yes	complemented
547	#3117	C₂×C₃₁	1	2	yes	complemented
548	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3110	C₂×C₃₁	1	2	yes	complemented
551	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
552	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
553	C₂×#440	C₂×C₃₁	1	2	yes	complemented
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	1	no	—
557	C₂²×C₃₁	—	2	1	no	—
558	C₂²×C₃₁	—	2	2	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	4	2	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	8	8	no	—
566	C₂²×C₃₁	C₂×#137	1	4	yes	—
567	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	1	no	—
575	C₄×C₃₁	—	2	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	—	4	2	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	C₂×#137	1	2	yes	—
586	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
587	C₄×C₃₁	#585	1	1	yes	characteristic
588	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
589	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
590	#559	C₂²×C₃₁	1	1	yes	characteristic
591	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#557	—	2	1	no	—
593	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#554	—	2	1	no	—
595	#554	—	2	2	no	—
596	#554	C₂²×C₃₁	1	1	yes	characteristic
597	#554	C₂²×C₃₁	1	1	yes	characteristic
598	#554	C₂²×C₃₁	1	1	yes	characteristic
599	#554	C₂²×C₃₁	1	2	yes	complemented
600	#553	—	2	1	no	—
601	#553	C₂²×C₃₁	1	2	yes	—
602	#551	—	2	2	no	—
603	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
604	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
605	#546	—	2	1	no	—
606	#546	C₂²×C₃₁	1	2	yes	—
607	D₄²	C₂²×C₃₁	1	1	yes	characteristic
608	#533	—	2	2	no	—
609	#533	—	2	1	no	—
610	#533	C₂²×C₃₁	1	2	yes	complemented
611	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#532	C₂²×C₃₁	1	1	yes	characteristic
613	#529	—	2	1	no	—
614	#529	C₂²×C₃₁	1	2	yes	—
615	#525	—	2	2	no	—
616	C₄×#41	—	2	1	no	—
617	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
618	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
621	C₂×C₄×D₄	—	2	1	no	—
622	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
623	#501	C₂²×C₃₁	1	2	yes	complemented
624	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#497	C₂²×C₃₁	1	2	yes	complemented
626	#492	C₂²×C₃₁	1	1	yes	characteristic
627	#491	C₂²×C₃₁	1	2	yes	complemented
628	#489	C₂²×C₃₁	1	2	yes	complemented
629	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#486	C₂²×C₃₁	1	1	yes	characteristic
631	#485	C₂²×C₃₁	1	2	yes	complemented
632	#484	C₂²×C₃₁	1	2	yes	complemented
633	#484	C₂²×C₃₁	1	2	yes	complemented
634	#484	C₂²×C₃₁	1	2	yes	complemented
635	#481	C₂²×C₃₁	1	2	yes	—
636	#480	C₂²×C₃₁	1	2	yes	complemented
637	#479	C₂²×C₃₁	1	2	yes	complemented
638	#479	C₂²×C₃₁	1	2	yes	complemented
639	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#476	C₂²×C₃₁	1	1	yes	characteristic
643	#474	C₂²×C₃₁	1	2	yes	—
644	#474	C₂²×C₃₁	1	2	yes	complemented
645	#468	C₂²×C₃₁	1	2	yes	complemented
646	#468	C₂²×C₃₁	1	2	yes	complemented
647	#467	C₂²×C₃₁	1	2	yes	complemented
648	#467	C₂²×C₃₁	1	2	yes	complemented
649	#465	C₂²×C₃₁	1	2	yes	—
650	#465	C₂²×C₃₁	1	2	yes	—
651	#464	C₂²×C₃₁	1	2	yes	complemented
652	#464	C₂²×C₃₁	1	2	yes	complemented
653	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#461	C₂²×C₃₁	1	2	yes	—
655	#461	C₂²×C₃₁	1	1	yes	characteristic
656	#461	C₂²×C₃₁	1	2	yes	complemented
657	#460	C₂²×C₃₁	1	1	yes	characteristic
658	#460	C₂²×C₃₁	1	1	yes	characteristic
659	#452	C₂²×C₃₁	1	2	yes	—
660	#451	C₂²×C₃₁	1	2	yes	complemented
661	#450	C₂²×C₃₁	1	2	yes	—
662	#450	C₂²×C₃₁	1	2	yes	—
663	#448	C₂²×C₃₁	1	2	yes	—
664	#448	C₂²×C₃₁	1	2	yes	complemented
665	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#441	C₂²×C₃₁	1	2	yes	complemented
668	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#440	C₂²×C₃₁	1	1	yes	characteristic
671	#440	C₂²×C₃₁	1	2	yes	—
672	#440	C₂²×C₃₁	1	2	yes	—
673	#440	C₂²×C₃₁	1	2	yes	—
674	#440	C₂²×C₃₁	1	1	yes	characteristic
675	#440	C₂²×C₃₁	1	2	yes	complemented
676	#440	C₂²×C₃₁	1	2	yes	complemented
677	#440	C₂²×C₃₁	1	2	yes	complemented
678	#440	C₂²×C₃₁	1	2	yes	complemented
679	#440	C₂²×C₃₁	1	2	yes	complemented
680	#440	C₂²×C₃₁	1	2	yes	complemented
681	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
685	#435	C₂²×C₃₁	1	2	yes	complemented
686	#435	C₂²×C₃₁	1	2	yes	complemented
687	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
688	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
689	#432	C₂²×C₃₁	1	2	yes	complemented
690	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
693	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#417	C₂²×C₃₁	1	1	yes	characteristic
695	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#102	C₂²×C₃₁	1	2	yes	—
697	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
699	C₂×C₃₁	—	2	4	no	—
700	C₂×C₃₁	—	4	1	no	—
701	C₂×C₃₁	—	4	2	no	—
702	C₂×C₃₁	—	8	2	no	—
703	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
704	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
705	C₂×C₃₁	#3585	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
708	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
709	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
710	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂²×D₄	—	2	1	no	—
712	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
713	C₂³×C₄	—	2	2	no	—
714	#137	—	2	4	no	—
715	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	—	2	8	no	—
719	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
729	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
736	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
739	#127	C₂³×C₃₁	1	1	yes	characteristic
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#125	—	2	1	no	—
743	#125	—	2	1	no	—
744	#125	—	2	2	no	—
745	#125	—	2	1	no	—
746	#125	—	2	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	C₂³×C₃₁	1	2	yes	—
750	#124	—	2	1	no	—
751	#124	—	2	1	no	—
752	#124	C₂³×C₃₁	1	2	yes	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	C₂³×C₃₁	1	2	yes	—
777	#121	C₂³×C₃₁	1	2	yes	—
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	2	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
796	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
813	C₄×D₄	D₄×C₃₁	1	2	yes	—
814	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₃₁	1	2	yes	—
816	C₄×D₄	C₂³×C₃₁	1	2	yes	—
817	C₄×D₄	C₂³×C₃₁	1	2	yes	—
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	#117	—	2	2	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	D₄×C₃₁	1	2	yes	—
826	#117	D₄×C₃₁	1	1	yes	characteristic
827	#117	C₂³×C₃₁	1	1	yes	characteristic
828	C₂×C₄⋊C₄	—	2	2	no	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	—	2	2	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₄²	—	2	2	no	—
837	C₂×C₄²	—	2	1	no	—
838	C₂×C₄²	—	2	1	no	—
839	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
840	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
841	#107	C₂³×C₃₁	1	1	yes	characteristic
842	#107	C₂³×C₃₁	1	2	yes	—
843	#107	C₂³×C₃₁	1	2	yes	—
844	#107	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	1	yes	characteristic
846	#107	C₂³×C₃₁	1	2	yes	—
847	#107	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	1	yes	characteristic
849	#106	C₂³×C₃₁	1	1	yes	characteristic
850	#106	C₂³×C₃₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	1	yes	characteristic
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	1	yes	characteristic
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	1	yes	characteristic
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	#97	C₂³×C₃₁	1	1	yes	characteristic
879	#97	C₂³×C₃₁	1	2	yes	—
880	#97	C₂³×C₃₁	1	2	yes	—
881	#97	C₂³×C₃₁	1	2	yes	—
882	#97	C₂³×C₃₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₃₁	#61453	1	1	yes	characteristic, direct product factor, Sylow
886	C₂⁴	—	2	2	no	—
887	#41	—	2	4	no	—
888	#41	—	2	2	no	—
889	#41	—	4	1	no	—
890	#41	—	8	2	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	4	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	4	1	no	—
900	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂×D₄	—	2	4	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	4	no	—
914	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
917	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	8	4	no	—
930	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	Q₁₆	—	2	2	no	—
937	Q₁₆	—	2	2	no	—
938	Q₁₆	—	4	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	2	4	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	#41×C₃₁	1	4	yes	complemented
946	M₁₆	—	2	2	no	—
947	M₁₆	—	4	1	no	—
948	C₂×C₈	—	2	4	no	—
949	C₂×C₈	—	4	2	no	—
950	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
954	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
955	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1020	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1021	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1022	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₃₁	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	4	4	no	—
1028	C₂³	—	4	4	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	4	4	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	—	8	1	no	—
1045	Q₈	C₂×#41×C₃₁	1	2	yes	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	4	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	8	2	no	—
1056	D₄	C₃₁×#137	1	4	yes	complemented
1057	D₄	C₂×#41×C₃₁	1	2	yes	—
1058	C₂×C₄	—	2	4	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1095	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	C₂×#41×C₃₁	1	2	yes	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	8	8	no	—
1114	C₂²	C₂×C₃₁×#137	1	4	yes	—
1115	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	C₂×C₃₁×#137	1	2	yes	—
1134	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1135	C₄	C₃₁×#585	1	1	yes	characteristic
1136	C₂	—	2	4	no	—
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	2	no	—
1140	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1141	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
1142	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3481	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
2. Q₈×#41×C₃₁	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3385	C₂	semidirect
5. C₃₁×#3375	C₂	semidirect
6. C₃₁×#3372	C₂	semidirect
7. C₃₁×#3346	C₂	semidirect
8. C₃₁×#3338	C₂	semidirect
9. C₃₁×#3320	C₂	semidirect
10. C₃₁×#3314	C₂	semidirect
11. C₃₁×#3299	C₂	semidirect
12. C₃₁×#3295	C₂	semidirect
13. D₄×SD₁₆×C₃₁	C₂	semidirect
14. C₃₁×#3266	C₂	semidirect
15. C₃₁×#3182	C₂	semidirect
16. C₃₁×#3181	C₂	semidirect
17. C₃₁×#3117	C₂	semidirect
18. C₃₁×#3116	C₂	semidirect
19. C₃₁×#3112	C₂	semidirect
20. C₃₁×#3110	C₂	semidirect
21. C₃₁×#2970	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. C₂×C₃₁×#440	C₂	semidirect
27. Q₈²×C₃₁	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
35. C₃₁×#554	C₂²	semidirect
40. D₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
47. C₃₁×#533	C₂²	semidirect
55. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
56. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
61. C₃₁×#497	C₂²	semidirect
63. C₃₁×#491	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
69. C₃₁×#484	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
84. C₃₁×#467	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
92. C₃₁×#461	C₂²	semidirect
96. C₃₁×#451	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#441	C₂²	semidirect
105. C₃₁×#441	C₂²	semidirect
111. C₃₁×#440	C₂²	semidirect
112. C₃₁×#440	C₂²	semidirect
113. C₃₁×#440	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₃₁×#440	C₂²	semidirect
116. C₃₁×#440	C₂²	semidirect
117. C₄×Q₁₆×C₃₁	C₂²	semidirect
118. C₄×Q₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#435	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₂×C₃₁×#107	C₂²	semidirect
129. C₃₁×#419	C₂²	semidirect
131. C₂×C₃₁×#103	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₂×C₃₁×#97	C₂²	semidirect
373. SD₁₆×C₃₁	#41	semidirect
453. #61453	C₃₁	direct (N × H)
485. D₄×C₃₁	#137	semidirect
532. Q₈×#41	C₂×C₃₁	semidirect
533. #3400	C₂×C₃₁	semidirect
534. #3385	C₂×C₃₁	semidirect
535. #3375	C₂×C₃₁	semidirect
536. #3372	C₂×C₃₁	semidirect
537. #3346	C₂×C₃₁	semidirect
538. #3338	C₂×C₃₁	semidirect
539. #3320	C₂×C₃₁	semidirect
540. #3314	C₂×C₃₁	semidirect
541. #3299	C₂×C₃₁	semidirect
542. #3295	C₂×C₃₁	semidirect
543. D₄×SD₁₆	C₂×C₃₁	semidirect
544. #3266	C₂×C₃₁	semidirect
545. #3182	C₂×C₃₁	semidirect
546. #3181	C₂×C₃₁	semidirect
547. #3117	C₂×C₃₁	semidirect
548. #3116	C₂×C₃₁	semidirect
549. #3112	C₂×C₃₁	semidirect
550. #3110	C₂×C₃₁	semidirect
551. #2970	C₂×C₃₁	semidirect
552. C₄×#137	C₂×C₃₁	semidirect
553. C₂×#440	C₂×C₃₁	semidirect
591. Q₈²	C₂²×C₃₁	semidirect
593. #557	C₂²×C₃₁	semidirect
599. #554	C₂²×C₃₁	semidirect
604. D₄×Q₈	C₂²×C₃₁	semidirect
610. #533	C₂²×C₃₁	semidirect
611. #533	C₂²×C₃₁	semidirect
619. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
620. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
623. #501	C₂²×C₃₁	semidirect
624. #500	C₂²×C₃₁	semidirect
625. #497	C₂²×C₃₁	semidirect
627. #491	C₂²×C₃₁	semidirect
628. #489	C₂²×C₃₁	semidirect
629. #487	C₂²×C₃₁	semidirect
631. #485	C₂²×C₃₁	semidirect
632. #484	C₂²×C₃₁	semidirect
633. #484	C₂²×C₃₁	semidirect
634. #484	C₂²×C₃₁	semidirect
636. #480	C₂²×C₃₁	semidirect
637. #479	C₂²×C₃₁	semidirect
638. #479	C₂²×C₃₁	semidirect
639. #477	C₂²×C₃₁	semidirect
640. #477	C₂²×C₃₁	semidirect
641. #477	C₂²×C₃₁	semidirect
644. #474	C₂²×C₃₁	semidirect
645. #468	C₂²×C₃₁	semidirect
646. #468	C₂²×C₃₁	semidirect
647. #467	C₂²×C₃₁	semidirect
648. #467	C₂²×C₃₁	semidirect
651. #464	C₂²×C₃₁	semidirect
652. #464	C₂²×C₃₁	semidirect
653. #462	C₂²×C₃₁	semidirect
656. #461	C₂²×C₃₁	semidirect
660. #451	C₂²×C₃₁	semidirect
664. #448	C₂²×C₃₁	semidirect
665. #446	C₂²×C₃₁	semidirect
666. #446	C₂²×C₃₁	semidirect
667. #441	C₂²×C₃₁	semidirect
668. #441	C₂²×C₃₁	semidirect
669. #441	C₂²×C₃₁	semidirect
675. #440	C₂²×C₃₁	semidirect
676. #440	C₂²×C₃₁	semidirect
677. #440	C₂²×C₃₁	semidirect
678. #440	C₂²×C₃₁	semidirect
679. #440	C₂²×C₃₁	semidirect
680. #440	C₂²×C₃₁	semidirect
681. C₄×Q₁₆	C₂²×C₃₁	semidirect
682. C₄×Q₁₆	C₂²×C₃₁	semidirect
685. #435	C₂²×C₃₁	semidirect
686. #435	C₂²×C₃₁	semidirect
689. #432	C₂²×C₃₁	semidirect
690. #432	C₂²×C₃₁	semidirect
691. #428	C₂²×C₃₁	semidirect
692. C₂×#107	C₂²×C₃₁	semidirect
693. #419	C₂²×C₃₁	semidirect
695. C₂×#103	C₂²×C₃₁	semidirect
697. C₄×M₁₆	C₂²×C₃₁	semidirect
698. C₂×#97	C₂²×C₃₁	semidirect
885. C₃₁	#61453	direct (N × H)
945. SD₁₆	#41×C₃₁	semidirect
1056. D₄	C₃₁×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3481	2
Q₈×#41×C₃₁	2
C₃₁×#3400	2
C₃₁×#3385	2
C₃₁×#3375	2
C₃₁×#3372	2
C₃₁×#3346	2
C₃₁×#3338	2
C₃₁×#3320	2
C₃₁×#3314	2
C₃₁×#3299	2
C₃₁×#3295	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3266	2
C₃₁×#3182	2
C₃₁×#3181	2
C₃₁×#3117	2
C₃₁×#3116	2
C₃₁×#3112	2
C₃₁×#3110	2
C₃₁×#2970	2
C₄×C₃₁×#137	2
C₂×C₃₁×#440	2
#61453	31

Subgroups — C31×#61453 #21518212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61453 #21518212