Subgroups — C₃₁×#61980 #21518739

Order 7936.

1894 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3372	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3320	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3218	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3110	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#461	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	—
20	C₃₁×#559	C₂²	1	1	yes	characteristic
21	Q₈²×C₃₁	—	2	1	no	—
22	C₃₁×#557	C₂²	1	2	yes	complemented
23	C₃₁×#554	—	2	1	no	—
24	C₃₁×#554	—	2	2	no	—
25	C₃₁×#554	C₂²	1	1	yes	characteristic
26	C₃₁×#554	C₂²	1	1	yes	characteristic
27	C₃₁×#553	—	2	1	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#551	—	2	2	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
32	C₃₁×#546	—	2	1	no	—
33	C₃₁×#546	C₂²	1	2	yes	—
34	D₄²×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#544	—	2	2	no	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#533	C₂²	1	2	yes	complemented
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₃₁×#529	—	2	1	no	—
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₃₁×#525	—	2	2	no	—
45	C₃₁×#520	—	2	1	no	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
50	C₃₁×#497	C₂²	1	4	yes	complemented
51	C₃₁×#492	C₂²	1	2	yes	—
52	C₃₁×#491	C₂²	1	4	yes	complemented
53	C₃₁×#487	C₂²	1	2	yes	complemented
54	C₃₁×#485	C₂²	1	2	yes	complemented
55	C₃₁×#484	C₂²	1	4	yes	complemented
56	C₃₁×#479	C₂²	1	4	yes	complemented
57	C₃₁×#477	C₂²	1	2	yes	complemented
58	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#474	C₂²	1	1	yes	characteristic
60	C₃₁×#474	C₂²	1	2	yes	complemented
61	C₃₁×#468	C₂²	1	4	yes	complemented
62	C₃₁×#467	C₂²	1	4	yes	complemented
63	C₃₁×#465	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#462	C₂²	1	2	yes	complemented
67	C₃₁×#462	C₂²	1	2	yes	complemented
68	C₃₁×#461	C₂²	1	1	yes	characteristic
69	C₃₁×#461	C₂²	1	2	yes	—
70	C₃₁×#461	C₂²	1	4	yes	—
71	C₃₁×#461	C₂²	1	2	yes	—
72	C₃₁×#461	C₂²	1	2	yes	complemented
73	C₃₁×#461	C₂²	1	4	yes	complemented
74	C₃₁×#461	C₂²	1	2	yes	complemented
75	C₃₁×#461	C₂²	1	2	yes	complemented
76	C₃₁×#460	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#451	C₂²	1	4	yes	complemented
79	C₃₁×#450	C₂²	1	4	yes	—
80	C₃₁×#448	C₂²	1	4	yes	—
81	C₃₁×#448	C₂²	1	4	yes	complemented
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	—
84	C₃₁×#440	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
87	C₃₁×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₃₁	C₂²	1	2	yes	—
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#419	C₂²	1	2	yes	complemented
94	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
102	C₂³×C₄×C₃₁	—	2	2	no	—
103	C₃₁×#137	—	4	4	no	—
104	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₃₁	—	4	8	no	—
107	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
113	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
114	C₃₁×C₄⋊Q₈	—	2	2	no	—
115	C₃₁×C₄⋊Q₈	—	2	4	no	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	—	2	2	no	—
118	C₃₁×C₄⋊Q₈	—	2	1	no	—
119	C₃₁×C₄⋊Q₈	—	2	2	no	—
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
123	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×#127	C₂³	1	1	yes	characteristic
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#125	—	2	1	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	4	no	—
132	C₃₁×#125	—	2	1	no	—
133	C₃₁×#125	—	2	2	no	—
134	C₃₁×#125	C₂³	1	2	yes	—
135	C₃₁×#124	—	2	1	no	—
136	C₃₁×#124	—	2	1	no	—
137	C₃₁×#124	C₂³	1	2	yes	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	4	no	—
148	C₃₁×C₂²⋊Q₈	—	2	4	no	—
149	C₃₁×C₂²⋊Q₈	—	2	4	no	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	C₂³	1	2	yes	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#120	—	2	2	no	—
160	C₃₁×#120	—	2	2	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	2	no	—
164	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	4	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
182	C₄×D₄×C₃₁	D₄	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	2	yes	—
186	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₃₁×#117	—	2	2	no	—
191	C₃₁×#117	—	2	1	no	—
192	C₃₁×#117	—	2	1	no	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	D₄	1	2	yes	—
195	C₃₁×#117	D₄	1	1	yes	characteristic
196	C₃₁×#117	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	2	yes	—
222	C₃₁×#103	C₂³	1	2	yes	—
223	C₃₁×#103	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃₁×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₃₁	C₂³	1	2	yes	—
230	C₂⁴×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	4	1	no	—
234	#41×C₃₁	—	8	2	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	4	no	—
239	C₂×Q₈×C₃₁	—	4	4	no	—
240	C₂×Q₈×C₃₁	—	4	2	no	—
241	C₂×Q₈×C₃₁	—	4	4	no	—
242	C₂×Q₈×C₃₁	—	4	2	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	—	4	4	no	—
256	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	4	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	1	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	2	no	—
269	C₂²×C₄×C₃₁	—	8	4	no	—
270	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	Q₁₆×C₃₁	—	4	2	no	—
277	Q₁₆×C₃₁	—	4	4	no	—
278	SD₁₆×C₃₁	—	2	4	no	—
279	SD₁₆×C₃₁	—	2	8	no	—
280	SD₁₆×C₃₁	—	4	4	no	—
281	SD₁₆×C₃₁	—	4	4	no	—
282	SD₁₆×C₃₁	—	4	4	no	—
283	M₁₆×C₃₁	—	4	2	no	—
284	C₂×C₈×C₃₁	—	4	4	no	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	4	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	1	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	—	2	1	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	1	no	—
335	C₄²×C₃₁	—	2	4	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂×D₄	1	2	yes	—
340	C₄²×C₃₁	C₂×D₄	1	2	yes	—
341	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₄²×C₃₁	C₂⁴	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	#61980	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂³×C₃₁	—	2	1	no	—
346	C₂³×C₃₁	—	2	2	no	—
347	C₂³×C₃₁	—	4	4	no	—
348	C₂³×C₃₁	—	4	4	no	—
349	C₂³×C₃₁	—	8	2	no	—
350	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
352	Q₈×C₃₁	—	2	2	no	—
353	Q₈×C₃₁	—	2	2	no	—
354	Q₈×C₃₁	—	2	4	no	—
355	Q₈×C₃₁	—	2	1	no	—
356	Q₈×C₃₁	—	2	4	no	—
357	Q₈×C₃₁	—	2	1	no	—
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	4	2	no	—
360	Q₈×C₃₁	—	8	2	no	—
361	Q₈×C₃₁	—	8	4	no	—
362	Q₈×C₃₁	—	8	1	no	—
363	D₄×C₃₁	—	2	4	no	—
364	D₄×C₃₁	—	2	2	no	—
365	D₄×C₃₁	—	2	1	no	—
366	D₄×C₃₁	—	2	2	no	—
367	D₄×C₃₁	—	4	4	no	—
368	D₄×C₃₁	—	4	2	no	—
369	D₄×C₃₁	—	4	4	no	—
370	D₄×C₃₁	—	4	2	no	—
371	D₄×C₃₁	—	8	1	no	—
372	D₄×C₃₁	—	8	2	no	—
373	D₄×C₃₁	#137	1	4	yes	complemented
374	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	4	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	4	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	—	4	2	no	—
393	C₂×C₄×C₃₁	—	4	4	no	—
394	C₂×C₄×C₃₁	—	8	2	no	—
395	C₂×C₄×C₃₁	—	8	2	no	—
396	C₂×C₄×C₃₁	—	8	2	no	—
397	C₂×C₄×C₃₁	—	8	4	no	—
398	C₂×C₄×C₃₁	—	8	2	no	—
399	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
408	C₈×C₃₁	—	2	2	no	—
409	C₈×C₃₁	—	2	4	no	—
410	C₈×C₃₁	—	2	2	no	—
411	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3481	C₂×C₃₁	1	1	yes	characteristic
413	#3400	C₂×C₃₁	1	2	yes	complemented
414	#3372	C₂×C₃₁	1	2	yes	complemented
415	#3320	C₂×C₃₁	1	4	yes	complemented
416	#3299	C₂×C₃₁	1	2	yes	complemented
417	D₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
418	#3266	C₂×C₃₁	1	4	yes	complemented
419	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#3248	C₂×C₃₁	1	2	yes	complemented
421	#3218	C₂×C₃₁	1	2	yes	complemented
422	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#3110	C₂×C₃₁	1	2	yes	complemented
424	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
426	C₂×#461	C₂×C₃₁	1	2	yes	complemented
427	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
428	C₂²×C₃₁	—	2	2	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	1	no	—
431	C₂²×C₃₁	—	2	2	no	—
432	C₂²×C₃₁	—	2	1	no	—
433	C₂²×C₃₁	—	2	1	no	—
434	C₂²×C₃₁	—	4	1	no	—
435	C₂²×C₃₁	—	4	1	no	—
436	C₂²×C₃₁	—	4	2	no	—
437	C₂²×C₃₁	—	4	2	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	8	8	no	—
440	C₂²×C₃₁	C₂×#137	1	4	yes	—
441	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
442	C₄×C₃₁	—	2	1	no	—
443	C₄×C₃₁	—	2	2	no	—
444	C₄×C₃₁	—	2	1	no	—
445	C₄×C₃₁	—	2	2	no	—
446	C₄×C₃₁	—	2	2	no	—
447	C₄×C₃₁	—	2	1	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	2	no	—
450	C₄×C₃₁	—	4	4	no	—
451	C₄×C₃₁	—	4	1	no	—
452	C₄×C₃₁	—	4	1	no	—
453	C₄×C₃₁	—	4	2	no	—
454	C₄×C₃₁	—	4	2	no	—
455	C₄×C₃₁	C₂×#137	1	2	yes	—
456	C₄×C₃₁	#577	1	2	yes	—
457	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₄×C₃₁	#585	1	1	yes	characteristic
459	C₂×#137	C₂²×C₃₁	1	2	yes	—
460	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	—
461	#559	C₂²×C₃₁	1	1	yes	characteristic
462	Q₈²	—	2	1	no	—
463	#557	C₂²×C₃₁	1	2	yes	complemented
464	#554	—	2	1	no	—
465	#554	—	2	2	no	—
466	#554	C₂²×C₃₁	1	1	yes	characteristic
467	#554	C₂²×C₃₁	1	1	yes	characteristic
468	#553	—	2	1	no	—
469	#553	C₂²×C₃₁	1	2	yes	—
470	#551	—	2	2	no	—
471	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
472	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
473	#546	—	2	1	no	—
474	#546	C₂²×C₃₁	1	2	yes	—
475	D₄²	C₂²×C₃₁	1	1	yes	characteristic
476	#544	—	2	2	no	—
477	#544	—	2	1	no	—
478	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	#533	C₂²×C₃₁	1	2	yes	complemented
480	#532	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
482	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
483	#529	—	2	1	no	—
484	#529	C₂²×C₃₁	1	2	yes	—
485	#525	—	2	2	no	—
486	#520	—	2	1	no	—
487	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
488	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×C₄×D₄	—	2	1	no	—
490	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
491	#497	C₂²×C₃₁	1	4	yes	complemented
492	#492	C₂²×C₃₁	1	2	yes	—
493	#491	C₂²×C₃₁	1	4	yes	complemented
494	#487	C₂²×C₃₁	1	2	yes	complemented
495	#485	C₂²×C₃₁	1	2	yes	complemented
496	#484	C₂²×C₃₁	1	4	yes	complemented
497	#479	C₂²×C₃₁	1	4	yes	complemented
498	#477	C₂²×C₃₁	1	2	yes	complemented
499	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#474	C₂²×C₃₁	1	1	yes	characteristic
501	#474	C₂²×C₃₁	1	2	yes	complemented
502	#468	C₂²×C₃₁	1	4	yes	complemented
503	#467	C₂²×C₃₁	1	4	yes	complemented
504	#465	C₂²×C₃₁	1	4	yes	—
505	#464	C₂²×C₃₁	1	4	yes	complemented
506	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	#462	C₂²×C₃₁	1	2	yes	complemented
508	#462	C₂²×C₃₁	1	2	yes	complemented
509	#461	C₂²×C₃₁	1	1	yes	characteristic
510	#461	C₂²×C₃₁	1	2	yes	—
511	#461	C₂²×C₃₁	1	4	yes	—
512	#461	C₂²×C₃₁	1	2	yes	—
513	#461	C₂²×C₃₁	1	2	yes	complemented
514	#461	C₂²×C₃₁	1	4	yes	complemented
515	#461	C₂²×C₃₁	1	2	yes	complemented
516	#461	C₂²×C₃₁	1	2	yes	complemented
517	#460	C₂²×C₃₁	1	2	yes	—
518	#452	C₂²×C₃₁	1	2	yes	—
519	#451	C₂²×C₃₁	1	4	yes	complemented
520	#450	C₂²×C₃₁	1	4	yes	—
521	#448	C₂²×C₃₁	1	4	yes	—
522	#448	C₂²×C₃₁	1	4	yes	complemented
523	#446	C₂²×C₃₁	1	2	yes	complemented
524	#440	C₂²×C₃₁	1	4	yes	—
525	#440	C₂²×C₃₁	1	4	yes	complemented
526	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
527	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
528	#435	C₂²×C₃₁	1	4	yes	complemented
529	C₈×D₄	C₂²×C₃₁	1	2	yes	—
530	#432	C₂²×C₃₁	1	2	yes	complemented
531	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
533	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
534	#419	C₂²×C₃₁	1	2	yes	complemented
535	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
536	C₂×C₃₁	—	2	4	no	—
537	C₂×C₃₁	—	4	1	no	—
538	C₂×C₃₁	—	4	2	no	—
539	C₂×C₃₁	—	8	2	no	—
540	C₂×C₃₁	#3488	1	1	yes	characteristic
541	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
542	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
543	C₂×#41	—	2	1	no	—
544	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
545	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
547	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
550	C₂³×C₄	—	2	2	no	—
551	#137	—	4	4	no	—
552	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
553	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
554	C₂×SD₁₆	—	4	8	no	—
555	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
559	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
560	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
561	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	—	2	4	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	2	no	—
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	—	2	2	no	—
568	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
571	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
572	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
574	#127	C₂³×C₃₁	1	1	yes	characteristic
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#125	—	2	1	no	—
578	#125	—	2	2	no	—
579	#125	—	2	4	no	—
580	#125	—	2	1	no	—
581	#125	—	2	2	no	—
582	#125	C₂³×C₃₁	1	2	yes	—
583	#124	—	2	1	no	—
584	#124	—	2	1	no	—
585	#124	C₂³×C₃₁	1	2	yes	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	4	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
600	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
601	#121	—	2	2	no	—
602	#121	—	2	1	no	—
603	#121	—	2	1	no	—
604	#121	—	2	2	no	—
605	#121	C₂³×C₃₁	1	2	yes	—
606	#121	C₂³×C₃₁	1	2	yes	—
607	#120	—	2	2	no	—
608	#120	—	2	2	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
616	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
617	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
630	C₄×D₄	D₄×C₃₁	1	2	yes	—
631	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₃₁	1	2	yes	—
633	C₄×D₄	C₂³×C₃₁	1	2	yes	—
634	C₄×D₄	C₂³×C₃₁	1	2	yes	—
635	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₃₁	1	2	yes	—
638	#117	—	2	2	no	—
639	#117	—	2	1	no	—
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	D₄×C₃₁	1	2	yes	—
643	#117	D₄×C₃₁	1	1	yes	characteristic
644	#117	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₂²⋊C₄	—	2	2	no	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
656	#107	C₂³×C₃₁	1	2	yes	—
657	#107	C₂³×C₃₁	1	4	yes	—
658	#106	C₂³×C₃₁	1	2	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
660	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
661	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
662	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
663	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
664	#103	C₂³×C₃₁	1	2	yes	—
665	#103	C₂³×C₃₁	1	4	yes	—
666	#103	C₂³×C₃₁	1	4	yes	—
667	#103	C₂³×C₃₁	1	4	yes	—
668	#103	C₂³×C₃₁	1	4	yes	—
669	#103	C₂³×C₃₁	1	2	yes	—
670	#103	C₂³×C₃₁	1	2	yes	—
671	#103	C₂³×C₃₁	1	4	yes	—
672	#102	C₂³×C₃₁	1	2	yes	—
673	#102	C₂³×C₃₁	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
676	#97	C₂³×C₃₁	1	4	yes	—
677	C₄×C₈	C₂³×C₃₁	1	2	yes	—
678	C₃₁	#61980	1	1	yes	characteristic, direct product factor, Sylow
679	C₂⁴	—	2	2	no	—
680	#41	—	2	4	no	—
681	#41	—	2	2	no	—
682	#41	—	4	1	no	—
683	#41	—	8	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	4	no	—
691	C₂×Q₈	—	4	2	no	—
692	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
695	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
708	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	8	4	no	—
719	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
720	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	Q₁₆	—	4	2	no	—
726	Q₁₆	—	4	4	no	—
727	SD₁₆	—	2	4	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	4	4	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	—	4	4	no	—
732	M₁₆	—	4	2	no	—
733	C₂×C₈	—	4	4	no	—
734	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
735	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
736	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
759	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	1	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
787	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₃₁	1	2	yes	—
789	C₄²	C₂×D₄×C₃₁	1	2	yes	—
790	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₄²	C₂⁴×C₃₁	1	2	yes	—
792	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	4	4	no	—
797	C₂³	—	8	2	no	—
798	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
799	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	4	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	2	4	no	—
805	Q₈	—	2	1	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	—	8	4	no	—
810	Q₈	—	8	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	2	no	—
819	D₄	—	8	1	no	—
820	D₄	—	8	2	no	—
821	D₄	C₃₁×#137	1	4	yes	complemented
822	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	2	no	—
844	C₂×C₄	—	8	2	no	—
845	C₂×C₄	—	8	4	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
851	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
855	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
856	C₈	—	2	2	no	—
857	C₈	—	2	4	no	—
858	C₈	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	8	8	no	—
871	C₂²	C₂×C₃₁×#137	1	4	yes	—
872	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	4	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	C₂×C₃₁×#137	1	2	yes	—
887	C₄	C₃₁×#577	1	2	yes	—
888	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
889	C₄	C₃₁×#585	1	1	yes	characteristic
890	C₂	—	2	4	no	—
891	C₂	—	4	1	no	—
892	C₂	—	4	2	no	—
893	C₂	—	8	2	no	—
894	C₂	C₃₁×#3488	1	1	yes	characteristic
895	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
896	C₂	C₂×C₃₁×#577	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
1. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3372	C₂	semidirect
5. C₃₁×#3320	C₂	semidirect
6. C₃₁×#3299	C₂	semidirect
7. D₄×SD₁₆×C₃₁	C₂	semidirect
8. C₃₁×#3266	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3248	C₂	semidirect
11. C₃₁×#3218	C₂	semidirect
12. C₃₁×#3206	C₂	semidirect
13. C₃₁×#3110	C₂	semidirect
14. C₃₁×#3107	C₂	semidirect
15. C₃₁×#3039	C₂	semidirect
16. C₂×C₃₁×#461	C₂	semidirect
17. C₃₁×#2990	C₂	semidirect
22. C₃₁×#557	C₂²	semidirect
31. D₄×Q₈×C₃₁	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
40. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
50. C₃₁×#497	C₂²	semidirect
52. C₃₁×#491	C₂²	semidirect
53. C₃₁×#487	C₂²	semidirect
54. C₃₁×#485	C₂²	semidirect
55. C₃₁×#484	C₂²	semidirect
56. C₃₁×#479	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#468	C₂²	semidirect
62. C₃₁×#467	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
65. C₃₁×#462	C₂²	semidirect
66. C₃₁×#462	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
72. C₃₁×#461	C₂²	semidirect
73. C₃₁×#461	C₂²	semidirect
74. C₃₁×#461	C₂²	semidirect
75. C₃₁×#461	C₂²	semidirect
78. C₃₁×#451	C₂²	semidirect
81. C₃₁×#448	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
84. C₃₁×#440	C₂²	semidirect
85. C₄×Q₁₆×C₃₁	C₂²	semidirect
87. C₃₁×#435	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
93. C₃₁×#419	C₂²	semidirect
94. C₂×C₃₁×#103	C₂²	semidirect
344. #61980	C₃₁	direct (N × H)
373. D₄×C₃₁	#137	semidirect
411. #3503	C₂×C₃₁	semidirect
413. #3400	C₂×C₃₁	semidirect
414. #3372	C₂×C₃₁	semidirect
415. #3320	C₂×C₃₁	semidirect
416. #3299	C₂×C₃₁	semidirect
417. D₄×SD₁₆	C₂×C₃₁	semidirect
418. #3266	C₂×C₃₁	semidirect
419. #3254	C₂×C₃₁	semidirect
420. #3248	C₂×C₃₁	semidirect
421. #3218	C₂×C₃₁	semidirect
422. #3206	C₂×C₃₁	semidirect
423. #3110	C₂×C₃₁	semidirect
424. #3107	C₂×C₃₁	semidirect
425. #3039	C₂×C₃₁	semidirect
426. C₂×#461	C₂×C₃₁	semidirect
427. #2990	C₂×C₃₁	semidirect
463. #557	C₂²×C₃₁	semidirect
472. D₄×Q₈	C₂²×C₃₁	semidirect
478. #533	C₂²×C₃₁	semidirect
479. #533	C₂²×C₃₁	semidirect
481. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
482. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
491. #497	C₂²×C₃₁	semidirect
493. #491	C₂²×C₃₁	semidirect
494. #487	C₂²×C₃₁	semidirect
495. #485	C₂²×C₃₁	semidirect
496. #484	C₂²×C₃₁	semidirect
497. #479	C₂²×C₃₁	semidirect
498. #477	C₂²×C₃₁	semidirect
499. #475	C₂²×C₃₁	semidirect
501. #474	C₂²×C₃₁	semidirect
502. #468	C₂²×C₃₁	semidirect
503. #467	C₂²×C₃₁	semidirect
505. #464	C₂²×C₃₁	semidirect
506. #462	C₂²×C₃₁	semidirect
507. #462	C₂²×C₃₁	semidirect
508. #462	C₂²×C₃₁	semidirect
513. #461	C₂²×C₃₁	semidirect
514. #461	C₂²×C₃₁	semidirect
515. #461	C₂²×C₃₁	semidirect
516. #461	C₂²×C₃₁	semidirect
519. #451	C₂²×C₃₁	semidirect
522. #448	C₂²×C₃₁	semidirect
523. #446	C₂²×C₃₁	semidirect
525. #440	C₂²×C₃₁	semidirect
526. C₄×Q₁₆	C₂²×C₃₁	semidirect
528. #435	C₂²×C₃₁	semidirect
530. #432	C₂²×C₃₁	semidirect
531. #431	C₂²×C₃₁	semidirect
532. #423	C₂²×C₃₁	semidirect
533. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
534. #419	C₂²×C₃₁	semidirect
535. C₂×#103	C₂²×C₃₁	semidirect
678. C₃₁	#61980	direct (N × H)
821. 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×#3503	2
C₃₁×#3481	2
C₃₁×#3400	2
C₃₁×#3372	2
C₃₁×#3320	2
C₃₁×#3299	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3266	2
C₃₁×#3254	2
C₃₁×#3248	2
C₃₁×#3218	2
C₃₁×#3206	2
C₃₁×#3110	2
C₃₁×#3107	2
C₃₁×#3039	2
C₂×C₃₁×#461	2
C₃₁×#2990	2
#61980	31

Subgroups — C31×#61980 #21518739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61980 #21518739