Subgroups — C₃₁×#61491 #21518250

Order 7936.

1770 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3516	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#557	C₂²	1	2	yes	—
23	C₃₁×#556	—	2	2	no	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#554	—	2	2	no	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#552	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#548	C₂²	1	2	yes	—
34	C₃₁×#542	—	2	2	no	—
35	C₃₁×#542	C₂²	1	2	yes	—
36	C₃₁×#541	—	2	2	no	—
37	C₃₁×#541	C₂²	1	2	yes	—
38	C₃₁×#529	—	2	2	no	—
39	C₃₁×#529	—	2	2	no	—
40	C₃₁×#529	C₂²	1	2	yes	—
41	C₃₁×#529	C₂²	1	1	yes	characteristic
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₃₁×#519	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
45	C₃₁×#501	C₂²	1	2	yes	—
46	C₃₁×#499	C₂²	1	1	yes	characteristic
47	C₃₁×#497	C₂²	1	2	yes	—
48	C₃₁×#495	C₂²	1	1	yes	characteristic
49	C₃₁×#488	C₂²	1	2	yes	—
50	C₃₁×#488	C₂²	1	2	yes	—
51	C₃₁×#487	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	2	yes	—
53	C₃₁×#485	C₂²	1	2	yes	—
54	C₃₁×#484	C₂²	1	2	yes	—
55	C₃₁×#484	C₂²	1	2	yes	—
56	C₃₁×#481	C₂²	1	2	yes	—
57	C₃₁×#480	C₂²	1	2	yes	—
58	C₃₁×#479	C₂²	1	2	yes	—
59	C₃₁×#479	C₂²	1	2	yes	—
60	C₃₁×#479	C₂²	1	2	yes	—
61	C₃₁×#479	C₂²	1	2	yes	—
62	C₃₁×#477	C₂²	1	2	yes	—
63	C₃₁×#474	C₂²	1	2	yes	—
64	C₃₁×#470	C₂²	1	2	yes	—
65	C₃₁×#468	C₂²	1	2	yes	—
66	C₃₁×#467	C₂²	1	1	yes	characteristic
67	C₃₁×#467	C₂²	1	2	yes	—
68	C₃₁×#466	C₂²	1	1	yes	characteristic
69	C₃₁×#465	C₂²	1	2	yes	—
70	C₃₁×#465	C₂²	1	2	yes	—
71	C₃₁×#464	C₂²	1	2	yes	—
72	C₃₁×#464	C₂²	1	2	yes	—
73	C₃₁×#464	C₂²	1	2	yes	—
74	C₃₁×#463	C₂²	1	2	yes	—
75	C₃₁×#462	C₂²	1	2	yes	—
76	C₃₁×#462	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#451	C₂²	1	2	yes	—
79	C₃₁×#451	C₂²	1	2	yes	—
80	C₃₁×#451	C₂²	1	2	yes	—
81	C₃₁×#449	C₂²	1	2	yes	—
82	C₃₁×#448	C₂²	1	2	yes	—
83	C₃₁×#446	C₂²	1	1	yes	characteristic
84	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
85	C₃₁×#441	C₂²	1	2	yes	—
86	C₃₁×#441	C₂²	1	2	yes	—
87	C₃₁×#441	C₂²	1	2	yes	—
88	C₃₁×#440	C₂²	1	2	yes	—
89	C₃₁×#440	C₂²	1	2	yes	—
90	C₃₁×#440	C₂²	1	2	yes	—
91	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
92	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
93	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
94	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
95	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
96	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
97	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
99	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
100	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
101	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
102	C₃₁×#436	C₂²	1	1	yes	characteristic
103	C₃₁×#435	C₂²	1	2	yes	—
104	C₈×D₄×C₃₁	C₂²	1	2	yes	—
105	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₃₁×#433	C₂²	1	2	yes	—
107	C₃₁×#432	C₂²	1	1	yes	characteristic
108	C₃₁×#428	C₂²	1	2	yes	—
109	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
110	C₃₁×#416	C₂²	1	2	yes	—
111	C₂×C₃₁×#103	C₂²	1	2	yes	—
112	C₂×C₃₁×#103	C₂²	1	2	yes	—
113	C₃₁×#405	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
117	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
118	C₃₁×#137	—	2	8	no	—
119	C₂×Q₁₆×C₃₁	—	2	4	no	—
120	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	D₄	1	2	yes	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	D₄	1	1	yes	characteristic
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#125	C₂³	1	2	yes	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	2	no	—
159	C₃₁×#124	D₄	1	1	yes	characteristic
160	C₃₁×#124	C₂³	1	2	yes	—
161	C₃₁×#124	C₂³	1	2	yes	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	D₄	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	—	2	2	no	—
182	C₃₁×#121	—	2	2	no	—
183	C₃₁×#121	D₄	1	1	yes	characteristic
184	C₃₁×#121	C₂³	1	2	yes	—
185	C₃₁×#121	C₂³	1	2	yes	—
186	C₄×Q₈×C₃₁	—	2	2	no	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	—	2	2	no	—
189	C₄×Q₈×C₃₁	—	2	2	no	—
190	C₄×Q₈×C₃₁	—	2	2	no	—
191	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
194	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
195	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
196	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
197	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
198	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₃₁	—	2	2	no	—
201	C₄×D₄×C₃₁	—	2	2	no	—
202	C₄×D₄×C₃₁	—	2	2	no	—
203	C₄×D₄×C₃₁	—	2	2	no	—
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	C₂³	1	2	yes	—
209	C₄×D₄×C₃₁	C₂³	1	2	yes	—
210	C₄×D₄×C₃₁	C₂³	1	2	yes	—
211	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×#117	—	2	2	no	—
213	C₃₁×#117	—	2	2	no	—
214	C₃₁×#117	—	2	2	no	—
215	C₃₁×#117	—	2	2	no	—
216	C₃₁×#117	—	2	2	no	—
217	C₃₁×#117	—	2	2	no	—
218	C₃₁×#117	C₂³	1	2	yes	—
219	C₃₁×#117	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
221	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
222	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	2	yes	—
229	C₃₁×#107	C₂³	1	2	yes	—
230	C₃₁×#107	C₂³	1	1	yes	characteristic
231	C₃₁×#107	C₂³	1	1	yes	characteristic
232	C₃₁×#107	C₂³	1	2	yes	—
233	C₃₁×#106	C₂³	1	2	yes	—
234	C₃₁×#106	C₂³	1	2	yes	—
235	C₃₁×#106	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
239	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
240	C₃₁×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#103	C₂³	1	2	yes	—
245	C₃₁×#103	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₃₁×#97	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	2	yes	—
266	#41×C₃₁	—	2	4	no	—
267	#41×C₃₁	—	4	2	no	—
268	C₂×Q₈×C₃₁	—	2	2	no	—
269	C₂×Q₈×C₃₁	—	2	2	no	—
270	C₂×Q₈×C₃₁	—	2	2	no	—
271	C₂×Q₈×C₃₁	—	2	4	no	—
272	C₂×Q₈×C₃₁	—	2	4	no	—
273	C₂×Q₈×C₃₁	—	4	2	no	—
274	C₂×Q₈×C₃₁	—	4	2	no	—
275	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
276	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
277	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
278	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
296	Q₁₆×C₃₁	—	2	4	no	—
297	Q₁₆×C₃₁	—	2	4	no	—
298	Q₁₆×C₃₁	—	2	2	no	—
299	Q₁₆×C₃₁	—	4	1	no	—
300	Q₁₆×C₃₁	—	4	2	no	—
301	Q₁₆×C₃₁	#41	1	4	yes	—
302	SD₁₆×C₃₁	—	2	4	no	—
303	SD₁₆×C₃₁	—	2	4	no	—
304	SD₁₆×C₃₁	—	4	2	no	—
305	D₈×C₃₁	—	4	1	no	—
306	M₁₆×C₃₁	—	2	4	no	—
307	C₂×C₈×C₃₁	—	2	2	no	—
308	C₂×C₈×C₃₁	—	4	1	no	—
309	C₂×C₈×C₃₁	—	4	2	no	—
310	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
314	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
315	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	2	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	—	2	2	no	—
371	C₄²×C₃₁	—	2	2	no	—
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄²×C₃₁	C₂⁴	1	2	yes	—
379	#61491	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
382	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₃₁	—	2	2	no	—
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	2	2	no	—
386	Q₈×C₃₁	—	2	2	no	—
387	Q₈×C₃₁	—	2	2	no	—
388	Q₈×C₃₁	—	4	1	no	—
389	Q₈×C₃₁	—	4	4	no	—
390	Q₈×C₃₁	—	4	4	no	—
391	Q₈×C₃₁	—	8	2	no	—
392	Q₈×C₃₁	C₂×#41	1	4	yes	—
393	D₄×C₃₁	—	2	4	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	2	2	no	—
396	D₄×C₃₁	—	4	1	no	—
397	D₄×C₃₁	—	4	4	no	—
398	D₄×C₃₁	—	4	4	no	—
399	D₄×C₃₁	—	8	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	4	1	no	—
413	C₂×C₄×C₃₁	—	4	4	no	—
414	C₂×C₄×C₃₁	—	4	4	no	—
415	C₂×C₄×C₃₁	—	4	4	no	—
416	C₂×C₄×C₃₁	—	8	2	no	—
417	C₂×C₄×C₃₁	—	8	2	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	—	8	2	no	—
420	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
429	C₈×C₃₁	—	2	1	no	—
430	C₈×C₃₁	—	2	2	no	—
431	C₈×C₃₁	—	2	1	no	—
432	C₈×C₃₁	—	2	1	no	—
433	C₈×C₃₁	—	2	2	no	—
434	C₈×C₃₁	C₂×#41	1	2	yes	—
435	#3516	C₂×C₃₁	1	2	yes	complemented
436	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3364	C₂×C₃₁	1	2	yes	complemented
439	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
440	#3346	C₂×C₃₁	1	2	yes	complemented
441	#3301	C₂×C₃₁	1	2	yes	complemented
442	#3300	C₂×C₃₁	1	2	yes	complemented
443	#3299	C₂×C₃₁	1	2	yes	complemented
444	#3277	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3270	C₂×C₃₁	1	2	yes	complemented
446	#3178	C₂×C₃₁	1	2	yes	complemented
447	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#3127	C₂×C₃₁	1	2	yes	complemented
449	#3124	C₂×C₃₁	1	2	yes	complemented
450	#3117	C₂×C₃₁	1	2	yes	complemented
451	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#2947	C₂×C₃₁	1	2	yes	complemented
453	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₂²×C₃₁	—	2	1	no	—
455	C₂²×C₃₁	—	2	1	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	2	2	no	—
459	C₂²×C₃₁	—	4	2	no	—
460	C₂²×C₃₁	—	4	2	no	—
461	C₂²×C₃₁	—	4	2	no	—
462	C₂²×C₃₁	#578	1	2	yes	—
463	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₃₁	—	2	1	no	—
465	C₄×C₃₁	—	2	1	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	2	1	no	—
469	C₄×C₃₁	—	2	4	no	—
470	C₄×C₃₁	—	2	1	no	—
471	C₄×C₃₁	—	2	1	no	—
472	C₄×C₃₁	—	2	2	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	2	no	—
475	C₄×C₃₁	—	4	2	no	—
476	C₄×C₃₁	—	4	2	no	—
477	C₄×C₃₁	—	4	2	no	—
478	C₄×C₃₁	—	4	2	no	—
479	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
480	C₄×C₃₁	#585	1	1	yes	characteristic
481	C₂×#137	C₂²×C₃₁	1	2	yes	—
482	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
483	#557	C₂²×C₃₁	1	2	yes	—
484	#556	—	2	2	no	—
485	#556	C₂²×C₃₁	1	2	yes	—
486	#554	—	2	2	no	—
487	#554	C₂²×C₃₁	1	2	yes	—
488	#553	—	2	2	no	—
489	#553	C₂²×C₃₁	1	2	yes	—
490	#552	—	2	2	no	—
491	#552	C₂²×C₃₁	1	2	yes	—
492	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
493	#548	C₂²×C₃₁	1	2	yes	—
494	#548	C₂²×C₃₁	1	2	yes	—
495	#542	—	2	2	no	—
496	#542	C₂²×C₃₁	1	2	yes	—
497	#541	—	2	2	no	—
498	#541	C₂²×C₃₁	1	2	yes	—
499	#529	—	2	2	no	—
500	#529	—	2	2	no	—
501	#529	C₂²×C₃₁	1	2	yes	—
502	#529	C₂²×C₃₁	1	1	yes	characteristic
503	#520	C₂²×C₃₁	1	2	yes	—
504	#519	C₂²×C₃₁	1	2	yes	—
505	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
506	#501	C₂²×C₃₁	1	2	yes	—
507	#499	C₂²×C₃₁	1	1	yes	characteristic
508	#497	C₂²×C₃₁	1	2	yes	—
509	#495	C₂²×C₃₁	1	1	yes	characteristic
510	#488	C₂²×C₃₁	1	2	yes	—
511	#488	C₂²×C₃₁	1	2	yes	—
512	#487	C₂²×C₃₁	1	2	yes	—
513	#485	C₂²×C₃₁	1	2	yes	—
514	#485	C₂²×C₃₁	1	2	yes	—
515	#484	C₂²×C₃₁	1	2	yes	—
516	#484	C₂²×C₃₁	1	2	yes	—
517	#481	C₂²×C₃₁	1	2	yes	—
518	#480	C₂²×C₃₁	1	2	yes	—
519	#479	C₂²×C₃₁	1	2	yes	—
520	#479	C₂²×C₃₁	1	2	yes	—
521	#479	C₂²×C₃₁	1	2	yes	—
522	#479	C₂²×C₃₁	1	2	yes	—
523	#477	C₂²×C₃₁	1	2	yes	—
524	#474	C₂²×C₃₁	1	2	yes	—
525	#470	C₂²×C₃₁	1	2	yes	—
526	#468	C₂²×C₃₁	1	2	yes	—
527	#467	C₂²×C₃₁	1	1	yes	characteristic
528	#467	C₂²×C₃₁	1	2	yes	—
529	#466	C₂²×C₃₁	1	1	yes	characteristic
530	#465	C₂²×C₃₁	1	2	yes	—
531	#465	C₂²×C₃₁	1	2	yes	—
532	#464	C₂²×C₃₁	1	2	yes	—
533	#464	C₂²×C₃₁	1	2	yes	—
534	#464	C₂²×C₃₁	1	2	yes	—
535	#463	C₂²×C₃₁	1	2	yes	—
536	#462	C₂²×C₃₁	1	2	yes	—
537	#462	C₂²×C₃₁	1	2	yes	—
538	#452	C₂²×C₃₁	1	2	yes	—
539	#451	C₂²×C₃₁	1	2	yes	—
540	#451	C₂²×C₃₁	1	2	yes	—
541	#451	C₂²×C₃₁	1	2	yes	—
542	#449	C₂²×C₃₁	1	2	yes	—
543	#448	C₂²×C₃₁	1	2	yes	—
544	#446	C₂²×C₃₁	1	1	yes	characteristic
545	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
546	#441	C₂²×C₃₁	1	2	yes	—
547	#441	C₂²×C₃₁	1	2	yes	—
548	#441	C₂²×C₃₁	1	2	yes	—
549	#440	C₂²×C₃₁	1	2	yes	—
550	#440	C₂²×C₃₁	1	2	yes	—
551	#440	C₂²×C₃₁	1	2	yes	—
552	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
553	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
554	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
555	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
556	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
557	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
558	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
559	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
560	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
561	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
562	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
563	#436	C₂²×C₃₁	1	1	yes	characteristic
564	#435	C₂²×C₃₁	1	2	yes	—
565	C₈×D₄	C₂²×C₃₁	1	2	yes	—
566	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
567	#433	C₂²×C₃₁	1	2	yes	—
568	#432	C₂²×C₃₁	1	1	yes	characteristic
569	#428	C₂²×C₃₁	1	2	yes	—
570	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
571	#416	C₂²×C₃₁	1	2	yes	—
572	C₂×#103	C₂²×C₃₁	1	2	yes	—
573	C₂×#103	C₂²×C₃₁	1	2	yes	—
574	#405	C₂²×C₃₁	1	2	yes	—
575	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
576	C₂×C₃₁	—	2	2	no	—
577	C₂×C₃₁	—	4	2	no	—
578	C₂×C₃₁	—	8	2	no	—
579	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
580	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
581	C₂×C₃₁	#3584	1	1	yes	characteristic
582	C₂×#41	C₂³×C₃₁	1	2	yes	—
583	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
584	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
585	#137	—	2	8	no	—
586	C₂×Q₁₆	—	2	4	no	—
587	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
588	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
589	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
590	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
593	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
596	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
598	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	D₄×C₃₁	1	2	yes	—
614	#125	—	2	2	no	—
615	#125	—	2	2	no	—
616	#125	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	D₄×C₃₁	1	1	yes	characteristic
621	#125	C₂³×C₃₁	1	2	yes	—
622	#125	C₂³×C₃₁	1	2	yes	—
623	#124	—	2	2	no	—
624	#124	—	2	2	no	—
625	#124	—	2	2	no	—
626	#124	D₄×C₃₁	1	1	yes	characteristic
627	#124	C₂³×C₃₁	1	2	yes	—
628	#124	C₂³×C₃₁	1	2	yes	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	D₄×C₃₁	1	2	yes	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
643	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	D₄×C₃₁	1	1	yes	characteristic
651	#121	C₂³×C₃₁	1	2	yes	—
652	#121	C₂³×C₃₁	1	2	yes	—
653	C₄×Q₈	—	2	2	no	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	—	2	2	no	—
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
659	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
660	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
661	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
662	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
663	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
664	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
665	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
666	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	C₂³×C₃₁	1	2	yes	—
676	C₄×D₄	C₂³×C₃₁	1	2	yes	—
677	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	2	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	C₂³×C₃₁	1	2	yes	—
686	#117	C₂³×C₃₁	1	2	yes	—
687	C₂×C₄⋊C₄	—	2	2	no	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄²	—	2	2	no	—
692	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
693	#107	C₂³×C₃₁	1	1	yes	characteristic
694	#107	C₂³×C₃₁	1	1	yes	characteristic
695	#107	C₂³×C₃₁	1	2	yes	—
696	#107	C₂³×C₃₁	1	2	yes	—
697	#107	C₂³×C₃₁	1	1	yes	characteristic
698	#107	C₂³×C₃₁	1	1	yes	characteristic
699	#107	C₂³×C₃₁	1	2	yes	—
700	#106	C₂³×C₃₁	1	2	yes	—
701	#106	C₂³×C₃₁	1	2	yes	—
702	#106	C₂³×C₃₁	1	2	yes	—
703	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
706	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
707	#103	C₂³×C₃₁	1	2	yes	—
708	#103	C₂³×C₃₁	1	2	yes	—
709	#103	C₂³×C₃₁	1	2	yes	—
710	#103	C₂³×C₃₁	1	2	yes	—
711	#103	C₂³×C₃₁	1	2	yes	—
712	#103	C₂³×C₃₁	1	2	yes	—
713	#103	C₂³×C₃₁	1	2	yes	—
714	#103	C₂³×C₃₁	1	2	yes	—
715	#103	C₂³×C₃₁	1	2	yes	—
716	#103	C₂³×C₃₁	1	2	yes	—
717	#103	C₂³×C₃₁	1	2	yes	—
718	#103	C₂³×C₃₁	1	2	yes	—
719	#102	C₂³×C₃₁	1	2	yes	—
720	#102	C₂³×C₃₁	1	2	yes	—
721	#102	C₂³×C₃₁	1	2	yes	—
722	#102	C₂³×C₃₁	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
726	#97	C₂³×C₃₁	1	2	yes	—
727	#97	C₂³×C₃₁	1	2	yes	—
728	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₃₁	1	2	yes	—
733	C₃₁	#61491	1	1	yes	characteristic, direct product factor, Sylow
734	#41	—	2	4	no	—
735	#41	—	4	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	4	no	—
740	C₂×Q₈	—	2	4	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×Q₈	—	4	2	no	—
743	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
744	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
745	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
751	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
752	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
764	Q₁₆	—	2	4	no	—
765	Q₁₆	—	2	4	no	—
766	Q₁₆	—	2	2	no	—
767	Q₁₆	—	4	1	no	—
768	Q₁₆	—	4	2	no	—
769	Q₁₆	#41×C₃₁	1	4	yes	—
770	SD₁₆	—	2	4	no	—
771	SD₁₆	—	2	4	no	—
772	SD₁₆	—	4	2	no	—
773	D₈	—	4	1	no	—
774	M₁₆	—	2	4	no	—
775	C₂×C₈	—	2	2	no	—
776	C₂×C₈	—	4	1	no	—
777	C₂×C₈	—	4	2	no	—
778	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
781	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
782	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
783	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
807	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
808	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
809	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
810	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
811	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
814	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
829	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
843	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
844	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
846	C₄²	C₂⁴×C₃₁	1	2	yes	—
847	C₂³	—	2	2	no	—
848	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
849	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	4	1	no	—
856	Q₈	—	4	4	no	—
857	Q₈	—	4	4	no	—
858	Q₈	—	8	2	no	—
859	Q₈	C₂×#41×C₃₁	1	4	yes	—
860	D₄	—	2	4	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	1	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	8	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	—	8	2	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
895	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
896	C₈	—	2	1	no	—
897	C₈	—	2	2	no	—
898	C₈	—	2	1	no	—
899	C₈	—	2	1	no	—
900	C₈	—	2	2	no	—
901	C₈	C₂×#41×C₃₁	1	2	yes	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	C₃₁×#578	1	2	yes	—
911	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
912	C₄	—	2	2	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
928	C₄	C₃₁×#585	1	1	yes	characteristic
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	8	2	no	—
932	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
933	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
934	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3516	C₂	semidirect
2. C₃₁×#3402	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3364	C₂	semidirect
5. C₃₁×#3352	C₂	semidirect
6. C₃₁×#3346	C₂	semidirect
7. C₃₁×#3301	C₂	semidirect
8. C₃₁×#3300	C₂	semidirect
9. C₃₁×#3299	C₂	semidirect
10. C₃₁×#3277	C₂	semidirect
11. C₃₁×#3270	C₂	semidirect
12. C₃₁×#3178	C₂	semidirect
13. C₃₁×#3168	C₂	semidirect
14. C₃₁×#3127	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3117	C₂	semidirect
17. C₃₁×#2966	C₂	semidirect
18. C₃₁×#2947	C₂	semidirect
19. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
379. #61491	C₃₁	direct (N × H)
435. #3516	C₂×C₃₁	semidirect
436. #3402	C₂×C₃₁	semidirect
437. #3390	C₂×C₃₁	semidirect
438. #3364	C₂×C₃₁	semidirect
439. #3352	C₂×C₃₁	semidirect
440. #3346	C₂×C₃₁	semidirect
441. #3301	C₂×C₃₁	semidirect
442. #3300	C₂×C₃₁	semidirect
443. #3299	C₂×C₃₁	semidirect
444. #3277	C₂×C₃₁	semidirect
445. #3270	C₂×C₃₁	semidirect
446. #3178	C₂×C₃₁	semidirect
447. #3168	C₂×C₃₁	semidirect
448. #3127	C₂×C₃₁	semidirect
449. #3124	C₂×C₃₁	semidirect
450. #3117	C₂×C₃₁	semidirect
451. #2966	C₂×C₃₁	semidirect
452. #2947	C₂×C₃₁	semidirect
453. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
733. C₃₁	#61491	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×#3516	2
C₃₁×#3402	2
C₃₁×#3390	2
C₃₁×#3364	2
C₃₁×#3352	2
C₃₁×#3346	2
C₃₁×#3301	2
C₃₁×#3300	2
C₃₁×#3299	2
C₃₁×#3277	2
C₃₁×#3270	2
C₃₁×#3178	2
C₃₁×#3168	2
C₃₁×#3127	2
C₃₁×#3124	2
C₃₁×#3117	2
C₃₁×#2966	2
C₃₁×#2947	2
C₂×C₄×Q₁₆×C₃₁	2
#61491	31

Subgroups — C31×#61491 #21518250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61491 #21518250