Subgroups — C₃₁×#60829 #21517588

Order 7936.

2082 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3225	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3224	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3216	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3214	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3150	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3046	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3045	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3012	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
21	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₃₁×#135	C₂²	1	2	yes	—
23	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#555	—	2	1	no	—
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#548	—	2	1	no	—
29	C₃₁×#548	—	2	1	no	—
30	C₃₁×#548	—	2	2	no	—
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#546	—	2	1	no	—
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	—	2	2	no	—
35	C₃₁×#546	—	2	1	no	—
36	C₃₁×#542	C₂²	1	4	yes	complemented
37	C₃₁×#537	C₂²	1	2	yes	—
38	C₃₁×#536	C₂²	1	2	yes	—
39	C₃₁×#536	C₂²	1	1	yes	characteristic
40	C₃₁×#535	C₂²	1	2	yes	—
41	C₃₁×#535	C₂²	1	1	yes	characteristic
42	C₃₁×#533	C₂²	1	2	yes	complemented
43	C₃₁×#532	C₂²	1	1	yes	characteristic
44	C₃₁×#532	C₂²	1	2	yes	—
45	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#532	C₂²	1	2	yes	complemented
47	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#124	C₂²	1	2	yes	—
50	C₃₁×#520	C₂²	1	2	yes	complemented
51	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
52	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#497	C₂²	1	2	yes	complemented
55	C₃₁×#497	C₂²	1	2	yes	complemented
56	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#496	C₂²	1	2	yes	complemented
59	C₃₁×#496	C₂²	1	2	yes	complemented
60	C₃₁×#495	C₂²	1	4	yes	complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#489	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	4	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#489	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	2	yes	complemented
67	C₃₁×#486	C₂²	1	2	yes	complemented
68	C₃₁×#464	C₂²	1	4	yes	complemented
69	C₃₁×#464	C₂²	1	4	yes	complemented
70	C₃₁×#463	C₂²	1	4	yes	complemented
71	C₃₁×#463	C₂²	1	4	yes	complemented
72	C₃₁×#462	C₂²	1	4	yes	complemented
73	C₃₁×#461	C₂²	1	4	yes	complemented
74	C₃₁×#460	C₂²	1	4	yes	complemented
75	C₃₁×#459	C₂²	1	4	yes	complemented
76	C₃₁×#452	C₂²	1	4	yes	—
77	C₃₁×#452	C₂²	1	4	yes	complemented
78	C₃₁×#451	C₂²	1	4	yes	complemented
79	C₃₁×#450	C₂²	1	4	yes	—
80	C₃₁×#449	C₂²	1	4	yes	—
81	C₃₁×#449	C₂²	1	4	yes	complemented
82	C₃₁×#448	C₂²	1	4	yes	complemented
83	C₃₁×#447	C₂²	1	4	yes	—
84	C₃₁×#433	C₂²	1	4	yes	complemented
85	C₃₁×#432	C₂²	1	2	yes	complemented
86	C₃₁×#432	C₂²	1	2	yes	complemented
87	C₃₁×#424	C₂²	1	2	yes	complemented
88	C₃₁×#417	C₂²	1	2	yes	—
89	C₃₁×#417	C₂²	1	2	yes	complemented
90	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
91	C₂×C₃₁×#102	C₂²	1	2	yes	—
92	C₃₁×#408	C₂²	1	2	yes	—
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×2₋¹⁺⁴	—	4	4	no	—
96	C₃₁×H(5,𝔽₂)	—	4	4	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	2	1	no	—
99	C₂×#41×C₃₁	—	2	2	no	—
100	C₂×#41×C₃₁	—	2	2	no	—
101	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×#41×C₃₁	C₂³	1	2	yes	—
104	C₂×#41×C₃₁	C₂³	1	2	yes	—
105	C₂×#41×C₃₁	C₂³	1	2	yes	—
106	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₃₁	—	2	1	no	—
108	C₂²×Q₈×C₃₁	—	2	1	no	—
109	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	—	2	2	no	—
112	C₂²×D₄×C₃₁	—	2	1	no	—
113	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₃₁×#137	—	4	4	no	—
116	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
117	C₃₁×#135	—	4	4	no	—
118	C₃₁×#135	—	4	4	no	—
119	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	4	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	1	no	—
134	C₃₁×C₄⋊Q₈	—	2	1	no	—
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×#127	C₂³	1	2	yes	—
141	C₃₁×#127	C₂³	1	1	yes	characteristic
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#126	—	2	4	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#124	—	2	4	no	—
146	C₃₁×#124	—	2	2	no	—
147	C₃₁×#124	—	2	1	no	—
148	C₃₁×#124	—	2	1	no	—
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	—	2	2	no	—
151	C₃₁×#124	C₂³	1	2	yes	—
152	C₃₁×#124	C₂³	1	2	yes	—
153	C₃₁×#124	C₂³	1	2	yes	—
154	C₃₁×#124	C₂³	1	2	yes	—
155	C₃₁×#124	C₂³	1	1	yes	characteristic
156	C₃₁×#124	C₂³	1	1	yes	characteristic
157	C₃₁×#124	C₂³	1	2	yes	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	4	no	—
162	C₃₁×C₂²⋊Q₈	—	2	2	no	—
163	C₃₁×C₂²⋊Q₈	—	2	2	no	—
164	C₃₁×C₂²⋊Q₈	—	2	1	no	—
165	C₃₁×C₂²⋊Q₈	—	2	1	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	4	no	—
169	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
170	C₃₁×#121	—	2	2	no	—
171	C₃₁×#121	—	2	4	no	—
172	C₃₁×#121	—	2	1	no	—
173	C₃₁×#121	—	2	2	no	—
174	C₃₁×#121	—	2	1	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	1	no	—
177	C₃₁×#121	—	2	1	no	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	1	no	—
180	C₃₁×#121	—	2	1	no	—
181	C₃₁×#121	—	2	2	no	—
182	C₃₁×#121	—	2	2	no	—
183	C₃₁×#121	C₂³	1	4	yes	—
184	C₃₁×#120	—	2	2	no	—
185	C₃₁×#120	—	2	2	no	—
186	C₃₁×#120	—	2	2	no	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
189	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
190	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
191	C₄×D₄×C₃₁	—	2	4	no	—
192	C₄×D₄×C₃₁	—	2	2	no	—
193	C₄×D₄×C₃₁	—	2	1	no	—
194	C₄×D₄×C₃₁	—	2	1	no	—
195	C₄×D₄×C₃₁	—	2	2	no	—
196	C₄×D₄×C₃₁	—	2	1	no	—
197	C₄×D₄×C₃₁	—	2	2	no	—
198	C₄×D₄×C₃₁	—	2	1	no	—
199	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
200	C₄×D₄×C₃₁	D₄	1	2	yes	—
201	C₄×D₄×C₃₁	D₄	1	2	yes	—
202	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
203	C₄×D₄×C₃₁	C₂³	1	4	yes	—
204	C₃₁×#117	—	2	2	no	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	C₂³	1	1	yes	characteristic
207	C₃₁×#117	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
209	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
210	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
212	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
213	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
214	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
215	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
217	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
218	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	4	yes	—
222	C₃₁×#103	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃₁×#97	C₂³	1	1	yes	characteristic
230	C₃₁×#97	C₂³	1	1	yes	characteristic
231	C₃₁×#97	C₂³	1	2	yes	—
232	C₃₁×#97	C₂³	1	2	yes	—
233	C₄×C₈×C₃₁	C₂³	1	2	yes	—
234	C₂⁴×C₃₁	—	2	2	no	—
235	C₂⁴×C₃₁	—	2	1	no	—
236	#41×C₃₁	—	2	4	no	—
237	#41×C₃₁	—	2	4	no	—
238	#41×C₃₁	—	2	4	no	—
239	#41×C₃₁	—	2	4	no	—
240	#41×C₃₁	—	2	4	no	—
241	#41×C₃₁	—	4	4	no	—
242	#41×C₃₁	—	4	4	no	—
243	#41×C₃₁	—	4	8	no	—
244	#41×C₃₁	—	4	4	no	—
245	#41×C₃₁	—	4	4	no	—
246	#41×C₃₁	—	8	4	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	—	2	2	no	—
249	C₂×Q₈×C₃₁	—	2	1	no	—
250	C₂×Q₈×C₃₁	—	2	2	no	—
251	C₂×Q₈×C₃₁	—	2	4	no	—
252	C₂×Q₈×C₃₁	—	4	4	no	—
253	C₂×Q₈×C₃₁	—	4	4	no	—
254	C₂×Q₈×C₃₁	—	8	2	no	—
255	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	2	1	no	—
263	C₂×D₄×C₃₁	—	2	2	no	—
264	C₂×D₄×C₃₁	—	2	1	no	—
265	C₂×D₄×C₃₁	—	2	4	no	—
266	C₂×D₄×C₃₁	—	2	1	no	—
267	C₂×D₄×C₃₁	—	2	1	no	—
268	C₂×D₄×C₃₁	—	2	2	no	—
269	C₂×D₄×C₃₁	—	2	1	no	—
270	C₂×D₄×C₃₁	—	2	2	no	—
271	C₂×D₄×C₃₁	—	2	1	no	—
272	C₂×D₄×C₃₁	—	2	1	no	—
273	C₂×D₄×C₃₁	—	2	2	no	—
274	C₂×D₄×C₃₁	—	2	4	no	—
275	C₂×D₄×C₃₁	—	4	4	no	—
276	C₂×D₄×C₃₁	—	4	8	no	—
277	C₂×D₄×C₃₁	—	4	4	no	—
278	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	—	2	2	no	—
285	C₂²×C₄×C₃₁	—	2	1	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	1	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	1	no	—
292	C₂²×C₄×C₃₁	—	2	4	no	—
293	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	Q₁₆×C₃₁	—	4	2	no	—
300	Q₁₆×C₃₁	—	4	2	no	—
301	Q₁₆×C₃₁	—	4	4	no	—
302	SD₁₆×C₃₁	—	4	2	no	—
303	SD₁₆×C₃₁	—	4	2	no	—
304	SD₁₆×C₃₁	—	4	2	no	—
305	SD₁₆×C₃₁	—	4	2	no	—
306	SD₁₆×C₃₁	—	4	4	no	—
307	SD₁₆×C₃₁	—	4	4	no	—
308	D₈×C₃₁	—	4	2	no	—
309	D₈×C₃₁	—	4	2	no	—
310	D₈×C₃₁	—	4	4	no	—
311	M₁₆×C₃₁	—	2	4	no	—
312	C₂×C₈×C₃₁	—	2	4	no	—
313	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
314	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
315	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	4	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	1	no	—
321	C₄⋊C₄×C₃₁	—	2	1	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	1	no	—
324	C₄⋊C₄×C₃₁	—	2	1	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	4	no	—
327	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	1	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	2	1	no	—
337	C₂²⋊C₄×C₃₁	—	2	2	no	—
338	C₂²⋊C₄×C₃₁	—	2	2	no	—
339	C₂²⋊C₄×C₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₃₁	—	2	2	no	—
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	4	no	—
344	C₂²⋊C₄×C₃₁	—	2	1	no	—
345	C₂²⋊C₄×C₃₁	—	2	1	no	—
346	C₂²⋊C₄×C₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₄²×C₃₁	—	2	4	no	—
353	C₄²×C₃₁	C₂×D₄	1	2	yes	—
354	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₃₁	C₂×D₄	1	2	yes	—
357	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₄²×C₃₁	C₂⁴	1	2	yes	—
360	#60829	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	—	2	1	no	—
364	C₂³×C₃₁	—	2	1	no	—
365	C₂³×C₃₁	—	4	4	no	—
366	C₂³×C₃₁	—	4	2	no	—
367	C₂³×C₃₁	—	8	1	no	—
368	C₂³×C₃₁	—	8	1	no	—
369	C₂³×C₃₁	—	8	2	no	—
370	C₂³×C₃₁	—	8	2	no	—
371	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
372	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	Q₈×C₃₁	—	2	2	no	—
374	Q₈×C₃₁	—	2	2	no	—
375	Q₈×C₃₁	—	2	2	no	—
376	Q₈×C₃₁	—	2	4	no	—
377	Q₈×C₃₁	—	2	2	no	—
378	Q₈×C₃₁	—	2	2	no	—
379	Q₈×C₃₁	—	4	4	no	—
380	Q₈×C₃₁	—	4	4	no	—
381	Q₈×C₃₁	—	4	2	no	—
382	Q₈×C₃₁	—	8	2	no	—
383	D₄×C₃₁	—	2	4	no	—
384	D₄×C₃₁	—	2	2	no	—
385	D₄×C₃₁	—	2	2	no	—
386	D₄×C₃₁	—	2	2	no	—
387	D₄×C₃₁	—	2	4	no	—
388	D₄×C₃₁	—	2	2	no	—
389	D₄×C₃₁	—	2	2	no	—
390	D₄×C₃₁	—	4	2	no	—
391	D₄×C₃₁	—	4	4	no	—
392	D₄×C₃₁	—	4	2	no	—
393	D₄×C₃₁	—	4	4	no	—
394	D₄×C₃₁	—	4	4	no	—
395	D₄×C₃₁	—	4	2	no	—
396	D₄×C₃₁	—	4	4	no	—
397	D₄×C₃₁	—	4	2	no	—
398	D₄×C₃₁	—	4	2	no	—
399	D₄×C₃₁	—	8	2	no	—
400	D₄×C₃₁	—	8	1	no	—
401	D₄×C₃₁	—	8	2	no	—
402	D₄×C₃₁	—	8	1	no	—
403	D₄×C₃₁	—	8	4	no	—
404	C₂×C₄×C₃₁	—	2	4	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	4	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	4	1	no	—
411	C₂×C₄×C₃₁	—	4	2	no	—
412	C₂×C₄×C₃₁	—	4	1	no	—
413	C₂×C₄×C₃₁	—	4	2	no	—
414	C₂×C₄×C₃₁	—	4	4	no	—
415	C₂×C₄×C₃₁	—	4	4	no	—
416	C₂×C₄×C₃₁	—	4	4	no	—
417	C₂×C₄×C₃₁	—	4	2	no	—
418	C₂×C₄×C₃₁	—	4	2	no	—
419	C₂×C₄×C₃₁	—	4	2	no	—
420	C₂×C₄×C₃₁	—	4	4	no	—
421	C₂×C₄×C₃₁	—	8	4	no	—
422	C₂×C₄×C₃₁	—	8	2	no	—
423	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
432	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
433	C₈×C₃₁	—	2	2	no	—
434	C₈×C₃₁	—	2	2	no	—
435	C₈×C₃₁	—	2	4	no	—
436	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3500	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3225	C₂×C₃₁	1	4	yes	complemented
439	#3224	C₂×C₃₁	1	4	yes	complemented
440	#3216	C₂×C₃₁	1	2	yes	complemented
441	#3215	C₂×C₃₁	1	2	yes	complemented
442	#3214	C₂×C₃₁	1	2	yes	complemented
443	#3213	C₂×C₃₁	1	2	yes	complemented
444	#3153	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3150	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
447	C₂×#489	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#3046	C₂×C₃₁	1	2	yes	complemented
449	#3045	C₂×C₃₁	1	2	yes	complemented
450	#3013	C₂×C₃₁	1	2	yes	complemented
451	#3012	C₂×C₃₁	1	2	yes	complemented
452	#2923	C₂×C₃₁	1	1	yes	characteristic, complemented
453	C₂²×C₃₁	—	2	1	no	—
454	C₂²×C₃₁	—	2	1	no	—
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	4	2	no	—
459	C₂²×C₃₁	—	4	1	no	—
460	C₂²×C₃₁	—	4	2	no	—
461	C₂²×C₃₁	—	4	1	no	—
462	C₂²×C₃₁	—	4	2	no	—
463	C₂²×C₃₁	—	4	1	no	—
464	C₂²×C₃₁	—	4	2	no	—
465	C₂²×C₃₁	—	4	1	no	—
466	C₂²×C₃₁	—	4	1	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	1	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	16	2	no	—
471	C₂²×C₃₁	—	16	4	no	—
472	C₂²×C₃₁	#535	1	2	yes	—
473	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
474	C₄×C₃₁	—	2	1	no	—
475	C₄×C₃₁	—	2	2	no	—
476	C₄×C₃₁	—	2	1	no	—
477	C₄×C₃₁	—	2	1	no	—
478	C₄×C₃₁	—	2	2	no	—
479	C₄×C₃₁	—	2	1	no	—
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	4	4	no	—
482	C₄×C₃₁	—	4	1	no	—
483	C₄×C₃₁	—	4	2	no	—
484	C₄×C₃₁	—	4	1	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	#535	1	2	yes	—
487	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
488	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
490	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
491	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
492	C₂×#135	C₂²×C₃₁	1	2	yes	—
493	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
494	#556	—	2	1	no	—
495	#555	—	2	1	no	—
496	#554	—	2	1	no	—
497	#553	—	2	2	no	—
498	#548	—	2	1	no	—
499	#548	—	2	1	no	—
500	#548	—	2	2	no	—
501	#547	—	2	1	no	—
502	#546	—	2	1	no	—
503	#546	—	2	2	no	—
504	#546	—	2	2	no	—
505	#546	—	2	1	no	—
506	#542	C₂²×C₃₁	1	4	yes	complemented
507	#537	C₂²×C₃₁	1	2	yes	—
508	#536	C₂²×C₃₁	1	2	yes	—
509	#536	C₂²×C₃₁	1	1	yes	characteristic
510	#535	C₂²×C₃₁	1	2	yes	—
511	#535	C₂²×C₃₁	1	1	yes	characteristic
512	#533	C₂²×C₃₁	1	2	yes	complemented
513	#532	C₂²×C₃₁	1	1	yes	characteristic
514	#532	C₂²×C₃₁	1	2	yes	—
515	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	#532	C₂²×C₃₁	1	2	yes	complemented
517	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×#124	C₂²×C₃₁	1	2	yes	—
520	#520	C₂²×C₃₁	1	2	yes	complemented
521	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
522	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
523	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
524	#497	C₂²×C₃₁	1	2	yes	complemented
525	#497	C₂²×C₃₁	1	2	yes	complemented
526	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
527	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#496	C₂²×C₃₁	1	2	yes	complemented
529	#496	C₂²×C₃₁	1	2	yes	complemented
530	#495	C₂²×C₃₁	1	4	yes	complemented
531	#489	C₂²×C₃₁	1	2	yes	complemented
532	#489	C₂²×C₃₁	1	2	yes	complemented
533	#489	C₂²×C₃₁	1	4	yes	complemented
534	#489	C₂²×C₃₁	1	2	yes	complemented
535	#489	C₂²×C₃₁	1	2	yes	complemented
536	#487	C₂²×C₃₁	1	2	yes	complemented
537	#486	C₂²×C₃₁	1	2	yes	complemented
538	#464	C₂²×C₃₁	1	4	yes	complemented
539	#464	C₂²×C₃₁	1	4	yes	complemented
540	#463	C₂²×C₃₁	1	4	yes	complemented
541	#463	C₂²×C₃₁	1	4	yes	complemented
542	#462	C₂²×C₃₁	1	4	yes	complemented
543	#461	C₂²×C₃₁	1	4	yes	complemented
544	#460	C₂²×C₃₁	1	4	yes	complemented
545	#459	C₂²×C₃₁	1	4	yes	complemented
546	#452	C₂²×C₃₁	1	4	yes	—
547	#452	C₂²×C₃₁	1	4	yes	complemented
548	#451	C₂²×C₃₁	1	4	yes	complemented
549	#450	C₂²×C₃₁	1	4	yes	—
550	#449	C₂²×C₃₁	1	4	yes	—
551	#449	C₂²×C₃₁	1	4	yes	complemented
552	#448	C₂²×C₃₁	1	4	yes	complemented
553	#447	C₂²×C₃₁	1	4	yes	—
554	#433	C₂²×C₃₁	1	4	yes	complemented
555	#432	C₂²×C₃₁	1	2	yes	complemented
556	#432	C₂²×C₃₁	1	2	yes	complemented
557	#424	C₂²×C₃₁	1	2	yes	complemented
558	#417	C₂²×C₃₁	1	2	yes	—
559	#417	C₂²×C₃₁	1	2	yes	complemented
560	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
561	C₂×#102	C₂²×C₃₁	1	2	yes	—
562	#408	C₂²×C₃₁	1	2	yes	—
563	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	C₂×C₃₁	—	2	2	no	—
566	C₂×C₃₁	—	4	2	no	—
567	C₂×C₃₁	—	8	2	no	—
568	C₂×C₃₁	—	8	1	no	—
569	C₂×C₃₁	—	8	2	no	—
570	C₂×C₃₁	—	8	1	no	—
571	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
572	C₂×C₃₁	#3585	1	1	yes	characteristic
573	C₂×C₃₁	#3586	1	1	yes	characteristic
574	2₋¹⁺⁴	—	4	4	no	—
575	H(5,𝔽₂)	—	4	4	no	—
576	C₂×#41	—	2	1	no	—
577	C₂×#41	—	2	1	no	—
578	C₂×#41	—	2	2	no	—
579	C₂×#41	—	2	2	no	—
580	C₂×#41	C₂³×C₃₁	1	2	yes	—
581	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
582	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×#41	C₂³×C₃₁	1	2	yes	—
584	C₂×#41	C₂³×C₃₁	1	2	yes	—
585	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
586	C₂²×Q₈	—	2	1	no	—
587	C₂²×Q₈	—	2	1	no	—
588	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
589	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	2	1	no	—
592	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
594	#137	—	4	4	no	—
595	AGL(1,ℤ/8)	—	4	4	no	—
596	#135	—	4	4	no	—
597	#135	—	4	4	no	—
598	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
599	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
600	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
601	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
606	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
607	C₂×D₈	C₂³×C₃₁	1	2	yes	—
608	C₂×D₈	C₂³×C₃₁	1	2	yes	—
609	C₂×D₈	C₂³×C₃₁	1	4	yes	—
610	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
611	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
612	C₄⋊Q₈	—	2	1	no	—
613	C₄⋊Q₈	—	2	1	no	—
614	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
615	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
618	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
619	#127	C₂³×C₃₁	1	2	yes	—
620	#127	C₂³×C₃₁	1	1	yes	characteristic
621	#127	C₂³×C₃₁	1	1	yes	characteristic
622	#126	—	2	4	no	—
623	#125	—	2	2	no	—
624	#124	—	2	4	no	—
625	#124	—	2	2	no	—
626	#124	—	2	1	no	—
627	#124	—	2	1	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	C₂³×C₃₁	1	2	yes	—
631	#124	C₂³×C₃₁	1	1	yes	characteristic
632	#124	C₂³×C₃₁	1	2	yes	—
633	#124	C₂³×C₃₁	1	2	yes	—
634	#124	C₂³×C₃₁	1	2	yes	—
635	#124	C₂³×C₃₁	1	1	yes	characteristic
636	#124	C₂³×C₃₁	1	2	yes	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	4	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	4	no	—
648	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
649	#121	—	2	2	no	—
650	#121	—	2	4	no	—
651	#121	—	2	1	no	—
652	#121	—	2	2	no	—
653	#121	—	2	1	no	—
654	#121	—	2	2	no	—
655	#121	—	2	1	no	—
656	#121	—	2	1	no	—
657	#121	—	2	2	no	—
658	#121	—	2	1	no	—
659	#121	—	2	1	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	C₂³×C₃₁	1	4	yes	—
663	#120	—	2	2	no	—
664	#120	—	2	2	no	—
665	#120	—	2	2	no	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
668	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
669	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
670	C₄×D₄	—	2	4	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	—	2	1	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	1	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
679	C₄×D₄	D₄×C₃₁	1	2	yes	—
680	C₄×D₄	D₄×C₃₁	1	2	yes	—
681	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
682	C₄×D₄	C₂³×C₃₁	1	4	yes	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	C₂³×C₃₁	1	1	yes	characteristic
686	#117	C₂³×C₃₁	1	2	yes	—
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	—	2	2	no	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
696	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
697	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
698	#103	C₂³×C₃₁	1	4	yes	—
699	#103	C₂³×C₃₁	1	4	yes	—
700	#103	C₂³×C₃₁	1	4	yes	—
701	#103	C₂³×C₃₁	1	4	yes	—
702	#102	C₂³×C₃₁	1	4	yes	—
703	#102	C₂³×C₃₁	1	4	yes	—
704	#102	C₂³×C₃₁	1	4	yes	—
705	#102	C₂³×C₃₁	1	4	yes	—
706	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
707	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
708	#97	C₂³×C₃₁	1	1	yes	characteristic
709	#97	C₂³×C₃₁	1	1	yes	characteristic
710	#97	C₂³×C₃₁	1	2	yes	—
711	#97	C₂³×C₃₁	1	2	yes	—
712	C₄×C₈	C₂³×C₃₁	1	2	yes	—
713	C₃₁	#60829	1	1	yes	characteristic, direct product factor, Sylow
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	1	no	—
716	#41	—	2	4	no	—
717	#41	—	2	4	no	—
718	#41	—	2	4	no	—
719	#41	—	2	4	no	—
720	#41	—	2	4	no	—
721	#41	—	4	4	no	—
722	#41	—	4	4	no	—
723	#41	—	4	8	no	—
724	#41	—	4	4	no	—
725	#41	—	4	4	no	—
726	#41	—	8	4	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	1	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	4	4	no	—
733	C₂×Q₈	—	4	4	no	—
734	C₂×Q₈	—	8	2	no	—
735	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
736	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
737	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
739	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	4	no	—
755	C₂×D₄	—	4	4	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	4	4	no	—
758	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
759	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
760	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
761	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
776	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
779	Q₁₆	—	4	2	no	—
780	Q₁₆	—	4	2	no	—
781	Q₁₆	—	4	4	no	—
782	SD₁₆	—	4	2	no	—
783	SD₁₆	—	4	2	no	—
784	SD₁₆	—	4	2	no	—
785	SD₁₆	—	4	2	no	—
786	SD₁₆	—	4	4	no	—
787	SD₁₆	—	4	4	no	—
788	D₈	—	4	2	no	—
789	D₈	—	4	2	no	—
790	D₈	—	4	4	no	—
791	M₁₆	—	2	4	no	—
792	C₂×C₈	—	2	4	no	—
793	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
794	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
811	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	1	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	4	no	—
824	C₂²⋊C₄	—	2	1	no	—
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
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	C₄²	—	2	4	no	—
833	C₄²	C₂×D₄×C₃₁	1	2	yes	—
834	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
835	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
836	C₄²	C₂×D₄×C₃₁	1	2	yes	—
837	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
839	C₄²	C₂⁴×C₃₁	1	2	yes	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	4	4	no	—
845	C₂³	—	4	2	no	—
846	C₂³	—	8	1	no	—
847	C₂³	—	8	1	no	—
848	C₂³	—	8	2	no	—
849	C₂³	—	8	2	no	—
850	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
851	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	4	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	4	4	no	—
860	Q₈	—	4	2	no	—
861	Q₈	—	8	2	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	2	no	—
865	D₄	—	2	2	no	—
866	D₄	—	2	4	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	4	2	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	2	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	2	no	—
877	D₄	—	4	2	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	1	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	1	no	—
882	D₄	—	8	4	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	8	4	no	—
901	C₂×C₄	—	8	2	no	—
902	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
905	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
907	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
909	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
910	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
911	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
912	C₈	—	2	2	no	—
913	C₈	—	2	2	no	—
914	C₈	—	2	4	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	16	2	no	—
933	C₂²	—	16	4	no	—
934	C₂²	C₃₁×#535	1	2	yes	—
935	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
936	C₄	—	2	2	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	4	no	—
948	C₄	C₃₁×#535	1	2	yes	—
949	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
950	C₂	—	2	2	no	—
951	C₂	—	4	2	no	—
952	C₂	—	8	2	no	—
953	C₂	—	8	1	no	—
954	C₂	—	8	1	no	—
955	C₂	—	8	2	no	—
956	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
957	C₂	C₃₁×#3585	1	1	yes	characteristic
958	C₂	C₃₁×#3586	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3500	C₂	semidirect
3. C₃₁×#3225	C₂	semidirect
4. C₃₁×#3224	C₂	semidirect
5. C₃₁×#3216	C₂	semidirect
6. C₃₁×#3215	C₂	semidirect
7. C₃₁×#3214	C₂	semidirect
8. C₃₁×#3213	C₂	semidirect
9. C₃₁×#3153	C₂	semidirect
10. C₃₁×#3150	C₂	semidirect
11. C₃₁×#3141	C₂	semidirect
12. C₂×C₃₁×#489	C₂	semidirect
13. C₃₁×#3046	C₂	semidirect
14. C₃₁×#3045	C₂	semidirect
15. C₃₁×#3013	C₂	semidirect
16. C₃₁×#3012	C₂	semidirect
17. C₃₁×#2923	C₂	semidirect
20. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×#135	C₂²	semidirect
36. C₃₁×#542	C₂²	semidirect
42. C₃₁×#533	C₂²	semidirect
45. C₃₁×#532	C₂²	semidirect
46. C₃₁×#532	C₂²	semidirect
47. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
50. C₃₁×#520	C₂²	semidirect
52. C₃₁×#497	C₂²	semidirect
53. C₃₁×#497	C₂²	semidirect
54. C₃₁×#497	C₂²	semidirect
55. C₃₁×#497	C₂²	semidirect
56. C₃₁×#496	C₂²	semidirect
57. C₃₁×#496	C₂²	semidirect
58. C₃₁×#496	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
63. C₃₁×#489	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#464	C₂²	semidirect
69. C₃₁×#464	C₂²	semidirect
70. C₃₁×#463	C₂²	semidirect
71. C₃₁×#463	C₂²	semidirect
72. C₃₁×#462	C₂²	semidirect
73. C₃₁×#461	C₂²	semidirect
74. C₃₁×#460	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
78. C₃₁×#451	C₂²	semidirect
81. C₃₁×#449	C₂²	semidirect
82. C₃₁×#448	C₂²	semidirect
84. C₃₁×#433	C₂²	semidirect
85. C₃₁×#432	C₂²	semidirect
86. C₃₁×#432	C₂²	semidirect
87. C₃₁×#424	C₂²	semidirect
89. C₃₁×#417	C₂²	semidirect
90. C₂×C₃₁×#103	C₂²	semidirect
93. C₄×M₁₆×C₃₁	C₂²	semidirect
94. C₂×C₃₁×#97	C₂²	semidirect
360. #60829	C₃₁	direct (N × H)
436. #3511	C₂×C₃₁	semidirect
437. #3500	C₂×C₃₁	semidirect
438. #3225	C₂×C₃₁	semidirect
439. #3224	C₂×C₃₁	semidirect
440. #3216	C₂×C₃₁	semidirect
441. #3215	C₂×C₃₁	semidirect
442. #3214	C₂×C₃₁	semidirect
443. #3213	C₂×C₃₁	semidirect
444. #3153	C₂×C₃₁	semidirect
445. #3150	C₂×C₃₁	semidirect
446. #3141	C₂×C₃₁	semidirect
447. C₂×#489	C₂×C₃₁	semidirect
448. #3046	C₂×C₃₁	semidirect
449. #3045	C₂×C₃₁	semidirect
450. #3013	C₂×C₃₁	semidirect
451. #3012	C₂×C₃₁	semidirect
452. #2923	C₂×C₃₁	semidirect
490. C₂×#137	C₂²×C₃₁	semidirect
493. C₂×#135	C₂²×C₃₁	semidirect
506. #542	C₂²×C₃₁	semidirect
512. #533	C₂²×C₃₁	semidirect
515. #532	C₂²×C₃₁	semidirect
516. #532	C₂²×C₃₁	semidirect
517. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
520. #520	C₂²×C₃₁	semidirect
522. #497	C₂²×C₃₁	semidirect
523. #497	C₂²×C₃₁	semidirect
524. #497	C₂²×C₃₁	semidirect
525. #497	C₂²×C₃₁	semidirect
526. #496	C₂²×C₃₁	semidirect
527. #496	C₂²×C₃₁	semidirect
528. #496	C₂²×C₃₁	semidirect
529. #496	C₂²×C₃₁	semidirect
530. #495	C₂²×C₃₁	semidirect
531. #489	C₂²×C₃₁	semidirect
532. #489	C₂²×C₃₁	semidirect
533. #489	C₂²×C₃₁	semidirect
534. #489	C₂²×C₃₁	semidirect
535. #489	C₂²×C₃₁	semidirect
536. #487	C₂²×C₃₁	semidirect
537. #486	C₂²×C₃₁	semidirect
538. #464	C₂²×C₃₁	semidirect
539. #464	C₂²×C₃₁	semidirect
540. #463	C₂²×C₃₁	semidirect
541. #463	C₂²×C₃₁	semidirect
542. #462	C₂²×C₃₁	semidirect
543. #461	C₂²×C₃₁	semidirect
544. #460	C₂²×C₃₁	semidirect
545. #459	C₂²×C₃₁	semidirect
547. #452	C₂²×C₃₁	semidirect
548. #451	C₂²×C₃₁	semidirect
551. #449	C₂²×C₃₁	semidirect
552. #448	C₂²×C₃₁	semidirect
554. #433	C₂²×C₃₁	semidirect
555. #432	C₂²×C₃₁	semidirect
556. #432	C₂²×C₃₁	semidirect
557. #424	C₂²×C₃₁	semidirect
559. #417	C₂²×C₃₁	semidirect
560. C₂×#103	C₂²×C₃₁	semidirect
563. C₄×M₁₆	C₂²×C₃₁	semidirect
564. C₂×#97	C₂²×C₃₁	semidirect
713. C₃₁	#60829	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×#3511	2
C₃₁×#3500	2
C₃₁×#3225	2
C₃₁×#3224	2
C₃₁×#3216	2
C₃₁×#3215	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3153	2
C₃₁×#3150	2
C₃₁×#3141	2
C₂×C₃₁×#489	2
C₃₁×#3046	2
C₃₁×#3045	2
C₃₁×#3013	2
C₃₁×#3012	2
C₃₁×#2923	2
#60829	31

Subgroups — C31×#60829 #21517588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60829 #21517588