Subgroups — C₃₁×#60835 #21517594

Order 7936.

2040 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3210	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#546	—	2	2	no	—
37	C₃₁×#546	—	2	1	no	—
38	C₃₁×#546	—	2	2	no	—
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#542	—	2	1	no	—
42	C₃₁×#542	C₂²	1	2	yes	complemented
43	C₃₁×#541	—	2	1	no	—
44	C₃₁×#541	C₂²	1	2	yes	complemented
45	C₃₁×#539	—	2	2	no	—
46	C₃₁×#537	C₂²	1	1	yes	characteristic
47	C₃₁×#536	C₂²	1	1	yes	characteristic
48	C₃₁×#536	C₂²	1	2	yes	—
49	C₃₁×#536	C₂²	1	1	yes	characteristic
50	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#535	C₂²	1	1	yes	characteristic
52	C₃₁×#535	C₂²	1	2	yes	—
53	C₃₁×#533	—	2	1	no	—
54	C₃₁×#533	C₂²	1	2	yes	complemented
55	C₃₁×#532	C₂²	1	2	yes	—
56	C₃₁×#532	C₂²	1	1	yes	characteristic
57	C₃₁×#529	—	2	2	no	—
58	C₃₁×#529	—	2	1	no	—
59	C₃₁×#529	C₂²	1	2	yes	complemented
60	C₂×C₃₁×#124	C₂²	1	2	yes	—
61	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#497	C₂²	1	2	yes	complemented
66	C₃₁×#497	C₂²	1	2	yes	complemented
67	C₃₁×#497	C₂²	1	2	yes	complemented
68	C₃₁×#496	C₂²	1	2	yes	complemented
69	C₃₁×#495	C₂²	1	2	yes	complemented
70	C₃₁×#495	C₂²	1	2	yes	complemented
71	C₃₁×#494	C₂²	1	2	yes	complemented
72	C₃₁×#492	C₂²	1	2	yes	complemented
73	C₃₁×#491	C₂²	1	2	yes	complemented
74	C₃₁×#490	C₂²	1	2	yes	complemented
75	C₃₁×#489	C₂²	1	2	yes	complemented
76	C₃₁×#489	C₂²	1	2	yes	complemented
77	C₃₁×#488	C₂²	1	2	yes	complemented
78	C₃₁×#488	C₂²	1	2	yes	complemented
79	C₃₁×#487	C₂²	1	2	yes	complemented
80	C₃₁×#486	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#464	C₂²	1	2	yes	complemented
83	C₃₁×#464	C₂²	1	2	yes	complemented
84	C₃₁×#464	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	2	yes	complemented
86	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#464	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#463	C₂²	1	2	yes	complemented
93	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#463	C₂²	1	2	yes	complemented
95	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#462	C₂²	1	2	yes	complemented
97	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#460	C₂²	1	2	yes	complemented
100	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#452	C₂²	1	2	yes	—
102	C₃₁×#452	C₂²	1	2	yes	—
103	C₃₁×#452	C₂²	1	2	yes	—
104	C₃₁×#452	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#451	C₂²	1	2	yes	complemented
108	C₃₁×#451	C₂²	1	2	yes	complemented
109	C₃₁×#451	C₂²	1	2	yes	complemented
110	C₃₁×#450	C₂²	1	2	yes	—
111	C₃₁×#450	C₂²	1	2	yes	—
112	C₃₁×#450	C₂²	1	2	yes	—
113	C₃₁×#449	C₂²	1	2	yes	—
114	C₃₁×#449	C₂²	1	2	yes	complemented
115	C₃₁×#448	C₂²	1	2	yes	complemented
116	C₃₁×#447	C₂²	1	2	yes	—
117	C₃₁×#433	C₂²	1	2	yes	complemented
118	C₃₁×#433	C₂²	1	2	yes	complemented
119	C₃₁×#432	C₂²	1	2	yes	complemented
120	C₃₁×#431	C₂²	1	2	yes	complemented
121	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#418	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₃₁×#408	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×2₋¹⁺⁴	—	4	2	no	—
136	C₃₁×2₋¹⁺⁴	—	4	2	no	—
137	C₃₁×H(5,𝔽₂)	—	4	2	no	—
138	C₃₁×H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	2	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×#41×C₃₁	C₂³	1	2	yes	—
146	C₂×#41×C₃₁	C₂³	1	2	yes	—
147	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₃₁	—	2	1	no	—
149	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₂²×D₄×C₃₁	—	2	2	no	—
153	C₂²×D₄×C₃₁	—	2	1	no	—
154	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
156	C₃₁×#137	—	4	2	no	—
157	C₃₁×#137	—	4	2	no	—
158	C₃₁×#137	—	4	2	no	—
159	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
160	C₃₁×#135	—	4	2	no	—
161	C₃₁×#135	—	4	2	no	—
162	C₂×Q₁₆×C₃₁	—	4	2	no	—
163	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
168	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₃₁	—	4	2	no	—
171	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
181	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×D₈×C₃₁	C₂³	1	2	yes	—
183	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
188	C₃₁×C₄⋊Q₈	—	2	1	no	—
189	C₃₁×C₄⋊Q₈	—	2	1	no	—
190	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
191	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
192	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×#127	C₂³	1	1	yes	characteristic
195	C₃₁×#127	C₂³	1	2	yes	—
196	C₃₁×#126	—	2	2	no	—
197	C₃₁×#126	—	2	2	no	—
198	C₃₁×#126	—	2	2	no	—
199	C₃₁×#126	—	2	2	no	—
200	C₃₁×#125	—	2	2	no	—
201	C₃₁×#125	—	2	1	no	—
202	C₃₁×#125	—	2	2	no	—
203	C₃₁×#125	—	2	2	no	—
204	C₃₁×#125	C₂³	1	2	yes	—
205	C₃₁×#124	—	2	1	no	—
206	C₃₁×#124	—	2	2	no	—
207	C₃₁×#124	—	2	1	no	—
208	C₃₁×#124	—	2	2	no	—
209	C₃₁×#124	—	2	1	no	—
210	C₃₁×#124	—	2	2	no	—
211	C₃₁×#124	C₂³	1	1	yes	characteristic
212	C₃₁×#124	C₂³	1	2	yes	—
213	C₃₁×#124	C₂³	1	2	yes	—
214	C₃₁×#124	C₂³	1	1	yes	characteristic
215	C₃₁×#124	C₂³	1	2	yes	—
216	C₃₁×#124	C₂³	1	2	yes	—
217	C₃₁×#124	C₂³	1	2	yes	—
218	C₃₁×#123	—	2	2	no	—
219	C₃₁×#123	—	2	2	no	—
220	C₃₁×#123	—	2	2	no	—
221	C₃₁×#123	—	2	2	no	—
222	C₃₁×#123	—	2	2	no	—
223	C₃₁×#123	—	2	2	no	—
224	C₃₁×#123	—	2	2	no	—
225	C₃₁×C₂²⋊Q₈	—	2	1	no	—
226	C₃₁×C₂²⋊Q₈	—	2	2	no	—
227	C₃₁×C₂²⋊Q₈	—	2	1	no	—
228	C₃₁×C₂²⋊Q₈	—	2	1	no	—
229	C₃₁×C₂²⋊Q₈	—	2	2	no	—
230	C₃₁×C₂²⋊Q₈	—	2	1	no	—
231	C₃₁×C₂²⋊Q₈	—	2	2	no	—
232	C₃₁×C₂²⋊Q₈	—	2	1	no	—
233	C₃₁×C₂²⋊Q₈	—	2	2	no	—
234	C₃₁×C₂²⋊Q₈	—	2	2	no	—
235	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
236	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
237	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
238	C₃₁×#121	—	2	2	no	—
239	C₃₁×#121	—	2	1	no	—
240	C₃₁×#121	—	2	1	no	—
241	C₃₁×#121	—	2	1	no	—
242	C₃₁×#121	—	2	2	no	—
243	C₃₁×#121	—	2	2	no	—
244	C₃₁×#121	—	2	1	no	—
245	C₃₁×#121	—	2	2	no	—
246	C₃₁×#121	—	2	1	no	—
247	C₃₁×#121	—	2	2	no	—
248	C₃₁×#121	C₂³	1	2	yes	—
249	C₃₁×#120	—	2	2	no	—
250	C₃₁×#120	—	2	2	no	—
251	C₃₁×#120	—	2	2	no	—
252	C₄×Q₈×C₃₁	—	2	1	no	—
253	C₄×Q₈×C₃₁	—	2	1	no	—
254	C₄×Q₈×C₃₁	—	2	2	no	—
255	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
257	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
258	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
260	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	2	2	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	2	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	2	no	—
268	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
269	C₄×D₄×C₃₁	D₄	1	2	yes	—
270	C₄×D₄×C₃₁	D₄	1	2	yes	—
271	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
272	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#117	—	2	2	no	—
275	C₃₁×#117	—	2	1	no	—
276	C₃₁×#117	—	2	2	no	—
277	C₃₁×#117	C₂³	1	1	yes	characteristic
278	C₃₁×#117	C₂³	1	1	yes	characteristic
279	C₃₁×#117	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
284	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂×C₄²×C₃₁	—	2	1	no	—
287	C₂×C₄²×C₃₁	—	2	1	no	—
288	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
290	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
294	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
295	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	C₂³	1	1	yes	characteristic
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	2	yes	—
303	C₃₁×#103	C₂³	1	2	yes	—
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	1	yes	characteristic
309	C₃₁×#102	C₂³	1	1	yes	characteristic
310	C₃₁×#102	C₂³	1	1	yes	characteristic
311	C₃₁×#102	C₂³	1	1	yes	characteristic
312	C₃₁×#102	C₂³	1	2	yes	—
313	C₃₁×#102	C₂³	1	2	yes	—
314	C₃₁×#102	C₂³	1	2	yes	—
315	C₃₁×#102	C₂³	1	2	yes	—
316	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₃₁×#97	C₂³	1	2	yes	—
321	C₃₁×#97	C₂³	1	2	yes	—
322	C₄×C₈×C₃₁	C₂³	1	2	yes	—
323	C₄×C₈×C₃₁	C₂³	1	2	yes	—
324	C₂⁴×C₃₁	—	2	2	no	—
325	C₂⁴×C₃₁	—	2	1	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	2	2	no	—
333	#41×C₃₁	—	2	2	no	—
334	#41×C₃₁	—	4	2	no	—
335	#41×C₃₁	—	4	2	no	—
336	#41×C₃₁	—	4	2	no	—
337	#41×C₃₁	—	4	2	no	—
338	#41×C₃₁	—	4	8	no	—
339	#41×C₃₁	—	4	4	no	—
340	#41×C₃₁	—	4	4	no	—
341	C₂×Q₈×C₃₁	—	2	1	no	—
342	C₂×Q₈×C₃₁	—	2	2	no	—
343	C₂×Q₈×C₃₁	—	2	1	no	—
344	C₂×Q₈×C₃₁	—	2	2	no	—
345	C₂×Q₈×C₃₁	—	2	2	no	—
346	C₂×Q₈×C₃₁	—	2	2	no	—
347	C₂×Q₈×C₃₁	—	2	2	no	—
348	C₂×Q₈×C₃₁	—	2	2	no	—
349	C₂×Q₈×C₃₁	—	4	2	no	—
350	C₂×Q₈×C₃₁	—	4	2	no	—
351	C₂×Q₈×C₃₁	—	4	4	no	—
352	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
354	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₃₁	—	2	1	no	—
359	C₂×D₄×C₃₁	—	2	2	no	—
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	—	2	2	no	—
362	C₂×D₄×C₃₁	—	2	1	no	—
363	C₂×D₄×C₃₁	—	2	2	no	—
364	C₂×D₄×C₃₁	—	2	2	no	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	1	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	2	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	4	2	no	—
373	C₂×D₄×C₃₁	—	4	2	no	—
374	C₂×D₄×C₃₁	—	4	8	no	—
375	C₂×D₄×C₃₁	—	4	4	no	—
376	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
379	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	—	2	1	no	—
383	C₂²×C₄×C₃₁	—	2	2	no	—
384	C₂²×C₄×C₃₁	—	2	1	no	—
385	C₂²×C₄×C₃₁	—	2	1	no	—
386	C₂²×C₄×C₃₁	—	2	1	no	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
388	C₂²×C₄×C₃₁	—	2	2	no	—
389	C₂²×C₄×C₃₁	—	2	1	no	—
390	C₂²×C₄×C₃₁	—	2	2	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	—	2	1	no	—
393	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₃₁	—	4	2	no	—
400	Q₁₆×C₃₁	—	4	2	no	—
401	Q₁₆×C₃₁	—	4	1	no	—
402	Q₁₆×C₃₁	—	4	1	no	—
403	Q₁₆×C₃₁	—	4	2	no	—
404	Q₁₆×C₃₁	—	4	2	no	—
405	Q₁₆×C₃₁	—	4	2	no	—
406	SD₁₆×C₃₁	—	4	2	no	—
407	SD₁₆×C₃₁	—	4	2	no	—
408	SD₁₆×C₃₁	—	4	1	no	—
409	SD₁₆×C₃₁	—	4	1	no	—
410	SD₁₆×C₃₁	—	4	1	no	—
411	SD₁₆×C₃₁	—	4	1	no	—
412	SD₁₆×C₃₁	—	4	2	no	—
413	SD₁₆×C₃₁	—	4	2	no	—
414	SD₁₆×C₃₁	—	4	2	no	—
415	SD₁₆×C₃₁	—	4	2	no	—
416	D₈×C₃₁	—	4	1	no	—
417	D₈×C₃₁	—	4	1	no	—
418	D₈×C₃₁	—	4	2	no	—
419	M₁₆×C₃₁	—	2	2	no	—
420	M₁₆×C₃₁	—	2	2	no	—
421	C₂×C₈×C₃₁	—	2	2	no	—
422	C₂×C₈×C₃₁	—	2	2	no	—
423	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
426	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
427	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	2	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	—	2	2	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	1	no	—
439	C₄⋊C₄×C₃₁	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	2	no	—
441	C₄⋊C₄×C₃₁	—	2	2	no	—
442	C₄⋊C₄×C₃₁	—	2	2	no	—
443	C₄⋊C₄×C₃₁	—	2	2	no	—
444	C₄⋊C₄×C₃₁	—	2	2	no	—
445	C₄⋊C₄×C₃₁	—	2	2	no	—
446	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	2	no	—
455	C₂²⋊C₄×C₃₁	—	2	1	no	—
456	C₂²⋊C₄×C₃₁	—	2	2	no	—
457	C₂²⋊C₄×C₃₁	—	2	2	no	—
458	C₂²⋊C₄×C₃₁	—	2	1	no	—
459	C₂²⋊C₄×C₃₁	—	2	2	no	—
460	C₂²⋊C₄×C₃₁	—	2	1	no	—
461	C₂²⋊C₄×C₃₁	—	2	2	no	—
462	C₂²⋊C₄×C₃₁	—	2	2	no	—
463	C₂²⋊C₄×C₃₁	—	2	2	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	2	no	—
470	C₂²⋊C₄×C₃₁	—	2	2	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
477	C₄²×C₃₁	—	2	2	no	—
478	C₄²×C₃₁	—	2	1	no	—
479	C₄²×C₃₁	—	2	1	no	—
480	C₄²×C₃₁	—	2	1	no	—
481	C₄²×C₃₁	—	2	2	no	—
482	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₃₁	C₂×D₄	1	2	yes	—
484	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₃₁	C₂×D₄	1	2	yes	—
486	C₄²×C₃₁	C₂⁴	1	2	yes	—
487	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
488	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
489	#60835	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
490	C₂³×C₃₁	—	2	1	no	—
491	C₂³×C₃₁	—	2	2	no	—
492	C₂³×C₃₁	—	2	1	no	—
493	C₂³×C₃₁	—	2	1	no	—
494	C₂³×C₃₁	—	4	4	no	—
495	C₂³×C₃₁	—	4	2	no	—
496	C₂³×C₃₁	—	8	1	no	—
497	C₂³×C₃₁	—	8	1	no	—
498	C₂³×C₃₁	—	8	2	no	—
499	C₂³×C₃₁	—	8	2	no	—
500	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
501	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	Q₈×C₃₁	—	2	2	no	—
503	Q₈×C₃₁	—	2	2	no	—
504	Q₈×C₃₁	—	2	2	no	—
505	Q₈×C₃₁	—	2	1	no	—
506	Q₈×C₃₁	—	2	1	no	—
507	Q₈×C₃₁	—	2	2	no	—
508	Q₈×C₃₁	—	2	1	no	—
509	Q₈×C₃₁	—	2	1	no	—
510	Q₈×C₃₁	—	2	2	no	—
511	Q₈×C₃₁	—	2	1	no	—
512	Q₈×C₃₁	—	2	1	no	—
513	Q₈×C₃₁	—	4	4	no	—
514	Q₈×C₃₁	—	4	2	no	—
515	Q₈×C₃₁	—	4	2	no	—
516	Q₈×C₃₁	—	8	2	no	—
517	D₄×C₃₁	—	2	4	no	—
518	D₄×C₃₁	—	2	2	no	—
519	D₄×C₃₁	—	2	1	no	—
520	D₄×C₃₁	—	2	1	no	—
521	D₄×C₃₁	—	2	2	no	—
522	D₄×C₃₁	—	2	1	no	—
523	D₄×C₃₁	—	2	1	no	—
524	D₄×C₃₁	—	2	2	no	—
525	D₄×C₃₁	—	2	1	no	—
526	D₄×C₃₁	—	2	1	no	—
527	D₄×C₃₁	—	4	4	no	—
528	D₄×C₃₁	—	4	4	no	—
529	D₄×C₃₁	—	4	4	no	—
530	D₄×C₃₁	—	4	2	no	—
531	D₄×C₃₁	—	4	2	no	—
532	D₄×C₃₁	—	4	2	no	—
533	D₄×C₃₁	—	4	2	no	—
534	D₄×C₃₁	—	8	1	no	—
535	D₄×C₃₁	—	8	2	no	—
536	D₄×C₃₁	—	8	1	no	—
537	D₄×C₃₁	—	8	2	no	—
538	D₄×C₃₁	—	8	2	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	2	no	—
541	C₂×C₄×C₃₁	—	2	1	no	—
542	C₂×C₄×C₃₁	—	2	2	no	—
543	C₂×C₄×C₃₁	—	2	1	no	—
544	C₂×C₄×C₃₁	—	2	1	no	—
545	C₂×C₄×C₃₁	—	2	2	no	—
546	C₂×C₄×C₃₁	—	2	2	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	4	1	no	—
550	C₂×C₄×C₃₁	—	4	2	no	—
551	C₂×C₄×C₃₁	—	4	1	no	—
552	C₂×C₄×C₃₁	—	4	2	no	—
553	C₂×C₄×C₃₁	—	4	2	no	—
554	C₂×C₄×C₃₁	—	4	4	no	—
555	C₂×C₄×C₃₁	—	4	4	no	—
556	C₂×C₄×C₃₁	—	4	4	no	—
557	C₂×C₄×C₃₁	—	4	2	no	—
558	C₂×C₄×C₃₁	—	4	2	no	—
559	C₂×C₄×C₃₁	—	4	2	no	—
560	C₂×C₄×C₃₁	—	4	2	no	—
561	C₂×C₄×C₃₁	—	4	2	no	—
562	C₂×C₄×C₃₁	—	8	1	no	—
563	C₂×C₄×C₃₁	—	8	1	no	—
564	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
569	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
573	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
574	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
575	C₈×C₃₁	—	2	1	no	—
576	C₈×C₃₁	—	2	1	no	—
577	C₈×C₃₁	—	2	1	no	—
578	C₈×C₃₁	—	2	1	no	—
579	C₈×C₃₁	—	2	2	no	—
580	C₈×C₃₁	—	2	2	no	—
581	#3500	C₂×C₃₁	1	1	yes	characteristic, complemented
582	#3461	C₂×C₃₁	1	1	yes	characteristic, complemented
583	#3225	C₂×C₃₁	1	2	yes	complemented
584	#3224	C₂×C₃₁	1	2	yes	complemented
585	#3223	C₂×C₃₁	1	2	yes	complemented
586	#3222	C₂×C₃₁	1	2	yes	complemented
587	#3219	C₂×C₃₁	1	2	yes	complemented
588	#3215	C₂×C₃₁	1	2	yes	complemented
589	#3211	C₂×C₃₁	1	2	yes	complemented
590	#3210	C₂×C₃₁	1	2	yes	complemented
591	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
594	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
598	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
601	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3009	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
604	C₂²×C₃₁	—	2	1	no	—
605	C₂²×C₃₁	—	2	1	no	—
606	C₂²×C₃₁	—	2	2	no	—
607	C₂²×C₃₁	—	2	2	no	—
608	C₂²×C₃₁	—	2	2	no	—
609	C₂²×C₃₁	—	4	1	no	—
610	C₂²×C₃₁	—	4	1	no	—
611	C₂²×C₃₁	—	4	2	no	—
612	C₂²×C₃₁	—	4	1	no	—
613	C₂²×C₃₁	—	4	1	no	—
614	C₂²×C₃₁	—	4	1	no	—
615	C₂²×C₃₁	—	4	2	no	—
616	C₂²×C₃₁	—	4	1	no	—
617	C₂²×C₃₁	—	4	1	no	—
618	C₂²×C₃₁	—	4	2	no	—
619	C₂²×C₃₁	—	4	1	no	—
620	C₂²×C₃₁	—	4	1	no	—
621	C₂²×C₃₁	—	16	2	no	—
622	C₂²×C₃₁	—	16	4	no	—
623	C₂²×C₃₁	#535	1	2	yes	—
624	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
625	C₄×C₃₁	—	2	1	no	—
626	C₄×C₃₁	—	2	1	no	—
627	C₄×C₃₁	—	2	2	no	—
628	C₄×C₃₁	—	2	1	no	—
629	C₄×C₃₁	—	2	1	no	—
630	C₄×C₃₁	—	2	2	no	—
631	C₄×C₃₁	—	2	2	no	—
632	C₄×C₃₁	—	4	2	no	—
633	C₄×C₃₁	—	4	1	no	—
634	C₄×C₃₁	—	4	1	no	—
635	C₄×C₃₁	—	4	1	no	—
636	C₄×C₃₁	—	4	2	no	—
637	C₄×C₃₁	—	4	1	no	—
638	C₄×C₃₁	—	4	1	no	—
639	C₄×C₃₁	—	4	2	no	—
640	C₄×C₃₁	#535	1	2	yes	—
641	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
642	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
644	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
645	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
646	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
649	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
650	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
653	#548	—	2	1	no	—
654	#548	—	2	1	no	—
655	#546	—	2	2	no	—
656	#546	—	2	1	no	—
657	#546	—	2	2	no	—
658	#546	—	2	1	no	—
659	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#542	—	2	1	no	—
661	#542	C₂²×C₃₁	1	2	yes	complemented
662	#541	—	2	1	no	—
663	#541	C₂²×C₃₁	1	2	yes	complemented
664	#539	—	2	2	no	—
665	#537	C₂²×C₃₁	1	1	yes	characteristic
666	#536	C₂²×C₃₁	1	1	yes	characteristic
667	#536	C₂²×C₃₁	1	2	yes	—
668	#536	C₂²×C₃₁	1	1	yes	characteristic
669	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#535	C₂²×C₃₁	1	1	yes	characteristic
671	#535	C₂²×C₃₁	1	2	yes	—
672	#533	—	2	1	no	—
673	#533	C₂²×C₃₁	1	2	yes	complemented
674	#532	C₂²×C₃₁	1	2	yes	—
675	#532	C₂²×C₃₁	1	1	yes	characteristic
676	#529	—	2	2	no	—
677	#529	—	2	1	no	—
678	#529	C₂²×C₃₁	1	2	yes	complemented
679	C₂×#124	C₂²×C₃₁	1	2	yes	—
680	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
682	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#497	C₂²×C₃₁	1	2	yes	complemented
685	#497	C₂²×C₃₁	1	2	yes	complemented
686	#497	C₂²×C₃₁	1	2	yes	complemented
687	#496	C₂²×C₃₁	1	2	yes	complemented
688	#495	C₂²×C₃₁	1	2	yes	complemented
689	#495	C₂²×C₃₁	1	2	yes	complemented
690	#494	C₂²×C₃₁	1	2	yes	complemented
691	#492	C₂²×C₃₁	1	2	yes	complemented
692	#491	C₂²×C₃₁	1	2	yes	complemented
693	#490	C₂²×C₃₁	1	2	yes	complemented
694	#489	C₂²×C₃₁	1	2	yes	complemented
695	#489	C₂²×C₃₁	1	2	yes	complemented
696	#488	C₂²×C₃₁	1	2	yes	complemented
697	#488	C₂²×C₃₁	1	2	yes	complemented
698	#487	C₂²×C₃₁	1	2	yes	complemented
699	#486	C₂²×C₃₁	1	2	yes	complemented
700	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#464	C₂²×C₃₁	1	2	yes	complemented
702	#464	C₂²×C₃₁	1	2	yes	complemented
703	#464	C₂²×C₃₁	1	2	yes	complemented
704	#464	C₂²×C₃₁	1	2	yes	complemented
705	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#464	C₂²×C₃₁	1	2	yes	complemented
707	#464	C₂²×C₃₁	1	2	yes	complemented
708	#464	C₂²×C₃₁	1	2	yes	complemented
709	#464	C₂²×C₃₁	1	2	yes	complemented
710	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	#463	C₂²×C₃₁	1	2	yes	complemented
712	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	#463	C₂²×C₃₁	1	2	yes	complemented
714	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#462	C₂²×C₃₁	1	2	yes	complemented
716	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#460	C₂²×C₃₁	1	2	yes	complemented
719	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#452	C₂²×C₃₁	1	2	yes	—
721	#452	C₂²×C₃₁	1	2	yes	—
722	#452	C₂²×C₃₁	1	2	yes	—
723	#452	C₂²×C₃₁	1	2	yes	complemented
724	#452	C₂²×C₃₁	1	2	yes	complemented
725	#452	C₂²×C₃₁	1	2	yes	complemented
726	#451	C₂²×C₃₁	1	2	yes	complemented
727	#451	C₂²×C₃₁	1	2	yes	complemented
728	#451	C₂²×C₃₁	1	2	yes	complemented
729	#450	C₂²×C₃₁	1	2	yes	—
730	#450	C₂²×C₃₁	1	2	yes	—
731	#450	C₂²×C₃₁	1	2	yes	—
732	#449	C₂²×C₃₁	1	2	yes	—
733	#449	C₂²×C₃₁	1	2	yes	complemented
734	#448	C₂²×C₃₁	1	2	yes	complemented
735	#447	C₂²×C₃₁	1	2	yes	—
736	#433	C₂²×C₃₁	1	2	yes	complemented
737	#433	C₂²×C₃₁	1	2	yes	complemented
738	#432	C₂²×C₃₁	1	2	yes	complemented
739	#431	C₂²×C₃₁	1	2	yes	complemented
740	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
741	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
743	#418	C₂²×C₃₁	1	1	yes	characteristic
744	#417	C₂²×C₃₁	1	1	yes	characteristic
745	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
746	#416	C₂²×C₃₁	1	1	yes	characteristic
747	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
750	#408	C₂²×C₃₁	1	1	yes	characteristic
751	#408	C₂²×C₃₁	1	1	yes	characteristic
752	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
754	C₂×C₃₁	—	2	2	no	—
755	C₂×C₃₁	—	4	2	no	—
756	C₂×C₃₁	—	8	1	no	—
757	C₂×C₃₁	—	8	1	no	—
758	C₂×C₃₁	—	8	2	no	—
759	C₂×C₃₁	—	8	1	no	—
760	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
761	C₂×C₃₁	#3584	1	1	yes	characteristic
762	C₂×C₃₁	#3586	1	1	yes	characteristic
763	2₋¹⁺⁴	—	4	2	no	—
764	2₋¹⁺⁴	—	4	2	no	—
765	H(5,𝔽₂)	—	4	2	no	—
766	H(5,𝔽₂)	—	4	2	no	—
767	C₂×#41	—	2	1	no	—
768	C₂×#41	—	2	2	no	—
769	C₂×#41	—	2	1	no	—
770	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
773	C₂×#41	C₂³×C₃₁	1	2	yes	—
774	C₂×#41	C₂³×C₃₁	1	2	yes	—
775	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²×Q₈	—	2	1	no	—
777	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
780	C₂²×D₄	—	2	2	no	—
781	C₂²×D₄	—	2	1	no	—
782	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
784	#137	—	4	2	no	—
785	#137	—	4	2	no	—
786	#137	—	4	2	no	—
787	AGL(1,ℤ/8)	—	4	2	no	—
788	#135	—	4	2	no	—
789	#135	—	4	2	no	—
790	C₂×Q₁₆	—	4	2	no	—
791	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
792	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
793	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
794	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
795	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
796	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
797	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
798	C₂×SD₁₆	—	4	2	no	—
799	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
802	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
803	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
804	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
805	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
806	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
808	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
809	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₂×D₈	C₂³×C₃₁	1	2	yes	—
812	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
814	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄⋊Q₈	—	2	1	no	—
817	C₄⋊Q₈	—	2	1	no	—
818	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
820	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
821	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
822	#127	C₂³×C₃₁	1	1	yes	characteristic
823	#127	C₂³×C₃₁	1	2	yes	—
824	#126	—	2	2	no	—
825	#126	—	2	2	no	—
826	#126	—	2	2	no	—
827	#126	—	2	2	no	—
828	#125	—	2	2	no	—
829	#125	—	2	1	no	—
830	#125	—	2	2	no	—
831	#125	—	2	2	no	—
832	#125	C₂³×C₃₁	1	2	yes	—
833	#124	—	2	1	no	—
834	#124	—	2	2	no	—
835	#124	—	2	1	no	—
836	#124	—	2	2	no	—
837	#124	—	2	1	no	—
838	#124	—	2	2	no	—
839	#124	C₂³×C₃₁	1	1	yes	characteristic
840	#124	C₂³×C₃₁	1	2	yes	—
841	#124	C₂³×C₃₁	1	2	yes	—
842	#124	C₂³×C₃₁	1	2	yes	—
843	#124	C₂³×C₃₁	1	2	yes	—
844	#124	C₂³×C₃₁	1	2	yes	—
845	#124	C₂³×C₃₁	1	1	yes	characteristic
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	2	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	2	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	2	no	—
862	C₂²⋊Q₈	—	2	2	no	—
863	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
864	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
865	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
866	#121	—	2	2	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	2	no	—
871	#121	—	2	2	no	—
872	#121	—	2	1	no	—
873	#121	—	2	2	no	—
874	#121	—	2	1	no	—
875	#121	—	2	2	no	—
876	#121	C₂³×C₃₁	1	2	yes	—
877	#120	—	2	2	no	—
878	#120	—	2	2	no	—
879	#120	—	2	2	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	—	2	2	no	—
883	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
884	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
885	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
886	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
887	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	2	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	2	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	2	no	—
896	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
897	C₄×D₄	D₄×C₃₁	1	2	yes	—
898	C₄×D₄	D₄×C₃₁	1	2	yes	—
899	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
900	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
901	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
902	#117	—	2	2	no	—
903	#117	—	2	1	no	—
904	#117	—	2	2	no	—
905	#117	C₂³×C₃₁	1	1	yes	characteristic
906	#117	C₂³×C₃₁	1	1	yes	characteristic
907	#117	C₂³×C₃₁	1	2	yes	—
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
910	C₂×C₂²⋊C₄	—	2	1	no	—
911	C₂×C₂²⋊C₄	—	2	1	no	—
912	C₂×C₂²⋊C₄	—	2	2	no	—
913	C₂×C₂²⋊C₄	—	2	2	no	—
914	C₂×C₄²	—	2	1	no	—
915	C₂×C₄²	—	2	1	no	—
916	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
917	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
918	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
919	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
920	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
921	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
922	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
923	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
924	#103	C₂³×C₃₁	1	2	yes	—
925	#103	C₂³×C₃₁	1	2	yes	—
926	#103	C₂³×C₃₁	1	1	yes	characteristic
927	#103	C₂³×C₃₁	1	1	yes	characteristic
928	#103	C₂³×C₃₁	1	1	yes	characteristic
929	#103	C₂³×C₃₁	1	1	yes	characteristic
930	#103	C₂³×C₃₁	1	2	yes	—
931	#103	C₂³×C₃₁	1	2	yes	—
932	#103	C₂³×C₃₁	1	2	yes	—
933	#103	C₂³×C₃₁	1	2	yes	—
934	#102	C₂³×C₃₁	1	2	yes	—
935	#102	C₂³×C₃₁	1	2	yes	—
936	#102	C₂³×C₃₁	1	1	yes	characteristic
937	#102	C₂³×C₃₁	1	1	yes	characteristic
938	#102	C₂³×C₃₁	1	1	yes	characteristic
939	#102	C₂³×C₃₁	1	1	yes	characteristic
940	#102	C₂³×C₃₁	1	2	yes	—
941	#102	C₂³×C₃₁	1	2	yes	—
942	#102	C₂³×C₃₁	1	2	yes	—
943	#102	C₂³×C₃₁	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
948	#97	C₂³×C₃₁	1	2	yes	—
949	#97	C₂³×C₃₁	1	2	yes	—
950	C₄×C₈	C₂³×C₃₁	1	2	yes	—
951	C₄×C₈	C₂³×C₃₁	1	2	yes	—
952	C₃₁	#60835	1	1	yes	characteristic, direct product factor, Sylow
953	C₂⁴	—	2	2	no	—
954	C₂⁴	—	2	1	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	2	no	—
965	#41	—	4	2	no	—
966	#41	—	4	2	no	—
967	#41	—	4	8	no	—
968	#41	—	4	4	no	—
969	#41	—	4	4	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	2	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	2	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	2	2	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	4	2	no	—
979	C₂×Q₈	—	4	2	no	—
980	C₂×Q₈	—	4	4	no	—
981	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
983	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
986	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	4	2	no	—
1002	C₂×D₄	—	4	2	no	—
1003	C₂×D₄	—	4	8	no	—
1004	C₂×D₄	—	4	4	no	—
1005	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1006	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1008	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1027	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1028	Q₁₆	—	4	2	no	—
1029	Q₁₆	—	4	2	no	—
1030	Q₁₆	—	4	1	no	—
1031	Q₁₆	—	4	1	no	—
1032	Q₁₆	—	4	2	no	—
1033	Q₁₆	—	4	2	no	—
1034	Q₁₆	—	4	2	no	—
1035	SD₁₆	—	4	2	no	—
1036	SD₁₆	—	4	2	no	—
1037	SD₁₆	—	4	1	no	—
1038	SD₁₆	—	4	1	no	—
1039	SD₁₆	—	4	1	no	—
1040	SD₁₆	—	4	1	no	—
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	D₈	—	4	1	no	—
1046	D₈	—	4	1	no	—
1047	D₈	—	4	2	no	—
1048	M₁₆	—	2	2	no	—
1049	M₁₆	—	2	2	no	—
1050	C₂×C₈	—	2	2	no	—
1051	C₂×C₈	—	2	2	no	—
1052	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1055	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1056	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1057	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1076	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1080	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1104	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1106	C₄²	—	2	2	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	1	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1112	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1113	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1114	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1115	C₄²	C₂⁴×C₃₁	1	2	yes	—
1116	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1117	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	4	4	no	—
1123	C₂³	—	4	2	no	—
1124	C₂³	—	8	1	no	—
1125	C₂³	—	8	1	no	—
1126	C₂³	—	8	2	no	—
1127	C₂³	—	8	2	no	—
1128	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1129	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1130	Q₈	—	2	2	no	—
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	2	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	4	4	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	8	2	no	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	1	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	4	no	—
1184	C₂×C₄	—	4	4	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1198	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1199	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1200	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1201	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1202	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1203	C₈	—	2	1	no	—
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	1	no	—
1207	C₈	—	2	2	no	—
1208	C₈	—	2	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	16	2	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₃₁×#535	1	2	yes	—
1229	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1230	C₄	—	2	2	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	2	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	C₃₁×#535	1	2	yes	—
1246	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1247	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1248	C₂	—	2	2	no	—
1249	C₂	—	4	2	no	—
1250	C₂	—	8	2	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
1255	C₂	C₃₁×#3584	1	1	yes	characteristic
1256	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×#3500	C₂	semidirect
2. C₃₁×#3461	C₂	semidirect
3. C₃₁×#3225	C₂	semidirect
4. C₃₁×#3224	C₂	semidirect
5. C₃₁×#3223	C₂	semidirect
6. C₃₁×#3222	C₂	semidirect
7. C₃₁×#3219	C₂	semidirect
8. C₃₁×#3215	C₂	semidirect
9. C₃₁×#3211	C₂	semidirect
10. C₃₁×#3210	C₂	semidirect
11. C₃₁×#3156	C₂	semidirect
12. C₃₁×#3154	C₂	semidirect
13. C₃₁×#3137	C₂	semidirect
14. C₃₁×#3136	C₂	semidirect
15. C₃₁×#3040	C₂	semidirect
16. C₃₁×#3037	C₂	semidirect
17. C₃₁×#3035	C₂	semidirect
18. C₂×C₃₁×#464	C₂	semidirect
19. C₃₁×#3013	C₂	semidirect
20. C₃₁×#3012	C₂	semidirect
21. C₃₁×#3011	C₂	semidirect
22. C₃₁×#3009	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
28. C₂×C₃₁×#137	C₂²	semidirect
31. C₂×C₃₁×#135	C₂²	semidirect
32. C₂²×Q₁₆×C₃₁	C₂²	semidirect
40. C₃₁×#544	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
44. C₃₁×#541	C₂²	semidirect
50. C₃₁×#536	C₂²	semidirect
54. C₃₁×#533	C₂²	semidirect
59. C₃₁×#529	C₂²	semidirect
63. C₄×#41×C₃₁	C₂²	semidirect
64. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
65. C₃₁×#497	C₂²	semidirect
66. C₃₁×#497	C₂²	semidirect
67. C₃₁×#497	C₂²	semidirect
68. C₃₁×#496	C₂²	semidirect
69. C₃₁×#495	C₂²	semidirect
70. C₃₁×#495	C₂²	semidirect
71. C₃₁×#494	C₂²	semidirect
72. C₃₁×#492	C₂²	semidirect
73. C₃₁×#491	C₂²	semidirect
74. C₃₁×#490	C₂²	semidirect
75. C₃₁×#489	C₂²	semidirect
76. C₃₁×#489	C₂²	semidirect
77. C₃₁×#488	C₂²	semidirect
78. C₃₁×#488	C₂²	semidirect
79. C₃₁×#487	C₂²	semidirect
80. C₃₁×#486	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
83. C₃₁×#464	C₂²	semidirect
84. C₃₁×#464	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
89. C₃₁×#464	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#463	C₂²	semidirect
93. C₃₁×#463	C₂²	semidirect
94. C₃₁×#463	C₂²	semidirect
95. C₃₁×#462	C₂²	semidirect
96. C₃₁×#462	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
98. C₃₁×#460	C₂²	semidirect
99. C₃₁×#460	C₂²	semidirect
100. C₃₁×#459	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#451	C₂²	semidirect
108. C₃₁×#451	C₂²	semidirect
109. C₃₁×#451	C₂²	semidirect
114. C₃₁×#449	C₂²	semidirect
115. C₃₁×#448	C₂²	semidirect
117. C₃₁×#433	C₂²	semidirect
118. C₃₁×#433	C₂²	semidirect
119. C₃₁×#432	C₂²	semidirect
120. C₃₁×#431	C₂²	semidirect
121. C₃₁×#423	C₂²	semidirect
122. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
123. C₃₁×#419	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
128. C₃₁×#416	C₂²	semidirect
129. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₃₁×#405	C₂²	semidirect
489. #60835	C₃₁	direct (N × H)
581. #3500	C₂×C₃₁	semidirect
582. #3461	C₂×C₃₁	semidirect
583. #3225	C₂×C₃₁	semidirect
584. #3224	C₂×C₃₁	semidirect
585. #3223	C₂×C₃₁	semidirect
586. #3222	C₂×C₃₁	semidirect
587. #3219	C₂×C₃₁	semidirect
588. #3215	C₂×C₃₁	semidirect
589. #3211	C₂×C₃₁	semidirect
590. #3210	C₂×C₃₁	semidirect
591. #3156	C₂×C₃₁	semidirect
592. #3154	C₂×C₃₁	semidirect
593. #3137	C₂×C₃₁	semidirect
594. #3136	C₂×C₃₁	semidirect
595. #3040	C₂×C₃₁	semidirect
596. #3037	C₂×C₃₁	semidirect
597. #3035	C₂×C₃₁	semidirect
598. C₂×#464	C₂×C₃₁	semidirect
599. #3013	C₂×C₃₁	semidirect
600. #3012	C₂×C₃₁	semidirect
601. #3011	C₂×C₃₁	semidirect
602. #3009	C₂×C₃₁	semidirect
603. #2925	C₂×C₃₁	semidirect
646. C₂×#137	C₂²×C₃₁	semidirect
647. C₂×#137	C₂²×C₃₁	semidirect
650. C₂×#135	C₂²×C₃₁	semidirect
651. C₂²×Q₁₆	C₂²×C₃₁	semidirect
659. #544	C₂²×C₃₁	semidirect
661. #542	C₂²×C₃₁	semidirect
663. #541	C₂²×C₃₁	semidirect
669. #536	C₂²×C₃₁	semidirect
673. #533	C₂²×C₃₁	semidirect
678. #529	C₂²×C₃₁	semidirect
682. C₄×#41	C₂²×C₃₁	semidirect
683. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
684. #497	C₂²×C₃₁	semidirect
685. #497	C₂²×C₃₁	semidirect
686. #497	C₂²×C₃₁	semidirect
687. #496	C₂²×C₃₁	semidirect
688. #495	C₂²×C₃₁	semidirect
689. #495	C₂²×C₃₁	semidirect
690. #494	C₂²×C₃₁	semidirect
691. #492	C₂²×C₃₁	semidirect
692. #491	C₂²×C₃₁	semidirect
693. #490	C₂²×C₃₁	semidirect
694. #489	C₂²×C₃₁	semidirect
695. #489	C₂²×C₃₁	semidirect
696. #488	C₂²×C₃₁	semidirect
697. #488	C₂²×C₃₁	semidirect
698. #487	C₂²×C₃₁	semidirect
699. #486	C₂²×C₃₁	semidirect
700. #464	C₂²×C₃₁	semidirect
701. #464	C₂²×C₃₁	semidirect
702. #464	C₂²×C₃₁	semidirect
703. #464	C₂²×C₃₁	semidirect
704. #464	C₂²×C₃₁	semidirect
705. #464	C₂²×C₃₁	semidirect
706. #464	C₂²×C₃₁	semidirect
707. #464	C₂²×C₃₁	semidirect
708. #464	C₂²×C₃₁	semidirect
709. #464	C₂²×C₃₁	semidirect
710. #463	C₂²×C₃₁	semidirect
711. #463	C₂²×C₃₁	semidirect
712. #463	C₂²×C₃₁	semidirect
713. #463	C₂²×C₃₁	semidirect
714. #462	C₂²×C₃₁	semidirect
715. #462	C₂²×C₃₁	semidirect
716. #461	C₂²×C₃₁	semidirect
717. #460	C₂²×C₃₁	semidirect
718. #460	C₂²×C₃₁	semidirect
719. #459	C₂²×C₃₁	semidirect
723. #452	C₂²×C₃₁	semidirect
724. #452	C₂²×C₃₁	semidirect
725. #452	C₂²×C₃₁	semidirect
726. #451	C₂²×C₃₁	semidirect
727. #451	C₂²×C₃₁	semidirect
728. #451	C₂²×C₃₁	semidirect
733. #449	C₂²×C₃₁	semidirect
734. #448	C₂²×C₃₁	semidirect
736. #433	C₂²×C₃₁	semidirect
737. #433	C₂²×C₃₁	semidirect
738. #432	C₂²×C₃₁	semidirect
739. #431	C₂²×C₃₁	semidirect
740. #423	C₂²×C₃₁	semidirect
741. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
742. #419	C₂²×C₃₁	semidirect
745. #417	C₂²×C₃₁	semidirect
747. #416	C₂²×C₃₁	semidirect
748. C₂×#103	C₂²×C₃₁	semidirect
752. #405	C₂²×C₃₁	semidirect
753. #405	C₂²×C₃₁	semidirect
952. C₃₁	#60835	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×#3500	2
C₃₁×#3461	2
C₃₁×#3225	2
C₃₁×#3224	2
C₃₁×#3223	2
C₃₁×#3222	2
C₃₁×#3219	2
C₃₁×#3215	2
C₃₁×#3211	2
C₃₁×#3210	2
C₃₁×#3156	2
C₃₁×#3154	2
C₃₁×#3137	2
C₃₁×#3136	2
C₃₁×#3040	2
C₃₁×#3037	2
C₃₁×#3035	2
C₂×C₃₁×#464	2
C₃₁×#3013	2
C₃₁×#3012	2
C₃₁×#3011	2
C₃₁×#3009	2
C₃₁×#2925	2
#60835	31

Subgroups — C31×#60835 #21517594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60835 #21517594