Subgroups — C₃₁×#60834 #21517593

Order 7936.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1286 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×#3460	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×#3221	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3155	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×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#463	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×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3008	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, complemented
27	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₈×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	2	no	—
38	C₃₁×#546	—	2	1	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×#540	—	2	1	no	—
44	C₃₁×#540	C₂²	1	2	yes	complemented
45	C₃₁×#538	—	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	complemented
49	C₃₁×#535	C₂²	1	1	yes	characteristic
50	C₃₁×#535	C₂²	1	1	yes	characteristic
51	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#535	C₂²	1	2	yes	complemented
53	C₃₁×#532	—	2	1	no	—
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₃₁×#532	C₂²	1	2	yes	complemented
56	C₃₁×#532	C₂²	1	2	yes	complemented
57	C₃₁×#529	—	2	1	no	—
58	C₃₁×#529	C₂²	1	2	yes	complemented
59	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
61	C₃₁×#525	—	2	2	no	—
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#497	C₂²	1	2	yes	complemented
66	C₃₁×#496	C₂²	1	2	yes	complemented
67	C₃₁×#496	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×#493	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	1	yes	characteristic, complemented
84	C₃₁×#464	C₂²	1	2	yes	complemented
85	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#463	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#463	C₂²	1	2	yes	complemented
92	C₃₁×#463	C₂²	1	2	yes	complemented
93	C₃₁×#463	C₂²	1	2	yes	complemented
94	C₃₁×#463	C₂²	1	2	yes	complemented
95	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#461	C₂²	1	2	yes	complemented
98	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#459	C₂²	1	2	yes	complemented
101	C₃₁×#452	C₂²	1	2	yes	complemented
102	C₃₁×#452	C₂²	1	2	yes	complemented
103	C₃₁×#451	C₂²	1	2	yes	complemented
104	C₃₁×#450	C₂²	1	2	yes	complemented
105	C₃₁×#449	C₂²	1	2	yes	—
106	C₃₁×#449	C₂²	1	2	yes	—
107	C₃₁×#449	C₂²	1	2	yes	complemented
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#448	C₂²	1	2	yes	complemented
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	2	yes	complemented
114	C₃₁×#447	C₂²	1	2	yes	—
115	C₃₁×#447	C₂²	1	2	yes	—
116	C₃₁×#447	C₂²	1	2	yes	complemented
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	—	2	2	no	—
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₃₁	C₂³	1	2	yes	—
147	C₂×#41×C₃₁	C₂³	1	2	yes	—
148	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₃₁	—	2	1	no	—
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	1	yes	characteristic
156	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
157	C₂³×C₄×C₃₁	—	2	1	no	—
158	C₃₁×#137	—	4	2	no	—
159	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
160	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
161	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
162	C₃₁×#135	—	4	2	no	—
163	C₃₁×#135	—	4	2	no	—
164	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₃₁	—	4	2	no	—
168	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
171	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
172	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×D₈×C₃₁	—	4	2	no	—
179	C₂×D₈×C₃₁	C₂³	1	2	yes	—
180	C₂×D₈×C₃₁	C₂³	1	2	yes	—
181	C₂×D₈×C₃₁	C₂³	1	2	yes	—
182	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×D₈×C₃₁	C₂³	1	2	yes	—
184	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×D₈×C₃₁	C₂³	1	2	yes	—
186	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
188	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
190	C₃₁×C₄⋊Q₈	—	2	1	no	—
191	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×#127	—	2	1	no	—
195	C₃₁×#127	C₂³	1	1	yes	characteristic
196	C₃₁×#127	C₂³	1	2	yes	—
197	C₃₁×#127	C₂³	1	2	yes	—
198	C₃₁×#126	—	2	2	no	—
199	C₃₁×#126	—	2	2	no	—
200	C₃₁×#125	—	2	1	no	—
201	C₃₁×#125	C₂³	1	2	yes	—
202	C₃₁×#124	—	2	1	no	—
203	C₃₁×#124	—	2	2	no	—
204	C₃₁×#124	—	2	1	no	—
205	C₃₁×#124	—	2	1	no	—
206	C₃₁×#124	—	2	2	no	—
207	C₃₁×#124	—	2	2	no	—
208	C₃₁×#124	—	2	2	no	—
209	C₃₁×#124	C₂³	1	2	yes	—
210	C₃₁×#124	C₂³	1	2	yes	—
211	C₃₁×#124	C₂³	1	1	yes	characteristic
212	C₃₁×#124	C₂³	1	1	yes	characteristic
213	C₃₁×#124	C₂³	1	2	yes	—
214	C₃₁×#124	C₂³	1	2	yes	—
215	C₃₁×#124	C₂³	1	2	yes	—
216	C₃₁×#123	—	2	2	no	—
217	C₃₁×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	1	no	—
224	C₃₁×C₂²⋊Q₈	—	2	2	no	—
225	C₃₁×C₂²⋊Q₈	—	2	1	no	—
226	C₃₁×C₂²⋊Q₈	—	2	1	no	—
227	C₃₁×C₂²⋊Q₈	—	2	2	no	—
228	C₃₁×C₂²⋊Q₈	—	2	2	no	—
229	C₃₁×C₂²⋊Q₈	—	2	2	no	—
230	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₃₁×#121	—	2	2	no	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	—	2	2	no	—
237	C₃₁×#121	—	2	2	no	—
238	C₃₁×#121	—	2	1	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	2	no	—
245	C₃₁×#121	—	2	2	no	—
246	C₃₁×#121	C₂³	1	2	yes	—
247	C₃₁×#121	C₂³	1	2	yes	—
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	C₃₁×#120	—	2	2	no	—
253	C₃₁×#120	—	2	2	no	—
254	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
255	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₃₁	—	2	1	no	—
259	C₄×D₄×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	2	no	—
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	1	no	—
266	C₄×D₄×C₃₁	—	2	2	no	—
267	C₄×D₄×C₃₁	—	2	2	no	—
268	C₄×D₄×C₃₁	D₄	1	2	yes	—
269	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
270	C₄×D₄×C₃₁	D₄	1	2	yes	—
271	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
272	C₄×D₄×C₃₁	C₂³	1	2	yes	—
273	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₃₁	C₂³	1	2	yes	—
275	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₃₁×#117	—	2	1	no	—
277	C₃₁×#117	—	2	2	no	—
278	C₃₁×#117	C₂³	1	1	yes	characteristic
279	C₃₁×#117	C₂³	1	1	yes	characteristic
280	C₃₁×#117	C₂³	1	2	yes	—
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	1	no	—
285	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂×C₂²⋊C₄×C₃₁	—	2	2	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	C₂⁴×C₃₁	—	2	1	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	—	2	2	no	—
335	#41×C₃₁	—	4	2	no	—
336	#41×C₃₁	—	4	2	no	—
337	#41×C₃₁	—	4	2	no	—
338	#41×C₃₁	—	4	2	no	—
339	#41×C₃₁	—	4	8	no	—
340	#41×C₃₁	—	4	4	no	—
341	#41×C₃₁	—	4	4	no	—
342	#41×C₃₁	—	8	4	no	—
343	C₂×Q₈×C₃₁	—	2	2	no	—
344	C₂×Q₈×C₃₁	—	2	1	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	—	4	2	no	—
349	C₂×Q₈×C₃₁	—	4	2	no	—
350	C₂×Q₈×C₃₁	—	4	4	no	—
351	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
353	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₃₁	—	2	1	no	—
357	C₂×D₄×C₃₁	—	2	2	no	—
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	2	no	—
363	C₂×D₄×C₃₁	—	2	2	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	2	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	1	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	2	2	no	—
373	C₂×D₄×C₃₁	—	2	2	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	2	no	—
376	C₂×D₄×C₃₁	—	2	2	no	—
377	C₂×D₄×C₃₁	—	4	2	no	—
378	C₂×D₄×C₃₁	—	4	2	no	—
379	C₂×D₄×C₃₁	—	4	8	no	—
380	C₂×D₄×C₃₁	—	4	4	no	—
381	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
384	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
387	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	—	2	2	no	—
389	C₂²×C₄×C₃₁	—	2	1	no	—
390	C₂²×C₄×C₃₁	—	2	1	no	—
391	C₂²×C₄×C₃₁	—	2	1	no	—
392	C₂²×C₄×C₃₁	—	2	1	no	—
393	C₂²×C₄×C₃₁	—	2	2	no	—
394	C₂²×C₄×C₃₁	—	2	2	no	—
395	C₂²×C₄×C₃₁	—	2	1	no	—
396	C₂²×C₄×C₃₁	—	2	2	no	—
397	C₂²×C₄×C₃₁	—	2	1	no	—
398	C₂²×C₄×C₃₁	—	2	1	no	—
399	C₂²×C₄×C₃₁	—	2	2	no	—
400	C₂²×C₄×C₃₁	—	8	2	no	—
401	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₃₁	—	4	1	no	—
408	Q₁₆×C₃₁	—	4	1	no	—
409	Q₁₆×C₃₁	—	4	2	no	—
410	SD₁₆×C₃₁	—	4	2	no	—
411	SD₁₆×C₃₁	—	4	2	no	—
412	SD₁₆×C₃₁	—	4	1	no	—
413	SD₁₆×C₃₁	—	4	1	no	—
414	SD₁₆×C₃₁	—	4	1	no	—
415	SD₁₆×C₃₁	—	4	1	no	—
416	SD₁₆×C₃₁	—	4	2	no	—
417	SD₁₆×C₃₁	—	4	2	no	—
418	SD₁₆×C₃₁	—	4	2	no	—
419	SD₁₆×C₃₁	—	4	2	no	—
420	D₈×C₃₁	—	4	2	no	—
421	D₈×C₃₁	—	4	2	no	—
422	D₈×C₃₁	—	4	1	no	—
423	D₈×C₃₁	—	4	1	no	—
424	D₈×C₃₁	—	4	2	no	—
425	D₈×C₃₁	—	4	2	no	—
426	D₈×C₃₁	—	4	2	no	—
427	M₁₆×C₃₁	—	2	2	no	—
428	M₁₆×C₃₁	—	2	2	no	—
429	C₂×C₈×C₃₁	—	2	2	no	—
430	C₂×C₈×C₃₁	—	2	2	no	—
431	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
434	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
435	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
443	C₄⋊C₄×C₃₁	—	2	2	no	—
444	C₄⋊C₄×C₃₁	—	2	1	no	—
445	C₄⋊C₄×C₃₁	—	2	2	no	—
446	C₄⋊C₄×C₃₁	—	2	2	no	—
447	C₄⋊C₄×C₃₁	—	2	2	no	—
448	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	2	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	1	no	—
475	C₂²⋊C₄×C₃₁	—	2	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
479	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
480	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
481	C₄²×C₃₁	—	2	1	no	—
482	C₄²×C₃₁	—	2	1	no	—
483	C₄²×C₃₁	—	2	1	no	—
484	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₃₁	C₂×D₄	1	2	yes	—
486	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₃₁	C₂×D₄	1	2	yes	—
488	C₄²×C₃₁	C₂⁴	1	2	yes	—
489	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
490	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
491	#60834	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
492	C₂³×C₃₁	—	2	2	no	—
493	C₂³×C₃₁	—	2	2	no	—
494	C₂³×C₃₁	—	2	1	no	—
495	C₂³×C₃₁	—	2	1	no	—
496	C₂³×C₃₁	—	2	1	no	—
497	C₂³×C₃₁	—	4	4	no	—
498	C₂³×C₃₁	—	4	2	no	—
499	C₂³×C₃₁	—	4	2	no	—
500	C₂³×C₃₁	—	8	1	no	—
501	C₂³×C₃₁	—	8	1	no	—
502	C₂³×C₃₁	—	8	1	no	—
503	C₂³×C₃₁	—	8	1	no	—
504	C₂³×C₃₁	—	8	2	no	—
505	C₂³×C₃₁	—	8	2	no	—
506	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	Q₈×C₃₁	—	2	2	no	—
509	Q₈×C₃₁	—	2	1	no	—
510	Q₈×C₃₁	—	2	1	no	—
511	Q₈×C₃₁	—	2	2	no	—
512	Q₈×C₃₁	—	2	1	no	—
513	Q₈×C₃₁	—	2	1	no	—
514	Q₈×C₃₁	—	2	2	no	—
515	Q₈×C₃₁	—	2	1	no	—
516	Q₈×C₃₁	—	2	1	no	—
517	Q₈×C₃₁	—	4	4	no	—
518	Q₈×C₃₁	—	4	2	no	—
519	Q₈×C₃₁	—	8	2	no	—
520	D₄×C₃₁	—	2	4	no	—
521	D₄×C₃₁	—	2	2	no	—
522	D₄×C₃₁	—	2	2	no	—
523	D₄×C₃₁	—	2	2	no	—
524	D₄×C₃₁	—	2	1	no	—
525	D₄×C₃₁	—	2	1	no	—
526	D₄×C₃₁	—	2	2	no	—
527	D₄×C₃₁	—	2	1	no	—
528	D₄×C₃₁	—	2	1	no	—
529	D₄×C₃₁	—	2	2	no	—
530	D₄×C₃₁	—	2	1	no	—
531	D₄×C₃₁	—	2	1	no	—
532	D₄×C₃₁	—	4	4	no	—
533	D₄×C₃₁	—	4	4	no	—
534	D₄×C₃₁	—	4	4	no	—
535	D₄×C₃₁	—	4	2	no	—
536	D₄×C₃₁	—	4	2	no	—
537	D₄×C₃₁	—	4	2	no	—
538	D₄×C₃₁	—	4	2	no	—
539	D₄×C₃₁	—	4	2	no	—
540	D₄×C₃₁	—	8	1	no	—
541	D₄×C₃₁	—	8	2	no	—
542	D₄×C₃₁	—	8	2	no	—
543	D₄×C₃₁	—	8	1	no	—
544	D₄×C₃₁	—	8	2	no	—
545	D₄×C₃₁	—	8	2	no	—
546	D₄×C₃₁	—	8	2	no	—
547	D₄×C₃₁	—	8	2	no	—
548	D₄×C₃₁	—	8	2	no	—
549	C₂×C₄×C₃₁	—	2	2	no	—
550	C₂×C₄×C₃₁	—	2	2	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	2	2	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	2	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	4	1	no	—
559	C₂×C₄×C₃₁	—	4	1	no	—
560	C₂×C₄×C₃₁	—	4	2	no	—
561	C₂×C₄×C₃₁	—	4	2	no	—
562	C₂×C₄×C₃₁	—	4	4	no	—
563	C₂×C₄×C₃₁	—	4	4	no	—
564	C₂×C₄×C₃₁	—	4	4	no	—
565	C₂×C₄×C₃₁	—	4	2	no	—
566	C₂×C₄×C₃₁	—	4	4	no	—
567	C₂×C₄×C₃₁	—	4	2	no	—
568	C₂×C₄×C₃₁	—	4	2	no	—
569	C₂×C₄×C₃₁	—	4	2	no	—
570	C₂×C₄×C₃₁	—	4	2	no	—
571	C₂×C₄×C₃₁	—	8	1	no	—
572	C₂×C₄×C₃₁	—	8	2	no	—
573	C₂×C₄×C₃₁	—	8	1	no	—
574	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
583	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
584	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
585	C₈×C₃₁	—	2	1	no	—
586	C₈×C₃₁	—	2	1	no	—
587	C₈×C₃₁	—	2	1	no	—
588	C₈×C₃₁	—	2	1	no	—
589	C₈×C₃₁	—	2	2	no	—
590	C₈×C₃₁	—	2	2	no	—
591	#3500	C₂×C₃₁	1	1	yes	characteristic, complemented
592	#3460	C₂×C₃₁	1	1	yes	characteristic, complemented
593	#3225	C₂×C₃₁	1	2	yes	complemented
594	#3224	C₂×C₃₁	1	2	yes	complemented
595	#3221	C₂×C₃₁	1	2	yes	complemented
596	#3220	C₂×C₃₁	1	2	yes	complemented
597	#3219	C₂×C₃₁	1	2	yes	complemented
598	#3213	C₂×C₃₁	1	2	yes	complemented
599	#3211	C₂×C₃₁	1	2	yes	complemented
600	#3207	C₂×C₃₁	1	2	yes	complemented
601	#3155	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
608	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
609	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
610	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
611	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
612	#3008	C₂×C₃₁	1	1	yes	characteristic, complemented
613	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
614	C₂²×C₃₁	—	2	1	no	—
615	C₂²×C₃₁	—	2	1	no	—
616	C₂²×C₃₁	—	2	2	no	—
617	C₂²×C₃₁	—	2	2	no	—
618	C₂²×C₃₁	—	2	2	no	—
619	C₂²×C₃₁	—	4	1	no	—
620	C₂²×C₃₁	—	4	1	no	—
621	C₂²×C₃₁	—	4	2	no	—
622	C₂²×C₃₁	—	4	2	no	—
623	C₂²×C₃₁	—	4	1	no	—
624	C₂²×C₃₁	—	4	2	no	—
625	C₂²×C₃₁	—	4	1	no	—
626	C₂²×C₃₁	—	4	1	no	—
627	C₂²×C₃₁	—	4	2	no	—
628	C₂²×C₃₁	—	4	1	no	—
629	C₂²×C₃₁	—	4	1	no	—
630	C₂²×C₃₁	—	4	2	no	—
631	C₂²×C₃₁	—	4	1	no	—
632	C₂²×C₃₁	—	4	1	no	—
633	C₂²×C₃₁	—	4	2	no	—
634	C₂²×C₃₁	—	8	4	no	—
635	C₂²×C₃₁	—	16	2	no	—
636	C₂²×C₃₁	—	16	4	no	—
637	C₂²×C₃₁	#535	1	2	yes	—
638	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
639	C₄×C₃₁	—	2	1	no	—
640	C₄×C₃₁	—	2	1	no	—
641	C₄×C₃₁	—	2	2	no	—
642	C₄×C₃₁	—	2	1	no	—
643	C₄×C₃₁	—	2	1	no	—
644	C₄×C₃₁	—	2	2	no	—
645	C₄×C₃₁	—	2	2	no	—
646	C₄×C₃₁	—	4	1	no	—
647	C₄×C₃₁	—	4	2	no	—
648	C₄×C₃₁	—	4	1	no	—
649	C₄×C₃₁	—	4	1	no	—
650	C₄×C₃₁	—	4	2	no	—
651	C₄×C₃₁	—	4	1	no	—
652	C₄×C₃₁	—	4	1	no	—
653	C₄×C₃₁	#535	1	2	yes	—
654	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
655	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
657	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
660	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
663	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
666	#548	—	2	1	no	—
667	#548	—	2	1	no	—
668	#546	—	2	2	no	—
669	#546	—	2	2	no	—
670	#546	—	2	1	no	—
671	#546	—	2	1	no	—
672	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#542	—	2	1	no	—
674	#542	C₂²×C₃₁	1	2	yes	complemented
675	#540	—	2	1	no	—
676	#540	C₂²×C₃₁	1	2	yes	complemented
677	#538	—	2	2	no	—
678	#537	C₂²×C₃₁	1	1	yes	characteristic
679	#536	C₂²×C₃₁	1	1	yes	characteristic
680	#536	C₂²×C₃₁	1	2	yes	complemented
681	#535	C₂²×C₃₁	1	1	yes	characteristic
682	#535	C₂²×C₃₁	1	1	yes	characteristic
683	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#535	C₂²×C₃₁	1	2	yes	complemented
685	#532	—	2	1	no	—
686	#532	C₂²×C₃₁	1	1	yes	characteristic
687	#532	C₂²×C₃₁	1	2	yes	complemented
688	#532	C₂²×C₃₁	1	2	yes	complemented
689	#529	—	2	1	no	—
690	#529	C₂²×C₃₁	1	2	yes	complemented
691	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
692	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
693	#525	—	2	2	no	—
694	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	#497	C₂²×C₃₁	1	2	yes	complemented
698	#496	C₂²×C₃₁	1	2	yes	complemented
699	#496	C₂²×C₃₁	1	2	yes	complemented
700	#496	C₂²×C₃₁	1	2	yes	complemented
701	#495	C₂²×C₃₁	1	2	yes	complemented
702	#495	C₂²×C₃₁	1	2	yes	complemented
703	#493	C₂²×C₃₁	1	2	yes	complemented
704	#492	C₂²×C₃₁	1	2	yes	complemented
705	#491	C₂²×C₃₁	1	2	yes	complemented
706	#490	C₂²×C₃₁	1	2	yes	complemented
707	#489	C₂²×C₃₁	1	2	yes	complemented
708	#489	C₂²×C₃₁	1	2	yes	complemented
709	#488	C₂²×C₃₁	1	2	yes	complemented
710	#488	C₂²×C₃₁	1	2	yes	complemented
711	#487	C₂²×C₃₁	1	2	yes	complemented
712	#486	C₂²×C₃₁	1	2	yes	complemented
713	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#464	C₂²×C₃₁	1	2	yes	complemented
715	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#464	C₂²×C₃₁	1	2	yes	complemented
717	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#463	C₂²×C₃₁	1	2	yes	complemented
719	#463	C₂²×C₃₁	1	2	yes	complemented
720	#463	C₂²×C₃₁	1	2	yes	complemented
721	#463	C₂²×C₃₁	1	2	yes	complemented
722	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
723	#463	C₂²×C₃₁	1	2	yes	complemented
724	#463	C₂²×C₃₁	1	2	yes	complemented
725	#463	C₂²×C₃₁	1	2	yes	complemented
726	#463	C₂²×C₃₁	1	2	yes	complemented
727	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
729	#461	C₂²×C₃₁	1	2	yes	complemented
730	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	#459	C₂²×C₃₁	1	2	yes	complemented
733	#452	C₂²×C₃₁	1	2	yes	complemented
734	#452	C₂²×C₃₁	1	2	yes	complemented
735	#451	C₂²×C₃₁	1	2	yes	complemented
736	#450	C₂²×C₃₁	1	2	yes	complemented
737	#449	C₂²×C₃₁	1	2	yes	—
738	#449	C₂²×C₃₁	1	2	yes	—
739	#449	C₂²×C₃₁	1	2	yes	complemented
740	#449	C₂²×C₃₁	1	2	yes	complemented
741	#449	C₂²×C₃₁	1	2	yes	complemented
742	#449	C₂²×C₃₁	1	2	yes	complemented
743	#448	C₂²×C₃₁	1	2	yes	complemented
744	#448	C₂²×C₃₁	1	2	yes	complemented
745	#448	C₂²×C₃₁	1	2	yes	complemented
746	#447	C₂²×C₃₁	1	2	yes	—
747	#447	C₂²×C₃₁	1	2	yes	—
748	#447	C₂²×C₃₁	1	2	yes	complemented
749	#433	C₂²×C₃₁	1	2	yes	complemented
750	#433	C₂²×C₃₁	1	2	yes	complemented
751	#432	C₂²×C₃₁	1	2	yes	complemented
752	#431	C₂²×C₃₁	1	2	yes	complemented
753	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
754	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
755	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
756	#418	C₂²×C₃₁	1	1	yes	characteristic
757	#417	C₂²×C₃₁	1	1	yes	characteristic
758	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#416	C₂²×C₃₁	1	1	yes	characteristic
760	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
761	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
762	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
763	#408	C₂²×C₃₁	1	1	yes	characteristic
764	#408	C₂²×C₃₁	1	1	yes	characteristic
765	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
767	C₂×C₃₁	—	2	2	no	—
768	C₂×C₃₁	—	4	2	no	—
769	C₂×C₃₁	—	8	1	no	—
770	C₂×C₃₁	—	8	1	no	—
771	C₂×C₃₁	—	8	2	no	—
772	C₂×C₃₁	—	8	2	no	—
773	C₂×C₃₁	—	8	1	no	—
774	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
775	C₂×C₃₁	#3584	1	1	yes	characteristic
776	C₂×C₃₁	#3585	1	1	yes	characteristic
777	2₋¹⁺⁴	—	4	2	no	—
778	2₋¹⁺⁴	—	4	2	no	—
779	H(5,𝔽₂)	—	4	2	no	—
780	H(5,𝔽₂)	—	4	2	no	—
781	C₂×#41	—	2	1	no	—
782	C₂×#41	—	2	2	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	2	2	no	—
785	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
786	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
787	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
788	C₂×#41	C₂³×C₃₁	1	2	yes	—
789	C₂×#41	C₂³×C₃₁	1	2	yes	—
790	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
791	C₂²×Q₈	—	2	1	no	—
792	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₂²×D₄	—	2	2	no	—
795	C₂²×D₄	—	2	1	no	—
796	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
798	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
799	C₂³×C₄	—	2	1	no	—
800	#137	—	4	2	no	—
801	AGL(1,ℤ/8)	—	4	2	no	—
802	AGL(1,ℤ/8)	—	4	2	no	—
803	AGL(1,ℤ/8)	—	4	2	no	—
804	#135	—	4	2	no	—
805	#135	—	4	2	no	—
806	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
807	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
808	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
809	C₂×SD₁₆	—	4	2	no	—
810	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
811	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
812	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
814	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
816	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
817	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
818	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
819	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
820	C₂×D₈	—	4	2	no	—
821	C₂×D₈	C₂³×C₃₁	1	2	yes	—
822	C₂×D₈	C₂³×C₃₁	1	2	yes	—
823	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
824	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₂×D₈	C₂³×C₃₁	1	2	yes	—
826	C₂×D₈	C₂³×C₃₁	1	2	yes	—
827	C₂×D₈	C₂³×C₃₁	1	2	yes	—
828	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
829	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
830	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄⋊Q₈	—	2	1	no	—
833	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
835	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
836	#127	—	2	1	no	—
837	#127	C₂³×C₃₁	1	1	yes	characteristic
838	#127	C₂³×C₃₁	1	2	yes	—
839	#127	C₂³×C₃₁	1	2	yes	—
840	#126	—	2	2	no	—
841	#126	—	2	2	no	—
842	#125	—	2	1	no	—
843	#125	C₂³×C₃₁	1	2	yes	—
844	#124	—	2	1	no	—
845	#124	—	2	2	no	—
846	#124	—	2	1	no	—
847	#124	—	2	1	no	—
848	#124	—	2	2	no	—
849	#124	—	2	2	no	—
850	#124	—	2	2	no	—
851	#124	C₂³×C₃₁	1	2	yes	—
852	#124	C₂³×C₃₁	1	2	yes	—
853	#124	C₂³×C₃₁	1	1	yes	characteristic
854	#124	C₂³×C₃₁	1	2	yes	—
855	#124	C₂³×C₃₁	1	2	yes	—
856	#124	C₂³×C₃₁	1	2	yes	—
857	#124	C₂³×C₃₁	1	1	yes	characteristic
858	#123	—	2	2	no	—
859	#123	—	2	2	no	—
860	#123	—	2	2	no	—
861	#123	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	2	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	2	no	—
870	C₂²⋊Q₈	—	2	2	no	—
871	C₂²⋊Q₈	—	2	2	no	—
872	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
873	#121	—	2	2	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	—	2	2	no	—
878	#121	—	2	2	no	—
879	#121	—	2	2	no	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	2	no	—
885	#121	—	2	2	no	—
886	#121	—	2	2	no	—
887	#121	—	2	2	no	—
888	#121	C₂³×C₃₁	1	2	yes	—
889	#121	C₂³×C₃₁	1	2	yes	—
890	#121	C₂³×C₃₁	1	2	yes	—
891	#120	—	2	2	no	—
892	#120	—	2	2	no	—
893	#120	—	2	2	no	—
894	#120	—	2	2	no	—
895	#120	—	2	2	no	—
896	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
897	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
898	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	2	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	2	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	—	2	1	no	—
908	C₄×D₄	—	2	2	no	—
909	C₄×D₄	—	2	2	no	—
910	C₄×D₄	D₄×C₃₁	1	2	yes	—
911	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
912	C₄×D₄	D₄×C₃₁	1	2	yes	—
913	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₃₁	1	2	yes	—
915	C₄×D₄	C₂³×C₃₁	1	2	yes	—
916	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
918	#117	—	2	1	no	—
919	#117	—	2	2	no	—
920	#117	C₂³×C₃₁	1	1	yes	characteristic
921	#117	C₂³×C₃₁	1	1	yes	characteristic
922	#117	C₂³×C₃₁	1	2	yes	—
923	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	—	2	1	no	—
925	C₂×C₂²⋊C₄	—	2	1	no	—
926	C₂×C₂²⋊C₄	—	2	1	no	—
927	C₂×C₂²⋊C₄	—	2	2	no	—
928	C₂×C₂²⋊C₄	—	2	2	no	—
929	C₂×C₄²	—	2	1	no	—
930	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
931	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
932	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
933	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
934	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
935	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
936	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
937	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
938	#103	C₂³×C₃₁	1	2	yes	—
939	#103	C₂³×C₃₁	1	2	yes	—
940	#103	C₂³×C₃₁	1	1	yes	characteristic
941	#103	C₂³×C₃₁	1	1	yes	characteristic
942	#103	C₂³×C₃₁	1	1	yes	characteristic
943	#103	C₂³×C₃₁	1	1	yes	characteristic
944	#103	C₂³×C₃₁	1	2	yes	—
945	#103	C₂³×C₃₁	1	2	yes	—
946	#103	C₂³×C₃₁	1	2	yes	—
947	#103	C₂³×C₃₁	1	2	yes	—
948	#102	C₂³×C₃₁	1	2	yes	—
949	#102	C₂³×C₃₁	1	2	yes	—
950	#102	C₂³×C₃₁	1	1	yes	characteristic
951	#102	C₂³×C₃₁	1	1	yes	characteristic
952	#102	C₂³×C₃₁	1	1	yes	characteristic
953	#102	C₂³×C₃₁	1	1	yes	characteristic
954	#102	C₂³×C₃₁	1	2	yes	—
955	#102	C₂³×C₃₁	1	2	yes	—
956	#102	C₂³×C₃₁	1	2	yes	—
957	#102	C₂³×C₃₁	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
962	#97	C₂³×C₃₁	1	2	yes	—
963	#97	C₂³×C₃₁	1	2	yes	—
964	C₄×C₈	C₂³×C₃₁	1	2	yes	—
965	C₄×C₈	C₂³×C₃₁	1	2	yes	—
966	C₃₁	#60834	1	1	yes	characteristic, direct product factor, Sylow
967	C₂⁴	—	2	2	no	—
968	C₂⁴	—	2	1	no	—
969	C₂⁴	—	2	1	no	—
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	2	2	no	—
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	2	no	—
981	#41	—	4	2	no	—
982	#41	—	4	8	no	—
983	#41	—	4	4	no	—
984	#41	—	4	4	no	—
985	#41	—	8	4	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	2	2	no	—
990	C₂×Q₈	—	2	2	no	—
991	C₂×Q₈	—	4	2	no	—
992	C₂×Q₈	—	4	2	no	—
993	C₂×Q₈	—	4	4	no	—
994	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
996	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	4	2	no	—
1021	C₂×D₄	—	4	2	no	—
1022	C₂×D₄	—	4	8	no	—
1023	C₂×D₄	—	4	4	no	—
1024	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1026	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1027	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1030	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	8	2	no	—
1044	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1047	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1048	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1049	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1050	Q₁₆	—	4	1	no	—
1051	Q₁₆	—	4	1	no	—
1052	Q₁₆	—	4	2	no	—
1053	SD₁₆	—	4	2	no	—
1054	SD₁₆	—	4	2	no	—
1055	SD₁₆	—	4	1	no	—
1056	SD₁₆	—	4	1	no	—
1057	SD₁₆	—	4	1	no	—
1058	SD₁₆	—	4	1	no	—
1059	SD₁₆	—	4	2	no	—
1060	SD₁₆	—	4	2	no	—
1061	SD₁₆	—	4	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	D₈	—	4	2	no	—
1064	D₈	—	4	2	no	—
1065	D₈	—	4	1	no	—
1066	D₈	—	4	1	no	—
1067	D₈	—	4	2	no	—
1068	D₈	—	4	2	no	—
1069	D₈	—	4	2	no	—
1070	M₁₆	—	2	2	no	—
1071	M₁₆	—	2	2	no	—
1072	C₂×C₈	—	2	2	no	—
1073	C₂×C₈	—	2	2	no	—
1074	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1075	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1076	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1077	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1092	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1094	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1123	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1129	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1130	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1131	C₄²	C₂⁴×C₃₁	1	2	yes	—
1132	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1133	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	2	1	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	2	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	1	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1149	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1150	Q₈	—	2	2	no	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	1	no	—
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	1	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	4	4	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	8	2	no	—
1162	D₄	—	2	4	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	4	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	4	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	4	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	2	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1220	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1221	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1223	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1224	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1225	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1226	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	1	no	—
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	2	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	4	2	no	—
1240	C₂²	—	4	1	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	2	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	2	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	8	4	no	—
1254	C₂²	—	16	2	no	—
1255	C₂²	—	16	4	no	—
1256	C₂²	C₃₁×#535	1	2	yes	—
1257	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1258	C₄	—	2	2	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	2	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	—	4	1	no	—
1272	C₄	C₃₁×#535	1	2	yes	—
1273	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1274	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1275	C₂	—	2	2	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	8	2	no	—
1278	C₂	—	8	2	no	—
1279	C₂	—	8	1	no	—
1280	C₂	—	8	1	no	—
1281	C₂	—	8	1	no	—
1282	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
1283	C₂	C₃₁×#3584	1	1	yes	characteristic
1284	C₂	C₃₁×#3585	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×#3460	C₂	semidirect
3. C₃₁×#3225	C₂	semidirect
4. C₃₁×#3224	C₂	semidirect
5. C₃₁×#3221	C₂	semidirect
6. C₃₁×#3220	C₂	semidirect
7. C₃₁×#3219	C₂	semidirect
8. C₃₁×#3213	C₂	semidirect
9. C₃₁×#3211	C₂	semidirect
10. C₃₁×#3207	C₂	semidirect
11. C₃₁×#3155	C₂	semidirect
12. C₃₁×#3154	C₂	semidirect
13. C₃₁×#3137	C₂	semidirect
14. C₃₁×#3136	C₂	semidirect
15. C₃₁×#3040	C₂	semidirect
16. C₃₁×#3036	C₂	semidirect
17. C₃₁×#3035	C₂	semidirect
18. C₂×C₃₁×#463	C₂	semidirect
19. C₃₁×#3013	C₂	semidirect
20. C₃₁×#3012	C₂	semidirect
21. C₃₁×#3010	C₂	semidirect
22. C₃₁×#3008	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
26. C₂×C₃₁×#137	C₂²	semidirect
29. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
31. C₂×C₃₁×#135	C₂²	semidirect
32. C₂²×SD₁₆×C₃₁	C₂²	semidirect
40. C₃₁×#544	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
44. C₃₁×#540	C₂²	semidirect
48. C₃₁×#536	C₂²	semidirect
51. C₃₁×#535	C₂²	semidirect
52. C₃₁×#535	C₂²	semidirect
55. C₃₁×#532	C₂²	semidirect
56. C₃₁×#532	C₂²	semidirect
58. C₃₁×#529	C₂²	semidirect
60. C₂×C₃₁×#124	C₂²	semidirect
63. C₄×#41×C₃₁	C₂²	semidirect
64. C₂×C₄×D₄×C₃₁	C₂²	semidirect
65. C₃₁×#497	C₂²	semidirect
66. C₃₁×#496	C₂²	semidirect
67. C₃₁×#496	C₂²	semidirect
68. C₃₁×#496	C₂²	semidirect
69. C₃₁×#495	C₂²	semidirect
70. C₃₁×#495	C₂²	semidirect
71. C₃₁×#493	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×#463	C₂²	semidirect
86. C₃₁×#463	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#463	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×#461	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
98. C₃₁×#460	C₂²	semidirect
99. C₃₁×#459	C₂²	semidirect
100. C₃₁×#459	C₂²	semidirect
101. C₃₁×#452	C₂²	semidirect
102. C₃₁×#452	C₂²	semidirect
103. C₃₁×#451	C₂²	semidirect
104. C₃₁×#450	C₂²	semidirect
107. C₃₁×#449	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
111. C₃₁×#448	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
116. C₃₁×#447	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
491. #60834	C₃₁	direct (N × H)
591. #3500	C₂×C₃₁	semidirect
592. #3460	C₂×C₃₁	semidirect
593. #3225	C₂×C₃₁	semidirect
594. #3224	C₂×C₃₁	semidirect
595. #3221	C₂×C₃₁	semidirect
596. #3220	C₂×C₃₁	semidirect
597. #3219	C₂×C₃₁	semidirect
598. #3213	C₂×C₃₁	semidirect
599. #3211	C₂×C₃₁	semidirect
600. #3207	C₂×C₃₁	semidirect
601. #3155	C₂×C₃₁	semidirect
602. #3154	C₂×C₃₁	semidirect
603. #3137	C₂×C₃₁	semidirect
604. #3136	C₂×C₃₁	semidirect
605. #3040	C₂×C₃₁	semidirect
606. #3036	C₂×C₃₁	semidirect
607. #3035	C₂×C₃₁	semidirect
608. C₂×#463	C₂×C₃₁	semidirect
609. #3013	C₂×C₃₁	semidirect
610. #3012	C₂×C₃₁	semidirect
611. #3010	C₂×C₃₁	semidirect
612. #3008	C₂×C₃₁	semidirect
613. #2925	C₂×C₃₁	semidirect
658. C₂×#137	C₂²×C₃₁	semidirect
661. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
663. C₂×#135	C₂²×C₃₁	semidirect
664. C₂²×SD₁₆	C₂²×C₃₁	semidirect
672. #544	C₂²×C₃₁	semidirect
674. #542	C₂²×C₃₁	semidirect
676. #540	C₂²×C₃₁	semidirect
680. #536	C₂²×C₃₁	semidirect
683. #535	C₂²×C₃₁	semidirect
684. #535	C₂²×C₃₁	semidirect
687. #532	C₂²×C₃₁	semidirect
688. #532	C₂²×C₃₁	semidirect
690. #529	C₂²×C₃₁	semidirect
692. C₂×#124	C₂²×C₃₁	semidirect
695. C₄×#41	C₂²×C₃₁	semidirect
696. C₂×C₄×D₄	C₂²×C₃₁	semidirect
697. #497	C₂²×C₃₁	semidirect
698. #496	C₂²×C₃₁	semidirect
699. #496	C₂²×C₃₁	semidirect
700. #496	C₂²×C₃₁	semidirect
701. #495	C₂²×C₃₁	semidirect
702. #495	C₂²×C₃₁	semidirect
703. #493	C₂²×C₃₁	semidirect
704. #492	C₂²×C₃₁	semidirect
705. #491	C₂²×C₃₁	semidirect
706. #490	C₂²×C₃₁	semidirect
707. #489	C₂²×C₃₁	semidirect
708. #489	C₂²×C₃₁	semidirect
709. #488	C₂²×C₃₁	semidirect
710. #488	C₂²×C₃₁	semidirect
711. #487	C₂²×C₃₁	semidirect
712. #486	C₂²×C₃₁	semidirect
713. #464	C₂²×C₃₁	semidirect
714. #464	C₂²×C₃₁	semidirect
715. #464	C₂²×C₃₁	semidirect
716. #464	C₂²×C₃₁	semidirect
717. #463	C₂²×C₃₁	semidirect
718. #463	C₂²×C₃₁	semidirect
719. #463	C₂²×C₃₁	semidirect
720. #463	C₂²×C₃₁	semidirect
721. #463	C₂²×C₃₁	semidirect
722. #463	C₂²×C₃₁	semidirect
723. #463	C₂²×C₃₁	semidirect
724. #463	C₂²×C₃₁	semidirect
725. #463	C₂²×C₃₁	semidirect
726. #463	C₂²×C₃₁	semidirect
727. #462	C₂²×C₃₁	semidirect
728. #461	C₂²×C₃₁	semidirect
729. #461	C₂²×C₃₁	semidirect
730. #460	C₂²×C₃₁	semidirect
731. #459	C₂²×C₃₁	semidirect
732. #459	C₂²×C₃₁	semidirect
733. #452	C₂²×C₃₁	semidirect
734. #452	C₂²×C₃₁	semidirect
735. #451	C₂²×C₃₁	semidirect
736. #450	C₂²×C₃₁	semidirect
739. #449	C₂²×C₃₁	semidirect
740. #449	C₂²×C₃₁	semidirect
741. #449	C₂²×C₃₁	semidirect
742. #449	C₂²×C₃₁	semidirect
743. #448	C₂²×C₃₁	semidirect
744. #448	C₂²×C₃₁	semidirect
745. #448	C₂²×C₃₁	semidirect
748. #447	C₂²×C₃₁	semidirect
749. #433	C₂²×C₃₁	semidirect
750. #433	C₂²×C₃₁	semidirect
751. #432	C₂²×C₃₁	semidirect
752. #431	C₂²×C₃₁	semidirect
753. #423	C₂²×C₃₁	semidirect
754. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
755. #419	C₂²×C₃₁	semidirect
758. #417	C₂²×C₃₁	semidirect
760. #416	C₂²×C₃₁	semidirect
761. C₂×#103	C₂²×C₃₁	semidirect
765. #405	C₂²×C₃₁	semidirect
766. #405	C₂²×C₃₁	semidirect
966. C₃₁	#60834	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×#3460	2
C₃₁×#3225	2
C₃₁×#3224	2
C₃₁×#3221	2
C₃₁×#3220	2
C₃₁×#3219	2
C₃₁×#3213	2
C₃₁×#3211	2
C₃₁×#3207	2
C₃₁×#3155	2
C₃₁×#3154	2
C₃₁×#3137	2
C₃₁×#3136	2
C₃₁×#3040	2
C₃₁×#3036	2
C₃₁×#3035	2
C₂×C₃₁×#463	2
C₃₁×#3013	2
C₃₁×#3012	2
C₃₁×#3010	2
C₃₁×#3008	2
C₃₁×#2925	2
#60834	31

Subgroups — C31×#60834 #21517593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60834 #21517593