Subgroups — C₃₁×#61483 #21518242

Order 7936.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3173	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2952	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#559	—	2	1	no	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#554	C₂²	1	2	yes	—
32	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#547	—	2	2	no	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#547	C₂²	1	2	yes	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	C₃₁×#542	—	2	2	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#542	C₂²	1	2	yes	complemented
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#532	—	2	1	no	—
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₃₁×#520	C₂²	1	2	yes	complemented
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#498	C₂²	1	2	yes	complemented
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#483	C₂²	1	2	yes	—
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	2	yes	—
71	C₃₁×#481	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#476	C₂²	1	1	yes	characteristic
74	C₃₁×#476	C₂²	1	1	yes	characteristic
75	C₃₁×#476	C₂²	1	2	yes	—
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#475	C₂²	1	2	yes	complemented
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	—
83	C₃₁×#465	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#459	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	complemented
97	C₃₁×#451	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#449	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#442	C₂²	1	2	yes	—
106	C₃₁×#441	C₂²	1	2	yes	complemented
107	C₃₁×#441	C₂²	1	2	yes	complemented
108	C₃₁×#441	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic
127	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
128	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
129	C₃₁×#417	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	2	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	—	2	1	no	—
144	C₃₁×#135	—	2	8	no	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	—	2	4	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	2	no	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	D₄	1	2	yes	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	1	no	—
176	C₃₁×#125	D₄	1	1	yes	characteristic
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	D₄	1	1	yes	characteristic
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	D₄	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#120	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	1	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	8	2	no	—
320	#41×C₃₁	—	8	4	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	4	1	no	—
329	C₂×Q₈×C₃₁	—	8	2	no	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	4	1	no	—
344	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	8	2	no	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
368	Q₁₆×C₃₁	—	2	4	no	—
369	Q₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	2	2	no	—
371	SD₁₆×C₃₁	—	2	2	no	—
372	SD₁₆×C₃₁	—	2	2	no	—
373	SD₁₆×C₃₁	—	2	4	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	#41	1	4	yes	complemented
376	D₈×C₃₁	—	2	4	no	—
377	D₈×C₃₁	—	4	2	no	—
378	M₁₆×C₃₁	—	4	2	no	—
379	C₂×C₈×C₃₁	—	2	2	no	—
380	C₂×C₈×C₃₁	—	2	4	no	—
381	C₂×C₈×C₃₁	—	4	1	no	—
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	2	yes	—
454	#61483	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	2	no	—
458	C₂³×C₃₁	—	4	2	no	—
459	C₂³×C₃₁	—	4	2	no	—
460	C₂³×C₃₁	—	8	1	no	—
461	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
462	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	2	no	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	4	2	no	—
470	Q₈×C₃₁	—	4	2	no	—
471	Q₈×C₃₁	—	8	2	no	—
472	Q₈×C₃₁	—	8	1	no	—
473	Q₈×C₃₁	—	8	2	no	—
474	Q₈×C₃₁	C₂×#41	1	2	yes	—
475	D₄×C₃₁	—	2	4	no	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	1	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	4	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	4	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	8	1	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	C₂×#41	1	2	yes	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	4	4	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	4	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	8	1	no	—
513	C₂×C₄×C₃₁	—	8	1	no	—
514	C₂×C₄×C₃₁	—	8	2	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	1	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₃₁	—	2	2	no	—
530	C₈×C₃₁	—	2	1	no	—
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	2	no	—
534	C₈×C₃₁	C₂×#41	1	2	yes	—
535	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
538	Q₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3335	C₂×C₃₁	1	2	yes	complemented
542	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3316	C₂×C₃₁	1	2	yes	complemented
546	#3306	C₂×C₃₁	1	2	yes	complemented
547	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3282	C₂×C₃₁	1	2	yes	complemented
549	#3173	C₂×C₃₁	1	2	yes	complemented
550	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3125	C₂×C₃₁	1	2	yes	complemented
552	#3125	C₂×C₃₁	1	2	yes	complemented
553	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#2952	C₂×C₃₁	1	2	yes	complemented
557	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	2	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	8	4	no	—
573	C₂²×C₃₁	#577	1	2	yes	—
574	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₃₁	—	2	2	no	—
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	4	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	#577	1	2	yes	—
592	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
593	C₄×C₃₁	#585	1	1	yes	characteristic
594	C₂×#135	C₂²×C₃₁	1	2	yes	—
595	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
596	#559	—	2	1	no	—
597	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#556	C₂²×C₃₁	1	1	yes	characteristic
600	#554	—	2	1	no	—
601	#554	C₂²×C₃₁	1	2	yes	—
602	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#552	—	2	1	no	—
604	#551	—	2	2	no	—
605	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
607	#548	—	2	1	no	—
608	#548	C₂²×C₃₁	1	2	yes	—
609	#547	—	2	2	no	—
610	#547	C₂²×C₃₁	1	1	yes	characteristic
611	#547	C₂²×C₃₁	1	1	yes	characteristic
612	#547	C₂²×C₃₁	1	2	yes	—
613	#546	C₂²×C₃₁	1	2	yes	—
614	#542	—	2	2	no	—
615	#542	C₂²×C₃₁	1	2	yes	—
616	#542	C₂²×C₃₁	1	2	yes	complemented
617	#539	—	2	2	no	—
618	#533	C₂²×C₃₁	1	1	yes	characteristic
619	#532	—	2	1	no	—
620	#532	C₂²×C₃₁	1	1	yes	characteristic
621	#529	—	2	1	no	—
622	#529	C₂²×C₃₁	1	1	yes	characteristic
623	#525	—	2	1	no	—
624	C₂×C₂²⋊Q₈	—	2	1	no	—
625	#520	C₂²×C₃₁	1	2	yes	—
626	#520	C₂²×C₃₁	1	2	yes	complemented
627	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
628	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
629	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#498	C₂²×C₃₁	1	2	yes	complemented
631	#495	C₂²×C₃₁	1	2	yes	—
632	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#489	C₂²×C₃₁	1	2	yes	—
634	#489	C₂²×C₃₁	1	2	yes	complemented
635	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#483	C₂²×C₃₁	1	2	yes	—
638	#483	C₂²×C₃₁	1	2	yes	complemented
639	#483	C₂²×C₃₁	1	2	yes	complemented
640	#481	C₂²×C₃₁	1	2	yes	—
641	#481	C₂²×C₃₁	1	2	yes	—
642	#481	C₂²×C₃₁	1	2	yes	complemented
643	#476	C₂²×C₃₁	1	1	yes	characteristic
644	#476	C₂²×C₃₁	1	1	yes	characteristic
645	#476	C₂²×C₃₁	1	2	yes	—
646	#476	C₂²×C₃₁	1	2	yes	complemented
647	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#475	C₂²×C₃₁	1	2	yes	complemented
650	#475	C₂²×C₃₁	1	2	yes	complemented
651	#470	C₂²×C₃₁	1	2	yes	complemented
652	#469	C₂²×C₃₁	1	2	yes	—
653	#465	C₂²×C₃₁	1	2	yes	—
654	#465	C₂²×C₃₁	1	2	yes	—
655	#465	C₂²×C₃₁	1	2	yes	—
656	#465	C₂²×C₃₁	1	2	yes	complemented
657	#464	C₂²×C₃₁	1	2	yes	—
658	#464	C₂²×C₃₁	1	2	yes	complemented
659	#463	C₂²×C₃₁	1	2	yes	—
660	#463	C₂²×C₃₁	1	2	yes	—
661	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#459	C₂²×C₃₁	1	1	yes	characteristic
664	#459	C₂²×C₃₁	1	1	yes	characteristic
665	#452	C₂²×C₃₁	1	2	yes	—
666	#452	C₂²×C₃₁	1	2	yes	complemented
667	#451	C₂²×C₃₁	1	2	yes	—
668	#449	C₂²×C₃₁	1	2	yes	—
669	#449	C₂²×C₃₁	1	2	yes	—
670	#447	C₂²×C₃₁	1	2	yes	—
671	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#442	C₂²×C₃₁	1	2	yes	—
674	#442	C₂²×C₃₁	1	2	yes	—
675	#442	C₂²×C₃₁	1	2	yes	—
676	#441	C₂²×C₃₁	1	2	yes	complemented
677	#441	C₂²×C₃₁	1	2	yes	complemented
678	#441	C₂²×C₃₁	1	2	yes	complemented
679	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
691	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#435	C₂²×C₃₁	1	2	yes	—
693	C₈×D₄	C₂²×C₃₁	1	2	yes	—
694	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#433	C₂²×C₃₁	1	2	yes	complemented
696	#432	C₂²×C₃₁	1	1	yes	characteristic
697	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
698	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
699	#417	C₂²×C₃₁	1	2	yes	—
700	#417	C₂²×C₃₁	1	2	yes	complemented
701	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
702	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
703	#405	C₂²×C₃₁	1	2	yes	complemented
704	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
705	C₂×C₃₁	—	2	2	no	—
706	C₂×C₃₁	—	4	2	no	—
707	C₂×C₃₁	—	4	2	no	—
708	C₂×C₃₁	—	8	2	no	—
709	C₂×C₃₁	—	8	1	no	—
710	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
711	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
712	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
713	C₂×#41	—	2	1	no	—
714	C₂×#41	—	2	2	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	C₂³×C₃₁	1	2	yes	—
717	C₂×#41	C₂³×C₃₁	1	2	yes	—
718	C₂²×Q₈	—	2	1	no	—
719	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
721	C₂³×C₄	—	2	1	no	—
722	#135	—	2	8	no	—
723	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
724	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×SD₁₆	—	2	4	no	—
726	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₃₁	1	2	yes	—
733	C₂×D₈	C₂³×C₃₁	1	2	yes	—
734	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
737	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	—	2	2	no	—
740	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
744	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
745	#127	—	2	1	no	—
746	#127	C₂³×C₃₁	1	1	yes	characteristic
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	D₄×C₃₁	1	2	yes	—
751	#125	—	2	1	no	—
752	#125	—	2	2	no	—
753	#125	—	2	1	no	—
754	#125	D₄×C₃₁	1	1	yes	characteristic
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	D₄×C₃₁	1	1	yes	characteristic
761	#124	C₂³×C₃₁	1	2	yes	—
762	#124	C₂³×C₃₁	1	2	yes	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	D₄×C₃₁	1	2	yes	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	D₄×C₃₁	1	1	yes	characteristic
794	#121	C₂³×C₃₁	1	2	yes	—
795	#121	C₂³×C₃₁	1	2	yes	—
796	#121	C₂³×C₃₁	1	2	yes	—
797	#120	—	2	2	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	C₂³×C₃₁	1	2	yes	—
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	2	2	no	—
834	#117	—	2	1	no	—
835	#117	C₂³×C₃₁	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	—	2	2	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
848	#106	C₂³×C₃₁	1	1	yes	characteristic
849	#106	C₂³×C₃₁	1	1	yes	characteristic
850	#106	C₂³×C₃₁	1	1	yes	characteristic
851	#106	C₂³×C₃₁	1	1	yes	characteristic
852	#106	C₂³×C₃₁	1	2	yes	—
853	#106	C₂³×C₃₁	1	2	yes	—
854	#106	C₂³×C₃₁	1	2	yes	—
855	#106	C₂³×C₃₁	1	2	yes	—
856	#106	C₂³×C₃₁	1	2	yes	—
857	#106	C₂³×C₃₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	1	yes	characteristic
864	#103	C₂³×C₃₁	1	1	yes	characteristic
865	#103	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	1	yes	characteristic
875	#102	C₂³×C₃₁	1	1	yes	characteristic
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
885	#97	C₂³×C₃₁	1	2	yes	—
886	#97	C₂³×C₃₁	1	2	yes	—
887	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₃₁	1	2	yes	—
892	C₃₁	#61483	1	1	yes	characteristic, direct product factor, Sylow
893	C₂⁴	—	2	1	no	—
894	#41	—	2	4	no	—
895	#41	—	2	4	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	8	2	no	—
899	#41	—	8	4	no	—
900	#41	—	8	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	4	1	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	4	1	no	—
923	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
927	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	8	2	no	—
943	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
947	Q₁₆	—	2	4	no	—
948	Q₁₆	—	4	2	no	—
949	SD₁₆	—	2	2	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	2	4	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	#41×C₃₁	1	4	yes	complemented
955	D₈	—	2	4	no	—
956	D₈	—	4	2	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	2	2	no	—
959	C₂×C₈	—	2	4	no	—
960	C₂×C₈	—	4	1	no	—
961	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
965	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
966	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₃₁	1	2	yes	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	4	2	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	8	1	no	—
1039	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1040	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	8	2	no	—
1050	Q₈	—	8	1	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	C₂×#41×C₃₁	1	2	yes	—
1053	D₄	—	2	4	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	C₂×#41×C₃₁	1	2	yes	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	1	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1106	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1107	C₈	—	2	2	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	C₂×#41×C₃₁	1	2	yes	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	8	4	no	—
1128	C₂²	C₃₁×#577	1	2	yes	—
1129	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	2	no	—
1146	C₄	C₃₁×#577	1	2	yes	—
1147	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1148	C₄	C₃₁×#585	1	1	yes	characteristic
1149	C₂	—	2	2	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	4	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	2	no	—
1154	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1155	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1156	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3522	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3394	C₂	semidirect
4. Q₈×SD₁₆×C₃₁	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3369	C₂	semidirect
7. C₃₁×#3335	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3332	C₂	semidirect
10. C₃₁×#3331	C₂	semidirect
11. C₃₁×#3316	C₂	semidirect
12. C₃₁×#3306	C₂	semidirect
13. C₃₁×#3284	C₂	semidirect
14. C₃₁×#3282	C₂	semidirect
15. C₃₁×#3173	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3125	C₂	semidirect
18. C₃₁×#3125	C₂	semidirect
19. C₃₁×#3113	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2952	C₂	semidirect
23. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
28. Q₈²×C₃₁	C₂²	semidirect
32. C₃₁×#554	C₂²	semidirect
35. C₃₁×#550	C₂²	semidirect
46. C₃₁×#542	C₂²	semidirect
56. C₃₁×#520	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
91. C₃₁×#462	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
96. C₃₁×#452	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
106. C₃₁×#441	C₂²	semidirect
107. C₃₁×#441	C₂²	semidirect
108. C₃₁×#441	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
128. C₂×C₃₁×#106	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
375. SD₁₆×C₃₁	#41	semidirect
454. #61483	C₃₁	direct (N × H)
535. #3522	C₂×C₃₁	semidirect
536. #3520	C₂×C₃₁	semidirect
537. #3394	C₂×C₃₁	semidirect
538. Q₈×SD₁₆	C₂×C₃₁	semidirect
539. #3373	C₂×C₃₁	semidirect
540. #3369	C₂×C₃₁	semidirect
541. #3335	C₂×C₃₁	semidirect
542. #3335	C₂×C₃₁	semidirect
543. #3332	C₂×C₃₁	semidirect
544. #3331	C₂×C₃₁	semidirect
545. #3316	C₂×C₃₁	semidirect
546. #3306	C₂×C₃₁	semidirect
547. #3284	C₂×C₃₁	semidirect
548. #3282	C₂×C₃₁	semidirect
549. #3173	C₂×C₃₁	semidirect
550. #3167	C₂×C₃₁	semidirect
551. #3125	C₂×C₃₁	semidirect
552. #3125	C₂×C₃₁	semidirect
553. #3113	C₂×C₃₁	semidirect
554. #3109	C₂×C₃₁	semidirect
555. #2966	C₂×C₃₁	semidirect
556. #2952	C₂×C₃₁	semidirect
557. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
597. #559	C₂²×C₃₁	semidirect
598. Q₈²	C₂²×C₃₁	semidirect
602. #554	C₂²×C₃₁	semidirect
605. #550	C₂²×C₃₁	semidirect
616. #542	C₂²×C₃₁	semidirect
626. #520	C₂²×C₃₁	semidirect
629. #498	C₂²×C₃₁	semidirect
630. #498	C₂²×C₃₁	semidirect
632. #492	C₂²×C₃₁	semidirect
634. #489	C₂²×C₃₁	semidirect
635. #487	C₂²×C₃₁	semidirect
636. #486	C₂²×C₃₁	semidirect
638. #483	C₂²×C₃₁	semidirect
639. #483	C₂²×C₃₁	semidirect
642. #481	C₂²×C₃₁	semidirect
646. #476	C₂²×C₃₁	semidirect
647. #475	C₂²×C₃₁	semidirect
648. #475	C₂²×C₃₁	semidirect
649. #475	C₂²×C₃₁	semidirect
650. #475	C₂²×C₃₁	semidirect
651. #470	C₂²×C₃₁	semidirect
656. #465	C₂²×C₃₁	semidirect
658. #464	C₂²×C₃₁	semidirect
661. #462	C₂²×C₃₁	semidirect
662. #462	C₂²×C₃₁	semidirect
666. #452	C₂²×C₃₁	semidirect
671. #446	C₂²×C₃₁	semidirect
672. C₈×Q₈	C₂²×C₃₁	semidirect
676. #441	C₂²×C₃₁	semidirect
677. #441	C₂²×C₃₁	semidirect
678. #441	C₂²×C₃₁	semidirect
688. C₄×SD₁₆	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	C₂²×C₃₁	semidirect
691. #436	C₂²×C₃₁	semidirect
694. C₈×D₄	C₂²×C₃₁	semidirect
695. #433	C₂²×C₃₁	semidirect
698. C₂×#106	C₂²×C₃₁	semidirect
700. #417	C₂²×C₃₁	semidirect
703. #405	C₂²×C₃₁	semidirect
892. C₃₁	#61483	direct (N × H)
954. SD₁₆	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3522	2
C₃₁×#3520	2
C₃₁×#3394	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3373	2
C₃₁×#3369	2
C₃₁×#3335	2
C₃₁×#3332	2
C₃₁×#3331	2
C₃₁×#3316	2
C₃₁×#3306	2
C₃₁×#3284	2
C₃₁×#3282	2
C₃₁×#3173	2
C₃₁×#3167	2
C₃₁×#3125	2
C₃₁×#3113	2
C₃₁×#3109	2
C₃₁×#2966	2
C₃₁×#2952	2
C₂×C₄×SD₁₆×C₃₁	2
#61483	31

Subgroups — C31×#61483 #21518242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61483 #21518242