Subgroups — C₃₁×#61154 #21517913

Order 7936.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3091	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3054	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3002	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2896	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₃₁	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
27	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	C₂²	1	2	yes	complemented
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#548	C₂²	1	2	yes	—
38	C₃₁×#547	—	2	1	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	—	2	2	no	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	D₄²×C₃₁	—	2	1	no	—
45	D₄²×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#532	—	2	1	no	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#529	—	2	2	no	—
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#525	—	2	2	no	—
52	C₃₁×#525	C₂²	1	2	yes	—
53	C₃₁×#525	C₂²	1	2	yes	complemented
54	C₄×#41×C₃₁	—	2	1	no	—
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₃₁	—	2	1	no	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#488	C₂²	1	2	yes	complemented
62	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#470	C₂²	1	2	yes	complemented
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	complemented
83	C₃₁×#469	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#468	C₂²	1	2	yes	complemented
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#452	C₂²	1	2	yes	complemented
95	C₃₁×#452	C₂²	1	2	yes	complemented
96	C₃₁×#451	C₂²	1	2	yes	complemented
97	C₃₁×#450	C₂²	1	2	yes	complemented
98	C₃₁×#449	C₂²	1	2	yes	complemented
99	C₃₁×#449	C₂²	1	2	yes	complemented
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#447	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#436	C₂²	1	1	yes	characteristic
111	C₃₁×#436	C₂²	1	1	yes	characteristic
112	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#436	C₂²	1	2	yes	complemented
115	C₃₁×#436	C₂²	1	2	yes	complemented
116	C₃₁×#427	C₂²	1	2	yes	complemented
117	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#419	C₂²	1	2	yes	complemented
120	C₃₁×#419	C₂²	1	2	yes	complemented
121	C₃₁×#418	C₂²	1	2	yes	complemented
122	C₃₁×#418	C₂²	1	2	yes	complemented
123	C₃₁×#417	C₂²	1	2	yes	complemented
124	C₃₁×#417	C₂²	1	2	yes	complemented
125	C₃₁×#417	C₂²	1	2	yes	complemented
126	C₃₁×#417	C₂²	1	2	yes	complemented
127	C₃₁×#416	C₂²	1	2	yes	—
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₃₁×#416	C₂²	1	2	yes	complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	2	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	8	no	—
139	C₂×#41×C₃₁	—	4	4	no	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	2	yes	—
143	C₂×#41×C₃₁	C₂³	1	2	yes	—
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	—	2	2	no	—
147	C₂²×D₄×C₃₁	—	2	1	no	—
148	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
149	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂³×C₄×C₃₁	—	2	2	no	—
151	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
152	C₃₁×#135	—	2	4	no	—
153	C₃₁×#135	—	4	4	no	—
154	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₃₁	—	4	4	no	—
163	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
165	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
170	C₃₁×C₄⋊Q₈	—	2	1	no	—
171	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₃₁×#127	—	2	1	no	—
175	C₃₁×#127	C₂³	1	1	yes	characteristic
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	C₂³	1	2	yes	—
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×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	—	2	2	no	—
218	C₃₁×#120	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
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×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
243	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
244	C₄×D₄×C₃₁	D₄	1	2	yes	—
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	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	C₂³	1	1	yes	characteristic
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	1	yes	characteristic
261	C₃₁×#117	C₂³	1	2	yes	—
262	C₃₁×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
270	C₂×C₄²×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	—	2	1	no	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	1	yes	characteristic
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
317	C₂⁴×C₃₁	—	2	2	no	—
318	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
319	#41×C₃₁	—	2	2	no	—
320	#41×C₃₁	—	2	4	no	—
321	#41×C₃₁	—	2	4	no	—
322	#41×C₃₁	—	2	2	no	—
323	#41×C₃₁	—	2	4	no	—
324	#41×C₃₁	—	2	2	no	—
325	#41×C₃₁	—	2	4	no	—
326	#41×C₃₁	—	4	8	no	—
327	#41×C₃₁	—	4	2	no	—
328	#41×C₃₁	—	4	2	no	—
329	#41×C₃₁	—	4	8	no	—
330	#41×C₃₁	—	4	4	no	—
331	#41×C₃₁	#41	1	4	yes	complemented
332	C₂×Q₈×C₃₁	—	2	1	no	—
333	C₂×Q₈×C₃₁	—	2	2	no	—
334	C₂×Q₈×C₃₁	—	2	1	no	—
335	C₂×Q₈×C₃₁	—	2	4	no	—
336	C₂×Q₈×C₃₁	—	4	2	no	—
337	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
338	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	4	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	2	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	—	2	2	no	—
349	C₂×D₄×C₃₁	—	2	2	no	—
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	2	2	no	—
352	C₂×D₄×C₃₁	—	2	1	no	—
353	C₂×D₄×C₃₁	—	4	2	no	—
354	C₂×D₄×C₃₁	—	4	2	no	—
355	C₂×D₄×C₃₁	—	4	8	no	—
356	C₂×D₄×C₃₁	—	4	4	no	—
357	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
361	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	4	no	—
365	C₂²×C₄×C₃₁	—	2	4	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	1	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	1	no	—
377	C₂²×C₄×C₃₁	—	4	8	no	—
378	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
380	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	Q₁₆×C₃₁	—	2	2	no	—
387	Q₁₆×C₃₁	—	4	2	no	—
388	SD₁₆×C₃₁	—	2	2	no	—
389	SD₁₆×C₃₁	—	2	2	no	—
390	SD₁₆×C₃₁	—	4	2	no	—
391	SD₁₆×C₃₁	—	4	2	no	—
392	D₈×C₃₁	—	2	2	no	—
393	D₈×C₃₁	—	4	2	no	—
394	M₁₆×C₃₁	—	4	2	no	—
395	M₁₆×C₃₁	—	4	2	no	—
396	M₁₆×C₃₁	—	4	2	no	—
397	M₁₆×C₃₁	—	4	2	no	—
398	C₂×C₈×C₃₁	—	2	2	no	—
399	C₂×C₈×C₃₁	—	2	2	no	—
400	C₂×C₈×C₃₁	—	2	4	no	—
401	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
406	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
430	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
432	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	1	no	—
445	C₂²⋊C₄×C₃₁	—	2	1	no	—
446	C₂²⋊C₄×C₃₁	—	2	1	no	—
447	C₂²⋊C₄×C₃₁	—	2	1	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
455	C₄²×C₃₁	—	2	2	no	—
456	C₄²×C₃₁	—	2	1	no	—
457	C₄²×C₃₁	—	2	2	no	—
458	C₄²×C₃₁	—	2	1	no	—
459	C₄²×C₃₁	—	2	1	no	—
460	C₄²×C₃₁	—	2	1	no	—
461	C₄²×C₃₁	—	2	1	no	—
462	C₄²×C₃₁	—	2	1	no	—
463	C₄²×C₃₁	—	2	2	no	—
464	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
465	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
466	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
467	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
468	#61154	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
469	C₂³×C₃₁	—	2	1	no	—
470	C₂³×C₃₁	—	2	4	no	—
471	C₂³×C₃₁	—	2	1	no	—
472	C₂³×C₃₁	—	2	2	no	—
473	C₂³×C₃₁	—	4	2	no	—
474	C₂³×C₃₁	—	4	2	no	—
475	C₂³×C₃₁	—	4	4	no	—
476	C₂³×C₃₁	—	4	4	no	—
477	C₂³×C₃₁	—	8	2	no	—
478	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
480	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
481	Q₈×C₃₁	—	2	1	no	—
482	Q₈×C₃₁	—	2	1	no	—
483	Q₈×C₃₁	—	2	2	no	—
484	Q₈×C₃₁	—	2	1	no	—
485	Q₈×C₃₁	—	2	2	no	—
486	Q₈×C₃₁	—	4	4	no	—
487	Q₈×C₃₁	—	4	2	no	—
488	Q₈×C₃₁	—	8	1	no	—
489	Q₈×C₃₁	C₂×#41	1	2	yes	—
490	D₄×C₃₁	—	2	4	no	—
491	D₄×C₃₁	—	2	2	no	—
492	D₄×C₃₁	—	2	2	no	—
493	D₄×C₃₁	—	2	1	no	—
494	D₄×C₃₁	—	2	2	no	—
495	D₄×C₃₁	—	2	1	no	—
496	D₄×C₃₁	—	2	1	no	—
497	D₄×C₃₁	—	2	2	no	—
498	D₄×C₃₁	—	4	2	no	—
499	D₄×C₃₁	—	4	4	no	—
500	D₄×C₃₁	—	4	4	no	—
501	D₄×C₃₁	—	4	4	no	—
502	D₄×C₃₁	—	4	4	no	—
503	D₄×C₃₁	—	4	4	no	—
504	D₄×C₃₁	—	4	4	no	—
505	D₄×C₃₁	—	4	2	no	—
506	D₄×C₃₁	—	4	2	no	—
507	D₄×C₃₁	—	8	1	no	—
508	D₄×C₃₁	—	8	2	no	—
509	D₄×C₃₁	—	8	2	no	—
510	D₄×C₃₁	C₂×#41	1	2	yes	—
511	C₂×C₄×C₃₁	—	2	4	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	4	no	—
514	C₂×C₄×C₃₁	—	2	4	no	—
515	C₂×C₄×C₃₁	—	2	4	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	2	no	—
519	C₂×C₄×C₃₁	—	2	2	no	—
520	C₂×C₄×C₃₁	—	2	2	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	1	no	—
523	C₂×C₄×C₃₁	—	2	1	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	1	no	—
526	C₂×C₄×C₃₁	—	2	2	no	—
527	C₂×C₄×C₃₁	—	2	2	no	—
528	C₂×C₄×C₃₁	—	2	2	no	—
529	C₂×C₄×C₃₁	—	4	1	no	—
530	C₂×C₄×C₃₁	—	4	4	no	—
531	C₂×C₄×C₃₁	—	4	4	no	—
532	C₂×C₄×C₃₁	—	4	4	no	—
533	C₂×C₄×C₃₁	—	4	4	no	—
534	C₂×C₄×C₃₁	—	4	4	no	—
535	C₂×C₄×C₃₁	—	4	2	no	—
536	C₂×C₄×C₃₁	—	4	2	no	—
537	C₂×C₄×C₃₁	—	4	2	no	—
538	C₂×C₄×C₃₁	—	8	1	no	—
539	C₂×C₄×C₃₁	—	8	1	no	—
540	C₂×C₄×C₃₁	—	8	2	no	—
541	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
549	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
550	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
551	C₈×C₃₁	—	2	1	no	—
552	C₈×C₃₁	—	2	1	no	—
553	C₈×C₃₁	—	2	1	no	—
554	C₈×C₃₁	—	2	1	no	—
555	C₈×C₃₁	—	2	2	no	—
556	C₈×C₃₁	—	2	2	no	—
557	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
558	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
563	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3327	C₂×C₃₁	1	2	yes	complemented
566	#3326	C₂×C₃₁	1	2	yes	complemented
567	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3323	C₂×C₃₁	1	2	yes	complemented
570	#3322	C₂×C₃₁	1	2	yes	complemented
571	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
572	#3091	C₂×C₃₁	1	2	yes	complemented
573	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
574	#3054	C₂×C₃₁	1	2	yes	complemented
575	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
576	#3002	C₂×C₃₁	1	2	yes	complemented
577	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
578	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#2896	C₂×C₃₁	1	2	yes	complemented
580	C₂²×C₃₁	—	2	1	no	—
581	C₂²×C₃₁	—	2	1	no	—
582	C₂²×C₃₁	—	2	2	no	—
583	C₂²×C₃₁	—	2	2	no	—
584	C₂²×C₃₁	—	2	2	no	—
585	C₂²×C₃₁	—	2	2	no	—
586	C₂²×C₃₁	—	2	2	no	—
587	C₂²×C₃₁	—	2	2	no	—
588	C₂²×C₃₁	—	2	2	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	4	1	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	2	no	—
593	C₂²×C₃₁	—	4	2	no	—
594	C₂²×C₃₁	—	4	1	no	—
595	C₂²×C₃₁	—	4	1	no	—
596	C₂²×C₃₁	—	4	2	no	—
597	C₂²×C₃₁	—	8	4	no	—
598	C₂²×C₃₁	—	8	8	no	—
599	C₂²×C₃₁	#546	1	2	yes	—
600	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
601	C₄×C₃₁	—	2	1	no	—
602	C₄×C₃₁	—	2	1	no	—
603	C₄×C₃₁	—	2	2	no	—
604	C₄×C₃₁	—	2	2	no	—
605	C₄×C₃₁	—	2	2	no	—
606	C₄×C₃₁	—	2	1	no	—
607	C₄×C₃₁	—	4	1	no	—
608	C₄×C₃₁	—	4	1	no	—
609	C₄×C₃₁	—	4	2	no	—
610	C₄×C₃₁	—	4	2	no	—
611	C₄×C₃₁	—	4	1	no	—
612	C₄×C₃₁	—	4	1	no	—
613	C₄×C₃₁	—	4	1	no	—
614	C₄×C₃₁	—	4	2	no	—
615	C₄×C₃₁	#546	1	2	yes	—
616	C₄×C₃₁	#575	1	2	yes	—
617	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
618	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂²×#41	C₂²×C₃₁	1	2	yes	—
620	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
621	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
622	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
623	#556	C₂²×C₃₁	1	1	yes	characteristic
624	#555	C₂²×C₃₁	1	1	yes	characteristic
625	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#553	C₂²×C₃₁	1	2	yes	complemented
627	#552	—	2	1	no	—
628	#552	C₂²×C₃₁	1	2	yes	complemented
629	#551	—	2	2	no	—
630	#550	C₂²×C₃₁	1	1	yes	characteristic
631	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
632	#548	C₂²×C₃₁	1	2	yes	—
633	#547	—	2	1	no	—
634	#547	C₂²×C₃₁	1	1	yes	characteristic
635	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#546	—	2	1	no	—
637	#546	—	2	2	no	—
638	#546	C₂²×C₃₁	1	2	yes	—
639	D₄²	—	2	1	no	—
640	D₄²	C₂²×C₃₁	1	1	yes	characteristic
641	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#532	—	2	1	no	—
643	#532	C₂²×C₃₁	1	1	yes	characteristic
644	#529	—	2	2	no	—
645	#529	—	2	1	no	—
646	#525	—	2	2	no	—
647	#525	C₂²×C₃₁	1	2	yes	—
648	#525	C₂²×C₃₁	1	2	yes	complemented
649	C₄×#41	—	2	1	no	—
650	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
651	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	C₂×C₄×D₄	—	2	1	no	—
653	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
655	#488	C₂²×C₃₁	1	2	yes	complemented
656	#488	C₂²×C₃₁	1	2	yes	complemented
657	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#485	C₂²×C₃₁	1	2	yes	complemented
662	#485	C₂²×C₃₁	1	2	yes	complemented
663	#484	C₂²×C₃₁	1	2	yes	complemented
664	#483	C₂²×C₃₁	1	2	yes	complemented
665	#482	C₂²×C₃₁	1	2	yes	complemented
666	#482	C₂²×C₃₁	1	2	yes	complemented
667	#481	C₂²×C₃₁	1	2	yes	complemented
668	#480	C₂²×C₃₁	1	2	yes	complemented
669	#479	C₂²×C₃₁	1	2	yes	complemented
670	#478	C₂²×C₃₁	1	2	yes	complemented
671	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#470	C₂²×C₃₁	1	2	yes	complemented
676	#470	C₂²×C₃₁	1	2	yes	complemented
677	#469	C₂²×C₃₁	1	2	yes	complemented
678	#469	C₂²×C₃₁	1	2	yes	complemented
679	#468	C₂²×C₃₁	1	2	yes	complemented
680	#468	C₂²×C₃₁	1	2	yes	complemented
681	#468	C₂²×C₃₁	1	2	yes	complemented
682	#468	C₂²×C₃₁	1	2	yes	complemented
683	#464	C₂²×C₃₁	1	2	yes	complemented
684	#463	C₂²×C₃₁	1	2	yes	complemented
685	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#452	C₂²×C₃₁	1	2	yes	complemented
690	#452	C₂²×C₃₁	1	2	yes	complemented
691	#451	C₂²×C₃₁	1	2	yes	complemented
692	#450	C₂²×C₃₁	1	2	yes	complemented
693	#449	C₂²×C₃₁	1	2	yes	complemented
694	#449	C₂²×C₃₁	1	2	yes	complemented
695	#448	C₂²×C₃₁	1	2	yes	complemented
696	#447	C₂²×C₃₁	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#436	C₂²×C₃₁	1	1	yes	characteristic
706	#436	C₂²×C₃₁	1	1	yes	characteristic
707	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#436	C₂²×C₃₁	1	2	yes	complemented
710	#436	C₂²×C₃₁	1	2	yes	complemented
711	#427	C₂²×C₃₁	1	2	yes	complemented
712	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#419	C₂²×C₃₁	1	2	yes	complemented
715	#419	C₂²×C₃₁	1	2	yes	complemented
716	#418	C₂²×C₃₁	1	2	yes	complemented
717	#418	C₂²×C₃₁	1	2	yes	complemented
718	#417	C₂²×C₃₁	1	2	yes	complemented
719	#417	C₂²×C₃₁	1	2	yes	complemented
720	#417	C₂²×C₃₁	1	2	yes	complemented
721	#417	C₂²×C₃₁	1	2	yes	complemented
722	#416	C₂²×C₃₁	1	2	yes	—
723	#416	C₂²×C₃₁	1	1	yes	characteristic
724	#416	C₂²×C₃₁	1	2	yes	complemented
725	#416	C₂²×C₃₁	1	2	yes	complemented
726	#416	C₂²×C₃₁	1	2	yes	complemented
727	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
729	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	C₂×C₃₁	—	2	2	no	—
731	C₂×C₃₁	—	4	2	no	—
732	C₂×C₃₁	—	4	2	no	—
733	C₂×C₃₁	—	4	2	no	—
734	C₂×C₃₁	—	8	1	no	—
735	C₂×C₃₁	—	8	2	no	—
736	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
737	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
738	C₂×C₃₁	#3584	1	1	yes	characteristic
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	2	no	—
741	C₂×#41	—	2	2	no	—
742	C₂×#41	—	2	8	no	—
743	C₂×#41	—	4	4	no	—
744	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×#41	C₂³×C₃₁	1	2	yes	—
746	C₂×#41	C₂³×C₃₁	1	2	yes	—
747	C₂×#41	C₂³×C₃₁	1	2	yes	—
748	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
749	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
750	C₂²×D₄	—	2	2	no	—
751	C₂²×D₄	—	2	1	no	—
752	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
753	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
754	C₂³×C₄	—	2	2	no	—
755	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
756	#135	—	2	4	no	—
757	#135	—	4	4	no	—
758	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
764	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₂×D₈	C₂³×C₃₁	1	2	yes	—
766	C₂×M₁₆	—	4	4	no	—
767	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
768	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
769	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
770	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
771	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
773	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	#127	—	2	1	no	—
779	#127	C₂³×C₃₁	1	1	yes	characteristic
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#125	—	2	2	no	—
784	#125	—	2	1	no	—
785	#125	C₂³×C₃₁	1	2	yes	—
786	#124	—	2	1	no	—
787	#124	—	2	2	no	—
788	#124	—	2	2	no	—
789	#124	C₂³×C₃₁	1	2	yes	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	C₂³×C₃₁	1	2	yes	—
817	#121	C₂³×C₃₁	1	2	yes	—
818	#121	C₂³×C₃₁	1	2	yes	—
819	#121	C₂³×C₃₁	1	2	yes	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	—	2	1	no	—
827	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
847	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
848	C₄×D₄	D₄×C₃₁	1	2	yes	—
849	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₃₁	1	2	yes	—
855	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
856	#117	—	2	2	no	—
857	#117	—	2	2	no	—
858	#117	—	2	1	no	—
859	#117	—	2	2	no	—
860	#117	—	2	1	no	—
861	#117	—	2	1	no	—
862	#117	C₂³×C₃₁	1	1	yes	characteristic
863	#117	C₂³×C₃₁	1	2	yes	—
864	#117	C₂³×C₃₁	1	2	yes	—
865	#117	C₂³×C₃₁	1	2	yes	—
866	#117	C₂³×C₃₁	1	1	yes	characteristic
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
870	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
871	C₂×C₂²⋊C₄	—	2	2	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
874	C₂×C₄²	—	2	2	no	—
875	C₂×C₄²	—	2	1	no	—
876	C₂×C₄²	—	2	1	no	—
877	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
878	#107	C₂³×C₃₁	1	1	yes	characteristic
879	#107	C₂³×C₃₁	1	1	yes	characteristic
880	#107	C₂³×C₃₁	1	2	yes	—
881	#107	C₂³×C₃₁	1	2	yes	—
882	#106	C₂³×C₃₁	1	1	yes	characteristic
883	#106	C₂³×C₃₁	1	1	yes	characteristic
884	#106	C₂³×C₃₁	1	2	yes	—
885	#106	C₂³×C₃₁	1	2	yes	—
886	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
889	#103	C₂³×C₃₁	1	1	yes	characteristic
890	#103	C₂³×C₃₁	1	1	yes	characteristic
891	#103	C₂³×C₃₁	1	2	yes	—
892	#103	C₂³×C₃₁	1	2	yes	—
893	#103	C₂³×C₃₁	1	2	yes	—
894	#103	C₂³×C₃₁	1	2	yes	—
895	#103	C₂³×C₃₁	1	2	yes	—
896	#103	C₂³×C₃₁	1	2	yes	—
897	#103	C₂³×C₃₁	1	1	yes	characteristic
898	#103	C₂³×C₃₁	1	1	yes	characteristic
899	#103	C₂³×C₃₁	1	2	yes	—
900	#103	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	1	yes	characteristic
902	#102	C₂³×C₃₁	1	1	yes	characteristic
903	#102	C₂³×C₃₁	1	2	yes	—
904	#102	C₂³×C₃₁	1	2	yes	—
905	#102	C₂³×C₃₁	1	2	yes	—
906	#102	C₂³×C₃₁	1	2	yes	—
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	2	yes	—
909	#102	C₂³×C₃₁	1	1	yes	characteristic
910	#102	C₂³×C₃₁	1	1	yes	characteristic
911	#102	C₂³×C₃₁	1	2	yes	—
912	#102	C₂³×C₃₁	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
917	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
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	C₃₁	#61154	1	1	yes	characteristic, direct product factor, Sylow
922	C₂⁴	—	2	2	no	—
923	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
924	#41	—	2	2	no	—
925	#41	—	2	4	no	—
926	#41	—	2	4	no	—
927	#41	—	2	2	no	—
928	#41	—	2	4	no	—
929	#41	—	2	2	no	—
930	#41	—	2	4	no	—
931	#41	—	4	8	no	—
932	#41	—	4	2	no	—
933	#41	—	4	2	no	—
934	#41	—	4	8	no	—
935	#41	—	4	4	no	—
936	#41	#41×C₃₁	1	4	yes	complemented
937	C₂×Q₈	—	2	1	no	—
938	C₂×Q₈	—	2	2	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	4	no	—
941	C₂×Q₈	—	4	2	no	—
942	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
943	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	4	2	no	—
960	C₂×D₄	—	4	8	no	—
961	C₂×D₄	—	4	4	no	—
962	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
963	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
966	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	4	no	—
970	C₂²×C₄	—	2	4	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	4	8	no	—
983	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
988	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
989	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
990	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
991	Q₁₆	—	2	2	no	—
992	Q₁₆	—	4	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	2	no	—
997	D₈	—	2	2	no	—
998	D₈	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	M₁₆	—	4	2	no	—
1001	M₁₆	—	4	2	no	—
1002	M₁₆	—	4	2	no	—
1003	C₂×C₈	—	2	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	4	no	—
1006	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1011	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1034	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1070	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1071	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1072	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	4	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	4	2	no	—
1078	C₂³	—	4	2	no	—
1079	C₂³	—	4	4	no	—
1080	C₂³	—	4	4	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1083	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1084	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1085	Q₈	—	2	1	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	4	4	no	—
1091	Q₈	—	4	2	no	—
1092	Q₈	—	8	1	no	—
1093	Q₈	C₂×#41×C₃₁	1	2	yes	—
1094	D₄	—	2	4	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	1	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	4	2	no	—
1103	D₄	—	4	4	no	—
1104	D₄	—	4	4	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	4	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	8	1	no	—
1112	D₄	—	8	2	no	—
1113	D₄	—	8	2	no	—
1114	D₄	C₂×#41×C₃₁	1	2	yes	—
1115	C₂×C₄	—	2	4	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	4	no	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	4	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	4	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1146	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1147	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1148	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1150	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1152	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1153	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1154	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	2	no	—
1160	C₈	—	2	2	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	8	4	no	—
1179	C₂²	—	8	8	no	—
1180	C₂²	C₃₁×#546	1	2	yes	—
1181	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	1	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	C₃₁×#546	1	2	yes	—
1197	C₄	C₃₁×#575	1	2	yes	—
1198	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1199	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1200	C₂	—	2	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	8	2	no	—
1205	C₂	—	8	1	no	—
1206	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
1207	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1208	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3333	C₂	semidirect
4. C₃₁×#3332	C₂	semidirect
5. C₃₁×#3331	C₂	semidirect
6. C₃₁×#3330	C₂	semidirect
7. C₃₁×#3329	C₂	semidirect
8. C₃₁×#3328	C₂	semidirect
9. C₃₁×#3327	C₂	semidirect
10. C₃₁×#3326	C₂	semidirect
11. C₃₁×#3325	C₂	semidirect
12. C₃₁×#3324	C₂	semidirect
13. C₃₁×#3323	C₂	semidirect
14. C₃₁×#3322	C₂	semidirect
15. C₃₁×#3131	C₂	semidirect
16. C₃₁×#3091	C₂	semidirect
17. C₃₁×#3076	C₂	semidirect
18. C₃₁×#3054	C₂	semidirect
19. C₃₁×#3035	C₂	semidirect
20. C₃₁×#3002	C₂	semidirect
21. C₄×C₃₁×#135	C₂	semidirect
22. C₂×C₃₁×#436	C₂	semidirect
23. C₃₁×#2896	C₂	semidirect
26. C₂×C₃₁×#135	C₂²	semidirect
27. C₂²×M₁₆×C₃₁	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
33. C₃₁×#552	C₂²	semidirect
40. C₃₁×#547	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
53. C₃₁×#525	C₂²	semidirect
56. C₄×#41×C₃₁	C₂²	semidirect
59. C₂×C₃₁×#117	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#488	C₂²	semidirect
62. C₃₁×#487	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
79. C₃₁×#474	C₂²	semidirect
80. C₃₁×#470	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
82. C₃₁×#469	C₂²	semidirect
83. C₃₁×#469	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#468	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#461	C₂²	semidirect
92. C₃₁×#460	C₂²	semidirect
93. C₃₁×#459	C₂²	semidirect
94. C₃₁×#452	C₂²	semidirect
95. C₃₁×#452	C₂²	semidirect
96. C₃₁×#451	C₂²	semidirect
97. C₃₁×#450	C₂²	semidirect
98. C₃₁×#449	C₂²	semidirect
99. C₃₁×#449	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#447	C₂²	semidirect
102. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₄×Q₁₆×C₃₁	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₄×SD₁₆×C₃₁	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₄×D₈×C₃₁	C₂²	semidirect
109. C₄×D₈×C₃₁	C₂²	semidirect
112. C₃₁×#436	C₂²	semidirect
113. C₃₁×#436	C₂²	semidirect
114. C₃₁×#436	C₂²	semidirect
115. C₃₁×#436	C₂²	semidirect
116. C₃₁×#427	C₂²	semidirect
117. C₃₁×#427	C₂²	semidirect
118. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
119. C₃₁×#419	C₂²	semidirect
120. C₃₁×#419	C₂²	semidirect
121. C₃₁×#418	C₂²	semidirect
122. C₃₁×#418	C₂²	semidirect
123. C₃₁×#417	C₂²	semidirect
124. C₃₁×#417	C₂²	semidirect
125. C₃₁×#417	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
132. C₃₁×#416	C₂²	semidirect
133. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
331. #41×C₃₁	#41	semidirect
468. #61154	C₃₁	direct (N × H)
557. #3475	C₂×C₃₁	semidirect
558. D₄×#41	C₂×C₃₁	semidirect
559. #3333	C₂×C₃₁	semidirect
560. #3332	C₂×C₃₁	semidirect
561. #3331	C₂×C₃₁	semidirect
562. #3330	C₂×C₃₁	semidirect
563. #3329	C₂×C₃₁	semidirect
564. #3328	C₂×C₃₁	semidirect
565. #3327	C₂×C₃₁	semidirect
566. #3326	C₂×C₃₁	semidirect
567. #3325	C₂×C₃₁	semidirect
568. #3324	C₂×C₃₁	semidirect
569. #3323	C₂×C₃₁	semidirect
570. #3322	C₂×C₃₁	semidirect
571. #3131	C₂×C₃₁	semidirect
572. #3091	C₂×C₃₁	semidirect
573. #3076	C₂×C₃₁	semidirect
574. #3054	C₂×C₃₁	semidirect
575. #3035	C₂×C₃₁	semidirect
576. #3002	C₂×C₃₁	semidirect
577. C₄×#135	C₂×C₃₁	semidirect
578. C₂×#436	C₂×C₃₁	semidirect
579. #2896	C₂×C₃₁	semidirect
621. C₂×#135	C₂²×C₃₁	semidirect
622. C₂²×M₁₆	C₂²×C₃₁	semidirect
625. #554	C₂²×C₃₁	semidirect
626. #553	C₂²×C₃₁	semidirect
628. #552	C₂²×C₃₁	semidirect
635. #547	C₂²×C₃₁	semidirect
641. #533	C₂²×C₃₁	semidirect
648. #525	C₂²×C₃₁	semidirect
651. C₄×#41	C₂²×C₃₁	semidirect
654. C₂×#117	C₂²×C₃₁	semidirect
655. #488	C₂²×C₃₁	semidirect
656. #488	C₂²×C₃₁	semidirect
657. #487	C₂²×C₃₁	semidirect
658. #487	C₂²×C₃₁	semidirect
659. #486	C₂²×C₃₁	semidirect
660. #486	C₂²×C₃₁	semidirect
661. #485	C₂²×C₃₁	semidirect
662. #485	C₂²×C₃₁	semidirect
663. #484	C₂²×C₃₁	semidirect
664. #483	C₂²×C₃₁	semidirect
665. #482	C₂²×C₃₁	semidirect
666. #482	C₂²×C₃₁	semidirect
667. #481	C₂²×C₃₁	semidirect
668. #480	C₂²×C₃₁	semidirect
669. #479	C₂²×C₃₁	semidirect
670. #478	C₂²×C₃₁	semidirect
671. #477	C₂²×C₃₁	semidirect
672. #476	C₂²×C₃₁	semidirect
673. #475	C₂²×C₃₁	semidirect
674. #474	C₂²×C₃₁	semidirect
675. #470	C₂²×C₃₁	semidirect
676. #470	C₂²×C₃₁	semidirect
677. #469	C₂²×C₃₁	semidirect
678. #469	C₂²×C₃₁	semidirect
679. #468	C₂²×C₃₁	semidirect
680. #468	C₂²×C₃₁	semidirect
681. #468	C₂²×C₃₁	semidirect
682. #468	C₂²×C₃₁	semidirect
683. #464	C₂²×C₃₁	semidirect
684. #463	C₂²×C₃₁	semidirect
685. #462	C₂²×C₃₁	semidirect
686. #461	C₂²×C₃₁	semidirect
687. #460	C₂²×C₃₁	semidirect
688. #459	C₂²×C₃₁	semidirect
689. #452	C₂²×C₃₁	semidirect
690. #452	C₂²×C₃₁	semidirect
691. #451	C₂²×C₃₁	semidirect
692. #450	C₂²×C₃₁	semidirect
693. #449	C₂²×C₃₁	semidirect
694. #449	C₂²×C₃₁	semidirect
695. #448	C₂²×C₃₁	semidirect
696. #447	C₂²×C₃₁	semidirect
697. C₄×Q₁₆	C₂²×C₃₁	semidirect
698. C₄×Q₁₆	C₂²×C₃₁	semidirect
699. C₄×SD₁₆	C₂²×C₃₁	semidirect
700. C₄×SD₁₆	C₂²×C₃₁	semidirect
701. C₄×SD₁₆	C₂²×C₃₁	semidirect
702. C₄×SD₁₆	C₂²×C₃₁	semidirect
703. C₄×D₈	C₂²×C₃₁	semidirect
704. C₄×D₈	C₂²×C₃₁	semidirect
707. #436	C₂²×C₃₁	semidirect
708. #436	C₂²×C₃₁	semidirect
709. #436	C₂²×C₃₁	semidirect
710. #436	C₂²×C₃₁	semidirect
711. #427	C₂²×C₃₁	semidirect
712. #427	C₂²×C₃₁	semidirect
713. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
714. #419	C₂²×C₃₁	semidirect
715. #419	C₂²×C₃₁	semidirect
716. #418	C₂²×C₃₁	semidirect
717. #418	C₂²×C₃₁	semidirect
718. #417	C₂²×C₃₁	semidirect
719. #417	C₂²×C₃₁	semidirect
720. #417	C₂²×C₃₁	semidirect
721. #417	C₂²×C₃₁	semidirect
724. #416	C₂²×C₃₁	semidirect
725. #416	C₂²×C₃₁	semidirect
726. #416	C₂²×C₃₁	semidirect
727. #416	C₂²×C₃₁	semidirect
728. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
729. C₂×C₄×C₈	C₂²×C₃₁	semidirect
921. C₃₁	#61154	direct (N × H)
936. #41	#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×#3475	2
D₄×#41×C₃₁	2
C₃₁×#3333	2
C₃₁×#3332	2
C₃₁×#3331	2
C₃₁×#3330	2
C₃₁×#3329	2
C₃₁×#3328	2
C₃₁×#3327	2
C₃₁×#3326	2
C₃₁×#3325	2
C₃₁×#3324	2
C₃₁×#3323	2
C₃₁×#3322	2
C₃₁×#3131	2
C₃₁×#3091	2
C₃₁×#3076	2
C₃₁×#3054	2
C₃₁×#3035	2
C₃₁×#3002	2
C₄×C₃₁×#135	2
C₂×C₃₁×#436	2
C₃₁×#2896	2
#61154	31

Subgroups — C31×#61154 #21517913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61154 #21517913