Subgroups — C₃₁×#61003 #21517762

Order 7936.

1792 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3197	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3194	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3192	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#555	—	2	2	no	—
21	C₃₁×#553	—	2	2	no	—
22	C₃₁×#553	—	2	2	no	—
23	C₃₁×#551	—	2	2	no	—
24	C₃₁×#551	—	2	2	no	—
25	C₃₁×#547	—	2	2	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#546	—	2	2	no	—
28	C₃₁×#544	C₂²	1	2	yes	complemented
29	C₃₁×#542	C₂²	1	2	yes	—
30	C₃₁×#542	C₂²	1	2	yes	—
31	C₃₁×#540	C₂²	1	2	yes	—
32	C₃₁×#540	C₂²	1	2	yes	—
33	C₃₁×#535	C₂²	1	2	yes	complemented
34	C₃₁×#532	C₂²	1	2	yes	complemented
35	C₃₁×#532	C₂²	1	2	yes	complemented
36	C₃₁×#529	C₂²	1	2	yes	complemented
37	C₃₁×#529	C₂²	1	2	yes	complemented
38	C₃₁×#525	C₂²	1	2	yes	—
39	C₂×C₃₁×#121	C₂²	1	2	yes	—
40	C₃₁×#520	C₂²	1	2	yes	complemented
41	C₃₁×#518	C₂²	1	2	yes	complemented
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₃₁×#501	C₂²	1	2	yes	complemented
44	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#496	C₂²	1	2	yes	complemented
47	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#490	C₂²	1	2	yes	complemented
50	C₃₁×#489	C₂²	1	2	yes	complemented
51	C₃₁×#488	C₂²	1	2	yes	complemented
52	C₃₁×#486	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	2	yes	complemented
54	C₃₁×#483	C₂²	1	2	yes	complemented
55	C₃₁×#482	C₂²	1	2	yes	—
56	C₃₁×#482	C₂²	1	2	yes	—
57	C₃₁×#482	C₂²	1	2	yes	complemented
58	C₃₁×#481	C₂²	1	2	yes	—
59	C₃₁×#481	C₂²	1	2	yes	—
60	C₃₁×#480	C₂²	1	2	yes	complemented
61	C₃₁×#479	C₂²	1	2	yes	complemented
62	C₃₁×#478	C₂²	1	2	yes	complemented
63	C₃₁×#478	C₂²	1	2	yes	complemented
64	C₃₁×#478	C₂²	1	2	yes	complemented
65	C₃₁×#476	C₂²	1	2	yes	complemented
66	C₃₁×#476	C₂²	1	2	yes	complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#469	C₂²	1	2	yes	—
71	C₃₁×#469	C₂²	1	1	yes	characteristic
72	C₃₁×#469	C₂²	1	1	yes	characteristic
73	C₃₁×#469	C₂²	1	2	yes	complemented
74	C₃₁×#469	C₂²	1	2	yes	complemented
75	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#468	C₂²	1	2	yes	complemented
77	C₃₁×#468	C₂²	1	2	yes	complemented
78	C₃₁×#468	C₂²	1	2	yes	complemented
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#460	C₂²	1	2	yes	complemented
84	C₃₁×#459	C₂²	1	2	yes	complemented
85	C₃₁×#459	C₂²	1	2	yes	complemented
86	C₃₁×#459	C₂²	1	2	yes	complemented
87	C₃₁×#452	C₂²	1	2	yes	complemented
88	C₃₁×#450	C₂²	1	2	yes	complemented
89	C₃₁×#449	C₂²	1	2	yes	—
90	C₃₁×#449	C₂²	1	2	yes	—
91	C₃₁×#449	C₂²	1	2	yes	complemented
92	C₃₁×#447	C₂²	1	2	yes	—
93	C₃₁×#447	C₂²	1	2	yes	—
94	C₃₁×#447	C₂²	1	2	yes	complemented
95	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#442	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
105	C₃₁×#433	C₂²	1	2	yes	complemented
106	C₃₁×#433	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#433	C₂²	1	2	yes	complemented
109	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#407	C₂²	1	1	yes	characteristic
112	C₃₁×#407	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₃₁	—	2	2	no	—
116	C₂×#41×C₃₁	—	2	2	no	—
117	C₂×#41×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	—	2	2	no	—
119	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×D₈×C₃₁	C₂³	1	2	yes	—
126	C₂×D₈×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
134	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×#127	C₂³	1	2	yes	—
139	C₃₁×#127	C₂³	1	2	yes	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	C₂³	1	2	yes	—
146	C₃₁×#125	C₂³	1	2	yes	—
147	C₃₁×#124	—	2	2	no	—
148	C₃₁×#124	—	2	2	no	—
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	—	2	2	no	—
151	C₃₁×#124	C₂³	1	2	yes	—
152	C₃₁×#124	C₂³	1	2	yes	—
153	C₃₁×#123	—	2	2	no	—
154	C₃₁×#123	—	2	2	no	—
155	C₃₁×#123	—	2	2	no	—
156	C₃₁×#123	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×C₂²⋊Q₈	—	2	2	no	—
163	C₃₁×C₂²⋊Q₈	—	2	2	no	—
164	C₃₁×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×#121	—	2	2	no	—
169	C₃₁×#121	—	2	2	no	—
170	C₃₁×#121	—	2	2	no	—
171	C₃₁×#121	—	2	2	no	—
172	C₃₁×#121	—	2	2	no	—
173	C₃₁×#121	—	2	2	no	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	2	no	—
177	C₃₁×#121	—	2	2	no	—
178	C₃₁×#121	C₂³	1	2	yes	—
179	C₃₁×#121	C₂³	1	2	yes	—
180	C₃₁×#121	C₂³	1	2	yes	—
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#121	C₂³	1	2	yes	—
184	C₃₁×#120	—	2	2	no	—
185	C₃₁×#120	—	2	2	no	—
186	C₃₁×#120	—	2	2	no	—
187	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
188	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	—	2	2	no	—
190	C₄×D₄×C₃₁	—	2	2	no	—
191	C₄×D₄×C₃₁	—	2	2	no	—
192	C₄×D₄×C₃₁	—	2	2	no	—
193	C₄×D₄×C₃₁	—	2	2	no	—
194	C₄×D₄×C₃₁	—	2	2	no	—
195	C₄×D₄×C₃₁	—	2	2	no	—
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	2	no	—
198	C₄×D₄×C₃₁	—	2	2	no	—
199	C₄×D₄×C₃₁	C₂³	1	2	yes	—
200	C₄×D₄×C₃₁	C₂³	1	2	yes	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₄×D₄×C₃₁	C₂³	1	2	yes	—
203	C₄×D₄×C₃₁	C₂³	1	2	yes	—
204	C₄×D₄×C₃₁	C₂³	1	2	yes	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	—	2	2	no	—
207	C₃₁×#117	—	2	2	no	—
208	C₃₁×#117	D₄	1	2	yes	—
209	C₃₁×#117	D₄	1	2	yes	—
210	C₃₁×#117	C₂³	1	2	yes	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₃₁×#117	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
214	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
215	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
217	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
218	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
220	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
222	C₃₁×#107	C₂³	1	2	yes	—
223	C₃₁×#107	C₂³	1	2	yes	—
224	C₃₁×#107	C₂³	1	2	yes	—
225	C₃₁×#106	C₂³	1	2	yes	—
226	C₃₁×#106	C₂³	1	2	yes	—
227	C₃₁×#106	C₂³	1	1	yes	characteristic
228	C₃₁×#106	C₂³	1	1	yes	characteristic
229	C₃₁×#106	C₂³	1	2	yes	—
230	C₃₁×#106	C₂³	1	1	yes	characteristic
231	C₃₁×#106	C₂³	1	1	yes	characteristic
232	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
233	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
234	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
235	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
236	C₃₁×#103	C₂³	1	2	yes	—
237	C₃₁×#103	C₂³	1	2	yes	—
238	C₃₁×#103	C₂³	1	2	yes	—
239	C₃₁×#103	C₂³	1	2	yes	—
240	C₃₁×#102	C₂³	1	2	yes	—
241	C₃₁×#102	C₂³	1	2	yes	—
242	C₃₁×#102	C₂³	1	2	yes	—
243	C₃₁×#102	C₂³	1	2	yes	—
244	C₃₁×#102	C₂³	1	2	yes	—
245	C₃₁×#102	C₂³	1	2	yes	—
246	C₃₁×#102	C₂³	1	2	yes	—
247	C₃₁×#102	C₂³	1	2	yes	—
248	C₃₁×#102	C₂³	1	2	yes	—
249	C₃₁×#102	C₂³	1	2	yes	—
250	C₃₁×#102	C₂³	1	2	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₃₁×#97	C₂³	1	1	yes	characteristic
257	C₃₁×#97	C₂³	1	1	yes	characteristic
258	C₃₁×#97	C₂³	1	2	yes	—
259	C₄×C₈×C₃₁	C₂³	1	2	yes	—
260	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₂⁴×C₃₁	—	2	2	no	—
263	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
264	#41×C₃₁	—	4	2	no	—
265	#41×C₃₁	—	4	2	no	—
266	#41×C₃₁	—	8	4	no	—
267	#41×C₃₁	—	8	4	no	—
268	C₂×Q₈×C₃₁	—	2	2	no	—
269	C₂×Q₈×C₃₁	—	2	2	no	—
270	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
271	C₂×D₄×C₃₁	—	2	2	no	—
272	C₂×D₄×C₃₁	—	2	2	no	—
273	C₂×D₄×C₃₁	—	2	2	no	—
274	C₂×D₄×C₃₁	—	2	2	no	—
275	C₂×D₄×C₃₁	—	2	2	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	4	2	no	—
284	C₂×D₄×C₃₁	—	4	2	no	—
285	C₂×D₄×C₃₁	—	8	4	no	—
286	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
288	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	—	2	2	no	—
297	C₂²×C₄×C₃₁	—	4	1	no	—
298	C₂²×C₄×C₃₁	—	4	1	no	—
299	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	Q₁₆×C₃₁	—	4	1	no	—
306	SD₁₆×C₃₁	—	4	2	no	—
307	SD₁₆×C₃₁	—	4	2	no	—
308	SD₁₆×C₃₁	—	4	2	no	—
309	D₈×C₃₁	—	4	2	no	—
310	D₈×C₃₁	—	4	1	no	—
311	D₈×C₃₁	—	4	1	no	—
312	D₈×C₃₁	—	4	2	no	—
313	D₈×C₃₁	—	4	2	no	—
314	D₈×C₃₁	—	4	1	no	—
315	M₁₆×C₃₁	—	4	1	no	—
316	M₁₆×C₃₁	—	4	1	no	—
317	M₁₆×C₃₁	—	4	1	no	—
318	M₁₆×C₃₁	—	4	1	no	—
319	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
322	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
323	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
341	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	2	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₃₁	C₂×D₄	1	2	yes	—
372	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₄²×C₃₁	C₂⁴	1	2	yes	—
376	#61003	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₃₁	—	2	2	no	—
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	—	2	2	no	—
380	C₂³×C₃₁	—	4	1	no	—
381	C₂³×C₃₁	—	4	2	no	—
382	C₂³×C₃₁	—	4	4	no	—
383	C₂³×C₃₁	—	8	2	no	—
384	C₂³×C₃₁	—	8	2	no	—
385	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
386	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₃₁	—	2	2	no	—
388	Q₈×C₃₁	—	2	2	no	—
389	Q₈×C₃₁	—	8	2	no	—
390	Q₈×C₃₁	—	8	2	no	—
391	D₄×C₃₁	—	2	2	no	—
392	D₄×C₃₁	—	2	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	2	2	no	—
396	D₄×C₃₁	—	2	2	no	—
397	D₄×C₃₁	—	4	4	no	—
398	D₄×C₃₁	—	4	4	no	—
399	D₄×C₃₁	—	4	4	no	—
400	D₄×C₃₁	—	4	4	no	—
401	D₄×C₃₁	—	4	4	no	—
402	D₄×C₃₁	—	8	2	no	—
403	D₄×C₃₁	—	8	2	no	—
404	D₄×C₃₁	—	8	2	no	—
405	D₄×C₃₁	—	8	2	no	—
406	D₄×C₃₁	—	8	2	no	—
407	D₄×C₃₁	—	8	2	no	—
408	D₄×C₃₁	—	8	2	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	4	1	no	—
419	C₂×C₄×C₃₁	—	4	2	no	—
420	C₂×C₄×C₃₁	—	4	2	no	—
421	C₂×C₄×C₃₁	—	4	2	no	—
422	C₂×C₄×C₃₁	—	4	4	no	—
423	C₂×C₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	—	8	2	no	—
425	C₂×C₄×C₃₁	—	8	2	no	—
426	C₂×C₄×C₃₁	—	8	2	no	—
427	C₂×C₄×C₃₁	—	8	2	no	—
428	C₂×C₄×C₃₁	—	8	2	no	—
429	C₂×C₄×C₃₁	—	8	2	no	—
430	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
437	C₈×C₃₁	—	2	1	no	—
438	C₈×C₃₁	—	2	1	no	—
439	C₈×C₃₁	—	2	2	no	—
440	C₈×C₃₁	—	2	2	no	—
441	C₈×C₃₁	—	2	1	no	—
442	C₈×C₃₁	—	2	1	no	—
443	#3494	C₂×C₃₁	1	2	yes	complemented
444	#3256	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3251	C₂×C₃₁	1	2	yes	complemented
447	#3244	C₂×C₃₁	1	2	yes	complemented
448	#3241	C₂×C₃₁	1	2	yes	complemented
449	#3224	C₂×C₃₁	1	2	yes	complemented
450	#3220	C₂×C₃₁	1	2	yes	complemented
451	#3197	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#3194	C₂×C₃₁	1	2	yes	complemented
453	#3192	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#3184	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#3183	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#3171	C₂×C₃₁	1	2	yes	complemented
457	#3125	C₂×C₃₁	1	2	yes	complemented
458	#3122	C₂×C₃₁	1	2	yes	complemented
459	#3119	C₂×C₃₁	1	2	yes	complemented
460	#3118	C₂×C₃₁	1	2	yes	complemented
461	#2921	C₂×C₃₁	1	1	yes	characteristic, complemented
462	C₂²×C₃₁	—	2	2	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	2	no	—
465	C₂²×C₃₁	—	2	2	no	—
466	C₂²×C₃₁	—	2	1	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	—	4	2	no	—
475	C₂²×C₃₁	—	4	2	no	—
476	C₂²×C₃₁	—	8	2	no	—
477	C₂²×C₃₁	—	16	4	no	—
478	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	2	2	no	—
482	C₄×C₃₁	—	2	2	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	2	1	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	—	4	2	no	—
487	C₄×C₃₁	—	4	2	no	—
488	C₄×C₃₁	—	4	2	no	—
489	C₄×C₃₁	—	4	2	no	—
490	C₄×C₃₁	#585	1	1	yes	characteristic
491	C₄×C₃₁	#585	1	1	yes	characteristic
492	#555	—	2	2	no	—
493	#553	—	2	2	no	—
494	#553	—	2	2	no	—
495	#551	—	2	2	no	—
496	#551	—	2	2	no	—
497	#547	—	2	2	no	—
498	#546	—	2	2	no	—
499	#546	—	2	2	no	—
500	#544	C₂²×C₃₁	1	2	yes	complemented
501	#542	C₂²×C₃₁	1	2	yes	—
502	#542	C₂²×C₃₁	1	2	yes	—
503	#540	C₂²×C₃₁	1	2	yes	—
504	#540	C₂²×C₃₁	1	2	yes	—
505	#535	C₂²×C₃₁	1	2	yes	complemented
506	#532	C₂²×C₃₁	1	2	yes	complemented
507	#532	C₂²×C₃₁	1	2	yes	complemented
508	#529	C₂²×C₃₁	1	2	yes	complemented
509	#529	C₂²×C₃₁	1	2	yes	complemented
510	#525	C₂²×C₃₁	1	2	yes	—
511	C₂×#121	C₂²×C₃₁	1	2	yes	—
512	#520	C₂²×C₃₁	1	2	yes	complemented
513	#518	C₂²×C₃₁	1	2	yes	complemented
514	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
515	#501	C₂²×C₃₁	1	2	yes	complemented
516	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
517	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	#496	C₂²×C₃₁	1	2	yes	complemented
519	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	#490	C₂²×C₃₁	1	2	yes	complemented
522	#489	C₂²×C₃₁	1	2	yes	complemented
523	#488	C₂²×C₃₁	1	2	yes	complemented
524	#486	C₂²×C₃₁	1	2	yes	complemented
525	#485	C₂²×C₃₁	1	2	yes	complemented
526	#483	C₂²×C₃₁	1	2	yes	complemented
527	#482	C₂²×C₃₁	1	2	yes	—
528	#482	C₂²×C₃₁	1	2	yes	—
529	#482	C₂²×C₃₁	1	2	yes	complemented
530	#481	C₂²×C₃₁	1	2	yes	—
531	#481	C₂²×C₃₁	1	2	yes	—
532	#480	C₂²×C₃₁	1	2	yes	complemented
533	#479	C₂²×C₃₁	1	2	yes	complemented
534	#478	C₂²×C₃₁	1	2	yes	complemented
535	#478	C₂²×C₃₁	1	2	yes	complemented
536	#478	C₂²×C₃₁	1	2	yes	complemented
537	#476	C₂²×C₃₁	1	2	yes	complemented
538	#476	C₂²×C₃₁	1	2	yes	complemented
539	#475	C₂²×C₃₁	1	2	yes	complemented
540	#474	C₂²×C₃₁	1	2	yes	complemented
541	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
542	#469	C₂²×C₃₁	1	2	yes	—
543	#469	C₂²×C₃₁	1	1	yes	characteristic
544	#469	C₂²×C₃₁	1	1	yes	characteristic
545	#469	C₂²×C₃₁	1	2	yes	complemented
546	#469	C₂²×C₃₁	1	2	yes	complemented
547	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#468	C₂²×C₃₁	1	2	yes	complemented
549	#468	C₂²×C₃₁	1	2	yes	complemented
550	#468	C₂²×C₃₁	1	2	yes	complemented
551	#464	C₂²×C₃₁	1	2	yes	complemented
552	#463	C₂²×C₃₁	1	2	yes	complemented
553	#463	C₂²×C₃₁	1	2	yes	complemented
554	#463	C₂²×C₃₁	1	2	yes	complemented
555	#460	C₂²×C₃₁	1	2	yes	complemented
556	#459	C₂²×C₃₁	1	2	yes	complemented
557	#459	C₂²×C₃₁	1	2	yes	complemented
558	#459	C₂²×C₃₁	1	2	yes	complemented
559	#452	C₂²×C₃₁	1	2	yes	complemented
560	#450	C₂²×C₃₁	1	2	yes	complemented
561	#449	C₂²×C₃₁	1	2	yes	—
562	#449	C₂²×C₃₁	1	2	yes	—
563	#449	C₂²×C₃₁	1	2	yes	complemented
564	#447	C₂²×C₃₁	1	2	yes	—
565	#447	C₂²×C₃₁	1	2	yes	—
566	#447	C₂²×C₃₁	1	2	yes	complemented
567	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#442	C₂²×C₃₁	1	2	yes	complemented
571	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#440	C₂²×C₃₁	1	2	yes	complemented
573	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
574	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
575	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
576	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
577	#433	C₂²×C₃₁	1	2	yes	complemented
578	#433	C₂²×C₃₁	1	2	yes	complemented
579	#433	C₂²×C₃₁	1	2	yes	complemented
580	#433	C₂²×C₃₁	1	2	yes	complemented
581	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#407	C₂²×C₃₁	1	1	yes	characteristic
584	#407	C₂²×C₃₁	1	1	yes	characteristic
585	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	C₂×C₃₁	—	4	1	no	—
588	C₂×C₃₁	—	4	2	no	—
589	C₂×C₃₁	—	8	2	no	—
590	C₂×C₃₁	—	8	2	no	—
591	C₂×C₃₁	—	8	2	no	—
592	C₂×C₃₁	#3449	1	1	yes	characteristic
593	C₂×C₃₁	#3585	1	2	yes	—
594	C₂×#41	—	2	2	no	—
595	C₂×#41	—	2	2	no	—
596	C₂×#41	C₂³×C₃₁	1	2	yes	—
597	C₂²×D₄	—	2	2	no	—
598	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
599	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
601	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
604	C₂×D₈	C₂³×C₃₁	1	2	yes	—
605	C₂×D₈	C₂³×C₃₁	1	2	yes	—
606	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×D₈	C₂³×C₃₁	1	2	yes	—
609	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
616	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
617	#127	C₂³×C₃₁	1	2	yes	—
618	#127	C₂³×C₃₁	1	2	yes	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#125	—	2	2	no	—
624	#125	C₂³×C₃₁	1	2	yes	—
625	#125	C₂³×C₃₁	1	2	yes	—
626	#124	—	2	2	no	—
627	#124	—	2	2	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	C₂³×C₃₁	1	2	yes	—
631	#124	C₂³×C₃₁	1	2	yes	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	C₂³×C₃₁	1	2	yes	—
658	#121	C₂³×C₃₁	1	2	yes	—
659	#121	C₂³×C₃₁	1	2	yes	—
660	#121	C₂³×C₃₁	1	2	yes	—
661	#121	C₂³×C₃₁	1	2	yes	—
662	#121	C₂³×C₃₁	1	2	yes	—
663	#120	—	2	2	no	—
664	#120	—	2	2	no	—
665	#120	—	2	2	no	—
666	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
667	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	C₄×D₄	C₂³×C₃₁	1	2	yes	—
680	C₄×D₄	C₂³×C₃₁	1	2	yes	—
681	C₄×D₄	C₂³×C₃₁	1	2	yes	—
682	C₄×D₄	C₂³×C₃₁	1	2	yes	—
683	C₄×D₄	C₂³×C₃₁	1	2	yes	—
684	#117	—	2	2	no	—
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	D₄×C₃₁	1	2	yes	—
688	#117	D₄×C₃₁	1	2	yes	—
689	#117	C₂³×C₃₁	1	2	yes	—
690	#117	C₂³×C₃₁	1	2	yes	—
691	#117	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄⋊C₄	—	2	2	no	—
693	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₂²⋊C₄	—	2	2	no	—
697	C₂×C₂²⋊C₄	—	2	2	no	—
698	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
699	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
701	#107	C₂³×C₃₁	1	2	yes	—
702	#107	C₂³×C₃₁	1	2	yes	—
703	#107	C₂³×C₃₁	1	2	yes	—
704	#106	C₂³×C₃₁	1	2	yes	—
705	#106	C₂³×C₃₁	1	2	yes	—
706	#106	C₂³×C₃₁	1	1	yes	characteristic
707	#106	C₂³×C₃₁	1	1	yes	characteristic
708	#106	C₂³×C₃₁	1	2	yes	—
709	#106	C₂³×C₃₁	1	1	yes	characteristic
710	#106	C₂³×C₃₁	1	1	yes	characteristic
711	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
712	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
713	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
714	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
715	#103	C₂³×C₃₁	1	2	yes	—
716	#103	C₂³×C₃₁	1	2	yes	—
717	#103	C₂³×C₃₁	1	2	yes	—
718	#103	C₂³×C₃₁	1	2	yes	—
719	#102	C₂³×C₃₁	1	2	yes	—
720	#102	C₂³×C₃₁	1	2	yes	—
721	#102	C₂³×C₃₁	1	2	yes	—
722	#102	C₂³×C₃₁	1	2	yes	—
723	#102	C₂³×C₃₁	1	2	yes	—
724	#102	C₂³×C₃₁	1	2	yes	—
725	#102	C₂³×C₃₁	1	2	yes	—
726	#102	C₂³×C₃₁	1	2	yes	—
727	#102	C₂³×C₃₁	1	2	yes	—
728	#102	C₂³×C₃₁	1	2	yes	—
729	#102	C₂³×C₃₁	1	2	yes	—
730	#102	C₂³×C₃₁	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
735	#97	C₂³×C₃₁	1	1	yes	characteristic
736	#97	C₂³×C₃₁	1	1	yes	characteristic
737	#97	C₂³×C₃₁	1	2	yes	—
738	C₄×C₈	C₂³×C₃₁	1	2	yes	—
739	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₃₁	#61003	1	1	yes	characteristic, direct product factor, Sylow
742	C₂⁴	—	2	2	no	—
743	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	—	8	4	no	—
747	#41	—	8	4	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	2	2	no	—
750	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	8	4	no	—
766	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
767	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	4	1	no	—
778	C₂²×C₄	—	4	1	no	—
779	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	Q₁₆	—	4	1	no	—
786	SD₁₆	—	4	2	no	—
787	SD₁₆	—	4	2	no	—
788	SD₁₆	—	4	2	no	—
789	D₈	—	4	2	no	—
790	D₈	—	4	1	no	—
791	D₈	—	4	1	no	—
792	D₈	—	4	2	no	—
793	D₈	—	4	2	no	—
794	D₈	—	4	1	no	—
795	M₁₆	—	4	1	no	—
796	M₁₆	—	4	1	no	—
797	M₁₆	—	4	1	no	—
798	M₁₆	—	4	1	no	—
799	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
802	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
803	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
817	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
819	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
823	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
851	C₄²	C₂×D₄×C₃₁	1	2	yes	—
852	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
853	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
854	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
855	C₄²	C₂⁴×C₃₁	1	2	yes	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	2	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	8	2	no	—
863	C₂³	—	8	2	no	—
864	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
865	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	8	2	no	—
869	Q₈	—	8	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	D₄	—	8	2	no	—
887	D₄	—	8	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	2	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
913	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
914	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
915	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
916	C₈	—	2	1	no	—
917	C₈	—	2	1	no	—
918	C₈	—	2	2	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	2	no	—
937	C₂²	—	16	4	no	—
938	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	C₃₁×#585	1	1	yes	characteristic
951	C₄	C₃₁×#585	1	1	yes	characteristic
952	C₂	—	4	2	no	—
953	C₂	—	4	1	no	—
954	C₂	—	8	2	no	—
955	C₂	—	8	2	no	—
956	C₂	—	8	2	no	—
957	C₂	C₃₁×#3449	1	1	yes	characteristic
958	C₂	C₃₁×#3585	1	2	yes	—

	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3494	C₂	semidirect
2. C₃₁×#3256	C₂	semidirect
3. C₃₁×#3253	C₂	semidirect
4. C₃₁×#3251	C₂	semidirect
5. C₃₁×#3244	C₂	semidirect
6. C₃₁×#3241	C₂	semidirect
7. C₃₁×#3224	C₂	semidirect
8. C₃₁×#3220	C₂	semidirect
9. C₃₁×#3197	C₂	semidirect
10. C₃₁×#3194	C₂	semidirect
11. C₃₁×#3192	C₂	semidirect
12. C₃₁×#3184	C₂	semidirect
13. C₃₁×#3183	C₂	semidirect
14. C₃₁×#3171	C₂	semidirect
15. C₃₁×#3125	C₂	semidirect
16. C₃₁×#3122	C₂	semidirect
17. C₃₁×#3119	C₂	semidirect
18. C₃₁×#3118	C₂	semidirect
19. C₃₁×#2921	C₂	semidirect
28. C₃₁×#544	C₂²	semidirect
33. C₃₁×#535	C₂²	semidirect
34. C₃₁×#532	C₂²	semidirect
35. C₃₁×#532	C₂²	semidirect
36. C₃₁×#529	C₂²	semidirect
37. C₃₁×#529	C₂²	semidirect
40. C₃₁×#520	C₂²	semidirect
41. C₃₁×#518	C₂²	semidirect
43. C₃₁×#501	C₂²	semidirect
44. C₃₁×#499	C₂²	semidirect
45. C₃₁×#498	C₂²	semidirect
46. C₃₁×#496	C₂²	semidirect
47. C₃₁×#495	C₂²	semidirect
48. C₃₁×#493	C₂²	semidirect
49. C₃₁×#490	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#488	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
57. C₃₁×#482	C₂²	semidirect
60. C₃₁×#480	C₂²	semidirect
61. C₃₁×#479	C₂²	semidirect
62. C₃₁×#478	C₂²	semidirect
63. C₃₁×#478	C₂²	semidirect
64. C₃₁×#478	C₂²	semidirect
65. C₃₁×#476	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#470	C₂²	semidirect
73. C₃₁×#469	C₂²	semidirect
74. C₃₁×#469	C₂²	semidirect
75. C₃₁×#469	C₂²	semidirect
76. C₃₁×#468	C₂²	semidirect
77. C₃₁×#468	C₂²	semidirect
78. C₃₁×#468	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#460	C₂²	semidirect
84. C₃₁×#459	C₂²	semidirect
85. C₃₁×#459	C₂²	semidirect
86. C₃₁×#459	C₂²	semidirect
87. C₃₁×#452	C₂²	semidirect
88. C₃₁×#450	C₂²	semidirect
91. C₃₁×#449	C₂²	semidirect
94. C₃₁×#447	C₂²	semidirect
95. C₃₁×#442	C₂²	semidirect
96. C₃₁×#442	C₂²	semidirect
97. C₃₁×#442	C₂²	semidirect
98. C₃₁×#442	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×SD₁₆×C₃₁	C₂²	semidirect
102. C₄×SD₁₆×C₃₁	C₂²	semidirect
103. C₄×D₈×C₃₁	C₂²	semidirect
104. C₄×D₈×C₃₁	C₂²	semidirect
105. C₃₁×#433	C₂²	semidirect
106. C₃₁×#433	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
108. C₃₁×#433	C₂²	semidirect
109. C₃₁×#423	C₂²	semidirect
110. C₃₁×#423	C₂²	semidirect
113. C₄×M₁₆×C₃₁	C₂²	semidirect
114. C₄×M₁₆×C₃₁	C₂²	semidirect
376. #61003	C₃₁	direct (N × H)
443. #3494	C₂×C₃₁	semidirect
444. #3256	C₂×C₃₁	semidirect
445. #3253	C₂×C₃₁	semidirect
446. #3251	C₂×C₃₁	semidirect
447. #3244	C₂×C₃₁	semidirect
448. #3241	C₂×C₃₁	semidirect
449. #3224	C₂×C₃₁	semidirect
450. #3220	C₂×C₃₁	semidirect
451. #3197	C₂×C₃₁	semidirect
452. #3194	C₂×C₃₁	semidirect
453. #3192	C₂×C₃₁	semidirect
454. #3184	C₂×C₃₁	semidirect
455. #3183	C₂×C₃₁	semidirect
456. #3171	C₂×C₃₁	semidirect
457. #3125	C₂×C₃₁	semidirect
458. #3122	C₂×C₃₁	semidirect
459. #3119	C₂×C₃₁	semidirect
460. #3118	C₂×C₃₁	semidirect
461. #2921	C₂×C₃₁	semidirect
500. #544	C₂²×C₃₁	semidirect
505. #535	C₂²×C₃₁	semidirect
506. #532	C₂²×C₃₁	semidirect
507. #532	C₂²×C₃₁	semidirect
508. #529	C₂²×C₃₁	semidirect
509. #529	C₂²×C₃₁	semidirect
512. #520	C₂²×C₃₁	semidirect
513. #518	C₂²×C₃₁	semidirect
515. #501	C₂²×C₃₁	semidirect
516. #499	C₂²×C₃₁	semidirect
517. #498	C₂²×C₃₁	semidirect
518. #496	C₂²×C₃₁	semidirect
519. #495	C₂²×C₃₁	semidirect
520. #493	C₂²×C₃₁	semidirect
521. #490	C₂²×C₃₁	semidirect
522. #489	C₂²×C₃₁	semidirect
523. #488	C₂²×C₃₁	semidirect
524. #486	C₂²×C₃₁	semidirect
525. #485	C₂²×C₃₁	semidirect
526. #483	C₂²×C₃₁	semidirect
529. #482	C₂²×C₃₁	semidirect
532. #480	C₂²×C₃₁	semidirect
533. #479	C₂²×C₃₁	semidirect
534. #478	C₂²×C₃₁	semidirect
535. #478	C₂²×C₃₁	semidirect
536. #478	C₂²×C₃₁	semidirect
537. #476	C₂²×C₃₁	semidirect
538. #476	C₂²×C₃₁	semidirect
539. #475	C₂²×C₃₁	semidirect
540. #474	C₂²×C₃₁	semidirect
541. #470	C₂²×C₃₁	semidirect
545. #469	C₂²×C₃₁	semidirect
546. #469	C₂²×C₃₁	semidirect
547. #469	C₂²×C₃₁	semidirect
548. #468	C₂²×C₃₁	semidirect
549. #468	C₂²×C₃₁	semidirect
550. #468	C₂²×C₃₁	semidirect
551. #464	C₂²×C₃₁	semidirect
552. #463	C₂²×C₃₁	semidirect
553. #463	C₂²×C₃₁	semidirect
554. #463	C₂²×C₃₁	semidirect
555. #460	C₂²×C₃₁	semidirect
556. #459	C₂²×C₃₁	semidirect
557. #459	C₂²×C₃₁	semidirect
558. #459	C₂²×C₃₁	semidirect
559. #452	C₂²×C₃₁	semidirect
560. #450	C₂²×C₃₁	semidirect
563. #449	C₂²×C₃₁	semidirect
566. #447	C₂²×C₃₁	semidirect
567. #442	C₂²×C₃₁	semidirect
568. #442	C₂²×C₃₁	semidirect
569. #442	C₂²×C₃₁	semidirect
570. #442	C₂²×C₃₁	semidirect
571. #441	C₂²×C₃₁	semidirect
572. #440	C₂²×C₃₁	semidirect
573. C₄×SD₁₆	C₂²×C₃₁	semidirect
574. C₄×SD₁₆	C₂²×C₃₁	semidirect
575. C₄×D₈	C₂²×C₃₁	semidirect
576. C₄×D₈	C₂²×C₃₁	semidirect
577. #433	C₂²×C₃₁	semidirect
578. #433	C₂²×C₃₁	semidirect
579. #433	C₂²×C₃₁	semidirect
580. #433	C₂²×C₃₁	semidirect
581. #423	C₂²×C₃₁	semidirect
582. #423	C₂²×C₃₁	semidirect
585. C₄×M₁₆	C₂²×C₃₁	semidirect
586. C₄×M₁₆	C₂²×C₃₁	semidirect
741. C₃₁	#61003	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×#3494	2
C₃₁×#3256	2
C₃₁×#3253	2
C₃₁×#3251	2
C₃₁×#3244	2
C₃₁×#3241	2
C₃₁×#3224	2
C₃₁×#3220	2
C₃₁×#3197	2
C₃₁×#3194	2
C₃₁×#3192	2
C₃₁×#3184	2
C₃₁×#3183	2
C₃₁×#3171	2
C₃₁×#3125	2
C₃₁×#3122	2
C₃₁×#3119	2
C₃₁×#3118	2
C₃₁×#2921	2
#61003	31

Subgroups — C31×#61003 #21517762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61003 #21517762