Subgroups — C₃₁×#61005 #21517764

Order 7936.

1672 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3197	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3195	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3172	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#556	—	2	2	no	—
21	C₃₁×#554	—	2	2	no	—
22	C₃₁×#552	—	2	2	no	—
23	C₃₁×#552	—	2	2	no	—
24	C₃₁×#552	—	2	2	no	—
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#551	—	2	2	no	—
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#544	C₂²	1	2	yes	—
29	C₃₁×#542	C₂²	1	2	yes	—
30	C₃₁×#542	C₂²	1	2	yes	—
31	C₃₁×#541	C₂²	1	2	yes	—
32	C₃₁×#541	C₂²	1	2	yes	—
33	C₃₁×#536	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	2	yes	—
35	C₃₁×#533	C₂²	1	2	yes	—
36	C₃₁×#529	C₂²	1	2	yes	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₃₁×#525	C₂²	1	2	yes	—
39	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₃₁×#520	C₂²	1	2	yes	—
41	C₃₁×#519	C₂²	1	2	yes	—
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×#497	C₂²	1	2	yes	complemented
47	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#491	C₂²	1	2	yes	complemented
50	C₃₁×#489	C₂²	1	2	yes	complemented
51	C₃₁×#488	C₂²	1	2	yes	complemented
52	C₃₁×#487	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	2	yes	—
54	C₃₁×#485	C₂²	1	2	yes	—
55	C₃₁×#485	C₂²	1	2	yes	—
56	C₃₁×#484	C₂²	1	2	yes	—
57	C₃₁×#483	C₂²	1	2	yes	—
58	C₃₁×#483	C₂²	1	2	yes	—
59	C₃₁×#482	C₂²	1	2	yes	—
60	C₃₁×#481	C₂²	1	2	yes	—
61	C₃₁×#479	C₂²	1	2	yes	complemented
62	C₃₁×#479	C₂²	1	2	yes	complemented
63	C₃₁×#479	C₂²	1	2	yes	complemented
64	C₃₁×#478	C₂²	1	2	yes	complemented
65	C₃₁×#477	C₂²	1	2	yes	complemented
66	C₃₁×#476	C₂²	1	2	yes	complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#470	C₂²	1	2	yes	—
70	C₃₁×#470	C₂²	1	2	yes	—
71	C₃₁×#470	C₂²	1	1	yes	characteristic
72	C₃₁×#470	C₂²	1	1	yes	characteristic
73	C₃₁×#470	C₂²	1	2	yes	—
74	C₃₁×#470	C₂²	1	1	yes	characteristic
75	C₃₁×#469	C₂²	1	1	yes	characteristic
76	C₃₁×#468	C₂²	1	2	yes	—
77	C₃₁×#468	C₂²	1	2	yes	—
78	C₃₁×#468	C₂²	1	2	yes	—
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#464	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#462	C₂²	1	2	yes	complemented
84	C₃₁×#462	C₂²	1	2	yes	complemented
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#461	C₂²	1	2	yes	complemented
87	C₃₁×#452	C₂²	1	2	yes	—
88	C₃₁×#452	C₂²	1	2	yes	—
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#451	C₂²	1	2	yes	—
91	C₃₁×#451	C₂²	1	2	yes	—
92	C₃₁×#451	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#448	C₂²	1	2	yes	—
95	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#441	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₃₁×#433	C₂²	1	2	yes	—
106	C₃₁×#433	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	—
108	C₃₁×#433	C₂²	1	2	yes	—
109	C₃₁×#423	C₂²	1	1	yes	characteristic
110	C₃₁×#423	C₂²	1	1	yes	characteristic
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
114	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
132	C₃₁×C₄⋊Q₈	—	2	2	no	—
133	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×#126	—	2	2	no	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
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×#126	—	2	2	no	—
145	C₃₁×#125	—	2	2	no	—
146	C₃₁×#125	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	C₂³	1	2	yes	—
157	C₃₁×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#120	—	2	2	no	—
184	C₄×Q₈×C₃₁	—	2	2	no	—
185	C₄×Q₈×C₃₁	—	2	2	no	—
186	C₄×Q₈×C₃₁	—	2	2	no	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
189	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
190	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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	—	2	2	no	—
200	C₄×D₄×C₃₁	C₂³	1	2	yes	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#117	—	2	2	no	—
203	C₃₁×#117	—	2	2	no	—
204	C₃₁×#117	—	2	2	no	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	—	2	2	no	—
207	C₃₁×#117	—	2	2	no	—
208	C₃₁×#117	—	2	2	no	—
209	C₃₁×#117	D₄	1	2	yes	—
210	C₃₁×#117	D₄	1	2	yes	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₃₁×#117	C₂³	1	2	yes	—
213	C₃₁×#117	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
215	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
216	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
217	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#103	C₂³	1	2	yes	—
245	C₃₁×#103	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	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	C₂×D₄	1	1	yes	characteristic
263	#41×C₃₁	—	4	2	no	—
264	#41×C₃₁	—	4	2	no	—
265	C₂×Q₈×C₃₁	—	2	2	no	—
266	C₂×Q₈×C₃₁	—	2	2	no	—
267	C₂×Q₈×C₃₁	—	2	2	no	—
268	C₂×Q₈×C₃₁	—	4	2	no	—
269	C₂×Q₈×C₃₁	—	4	2	no	—
270	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
272	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	2	no	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	2	no	—
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	4	1	no	—
283	C₂²×C₄×C₃₁	—	4	1	no	—
284	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	Q₁₆×C₃₁	—	4	1	no	—
291	Q₁₆×C₃₁	—	4	2	no	—
292	Q₁₆×C₃₁	—	4	2	no	—
293	Q₁₆×C₃₁	—	4	1	no	—
294	Q₁₆×C₃₁	—	4	2	no	—
295	Q₁₆×C₃₁	—	4	1	no	—
296	SD₁₆×C₃₁	—	4	2	no	—
297	SD₁₆×C₃₁	—	4	2	no	—
298	SD₁₆×C₃₁	—	4	2	no	—
299	D₈×C₃₁	—	4	1	no	—
300	M₁₆×C₃₁	—	4	1	no	—
301	M₁₆×C₃₁	—	4	1	no	—
302	M₁₆×C₃₁	—	4	1	no	—
303	M₁₆×C₃₁	—	4	1	no	—
304	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
307	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
308	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	2	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	2	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₄²×C₃₁	—	2	2	no	—
361	C₄²×C₃₁	—	2	2	no	—
362	C₄²×C₃₁	—	2	2	no	—
363	C₄²×C₃₁	—	2	2	no	—
364	C₄²×C₃₁	—	2	2	no	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₃₁	C₂×D₄	1	2	yes	—
369	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₄²×C₃₁	C₂⁴	1	2	yes	—
373	#61005	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₂³×C₃₁	—	2	2	no	—
375	C₂³×C₃₁	—	4	1	no	—
376	C₂³×C₃₁	—	4	2	no	—
377	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
379	Q₈×C₃₁	—	2	2	no	—
380	Q₈×C₃₁	—	2	2	no	—
381	Q₈×C₃₁	—	2	2	no	—
382	Q₈×C₃₁	—	2	2	no	—
383	Q₈×C₃₁	—	2	2	no	—
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	4	4	no	—
386	Q₈×C₃₁	—	8	2	no	—
387	Q₈×C₃₁	—	8	2	no	—
388	D₄×C₃₁	—	2	2	no	—
389	D₄×C₃₁	—	2	2	no	—
390	D₄×C₃₁	—	4	4	no	—
391	D₄×C₃₁	—	4	4	no	—
392	D₄×C₃₁	—	8	2	no	—
393	C₂×C₄×C₃₁	—	2	1	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	4	1	no	—
405	C₂×C₄×C₃₁	—	4	2	no	—
406	C₂×C₄×C₃₁	—	4	2	no	—
407	C₂×C₄×C₃₁	—	4	2	no	—
408	C₂×C₄×C₃₁	—	4	4	no	—
409	C₂×C₄×C₃₁	—	4	4	no	—
410	C₂×C₄×C₃₁	—	8	2	no	—
411	C₂×C₄×C₃₁	—	8	2	no	—
412	C₂×C₄×C₃₁	—	8	2	no	—
413	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
420	C₈×C₃₁	—	2	1	no	—
421	C₈×C₃₁	—	2	1	no	—
422	C₈×C₃₁	—	2	2	no	—
423	C₈×C₃₁	—	2	2	no	—
424	C₈×C₃₁	—	2	1	no	—
425	C₈×C₃₁	—	2	1	no	—
426	#3495	C₂×C₃₁	1	2	yes	complemented
427	#3256	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
429	#3252	C₂×C₃₁	1	2	yes	complemented
430	#3244	C₂×C₃₁	1	2	yes	complemented
431	#3242	C₂×C₃₁	1	2	yes	complemented
432	#3225	C₂×C₃₁	1	2	yes	complemented
433	#3223	C₂×C₃₁	1	2	yes	complemented
434	#3197	C₂×C₃₁	1	1	yes	characteristic
435	#3196	C₂×C₃₁	1	2	yes	complemented
436	#3195	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3185	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3183	C₂×C₃₁	1	1	yes	characteristic, complemented
439	#3172	C₂×C₃₁	1	2	yes	complemented
440	#3127	C₂×C₃₁	1	2	yes	complemented
441	#3125	C₂×C₃₁	1	2	yes	complemented
442	#3121	C₂×C₃₁	1	2	yes	complemented
443	#3120	C₂×C₃₁	1	2	yes	complemented
444	#2921	C₂×C₃₁	1	1	yes	characteristic, complemented
445	C₂²×C₃₁	—	2	2	no	—
446	C₂²×C₃₁	—	2	2	no	—
447	C₂²×C₃₁	—	2	2	no	—
448	C₂²×C₃₁	—	2	2	no	—
449	C₂²×C₃₁	—	2	1	no	—
450	C₂²×C₃₁	—	4	2	no	—
451	C₂²×C₃₁	—	4	2	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	—	8	2	no	—
454	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₃₁	—	2	2	no	—
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	2	no	—
460	C₄×C₃₁	—	2	1	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	2	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	—	4	2	no	—
468	C₄×C₃₁	#585	1	1	yes	characteristic
469	C₄×C₃₁	#585	1	1	yes	characteristic
470	#556	—	2	2	no	—
471	#554	—	2	2	no	—
472	#552	—	2	2	no	—
473	#552	—	2	2	no	—
474	#552	—	2	2	no	—
475	#552	—	2	2	no	—
476	#551	—	2	2	no	—
477	#551	—	2	2	no	—
478	#544	C₂²×C₃₁	1	2	yes	—
479	#542	C₂²×C₃₁	1	2	yes	—
480	#542	C₂²×C₃₁	1	2	yes	—
481	#541	C₂²×C₃₁	1	2	yes	—
482	#541	C₂²×C₃₁	1	2	yes	—
483	#536	C₂²×C₃₁	1	2	yes	—
484	#533	C₂²×C₃₁	1	2	yes	—
485	#533	C₂²×C₃₁	1	2	yes	—
486	#529	C₂²×C₃₁	1	2	yes	—
487	#529	C₂²×C₃₁	1	2	yes	—
488	#525	C₂²×C₃₁	1	2	yes	—
489	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
490	#520	C₂²×C₃₁	1	2	yes	—
491	#519	C₂²×C₃₁	1	2	yes	—
492	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
493	#501	C₂²×C₃₁	1	2	yes	complemented
494	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
495	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	#497	C₂²×C₃₁	1	2	yes	complemented
497	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
498	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
499	#491	C₂²×C₃₁	1	2	yes	complemented
500	#489	C₂²×C₃₁	1	2	yes	complemented
501	#488	C₂²×C₃₁	1	2	yes	complemented
502	#487	C₂²×C₃₁	1	2	yes	complemented
503	#485	C₂²×C₃₁	1	2	yes	—
504	#485	C₂²×C₃₁	1	2	yes	—
505	#485	C₂²×C₃₁	1	2	yes	—
506	#484	C₂²×C₃₁	1	2	yes	—
507	#483	C₂²×C₃₁	1	2	yes	—
508	#483	C₂²×C₃₁	1	2	yes	—
509	#482	C₂²×C₃₁	1	2	yes	—
510	#481	C₂²×C₃₁	1	2	yes	—
511	#479	C₂²×C₃₁	1	2	yes	complemented
512	#479	C₂²×C₃₁	1	2	yes	complemented
513	#479	C₂²×C₃₁	1	2	yes	complemented
514	#478	C₂²×C₃₁	1	2	yes	complemented
515	#477	C₂²×C₃₁	1	2	yes	complemented
516	#476	C₂²×C₃₁	1	2	yes	complemented
517	#475	C₂²×C₃₁	1	2	yes	complemented
518	#475	C₂²×C₃₁	1	2	yes	complemented
519	#470	C₂²×C₃₁	1	2	yes	—
520	#470	C₂²×C₃₁	1	2	yes	—
521	#470	C₂²×C₃₁	1	1	yes	characteristic
522	#470	C₂²×C₃₁	1	1	yes	characteristic
523	#470	C₂²×C₃₁	1	2	yes	—
524	#470	C₂²×C₃₁	1	1	yes	characteristic
525	#469	C₂²×C₃₁	1	1	yes	characteristic
526	#468	C₂²×C₃₁	1	2	yes	—
527	#468	C₂²×C₃₁	1	2	yes	—
528	#468	C₂²×C₃₁	1	2	yes	—
529	#464	C₂²×C₃₁	1	2	yes	complemented
530	#464	C₂²×C₃₁	1	2	yes	complemented
531	#464	C₂²×C₃₁	1	2	yes	complemented
532	#463	C₂²×C₃₁	1	2	yes	complemented
533	#462	C₂²×C₃₁	1	2	yes	complemented
534	#462	C₂²×C₃₁	1	2	yes	complemented
535	#462	C₂²×C₃₁	1	2	yes	complemented
536	#461	C₂²×C₃₁	1	2	yes	complemented
537	#452	C₂²×C₃₁	1	2	yes	—
538	#452	C₂²×C₃₁	1	2	yes	—
539	#452	C₂²×C₃₁	1	2	yes	—
540	#451	C₂²×C₃₁	1	2	yes	—
541	#451	C₂²×C₃₁	1	2	yes	—
542	#451	C₂²×C₃₁	1	2	yes	—
543	#449	C₂²×C₃₁	1	2	yes	—
544	#448	C₂²×C₃₁	1	2	yes	—
545	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
546	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#441	C₂²×C₃₁	1	2	yes	complemented
549	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	#440	C₂²×C₃₁	1	2	yes	complemented
551	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
552	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
553	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
554	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
555	#433	C₂²×C₃₁	1	2	yes	—
556	#433	C₂²×C₃₁	1	2	yes	—
557	#433	C₂²×C₃₁	1	2	yes	—
558	#433	C₂²×C₃₁	1	2	yes	—
559	#423	C₂²×C₃₁	1	1	yes	characteristic
560	#423	C₂²×C₃₁	1	1	yes	characteristic
561	#407	C₂²×C₃₁	1	1	yes	characteristic
562	#407	C₂²×C₃₁	1	1	yes	characteristic
563	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
564	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
565	C₂×C₃₁	—	4	1	no	—
566	C₂×C₃₁	—	4	2	no	—
567	C₂×C₃₁	—	8	2	no	—
568	C₂×C₃₁	#3449	1	1	yes	characteristic
569	C₂×C₃₁	#3586	1	2	yes	—
570	C₂×#41	C₂³×C₃₁	1	2	yes	—
571	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
572	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
574	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
575	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
577	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
578	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
579	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
582	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
587	C₄⋊Q₈	—	2	2	no	—
588	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#125	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	C₂³×C₃₁	1	2	yes	—
608	#125	C₂³×C₃₁	1	2	yes	—
609	#124	—	2	2	no	—
610	#124	—	2	2	no	—
611	#124	C₂³×C₃₁	1	2	yes	—
612	#124	C₂³×C₃₁	1	2	yes	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
631	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
632	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
633	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
634	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
636	#121	C₂³×C₃₁	1	2	yes	—
637	#121	C₂³×C₃₁	1	2	yes	—
638	#120	—	2	2	no	—
639	C₄×Q₈	—	2	2	no	—
640	C₄×Q₈	—	2	2	no	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	—	2	2	no	—
643	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
644	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
645	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
646	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
647	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
648	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	C₂³×C₃₁	1	2	yes	—
656	C₄×D₄	C₂³×C₃₁	1	2	yes	—
657	#117	—	2	2	no	—
658	#117	—	2	2	no	—
659	#117	—	2	2	no	—
660	#117	—	2	2	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	D₄×C₃₁	1	2	yes	—
665	#117	D₄×C₃₁	1	2	yes	—
666	#117	C₂³×C₃₁	1	2	yes	—
667	#117	C₂³×C₃₁	1	2	yes	—
668	#117	C₂³×C₃₁	1	2	yes	—
669	C₂×C₄⋊C₄	—	2	2	no	—
670	C₂×C₄⋊C₄	—	2	2	no	—
671	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
675	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
677	#107	C₂³×C₃₁	1	2	yes	—
678	#107	C₂³×C₃₁	1	2	yes	—
679	#107	C₂³×C₃₁	1	2	yes	—
680	#106	C₂³×C₃₁	1	2	yes	—
681	#106	C₂³×C₃₁	1	2	yes	—
682	#106	C₂³×C₃₁	1	1	yes	characteristic
683	#106	C₂³×C₃₁	1	1	yes	characteristic
684	#106	C₂³×C₃₁	1	2	yes	—
685	#106	C₂³×C₃₁	1	1	yes	characteristic
686	#106	C₂³×C₃₁	1	1	yes	characteristic
687	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
688	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
689	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
690	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
691	#103	C₂³×C₃₁	1	2	yes	—
692	#103	C₂³×C₃₁	1	2	yes	—
693	#103	C₂³×C₃₁	1	2	yes	—
694	#103	C₂³×C₃₁	1	2	yes	—
695	#103	C₂³×C₃₁	1	2	yes	—
696	#103	C₂³×C₃₁	1	2	yes	—
697	#103	C₂³×C₃₁	1	2	yes	—
698	#103	C₂³×C₃₁	1	2	yes	—
699	#103	C₂³×C₃₁	1	2	yes	—
700	#103	C₂³×C₃₁	1	2	yes	—
701	#103	C₂³×C₃₁	1	2	yes	—
702	#103	C₂³×C₃₁	1	2	yes	—
703	#102	C₂³×C₃₁	1	2	yes	—
704	#102	C₂³×C₃₁	1	2	yes	—
705	#102	C₂³×C₃₁	1	2	yes	—
706	#102	C₂³×C₃₁	1	2	yes	—
707	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
711	#97	C₂³×C₃₁	1	1	yes	characteristic
712	#97	C₂³×C₃₁	1	1	yes	characteristic
713	#97	C₂³×C₃₁	1	2	yes	—
714	C₄×C₈	C₂³×C₃₁	1	2	yes	—
715	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₃₁	#61005	1	1	yes	characteristic, direct product factor, Sylow
718	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
719	#41	—	4	2	no	—
720	#41	—	4	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
728	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
743	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
746	Q₁₆	—	4	1	no	—
747	Q₁₆	—	4	2	no	—
748	Q₁₆	—	4	2	no	—
749	Q₁₆	—	4	1	no	—
750	Q₁₆	—	4	2	no	—
751	Q₁₆	—	4	1	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	D₈	—	4	1	no	—
756	M₁₆	—	4	1	no	—
757	M₁₆	—	4	1	no	—
758	M₁₆	—	4	1	no	—
759	M₁₆	—	4	1	no	—
760	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
763	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
764	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₄²	C₂×D₄×C₃₁	1	2	yes	—
825	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
826	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
827	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₄²	C₂⁴×C₃₁	1	2	yes	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	2	no	—
832	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
833	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	4	4	no	—
841	Q₈	—	8	2	no	—
842	Q₈	—	8	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	8	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
874	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
875	C₈	—	2	1	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	1	no	—
880	C₈	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	2	no	—
890	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	C₃₁×#585	1	1	yes	characteristic
905	C₄	C₃₁×#585	1	1	yes	characteristic
906	C₂	—	4	2	no	—
907	C₂	—	4	1	no	—
908	C₂	—	8	2	no	—
909	C₂	C₃₁×#3449	1	1	yes	characteristic
910	C₂	C₃₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3197	C₂
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×#3495	C₂	semidirect
2. C₃₁×#3256	C₂	semidirect
3. C₃₁×#3255	C₂	semidirect
4. C₃₁×#3252	C₂	semidirect
5. C₃₁×#3244	C₂	semidirect
6. C₃₁×#3242	C₂	semidirect
7. C₃₁×#3225	C₂	semidirect
8. C₃₁×#3223	C₂	semidirect
10. C₃₁×#3196	C₂	semidirect
11. C₃₁×#3195	C₂	semidirect
12. C₃₁×#3185	C₂	semidirect
13. C₃₁×#3183	C₂	semidirect
14. C₃₁×#3172	C₂	semidirect
15. C₃₁×#3127	C₂	semidirect
16. C₃₁×#3125	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₃₁×#2921	C₂	semidirect
43. C₃₁×#501	C₂²	semidirect
44. C₃₁×#499	C₂²	semidirect
45. C₃₁×#498	C₂²	semidirect
46. C₃₁×#497	C₂²	semidirect
47. C₃₁×#495	C₂²	semidirect
48. C₃₁×#494	C₂²	semidirect
49. C₃₁×#491	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#488	C₂²	semidirect
52. C₃₁×#487	C₂²	semidirect
61. C₃₁×#479	C₂²	semidirect
62. C₃₁×#479	C₂²	semidirect
63. C₃₁×#479	C₂²	semidirect
64. C₃₁×#478	C₂²	semidirect
65. C₃₁×#477	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#464	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#462	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#461	C₂²	semidirect
95. C₃₁×#442	C₂²	semidirect
96. C₃₁×#441	C₂²	semidirect
97. C₃₁×#441	C₂²	semidirect
98. C₃₁×#441	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₄×SD₁₆×C₃₁	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
373. #61005	C₃₁	direct (N × H)
426. #3495	C₂×C₃₁	semidirect
427. #3256	C₂×C₃₁	semidirect
428. #3255	C₂×C₃₁	semidirect
429. #3252	C₂×C₃₁	semidirect
430. #3244	C₂×C₃₁	semidirect
431. #3242	C₂×C₃₁	semidirect
432. #3225	C₂×C₃₁	semidirect
433. #3223	C₂×C₃₁	semidirect
435. #3196	C₂×C₃₁	semidirect
436. #3195	C₂×C₃₁	semidirect
437. #3185	C₂×C₃₁	semidirect
438. #3183	C₂×C₃₁	semidirect
439. #3172	C₂×C₃₁	semidirect
440. #3127	C₂×C₃₁	semidirect
441. #3125	C₂×C₃₁	semidirect
442. #3121	C₂×C₃₁	semidirect
443. #3120	C₂×C₃₁	semidirect
444. #2921	C₂×C₃₁	semidirect
493. #501	C₂²×C₃₁	semidirect
494. #499	C₂²×C₃₁	semidirect
495. #498	C₂²×C₃₁	semidirect
496. #497	C₂²×C₃₁	semidirect
497. #495	C₂²×C₃₁	semidirect
498. #494	C₂²×C₃₁	semidirect
499. #491	C₂²×C₃₁	semidirect
500. #489	C₂²×C₃₁	semidirect
501. #488	C₂²×C₃₁	semidirect
502. #487	C₂²×C₃₁	semidirect
511. #479	C₂²×C₃₁	semidirect
512. #479	C₂²×C₃₁	semidirect
513. #479	C₂²×C₃₁	semidirect
514. #478	C₂²×C₃₁	semidirect
515. #477	C₂²×C₃₁	semidirect
516. #476	C₂²×C₃₁	semidirect
517. #475	C₂²×C₃₁	semidirect
518. #475	C₂²×C₃₁	semidirect
529. #464	C₂²×C₃₁	semidirect
530. #464	C₂²×C₃₁	semidirect
531. #464	C₂²×C₃₁	semidirect
532. #463	C₂²×C₃₁	semidirect
533. #462	C₂²×C₃₁	semidirect
534. #462	C₂²×C₃₁	semidirect
535. #462	C₂²×C₃₁	semidirect
536. #461	C₂²×C₃₁	semidirect
545. #442	C₂²×C₃₁	semidirect
546. #441	C₂²×C₃₁	semidirect
547. #441	C₂²×C₃₁	semidirect
548. #441	C₂²×C₃₁	semidirect
549. #441	C₂²×C₃₁	semidirect
550. #440	C₂²×C₃₁	semidirect
551. C₄×Q₁₆	C₂²×C₃₁	semidirect
552. C₄×Q₁₆	C₂²×C₃₁	semidirect
553. C₄×SD₁₆	C₂²×C₃₁	semidirect
554. C₄×SD₁₆	C₂²×C₃₁	semidirect
717. C₃₁	#61005	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×#3495	2
C₃₁×#3256	2
C₃₁×#3255	2
C₃₁×#3252	2
C₃₁×#3244	2
C₃₁×#3242	2
C₃₁×#3225	2
C₃₁×#3223	2
C₃₁×#3197	2
C₃₁×#3196	2
C₃₁×#3195	2
C₃₁×#3185	2
C₃₁×#3183	2
C₃₁×#3172	2
C₃₁×#3127	2
C₃₁×#3125	2
C₃₁×#3121	2
C₃₁×#3120	2
C₃₁×#2921	2
#61005	31

Subgroups — C31×#61005 #21517764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61005 #21517764