Subgroups — C₃₁×#62762 #21519521

Order 7936.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3566	C₂	1	8	yes	maximal, complemented
2	C₃₁×#3565	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3562	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3555	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3554	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3547	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3546	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3540	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3539	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3529	C₂	1	4	yes	maximal, complemented
11	C₃₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3482	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3480	C₂	1	4	yes	maximal, complemented
15	C₃₁×#3475	C₂	1	4	yes	maximal, complemented
16	C₃₁×#3461	C₂	1	4	yes	maximal, complemented
17	C₃₁×#3460	C₂	1	4	yes	maximal, complemented
18	C₃₁×#3455	C₂	1	4	yes	maximal, complemented
19	C₃₁×#3444	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3444	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#563	C₂²	1	8	yes	complemented
22	C₃₁×#563	C₂²	1	4	yes	complemented
23	C₃₁×#562	C₂²	1	8	yes	complemented
24	C₃₁×#562	C₂²	1	8	yes	complemented
25	C₃₁×#562	C₂²	1	8	yes	complemented
26	C₃₁×H(3,𝔽₄)	C₂²	1	4	yes	complemented
27	C₃₁×#560	C₂²	1	8	yes	—
28	C₃₁×#560	C₂²	1	4	yes	complemented
29	C₃₁×#560	C₂²	1	8	yes	complemented
30	C₃₁×#560	C₂²	1	4	yes	complemented
31	C₃₁×#559	C₂²	1	8	yes	complemented
32	C₃₁×#559	C₂²	1	4	yes	complemented
33	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
34	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#557	C₂²	1	4	yes	complemented
36	C₃₁×#557	C₂²	1	2	yes	complemented
37	C₃₁×#556	C₂²	1	4	yes	complemented
38	C₃₁×#556	C₂²	1	4	yes	complemented
39	C₃₁×#556	C₂²	1	8	yes	complemented
40	C₃₁×#556	C₂²	1	4	yes	complemented
41	C₃₁×#556	C₂²	1	2	yes	complemented
42	C₃₁×#555	C₂²	1	4	yes	—
43	C₃₁×#555	C₂²	1	4	yes	complemented
44	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#555	C₂²	1	4	yes	complemented
46	C₃₁×#554	C₂²	1	4	yes	complemented
47	C₃₁×#554	C₂²	1	2	yes	complemented
48	C₃₁×#553	C₂²	1	4	yes	—
49	C₃₁×#553	C₂²	1	8	yes	complemented
50	C₃₁×#553	C₂²	1	4	yes	complemented
51	C₃₁×#553	C₂²	1	8	yes	complemented
52	C₃₁×#553	C₂²	1	4	yes	complemented
53	C₃₁×#553	C₂²	1	8	yes	complemented
54	C₃₁×#552	C₂²	1	4	yes	complemented
55	C₃₁×#552	C₂²	1	4	yes	complemented
56	C₃₁×#552	C₂²	1	8	yes	complemented
57	C₃₁×#552	C₂²	1	4	yes	complemented
58	C₃₁×#552	C₂²	1	8	yes	complemented
59	C₃₁×#551	C₂²	1	8	yes	complemented
60	C₃₁×#551	C₂²	1	8	yes	complemented
61	C₃₁×#551	C₂²	1	4	yes	complemented
62	C₃₁×#550	C₂²	1	4	yes	—
63	C₃₁×#550	C₂²	1	4	yes	complemented
64	C₃₁×#550	C₂²	1	2	yes	complemented
65	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
66	C₃₁×#548	C₂²	1	4	yes	—
67	C₃₁×#548	C₂²	1	4	yes	complemented
68	C₃₁×#548	C₂²	1	4	yes	complemented
69	C₃₁×#547	C₂²	1	4	yes	complemented
70	C₃₁×#547	C₂²	1	4	yes	complemented
71	C₃₁×#547	C₂²	1	2	yes	complemented
72	C₃₁×#546	C₂²	1	4	yes	—
73	C₃₁×#546	C₂²	1	4	yes	—
74	C₃₁×#546	C₂²	1	4	yes	complemented
75	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#544	C₂²	1	4	yes	complemented
77	C₃₁×#544	C₂²	1	4	yes	complemented
78	C₃₁×#542	C₂²	1	4	yes	—
79	C₃₁×#542	C₂²	1	8	yes	complemented
80	C₃₁×#542	C₂²	1	8	yes	complemented
81	C₃₁×#542	C₂²	1	4	yes	complemented
82	C₃₁×#542	C₂²	1	8	yes	complemented
83	C₃₁×#542	C₂²	1	4	yes	complemented
84	C₃₁×#542	C₂²	1	8	yes	complemented
85	C₃₁×#542	C₂²	1	4	yes	complemented
86	C₃₁×#541	C₂²	1	8	yes	complemented
87	C₃₁×#541	C₂²	1	4	yes	complemented
88	C₃₁×#541	C₂²	1	4	yes	complemented
89	C₃₁×#541	C₂²	1	8	yes	complemented
90	C₃₁×#540	C₂²	1	8	yes	complemented
91	C₃₁×#540	C₂²	1	4	yes	complemented
92	C₃₁×#540	C₂²	1	8	yes	complemented
93	C₃₁×#540	C₂²	1	4	yes	complemented
94	C₃₁×#539	C₂²	1	8	yes	complemented
95	C₃₁×#539	C₂²	1	8	yes	complemented
96	C₃₁×#539	C₂²	1	8	yes	complemented
97	C₃₁×#539	C₂²	1	8	yes	complemented
98	C₃₁×#538	C₂²	1	8	yes	complemented
99	C₃₁×#538	C₂²	1	8	yes	complemented
100	C₃₁×#538	C₂²	1	8	yes	complemented
101	C₃₁×#538	C₂²	1	8	yes	complemented
102	C₃₁×#537	C₂²	1	4	yes	—
103	C₃₁×#537	C₂²	1	4	yes	complemented
104	C₃₁×#536	C₂²	1	4	yes	complemented
105	C₃₁×#536	C₂²	1	4	yes	complemented
106	C₃₁×#535	C₂²	1	4	yes	—
107	C₃₁×#535	C₂²	1	4	yes	complemented
108	C₃₁×#533	C₂²	1	2	yes	complemented
109	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#533	C₂²	1	2	yes	complemented
111	C₃₁×#533	C₂²	1	2	yes	complemented
112	C₃₁×#533	C₂²	1	2	yes	complemented
113	C₃₁×#533	C₂²	1	4	yes	complemented
114	C₃₁×#533	C₂²	1	4	yes	complemented
115	C₃₁×#532	C₂²	1	2	yes	—
116	C₃₁×#532	C₂²	1	1	yes	characteristic
117	C₃₁×#532	C₂²	1	2	yes	—
118	C₃₁×#532	C₂²	1	2	yes	—
119	C₃₁×#532	C₂²	1	2	yes	—
120	C₃₁×#532	C₂²	1	4	yes	complemented
121	C₃₁×#532	C₂²	1	4	yes	complemented
122	C₃₁×#532	C₂²	1	8	yes	complemented
123	C₃₁×#529	C₂²	1	2	yes	—
124	C₃₁×#529	C₂²	1	2	yes	—
125	C₃₁×#529	C₂²	1	4	yes	complemented
126	C₃₁×#529	C₂²	1	4	yes	complemented
127	C₃₁×#529	C₂²	1	2	yes	complemented
128	C₃₁×#529	C₂²	1	2	yes	complemented
129	C₃₁×#529	C₂²	1	4	yes	complemented
130	C₃₁×#529	C₂²	1	4	yes	complemented
131	C₃₁×#529	C₂²	1	4	yes	complemented
132	C₃₁×#529	C₂²	1	4	yes	complemented
133	C₃₁×#529	C₂²	1	4	yes	complemented
134	C₃₁×#529	C₂²	1	8	yes	complemented
135	C₃₁×#529	C₂²	1	8	yes	complemented
136	C₃₁×#529	C₂²	1	8	yes	complemented
137	C₃₁×#529	C₂²	1	4	yes	complemented
138	C₃₁×#529	C₂²	1	8	yes	complemented
139	C₃₁×#529	C₂²	1	4	yes	complemented
140	C₃₁×#529	C₂²	1	8	yes	complemented
141	C₃₁×#525	C₂²	1	2	yes	—
142	C₃₁×#525	C₂²	1	4	yes	—
143	C₃₁×#525	C₂²	1	4	yes	complemented
144	C₃₁×#525	C₂²	1	2	yes	complemented
145	C₃₁×#525	C₂²	1	2	yes	complemented
146	C₃₁×#525	C₂²	1	4	yes	complemented
147	C₃₁×#525	C₂²	1	4	yes	complemented
148	C₃₁×#525	C₂²	1	4	yes	complemented
149	C₃₁×#525	C₂²	1	8	yes	complemented
150	C₄×#41×C₃₁	C₂²	1	2	yes	—
151	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
152	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
153	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
154	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
155	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
156	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
157	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
158	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
159	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
160	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
161	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
162	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
163	C₂×#41×C₃₁	C₂³	1	2	yes	—
164	C₂×#41×C₃₁	C₂³	1	2	yes	—
165	C₂×#41×C₃₁	C₂³	1	4	yes	—
166	C₂×#41×C₃₁	C₂³	1	4	yes	—
167	C₂×#41×C₃₁	C₂³	1	4	yes	—
168	C₂×#41×C₃₁	C₂³	1	2	yes	—
169	C₂×#41×C₃₁	C₂³	1	4	yes	—
170	C₂×#41×C₃₁	C₂³	1	4	yes	—
171	C₂×#41×C₃₁	C₂³	1	4	yes	—
172	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
173	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
174	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
175	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
177	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
180	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
183	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
184	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
185	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
186	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
187	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
188	C₃₁×#127	C₂³	1	2	yes	—
189	C₃₁×#127	C₂³	1	1	yes	characteristic
190	C₃₁×#127	C₂³	1	8	yes	—
191	C₃₁×#127	C₂³	1	4	yes	—
192	C₃₁×#127	C₂³	1	4	yes	—
193	C₃₁×#126	C₂³	1	4	yes	—
194	C₃₁×#126	C₂³	1	4	yes	—
195	C₃₁×#126	C₂³	1	8	yes	—
196	C₃₁×#126	C₂³	1	4	yes	—
197	C₃₁×#126	C₂³	1	4	yes	—
198	C₃₁×#126	C₂³	1	8	yes	—
199	C₃₁×#126	C₂³	1	8	yes	—
200	C₃₁×#126	C₂³	1	8	yes	—
201	C₃₁×#126	C₂³	1	8	yes	—
202	C₃₁×#126	C₂³	1	8	yes	—
203	C₃₁×#126	C₂³	1	8	yes	—
204	C₃₁×#126	C₂³	1	8	yes	—
205	C₃₁×#126	C₂³	1	8	yes	—
206	C₃₁×#126	C₂³	1	8	yes	—
207	C₃₁×#126	C₂³	1	8	yes	—
208	C₃₁×#126	C₂³	1	8	yes	—
209	C₃₁×#126	C₂³	1	8	yes	—
210	C₃₁×#125	C₂³	1	2	yes	—
211	C₃₁×#125	C₂³	1	2	yes	—
212	C₃₁×#125	C₂³	1	4	yes	—
213	C₃₁×#125	C₂³	1	4	yes	—
214	C₃₁×#125	C₂³	1	4	yes	—
215	C₃₁×#125	C₂³	1	2	yes	—
216	C₃₁×#125	C₂³	1	8	yes	—
217	C₃₁×#125	C₂³	1	8	yes	—
218	C₃₁×#125	C₂³	1	8	yes	—
219	C₃₁×#125	C₂³	1	4	yes	—
220	C₃₁×#125	C₂³	1	8	yes	—
221	C₃₁×#125	C₂³	1	8	yes	—
222	C₃₁×#125	C₂³	1	4	yes	—
223	C₃₁×#125	C₂³	1	8	yes	—
224	C₃₁×#125	C₂³	1	8	yes	—
225	C₃₁×#124	C₂³	1	2	yes	—
226	C₃₁×#124	C₂³	1	4	yes	—
227	C₃₁×#124	C₂³	1	4	yes	—
228	C₃₁×#124	C₂³	1	4	yes	—
229	C₃₁×#124	C₂³	1	2	yes	—
230	C₃₁×#124	C₂³	1	2	yes	—
231	C₃₁×#124	C₂³	1	8	yes	—
232	C₃₁×#124	C₂³	1	4	yes	—
233	C₃₁×#124	C₂³	1	4	yes	—
234	C₃₁×#124	C₂³	1	8	yes	—
235	C₃₁×#124	C₂³	1	8	yes	—
236	C₃₁×#124	C₂³	1	8	yes	—
237	C₃₁×#124	C₂³	1	8	yes	—
238	C₃₁×#124	C₂³	1	8	yes	—
239	C₃₁×#124	C₂³	1	8	yes	—
240	C₃₁×#124	C₂³	1	8	yes	—
241	C₃₁×#124	C₂³	1	4	yes	—
242	C₃₁×#124	C₂³	1	4	yes	—
243	C₃₁×#123	C₂³	1	4	yes	—
244	C₃₁×#123	C₂³	1	4	yes	—
245	C₃₁×#123	C₂³	1	4	yes	—
246	C₃₁×#123	C₂³	1	4	yes	—
247	C₃₁×#123	C₂³	1	4	yes	—
248	C₃₁×#123	C₂³	1	8	yes	—
249	C₃₁×#123	C₂³	1	4	yes	—
250	C₃₁×#123	C₂³	1	4	yes	—
251	C₃₁×#123	C₂³	1	4	yes	—
252	C₃₁×#123	C₂³	1	4	yes	—
253	C₃₁×#123	C₂³	1	8	yes	—
254	C₃₁×#123	C₂³	1	8	yes	—
255	C₃₁×#123	C₂³	1	8	yes	—
256	C₃₁×#123	C₂³	1	8	yes	—
257	C₃₁×#123	C₂³	1	8	yes	—
258	C₃₁×#123	C₂³	1	8	yes	—
259	C₃₁×#123	C₂³	1	8	yes	—
260	C₃₁×#123	C₂³	1	8	yes	—
261	C₃₁×#123	C₂³	1	8	yes	—
262	C₃₁×#123	C₂³	1	8	yes	—
263	C₃₁×#123	C₂³	1	8	yes	—
264	C₃₁×#123	C₂³	1	8	yes	—
265	C₃₁×#123	C₂³	1	8	yes	—
266	C₃₁×#123	C₂³	1	8	yes	—
267	C₃₁×#123	C₂³	1	8	yes	—
268	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
269	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
271	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
274	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
275	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
276	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
277	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
278	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
279	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
280	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
281	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
282	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
283	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
284	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
285	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
286	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
287	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
288	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
289	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
290	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
291	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
292	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
293	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
294	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
295	C₃₁×#121	C₂³	1	2	yes	—
296	C₃₁×#121	C₂³	1	2	yes	—
297	C₃₁×#121	C₂³	1	8	yes	—
298	C₃₁×#121	C₂³	1	4	yes	—
299	C₃₁×#121	C₂³	1	2	yes	—
300	C₃₁×#121	C₂³	1	4	yes	—
301	C₃₁×#121	C₂³	1	4	yes	—
302	C₃₁×#121	C₂³	1	4	yes	—
303	C₃₁×#121	C₂³	1	2	yes	—
304	C₃₁×#121	C₂³	1	4	yes	—
305	C₃₁×#121	C₂³	1	4	yes	—
306	C₃₁×#121	C₂³	1	4	yes	—
307	C₃₁×#121	C₂³	1	8	yes	—
308	C₃₁×#121	C₂³	1	8	yes	—
309	C₃₁×#121	C₂³	1	8	yes	—
310	C₃₁×#121	C₂³	1	4	yes	—
311	C₃₁×#121	C₂³	1	8	yes	—
312	C₃₁×#121	C₂³	1	8	yes	—
313	C₃₁×#121	C₂³	1	4	yes	—
314	C₃₁×#121	C₂³	1	8	yes	—
315	C₃₁×#121	C₂³	1	8	yes	—
316	C₃₁×#121	C₂³	1	8	yes	—
317	C₃₁×#121	C₂³	1	4	yes	—
318	C₃₁×#121	C₂³	1	8	yes	—
319	C₃₁×#121	C₂³	1	4	yes	—
320	C₃₁×#121	C₂³	1	8	yes	—
321	C₃₁×#121	C₂³	1	8	yes	—
322	C₃₁×#121	C₂³	1	8	yes	—
323	C₃₁×#121	C₂³	1	8	yes	—
324	C₃₁×#121	C₂³	1	8	yes	—
325	C₃₁×#121	C₂³	1	8	yes	—
326	C₃₁×#120	C₂³	1	4	yes	—
327	C₃₁×#120	C₂³	1	4	yes	—
328	C₃₁×#120	C₂³	1	4	yes	—
329	C₃₁×#120	C₂³	1	4	yes	—
330	C₃₁×#120	C₂³	1	4	yes	—
331	C₃₁×#120	C₂³	1	8	yes	—
332	C₃₁×#120	C₂³	1	8	yes	—
333	C₃₁×#120	C₂³	1	8	yes	—
334	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
335	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
336	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
337	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
338	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
339	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
340	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
341	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
342	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
343	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
344	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
345	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
346	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
347	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
348	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
349	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
350	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
351	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
352	C₄×D₄×C₃₁	C₂³	1	2	yes	—
353	C₄×D₄×C₃₁	C₂³	1	4	yes	—
354	C₄×D₄×C₃₁	C₂³	1	8	yes	—
355	C₄×D₄×C₃₁	C₂³	1	4	yes	—
356	C₄×D₄×C₃₁	C₂³	1	4	yes	—
357	C₄×D₄×C₃₁	C₂³	1	8	yes	—
358	C₄×D₄×C₃₁	C₂³	1	4	yes	—
359	C₄×D₄×C₃₁	C₂³	1	4	yes	—
360	C₄×D₄×C₃₁	C₂³	1	2	yes	—
361	C₄×D₄×C₃₁	C₂³	1	2	yes	—
362	C₄×D₄×C₃₁	C₂³	1	4	yes	—
363	C₄×D₄×C₃₁	C₂³	1	4	yes	—
364	C₄×D₄×C₃₁	C₂³	1	4	yes	—
365	C₄×D₄×C₃₁	C₂³	1	4	yes	—
366	C₄×D₄×C₃₁	C₂³	1	8	yes	—
367	C₄×D₄×C₃₁	C₂³	1	8	yes	—
368	C₄×D₄×C₃₁	C₂³	1	4	yes	—
369	C₄×D₄×C₃₁	C₂³	1	4	yes	—
370	C₄×D₄×C₃₁	C₂³	1	4	yes	—
371	C₄×D₄×C₃₁	C₂³	1	8	yes	—
372	C₄×D₄×C₃₁	C₂³	1	8	yes	—
373	C₄×D₄×C₃₁	C₂³	1	4	yes	—
374	C₄×D₄×C₃₁	C₂³	1	4	yes	—
375	C₄×D₄×C₃₁	C₂³	1	4	yes	—
376	C₄×D₄×C₃₁	C₂³	1	8	yes	—
377	C₄×D₄×C₃₁	C₂³	1	4	yes	—
378	C₄×D₄×C₃₁	C₂³	1	4	yes	—
379	C₄×D₄×C₃₁	C₂³	1	4	yes	—
380	C₄×D₄×C₃₁	C₂³	1	4	yes	—
381	C₄×D₄×C₃₁	C₂³	1	4	yes	—
382	C₄×D₄×C₃₁	C₂³	1	2	yes	—
383	C₄×D₄×C₃₁	C₂³	1	4	yes	—
384	C₄×D₄×C₃₁	C₂³	1	8	yes	—
385	C₄×D₄×C₃₁	C₂³	1	8	yes	—
386	C₄×D₄×C₃₁	C₂³	1	8	yes	—
387	C₄×D₄×C₃₁	C₂³	1	8	yes	—
388	C₄×D₄×C₃₁	C₂³	1	4	yes	—
389	C₄×D₄×C₃₁	C₂³	1	8	yes	—
390	C₄×D₄×C₃₁	C₂³	1	4	yes	—
391	C₃₁×#117	C₂³	1	4	yes	—
392	C₃₁×#117	C₂³	1	8	yes	—
393	C₃₁×#117	C₂³	1	8	yes	—
394	C₃₁×#117	C₂³	1	8	yes	—
395	C₃₁×#117	C₂³	1	2	yes	—
396	C₃₁×#117	C₂³	1	4	yes	—
397	C₃₁×#117	C₂³	1	4	yes	—
398	C₃₁×#117	C₂³	1	4	yes	—
399	C₃₁×#117	C₂³	1	2	yes	—
400	C₃₁×#117	C₂³	1	4	yes	—
401	C₃₁×#117	C₂³	1	2	yes	—
402	C₃₁×#117	C₂³	1	4	yes	—
403	C₃₁×#117	C₂³	1	4	yes	—
404	C₃₁×#117	C₂³	1	4	yes	—
405	C₃₁×#117	C₂³	1	4	yes	—
406	C₃₁×#117	C₂³	1	4	yes	—
407	C₃₁×#117	C₂³	1	8	yes	—
408	C₃₁×#117	C₂³	1	4	yes	—
409	C₃₁×#117	C₂³	1	4	yes	—
410	C₃₁×#117	C₂³	1	4	yes	—
411	C₃₁×#117	C₂³	1	8	yes	—
412	C₃₁×#117	C₂³	1	8	yes	—
413	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
414	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
415	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
416	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
417	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
418	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
419	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
421	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
422	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
423	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
424	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
425	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
426	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
427	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
428	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
429	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
430	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
431	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
432	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
433	#41×C₃₁	—	4	8	no	—
434	#41×C₃₁	—	4	4	no	—
435	#41×C₃₁	—	4	8	no	—
436	#41×C₃₁	—	4	8	no	—
437	#41×C₃₁	—	4	4	no	—
438	#41×C₃₁	—	4	8	no	—
439	#41×C₃₁	—	4	4	no	—
440	#41×C₃₁	—	4	8	no	—
441	#41×C₃₁	—	4	8	no	—
442	C₂×Q₈×C₃₁	—	4	8	no	—
443	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
444	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
445	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
446	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
447	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
448	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
449	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
450	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
451	C₂×D₄×C₃₁	—	4	8	no	—
452	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
453	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
454	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
455	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
456	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
457	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
458	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
459	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
460	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
461	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
462	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
463	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
464	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
465	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
466	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
467	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
468	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
469	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
470	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
471	C₂²×C₄×C₃₁	—	4	8	no	—
472	C₂²×C₄×C₃₁	—	4	4	no	—
473	C₂²×C₄×C₃₁	—	4	2	no	—
474	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
475	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
476	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
477	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
478	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
479	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
480	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
482	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
483	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
484	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
485	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
486	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
487	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
488	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
490	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
491	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
492	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
493	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
494	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
495	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
496	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
497	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
498	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
499	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
500	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
501	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
502	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
503	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
504	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
505	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
506	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
507	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
508	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
509	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
510	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
511	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
512	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
513	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
514	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
515	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
516	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
517	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
518	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
519	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
520	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
521	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
522	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
523	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
524	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
525	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
526	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
527	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
528	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
529	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
530	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
531	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
532	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
533	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
534	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
535	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
536	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
537	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
538	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
539	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
540	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
541	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
542	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
543	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
544	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
545	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
546	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
547	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
548	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
549	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
550	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
551	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
552	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
553	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
554	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
555	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
556	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
557	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
558	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
559	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
560	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
561	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
562	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
563	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
564	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
565	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
566	C₄²×C₃₁	C₂⁴	1	2	yes	—
567	C₄²×C₃₁	C₂⁴	1	2	yes	—
568	C₄²×C₃₁	C₂⁴	1	2	yes	—
569	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
570	C₄²×C₃₁	C₂⁴	1	2	yes	—
571	C₄²×C₃₁	C₂⁴	1	2	yes	—
572	C₄²×C₃₁	C₂⁴	1	4	yes	—
573	C₄²×C₃₁	C₂⁴	1	4	yes	—
574	C₄²×C₃₁	C₂⁴	1	8	yes	—
575	C₄²×C₃₁	C₂⁴	1	4	yes	—
576	C₄²×C₃₁	C₂⁴	1	4	yes	—
577	C₄²×C₃₁	C₂⁴	1	4	yes	—
578	C₄²×C₃₁	C₂⁴	1	4	yes	—
579	C₄²×C₃₁	C₂⁴	1	8	yes	—
580	C₄²×C₃₁	C₂⁴	1	8	yes	—
581	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
582	C₄²×C₃₁	C₂⁴	1	2	yes	—
583	C₄²×C₃₁	C₂⁴	1	4	yes	—
584	C₄²×C₃₁	C₂⁴	1	4	yes	—
585	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
586	C₄²×C₃₁	C₂⁴	1	4	yes	—
587	#62762	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
588	C₂³×C₃₁	—	4	2	no	—
589	C₂³×C₃₁	—	4	1	no	—
590	C₂³×C₃₁	—	4	4	no	—
591	C₂³×C₃₁	—	4	8	no	—
592	C₂³×C₃₁	C₂⁵	1	4	yes	—
593	C₂³×C₃₁	C₂⁵	1	2	yes	—
594	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
595	C₂³×C₃₁	C₂⁵	1	4	yes	—
596	C₂³×C₃₁	C₂⁵	1	4	yes	—
597	Q₈×C₃₁	—	2	4	no	—
598	Q₈×C₃₁	—	2	8	no	—
599	Q₈×C₃₁	—	2	4	no	—
600	Q₈×C₃₁	—	4	8	no	—
601	Q₈×C₃₁	—	4	4	no	—
602	Q₈×C₃₁	—	4	4	no	—
603	Q₈×C₃₁	—	4	2	no	—
604	Q₈×C₃₁	—	4	4	no	—
605	D₄×C₃₁	—	2	4	no	—
606	D₄×C₃₁	—	2	8	no	—
607	D₄×C₃₁	—	2	4	no	—
608	D₄×C₃₁	—	4	8	no	—
609	D₄×C₃₁	—	4	4	no	—
610	D₄×C₃₁	—	4	4	no	—
611	D₄×C₃₁	—	4	4	no	—
612	D₄×C₃₁	—	4	4	no	—
613	D₄×C₃₁	—	4	4	no	—
614	D₄×C₃₁	—	4	2	no	—
615	D₄×C₃₁	—	4	4	no	—
616	D₄×C₃₁	—	4	4	no	—
617	D₄×C₃₁	—	4	4	no	—
618	D₄×C₃₁	—	4	8	no	—
619	D₄×C₃₁	—	4	8	no	—
620	D₄×C₃₁	—	4	4	no	—
621	D₄×C₃₁	—	4	8	no	—
622	D₄×C₃₁	—	4	8	no	—
623	D₄×C₃₁	—	4	4	no	—
624	C₂×C₄×C₃₁	—	2	8	no	—
625	C₂×C₄×C₃₁	—	2	4	no	—
626	C₂×C₄×C₃₁	—	2	4	no	—
627	C₂×C₄×C₃₁	—	2	2	no	—
628	C₂×C₄×C₃₁	—	2	4	no	—
629	C₂×C₄×C₃₁	—	2	8	no	—
630	C₂×C₄×C₃₁	—	2	4	no	—
631	C₂×C₄×C₃₁	—	2	8	no	—
632	C₂×C₄×C₃₁	—	2	8	no	—
633	C₂×C₄×C₃₁	—	2	8	no	—
634	C₂×C₄×C₃₁	—	4	2	no	—
635	C₂×C₄×C₃₁	—	4	2	no	—
636	C₂×C₄×C₃₁	—	4	2	no	—
637	C₂×C₄×C₃₁	—	4	4	no	—
638	C₂×C₄×C₃₁	—	4	8	no	—
639	C₂×C₄×C₃₁	—	4	2	no	—
640	C₂×C₄×C₃₁	—	4	1	no	—
641	C₂×C₄×C₃₁	—	4	8	no	—
642	C₂×C₄×C₃₁	—	4	4	no	—
643	C₂×C₄×C₃₁	—	4	8	no	—
644	C₂×C₄×C₃₁	—	4	4	no	—
645	C₂×C₄×C₃₁	—	4	8	no	—
646	C₂×C₄×C₃₁	—	4	8	no	—
647	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
648	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
649	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
650	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
651	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
652	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
653	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
654	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
655	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
656	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
657	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
658	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
659	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
660	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
661	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
662	#3566	C₂×C₃₁	1	8	yes	complemented
663	#3565	C₂×C₃₁	1	4	yes	complemented
664	#3562	C₂×C₃₁	1	4	yes	complemented
665	#3555	C₂×C₃₁	1	2	yes	complemented
666	#3554	C₂×C₃₁	1	2	yes	complemented
667	#3547	C₂×C₃₁	1	2	yes	complemented
668	#3546	C₂×C₃₁	1	2	yes	complemented
669	#3540	C₂×C₃₁	1	4	yes	complemented
670	#3539	C₂×C₃₁	1	4	yes	complemented
671	#3529	C₂×C₃₁	1	4	yes	complemented
672	#3483	C₂×C₃₁	1	1	yes	characteristic, complemented
673	#3482	C₂×C₃₁	1	2	yes	complemented
674	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
675	#3480	C₂×C₃₁	1	4	yes	complemented
676	#3475	C₂×C₃₁	1	4	yes	complemented
677	#3461	C₂×C₃₁	1	4	yes	complemented
678	#3460	C₂×C₃₁	1	4	yes	complemented
679	#3455	C₂×C₃₁	1	4	yes	complemented
680	#3444	C₂×C₃₁	1	2	yes	complemented
681	#3444	C₂×C₃₁	1	1	yes	characteristic, complemented
682	C₂²×C₃₁	—	2	4	no	—
683	C₂²×C₃₁	—	2	4	no	—
684	C₂²×C₃₁	—	2	2	no	—
685	C₂²×C₃₁	—	2	2	no	—
686	C₂²×C₃₁	—	2	2	no	—
687	C₂²×C₃₁	—	2	2	no	—
688	C₂²×C₃₁	—	2	1	no	—
689	C₂²×C₃₁	—	2	4	no	—
690	C₂²×C₃₁	—	2	4	no	—
691	C₂²×C₃₁	—	2	4	no	—
692	C₂²×C₃₁	—	2	4	no	—
693	C₂²×C₃₁	—	2	8	no	—
694	C₂²×C₃₁	—	2	4	no	—
695	C₂²×C₃₁	—	4	4	no	—
696	C₂²×C₃₁	—	8	8	no	—
697	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
698	C₄×C₃₁	—	2	2	no	—
699	C₄×C₃₁	—	2	2	no	—
700	C₄×C₃₁	—	2	4	no	—
701	C₄×C₃₁	—	2	4	no	—
702	C₄×C₃₁	—	2	2	no	—
703	C₄×C₃₁	—	2	4	no	—
704	C₄×C₃₁	—	2	1	no	—
705	C₄×C₃₁	—	2	2	no	—
706	C₄×C₃₁	—	2	4	no	—
707	C₄×C₃₁	—	2	4	no	—
708	C₄×C₃₁	—	2	4	no	—
709	C₄×C₃₁	—	2	8	no	—
710	C₄×C₃₁	—	2	4	no	—
711	C₄×C₃₁	#585	1	2	yes	—
712	C₄×C₃₁	#585	1	4	yes	—
713	#563	C₂²×C₃₁	1	8	yes	complemented
714	#563	C₂²×C₃₁	1	4	yes	complemented
715	#562	C₂²×C₃₁	1	8	yes	complemented
716	#562	C₂²×C₃₁	1	8	yes	complemented
717	#562	C₂²×C₃₁	1	8	yes	complemented
718	H(3,𝔽₄)	C₂²×C₃₁	1	4	yes	complemented
719	#560	C₂²×C₃₁	1	8	yes	—
720	#560	C₂²×C₃₁	1	4	yes	complemented
721	#560	C₂²×C₃₁	1	8	yes	complemented
722	#560	C₂²×C₃₁	1	4	yes	complemented
723	#559	C₂²×C₃₁	1	8	yes	complemented
724	#559	C₂²×C₃₁	1	4	yes	complemented
725	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#557	C₂²×C₃₁	1	4	yes	complemented
728	#557	C₂²×C₃₁	1	2	yes	complemented
729	#556	C₂²×C₃₁	1	4	yes	complemented
730	#556	C₂²×C₃₁	1	4	yes	complemented
731	#556	C₂²×C₃₁	1	8	yes	complemented
732	#556	C₂²×C₃₁	1	4	yes	complemented
733	#556	C₂²×C₃₁	1	2	yes	complemented
734	#555	C₂²×C₃₁	1	4	yes	—
735	#555	C₂²×C₃₁	1	4	yes	complemented
736	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
737	#555	C₂²×C₃₁	1	4	yes	complemented
738	#554	C₂²×C₃₁	1	4	yes	complemented
739	#554	C₂²×C₃₁	1	2	yes	complemented
740	#553	C₂²×C₃₁	1	4	yes	—
741	#553	C₂²×C₃₁	1	8	yes	complemented
742	#553	C₂²×C₃₁	1	4	yes	complemented
743	#553	C₂²×C₃₁	1	8	yes	complemented
744	#553	C₂²×C₃₁	1	4	yes	complemented
745	#553	C₂²×C₃₁	1	8	yes	complemented
746	#552	C₂²×C₃₁	1	4	yes	complemented
747	#552	C₂²×C₃₁	1	4	yes	complemented
748	#552	C₂²×C₃₁	1	8	yes	complemented
749	#552	C₂²×C₃₁	1	4	yes	complemented
750	#552	C₂²×C₃₁	1	8	yes	complemented
751	#551	C₂²×C₃₁	1	8	yes	complemented
752	#551	C₂²×C₃₁	1	8	yes	complemented
753	#551	C₂²×C₃₁	1	4	yes	complemented
754	#550	C₂²×C₃₁	1	4	yes	—
755	#550	C₂²×C₃₁	1	4	yes	complemented
756	#550	C₂²×C₃₁	1	2	yes	complemented
757	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
758	#548	C₂²×C₃₁	1	4	yes	—
759	#548	C₂²×C₃₁	1	4	yes	complemented
760	#548	C₂²×C₃₁	1	4	yes	complemented
761	#547	C₂²×C₃₁	1	4	yes	complemented
762	#547	C₂²×C₃₁	1	4	yes	complemented
763	#547	C₂²×C₃₁	1	2	yes	complemented
764	#546	C₂²×C₃₁	1	4	yes	—
765	#546	C₂²×C₃₁	1	4	yes	—
766	#546	C₂²×C₃₁	1	4	yes	complemented
767	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
768	#544	C₂²×C₃₁	1	4	yes	complemented
769	#544	C₂²×C₃₁	1	4	yes	complemented
770	#542	C₂²×C₃₁	1	4	yes	—
771	#542	C₂²×C₃₁	1	8	yes	complemented
772	#542	C₂²×C₃₁	1	8	yes	complemented
773	#542	C₂²×C₃₁	1	4	yes	complemented
774	#542	C₂²×C₃₁	1	8	yes	complemented
775	#542	C₂²×C₃₁	1	4	yes	complemented
776	#542	C₂²×C₃₁	1	8	yes	complemented
777	#542	C₂²×C₃₁	1	4	yes	complemented
778	#541	C₂²×C₃₁	1	8	yes	complemented
779	#541	C₂²×C₃₁	1	4	yes	complemented
780	#541	C₂²×C₃₁	1	4	yes	complemented
781	#541	C₂²×C₃₁	1	8	yes	complemented
782	#540	C₂²×C₃₁	1	8	yes	complemented
783	#540	C₂²×C₃₁	1	4	yes	complemented
784	#540	C₂²×C₃₁	1	8	yes	complemented
785	#540	C₂²×C₃₁	1	4	yes	complemented
786	#539	C₂²×C₃₁	1	8	yes	complemented
787	#539	C₂²×C₃₁	1	8	yes	complemented
788	#539	C₂²×C₃₁	1	8	yes	complemented
789	#539	C₂²×C₃₁	1	8	yes	complemented
790	#538	C₂²×C₃₁	1	8	yes	complemented
791	#538	C₂²×C₃₁	1	8	yes	complemented
792	#538	C₂²×C₃₁	1	8	yes	complemented
793	#538	C₂²×C₃₁	1	8	yes	complemented
794	#537	C₂²×C₃₁	1	4	yes	—
795	#537	C₂²×C₃₁	1	4	yes	complemented
796	#536	C₂²×C₃₁	1	4	yes	complemented
797	#536	C₂²×C₃₁	1	4	yes	complemented
798	#535	C₂²×C₃₁	1	4	yes	—
799	#535	C₂²×C₃₁	1	4	yes	complemented
800	#533	C₂²×C₃₁	1	2	yes	complemented
801	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
802	#533	C₂²×C₃₁	1	2	yes	complemented
803	#533	C₂²×C₃₁	1	2	yes	complemented
804	#533	C₂²×C₃₁	1	2	yes	complemented
805	#533	C₂²×C₃₁	1	4	yes	complemented
806	#533	C₂²×C₃₁	1	4	yes	complemented
807	#532	C₂²×C₃₁	1	2	yes	—
808	#532	C₂²×C₃₁	1	1	yes	characteristic
809	#532	C₂²×C₃₁	1	2	yes	—
810	#532	C₂²×C₃₁	1	2	yes	—
811	#532	C₂²×C₃₁	1	2	yes	—
812	#532	C₂²×C₃₁	1	4	yes	complemented
813	#532	C₂²×C₃₁	1	4	yes	complemented
814	#532	C₂²×C₃₁	1	8	yes	complemented
815	#529	C₂²×C₃₁	1	2	yes	—
816	#529	C₂²×C₃₁	1	2	yes	—
817	#529	C₂²×C₃₁	1	4	yes	complemented
818	#529	C₂²×C₃₁	1	4	yes	complemented
819	#529	C₂²×C₃₁	1	2	yes	complemented
820	#529	C₂²×C₃₁	1	2	yes	complemented
821	#529	C₂²×C₃₁	1	4	yes	complemented
822	#529	C₂²×C₃₁	1	4	yes	complemented
823	#529	C₂²×C₃₁	1	4	yes	complemented
824	#529	C₂²×C₃₁	1	4	yes	complemented
825	#529	C₂²×C₃₁	1	4	yes	complemented
826	#529	C₂²×C₃₁	1	8	yes	complemented
827	#529	C₂²×C₃₁	1	8	yes	complemented
828	#529	C₂²×C₃₁	1	8	yes	complemented
829	#529	C₂²×C₃₁	1	4	yes	complemented
830	#529	C₂²×C₃₁	1	8	yes	complemented
831	#529	C₂²×C₃₁	1	4	yes	complemented
832	#529	C₂²×C₃₁	1	8	yes	complemented
833	#525	C₂²×C₃₁	1	2	yes	—
834	#525	C₂²×C₃₁	1	4	yes	—
835	#525	C₂²×C₃₁	1	4	yes	complemented
836	#525	C₂²×C₃₁	1	2	yes	complemented
837	#525	C₂²×C₃₁	1	2	yes	complemented
838	#525	C₂²×C₃₁	1	4	yes	complemented
839	#525	C₂²×C₃₁	1	4	yes	complemented
840	#525	C₂²×C₃₁	1	4	yes	complemented
841	#525	C₂²×C₃₁	1	8	yes	complemented
842	C₄×#41	C₂²×C₃₁	1	2	yes	—
843	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
844	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
845	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
846	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
847	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
848	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
849	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
850	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
851	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
852	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
853	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
854	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
855	C₂×C₃₁	—	4	4	no	—
856	C₂×C₃₁	—	4	1	no	—
857	C₂×C₃₁	—	4	2	no	—
858	C₂×C₃₁	—	4	4	no	—
859	C₂×C₃₁	—	4	4	no	—
860	C₂×C₃₁	C₂×#585	1	2	yes	—
861	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
862	C₂×#41	C₂³×C₃₁	1	2	yes	—
863	C₂×#41	C₂³×C₃₁	1	2	yes	—
864	C₂×#41	C₂³×C₃₁	1	4	yes	—
865	C₂×#41	C₂³×C₃₁	1	4	yes	—
866	C₂×#41	C₂³×C₃₁	1	4	yes	—
867	C₂×#41	C₂³×C₃₁	1	2	yes	—
868	C₂×#41	C₂³×C₃₁	1	4	yes	—
869	C₂×#41	C₂³×C₃₁	1	4	yes	—
870	C₂×#41	C₂³×C₃₁	1	4	yes	—
871	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
872	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
873	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
874	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
875	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
876	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
877	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
878	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
879	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
880	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
882	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
883	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
884	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
885	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
886	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
887	#127	C₂³×C₃₁	1	2	yes	—
888	#127	C₂³×C₃₁	1	1	yes	characteristic
889	#127	C₂³×C₃₁	1	8	yes	—
890	#127	C₂³×C₃₁	1	4	yes	—
891	#127	C₂³×C₃₁	1	4	yes	—
892	#126	C₂³×C₃₁	1	4	yes	—
893	#126	C₂³×C₃₁	1	4	yes	—
894	#126	C₂³×C₃₁	1	8	yes	—
895	#126	C₂³×C₃₁	1	4	yes	—
896	#126	C₂³×C₃₁	1	4	yes	—
897	#126	C₂³×C₃₁	1	8	yes	—
898	#126	C₂³×C₃₁	1	8	yes	—
899	#126	C₂³×C₃₁	1	8	yes	—
900	#126	C₂³×C₃₁	1	8	yes	—
901	#126	C₂³×C₃₁	1	8	yes	—
902	#126	C₂³×C₃₁	1	8	yes	—
903	#126	C₂³×C₃₁	1	8	yes	—
904	#126	C₂³×C₃₁	1	8	yes	—
905	#126	C₂³×C₃₁	1	8	yes	—
906	#126	C₂³×C₃₁	1	8	yes	—
907	#126	C₂³×C₃₁	1	8	yes	—
908	#126	C₂³×C₃₁	1	8	yes	—
909	#125	C₂³×C₃₁	1	2	yes	—
910	#125	C₂³×C₃₁	1	2	yes	—
911	#125	C₂³×C₃₁	1	4	yes	—
912	#125	C₂³×C₃₁	1	4	yes	—
913	#125	C₂³×C₃₁	1	4	yes	—
914	#125	C₂³×C₃₁	1	2	yes	—
915	#125	C₂³×C₃₁	1	8	yes	—
916	#125	C₂³×C₃₁	1	8	yes	—
917	#125	C₂³×C₃₁	1	8	yes	—
918	#125	C₂³×C₃₁	1	4	yes	—
919	#125	C₂³×C₃₁	1	8	yes	—
920	#125	C₂³×C₃₁	1	8	yes	—
921	#125	C₂³×C₃₁	1	4	yes	—
922	#125	C₂³×C₃₁	1	8	yes	—
923	#125	C₂³×C₃₁	1	8	yes	—
924	#124	C₂³×C₃₁	1	2	yes	—
925	#124	C₂³×C₃₁	1	4	yes	—
926	#124	C₂³×C₃₁	1	4	yes	—
927	#124	C₂³×C₃₁	1	4	yes	—
928	#124	C₂³×C₃₁	1	2	yes	—
929	#124	C₂³×C₃₁	1	2	yes	—
930	#124	C₂³×C₃₁	1	8	yes	—
931	#124	C₂³×C₃₁	1	4	yes	—
932	#124	C₂³×C₃₁	1	4	yes	—
933	#124	C₂³×C₃₁	1	8	yes	—
934	#124	C₂³×C₃₁	1	8	yes	—
935	#124	C₂³×C₃₁	1	8	yes	—
936	#124	C₂³×C₃₁	1	8	yes	—
937	#124	C₂³×C₃₁	1	8	yes	—
938	#124	C₂³×C₃₁	1	8	yes	—
939	#124	C₂³×C₃₁	1	8	yes	—
940	#124	C₂³×C₃₁	1	4	yes	—
941	#124	C₂³×C₃₁	1	4	yes	—
942	#123	C₂³×C₃₁	1	4	yes	—
943	#123	C₂³×C₃₁	1	4	yes	—
944	#123	C₂³×C₃₁	1	4	yes	—
945	#123	C₂³×C₃₁	1	4	yes	—
946	#123	C₂³×C₃₁	1	4	yes	—
947	#123	C₂³×C₃₁	1	8	yes	—
948	#123	C₂³×C₃₁	1	4	yes	—
949	#123	C₂³×C₃₁	1	4	yes	—
950	#123	C₂³×C₃₁	1	4	yes	—
951	#123	C₂³×C₃₁	1	4	yes	—
952	#123	C₂³×C₃₁	1	8	yes	—
953	#123	C₂³×C₃₁	1	8	yes	—
954	#123	C₂³×C₃₁	1	8	yes	—
955	#123	C₂³×C₃₁	1	8	yes	—
956	#123	C₂³×C₃₁	1	8	yes	—
957	#123	C₂³×C₃₁	1	8	yes	—
958	#123	C₂³×C₃₁	1	8	yes	—
959	#123	C₂³×C₃₁	1	8	yes	—
960	#123	C₂³×C₃₁	1	8	yes	—
961	#123	C₂³×C₃₁	1	8	yes	—
962	#123	C₂³×C₃₁	1	8	yes	—
963	#123	C₂³×C₃₁	1	8	yes	—
964	#123	C₂³×C₃₁	1	8	yes	—
965	#123	C₂³×C₃₁	1	8	yes	—
966	#123	C₂³×C₃₁	1	8	yes	—
967	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
968	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
969	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
970	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
971	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
972	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
973	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
974	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
975	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
976	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
977	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
978	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
979	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
980	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
981	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
982	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
983	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
984	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
985	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
986	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
987	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
988	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
989	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
990	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
991	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
992	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
993	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
994	#121	C₂³×C₃₁	1	2	yes	—
995	#121	C₂³×C₃₁	1	2	yes	—
996	#121	C₂³×C₃₁	1	8	yes	—
997	#121	C₂³×C₃₁	1	4	yes	—
998	#121	C₂³×C₃₁	1	2	yes	—
999	#121	C₂³×C₃₁	1	4	yes	—
1000	#121	C₂³×C₃₁	1	4	yes	—
1001	#121	C₂³×C₃₁	1	4	yes	—
1002	#121	C₂³×C₃₁	1	2	yes	—
1003	#121	C₂³×C₃₁	1	4	yes	—
1004	#121	C₂³×C₃₁	1	4	yes	—
1005	#121	C₂³×C₃₁	1	4	yes	—
1006	#121	C₂³×C₃₁	1	8	yes	—
1007	#121	C₂³×C₃₁	1	8	yes	—
1008	#121	C₂³×C₃₁	1	8	yes	—
1009	#121	C₂³×C₃₁	1	4	yes	—
1010	#121	C₂³×C₃₁	1	8	yes	—
1011	#121	C₂³×C₃₁	1	8	yes	—
1012	#121	C₂³×C₃₁	1	4	yes	—
1013	#121	C₂³×C₃₁	1	8	yes	—
1014	#121	C₂³×C₃₁	1	8	yes	—
1015	#121	C₂³×C₃₁	1	8	yes	—
1016	#121	C₂³×C₃₁	1	4	yes	—
1017	#121	C₂³×C₃₁	1	8	yes	—
1018	#121	C₂³×C₃₁	1	4	yes	—
1019	#121	C₂³×C₃₁	1	8	yes	—
1020	#121	C₂³×C₃₁	1	8	yes	—
1021	#121	C₂³×C₃₁	1	8	yes	—
1022	#121	C₂³×C₃₁	1	8	yes	—
1023	#121	C₂³×C₃₁	1	8	yes	—
1024	#121	C₂³×C₃₁	1	8	yes	—
1025	#120	C₂³×C₃₁	1	4	yes	—
1026	#120	C₂³×C₃₁	1	4	yes	—
1027	#120	C₂³×C₃₁	1	4	yes	—
1028	#120	C₂³×C₃₁	1	4	yes	—
1029	#120	C₂³×C₃₁	1	4	yes	—
1030	#120	C₂³×C₃₁	1	8	yes	—
1031	#120	C₂³×C₃₁	1	8	yes	—
1032	#120	C₂³×C₃₁	1	8	yes	—
1033	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1034	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1035	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
1036	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1037	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1038	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
1039	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1040	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1041	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1042	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1043	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1044	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1045	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1046	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1047	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1048	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1049	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
1050	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
1051	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1052	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1053	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1054	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1055	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1056	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1057	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1058	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1059	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1060	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1061	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1062	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1063	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1064	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1065	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1066	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1067	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1068	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1069	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1070	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1071	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1072	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1073	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1074	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1075	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1076	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1077	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1078	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1079	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1080	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1081	C₄×D₄	C₂³×C₃₁	1	2	yes	—
1082	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1083	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1084	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1085	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1086	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1087	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1088	C₄×D₄	C₂³×C₃₁	1	8	yes	—
1089	C₄×D₄	C₂³×C₃₁	1	4	yes	—
1090	#117	C₂³×C₃₁	1	4	yes	—
1091	#117	C₂³×C₃₁	1	8	yes	—
1092	#117	C₂³×C₃₁	1	8	yes	—
1093	#117	C₂³×C₃₁	1	8	yes	—
1094	#117	C₂³×C₃₁	1	2	yes	—
1095	#117	C₂³×C₃₁	1	4	yes	—
1096	#117	C₂³×C₃₁	1	4	yes	—
1097	#117	C₂³×C₃₁	1	4	yes	—
1098	#117	C₂³×C₃₁	1	2	yes	—
1099	#117	C₂³×C₃₁	1	4	yes	—
1100	#117	C₂³×C₃₁	1	2	yes	—
1101	#117	C₂³×C₃₁	1	4	yes	—
1102	#117	C₂³×C₃₁	1	4	yes	—
1103	#117	C₂³×C₃₁	1	4	yes	—
1104	#117	C₂³×C₃₁	1	4	yes	—
1105	#117	C₂³×C₃₁	1	4	yes	—
1106	#117	C₂³×C₃₁	1	8	yes	—
1107	#117	C₂³×C₃₁	1	4	yes	—
1108	#117	C₂³×C₃₁	1	4	yes	—
1109	#117	C₂³×C₃₁	1	4	yes	—
1110	#117	C₂³×C₃₁	1	8	yes	—
1111	#117	C₂³×C₃₁	1	8	yes	—
1112	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
1113	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
1114	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
1115	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
1116	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
1117	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
1118	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
1119	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
1120	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
1121	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
1122	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
1123	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1124	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
1125	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1126	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
1127	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
1128	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
1129	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
1130	C₃₁	#62762	1	1	yes	characteristic, direct product factor, Sylow
1131	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
1132	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1133	#41	—	4	8	no	—
1134	#41	—	4	4	no	—
1135	#41	—	4	8	no	—
1136	#41	—	4	8	no	—
1137	#41	—	4	4	no	—
1138	#41	—	4	8	no	—
1139	#41	—	4	4	no	—
1140	#41	—	4	8	no	—
1141	#41	—	4	8	no	—
1142	C₂×Q₈	—	4	8	no	—
1143	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1144	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
1145	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1146	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
1147	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
1148	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
1149	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1150	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
1151	C₂×D₄	—	4	8	no	—
1152	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1153	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1154	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1155	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1156	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1157	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1158	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1159	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1160	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1161	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1162	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1163	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1164	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1165	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1166	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1167	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1168	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1169	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1170	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1171	C₂²×C₄	—	4	8	no	—
1172	C₂²×C₄	—	4	4	no	—
1173	C₂²×C₄	—	4	2	no	—
1174	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1175	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1176	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1178	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1179	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1180	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1181	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1182	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1183	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1184	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1185	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1186	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1187	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1188	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1189	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1190	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1191	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1192	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1193	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1194	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1195	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1196	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1197	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1198	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1199	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1200	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1201	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1202	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1203	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1204	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1205	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1206	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1207	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1208	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1209	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1210	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1211	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1212	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1213	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1214	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1215	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1216	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1217	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1218	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1219	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1220	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1221	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1222	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1223	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1224	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1225	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1226	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1227	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1228	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1229	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1230	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1231	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1232	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1233	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1234	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1235	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1236	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1237	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1238	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1239	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1240	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1241	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1242	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1243	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1244	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1245	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1246	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1247	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1248	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1249	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1250	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1251	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1252	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1253	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1254	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1255	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1256	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1257	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1258	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1259	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1260	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1261	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1262	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1263	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1264	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1265	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1266	C₄²	C₂⁴×C₃₁	1	2	yes	—
1267	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1268	C₄²	C₂⁴×C₃₁	1	4	yes	—
1269	C₄²	C₂⁴×C₃₁	1	4	yes	—
1270	C₄²	C₂⁴×C₃₁	1	4	yes	—
1271	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1272	C₄²	C₂⁴×C₃₁	1	2	yes	—
1273	C₄²	C₂⁴×C₃₁	1	2	yes	—
1274	C₄²	C₂⁴×C₃₁	1	2	yes	—
1275	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1276	C₄²	C₂⁴×C₃₁	1	2	yes	—
1277	C₄²	C₂⁴×C₃₁	1	2	yes	—
1278	C₄²	C₂⁴×C₃₁	1	4	yes	—
1279	C₄²	C₂⁴×C₃₁	1	4	yes	—
1280	C₄²	C₂⁴×C₃₁	1	8	yes	—
1281	C₄²	C₂⁴×C₃₁	1	4	yes	—
1282	C₄²	C₂⁴×C₃₁	1	4	yes	—
1283	C₄²	C₂⁴×C₃₁	1	4	yes	—
1284	C₄²	C₂⁴×C₃₁	1	4	yes	—
1285	C₄²	C₂⁴×C₃₁	1	8	yes	—
1286	C₄²	C₂⁴×C₃₁	1	8	yes	—
1287	C₂³	—	4	2	no	—
1288	C₂³	—	4	1	no	—
1289	C₂³	—	4	4	no	—
1290	C₂³	—	4	8	no	—
1291	C₂³	C₂⁵×C₃₁	1	4	yes	—
1292	C₂³	C₂⁵×C₃₁	1	2	yes	—
1293	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1294	C₂³	C₂⁵×C₃₁	1	4	yes	—
1295	C₂³	C₂⁵×C₃₁	1	4	yes	—
1296	Q₈	—	2	4	no	—
1297	Q₈	—	2	8	no	—
1298	Q₈	—	2	4	no	—
1299	Q₈	—	4	8	no	—
1300	Q₈	—	4	4	no	—
1301	Q₈	—	4	4	no	—
1302	Q₈	—	4	2	no	—
1303	Q₈	—	4	4	no	—
1304	D₄	—	2	4	no	—
1305	D₄	—	2	8	no	—
1306	D₄	—	2	4	no	—
1307	D₄	—	4	8	no	—
1308	D₄	—	4	4	no	—
1309	D₄	—	4	4	no	—
1310	D₄	—	4	4	no	—
1311	D₄	—	4	4	no	—
1312	D₄	—	4	4	no	—
1313	D₄	—	4	2	no	—
1314	D₄	—	4	4	no	—
1315	D₄	—	4	4	no	—
1316	D₄	—	4	4	no	—
1317	D₄	—	4	8	no	—
1318	D₄	—	4	8	no	—
1319	D₄	—	4	4	no	—
1320	D₄	—	4	8	no	—
1321	D₄	—	4	8	no	—
1322	D₄	—	4	4	no	—
1323	C₂×C₄	—	2	8	no	—
1324	C₂×C₄	—	2	4	no	—
1325	C₂×C₄	—	2	4	no	—
1326	C₂×C₄	—	2	2	no	—
1327	C₂×C₄	—	2	4	no	—
1328	C₂×C₄	—	2	8	no	—
1329	C₂×C₄	—	2	4	no	—
1330	C₂×C₄	—	2	8	no	—
1331	C₂×C₄	—	2	8	no	—
1332	C₂×C₄	—	2	8	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	4	2	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	4	4	no	—
1337	C₂×C₄	—	4	8	no	—
1338	C₂×C₄	—	4	2	no	—
1339	C₂×C₄	—	4	1	no	—
1340	C₂×C₄	—	4	8	no	—
1341	C₂×C₄	—	4	4	no	—
1342	C₂×C₄	—	4	8	no	—
1343	C₂×C₄	—	4	4	no	—
1344	C₂×C₄	—	4	8	no	—
1345	C₂×C₄	—	4	8	no	—
1346	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1347	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1348	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1349	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1350	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1351	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1352	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1353	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1354	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1355	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
1356	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1357	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1358	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1359	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1360	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1361	C₂²	—	2	4	no	—
1362	C₂²	—	2	4	no	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	2	2	no	—
1366	C₂²	—	2	2	no	—
1367	C₂²	—	2	1	no	—
1368	C₂²	—	2	4	no	—
1369	C₂²	—	2	4	no	—
1370	C₂²	—	2	4	no	—
1371	C₂²	—	2	4	no	—
1372	C₂²	—	2	8	no	—
1373	C₂²	—	2	4	no	—
1374	C₂²	—	4	4	no	—
1375	C₂²	—	8	8	no	—
1376	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1377	C₄	—	2	2	no	—
1378	C₄	—	2	2	no	—
1379	C₄	—	2	4	no	—
1380	C₄	—	2	4	no	—
1381	C₄	—	2	2	no	—
1382	C₄	—	2	4	no	—
1383	C₄	—	2	1	no	—
1384	C₄	—	2	2	no	—
1385	C₄	—	2	4	no	—
1386	C₄	—	2	4	no	—
1387	C₄	—	2	4	no	—
1388	C₄	—	2	8	no	—
1389	C₄	—	2	4	no	—
1390	C₄	C₃₁×#585	1	2	yes	—
1391	C₄	C₃₁×#585	1	4	yes	—
1392	C₂	—	4	1	no	—
1393	C₂	—	4	2	no	—
1394	C₂	—	4	4	no	—
1395	C₂	—	4	4	no	—
1396	C₂	—	4	4	no	—
1397	C₂	C₂×C₃₁×#585	1	2	yes	—
1398	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂²×C₃₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3566	C₂	semidirect
2. C₃₁×#3565	C₂	semidirect
3. C₃₁×#3562	C₂	semidirect
4. C₃₁×#3555	C₂	semidirect
5. C₃₁×#3554	C₂	semidirect
6. C₃₁×#3547	C₂	semidirect
7. C₃₁×#3546	C₂	semidirect
8. C₃₁×#3540	C₂	semidirect
9. C₃₁×#3539	C₂	semidirect
10. C₃₁×#3529	C₂	semidirect
11. C₃₁×#3483	C₂	semidirect
12. C₃₁×#3482	C₂	semidirect
13. C₃₁×#3481	C₂	semidirect
14. C₃₁×#3480	C₂	semidirect
15. C₃₁×#3475	C₂	semidirect
16. C₃₁×#3461	C₂	semidirect
17. C₃₁×#3460	C₂	semidirect
18. C₃₁×#3455	C₂	semidirect
19. C₃₁×#3444	C₂	semidirect
20. C₃₁×#3444	C₂	semidirect
21. C₃₁×#563	C₂²	semidirect
22. C₃₁×#563	C₂²	semidirect
23. C₃₁×#562	C₂²	semidirect
24. C₃₁×#562	C₂²	semidirect
25. C₃₁×#562	C₂²	semidirect
26. C₃₁×H(3,𝔽₄)	C₂²	semidirect
28. C₃₁×#560	C₂²	semidirect
29. C₃₁×#560	C₂²	semidirect
30. C₃₁×#560	C₂²	semidirect
31. C₃₁×#559	C₂²	semidirect
32. C₃₁×#559	C₂²	semidirect
33. C₃₁×#559	C₂²	semidirect
34. Q₈²×C₃₁	C₂²	semidirect
35. C₃₁×#557	C₂²	semidirect
36. C₃₁×#557	C₂²	semidirect
37. C₃₁×#556	C₂²	semidirect
38. C₃₁×#556	C₂²	semidirect
39. C₃₁×#556	C₂²	semidirect
40. C₃₁×#556	C₂²	semidirect
41. C₃₁×#556	C₂²	semidirect
43. C₃₁×#555	C₂²	semidirect
44. C₃₁×#555	C₂²	semidirect
45. C₃₁×#555	C₂²	semidirect
46. C₃₁×#554	C₂²	semidirect
47. C₃₁×#554	C₂²	semidirect
49. C₃₁×#553	C₂²	semidirect
50. C₃₁×#553	C₂²	semidirect
51. C₃₁×#553	C₂²	semidirect
52. C₃₁×#553	C₂²	semidirect
53. C₃₁×#553	C₂²	semidirect
54. C₃₁×#552	C₂²	semidirect
55. C₃₁×#552	C₂²	semidirect
56. C₃₁×#552	C₂²	semidirect
57. C₃₁×#552	C₂²	semidirect
58. C₃₁×#552	C₂²	semidirect
59. C₃₁×#551	C₂²	semidirect
60. C₃₁×#551	C₂²	semidirect
61. C₃₁×#551	C₂²	semidirect
63. C₃₁×#550	C₂²	semidirect
64. C₃₁×#550	C₂²	semidirect
65. D₄×Q₈×C₃₁	C₂²	semidirect
67. C₃₁×#548	C₂²	semidirect
68. C₃₁×#548	C₂²	semidirect
69. C₃₁×#547	C₂²	semidirect
70. C₃₁×#547	C₂²	semidirect
71. C₃₁×#547	C₂²	semidirect
74. C₃₁×#546	C₂²	semidirect
75. D₄²×C₃₁	C₂²	semidirect
76. C₃₁×#544	C₂²	semidirect
77. C₃₁×#544	C₂²	semidirect
79. C₃₁×#542	C₂²	semidirect
80. C₃₁×#542	C₂²	semidirect
81. C₃₁×#542	C₂²	semidirect
82. C₃₁×#542	C₂²	semidirect
83. C₃₁×#542	C₂²	semidirect
84. C₃₁×#542	C₂²	semidirect
85. C₃₁×#542	C₂²	semidirect
86. C₃₁×#541	C₂²	semidirect
87. C₃₁×#541	C₂²	semidirect
88. C₃₁×#541	C₂²	semidirect
89. C₃₁×#541	C₂²	semidirect
90. C₃₁×#540	C₂²	semidirect
91. C₃₁×#540	C₂²	semidirect
92. C₃₁×#540	C₂²	semidirect
93. C₃₁×#540	C₂²	semidirect
94. C₃₁×#539	C₂²	semidirect
95. C₃₁×#539	C₂²	semidirect
96. C₃₁×#539	C₂²	semidirect
97. C₃₁×#539	C₂²	semidirect
98. C₃₁×#538	C₂²	semidirect
99. C₃₁×#538	C₂²	semidirect
100. C₃₁×#538	C₂²	semidirect
101. C₃₁×#538	C₂²	semidirect
103. C₃₁×#537	C₂²	semidirect
104. C₃₁×#536	C₂²	semidirect
105. C₃₁×#536	C₂²	semidirect
107. C₃₁×#535	C₂²	semidirect
108. C₃₁×#533	C₂²	semidirect
109. C₃₁×#533	C₂²	semidirect
110. C₃₁×#533	C₂²	semidirect
111. C₃₁×#533	C₂²	semidirect
112. C₃₁×#533	C₂²	semidirect
113. C₃₁×#533	C₂²	semidirect
114. C₃₁×#533	C₂²	semidirect
120. C₃₁×#532	C₂²	semidirect
121. C₃₁×#532	C₂²	semidirect
122. C₃₁×#532	C₂²	semidirect
125. C₃₁×#529	C₂²	semidirect
126. C₃₁×#529	C₂²	semidirect
127. C₃₁×#529	C₂²	semidirect
128. C₃₁×#529	C₂²	semidirect
129. C₃₁×#529	C₂²	semidirect
130. C₃₁×#529	C₂²	semidirect
131. C₃₁×#529	C₂²	semidirect
132. C₃₁×#529	C₂²	semidirect
133. C₃₁×#529	C₂²	semidirect
134. C₃₁×#529	C₂²	semidirect
135. C₃₁×#529	C₂²	semidirect
136. C₃₁×#529	C₂²	semidirect
137. C₃₁×#529	C₂²	semidirect
138. C₃₁×#529	C₂²	semidirect
139. C₃₁×#529	C₂²	semidirect
140. C₃₁×#529	C₂²	semidirect
143. C₃₁×#525	C₂²	semidirect
144. C₃₁×#525	C₂²	semidirect
145. C₃₁×#525	C₂²	semidirect
146. C₃₁×#525	C₂²	semidirect
147. C₃₁×#525	C₂²	semidirect
148. C₃₁×#525	C₂²	semidirect
149. C₃₁×#525	C₂²	semidirect
151. C₄×#41×C₃₁	C₂²	semidirect
152. C₄×#41×C₃₁	C₂²	semidirect
153. C₄×#41×C₃₁	C₂²	semidirect
154. C₄×#41×C₃₁	C₂²	semidirect
155. C₄×#41×C₃₁	C₂²	semidirect
156. C₄×#41×C₃₁	C₂²	semidirect
157. C₄×#41×C₃₁	C₂²	semidirect
158. C₄×#41×C₃₁	C₂²	semidirect
159. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
160. C₂×C₄×D₄×C₃₁	C₂²	semidirect
161. C₂×C₃₁×#117	C₂²	semidirect
162. C₂²×C₄²×C₃₁	C₂²	semidirect
587. #62762	C₃₁	direct (N × H)
662. #3566	C₂×C₃₁	semidirect
663. #3565	C₂×C₃₁	semidirect
664. #3562	C₂×C₃₁	semidirect
665. #3555	C₂×C₃₁	semidirect
666. #3554	C₂×C₃₁	semidirect
667. #3547	C₂×C₃₁	semidirect
668. #3546	C₂×C₃₁	semidirect
669. #3540	C₂×C₃₁	semidirect
670. #3539	C₂×C₃₁	semidirect
671. #3529	C₂×C₃₁	semidirect
672. #3483	C₂×C₃₁	semidirect
673. #3482	C₂×C₃₁	semidirect
674. #3481	C₂×C₃₁	semidirect
675. #3480	C₂×C₃₁	semidirect
676. #3475	C₂×C₃₁	semidirect
677. #3461	C₂×C₃₁	semidirect
678. #3460	C₂×C₃₁	semidirect
679. #3455	C₂×C₃₁	semidirect
680. #3444	C₂×C₃₁	semidirect
681. #3444	C₂×C₃₁	semidirect
713. #563	C₂²×C₃₁	semidirect
714. #563	C₂²×C₃₁	semidirect
715. #562	C₂²×C₃₁	semidirect
716. #562	C₂²×C₃₁	semidirect
717. #562	C₂²×C₃₁	semidirect
718. H(3,𝔽₄)	C₂²×C₃₁	semidirect
720. #560	C₂²×C₃₁	semidirect
721. #560	C₂²×C₃₁	semidirect
722. #560	C₂²×C₃₁	semidirect
723. #559	C₂²×C₃₁	semidirect
724. #559	C₂²×C₃₁	semidirect
725. #559	C₂²×C₃₁	semidirect
726. Q₈²	C₂²×C₃₁	semidirect
727. #557	C₂²×C₃₁	semidirect
728. #557	C₂²×C₃₁	semidirect
729. #556	C₂²×C₃₁	semidirect
730. #556	C₂²×C₃₁	semidirect
731. #556	C₂²×C₃₁	semidirect
732. #556	C₂²×C₃₁	semidirect
733. #556	C₂²×C₃₁	semidirect
735. #555	C₂²×C₃₁	semidirect
736. #555	C₂²×C₃₁	semidirect
737. #555	C₂²×C₃₁	semidirect
738. #554	C₂²×C₃₁	semidirect
739. #554	C₂²×C₃₁	semidirect
741. #553	C₂²×C₃₁	semidirect
742. #553	C₂²×C₃₁	semidirect
743. #553	C₂²×C₃₁	semidirect
744. #553	C₂²×C₃₁	semidirect
745. #553	C₂²×C₃₁	semidirect
746. #552	C₂²×C₃₁	semidirect
747. #552	C₂²×C₃₁	semidirect
748. #552	C₂²×C₃₁	semidirect
749. #552	C₂²×C₃₁	semidirect
750. #552	C₂²×C₃₁	semidirect
751. #551	C₂²×C₃₁	semidirect
752. #551	C₂²×C₃₁	semidirect
753. #551	C₂²×C₃₁	semidirect
755. #550	C₂²×C₃₁	semidirect
756. #550	C₂²×C₃₁	semidirect
757. D₄×Q₈	C₂²×C₃₁	semidirect
759. #548	C₂²×C₃₁	semidirect
760. #548	C₂²×C₃₁	semidirect
761. #547	C₂²×C₃₁	semidirect
762. #547	C₂²×C₃₁	semidirect
763. #547	C₂²×C₃₁	semidirect
766. #546	C₂²×C₃₁	semidirect
767. D₄²	C₂²×C₃₁	semidirect
768. #544	C₂²×C₃₁	semidirect
769. #544	C₂²×C₃₁	semidirect
771. #542	C₂²×C₃₁	semidirect
772. #542	C₂²×C₃₁	semidirect
773. #542	C₂²×C₃₁	semidirect
774. #542	C₂²×C₃₁	semidirect
775. #542	C₂²×C₃₁	semidirect
776. #542	C₂²×C₃₁	semidirect
777. #542	C₂²×C₃₁	semidirect
778. #541	C₂²×C₃₁	semidirect
779. #541	C₂²×C₃₁	semidirect
780. #541	C₂²×C₃₁	semidirect
781. #541	C₂²×C₃₁	semidirect
782. #540	C₂²×C₃₁	semidirect
783. #540	C₂²×C₃₁	semidirect
784. #540	C₂²×C₃₁	semidirect
785. #540	C₂²×C₃₁	semidirect
786. #539	C₂²×C₃₁	semidirect
787. #539	C₂²×C₃₁	semidirect
788. #539	C₂²×C₃₁	semidirect
789. #539	C₂²×C₃₁	semidirect
790. #538	C₂²×C₃₁	semidirect
791. #538	C₂²×C₃₁	semidirect
792. #538	C₂²×C₃₁	semidirect
793. #538	C₂²×C₃₁	semidirect
795. #537	C₂²×C₃₁	semidirect
796. #536	C₂²×C₃₁	semidirect
797. #536	C₂²×C₃₁	semidirect
799. #535	C₂²×C₃₁	semidirect
800. #533	C₂²×C₃₁	semidirect
801. #533	C₂²×C₃₁	semidirect
802. #533	C₂²×C₃₁	semidirect
803. #533	C₂²×C₃₁	semidirect
804. #533	C₂²×C₃₁	semidirect
805. #533	C₂²×C₃₁	semidirect
806. #533	C₂²×C₃₁	semidirect
812. #532	C₂²×C₃₁	semidirect
813. #532	C₂²×C₃₁	semidirect
814. #532	C₂²×C₃₁	semidirect
817. #529	C₂²×C₃₁	semidirect
818. #529	C₂²×C₃₁	semidirect
819. #529	C₂²×C₃₁	semidirect
820. #529	C₂²×C₃₁	semidirect
821. #529	C₂²×C₃₁	semidirect
822. #529	C₂²×C₃₁	semidirect
823. #529	C₂²×C₃₁	semidirect
824. #529	C₂²×C₃₁	semidirect
825. #529	C₂²×C₃₁	semidirect
826. #529	C₂²×C₃₁	semidirect
827. #529	C₂²×C₃₁	semidirect
828. #529	C₂²×C₃₁	semidirect
829. #529	C₂²×C₃₁	semidirect
830. #529	C₂²×C₃₁	semidirect
831. #529	C₂²×C₃₁	semidirect
832. #529	C₂²×C₃₁	semidirect
835. #525	C₂²×C₃₁	semidirect
836. #525	C₂²×C₃₁	semidirect
837. #525	C₂²×C₃₁	semidirect
838. #525	C₂²×C₃₁	semidirect
839. #525	C₂²×C₃₁	semidirect
840. #525	C₂²×C₃₁	semidirect
841. #525	C₂²×C₃₁	semidirect
843. C₄×#41	C₂²×C₃₁	semidirect
844. C₄×#41	C₂²×C₃₁	semidirect
845. C₄×#41	C₂²×C₃₁	semidirect
846. C₄×#41	C₂²×C₃₁	semidirect
847. C₄×#41	C₂²×C₃₁	semidirect
848. C₄×#41	C₂²×C₃₁	semidirect
849. C₄×#41	C₂²×C₃₁	semidirect
850. C₄×#41	C₂²×C₃₁	semidirect
851. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
852. C₂×C₄×D₄	C₂²×C₃₁	semidirect
853. C₂×#117	C₂²×C₃₁	semidirect
854. C₂²×C₄²	C₂²×C₃₁	semidirect
1130. C₃₁	#62762	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×#3566	2
C₃₁×#3565	2
C₃₁×#3562	2
C₃₁×#3555	2
C₃₁×#3554	2
C₃₁×#3547	2
C₃₁×#3546	2
C₃₁×#3540	2
C₃₁×#3539	2
C₃₁×#3529	2
C₃₁×#3483	2
C₃₁×#3482	2
C₃₁×#3481	2
C₃₁×#3480	2
C₃₁×#3475	2
C₃₁×#3461	2
C₃₁×#3460	2
C₃₁×#3455	2
C₃₁×#3444	2
#62762	31

Subgroups — C31×#62762 #21519521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62762 #21519521