Subgroups — C₃₁×#62781 #21519540

Order 7936.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3521	C₂	1	8	yes	maximal, complemented
2	C₃₁×#3515	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3514	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3507	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3505	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3493	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3491	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3485	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3482	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3481	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3475	C₂	1	8	yes	maximal, complemented
14	C₃₁×#3461	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3459	C₂	1	4	yes	maximal, complemented
16	C₃₁×#3444	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#529	C₂	1	4	yes	maximal, complemented
18	C₄×C₃₁×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#559	C₂²	1	4	yes	complemented
23	C₃₁×#557	C₂²	1	4	yes	complemented
24	C₃₁×#556	C₂²	1	8	yes	complemented
25	C₃₁×#556	C₂²	1	8	yes	complemented
26	C₃₁×#556	C₂²	1	4	yes	complemented
27	C₃₁×#555	C₂²	1	8	yes	complemented
28	C₃₁×#554	C₂²	1	8	yes	complemented
29	C₃₁×#554	C₂²	1	4	yes	complemented
30	C₃₁×#554	C₂²	1	4	yes	complemented
31	C₃₁×#553	C₂²	1	16	yes	complemented
32	C₃₁×#553	C₂²	1	8	yes	complemented
33	C₃₁×#553	C₂²	1	8	yes	complemented
34	C₃₁×#552	C₂²	1	16	yes	complemented
35	C₃₁×#552	C₂²	1	8	yes	complemented
36	C₃₁×#552	C₂²	1	8	yes	complemented
37	C₃₁×#552	C₂²	1	16	yes	complemented
38	C₃₁×#552	C₂²	1	8	yes	complemented
39	C₃₁×#551	C₂²	1	16	yes	complemented
40	C₃₁×#551	C₂²	1	16	yes	complemented
41	C₃₁×#551	C₂²	1	16	yes	complemented
42	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
43	C₃₁×#548	C₂²	1	8	yes	complemented
44	C₃₁×#547	C₂²	1	8	yes	complemented
45	C₃₁×#547	C₂²	1	8	yes	complemented
46	C₃₁×#547	C₂²	1	4	yes	complemented
47	C₃₁×#546	C₂²	1	8	yes	complemented
48	C₃₁×#546	C₂²	1	8	yes	complemented
49	C₃₁×#546	C₂²	1	8	yes	complemented
50	C₃₁×#546	C₂²	1	8	yes	complemented
51	D₄²×C₃₁	C₂²	1	4	yes	complemented
52	C₃₁×#544	C₂²	1	2	yes	complemented
53	C₃₁×#543	C₂²	1	4	yes	complemented
54	C₃₁×#542	C₂²	1	8	yes	complemented
55	C₃₁×#541	C₂²	1	8	yes	complemented
56	C₃₁×#539	C₂²	1	8	yes	complemented
57	C₃₁×#539	C₂²	1	16	yes	complemented
58	C₃₁×#539	C₂²	1	8	yes	complemented
59	C₃₁×#538	C₂²	1	8	yes	complemented
60	C₃₁×#538	C₂²	1	16	yes	complemented
61	C₃₁×#537	C₂²	1	2	yes	—
62	C₃₁×#536	C₂²	1	4	yes	complemented
63	C₃₁×#534	C₂²	1	4	yes	—
64	C₃₁×#534	C₂²	1	8	yes	complemented
65	C₃₁×#533	C₂²	1	2	yes	complemented
66	C₃₁×#533	C₂²	1	2	yes	complemented
67	C₃₁×#533	C₂²	1	2	yes	complemented
68	C₃₁×#533	C₂²	1	8	yes	complemented
69	C₃₁×#532	C₂²	1	2	yes	—
70	C₃₁×#532	C₂²	1	2	yes	complemented
71	C₃₁×#532	C₂²	1	2	yes	complemented
72	C₃₁×#529	C₂²	1	4	yes	complemented
73	C₃₁×#529	C₂²	1	8	yes	complemented
74	C₃₁×#529	C₂²	1	8	yes	complemented
75	C₃₁×#529	C₂²	1	8	yes	complemented
76	C₃₁×#529	C₂²	1	8	yes	complemented
77	C₃₁×#529	C₂²	1	8	yes	complemented
78	C₃₁×#529	C₂²	1	8	yes	complemented
79	C₃₁×#529	C₂²	1	8	yes	complemented
80	C₃₁×#529	C₂²	1	4	yes	complemented
81	C₃₁×#529	C₂²	1	4	yes	complemented
82	C₃₁×#529	C₂²	1	4	yes	complemented
83	C₃₁×#529	C₂²	1	4	yes	complemented
84	C₃₁×#529	C₂²	1	4	yes	complemented
85	C₃₁×#529	C₂²	1	16	yes	complemented
86	C₃₁×#529	C₂²	1	8	yes	complemented
87	C₂×C₃₁×#126	C₂²	1	8	yes	complemented
88	C₂×C₃₁×#125	C₂²	1	4	yes	complemented
89	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
90	C₃₁×#525	C₂²	1	4	yes	complemented
91	C₃₁×#525	C₂²	1	4	yes	complemented
92	C₃₁×#525	C₂²	1	4	yes	complemented
93	C₃₁×#525	C₂²	1	16	yes	complemented
94	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
95	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
96	C₂×C₃₁×#121	C₂²	1	4	yes	—
97	C₃₁×#520	C₂²	1	4	yes	complemented
98	C₃₁×#520	C₂²	1	8	yes	complemented
99	C₃₁×#518	C₂²	1	2	yes	—
100	C₃₁×#518	C₂²	1	8	yes	complemented
101	C₃₁×#518	C₂²	1	8	yes	complemented
102	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
103	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
104	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
105	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
106	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
107	C₄×#41×C₃₁	C₂²	1	8	yes	complemented
108	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
109	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
110	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
113	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
116	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
117	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
118	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
119	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
120	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
121	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
123	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
124	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×H(5,𝔽₂)	—	2	16	no	—
126	C₂×#41×C₃₁	—	2	8	no	—
127	C₂×#41×C₃₁	C₂³	1	4	yes	—
128	C₂×#41×C₃₁	C₂³	1	4	yes	—
129	C₂×#41×C₃₁	C₂³	1	4	yes	—
130	C₂×#41×C₃₁	C₂³	1	8	yes	—
131	C₂×#41×C₃₁	C₂³	1	4	yes	—
132	C₂×#41×C₃₁	C₂³	1	4	yes	—
133	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
137	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
138	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
147	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
148	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
151	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
152	C₃₁×#127	C₂³	1	2	yes	—
153	C₃₁×#126	C₂³	1	8	yes	—
154	C₃₁×#126	C₂³	1	16	yes	—
155	C₃₁×#126	C₂³	1	16	yes	—
156	C₃₁×#126	C₂³	1	16	yes	—
157	C₃₁×#126	C₂³	1	8	yes	—
158	C₃₁×#126	C₂³	1	16	yes	—
159	C₃₁×#126	C₂³	1	16	yes	—
160	C₃₁×#126	C₂³	1	16	yes	—
161	C₃₁×#125	C₂³	1	4	yes	—
162	C₃₁×#125	C₂³	1	8	yes	—
163	C₃₁×#125	C₂³	1	8	yes	—
164	C₃₁×#125	C₂³	1	8	yes	—
165	C₃₁×#125	C₂³	1	4	yes	—
166	C₃₁×#125	C₂³	1	4	yes	—
167	C₃₁×#125	C₂³	1	16	yes	—
168	C₃₁×#125	C₂³	1	8	yes	—
169	C₃₁×#125	C₂³	1	16	yes	—
170	C₃₁×#124	C₂³	1	4	yes	—
171	C₃₁×#124	C₂³	1	8	yes	—
172	C₃₁×#124	C₂³	1	8	yes	—
173	C₃₁×#124	C₂³	1	8	yes	—
174	C₃₁×#124	C₂³	1	4	yes	—
175	C₃₁×#124	C₂³	1	4	yes	—
176	C₃₁×#124	C₂³	1	8	yes	—
177	C₃₁×#124	C₂³	1	16	yes	—
178	C₃₁×#123	C₂³	1	8	yes	—
179	C₃₁×#123	C₂³	1	16	yes	—
180	C₃₁×#123	C₂³	1	16	yes	—
181	C₃₁×#123	C₂³	1	16	yes	—
182	C₃₁×#123	C₂³	1	8	yes	—
183	C₃₁×#123	C₂³	1	8	yes	—
184	C₃₁×#123	C₂³	1	16	yes	—
185	C₃₁×#123	C₂³	1	16	yes	—
186	C₃₁×#123	C₂³	1	16	yes	—
187	C₃₁×#123	C₂³	1	16	yes	—
188	C₃₁×#123	C₂³	1	16	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
205	C₃₁×#121	C₂³	1	4	yes	—
206	C₃₁×#121	C₂³	1	8	yes	—
207	C₃₁×#121	C₂³	1	8	yes	—
208	C₃₁×#121	C₂³	1	8	yes	—
209	C₃₁×#121	C₂³	1	4	yes	—
210	C₃₁×#121	C₂³	1	4	yes	—
211	C₃₁×#121	C₂³	1	4	yes	—
212	C₃₁×#121	C₂³	1	4	yes	—
213	C₃₁×#121	C₂³	1	4	yes	—
214	C₃₁×#121	C₂³	1	16	yes	—
215	C₃₁×#121	C₂³	1	16	yes	—
216	C₃₁×#121	C₂³	1	16	yes	—
217	C₃₁×#121	C₂³	1	8	yes	—
218	C₃₁×#120	C₂³	1	8	yes	—
219	C₃₁×#120	C₂³	1	16	yes	—
220	C₃₁×#120	C₂³	1	16	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
235	C₄×D₄×C₃₁	C₂³	1	4	yes	—
236	C₄×D₄×C₃₁	C₂³	1	4	yes	—
237	C₄×D₄×C₃₁	C₂³	1	4	yes	—
238	C₄×D₄×C₃₁	C₂³	1	4	yes	—
239	C₄×D₄×C₃₁	C₂³	1	8	yes	—
240	C₄×D₄×C₃₁	C₂³	1	16	yes	—
241	C₄×D₄×C₃₁	C₂³	1	4	yes	—
242	C₄×D₄×C₃₁	C₂³	1	4	yes	—
243	C₄×D₄×C₃₁	C₂³	1	8	yes	—
244	C₄×D₄×C₃₁	C₂³	1	8	yes	—
245	C₄×D₄×C₃₁	C₂³	1	8	yes	—
246	C₄×D₄×C₃₁	C₂³	1	8	yes	—
247	C₄×D₄×C₃₁	C₂³	1	8	yes	—
248	C₄×D₄×C₃₁	C₂³	1	16	yes	—
249	C₄×D₄×C₃₁	C₂³	1	16	yes	—
250	C₄×D₄×C₃₁	C₂³	1	16	yes	—
251	C₄×D₄×C₃₁	C₂³	1	8	yes	—
252	C₄×D₄×C₃₁	C₂³	1	8	yes	—
253	C₄×D₄×C₃₁	C₂³	1	8	yes	—
254	C₄×D₄×C₃₁	C₂³	1	8	yes	—
255	C₄×D₄×C₃₁	C₂³	1	8	yes	—
256	C₄×D₄×C₃₁	C₂³	1	8	yes	—
257	C₄×D₄×C₃₁	C₂³	1	4	yes	—
258	C₄×D₄×C₃₁	C₂³	1	16	yes	—
259	C₄×D₄×C₃₁	C₂³	1	8	yes	—
260	C₄×D₄×C₃₁	C₂³	1	8	yes	—
261	C₄×D₄×C₃₁	C₂³	1	8	yes	—
262	C₄×D₄×C₃₁	C₂³	1	8	yes	—
263	C₄×D₄×C₃₁	C₂³	1	4	yes	—
264	C₄×D₄×C₃₁	C₂³	1	4	yes	—
265	C₄×D₄×C₃₁	C₂³	1	4	yes	—
266	C₃₁×#117	C₂³	1	8	yes	—
267	C₃₁×#117	C₂³	1	8	yes	—
268	C₃₁×#117	C₂³	1	8	yes	—
269	C₃₁×#117	C₂³	1	4	yes	—
270	C₃₁×#117	C₂³	1	4	yes	—
271	C₃₁×#117	C₂³	1	16	yes	—
272	C₃₁×#117	C₂³	1	16	yes	—
273	C₃₁×#117	C₂³	1	16	yes	—
274	C₃₁×#117	C₂³	1	4	yes	—
275	C₃₁×#117	C₂³	1	8	yes	—
276	C₃₁×#117	C₂³	1	16	yes	—
277	C₃₁×#117	C₂³	1	8	yes	—
278	C₃₁×#117	C₂³	1	4	yes	—
279	C₃₁×#117	C₂³	1	4	yes	—
280	C₃₁×#117	C₂³	1	8	yes	—
281	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
284	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
286	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
288	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
289	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
290	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
291	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
292	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
296	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
297	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
298	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
299	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
300	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
303	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
304	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
308	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
309	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
310	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
311	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
312	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
313	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
314	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
315	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
316	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
317	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
318	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
319	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
321	#41×C₃₁	—	2	16	no	—
322	#41×C₃₁	—	2	16	no	—
323	#41×C₃₁	—	2	32	no	—
324	#41×C₃₁	—	2	16	no	—
325	#41×C₃₁	—	4	8	no	—
326	#41×C₃₁	—	4	8	no	—
327	C₂×Q₈×C₃₁	—	2	4	no	—
328	C₂×Q₈×C₃₁	—	4	8	no	—
329	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
331	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
334	C₂×D₄×C₃₁	—	2	8	no	—
335	C₂×D₄×C₃₁	—	2	32	no	—
336	C₂×D₄×C₃₁	—	2	32	no	—
337	C₂×D₄×C₃₁	—	4	8	no	—
338	C₂×D₄×C₃₁	#41	1	8	yes	complemented
339	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
340	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
341	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
346	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₃₁	—	2	8	no	—
350	C₂²×C₄×C₃₁	—	2	4	no	—
351	C₂²×C₄×C₃₁	—	4	4	no	—
352	C₂²×C₄×C₃₁	—	4	16	no	—
353	C₂²×C₄×C₃₁	—	4	4	no	—
354	C₂²×C₄×C₃₁	—	4	2	no	—
355	C₂²×C₄×C₃₁	—	4	2	no	—
356	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
366	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
369	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
371	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
374	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
375	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
380	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
381	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
382	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
383	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
385	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
388	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
390	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
391	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
393	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
394	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
395	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
397	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
409	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
411	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
412	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
415	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
418	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
419	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
420	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
421	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
422	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
423	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₄²×C₃₁	C₂⁴	1	4	yes	—
426	C₄²×C₃₁	C₂⁴	1	2	yes	—
427	C₄²×C₃₁	C₂⁴	1	2	yes	—
428	C₄²×C₃₁	C₂⁴	1	4	yes	—
429	C₄²×C₃₁	C₂⁴	1	4	yes	—
430	C₄²×C₃₁	C₂⁴	1	2	yes	—
431	C₄²×C₃₁	C₂⁴	1	2	yes	—
432	C₄²×C₃₁	C₂⁴	1	4	yes	—
433	C₄²×C₃₁	C₂⁴	1	2	yes	—
434	C₄²×C₃₁	C₂⁴	1	4	yes	—
435	C₄²×C₃₁	C₂⁴	1	8	yes	—
436	C₄²×C₃₁	C₂⁴	1	16	yes	—
437	C₄²×C₃₁	C₂⁴	1	8	yes	—
438	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₃₁	C₂⁴	1	2	yes	—
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	8	yes	—
442	C₄²×C₃₁	C₂⁴	1	4	yes	—
443	#62781	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	2	no	—
445	C₂³×C₃₁	—	2	16	no	—
446	C₂³×C₃₁	—	4	2	no	—
447	C₂³×C₃₁	—	4	2	no	—
448	C₂³×C₃₁	—	4	1	no	—
449	C₂³×C₃₁	—	4	1	no	—
450	C₂³×C₃₁	—	4	8	no	—
451	C₂³×C₃₁	—	4	8	no	—
452	C₂³×C₃₁	C₂×#41	1	8	yes	—
453	C₂³×C₃₁	C₂⁵	1	8	yes	—
454	C₂³×C₃₁	C₂⁵	1	2	yes	—
455	C₂³×C₃₁	C₂⁵	1	4	yes	—
456	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
457	Q₈×C₃₁	—	2	8	no	—
458	Q₈×C₃₁	—	2	8	no	—
459	Q₈×C₃₁	—	2	8	no	—
460	Q₈×C₃₁	—	4	8	no	—
461	Q₈×C₃₁	—	4	4	no	—
462	D₄×C₃₁	—	2	32	no	—
463	D₄×C₃₁	—	2	16	no	—
464	D₄×C₃₁	—	2	16	no	—
465	D₄×C₃₁	—	2	8	no	—
466	D₄×C₃₁	—	2	8	no	—
467	D₄×C₃₁	—	4	8	no	—
468	D₄×C₃₁	—	4	8	no	—
469	D₄×C₃₁	—	4	4	no	—
470	D₄×C₃₁	—	4	8	no	—
471	D₄×C₃₁	C₂×#41	1	16	yes	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	4	no	—
474	C₂×C₄×C₃₁	—	2	8	no	—
475	C₂×C₄×C₃₁	—	2	8	no	—
476	C₂×C₄×C₃₁	—	2	16	no	—
477	C₂×C₄×C₃₁	—	2	4	no	—
478	C₂×C₄×C₃₁	—	2	4	no	—
479	C₂×C₄×C₃₁	—	2	16	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	8	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	16	no	—
484	C₂×C₄×C₃₁	—	2	8	no	—
485	C₂×C₄×C₃₁	—	2	4	no	—
486	C₂×C₄×C₃₁	—	2	4	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	4	4	no	—
489	C₂×C₄×C₃₁	—	4	1	no	—
490	C₂×C₄×C₃₁	—	4	2	no	—
491	C₂×C₄×C₃₁	—	4	16	no	—
492	C₂×C₄×C₃₁	—	4	4	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	8	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	4	1	no	—
497	C₂×C₄×C₃₁	—	4	8	no	—
498	C₂×C₄×C₃₁	—	4	8	no	—
499	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
500	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
502	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
505	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
506	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
507	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
508	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
509	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
510	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
511	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
512	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
513	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
515	#3521	C₂×C₃₁	1	8	yes	complemented
516	#3515	C₂×C₃₁	1	4	yes	complemented
517	#3514	C₂×C₃₁	1	4	yes	complemented
518	#3507	C₂×C₃₁	1	2	yes	complemented
519	#3505	C₂×C₃₁	1	4	yes	complemented
520	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3496	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3493	C₂×C₃₁	1	2	yes	complemented
523	#3491	C₂×C₃₁	1	4	yes	complemented
524	#3485	C₂×C₃₁	1	2	yes	complemented
525	#3482	C₂×C₃₁	1	4	yes	complemented
526	#3481	C₂×C₃₁	1	4	yes	complemented
527	#3475	C₂×C₃₁	1	8	yes	complemented
528	#3461	C₂×C₃₁	1	2	yes	complemented
529	#3459	C₂×C₃₁	1	4	yes	complemented
530	#3444	C₂×C₃₁	1	2	yes	complemented
531	C₂×#529	C₂×C₃₁	1	4	yes	complemented
532	C₄×H(5,𝔽₂)	C₂×C₃₁	1	2	yes	complemented
533	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
534	C₂²×C₃₁	—	2	1	no	—
535	C₂²×C₃₁	—	2	1	no	—
536	C₂²×C₃₁	—	2	4	no	—
537	C₂²×C₃₁	—	2	4	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	2	8	no	—
540	C₂²×C₃₁	—	2	8	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	8	no	—
544	C₂²×C₃₁	—	4	8	no	—
545	C₂²×C₃₁	—	4	4	no	—
546	C₂²×C₃₁	—	8	16	no	—
547	C₂²×C₃₁	C₂²×#41	1	8	yes	—
548	C₂²×C₃₁	C₂²×#41	1	2	yes	—
549	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
550	C₄×C₃₁	—	2	1	no	—
551	C₄×C₃₁	—	2	1	no	—
552	C₄×C₃₁	—	2	8	no	—
553	C₄×C₃₁	—	2	4	no	—
554	C₄×C₃₁	—	2	1	no	—
555	C₄×C₃₁	—	2	4	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	8	no	—
559	C₄×C₃₁	—	2	4	no	—
560	C₄×C₃₁	—	2	2	no	—
561	C₄×C₃₁	—	2	8	no	—
562	C₄×C₃₁	C₂²×#41	1	4	yes	—
563	C₄×C₃₁	#585	1	2	yes	—
564	C₄×C₃₁	#585	1	2	yes	—
565	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
566	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
567	#559	C₂²×C₃₁	1	4	yes	complemented
568	#557	C₂²×C₃₁	1	4	yes	complemented
569	#556	C₂²×C₃₁	1	8	yes	complemented
570	#556	C₂²×C₃₁	1	8	yes	complemented
571	#556	C₂²×C₃₁	1	4	yes	complemented
572	#555	C₂²×C₃₁	1	8	yes	complemented
573	#554	C₂²×C₃₁	1	8	yes	complemented
574	#554	C₂²×C₃₁	1	4	yes	complemented
575	#554	C₂²×C₃₁	1	4	yes	complemented
576	#553	C₂²×C₃₁	1	16	yes	complemented
577	#553	C₂²×C₃₁	1	8	yes	complemented
578	#553	C₂²×C₃₁	1	8	yes	complemented
579	#552	C₂²×C₃₁	1	16	yes	complemented
580	#552	C₂²×C₃₁	1	8	yes	complemented
581	#552	C₂²×C₃₁	1	8	yes	complemented
582	#552	C₂²×C₃₁	1	16	yes	complemented
583	#552	C₂²×C₃₁	1	8	yes	complemented
584	#551	C₂²×C₃₁	1	16	yes	complemented
585	#551	C₂²×C₃₁	1	16	yes	complemented
586	#551	C₂²×C₃₁	1	16	yes	complemented
587	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
588	#548	C₂²×C₃₁	1	8	yes	complemented
589	#547	C₂²×C₃₁	1	8	yes	complemented
590	#547	C₂²×C₃₁	1	8	yes	complemented
591	#547	C₂²×C₃₁	1	4	yes	complemented
592	#546	C₂²×C₃₁	1	8	yes	complemented
593	#546	C₂²×C₃₁	1	8	yes	complemented
594	#546	C₂²×C₃₁	1	8	yes	complemented
595	#546	C₂²×C₃₁	1	8	yes	complemented
596	D₄²	C₂²×C₃₁	1	4	yes	complemented
597	#544	C₂²×C₃₁	1	2	yes	complemented
598	#543	C₂²×C₃₁	1	4	yes	complemented
599	#542	C₂²×C₃₁	1	8	yes	complemented
600	#541	C₂²×C₃₁	1	8	yes	complemented
601	#539	C₂²×C₃₁	1	8	yes	complemented
602	#539	C₂²×C₃₁	1	16	yes	complemented
603	#539	C₂²×C₃₁	1	8	yes	complemented
604	#538	C₂²×C₃₁	1	8	yes	complemented
605	#538	C₂²×C₃₁	1	16	yes	complemented
606	#537	C₂²×C₃₁	1	2	yes	—
607	#536	C₂²×C₃₁	1	4	yes	complemented
608	#534	C₂²×C₃₁	1	4	yes	—
609	#534	C₂²×C₃₁	1	8	yes	complemented
610	#533	C₂²×C₃₁	1	2	yes	complemented
611	#533	C₂²×C₃₁	1	2	yes	complemented
612	#533	C₂²×C₃₁	1	2	yes	complemented
613	#533	C₂²×C₃₁	1	8	yes	complemented
614	#532	C₂²×C₃₁	1	2	yes	—
615	#532	C₂²×C₃₁	1	2	yes	complemented
616	#532	C₂²×C₃₁	1	2	yes	complemented
617	#529	C₂²×C₃₁	1	4	yes	complemented
618	#529	C₂²×C₃₁	1	8	yes	complemented
619	#529	C₂²×C₃₁	1	8	yes	complemented
620	#529	C₂²×C₃₁	1	8	yes	complemented
621	#529	C₂²×C₃₁	1	8	yes	complemented
622	#529	C₂²×C₃₁	1	8	yes	complemented
623	#529	C₂²×C₃₁	1	8	yes	complemented
624	#529	C₂²×C₃₁	1	8	yes	complemented
625	#529	C₂²×C₃₁	1	4	yes	complemented
626	#529	C₂²×C₃₁	1	4	yes	complemented
627	#529	C₂²×C₃₁	1	4	yes	complemented
628	#529	C₂²×C₃₁	1	4	yes	complemented
629	#529	C₂²×C₃₁	1	4	yes	complemented
630	#529	C₂²×C₃₁	1	16	yes	complemented
631	#529	C₂²×C₃₁	1	8	yes	complemented
632	C₂×#126	C₂²×C₃₁	1	8	yes	complemented
633	C₂×#125	C₂²×C₃₁	1	4	yes	complemented
634	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
635	#525	C₂²×C₃₁	1	4	yes	complemented
636	#525	C₂²×C₃₁	1	4	yes	complemented
637	#525	C₂²×C₃₁	1	4	yes	complemented
638	#525	C₂²×C₃₁	1	16	yes	complemented
639	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
640	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
641	C₂×#121	C₂²×C₃₁	1	4	yes	—
642	#520	C₂²×C₃₁	1	4	yes	complemented
643	#520	C₂²×C₃₁	1	8	yes	complemented
644	#518	C₂²×C₃₁	1	2	yes	—
645	#518	C₂²×C₃₁	1	8	yes	complemented
646	#518	C₂²×C₃₁	1	8	yes	complemented
647	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
648	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
649	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
650	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
651	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
652	C₄×#41	C₂²×C₃₁	1	8	yes	complemented
653	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
654	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
655	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
658	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
659	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
660	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
661	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
662	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
663	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
664	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
665	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
666	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
668	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
669	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	C₂×C₃₁	—	2	2	no	—
671	C₂×C₃₁	—	2	8	no	—
672	C₂×C₃₁	—	4	2	no	—
673	C₂×C₃₁	—	4	8	no	—
674	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
675	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
676	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
677	H(5,𝔽₂)	—	2	16	no	—
678	C₂×#41	—	2	8	no	—
679	C₂×#41	C₂³×C₃₁	1	4	yes	—
680	C₂×#41	C₂³×C₃₁	1	4	yes	—
681	C₂×#41	C₂³×C₃₁	1	4	yes	—
682	C₂×#41	C₂³×C₃₁	1	8	yes	—
683	C₂×#41	C₂³×C₃₁	1	4	yes	—
684	C₂×#41	C₂³×C₃₁	1	4	yes	—
685	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
687	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
688	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
689	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
690	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
691	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
693	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
695	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
696	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
697	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
703	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
704	#127	C₂³×C₃₁	1	2	yes	—
705	#126	C₂³×C₃₁	1	8	yes	—
706	#126	C₂³×C₃₁	1	16	yes	—
707	#126	C₂³×C₃₁	1	16	yes	—
708	#126	C₂³×C₃₁	1	16	yes	—
709	#126	C₂³×C₃₁	1	8	yes	—
710	#126	C₂³×C₃₁	1	16	yes	—
711	#126	C₂³×C₃₁	1	16	yes	—
712	#126	C₂³×C₃₁	1	16	yes	—
713	#125	C₂³×C₃₁	1	4	yes	—
714	#125	C₂³×C₃₁	1	8	yes	—
715	#125	C₂³×C₃₁	1	8	yes	—
716	#125	C₂³×C₃₁	1	8	yes	—
717	#125	C₂³×C₃₁	1	4	yes	—
718	#125	C₂³×C₃₁	1	4	yes	—
719	#125	C₂³×C₃₁	1	16	yes	—
720	#125	C₂³×C₃₁	1	8	yes	—
721	#125	C₂³×C₃₁	1	16	yes	—
722	#124	C₂³×C₃₁	1	4	yes	—
723	#124	C₂³×C₃₁	1	8	yes	—
724	#124	C₂³×C₃₁	1	8	yes	—
725	#124	C₂³×C₃₁	1	8	yes	—
726	#124	C₂³×C₃₁	1	4	yes	—
727	#124	C₂³×C₃₁	1	4	yes	—
728	#124	C₂³×C₃₁	1	8	yes	—
729	#124	C₂³×C₃₁	1	16	yes	—
730	#123	C₂³×C₃₁	1	8	yes	—
731	#123	C₂³×C₃₁	1	16	yes	—
732	#123	C₂³×C₃₁	1	16	yes	—
733	#123	C₂³×C₃₁	1	16	yes	—
734	#123	C₂³×C₃₁	1	8	yes	—
735	#123	C₂³×C₃₁	1	8	yes	—
736	#123	C₂³×C₃₁	1	16	yes	—
737	#123	C₂³×C₃₁	1	16	yes	—
738	#123	C₂³×C₃₁	1	16	yes	—
739	#123	C₂³×C₃₁	1	16	yes	—
740	#123	C₂³×C₃₁	1	16	yes	—
741	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
742	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
743	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
744	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
745	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
746	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
747	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
748	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
749	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
750	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
751	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
752	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
753	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
754	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
755	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
756	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
757	#121	C₂³×C₃₁	1	4	yes	—
758	#121	C₂³×C₃₁	1	8	yes	—
759	#121	C₂³×C₃₁	1	8	yes	—
760	#121	C₂³×C₃₁	1	8	yes	—
761	#121	C₂³×C₃₁	1	4	yes	—
762	#121	C₂³×C₃₁	1	4	yes	—
763	#121	C₂³×C₃₁	1	4	yes	—
764	#121	C₂³×C₃₁	1	4	yes	—
765	#121	C₂³×C₃₁	1	4	yes	—
766	#121	C₂³×C₃₁	1	16	yes	—
767	#121	C₂³×C₃₁	1	16	yes	—
768	#121	C₂³×C₃₁	1	16	yes	—
769	#121	C₂³×C₃₁	1	8	yes	—
770	#120	C₂³×C₃₁	1	8	yes	—
771	#120	C₂³×C₃₁	1	16	yes	—
772	#120	C₂³×C₃₁	1	16	yes	—
773	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
774	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
775	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
776	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
777	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
778	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
779	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
780	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
781	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
782	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
783	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
784	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
786	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
787	C₄×D₄	C₂³×C₃₁	1	4	yes	—
788	C₄×D₄	C₂³×C₃₁	1	4	yes	—
789	C₄×D₄	C₂³×C₃₁	1	4	yes	—
790	C₄×D₄	C₂³×C₃₁	1	4	yes	—
791	C₄×D₄	C₂³×C₃₁	1	8	yes	—
792	C₄×D₄	C₂³×C₃₁	1	16	yes	—
793	C₄×D₄	C₂³×C₃₁	1	4	yes	—
794	C₄×D₄	C₂³×C₃₁	1	4	yes	—
795	C₄×D₄	C₂³×C₃₁	1	8	yes	—
796	C₄×D₄	C₂³×C₃₁	1	8	yes	—
797	C₄×D₄	C₂³×C₃₁	1	8	yes	—
798	C₄×D₄	C₂³×C₃₁	1	8	yes	—
799	C₄×D₄	C₂³×C₃₁	1	8	yes	—
800	C₄×D₄	C₂³×C₃₁	1	16	yes	—
801	C₄×D₄	C₂³×C₃₁	1	16	yes	—
802	C₄×D₄	C₂³×C₃₁	1	16	yes	—
803	C₄×D₄	C₂³×C₃₁	1	8	yes	—
804	C₄×D₄	C₂³×C₃₁	1	8	yes	—
805	C₄×D₄	C₂³×C₃₁	1	8	yes	—
806	C₄×D₄	C₂³×C₃₁	1	8	yes	—
807	C₄×D₄	C₂³×C₃₁	1	8	yes	—
808	C₄×D₄	C₂³×C₃₁	1	8	yes	—
809	C₄×D₄	C₂³×C₃₁	1	4	yes	—
810	C₄×D₄	C₂³×C₃₁	1	16	yes	—
811	C₄×D₄	C₂³×C₃₁	1	8	yes	—
812	C₄×D₄	C₂³×C₃₁	1	8	yes	—
813	C₄×D₄	C₂³×C₃₁	1	8	yes	—
814	C₄×D₄	C₂³×C₃₁	1	8	yes	—
815	C₄×D₄	C₂³×C₃₁	1	4	yes	—
816	C₄×D₄	C₂³×C₃₁	1	4	yes	—
817	C₄×D₄	C₂³×C₃₁	1	4	yes	—
818	#117	C₂³×C₃₁	1	8	yes	—
819	#117	C₂³×C₃₁	1	8	yes	—
820	#117	C₂³×C₃₁	1	8	yes	—
821	#117	C₂³×C₃₁	1	4	yes	—
822	#117	C₂³×C₃₁	1	4	yes	—
823	#117	C₂³×C₃₁	1	16	yes	—
824	#117	C₂³×C₃₁	1	16	yes	—
825	#117	C₂³×C₃₁	1	16	yes	—
826	#117	C₂³×C₃₁	1	4	yes	—
827	#117	C₂³×C₃₁	1	8	yes	—
828	#117	C₂³×C₃₁	1	16	yes	—
829	#117	C₂³×C₃₁	1	8	yes	—
830	#117	C₂³×C₃₁	1	4	yes	—
831	#117	C₂³×C₃₁	1	4	yes	—
832	#117	C₂³×C₃₁	1	8	yes	—
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
836	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
844	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
847	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
848	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
849	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
850	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
851	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
852	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
853	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
854	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
855	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
856	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
857	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
858	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
859	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
860	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
861	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
862	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
863	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
864	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
865	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
866	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
867	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
868	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
869	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
870	C₃₁	#62781	1	1	yes	characteristic, direct product factor, Sylow
871	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
872	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
874	#41	—	2	16	no	—
875	#41	—	2	16	no	—
876	#41	—	2	32	no	—
877	#41	—	2	16	no	—
878	#41	—	4	8	no	—
879	#41	—	4	8	no	—
880	C₂×Q₈	—	2	4	no	—
881	C₂×Q₈	—	4	8	no	—
882	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
883	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
884	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
885	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
886	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
887	C₂×D₄	—	2	8	no	—
888	C₂×D₄	—	2	32	no	—
889	C₂×D₄	—	2	32	no	—
890	C₂×D₄	—	4	8	no	—
891	C₂×D₄	#41×C₃₁	1	8	yes	complemented
892	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
893	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
894	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
895	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
896	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
897	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
898	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
899	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
900	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
901	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
902	C₂²×C₄	—	2	8	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	4	4	no	—
905	C₂²×C₄	—	4	16	no	—
906	C₂²×C₄	—	4	4	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
910	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
914	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
915	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
916	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
922	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
923	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
924	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
927	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
928	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
933	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
934	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
935	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
936	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
938	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
939	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
941	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
942	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
943	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
944	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
945	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
946	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
947	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
948	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
949	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
950	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
951	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
952	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
953	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
954	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
955	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
956	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
957	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
958	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
962	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
963	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
964	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
965	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
966	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
967	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
968	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
969	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
970	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
971	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
972	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
973	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
974	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
975	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
976	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₄²	C₂⁴×C₃₁	1	2	yes	—
978	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₄²	C₂⁴×C₃₁	1	4	yes	—
982	C₄²	C₂⁴×C₃₁	1	2	yes	—
983	C₄²	C₂⁴×C₃₁	1	2	yes	—
984	C₄²	C₂⁴×C₃₁	1	8	yes	—
985	C₄²	C₂⁴×C₃₁	1	4	yes	—
986	C₄²	C₂⁴×C₃₁	1	4	yes	—
987	C₄²	C₂⁴×C₃₁	1	4	yes	—
988	C₄²	C₂⁴×C₃₁	1	2	yes	—
989	C₄²	C₂⁴×C₃₁	1	2	yes	—
990	C₄²	C₂⁴×C₃₁	1	4	yes	—
991	C₄²	C₂⁴×C₃₁	1	2	yes	—
992	C₄²	C₂⁴×C₃₁	1	4	yes	—
993	C₄²	C₂⁴×C₃₁	1	8	yes	—
994	C₄²	C₂⁴×C₃₁	1	16	yes	—
995	C₄²	C₂⁴×C₃₁	1	8	yes	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	16	no	—
998	C₂³	—	4	2	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	—	4	8	no	—
1004	C₂³	C₂×#41×C₃₁	1	8	yes	—
1005	C₂³	C₂⁵×C₃₁	1	8	yes	—
1006	C₂³	C₂⁵×C₃₁	1	2	yes	—
1007	C₂³	C₂⁵×C₃₁	1	4	yes	—
1008	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1009	Q₈	—	2	8	no	—
1010	Q₈	—	2	8	no	—
1011	Q₈	—	2	8	no	—
1012	Q₈	—	4	8	no	—
1013	Q₈	—	4	4	no	—
1014	D₄	—	2	32	no	—
1015	D₄	—	2	16	no	—
1016	D₄	—	2	16	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	2	8	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	8	no	—
1023	D₄	C₂×#41×C₃₁	1	16	yes	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	4	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	8	no	—
1028	C₂×C₄	—	2	16	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	4	no	—
1031	C₂×C₄	—	2	16	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	8	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	16	no	—
1036	C₂×C₄	—	2	8	no	—
1037	C₂×C₄	—	2	4	no	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	4	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	16	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	8	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	8	no	—
1051	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
1052	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1053	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1054	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1055	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1056	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1057	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1058	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
1059	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1060	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1061	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1062	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
1063	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
1064	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1065	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1066	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	8	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	8	no	—
1077	C₂²	—	4	8	no	—
1078	C₂²	—	4	4	no	—
1079	C₂²	—	8	16	no	—
1080	C₂²	C₂²×#41×C₃₁	1	8	yes	—
1081	C₂²	C₂²×#41×C₃₁	1	2	yes	—
1082	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	8	no	—
1086	C₄	—	2	4	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	4	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	8	no	—
1092	C₄	—	2	4	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	C₂²×#41×C₃₁	1	4	yes	—
1096	C₄	C₃₁×#585	1	2	yes	—
1097	C₄	C₃₁×#585	1	2	yes	—
1098	C₂	—	2	2	no	—
1099	C₂	—	2	8	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	4	8	no	—
1102	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
1103	C₂	C₂×C₃₁×#585	1	1	yes	characteristic
1104	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×#3521	C₂	semidirect
2. C₃₁×#3515	C₂	semidirect
3. C₃₁×#3514	C₂	semidirect
4. C₃₁×#3507	C₂	semidirect
5. C₃₁×#3505	C₂	semidirect
6. C₃₁×#3501	C₂	semidirect
7. C₃₁×#3496	C₂	semidirect
8. C₃₁×#3493	C₂	semidirect
9. C₃₁×#3491	C₂	semidirect
10. C₃₁×#3485	C₂	semidirect
11. C₃₁×#3482	C₂	semidirect
12. C₃₁×#3481	C₂	semidirect
13. C₃₁×#3475	C₂	semidirect
14. C₃₁×#3461	C₂	semidirect
15. C₃₁×#3459	C₂	semidirect
16. C₃₁×#3444	C₂	semidirect
17. C₂×C₃₁×#529	C₂	semidirect
18. C₄×C₃₁×H(5,𝔽₂)	C₂	semidirect
19. C₂×C₄×#41×C₃₁	C₂	semidirect
22. C₃₁×#559	C₂²	semidirect
23. C₃₁×#557	C₂²	semidirect
24. C₃₁×#556	C₂²	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
33. C₃₁×#553	C₂²	semidirect
34. C₃₁×#552	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
37. C₃₁×#552	C₂²	semidirect
38. C₃₁×#552	C₂²	semidirect
39. C₃₁×#551	C₂²	semidirect
40. C₃₁×#551	C₂²	semidirect
41. C₃₁×#551	C₂²	semidirect
42. D₄×Q₈×C₃₁	C₂²	semidirect
43. C₃₁×#548	C₂²	semidirect
44. C₃₁×#547	C₂²	semidirect
45. C₃₁×#547	C₂²	semidirect
46. C₃₁×#547	C₂²	semidirect
47. C₃₁×#546	C₂²	semidirect
48. C₃₁×#546	C₂²	semidirect
49. C₃₁×#546	C₂²	semidirect
50. C₃₁×#546	C₂²	semidirect
51. D₄²×C₃₁	C₂²	semidirect
52. C₃₁×#544	C₂²	semidirect
53. C₃₁×#543	C₂²	semidirect
54. C₃₁×#542	C₂²	semidirect
55. C₃₁×#541	C₂²	semidirect
56. C₃₁×#539	C₂²	semidirect
57. C₃₁×#539	C₂²	semidirect
58. C₃₁×#539	C₂²	semidirect
59. C₃₁×#538	C₂²	semidirect
60. C₃₁×#538	C₂²	semidirect
62. C₃₁×#536	C₂²	semidirect
64. C₃₁×#534	C₂²	semidirect
65. C₃₁×#533	C₂²	semidirect
66. C₃₁×#533	C₂²	semidirect
67. C₃₁×#533	C₂²	semidirect
68. C₃₁×#533	C₂²	semidirect
70. C₃₁×#532	C₂²	semidirect
71. C₃₁×#532	C₂²	semidirect
72. C₃₁×#529	C₂²	semidirect
73. C₃₁×#529	C₂²	semidirect
74. C₃₁×#529	C₂²	semidirect
75. C₃₁×#529	C₂²	semidirect
76. C₃₁×#529	C₂²	semidirect
77. C₃₁×#529	C₂²	semidirect
78. C₃₁×#529	C₂²	semidirect
79. C₃₁×#529	C₂²	semidirect
80. C₃₁×#529	C₂²	semidirect
81. C₃₁×#529	C₂²	semidirect
82. C₃₁×#529	C₂²	semidirect
83. C₃₁×#529	C₂²	semidirect
84. C₃₁×#529	C₂²	semidirect
85. C₃₁×#529	C₂²	semidirect
86. C₃₁×#529	C₂²	semidirect
87. C₂×C₃₁×#126	C₂²	semidirect
88. C₂×C₃₁×#125	C₂²	semidirect
89. C₂×C₃₁×#124	C₂²	semidirect
90. C₃₁×#525	C₂²	semidirect
91. C₃₁×#525	C₂²	semidirect
92. C₃₁×#525	C₂²	semidirect
93. C₃₁×#525	C₂²	semidirect
94. C₂×C₃₁×#123	C₂²	semidirect
95. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
97. C₃₁×#520	C₂²	semidirect
98. C₃₁×#520	C₂²	semidirect
100. C₃₁×#518	C₂²	semidirect
101. C₃₁×#518	C₂²	semidirect
102. C₄×#41×C₃₁	C₂²	semidirect
103. C₄×#41×C₃₁	C₂²	semidirect
104. C₄×#41×C₃₁	C₂²	semidirect
105. C₄×#41×C₃₁	C₂²	semidirect
106. C₄×#41×C₃₁	C₂²	semidirect
107. C₄×#41×C₃₁	C₂²	semidirect
108. C₄×#41×C₃₁	C₂²	semidirect
109. C₄×#41×C₃₁	C₂²	semidirect
110. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
111. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
112. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
115. C₂×C₄×D₄×C₃₁	C₂²	semidirect
116. C₂×C₄×D₄×C₃₁	C₂²	semidirect
117. C₂×C₄×D₄×C₃₁	C₂²	semidirect
118. C₂×C₄×D₄×C₃₁	C₂²	semidirect
119. C₂×C₄×D₄×C₃₁	C₂²	semidirect
120. C₂×C₃₁×#117	C₂²	semidirect
121. C₂×C₃₁×#117	C₂²	semidirect
122. C₂×C₃₁×#117	C₂²	semidirect
123. C₂²×C₄²×C₃₁	C₂²	semidirect
124. C₂²×C₄²×C₃₁	C₂²	semidirect
338. C₂×D₄×C₃₁	#41	semidirect
443. #62781	C₃₁	direct (N × H)
515. #3521	C₂×C₃₁	semidirect
516. #3515	C₂×C₃₁	semidirect
517. #3514	C₂×C₃₁	semidirect
518. #3507	C₂×C₃₁	semidirect
519. #3505	C₂×C₃₁	semidirect
520. #3501	C₂×C₃₁	semidirect
521. #3496	C₂×C₃₁	semidirect
522. #3493	C₂×C₃₁	semidirect
523. #3491	C₂×C₃₁	semidirect
524. #3485	C₂×C₃₁	semidirect
525. #3482	C₂×C₃₁	semidirect
526. #3481	C₂×C₃₁	semidirect
527. #3475	C₂×C₃₁	semidirect
528. #3461	C₂×C₃₁	semidirect
529. #3459	C₂×C₃₁	semidirect
530. #3444	C₂×C₃₁	semidirect
531. C₂×#529	C₂×C₃₁	semidirect
532. C₄×H(5,𝔽₂)	C₂×C₃₁	semidirect
533. C₂×C₄×#41	C₂×C₃₁	semidirect
567. #559	C₂²×C₃₁	semidirect
568. #557	C₂²×C₃₁	semidirect
569. #556	C₂²×C₃₁	semidirect
570. #556	C₂²×C₃₁	semidirect
571. #556	C₂²×C₃₁	semidirect
572. #555	C₂²×C₃₁	semidirect
573. #554	C₂²×C₃₁	semidirect
574. #554	C₂²×C₃₁	semidirect
575. #554	C₂²×C₃₁	semidirect
576. #553	C₂²×C₃₁	semidirect
577. #553	C₂²×C₃₁	semidirect
578. #553	C₂²×C₃₁	semidirect
579. #552	C₂²×C₃₁	semidirect
580. #552	C₂²×C₃₁	semidirect
581. #552	C₂²×C₃₁	semidirect
582. #552	C₂²×C₃₁	semidirect
583. #552	C₂²×C₃₁	semidirect
584. #551	C₂²×C₃₁	semidirect
585. #551	C₂²×C₃₁	semidirect
586. #551	C₂²×C₃₁	semidirect
587. D₄×Q₈	C₂²×C₃₁	semidirect
588. #548	C₂²×C₃₁	semidirect
589. #547	C₂²×C₃₁	semidirect
590. #547	C₂²×C₃₁	semidirect
591. #547	C₂²×C₃₁	semidirect
592. #546	C₂²×C₃₁	semidirect
593. #546	C₂²×C₃₁	semidirect
594. #546	C₂²×C₃₁	semidirect
595. #546	C₂²×C₃₁	semidirect
596. D₄²	C₂²×C₃₁	semidirect
597. #544	C₂²×C₃₁	semidirect
598. #543	C₂²×C₃₁	semidirect
599. #542	C₂²×C₃₁	semidirect
600. #541	C₂²×C₃₁	semidirect
601. #539	C₂²×C₃₁	semidirect
602. #539	C₂²×C₃₁	semidirect
603. #539	C₂²×C₃₁	semidirect
604. #538	C₂²×C₃₁	semidirect
605. #538	C₂²×C₃₁	semidirect
607. #536	C₂²×C₃₁	semidirect
609. #534	C₂²×C₃₁	semidirect
610. #533	C₂²×C₃₁	semidirect
611. #533	C₂²×C₃₁	semidirect
612. #533	C₂²×C₃₁	semidirect
613. #533	C₂²×C₃₁	semidirect
615. #532	C₂²×C₃₁	semidirect
616. #532	C₂²×C₃₁	semidirect
617. #529	C₂²×C₃₁	semidirect
618. #529	C₂²×C₃₁	semidirect
619. #529	C₂²×C₃₁	semidirect
620. #529	C₂²×C₃₁	semidirect
621. #529	C₂²×C₃₁	semidirect
622. #529	C₂²×C₃₁	semidirect
623. #529	C₂²×C₃₁	semidirect
624. #529	C₂²×C₃₁	semidirect
625. #529	C₂²×C₃₁	semidirect
626. #529	C₂²×C₃₁	semidirect
627. #529	C₂²×C₃₁	semidirect
628. #529	C₂²×C₃₁	semidirect
629. #529	C₂²×C₃₁	semidirect
630. #529	C₂²×C₃₁	semidirect
631. #529	C₂²×C₃₁	semidirect
632. C₂×#126	C₂²×C₃₁	semidirect
633. C₂×#125	C₂²×C₃₁	semidirect
634. C₂×#124	C₂²×C₃₁	semidirect
635. #525	C₂²×C₃₁	semidirect
636. #525	C₂²×C₃₁	semidirect
637. #525	C₂²×C₃₁	semidirect
638. #525	C₂²×C₃₁	semidirect
639. C₂×#123	C₂²×C₃₁	semidirect
640. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
642. #520	C₂²×C₃₁	semidirect
643. #520	C₂²×C₃₁	semidirect
645. #518	C₂²×C₃₁	semidirect
646. #518	C₂²×C₃₁	semidirect
647. C₄×#41	C₂²×C₃₁	semidirect
648. C₄×#41	C₂²×C₃₁	semidirect
649. C₄×#41	C₂²×C₃₁	semidirect
650. C₄×#41	C₂²×C₃₁	semidirect
651. C₄×#41	C₂²×C₃₁	semidirect
652. C₄×#41	C₂²×C₃₁	semidirect
653. C₄×#41	C₂²×C₃₁	semidirect
654. C₄×#41	C₂²×C₃₁	semidirect
655. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
656. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
657. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
660. C₂×C₄×D₄	C₂²×C₃₁	semidirect
661. C₂×C₄×D₄	C₂²×C₃₁	semidirect
662. C₂×C₄×D₄	C₂²×C₃₁	semidirect
663. C₂×C₄×D₄	C₂²×C₃₁	semidirect
664. C₂×C₄×D₄	C₂²×C₃₁	semidirect
665. C₂×#117	C₂²×C₃₁	semidirect
666. C₂×#117	C₂²×C₃₁	semidirect
667. C₂×#117	C₂²×C₃₁	semidirect
668. C₂²×C₄²	C₂²×C₃₁	semidirect
669. C₂²×C₄²	C₂²×C₃₁	semidirect
870. C₃₁	#62781	direct (N × H)
891. C₂×D₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3521	2
C₃₁×#3515	2
C₃₁×#3514	2
C₃₁×#3507	2
C₃₁×#3505	2
C₃₁×#3501	2
C₃₁×#3496	2
C₃₁×#3493	2
C₃₁×#3491	2
C₃₁×#3485	2
C₃₁×#3482	2
C₃₁×#3481	2
C₃₁×#3475	2
C₃₁×#3461	2
C₃₁×#3459	2
C₃₁×#3444	2
C₂×C₃₁×#529	2
C₄×C₃₁×H(5,𝔽₂)	2
C₂×C₄×#41×C₃₁	2
#62781	31

Subgroups — C31×#62781 #21519540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62781 #21519540