Subgroups — C₃₁×#62800 #21519559

Order 7936.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3522	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3519	C₂	1	6	yes	maximal, complemented
3	C₃₁×#3517	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3514	C₂	1	6	yes	maximal, complemented
5	C₃₁×#3511	C₂	1	3	yes	maximal, complemented
6	C₃₁×#3508	C₂	1	3	yes	maximal, complemented
7	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3494	C₂	1	6	yes	maximal, complemented
10	C₃₁×#3488	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3483	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3481	C₂	1	6	yes	maximal, complemented
13	C₃₁×#3480	C₂	1	2	yes	maximal, complemented
14	D₄×#41×C₃₁	C₂	1	6	yes	maximal, complemented
15	C₃₁×#3460	C₂	1	6	yes	maximal, complemented
16	C₃₁×#3444	C₂	1	3	yes	maximal, complemented
17	C₂×C₃₁×#532	C₂	1	3	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	C₂²×#41×C₃₁	C₂²	1	6	yes	complemented
23	C₃₁×#559	C₂²	1	6	yes	complemented
24	C₃₁×#559	C₂²	1	6	yes	complemented
25	Q₈²×C₃₁	C₂²	1	2	yes	complemented
26	C₃₁×#557	C₂²	1	2	yes	complemented
27	C₃₁×#556	C₂²	1	6	yes	complemented
28	C₃₁×#555	C₂²	1	12	yes	complemented
29	C₃₁×#555	C₂²	1	6	yes	complemented
30	C₃₁×#554	C₂²	1	6	yes	complemented
31	C₃₁×#554	C₂²	1	6	yes	complemented
32	C₃₁×#553	C₂²	1	12	yes	complemented
33	C₃₁×#553	C₂²	1	12	yes	complemented
34	C₃₁×#553	C₂²	1	12	yes	complemented
35	C₃₁×#551	C₂²	1	24	yes	complemented
36	C₃₁×#550	C₂²	1	6	yes	complemented
37	C₃₁×#550	C₂²	1	2	yes	complemented
38	C₃₁×#550	C₂²	1	4	yes	complemented
39	C₃₁×#550	C₂²	1	2	yes	complemented
40	C₃₁×#550	C₂²	1	6	yes	complemented
41	D₄×Q₈×C₃₁	C₂²	1	6	yes	complemented
42	C₃₁×#548	C₂²	1	12	yes	complemented
43	C₃₁×#548	C₂²	1	4	yes	complemented
44	C₃₁×#547	C₂²	1	12	yes	complemented
45	C₃₁×#547	C₂²	1	6	yes	complemented
46	C₃₁×#546	C₂²	1	24	yes	complemented
47	C₃₁×#546	C₂²	1	12	yes	complemented
48	C₃₁×#546	C₂²	1	12	yes	complemented
49	C₃₁×#546	C₂²	1	12	yes	complemented
50	D₄²×C₃₁	C₂²	1	12	yes	complemented
51	D₄²×C₃₁	C₂²	1	6	yes	complemented
52	D₄²×C₃₁	C₂²	1	6	yes	complemented
53	C₃₁×#544	C₂²	1	6	yes	complemented
54	C₃₁×#542	C₂²	1	12	yes	complemented
55	C₃₁×#542	C₂²	1	12	yes	complemented
56	C₃₁×#540	C₂²	1	12	yes	complemented
57	C₃₁×#540	C₂²	1	12	yes	complemented
58	C₃₁×#538	C₂²	1	24	yes	complemented
59	C₃₁×#537	C₂²	1	6	yes	complemented
60	C₃₁×#535	C₂²	1	6	yes	complemented
61	C₃₁×#535	C₂²	1	6	yes	complemented
62	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#533	C₂²	1	3	yes	complemented
64	C₃₁×#533	C₂²	1	3	yes	complemented
65	C₃₁×#532	C₂²	1	3	yes	complemented
66	C₃₁×#532	C₂²	1	6	yes	complemented
67	C₃₁×#532	C₂²	1	6	yes	complemented
68	C₃₁×#532	C₂²	1	6	yes	complemented
69	C₃₁×#532	C₂²	1	6	yes	complemented
70	C₃₁×#532	C₂²	1	6	yes	complemented
71	C₃₁×#532	C₂²	1	6	yes	complemented
72	C₃₁×#532	C₂²	1	6	yes	complemented
73	C₃₁×#532	C₂²	1	3	yes	complemented
74	C₃₁×#532	C₂²	1	3	yes	complemented
75	C₃₁×#532	C₂²	1	12	yes	complemented
76	C₂×C₃₁×C₄⋊Q₈	C₂²	1	3	yes	complemented
77	C₂×C₃₁×#127	C₂²	1	3	yes	complemented
78	C₃₁×#529	C₂²	1	6	yes	complemented
79	C₃₁×#529	C₂²	1	6	yes	complemented
80	C₃₁×#529	C₂²	1	6	yes	complemented
81	C₃₁×#529	C₂²	1	6	yes	complemented
82	C₃₁×#529	C₂²	1	6	yes	complemented
83	C₃₁×#529	C₂²	1	6	yes	complemented
84	C₃₁×#529	C₂²	1	12	yes	complemented
85	C₂×C₃₁×#124	C₂²	1	6	yes	complemented
86	C₃₁×#525	C₂²	1	6	yes	complemented
87	C₃₁×#525	C₂²	1	6	yes	complemented
88	C₃₁×#525	C₂²	1	6	yes	complemented
89	C₃₁×#525	C₂²	1	24	yes	complemented
90	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
91	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
92	C₃₁×#520	C₂²	1	2	yes	—
93	C₃₁×#520	C₂²	1	6	yes	complemented
94	C₃₁×#520	C₂²	1	4	yes	complemented
95	C₃₁×#518	C₂²	1	6	yes	complemented
96	C₃₁×#518	C₂²	1	12	yes	complemented
97	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
99	C₄×#41×C₃₁	C₂²	1	3	yes	complemented
100	C₄×#41×C₃₁	C₂²	1	3	yes	complemented
101	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×#41×C₃₁	C₂²	1	3	yes	complemented
103	C₄×#41×C₃₁	C₂²	1	3	yes	complemented
104	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×#41×C₃₁	C₂²	1	6	yes	complemented
106	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
107	C₄×#41×C₃₁	C₂²	1	6	yes	complemented
108	C₄×#41×C₃₁	C₂²	1	6	yes	complemented
109	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	complemented
112	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	complemented
113	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
114	C₂×C₄×D₄×C₃₁	C₂²	1	12	yes	complemented
115	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
116	C₂×C₃₁×#117	C₂²	1	3	yes	complemented
117	C₂²×C₄²×C₃₁	C₂²	1	3	yes	complemented
118	C₃₁×H(5,𝔽₂)	—	2	16	no	—
119	C₂×#41×C₃₁	—	2	8	no	—
120	C₂×#41×C₃₁	—	4	24	no	—
121	C₂×#41×C₃₁	C₂³	1	3	yes	—
122	C₂×#41×C₃₁	C₂³	1	3	yes	—
123	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×#41×C₃₁	C₂³	1	6	yes	—
125	C₂×#41×C₃₁	C₂³	1	4	yes	—
126	C₂×#41×C₃₁	C₂³	1	6	yes	—
127	C₂×#41×C₃₁	C₂³	1	6	yes	—
128	C₂×#41×C₃₁	C₂³	1	12	yes	—
129	C₂×#41×C₃₁	C₂³	1	12	yes	—
130	C₂×#41×C₃₁	C₂³	1	12	yes	—
131	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
134	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
136	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
137	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
138	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
139	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
140	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
142	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
143	C₂³×C₄×C₃₁	C₂³	1	12	yes	—
144	C₃₁×C₄⋊Q₈	C₂³	1	3	yes	—
145	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
146	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
147	C₃₁×C₄⋊Q₈	C₂³	1	6	yes	—
148	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
149	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₄⋊Q₈	C₂³	1	12	yes	—
151	C₃₁×#127	C₂³	1	3	yes	—
152	C₃₁×#127	C₂³	1	6	yes	—
153	C₃₁×#127	C₂³	1	6	yes	—
154	C₃₁×#127	C₂³	1	6	yes	—
155	C₃₁×#127	C₂³	1	12	yes	—
156	C₃₁×#126	C₂³	1	12	yes	—
157	C₃₁×#126	C₂³	1	12	yes	—
158	C₃₁×#126	C₂³	1	24	yes	—
159	C₃₁×#125	C₂³	1	2	yes	—
160	C₃₁×#125	C₂³	1	6	yes	—
161	C₃₁×#125	C₂³	1	6	yes	—
162	C₃₁×#125	C₂³	1	12	yes	—
163	C₃₁×#124	C₂³	1	6	yes	—
164	C₃₁×#124	C₂³	1	12	yes	—
165	C₃₁×#124	C₂³	1	12	yes	—
166	C₃₁×#124	C₂³	1	12	yes	—
167	C₃₁×#124	C₂³	1	6	yes	—
168	C₃₁×#124	C₂³	1	6	yes	—
169	C₃₁×#124	C₂³	1	12	yes	—
170	C₃₁×#124	C₂³	1	24	yes	—
171	C₃₁×#123	C₂³	1	12	yes	—
172	C₃₁×#123	C₂³	1	12	yes	—
173	C₃₁×#123	C₂³	1	12	yes	—
174	C₃₁×#123	C₂³	1	24	yes	—
175	C₃₁×#123	C₂³	1	24	yes	—
176	C₃₁×#123	C₂³	1	24	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
180	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
181	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
183	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	—
184	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	—
185	C₃₁×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₃₁×#121	C₂³	1	6	yes	—
187	C₃₁×#121	C₂³	1	6	yes	—
188	C₃₁×#121	C₂³	1	12	yes	—
189	C₃₁×#121	C₂³	1	12	yes	—
190	C₃₁×#121	C₂³	1	12	yes	—
191	C₃₁×#121	C₂³	1	12	yes	—
192	C₃₁×#121	C₂³	1	12	yes	—
193	C₃₁×#121	C₂³	1	12	yes	—
194	C₃₁×#121	C₂³	1	6	yes	—
195	C₃₁×#121	C₂³	1	6	yes	—
196	C₃₁×#121	C₂³	1	6	yes	—
197	C₃₁×#121	C₂³	1	6	yes	—
198	C₃₁×#121	C₂³	1	24	yes	—
199	C₃₁×#121	C₂³	1	24	yes	—
200	C₃₁×#121	C₂³	1	12	yes	—
201	C₃₁×#121	C₂³	1	12	yes	—
202	C₃₁×#121	C₂³	1	12	yes	—
203	C₃₁×#121	C₂³	1	24	yes	—
204	C₃₁×#120	C₂³	1	12	yes	—
205	C₃₁×#120	C₂³	1	24	yes	—
206	C₃₁×#120	C₂³	1	24	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	3	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	6	yes	—
222	C₄×D₄×C₃₁	C₂³	1	3	yes	—
223	C₄×D₄×C₃₁	C₂³	1	12	yes	—
224	C₄×D₄×C₃₁	C₂³	1	6	yes	—
225	C₄×D₄×C₃₁	C₂³	1	12	yes	—
226	C₄×D₄×C₃₁	C₂³	1	6	yes	—
227	C₄×D₄×C₃₁	C₂³	1	3	yes	—
228	C₄×D₄×C₃₁	C₂³	1	3	yes	—
229	C₄×D₄×C₃₁	C₂³	1	3	yes	—
230	C₄×D₄×C₃₁	C₂³	1	6	yes	—
231	C₄×D₄×C₃₁	C₂³	1	3	yes	—
232	C₄×D₄×C₃₁	C₂³	1	6	yes	—
233	C₄×D₄×C₃₁	C₂³	1	3	yes	—
234	C₄×D₄×C₃₁	C₂³	1	6	yes	—
235	C₄×D₄×C₃₁	C₂³	1	6	yes	—
236	C₄×D₄×C₃₁	C₂³	1	3	yes	—
237	C₄×D₄×C₃₁	C₂³	1	3	yes	—
238	C₄×D₄×C₃₁	C₂³	1	12	yes	—
239	C₄×D₄×C₃₁	C₂³	1	12	yes	—
240	C₄×D₄×C₃₁	C₂³	1	12	yes	—
241	C₄×D₄×C₃₁	C₂³	1	24	yes	—
242	C₄×D₄×C₃₁	C₂³	1	12	yes	—
243	C₄×D₄×C₃₁	C₂³	1	12	yes	—
244	C₄×D₄×C₃₁	C₂³	1	12	yes	—
245	C₄×D₄×C₃₁	C₂³	1	12	yes	—
246	C₄×D₄×C₃₁	C₂³	1	12	yes	—
247	C₄×D₄×C₃₁	C₂³	1	6	yes	—
248	C₄×D₄×C₃₁	C₂³	1	12	yes	—
249	C₄×D₄×C₃₁	C₂³	1	12	yes	—
250	C₄×D₄×C₃₁	C₂³	1	12	yes	—
251	C₄×D₄×C₃₁	C₂³	1	12	yes	—
252	C₄×D₄×C₃₁	C₂³	1	12	yes	—
253	C₄×D₄×C₃₁	C₂³	1	6	yes	—
254	C₄×D₄×C₃₁	C₂³	1	6	yes	—
255	C₄×D₄×C₃₁	C₂³	1	6	yes	—
256	C₃₁×#117	C₂³	1	3	yes	—
257	C₃₁×#117	C₂³	1	3	yes	—
258	C₃₁×#117	C₂³	1	6	yes	—
259	C₃₁×#117	C₂³	1	6	yes	—
260	C₃₁×#117	C₂³	1	3	yes	—
261	C₃₁×#117	C₂³	1	3	yes	—
262	C₃₁×#117	C₂³	1	2	yes	—
263	C₃₁×#117	C₂³	1	6	yes	—
264	C₃₁×#117	C₂³	1	12	yes	—
265	C₃₁×#117	C₂³	1	12	yes	—
266	C₃₁×#117	C₂³	1	12	yes	—
267	C₃₁×#117	C₂³	1	6	yes	—
268	C₃₁×#117	C₂³	1	12	yes	—
269	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
270	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
271	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
272	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
273	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
276	C₂×C₂²⋊C₄×C₃₁	C₂³	1	24	yes	—
277	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
278	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
280	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
281	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
282	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
283	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
284	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
285	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
286	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
287	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
288	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
289	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
290	C₂×C₄²×C₃₁	C₂³	1	12	yes	—
291	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
292	C₂⁴×C₃₁	C₂⁴	1	12	yes	—
293	#41×C₃₁	—	2	4	no	—
294	#41×C₃₁	—	2	16	no	—
295	#41×C₃₁	—	2	12	no	—
296	#41×C₃₁	—	2	12	no	—
297	#41×C₃₁	—	2	24	no	—
298	#41×C₃₁	—	2	24	no	—
299	#41×C₃₁	—	4	24	no	—
300	#41×C₃₁	—	4	24	no	—
301	#41×C₃₁	—	4	24	no	—
302	#41×C₃₁	—	4	12	no	—
303	#41×C₃₁	#41	1	8	yes	complemented
304	C₂×Q₈×C₃₁	—	2	4	no	—
305	C₂×Q₈×C₃₁	—	4	12	no	—
306	C₂×Q₈×C₃₁	C₂⁴	1	3	yes	—
307	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
308	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₃₁	C₂⁴	1	6	yes	—
310	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
311	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂×D₄×C₃₁	—	2	12	no	—
313	C₂×D₄×C₃₁	—	2	48	no	—
314	C₂×D₄×C₃₁	—	2	24	no	—
315	C₂×D₄×C₃₁	—	4	12	no	—
316	C₂×D₄×C₃₁	—	4	12	no	—
317	C₂×D₄×C₃₁	—	4	24	no	—
318	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
319	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
320	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
321	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
322	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
323	C₂×D₄×C₃₁	C₂⁴	1	3	yes	—
324	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
325	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
326	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
327	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
328	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
329	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
330	C₂×D₄×C₃₁	C₂⁴	1	3	yes	—
331	C₂²×C₄×C₃₁	—	2	12	no	—
332	C₂²×C₄×C₃₁	—	2	12	no	—
333	C₂²×C₄×C₃₁	—	4	6	no	—
334	C₂²×C₄×C₃₁	—	4	24	no	—
335	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
338	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
339	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
340	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
341	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
342	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
343	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
345	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
346	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
347	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
348	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
349	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
350	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
351	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
352	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
353	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
354	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
355	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
356	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
357	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
359	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
360	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
361	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
362	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	6	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
372	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
373	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
376	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
378	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
379	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
381	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
382	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
383	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
384	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
385	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
386	C₂²⋊C₄×C₃₁	C₂⁴	1	6	yes	—
387	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
388	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
389	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
390	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
391	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
392	C₂²⋊C₄×C₃₁	C₂⁴	1	12	yes	—
393	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₄²×C₃₁	C₂⁴	1	3	yes	—
396	C₄²×C₃₁	C₂⁴	1	3	yes	—
397	C₄²×C₃₁	C₂⁴	1	3	yes	—
398	C₄²×C₃₁	C₂⁴	1	3	yes	—
399	C₄²×C₃₁	C₂⁴	1	3	yes	—
400	C₄²×C₃₁	C₂⁴	1	3	yes	—
401	C₄²×C₃₁	C₂⁴	1	3	yes	—
402	C₄²×C₃₁	C₂⁴	1	3	yes	—
403	C₄²×C₃₁	C₂⁴	1	3	yes	—
404	C₄²×C₃₁	C₂⁴	1	3	yes	—
405	C₄²×C₃₁	C₂⁴	1	12	yes	—
406	C₄²×C₃₁	C₂⁴	1	12	yes	—
407	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄²×C₃₁	C₂⁴	1	3	yes	—
409	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄²×C₃₁	C₂⁴	1	3	yes	—
411	C₄²×C₃₁	C₂⁴	1	4	yes	—
412	#62800	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂³×C₃₁	—	2	6	no	—
414	C₂³×C₃₁	—	2	6	no	—
415	C₂³×C₃₁	—	2	24	no	—
416	C₂³×C₃₁	—	4	3	no	—
417	C₂³×C₃₁	—	4	12	no	—
418	C₂³×C₃₁	—	4	12	no	—
419	C₂³×C₃₁	C₂⁵	1	12	yes	—
420	C₂³×C₃₁	C₂⁵	1	3	yes	—
421	C₂³×C₃₁	C₂⁵	1	3	yes	—
422	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
423	Q₈×C₃₁	—	2	6	no	—
424	Q₈×C₃₁	—	2	4	no	—
425	Q₈×C₃₁	—	2	12	no	—
426	Q₈×C₃₁	—	2	4	no	—
427	Q₈×C₃₁	—	4	12	no	—
428	Q₈×C₃₁	C₂×#41	1	4	yes	complemented
429	D₄×C₃₁	—	2	24	no	—
430	D₄×C₃₁	—	2	12	no	—
431	D₄×C₃₁	—	2	24	no	—
432	D₄×C₃₁	—	2	24	no	—
433	D₄×C₃₁	—	2	12	no	—
434	D₄×C₃₁	—	2	6	no	—
435	D₄×C₃₁	—	2	12	no	—
436	D₄×C₃₁	—	2	12	no	—
437	D₄×C₃₁	—	4	12	no	—
438	D₄×C₃₁	—	4	12	no	—
439	D₄×C₃₁	—	4	24	no	—
440	D₄×C₃₁	—	4	12	no	—
441	D₄×C₃₁	C₂×#41	1	12	yes	complemented
442	C₂×C₄×C₃₁	—	2	6	no	—
443	C₂×C₄×C₃₁	—	2	6	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	6	no	—
446	C₂×C₄×C₃₁	—	2	6	no	—
447	C₂×C₄×C₃₁	—	2	6	no	—
448	C₂×C₄×C₃₁	—	2	24	no	—
449	C₂×C₄×C₃₁	—	2	6	no	—
450	C₂×C₄×C₃₁	—	2	6	no	—
451	C₂×C₄×C₃₁	—	2	6	no	—
452	C₂×C₄×C₃₁	—	2	6	no	—
453	C₂×C₄×C₃₁	—	2	24	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	6	no	—
456	C₂×C₄×C₃₁	—	2	6	no	—
457	C₂×C₄×C₃₁	—	4	3	no	—
458	C₂×C₄×C₃₁	—	4	3	no	—
459	C₂×C₄×C₃₁	—	4	3	no	—
460	C₂×C₄×C₃₁	—	4	12	no	—
461	C₂×C₄×C₃₁	—	4	24	no	—
462	C₂×C₄×C₃₁	—	4	12	no	—
463	C₂×C₄×C₃₁	C₂×#41	1	12	yes	complemented
464	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	complemented
465	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
466	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
467	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
468	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
469	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
470	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
471	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
472	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
473	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
474	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
475	C₂×C₄×C₃₁	C₂⁵	1	3	yes	—
476	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
479	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
480	#3522	C₂×C₃₁	1	2	yes	complemented
481	#3519	C₂×C₃₁	1	6	yes	complemented
482	#3517	C₂×C₃₁	1	2	yes	complemented
483	#3514	C₂×C₃₁	1	6	yes	complemented
484	#3511	C₂×C₃₁	1	3	yes	complemented
485	#3508	C₂×C₃₁	1	3	yes	complemented
486	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3494	C₂×C₃₁	1	6	yes	complemented
489	#3488	C₂×C₃₁	1	2	yes	complemented
490	#3483	C₂×C₃₁	1	2	yes	complemented
491	#3481	C₂×C₃₁	1	6	yes	complemented
492	#3480	C₂×C₃₁	1	2	yes	complemented
493	D₄×#41	C₂×C₃₁	1	6	yes	complemented
494	#3460	C₂×C₃₁	1	6	yes	complemented
495	#3444	C₂×C₃₁	1	3	yes	complemented
496	C₂×#532	C₂×C₃₁	1	3	yes	complemented
497	C₄×H(5,𝔽₂)	C₂×C₃₁	1	2	yes	complemented
498	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
499	C₂²×C₃₁	—	2	1	no	—
500	C₂²×C₃₁	—	2	3	no	—
501	C₂²×C₃₁	—	2	1	no	—
502	C₂²×C₃₁	—	2	3	no	—
503	C₂²×C₃₁	—	2	3	no	—
504	C₂²×C₃₁	—	2	12	no	—
505	C₂²×C₃₁	—	2	3	no	—
506	C₂²×C₃₁	—	2	12	no	—
507	C₂²×C₃₁	—	2	3	no	—
508	C₂²×C₃₁	—	2	12	no	—
509	C₂²×C₃₁	—	4	12	no	—
510	C₂²×C₃₁	—	8	24	no	—
511	C₂²×C₃₁	C₂²×#41	1	6	yes	—
512	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
513	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
514	C₄×C₃₁	—	2	1	no	—
515	C₄×C₃₁	—	2	4	no	—
516	C₄×C₃₁	—	2	3	no	—
517	C₄×C₃₁	—	2	3	no	—
518	C₄×C₃₁	—	2	3	no	—
519	C₄×C₃₁	—	2	12	no	—
520	C₄×C₃₁	—	2	1	no	—
521	C₄×C₃₁	—	2	3	no	—
522	C₄×C₃₁	—	2	3	no	—
523	C₄×C₃₁	—	2	4	no	—
524	C₄×C₃₁	C₂²×#41	1	6	yes	—
525	C₄×C₃₁	C₂²×#41	1	2	yes	—
526	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
527	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
528	C₄×C₃₁	#585	1	2	yes	—
529	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
530	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
531	C₂²×#41	C₂²×C₃₁	1	6	yes	complemented
532	#559	C₂²×C₃₁	1	6	yes	complemented
533	#559	C₂²×C₃₁	1	6	yes	complemented
534	Q₈²	C₂²×C₃₁	1	2	yes	complemented
535	#557	C₂²×C₃₁	1	2	yes	complemented
536	#556	C₂²×C₃₁	1	6	yes	complemented
537	#555	C₂²×C₃₁	1	12	yes	complemented
538	#555	C₂²×C₃₁	1	6	yes	complemented
539	#554	C₂²×C₃₁	1	6	yes	complemented
540	#554	C₂²×C₃₁	1	6	yes	complemented
541	#553	C₂²×C₃₁	1	12	yes	complemented
542	#553	C₂²×C₃₁	1	12	yes	complemented
543	#553	C₂²×C₃₁	1	12	yes	complemented
544	#551	C₂²×C₃₁	1	24	yes	complemented
545	#550	C₂²×C₃₁	1	6	yes	complemented
546	#550	C₂²×C₃₁	1	2	yes	complemented
547	#550	C₂²×C₃₁	1	4	yes	complemented
548	#550	C₂²×C₃₁	1	2	yes	complemented
549	#550	C₂²×C₃₁	1	6	yes	complemented
550	D₄×Q₈	C₂²×C₃₁	1	6	yes	complemented
551	#548	C₂²×C₃₁	1	12	yes	complemented
552	#548	C₂²×C₃₁	1	4	yes	complemented
553	#547	C₂²×C₃₁	1	12	yes	complemented
554	#547	C₂²×C₃₁	1	6	yes	complemented
555	#546	C₂²×C₃₁	1	24	yes	complemented
556	#546	C₂²×C₃₁	1	12	yes	complemented
557	#546	C₂²×C₃₁	1	12	yes	complemented
558	#546	C₂²×C₃₁	1	12	yes	complemented
559	D₄²	C₂²×C₃₁	1	12	yes	complemented
560	D₄²	C₂²×C₃₁	1	6	yes	complemented
561	D₄²	C₂²×C₃₁	1	6	yes	complemented
562	#544	C₂²×C₃₁	1	6	yes	complemented
563	#542	C₂²×C₃₁	1	12	yes	complemented
564	#542	C₂²×C₃₁	1	12	yes	complemented
565	#540	C₂²×C₃₁	1	12	yes	complemented
566	#540	C₂²×C₃₁	1	12	yes	complemented
567	#538	C₂²×C₃₁	1	24	yes	complemented
568	#537	C₂²×C₃₁	1	6	yes	complemented
569	#535	C₂²×C₃₁	1	6	yes	complemented
570	#535	C₂²×C₃₁	1	6	yes	complemented
571	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#533	C₂²×C₃₁	1	3	yes	complemented
573	#533	C₂²×C₃₁	1	3	yes	complemented
574	#532	C₂²×C₃₁	1	3	yes	complemented
575	#532	C₂²×C₃₁	1	6	yes	complemented
576	#532	C₂²×C₃₁	1	6	yes	complemented
577	#532	C₂²×C₃₁	1	6	yes	complemented
578	#532	C₂²×C₃₁	1	6	yes	complemented
579	#532	C₂²×C₃₁	1	6	yes	complemented
580	#532	C₂²×C₃₁	1	6	yes	complemented
581	#532	C₂²×C₃₁	1	6	yes	complemented
582	#532	C₂²×C₃₁	1	3	yes	complemented
583	#532	C₂²×C₃₁	1	3	yes	complemented
584	#532	C₂²×C₃₁	1	12	yes	complemented
585	C₂×C₄⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
586	C₂×#127	C₂²×C₃₁	1	3	yes	complemented
587	#529	C₂²×C₃₁	1	6	yes	complemented
588	#529	C₂²×C₃₁	1	6	yes	complemented
589	#529	C₂²×C₃₁	1	6	yes	complemented
590	#529	C₂²×C₃₁	1	6	yes	complemented
591	#529	C₂²×C₃₁	1	6	yes	complemented
592	#529	C₂²×C₃₁	1	6	yes	complemented
593	#529	C₂²×C₃₁	1	12	yes	complemented
594	C₂×#124	C₂²×C₃₁	1	6	yes	complemented
595	#525	C₂²×C₃₁	1	6	yes	complemented
596	#525	C₂²×C₃₁	1	6	yes	complemented
597	#525	C₂²×C₃₁	1	6	yes	complemented
598	#525	C₂²×C₃₁	1	24	yes	complemented
599	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
600	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
601	#520	C₂²×C₃₁	1	2	yes	—
602	#520	C₂²×C₃₁	1	6	yes	complemented
603	#520	C₂²×C₃₁	1	4	yes	complemented
604	#518	C₂²×C₃₁	1	6	yes	complemented
605	#518	C₂²×C₃₁	1	12	yes	complemented
606	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
607	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
608	C₄×#41	C₂²×C₃₁	1	3	yes	complemented
609	C₄×#41	C₂²×C₃₁	1	3	yes	complemented
610	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	C₄×#41	C₂²×C₃₁	1	3	yes	complemented
612	C₄×#41	C₂²×C₃₁	1	3	yes	complemented
613	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	C₄×#41	C₂²×C₃₁	1	6	yes	complemented
615	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
616	C₄×#41	C₂²×C₃₁	1	6	yes	complemented
617	C₄×#41	C₂²×C₃₁	1	6	yes	complemented
618	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
619	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	complemented
621	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	complemented
622	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
623	C₂×C₄×D₄	C₂²×C₃₁	1	12	yes	complemented
624	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
625	C₂×#117	C₂²×C₃₁	1	3	yes	complemented
626	C₂²×C₄²	C₂²×C₃₁	1	3	yes	complemented
627	C₂×C₃₁	—	2	2	no	—
628	C₂×C₃₁	—	2	6	no	—
629	C₂×C₃₁	—	4	3	no	—
630	C₂×C₃₁	—	4	12	no	—
631	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
632	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
634	H(5,𝔽₂)	—	2	16	no	—
635	C₂×#41	—	2	8	no	—
636	C₂×#41	—	4	24	no	—
637	C₂×#41	C₂³×C₃₁	1	3	yes	—
638	C₂×#41	C₂³×C₃₁	1	3	yes	—
639	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×#41	C₂³×C₃₁	1	6	yes	—
641	C₂×#41	C₂³×C₃₁	1	4	yes	—
642	C₂×#41	C₂³×C₃₁	1	6	yes	—
643	C₂×#41	C₂³×C₃₁	1	6	yes	—
644	C₂×#41	C₂³×C₃₁	1	12	yes	—
645	C₂×#41	C₂³×C₃₁	1	12	yes	—
646	C₂×#41	C₂³×C₃₁	1	12	yes	—
647	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
649	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
650	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
651	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
652	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
653	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
654	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
655	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
656	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
657	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
658	C₂³×C₄	C₂³×C₃₁	1	12	yes	—
659	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
660	C₄⋊Q₈	C₂³×C₃₁	1	3	yes	—
661	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
662	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
663	C₄⋊Q₈	C₂³×C₃₁	1	6	yes	—
664	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
665	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
666	C₄⋊Q₈	C₂³×C₃₁	1	12	yes	—
667	#127	C₂³×C₃₁	1	3	yes	—
668	#127	C₂³×C₃₁	1	6	yes	—
669	#127	C₂³×C₃₁	1	6	yes	—
670	#127	C₂³×C₃₁	1	6	yes	—
671	#127	C₂³×C₃₁	1	12	yes	—
672	#126	C₂³×C₃₁	1	12	yes	—
673	#126	C₂³×C₃₁	1	12	yes	—
674	#126	C₂³×C₃₁	1	24	yes	—
675	#125	C₂³×C₃₁	1	2	yes	—
676	#125	C₂³×C₃₁	1	6	yes	—
677	#125	C₂³×C₃₁	1	6	yes	—
678	#125	C₂³×C₃₁	1	12	yes	—
679	#124	C₂³×C₃₁	1	6	yes	—
680	#124	C₂³×C₃₁	1	12	yes	—
681	#124	C₂³×C₃₁	1	12	yes	—
682	#124	C₂³×C₃₁	1	12	yes	—
683	#124	C₂³×C₃₁	1	6	yes	—
684	#124	C₂³×C₃₁	1	6	yes	—
685	#124	C₂³×C₃₁	1	12	yes	—
686	#124	C₂³×C₃₁	1	24	yes	—
687	#123	C₂³×C₃₁	1	12	yes	—
688	#123	C₂³×C₃₁	1	12	yes	—
689	#123	C₂³×C₃₁	1	12	yes	—
690	#123	C₂³×C₃₁	1	24	yes	—
691	#123	C₂³×C₃₁	1	24	yes	—
692	#123	C₂³×C₃₁	1	24	yes	—
693	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
696	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
697	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
698	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
699	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	—
700	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	—
701	C₂²⋊Q₈	C₂³×C₃₁	1	12	yes	—
702	#121	C₂³×C₃₁	1	6	yes	—
703	#121	C₂³×C₃₁	1	6	yes	—
704	#121	C₂³×C₃₁	1	12	yes	—
705	#121	C₂³×C₃₁	1	12	yes	—
706	#121	C₂³×C₃₁	1	12	yes	—
707	#121	C₂³×C₃₁	1	12	yes	—
708	#121	C₂³×C₃₁	1	12	yes	—
709	#121	C₂³×C₃₁	1	12	yes	—
710	#121	C₂³×C₃₁	1	6	yes	—
711	#121	C₂³×C₃₁	1	6	yes	—
712	#121	C₂³×C₃₁	1	6	yes	—
713	#121	C₂³×C₃₁	1	6	yes	—
714	#121	C₂³×C₃₁	1	24	yes	—
715	#121	C₂³×C₃₁	1	24	yes	—
716	#121	C₂³×C₃₁	1	12	yes	—
717	#121	C₂³×C₃₁	1	12	yes	—
718	#121	C₂³×C₃₁	1	12	yes	—
719	#121	C₂³×C₃₁	1	24	yes	—
720	#120	C₂³×C₃₁	1	12	yes	—
721	#120	C₂³×C₃₁	1	24	yes	—
722	#120	C₂³×C₃₁	1	24	yes	—
723	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
728	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
729	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
730	C₄×Q₈	C₂³×C₃₁	1	3	yes	—
731	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
732	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
733	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
734	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
735	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
736	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
737	C₄×Q₈	C₂³×C₃₁	1	6	yes	—
738	C₄×D₄	C₂³×C₃₁	1	3	yes	—
739	C₄×D₄	C₂³×C₃₁	1	12	yes	—
740	C₄×D₄	C₂³×C₃₁	1	6	yes	—
741	C₄×D₄	C₂³×C₃₁	1	12	yes	—
742	C₄×D₄	C₂³×C₃₁	1	6	yes	—
743	C₄×D₄	C₂³×C₃₁	1	3	yes	—
744	C₄×D₄	C₂³×C₃₁	1	3	yes	—
745	C₄×D₄	C₂³×C₃₁	1	3	yes	—
746	C₄×D₄	C₂³×C₃₁	1	6	yes	—
747	C₄×D₄	C₂³×C₃₁	1	3	yes	—
748	C₄×D₄	C₂³×C₃₁	1	6	yes	—
749	C₄×D₄	C₂³×C₃₁	1	3	yes	—
750	C₄×D₄	C₂³×C₃₁	1	6	yes	—
751	C₄×D₄	C₂³×C₃₁	1	6	yes	—
752	C₄×D₄	C₂³×C₃₁	1	3	yes	—
753	C₄×D₄	C₂³×C₃₁	1	3	yes	—
754	C₄×D₄	C₂³×C₃₁	1	12	yes	—
755	C₄×D₄	C₂³×C₃₁	1	12	yes	—
756	C₄×D₄	C₂³×C₃₁	1	12	yes	—
757	C₄×D₄	C₂³×C₃₁	1	24	yes	—
758	C₄×D₄	C₂³×C₃₁	1	12	yes	—
759	C₄×D₄	C₂³×C₃₁	1	12	yes	—
760	C₄×D₄	C₂³×C₃₁	1	12	yes	—
761	C₄×D₄	C₂³×C₃₁	1	12	yes	—
762	C₄×D₄	C₂³×C₃₁	1	12	yes	—
763	C₄×D₄	C₂³×C₃₁	1	6	yes	—
764	C₄×D₄	C₂³×C₃₁	1	12	yes	—
765	C₄×D₄	C₂³×C₃₁	1	12	yes	—
766	C₄×D₄	C₂³×C₃₁	1	12	yes	—
767	C₄×D₄	C₂³×C₃₁	1	12	yes	—
768	C₄×D₄	C₂³×C₃₁	1	12	yes	—
769	C₄×D₄	C₂³×C₃₁	1	6	yes	—
770	C₄×D₄	C₂³×C₃₁	1	6	yes	—
771	C₄×D₄	C₂³×C₃₁	1	6	yes	—
772	#117	C₂³×C₃₁	1	3	yes	—
773	#117	C₂³×C₃₁	1	3	yes	—
774	#117	C₂³×C₃₁	1	6	yes	—
775	#117	C₂³×C₃₁	1	6	yes	—
776	#117	C₂³×C₃₁	1	3	yes	—
777	#117	C₂³×C₃₁	1	3	yes	—
778	#117	C₂³×C₃₁	1	2	yes	—
779	#117	C₂³×C₃₁	1	6	yes	—
780	#117	C₂³×C₃₁	1	12	yes	—
781	#117	C₂³×C₃₁	1	12	yes	—
782	#117	C₂³×C₃₁	1	12	yes	—
783	#117	C₂³×C₃₁	1	6	yes	—
784	#117	C₂³×C₃₁	1	12	yes	—
785	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
786	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
787	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
788	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
789	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₃₁	1	24	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
794	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
795	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
796	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
797	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
798	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
799	C₂×C₄²	C₂³×C₃₁	1	12	yes	—
800	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
801	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
802	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
803	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
804	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
805	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
806	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
807	C₃₁	#62800	1	1	yes	characteristic, direct product factor, Sylow
808	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
809	C₂⁴	C₂⁴×C₃₁	1	12	yes	—
810	#41	—	2	4	no	—
811	#41	—	2	16	no	—
812	#41	—	2	12	no	—
813	#41	—	2	12	no	—
814	#41	—	2	24	no	—
815	#41	—	2	24	no	—
816	#41	—	4	24	no	—
817	#41	—	4	24	no	—
818	#41	—	4	24	no	—
819	#41	—	4	12	no	—
820	#41	#41×C₃₁	1	8	yes	complemented
821	C₂×Q₈	—	2	4	no	—
822	C₂×Q₈	—	4	12	no	—
823	C₂×Q₈	C₂⁴×C₃₁	1	3	yes	—
824	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
825	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
826	C₂×Q₈	C₂⁴×C₃₁	1	6	yes	—
827	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
828	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₂×D₄	—	2	12	no	—
830	C₂×D₄	—	2	48	no	—
831	C₂×D₄	—	2	24	no	—
832	C₂×D₄	—	4	12	no	—
833	C₂×D₄	—	4	12	no	—
834	C₂×D₄	—	4	24	no	—
835	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
836	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
837	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
838	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
839	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
840	C₂×D₄	C₂⁴×C₃₁	1	3	yes	—
841	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
842	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
843	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
844	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
845	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
846	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
847	C₂×D₄	C₂⁴×C₃₁	1	3	yes	—
848	C₂²×C₄	—	2	12	no	—
849	C₂²×C₄	—	2	12	no	—
850	C₂²×C₄	—	4	6	no	—
851	C₂²×C₄	—	4	24	no	—
852	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
855	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
856	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
857	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
858	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
859	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
860	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
861	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
862	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
863	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
864	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
865	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
866	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
867	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
868	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
869	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
870	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
871	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
872	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
873	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
874	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
876	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
877	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
878	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
879	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
880	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
881	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
882	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
883	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
884	C₄⋊C₄	C₂⁴×C₃₁	1	6	yes	—
885	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
886	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
887	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
888	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
889	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
890	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
891	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
892	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
893	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
894	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
895	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
896	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
897	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
898	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
899	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
900	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
901	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
902	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
903	C₂²⋊C₄	C₂⁴×C₃₁	1	6	yes	—
904	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
905	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
906	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
907	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
908	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
909	C₂²⋊C₄	C₂⁴×C₃₁	1	12	yes	—
910	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₄²	C₂⁴×C₃₁	1	3	yes	—
912	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₄²	C₂⁴×C₃₁	1	3	yes	—
916	C₄²	C₂⁴×C₃₁	1	3	yes	—
917	C₄²	C₂⁴×C₃₁	1	3	yes	—
918	C₄²	C₂⁴×C₃₁	1	3	yes	—
919	C₄²	C₂⁴×C₃₁	1	4	yes	—
920	C₄²	C₂⁴×C₃₁	1	3	yes	—
921	C₄²	C₂⁴×C₃₁	1	3	yes	—
922	C₄²	C₂⁴×C₃₁	1	3	yes	—
923	C₄²	C₂⁴×C₃₁	1	3	yes	—
924	C₄²	C₂⁴×C₃₁	1	3	yes	—
925	C₄²	C₂⁴×C₃₁	1	3	yes	—
926	C₄²	C₂⁴×C₃₁	1	3	yes	—
927	C₄²	C₂⁴×C₃₁	1	12	yes	—
928	C₄²	C₂⁴×C₃₁	1	12	yes	—
929	C₂³	—	2	6	no	—
930	C₂³	—	2	6	no	—
931	C₂³	—	2	24	no	—
932	C₂³	—	4	3	no	—
933	C₂³	—	4	12	no	—
934	C₂³	—	4	12	no	—
935	C₂³	C₂⁵×C₃₁	1	12	yes	—
936	C₂³	C₂⁵×C₃₁	1	3	yes	—
937	C₂³	C₂⁵×C₃₁	1	3	yes	—
938	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
939	Q₈	—	2	6	no	—
940	Q₈	—	2	4	no	—
941	Q₈	—	2	12	no	—
942	Q₈	—	2	4	no	—
943	Q₈	—	4	12	no	—
944	Q₈	C₂×#41×C₃₁	1	4	yes	complemented
945	D₄	—	2	24	no	—
946	D₄	—	2	12	no	—
947	D₄	—	2	24	no	—
948	D₄	—	2	24	no	—
949	D₄	—	2	12	no	—
950	D₄	—	2	6	no	—
951	D₄	—	2	12	no	—
952	D₄	—	2	12	no	—
953	D₄	—	4	12	no	—
954	D₄	—	4	12	no	—
955	D₄	—	4	24	no	—
956	D₄	—	4	12	no	—
957	D₄	C₂×#41×C₃₁	1	12	yes	complemented
958	C₂×C₄	—	2	6	no	—
959	C₂×C₄	—	2	6	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	6	no	—
962	C₂×C₄	—	2	6	no	—
963	C₂×C₄	—	2	6	no	—
964	C₂×C₄	—	2	24	no	—
965	C₂×C₄	—	2	6	no	—
966	C₂×C₄	—	2	6	no	—
967	C₂×C₄	—	2	6	no	—
968	C₂×C₄	—	2	6	no	—
969	C₂×C₄	—	2	24	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	6	no	—
972	C₂×C₄	—	2	6	no	—
973	C₂×C₄	—	4	3	no	—
974	C₂×C₄	—	4	3	no	—
975	C₂×C₄	—	4	3	no	—
976	C₂×C₄	—	4	12	no	—
977	C₂×C₄	—	4	24	no	—
978	C₂×C₄	—	4	12	no	—
979	C₂×C₄	C₂×#41×C₃₁	1	12	yes	complemented
980	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	complemented
981	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
982	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
983	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
984	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
985	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
986	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
987	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
988	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
989	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
990	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
991	C₂×C₄	C₂⁵×C₃₁	1	3	yes	—
992	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
993	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
994	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
995	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
996	C₂²	—	2	1	no	—
997	C₂²	—	2	3	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	3	no	—
1000	C₂²	—	2	3	no	—
1001	C₂²	—	2	12	no	—
1002	C₂²	—	2	3	no	—
1003	C₂²	—	2	12	no	—
1004	C₂²	—	2	3	no	—
1005	C₂²	—	2	12	no	—
1006	C₂²	—	4	12	no	—
1007	C₂²	—	8	24	no	—
1008	C₂²	C₂²×#41×C₃₁	1	6	yes	—
1009	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1010	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	4	no	—
1013	C₄	—	2	3	no	—
1014	C₄	—	2	3	no	—
1015	C₄	—	2	3	no	—
1016	C₄	—	2	12	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	3	no	—
1019	C₄	—	2	3	no	—
1020	C₄	—	2	4	no	—
1021	C₄	C₂²×#41×C₃₁	1	6	yes	—
1022	C₄	C₂²×#41×C₃₁	1	2	yes	—
1023	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1024	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1025	C₄	C₃₁×#585	1	2	yes	—
1026	C₂	—	2	2	no	—
1027	C₂	—	2	6	no	—
1028	C₂	—	4	3	no	—
1029	C₂	—	4	12	no	—
1030	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
1031	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1032	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×#3522	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3517	C₂	semidirect
4. C₃₁×#3514	C₂	semidirect
5. C₃₁×#3511	C₂	semidirect
6. C₃₁×#3508	C₂	semidirect
7. C₃₁×#3503	C₂	semidirect
8. C₃₁×#3498	C₂	semidirect
9. C₃₁×#3494	C₂	semidirect
10. C₃₁×#3488	C₂	semidirect
11. C₃₁×#3483	C₂	semidirect
12. C₃₁×#3481	C₂	semidirect
13. C₃₁×#3480	C₂	semidirect
14. D₄×#41×C₃₁	C₂	semidirect
15. C₃₁×#3460	C₂	semidirect
16. C₃₁×#3444	C₂	semidirect
17. C₂×C₃₁×#532	C₂	semidirect
18. C₄×C₃₁×H(5,𝔽₂)	C₂	semidirect
19. C₂×C₄×#41×C₃₁	C₂	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
23. C₃₁×#559	C₂²	semidirect
24. C₃₁×#559	C₂²	semidirect
25. Q₈²×C₃₁	C₂²	semidirect
26. C₃₁×#557	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
28. C₃₁×#555	C₂²	semidirect
29. C₃₁×#555	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
33. C₃₁×#553	C₂²	semidirect
34. C₃₁×#553	C₂²	semidirect
35. C₃₁×#551	C₂²	semidirect
36. C₃₁×#550	C₂²	semidirect
37. C₃₁×#550	C₂²	semidirect
38. C₃₁×#550	C₂²	semidirect
39. C₃₁×#550	C₂²	semidirect
40. C₃₁×#550	C₂²	semidirect
41. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#548	C₂²	semidirect
43. C₃₁×#548	C₂²	semidirect
44. C₃₁×#547	C₂²	semidirect
45. C₃₁×#547	C₂²	semidirect
46. C₃₁×#546	C₂²	semidirect
47. C₃₁×#546	C₂²	semidirect
48. C₃₁×#546	C₂²	semidirect
49. C₃₁×#546	C₂²	semidirect
50. D₄²×C₃₁	C₂²	semidirect
51. D₄²×C₃₁	C₂²	semidirect
52. D₄²×C₃₁	C₂²	semidirect
53. C₃₁×#544	C₂²	semidirect
54. C₃₁×#542	C₂²	semidirect
55. C₃₁×#542	C₂²	semidirect
56. C₃₁×#540	C₂²	semidirect
57. C₃₁×#540	C₂²	semidirect
58. C₃₁×#538	C₂²	semidirect
59. C₃₁×#537	C₂²	semidirect
60. C₃₁×#535	C₂²	semidirect
61. C₃₁×#535	C₂²	semidirect
62. C₃₁×#533	C₂²	semidirect
63. C₃₁×#533	C₂²	semidirect
64. C₃₁×#533	C₂²	semidirect
65. C₃₁×#532	C₂²	semidirect
66. C₃₁×#532	C₂²	semidirect
67. C₃₁×#532	C₂²	semidirect
68. C₃₁×#532	C₂²	semidirect
69. C₃₁×#532	C₂²	semidirect
70. C₃₁×#532	C₂²	semidirect
71. C₃₁×#532	C₂²	semidirect
72. C₃₁×#532	C₂²	semidirect
73. C₃₁×#532	C₂²	semidirect
74. C₃₁×#532	C₂²	semidirect
75. C₃₁×#532	C₂²	semidirect
76. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
77. C₂×C₃₁×#127	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. C₂×C₃₁×#124	C₂²	semidirect
86. C₃₁×#525	C₂²	semidirect
87. C₃₁×#525	C₂²	semidirect
88. C₃₁×#525	C₂²	semidirect
89. C₃₁×#525	C₂²	semidirect
90. C₂×C₃₁×#121	C₂²	semidirect
91. C₂×C₃₁×#121	C₂²	semidirect
93. C₃₁×#520	C₂²	semidirect
94. C₃₁×#520	C₂²	semidirect
95. C₃₁×#518	C₂²	semidirect
96. C₃₁×#518	C₂²	semidirect
99. C₄×#41×C₃₁	C₂²	semidirect
100. C₄×#41×C₃₁	C₂²	semidirect
101. C₄×#41×C₃₁	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. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
110. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
111. C₂×C₄×D₄×C₃₁	C₂²	semidirect
112. C₂×C₄×D₄×C₃₁	C₂²	semidirect
113. C₂×C₄×D₄×C₃₁	C₂²	semidirect
114. C₂×C₄×D₄×C₃₁	C₂²	semidirect
115. C₂×C₄×D₄×C₃₁	C₂²	semidirect
116. C₂×C₃₁×#117	C₂²	semidirect
117. C₂²×C₄²×C₃₁	C₂²	semidirect
303. #41×C₃₁	#41	semidirect
412. #62800	C₃₁	direct (N × H)
428. Q₈×C₃₁	C₂×#41	semidirect
441. D₄×C₃₁	C₂×#41	semidirect
463. C₂×C₄×C₃₁	C₂×#41	semidirect
464. C₂×C₄×C₃₁	H(5,𝔽₂)	semidirect
480. #3522	C₂×C₃₁	semidirect
481. #3519	C₂×C₃₁	semidirect
482. #3517	C₂×C₃₁	semidirect
483. #3514	C₂×C₃₁	semidirect
484. #3511	C₂×C₃₁	semidirect
485. #3508	C₂×C₃₁	semidirect
486. #3503	C₂×C₃₁	semidirect
487. #3498	C₂×C₃₁	semidirect
488. #3494	C₂×C₃₁	semidirect
489. #3488	C₂×C₃₁	semidirect
490. #3483	C₂×C₃₁	semidirect
491. #3481	C₂×C₃₁	semidirect
492. #3480	C₂×C₃₁	semidirect
493. D₄×#41	C₂×C₃₁	semidirect
494. #3460	C₂×C₃₁	semidirect
495. #3444	C₂×C₃₁	semidirect
496. C₂×#532	C₂×C₃₁	semidirect
497. C₄×H(5,𝔽₂)	C₂×C₃₁	semidirect
498. C₂×C₄×#41	C₂×C₃₁	semidirect
531. C₂²×#41	C₂²×C₃₁	semidirect
532. #559	C₂²×C₃₁	semidirect
533. #559	C₂²×C₃₁	semidirect
534. Q₈²	C₂²×C₃₁	semidirect
535. #557	C₂²×C₃₁	semidirect
536. #556	C₂²×C₃₁	semidirect
537. #555	C₂²×C₃₁	semidirect
538. #555	C₂²×C₃₁	semidirect
539. #554	C₂²×C₃₁	semidirect
540. #554	C₂²×C₃₁	semidirect
541. #553	C₂²×C₃₁	semidirect
542. #553	C₂²×C₃₁	semidirect
543. #553	C₂²×C₃₁	semidirect
544. #551	C₂²×C₃₁	semidirect
545. #550	C₂²×C₃₁	semidirect
546. #550	C₂²×C₃₁	semidirect
547. #550	C₂²×C₃₁	semidirect
548. #550	C₂²×C₃₁	semidirect
549. #550	C₂²×C₃₁	semidirect
550. D₄×Q₈	C₂²×C₃₁	semidirect
551. #548	C₂²×C₃₁	semidirect
552. #548	C₂²×C₃₁	semidirect
553. #547	C₂²×C₃₁	semidirect
554. #547	C₂²×C₃₁	semidirect
555. #546	C₂²×C₃₁	semidirect
556. #546	C₂²×C₃₁	semidirect
557. #546	C₂²×C₃₁	semidirect
558. #546	C₂²×C₃₁	semidirect
559. D₄²	C₂²×C₃₁	semidirect
560. D₄²	C₂²×C₃₁	semidirect
561. D₄²	C₂²×C₃₁	semidirect
562. #544	C₂²×C₃₁	semidirect
563. #542	C₂²×C₃₁	semidirect
564. #542	C₂²×C₃₁	semidirect
565. #540	C₂²×C₃₁	semidirect
566. #540	C₂²×C₃₁	semidirect
567. #538	C₂²×C₃₁	semidirect
568. #537	C₂²×C₃₁	semidirect
569. #535	C₂²×C₃₁	semidirect
570. #535	C₂²×C₃₁	semidirect
571. #533	C₂²×C₃₁	semidirect
572. #533	C₂²×C₃₁	semidirect
573. #533	C₂²×C₃₁	semidirect
574. #532	C₂²×C₃₁	semidirect
575. #532	C₂²×C₃₁	semidirect
576. #532	C₂²×C₃₁	semidirect
577. #532	C₂²×C₃₁	semidirect
578. #532	C₂²×C₃₁	semidirect
579. #532	C₂²×C₃₁	semidirect
580. #532	C₂²×C₃₁	semidirect
581. #532	C₂²×C₃₁	semidirect
582. #532	C₂²×C₃₁	semidirect
583. #532	C₂²×C₃₁	semidirect
584. #532	C₂²×C₃₁	semidirect
585. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
586. C₂×#127	C₂²×C₃₁	semidirect
587. #529	C₂²×C₃₁	semidirect
588. #529	C₂²×C₃₁	semidirect
589. #529	C₂²×C₃₁	semidirect
590. #529	C₂²×C₃₁	semidirect
591. #529	C₂²×C₃₁	semidirect
592. #529	C₂²×C₃₁	semidirect
593. #529	C₂²×C₃₁	semidirect
594. C₂×#124	C₂²×C₃₁	semidirect
595. #525	C₂²×C₃₁	semidirect
596. #525	C₂²×C₃₁	semidirect
597. #525	C₂²×C₃₁	semidirect
598. #525	C₂²×C₃₁	semidirect
599. C₂×#121	C₂²×C₃₁	semidirect
600. C₂×#121	C₂²×C₃₁	semidirect
602. #520	C₂²×C₃₁	semidirect
603. #520	C₂²×C₃₁	semidirect
604. #518	C₂²×C₃₁	semidirect
605. #518	C₂²×C₃₁	semidirect
608. C₄×#41	C₂²×C₃₁	semidirect
609. C₄×#41	C₂²×C₃₁	semidirect
610. C₄×#41	C₂²×C₃₁	semidirect
611. C₄×#41	C₂²×C₃₁	semidirect
612. C₄×#41	C₂²×C₃₁	semidirect
613. C₄×#41	C₂²×C₃₁	semidirect
614. C₄×#41	C₂²×C₃₁	semidirect
615. C₄×#41	C₂²×C₃₁	semidirect
616. C₄×#41	C₂²×C₃₁	semidirect
617. C₄×#41	C₂²×C₃₁	semidirect
618. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
619. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
620. C₂×C₄×D₄	C₂²×C₃₁	semidirect
621. C₂×C₄×D₄	C₂²×C₃₁	semidirect
622. C₂×C₄×D₄	C₂²×C₃₁	semidirect
623. C₂×C₄×D₄	C₂²×C₃₁	semidirect
624. C₂×C₄×D₄	C₂²×C₃₁	semidirect
625. C₂×#117	C₂²×C₃₁	semidirect
626. C₂²×C₄²	C₂²×C₃₁	semidirect
807. C₃₁	#62800	direct (N × H)
820. #41	#41×C₃₁	semidirect
944. Q₈	C₂×#41×C₃₁	semidirect
957. D₄	C₂×#41×C₃₁	semidirect
979. C₂×C₄	C₂×#41×C₃₁	semidirect
980. C₂×C₄	C₃₁×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3522	2
C₃₁×#3519	2
C₃₁×#3517	2
C₃₁×#3514	2
C₃₁×#3511	2
C₃₁×#3508	2
C₃₁×#3503	2
C₃₁×#3498	2
C₃₁×#3494	2
C₃₁×#3488	2
C₃₁×#3483	2
C₃₁×#3481	2
C₃₁×#3480	2
D₄×#41×C₃₁	2
C₃₁×#3460	2
C₃₁×#3444	2
C₂×C₃₁×#532	2
C₄×C₃₁×H(5,𝔽₂)	2
C₂×C₄×#41×C₃₁	2
#62800	31

Subgroups — C31×#62800 #21519559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62800 #21519559