Subgroups — C₃₁×#61632 #21518391

Order 7936.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3188	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
24	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#562	—	2	2	no	—
27	C₃₁×#554	C₂²	1	2	yes	—
28	D₄×Q₈×C₃₁	—	2	1	no	—
29	D₄×Q₈×C₃₁	—	2	1	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
32	C₃₁×#548	—	2	1	no	—
33	C₃₁×#548	—	2	1	no	—
34	C₃₁×#548	C₂²	1	2	yes	—
35	C₃₁×#548	C₂²	1	2	yes	—
36	C₃₁×#548	C₂²	1	2	yes	complemented
37	C₃₁×#547	C₂²	1	2	yes	—
38	C₃₁×#546	—	2	2	no	—
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	C₂²	1	2	yes	—
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#538	—	2	1	no	—
44	C₃₁×#537	—	2	1	no	—
45	C₃₁×#537	C₂²	1	2	yes	—
46	C₃₁×#536	—	2	2	no	—
47	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#525	—	2	2	no	—
50	C₃₁×#525	C₂²	1	1	yes	characteristic
51	C₃₁×#525	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
54	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#497	C₂²	1	2	yes	complemented
56	C₃₁×#495	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#487	C₂²	1	2	yes	complemented
59	C₃₁×#485	C₂²	1	2	yes	complemented
60	C₃₁×#484	C₂²	1	1	yes	characteristic
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#483	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#481	C₂²	1	1	yes	characteristic
66	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#470	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	complemented
71	C₃₁×#467	C₂²	1	2	yes	—
72	C₃₁×#467	C₂²	1	2	yes	complemented
73	C₃₁×#466	C₂²	1	2	yes	—
74	C₃₁×#465	C₂²	1	2	yes	—
75	C₃₁×#465	C₂²	1	2	yes	—
76	C₃₁×#465	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#462	C₂²	1	2	yes	complemented
82	C₃₁×#461	C₂²	1	2	yes	complemented
83	C₃₁×#452	C₂²	1	2	yes	complemented
84	C₃₁×#452	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#452	C₂²	1	2	yes	complemented
87	C₃₁×#451	C₂²	1	2	yes	—
88	C₃₁×#451	C₂²	1	2	yes	—
89	C₃₁×#451	C₂²	1	2	yes	complemented
90	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#451	C₂²	1	2	yes	complemented
92	C₃₁×#451	C₂²	1	2	yes	complemented
93	C₃₁×#450	C₂²	1	1	yes	characteristic
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	2	yes	—
98	C₃₁×#448	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#448	C₂²	1	2	yes	complemented
102	C₃₁×#447	C₂²	1	1	yes	characteristic
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	—
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₃₁	C₂²	1	2	yes	—
110	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#417	C₂²	1	2	yes	complemented
113	C₂×C₃₁×#103	C₂²	1	2	yes	—
114	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
119	C₃₁×2₋¹⁺⁴	—	4	4	no	—
120	C₂×#41×C₃₁	—	2	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	2	no	—
123	C₂×#41×C₃₁	C₂³	1	2	yes	—
124	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×#41×C₃₁	C₂³	1	2	yes	—
126	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₃₁	—	2	1	no	—
128	C₂²×Q₈×C₃₁	—	2	1	no	—
129	C₂²×Q₈×C₃₁	—	2	1	no	—
130	C₂²×Q₈×C₃₁	—	2	1	no	—
131	C₂²×Q₈×C₃₁	—	4	4	no	—
132	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	—	2	1	no	—
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	—	2	1	no	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×#137	—	4	4	no	—
143	C₃₁×#135	—	4	4	no	—
144	C₂×Q₁₆×C₃₁	—	4	4	no	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	—	4	4	no	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	—	2	1	no	—
163	C₃₁×C₄⋊Q₈	—	2	2	no	—
164	C₃₁×C₄⋊Q₈	—	2	2	no	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	1	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	D₄	1	2	yes	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
202	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	D₄	1	1	yes	characteristic
219	C₃₁×#121	D₄	1	1	yes	characteristic
220	C₃₁×#121	C₂³	1	1	yes	characteristic
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	1	yes	characteristic
225	C₃₁×#120	—	2	1	no	—
226	C₃₁×#120	—	2	2	no	—
227	C₃₁×#120	D₄	1	2	yes	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	C₂³	1	1	yes	characteristic
246	C₃₁×#117	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
251	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
254	C₃₁×#107	C₂³	1	2	yes	—
255	C₃₁×#107	C₂³	1	2	yes	—
256	C₃₁×#106	C₂³	1	2	yes	—
257	C₃₁×#106	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#97	C₂³	1	2	yes	—
285	C₄×C₈×C₃₁	C₂³	1	2	yes	—
286	C₂⁴×C₃₁	—	2	1	no	—
287	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
288	#41×C₃₁	—	2	4	no	—
289	#41×C₃₁	—	4	2	no	—
290	#41×C₃₁	—	4	2	no	—
291	#41×C₃₁	—	4	2	no	—
292	#41×C₃₁	—	4	8	no	—
293	#41×C₃₁	—	4	2	no	—
294	#41×C₃₁	—	4	2	no	—
295	#41×C₃₁	—	4	4	no	—
296	#41×C₃₁	—	8	4	no	—
297	C₂×Q₈×C₃₁	—	2	4	no	—
298	C₂×Q₈×C₃₁	—	2	1	no	—
299	C₂×Q₈×C₃₁	—	2	2	no	—
300	C₂×Q₈×C₃₁	—	2	2	no	—
301	C₂×Q₈×C₃₁	—	2	1	no	—
302	C₂×Q₈×C₃₁	—	2	2	no	—
303	C₂×Q₈×C₃₁	—	2	1	no	—
304	C₂×Q₈×C₃₁	—	2	2	no	—
305	C₂×Q₈×C₃₁	—	2	4	no	—
306	C₂×Q₈×C₃₁	—	2	4	no	—
307	C₂×Q₈×C₃₁	—	2	4	no	—
308	C₂×Q₈×C₃₁	—	4	2	no	—
309	C₂×Q₈×C₃₁	—	4	2	no	—
310	C₂×Q₈×C₃₁	—	4	2	no	—
311	C₂×Q₈×C₃₁	—	4	2	no	—
312	C₂×Q₈×C₃₁	—	4	4	no	—
313	C₂×Q₈×C₃₁	—	4	2	no	—
314	C₂×Q₈×C₃₁	—	4	4	no	—
315	C₂×Q₈×C₃₁	—	4	4	no	—
316	C₂×Q₈×C₃₁	—	4	4	no	—
317	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
319	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
321	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
322	C₂×D₄×C₃₁	—	2	1	no	—
323	C₂×D₄×C₃₁	—	2	1	no	—
324	C₂×D₄×C₃₁	—	2	2	no	—
325	C₂×D₄×C₃₁	—	2	1	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	4	2	no	—
332	C₂×D₄×C₃₁	—	8	2	no	—
333	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	4	2	no	—
353	C₂²×C₄×C₃₁	—	4	4	no	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
361	Q₁₆×C₃₁	—	2	4	no	—
362	Q₁₆×C₃₁	—	2	4	no	—
363	Q₁₆×C₃₁	—	4	2	no	—
364	Q₁₆×C₃₁	—	4	2	no	—
365	Q₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	2	4	no	—
367	SD₁₆×C₃₁	—	2	4	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	4	2	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	D₈×C₃₁	—	4	2	no	—
373	M₁₆×C₃₁	—	4	2	no	—
374	C₂×C₈×C₃₁	—	4	2	no	—
375	C₂×C₈×C₃₁	—	4	2	no	—
376	C₂×C₈×C₃₁	—	4	2	no	—
377	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	C₂⁴	1	2	yes	—
433	#61632	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂³×C₃₁	—	2	2	no	—
435	C₂³×C₃₁	—	2	2	no	—
436	C₂³×C₃₁	—	2	1	no	—
437	C₂³×C₃₁	—	2	2	no	—
438	C₂³×C₃₁	—	4	1	no	—
439	C₂³×C₃₁	—	4	2	no	—
440	C₂³×C₃₁	—	8	1	no	—
441	C₂³×C₃₁	—	8	1	no	—
442	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
444	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
445	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₃₁	—	2	4	no	—
447	Q₈×C₃₁	—	2	2	no	—
448	Q₈×C₃₁	—	2	2	no	—
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	2	no	—
451	Q₈×C₃₁	—	2	2	no	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	4	1	no	—
454	Q₈×C₃₁	—	4	4	no	—
455	Q₈×C₃₁	—	4	4	no	—
456	Q₈×C₃₁	—	4	4	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	8	1	no	—
459	Q₈×C₃₁	—	8	2	no	—
460	Q₈×C₃₁	H(5,𝔽₂)	1	4	yes	—
461	D₄×C₃₁	—	2	4	no	—
462	D₄×C₃₁	—	2	4	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	4	1	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	4	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	4	2	no	—
471	D₄×C₃₁	—	4	4	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	8	1	no	—
474	D₄×C₃₁	—	8	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	C₂×C₄×C₃₁	—	2	4	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	4	1	no	—
492	C₂×C₄×C₃₁	—	4	1	no	—
493	C₂×C₄×C₃₁	—	4	1	no	—
494	C₂×C₄×C₃₁	—	4	4	no	—
495	C₂×C₄×C₃₁	—	4	4	no	—
496	C₂×C₄×C₃₁	—	4	4	no	—
497	C₂×C₄×C₃₁	—	4	4	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	1	no	—
504	C₂×C₄×C₃₁	—	8	1	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
513	C₈×C₃₁	—	2	2	no	—
514	C₈×C₃₁	—	2	2	no	—
515	C₈×C₃₁	—	2	2	no	—
516	C₈×C₃₁	—	2	2	no	—
517	#3536	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3486	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3316	C₂×C₃₁	1	2	yes	complemented
520	#3308	C₂×C₃₁	1	2	yes	complemented
521	#3299	C₂×C₃₁	1	2	yes	complemented
522	#3298	C₂×C₃₁	1	2	yes	complemented
523	#3285	C₂×C₃₁	1	2	yes	complemented
524	#3282	C₂×C₃₁	1	2	yes	complemented
525	#3270	C₂×C₃₁	1	2	yes	complemented
526	#3266	C₂×C₃₁	1	2	yes	complemented
527	#3225	C₂×C₃₁	1	2	yes	complemented
528	#3201	C₂×C₃₁	1	2	yes	complemented
529	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3188	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3121	C₂×C₃₁	1	2	yes	complemented
532	#3013	C₂×C₃₁	1	2	yes	complemented
533	C₂×#451	C₂×C₃₁	1	1	yes	characteristic, complemented
534	C₂×#448	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
536	C₂²×C₃₁	—	2	1	no	—
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	1	no	—
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	4	4	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	2	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	16	2	no	—
554	C₂²×C₃₁	#577	1	2	yes	—
555	C₂²×C₃₁	#578	1	2	yes	—
556	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₃₁	—	2	4	no	—
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
572	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
574	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
575	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
576	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
577	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
578	#562	—	2	2	no	—
579	#554	C₂²×C₃₁	1	2	yes	—
580	D₄×Q₈	—	2	1	no	—
581	D₄×Q₈	—	2	1	no	—
582	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
583	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
584	#548	—	2	1	no	—
585	#548	—	2	1	no	—
586	#548	C₂²×C₃₁	1	2	yes	—
587	#548	C₂²×C₃₁	1	2	yes	—
588	#548	C₂²×C₃₁	1	2	yes	complemented
589	#547	C₂²×C₃₁	1	2	yes	—
590	#546	—	2	2	no	—
591	#546	C₂²×C₃₁	1	2	yes	—
592	#543	—	2	1	no	—
593	#542	C₂²×C₃₁	1	2	yes	—
594	#539	—	2	1	no	—
595	#538	—	2	1	no	—
596	#537	—	2	1	no	—
597	#537	C₂²×C₃₁	1	2	yes	—
598	#536	—	2	2	no	—
599	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#525	—	2	2	no	—
602	#525	C₂²×C₃₁	1	1	yes	characteristic
603	#525	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
605	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
606	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#497	C₂²×C₃₁	1	2	yes	complemented
608	#495	C₂²×C₃₁	1	2	yes	complemented
609	#489	C₂²×C₃₁	1	2	yes	complemented
610	#487	C₂²×C₃₁	1	2	yes	complemented
611	#485	C₂²×C₃₁	1	2	yes	complemented
612	#484	C₂²×C₃₁	1	1	yes	characteristic
613	#484	C₂²×C₃₁	1	2	yes	complemented
614	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#483	C₂²×C₃₁	1	2	yes	complemented
616	#482	C₂²×C₃₁	1	2	yes	—
617	#481	C₂²×C₃₁	1	1	yes	characteristic
618	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
619	#477	C₂²×C₃₁	1	2	yes	complemented
620	#475	C₂²×C₃₁	1	2	yes	complemented
621	#470	C₂²×C₃₁	1	2	yes	complemented
622	#468	C₂²×C₃₁	1	2	yes	complemented
623	#467	C₂²×C₃₁	1	2	yes	—
624	#467	C₂²×C₃₁	1	2	yes	complemented
625	#466	C₂²×C₃₁	1	2	yes	—
626	#465	C₂²×C₃₁	1	2	yes	—
627	#465	C₂²×C₃₁	1	2	yes	—
628	#465	C₂²×C₃₁	1	2	yes	complemented
629	#464	C₂²×C₃₁	1	2	yes	complemented
630	#464	C₂²×C₃₁	1	2	yes	complemented
631	#464	C₂²×C₃₁	1	2	yes	complemented
632	#463	C₂²×C₃₁	1	2	yes	complemented
633	#462	C₂²×C₃₁	1	2	yes	complemented
634	#461	C₂²×C₃₁	1	2	yes	complemented
635	#452	C₂²×C₃₁	1	2	yes	complemented
636	#452	C₂²×C₃₁	1	2	yes	complemented
637	#452	C₂²×C₃₁	1	2	yes	complemented
638	#452	C₂²×C₃₁	1	2	yes	complemented
639	#451	C₂²×C₃₁	1	2	yes	—
640	#451	C₂²×C₃₁	1	2	yes	—
641	#451	C₂²×C₃₁	1	2	yes	complemented
642	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#451	C₂²×C₃₁	1	2	yes	complemented
644	#451	C₂²×C₃₁	1	2	yes	complemented
645	#450	C₂²×C₃₁	1	1	yes	characteristic
646	#449	C₂²×C₃₁	1	2	yes	—
647	#449	C₂²×C₃₁	1	2	yes	complemented
648	#448	C₂²×C₃₁	1	2	yes	—
649	#448	C₂²×C₃₁	1	2	yes	—
650	#448	C₂²×C₃₁	1	2	yes	—
651	#448	C₂²×C₃₁	1	2	yes	—
652	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#448	C₂²×C₃₁	1	2	yes	complemented
654	#447	C₂²×C₃₁	1	1	yes	characteristic
655	#441	C₂²×C₃₁	1	2	yes	complemented
656	#440	C₂²×C₃₁	1	2	yes	complemented
657	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
658	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
659	#435	C₂²×C₃₁	1	2	yes	—
660	#435	C₂²×C₃₁	1	2	yes	complemented
661	C₈×D₄	C₂²×C₃₁	1	2	yes	—
662	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
663	#433	C₂²×C₃₁	1	2	yes	complemented
664	#417	C₂²×C₃₁	1	2	yes	complemented
665	C₂×#103	C₂²×C₃₁	1	2	yes	—
666	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
667	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
668	#408	C₂²×C₃₁	1	2	yes	complemented
669	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
670	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
671	C₂×C₃₁	—	2	2	no	—
672	C₂×C₃₁	—	2	2	no	—
673	C₂×C₃₁	—	4	2	no	—
674	C₂×C₃₁	—	4	1	no	—
675	C₂×C₃₁	—	8	1	no	—
676	C₂×C₃₁	—	8	2	no	—
677	C₂×C₃₁	#3484	1	1	yes	characteristic
678	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
679	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
680	2₋¹⁺⁴	—	4	4	no	—
681	C₂×#41	—	2	2	no	—
682	C₂×#41	—	2	1	no	—
683	C₂×#41	—	2	2	no	—
684	C₂×#41	C₂³×C₃₁	1	2	yes	—
685	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×#41	C₂³×C₃₁	1	2	yes	—
687	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
688	C₂²×Q₈	—	2	1	no	—
689	C₂²×Q₈	—	2	1	no	—
690	C₂²×Q₈	—	2	1	no	—
691	C₂²×Q₈	—	2	1	no	—
692	C₂²×Q₈	—	4	4	no	—
693	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
694	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
696	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
697	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₂²×D₄	—	2	1	no	—
700	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
701	C₂³×C₄	—	2	1	no	—
702	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
703	#137	—	4	4	no	—
704	#135	—	4	4	no	—
705	C₂×Q₁₆	—	4	4	no	—
706	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×SD₁₆	—	4	4	no	—
712	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×D₈	C₂³×C₃₁	1	2	yes	—
719	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
721	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
722	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
727	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
728	#126	—	2	2	no	—
729	#125	—	2	2	no	—
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	—	2	2	no	—
735	#124	C₂³×C₃₁	1	2	yes	—
736	#124	C₂³×C₃₁	1	2	yes	—
737	#123	—	2	2	no	—
738	#123	—	2	1	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	D₄×C₃₁	1	2	yes	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
762	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	D₄×C₃₁	1	1	yes	characteristic
780	#121	D₄×C₃₁	1	1	yes	characteristic
781	#121	C₂³×C₃₁	1	2	yes	—
782	#121	C₂³×C₃₁	1	2	yes	—
783	#121	C₂³×C₃₁	1	1	yes	characteristic
784	#121	C₂³×C₃₁	1	1	yes	characteristic
785	#121	C₂³×C₃₁	1	2	yes	—
786	#120	—	2	1	no	—
787	#120	—	2	2	no	—
788	#120	D₄×C₃₁	1	2	yes	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	C₂³×C₃₁	1	1	yes	characteristic
807	#117	C₂³×C₃₁	1	1	yes	characteristic
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
812	C₂×C₂²⋊C₄	—	2	1	no	—
813	C₂×C₂²⋊C₄	—	2	1	no	—
814	C₂×C₂²⋊C₄	—	2	2	no	—
815	#107	C₂³×C₃₁	1	2	yes	—
816	#107	C₂³×C₃₁	1	2	yes	—
817	#106	C₂³×C₃₁	1	2	yes	—
818	#106	C₂³×C₃₁	1	2	yes	—
819	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
820	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	2	yes	—
823	#103	C₂³×C₃₁	1	2	yes	—
824	#103	C₂³×C₃₁	1	2	yes	—
825	#103	C₂³×C₃₁	1	2	yes	—
826	#103	C₂³×C₃₁	1	2	yes	—
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	2	yes	—
829	#103	C₂³×C₃₁	1	2	yes	—
830	#103	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	2	yes	—
833	#102	C₂³×C₃₁	1	2	yes	—
834	#102	C₂³×C₃₁	1	2	yes	—
835	#102	C₂³×C₃₁	1	2	yes	—
836	#102	C₂³×C₃₁	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
845	#97	C₂³×C₃₁	1	2	yes	—
846	C₄×C₈	C₂³×C₃₁	1	2	yes	—
847	C₃₁	#61632	1	1	yes	characteristic, direct product factor, Sylow
848	C₂⁴	—	2	1	no	—
849	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
850	#41	—	2	4	no	—
851	#41	—	4	2	no	—
852	#41	—	4	2	no	—
853	#41	—	4	2	no	—
854	#41	—	4	8	no	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	#41	—	4	4	no	—
858	#41	—	8	4	no	—
859	C₂×Q₈	—	2	4	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	4	no	—
868	C₂×Q₈	—	2	4	no	—
869	C₂×Q₈	—	2	4	no	—
870	C₂×Q₈	—	4	2	no	—
871	C₂×Q₈	—	4	2	no	—
872	C₂×Q₈	—	4	2	no	—
873	C₂×Q₈	—	4	2	no	—
874	C₂×Q₈	—	4	4	no	—
875	C₂×Q₈	—	4	2	no	—
876	C₂×Q₈	—	4	4	no	—
877	C₂×Q₈	—	4	4	no	—
878	C₂×Q₈	—	4	4	no	—
879	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
880	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
881	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
883	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	4	2	no	—
894	C₂×D₄	—	8	2	no	—
895	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	4	no	—
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
923	Q₁₆	—	2	4	no	—
924	Q₁₆	—	2	4	no	—
925	Q₁₆	—	4	2	no	—
926	Q₁₆	—	4	2	no	—
927	Q₁₆	—	4	2	no	—
928	SD₁₆	—	2	4	no	—
929	SD₁₆	—	2	4	no	—
930	SD₁₆	—	4	2	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	—	4	2	no	—
934	D₈	—	4	2	no	—
935	M₁₆	—	4	2	no	—
936	C₂×C₈	—	4	2	no	—
937	C₂×C₈	—	4	2	no	—
938	C₂×C₈	—	4	2	no	—
939	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
940	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
941	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
942	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	2	no	—
994	C₄²	C₂⁴×C₃₁	1	2	yes	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	4	1	no	—
1000	C₂³	—	4	2	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	—	8	1	no	—
1003	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1004	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1005	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1006	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1007	Q₈	—	2	4	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	4	4	no	—
1016	Q₈	—	4	4	no	—
1017	Q₈	—	4	4	no	—
1018	Q₈	—	4	2	no	—
1019	Q₈	—	8	1	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	C₃₁×H(5,𝔽₂)	1	4	yes	—
1022	D₄	—	2	4	no	—
1023	D₄	—	2	4	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	4	1	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	4	1	no	—
1053	C₂×C₄	—	4	1	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1074	C₈	—	2	2	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	4	4	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	16	2	no	—
1096	C₂²	C₃₁×#577	1	2	yes	—
1097	C₂²	C₃₁×#578	1	2	yes	—
1098	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1099	C₄	—	2	4	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1114	C₂	—	2	2	no	—
1115	C₂	—	2	2	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	2	no	—
1118	C₂	—	8	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₃₁×#3484	1	1	yes	characteristic
1121	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1122	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3536	C₂	semidirect
2. C₃₁×#3486	C₂	semidirect
3. C₃₁×#3316	C₂	semidirect
4. C₃₁×#3308	C₂	semidirect
5. C₃₁×#3299	C₂	semidirect
6. C₃₁×#3298	C₂	semidirect
7. C₃₁×#3285	C₂	semidirect
8. C₃₁×#3282	C₂	semidirect
9. C₃₁×#3270	C₂	semidirect
10. C₃₁×#3266	C₂	semidirect
11. C₃₁×#3225	C₂	semidirect
12. C₃₁×#3201	C₂	semidirect
13. C₃₁×#3190	C₂	semidirect
14. C₃₁×#3188	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3013	C₂	semidirect
17. C₂×C₃₁×#451	C₂	semidirect
18. C₂×C₃₁×#448	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
20. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×#135	C₂²	semidirect
24. C₂²×Q₁₆×C₃₁	C₂²	semidirect
31. D₄×Q₈×C₃₁	C₂²	semidirect
36. C₃₁×#548	C₂²	semidirect
47. C₃₁×#536	C₂²	semidirect
48. C₃₁×#536	C₂²	semidirect
54. C₃₁×#519	C₂²	semidirect
55. C₃₁×#497	C₂²	semidirect
56. C₃₁×#495	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#487	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
62. C₃₁×#483	C₂²	semidirect
63. C₃₁×#483	C₂²	semidirect
66. C₃₁×#480	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
69. C₃₁×#470	C₂²	semidirect
70. C₃₁×#468	C₂²	semidirect
72. C₃₁×#467	C₂²	semidirect
76. C₃₁×#465	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#462	C₂²	semidirect
82. C₃₁×#461	C₂²	semidirect
83. C₃₁×#452	C₂²	semidirect
84. C₃₁×#452	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
89. C₃₁×#451	C₂²	semidirect
90. C₃₁×#451	C₂²	semidirect
91. C₃₁×#451	C₂²	semidirect
92. C₃₁×#451	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#448	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
110. C₈×D₄×C₃₁	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
112. C₃₁×#417	C₂²	semidirect
114. C₂×C₃₁×#103	C₂²	semidirect
115. C₂×C₃₁×#103	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
433. #61632	C₃₁	direct (N × H)
517. #3536	C₂×C₃₁	semidirect
518. #3486	C₂×C₃₁	semidirect
519. #3316	C₂×C₃₁	semidirect
520. #3308	C₂×C₃₁	semidirect
521. #3299	C₂×C₃₁	semidirect
522. #3298	C₂×C₃₁	semidirect
523. #3285	C₂×C₃₁	semidirect
524. #3282	C₂×C₃₁	semidirect
525. #3270	C₂×C₃₁	semidirect
526. #3266	C₂×C₃₁	semidirect
527. #3225	C₂×C₃₁	semidirect
528. #3201	C₂×C₃₁	semidirect
529. #3190	C₂×C₃₁	semidirect
530. #3188	C₂×C₃₁	semidirect
531. #3121	C₂×C₃₁	semidirect
532. #3013	C₂×C₃₁	semidirect
533. C₂×#451	C₂×C₃₁	semidirect
534. C₂×#448	C₂×C₃₁	semidirect
535. #2977	C₂×C₃₁	semidirect
572. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
574. C₂×#137	C₂²×C₃₁	semidirect
575. C₂×#135	C₂²×C₃₁	semidirect
576. C₂²×Q₁₆	C₂²×C₃₁	semidirect
583. D₄×Q₈	C₂²×C₃₁	semidirect
588. #548	C₂²×C₃₁	semidirect
599. #536	C₂²×C₃₁	semidirect
600. #536	C₂²×C₃₁	semidirect
606. #519	C₂²×C₃₁	semidirect
607. #497	C₂²×C₃₁	semidirect
608. #495	C₂²×C₃₁	semidirect
609. #489	C₂²×C₃₁	semidirect
610. #487	C₂²×C₃₁	semidirect
611. #485	C₂²×C₃₁	semidirect
613. #484	C₂²×C₃₁	semidirect
614. #483	C₂²×C₃₁	semidirect
615. #483	C₂²×C₃₁	semidirect
618. #480	C₂²×C₃₁	semidirect
619. #477	C₂²×C₃₁	semidirect
620. #475	C₂²×C₃₁	semidirect
621. #470	C₂²×C₃₁	semidirect
622. #468	C₂²×C₃₁	semidirect
624. #467	C₂²×C₃₁	semidirect
628. #465	C₂²×C₃₁	semidirect
629. #464	C₂²×C₃₁	semidirect
630. #464	C₂²×C₃₁	semidirect
631. #464	C₂²×C₃₁	semidirect
632. #463	C₂²×C₃₁	semidirect
633. #462	C₂²×C₃₁	semidirect
634. #461	C₂²×C₃₁	semidirect
635. #452	C₂²×C₃₁	semidirect
636. #452	C₂²×C₃₁	semidirect
637. #452	C₂²×C₃₁	semidirect
638. #452	C₂²×C₃₁	semidirect
641. #451	C₂²×C₃₁	semidirect
642. #451	C₂²×C₃₁	semidirect
643. #451	C₂²×C₃₁	semidirect
644. #451	C₂²×C₃₁	semidirect
647. #449	C₂²×C₃₁	semidirect
652. #448	C₂²×C₃₁	semidirect
653. #448	C₂²×C₃₁	semidirect
655. #441	C₂²×C₃₁	semidirect
656. #440	C₂²×C₃₁	semidirect
657. C₄×Q₁₆	C₂²×C₃₁	semidirect
658. C₄×SD₁₆	C₂²×C₃₁	semidirect
660. #435	C₂²×C₃₁	semidirect
662. C₈×D₄	C₂²×C₃₁	semidirect
663. #433	C₂²×C₃₁	semidirect
664. #417	C₂²×C₃₁	semidirect
666. C₂×#103	C₂²×C₃₁	semidirect
667. C₂×#103	C₂²×C₃₁	semidirect
668. #408	C₂²×C₃₁	semidirect
847. C₃₁	#61632	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×#3536	2
C₃₁×#3486	2
C₃₁×#3316	2
C₃₁×#3308	2
C₃₁×#3299	2
C₃₁×#3298	2
C₃₁×#3285	2
C₃₁×#3282	2
C₃₁×#3270	2
C₃₁×#3266	2
C₃₁×#3225	2
C₃₁×#3201	2
C₃₁×#3190	2
C₃₁×#3188	2
C₃₁×#3121	2
C₃₁×#3013	2
C₂×C₃₁×#451	2
C₂×C₃₁×#448	2
C₃₁×#2977	2
#61632	31

Subgroups — C31×#61632 #21518391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61632 #21518391