Subgroups — C₃₁×#3542 #16843475

Order 3968.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#562	C₂	1	2	yes	maximal, complemented
2	C₃₁×#560	C₂	1	2	yes	maximal, complemented
3	C₃₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#551	C₂	1	2	yes	maximal, complemented
7	C₃₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#546	C₂	1	2	yes	maximal, complemented
10	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#540	C₂	1	2	yes	maximal, complemented
16	C₃₁×#538	C₂	1	2	yes	maximal, complemented
17	C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#535	C₂	1	2	yes	maximal, complemented
19	C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#534	C₂	1	2	yes	maximal, complemented
21	C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
27	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂²×D₄×C₃₁	C₂²	1	2	yes	complemented
31	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#127	C₂²	1	2	yes	complemented
35	C₃₁×#127	C₂²	1	2	yes	complemented
36	C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#126	C₂²	1	2	yes	complemented
38	C₃₁×#126	C₂²	1	2	yes	complemented
39	C₃₁×#126	C₂²	1	2	yes	complemented
40	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#125	C₂²	1	2	yes	complemented
42	C₃₁×#124	C₂²	1	2	yes	complemented
43	C₃₁×#124	C₂²	1	2	yes	complemented
44	C₃₁×#124	C₂²	1	2	yes	complemented
45	C₃₁×#124	C₂²	1	2	yes	complemented
46	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#123	C₂²	1	2	yes	—
48	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#123	C₂²	1	2	yes	complemented
51	C₃₁×#123	C₂²	1	2	yes	complemented
52	C₃₁×#123	C₂²	1	2	yes	complemented
53	C₃₁×#123	C₂²	1	2	yes	complemented
54	C₃₁×#123	C₂²	1	2	yes	complemented
55	C₃₁×#123	C₂²	1	2	yes	complemented
56	C₃₁×#123	C₂²	1	2	yes	complemented
57	C₃₁×#123	C₂²	1	2	yes	complemented
58	C₃₁×#123	C₂²	1	2	yes	complemented
59	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₃₁×#121	C₂²	1	1	yes	characteristic
68	C₃₁×#121	C₂²	1	1	yes	characteristic
69	C₃₁×#121	C₂²	1	1	yes	characteristic
70	C₃₁×#121	C₂²	1	1	yes	characteristic
71	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#121	C₂²	1	2	yes	complemented
73	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#121	C₂²	1	2	yes	complemented
75	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#121	C₂²	1	2	yes	complemented
78	C₃₁×#121	C₂²	1	2	yes	complemented
79	C₃₁×#121	C₂²	1	2	yes	complemented
80	C₃₁×#121	C₂²	1	2	yes	complemented
81	C₃₁×#121	C₂²	1	2	yes	complemented
82	C₃₁×#121	C₂²	1	2	yes	complemented
83	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#121	C₂²	1	2	yes	complemented
85	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#121	C₂²	1	2	yes	complemented
87	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#121	C₂²	1	2	yes	complemented
89	C₃₁×#121	C₂²	1	2	yes	complemented
90	C₃₁×#121	C₂²	1	2	yes	complemented
91	C₃₁×#121	C₂²	1	2	yes	complemented
92	C₃₁×#120	C₂²	1	1	yes	characteristic
93	C₃₁×#120	C₂²	1	2	yes	—
94	C₃₁×#120	C₂²	1	2	yes	complemented
95	C₃₁×#120	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#120	C₂²	1	2	yes	complemented
97	C₃₁×#120	C₂²	1	2	yes	complemented
98	C₃₁×#120	C₂²	1	2	yes	complemented
99	C₃₁×#120	C₂²	1	2	yes	complemented
100	C₃₁×#120	C₂²	1	2	yes	complemented
101	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#117	C₂²	1	2	yes	complemented
116	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#117	C₂²	1	2	yes	complemented
118	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
123	C₂⁴×C₃₁	C₂³	1	2	yes	—
124	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
125	C₂⁴×C₃₁	C₂³	1	2	yes	—
126	#41×C₃₁	—	4	2	no	—
127	#41×C₃₁	—	4	4	no	—
128	#41×C₃₁	—	4	2	no	—
129	#41×C₃₁	—	4	2	no	—
130	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
133	C₂×D₄×C₃₁	—	4	2	no	—
134	C₂×D₄×C₃₁	—	4	2	no	—
135	C₂×D₄×C₃₁	—	4	4	no	—
136	C₂×D₄×C₃₁	—	4	4	no	—
137	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₃₁	C₂³	1	2	yes	—
139	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×D₄×C₃₁	C₂³	1	2	yes	—
152	C₂×D₄×C₃₁	C₂³	1	2	yes	—
153	C₂×D₄×C₃₁	C₂³	1	2	yes	—
154	C₂×D₄×C₃₁	C₂³	1	2	yes	—
155	C₂×D₄×C₃₁	C₂³	1	2	yes	—
156	C₂×D₄×C₃₁	C₂³	1	2	yes	—
157	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×D₄×C₃₁	C₂³	1	2	yes	—
159	C₂×D₄×C₃₁	C₂³	1	2	yes	—
160	C₂×D₄×C₃₁	C₂³	1	2	yes	—
161	C₂×D₄×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₄×C₃₁	—	4	2	no	—
163	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
171	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
172	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
173	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
174	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
175	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
177	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
208	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₄²×C₃₁	C₂³	1	2	yes	—
227	C₄²×C₃₁	C₂³	1	2	yes	—
228	C₄²×C₃₁	C₂³	1	1	yes	characteristic
229	C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₄²×C₃₁	C₂³	1	2	yes	—
231	C₂³×C₃₁	—	2	2	no	—
232	C₂³×C₃₁	—	2	4	no	—
233	C₂³×C₃₁	—	4	1	no	—
234	C₂³×C₃₁	—	4	1	no	—
235	C₂³×C₃₁	—	4	2	no	—
236	C₂³×C₃₁	—	4	2	no	—
237	C₂³×C₃₁	—	4	2	no	—
238	C₂³×C₃₁	—	4	2	no	—
239	C₂³×C₃₁	—	4	2	no	—
240	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂³×C₃₁	C₂⁴	1	2	yes	—
242	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂³×C₃₁	C₂⁴	1	2	yes	—
245	C₂³×C₃₁	C₂⁴	1	2	yes	—
246	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
248	Q₈×C₃₁	—	2	2	no	—
249	Q₈×C₃₁	—	4	1	no	—
250	Q₈×C₃₁	—	4	2	no	—
251	D₄×C₃₁	—	2	2	no	—
252	D₄×C₃₁	—	2	4	no	—
253	D₄×C₃₁	—	2	2	no	—
254	D₄×C₃₁	—	2	2	no	—
255	D₄×C₃₁	—	2	2	no	—
256	D₄×C₃₁	—	2	2	no	—
257	D₄×C₃₁	—	4	2	no	—
258	D₄×C₃₁	—	4	2	no	—
259	D₄×C₃₁	—	4	2	no	—
260	D₄×C₃₁	—	4	2	no	—
261	D₄×C₃₁	—	4	2	no	—
262	D₄×C₃₁	—	4	2	no	—
263	D₄×C₃₁	—	4	2	no	—
264	D₄×C₃₁	—	4	2	no	—
265	D₄×C₃₁	—	4	1	no	—
266	D₄×C₃₁	—	4	2	no	—
267	D₄×C₃₁	—	4	2	no	—
268	D₄×C₃₁	—	4	2	no	—
269	D₄×C₃₁	—	4	1	no	—
270	D₄×C₃₁	—	4	1	no	—
271	D₄×C₃₁	—	4	1	no	—
272	D₄×C₃₁	—	4	1	no	—
273	D₄×C₃₁	—	4	2	no	—
274	D₄×C₃₁	—	4	2	no	—
275	D₄×C₃₁	—	4	2	no	—
276	C₂×C₄×C₃₁	—	2	4	no	—
277	C₂×C₄×C₃₁	—	2	2	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	2	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	4	1	no	—
283	C₂×C₄×C₃₁	—	4	1	no	—
284	C₂×C₄×C₃₁	—	4	1	no	—
285	C₂×C₄×C₃₁	—	4	2	no	—
286	C₂×C₄×C₃₁	—	4	2	no	—
287	C₂×C₄×C₃₁	—	4	2	no	—
288	C₂×C₄×C₃₁	—	4	2	no	—
289	C₂×C₄×C₃₁	—	4	2	no	—
290	C₂×C₄×C₃₁	—	4	2	no	—
291	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	#3542	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂²×C₃₁	—	2	1	no	—
308	C₂²×C₃₁	—	2	1	no	—
309	C₂²×C₃₁	—	2	1	no	—
310	C₂²×C₃₁	—	2	1	no	—
311	C₂²×C₃₁	—	2	1	no	—
312	C₂²×C₃₁	—	2	1	no	—
313	C₂²×C₃₁	—	2	1	no	—
314	C₂²×C₃₁	—	2	2	no	—
315	C₂²×C₃₁	—	2	2	no	—
316	C₂²×C₃₁	—	2	2	no	—
317	C₂²×C₃₁	—	2	2	no	—
318	C₂²×C₃₁	—	2	1	no	—
319	C₂²×C₃₁	—	2	2	no	—
320	C₂²×C₃₁	—	2	1	no	—
321	C₂²×C₃₁	—	2	1	no	—
322	C₂²×C₃₁	—	2	2	no	—
323	C₂²×C₃₁	—	2	2	no	—
324	C₂²×C₃₁	—	2	1	no	—
325	C₂²×C₃₁	—	2	1	no	—
326	C₂²×C₃₁	—	2	1	no	—
327	C₂²×C₃₁	—	2	2	no	—
328	C₂²×C₃₁	—	2	1	no	—
329	C₂²×C₃₁	—	2	2	no	—
330	C₂²×C₃₁	—	4	4	no	—
331	C₂²×C₃₁	—	8	4	no	—
332	C₂²×C₃₁	—	8	4	no	—
333	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
334	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
335	C₄×C₃₁	—	2	1	no	—
336	C₄×C₃₁	—	2	2	no	—
337	C₄×C₃₁	—	2	1	no	—
338	C₄×C₃₁	—	2	1	no	—
339	C₄×C₃₁	—	2	1	no	—
340	C₄×C₃₁	—	2	2	no	—
341	C₄×C₃₁	—	2	1	no	—
342	C₄×C₃₁	—	2	1	no	—
343	C₄×C₃₁	—	2	2	no	—
344	C₄×C₃₁	—	2	1	no	—
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	1	no	—
347	C₄×C₃₁	—	2	2	no	—
348	C₄×C₃₁	—	2	1	no	—
349	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
350	#562	C₂×C₃₁	1	2	yes	complemented
351	#560	C₂×C₃₁	1	2	yes	complemented
352	#555	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#553	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#552	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#551	C₂×C₃₁	1	2	yes	complemented
356	#550	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#547	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#546	C₂×C₃₁	1	2	yes	complemented
359	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
361	D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#542	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#540	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#540	C₂×C₃₁	1	2	yes	complemented
365	#538	C₂×C₃₁	1	2	yes	complemented
366	#537	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#535	C₂×C₃₁	1	2	yes	complemented
368	#535	C₂×C₃₁	1	1	yes	characteristic, complemented
369	#534	C₂×C₃₁	1	2	yes	complemented
370	#525	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#525	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
373	C₂×C₃₁	—	2	2	no	—
374	C₂×C₃₁	—	4	1	no	—
375	C₂×C₃₁	—	4	1	no	—
376	C₂×C₃₁	—	4	1	no	—
377	C₂×C₃₁	—	4	2	no	—
378	C₂×C₃₁	—	4	2	no	—
379	C₂×C₃₁	—	4	1	no	—
380	C₂×C₃₁	—	4	2	no	—
381	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×C₃₁	#585	1	1	yes	characteristic
384	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
385	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
386	C₂×#41	C₂²×C₃₁	1	2	yes	complemented
387	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
388	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
389	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
390	C₂²×D₄	C₂²×C₃₁	1	2	yes	complemented
391	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
392	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
394	#127	C₂²×C₃₁	1	2	yes	complemented
395	#127	C₂²×C₃₁	1	2	yes	complemented
396	#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
397	#126	C₂²×C₃₁	1	2	yes	complemented
398	#126	C₂²×C₃₁	1	2	yes	complemented
399	#126	C₂²×C₃₁	1	2	yes	complemented
400	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
401	#125	C₂²×C₃₁	1	2	yes	complemented
402	#124	C₂²×C₃₁	1	2	yes	complemented
403	#124	C₂²×C₃₁	1	2	yes	complemented
404	#124	C₂²×C₃₁	1	2	yes	complemented
405	#124	C₂²×C₃₁	1	2	yes	complemented
406	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	#123	C₂²×C₃₁	1	2	yes	—
408	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
409	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	#123	C₂²×C₃₁	1	2	yes	complemented
411	#123	C₂²×C₃₁	1	2	yes	complemented
412	#123	C₂²×C₃₁	1	2	yes	complemented
413	#123	C₂²×C₃₁	1	2	yes	complemented
414	#123	C₂²×C₃₁	1	2	yes	complemented
415	#123	C₂²×C₃₁	1	2	yes	complemented
416	#123	C₂²×C₃₁	1	2	yes	complemented
417	#123	C₂²×C₃₁	1	2	yes	complemented
418	#123	C₂²×C₃₁	1	2	yes	complemented
419	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
421	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
425	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
426	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
427	#121	C₂²×C₃₁	1	1	yes	characteristic
428	#121	C₂²×C₃₁	1	1	yes	characteristic
429	#121	C₂²×C₃₁	1	1	yes	characteristic
430	#121	C₂²×C₃₁	1	1	yes	characteristic
431	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	#121	C₂²×C₃₁	1	2	yes	complemented
433	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	#121	C₂²×C₃₁	1	2	yes	complemented
435	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
436	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	#121	C₂²×C₃₁	1	2	yes	complemented
438	#121	C₂²×C₃₁	1	2	yes	complemented
439	#121	C₂²×C₃₁	1	2	yes	complemented
440	#121	C₂²×C₃₁	1	2	yes	complemented
441	#121	C₂²×C₃₁	1	2	yes	complemented
442	#121	C₂²×C₃₁	1	2	yes	complemented
443	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
444	#121	C₂²×C₃₁	1	2	yes	complemented
445	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
446	#121	C₂²×C₃₁	1	2	yes	complemented
447	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
448	#121	C₂²×C₃₁	1	2	yes	complemented
449	#121	C₂²×C₃₁	1	2	yes	complemented
450	#121	C₂²×C₃₁	1	2	yes	complemented
451	#121	C₂²×C₃₁	1	2	yes	complemented
452	#120	C₂²×C₃₁	1	1	yes	characteristic
453	#120	C₂²×C₃₁	1	2	yes	—
454	#120	C₂²×C₃₁	1	2	yes	complemented
455	#120	C₂²×C₃₁	1	1	yes	characteristic, complemented
456	#120	C₂²×C₃₁	1	2	yes	complemented
457	#120	C₂²×C₃₁	1	2	yes	complemented
458	#120	C₂²×C₃₁	1	2	yes	complemented
459	#120	C₂²×C₃₁	1	2	yes	complemented
460	#120	C₂²×C₃₁	1	2	yes	complemented
461	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
462	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
463	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
464	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
466	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
469	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
471	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
473	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
474	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	#117	C₂²×C₃₁	1	2	yes	complemented
476	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#117	C₂²×C₃₁	1	2	yes	complemented
478	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
480	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
481	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
482	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
483	C₃₁	#3542	1	1	yes	characteristic, direct product factor, Sylow
484	C₂⁴	C₂³×C₃₁	1	2	yes	—
485	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
486	C₂⁴	C₂³×C₃₁	1	2	yes	—
487	#41	—	4	2	no	—
488	#41	—	4	4	no	—
489	#41	—	4	2	no	—
490	#41	—	4	2	no	—
491	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
493	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
499	C₂×D₄	C₂³×C₃₁	1	2	yes	—
500	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
501	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
502	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
503	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
504	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₂×D₄	C₂³×C₃₁	1	2	yes	—
506	C₂×D₄	C₂³×C₃₁	1	2	yes	—
507	C₂×D₄	C₂³×C₃₁	1	2	yes	—
508	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
509	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂×D₄	C₂³×C₃₁	1	2	yes	—
511	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂×D₄	C₂³×C₃₁	1	2	yes	—
513	C₂×D₄	C₂³×C₃₁	1	2	yes	—
514	C₂×D₄	C₂³×C₃₁	1	2	yes	—
515	C₂×D₄	C₂³×C₃₁	1	2	yes	—
516	C₂×D₄	C₂³×C₃₁	1	2	yes	—
517	C₂×D₄	C₂³×C₃₁	1	2	yes	—
518	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₂×D₄	C₂³×C₃₁	1	2	yes	—
520	C₂×D₄	C₂³×C₃₁	1	2	yes	—
521	C₂×D₄	C₂³×C₃₁	1	2	yes	—
522	C₂×D₄	C₂³×C₃₁	1	2	yes	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
525	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
527	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
530	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
531	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
532	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
533	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
534	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
535	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
536	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
538	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
544	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
547	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
557	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
559	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
561	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
562	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
569	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
570	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
578	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
579	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
581	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
583	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₄²	C₂³×C₃₁	1	2	yes	—
588	C₄²	C₂³×C₃₁	1	2	yes	—
589	C₄²	C₂³×C₃₁	1	1	yes	characteristic
590	C₄²	C₂³×C₃₁	1	1	yes	characteristic
591	C₄²	C₂³×C₃₁	1	2	yes	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
602	C₂³	C₂⁴×C₃₁	1	2	yes	—
603	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
604	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
605	C₂³	C₂⁴×C₃₁	1	2	yes	—
606	C₂³	C₂⁴×C₃₁	1	2	yes	—
607	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	4	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	4	2	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	2	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	2	no	—
635	D₄	—	4	2	no	—
636	D₄	—	4	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
657	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
658	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
660	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
662	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	8	4	no	—
692	C₂²	—	8	4	no	—
693	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
694	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	1	no	—
709	C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	1	no	—
714	C₂	—	4	2	no	—
715	C₂	—	4	2	no	—
716	C₂	—	4	2	no	—
717	C₂	—	4	1	no	—
718	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂	C₃₁×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#562	C₂	semidirect
2. C₃₁×#560	C₂	semidirect
3. C₃₁×#555	C₂	semidirect
4. C₃₁×#553	C₂	semidirect
5. C₃₁×#552	C₂	semidirect
6. C₃₁×#551	C₂	semidirect
7. C₃₁×#550	C₂	semidirect
8. C₃₁×#547	C₂	semidirect
9. C₃₁×#546	C₂	semidirect
10. C₃₁×#546	C₂	semidirect
11. C₃₁×#546	C₂	semidirect
12. D₄²×C₃₁	C₂	semidirect
13. C₃₁×#542	C₂	semidirect
14. C₃₁×#540	C₂	semidirect
15. C₃₁×#540	C₂	semidirect
16. C₃₁×#538	C₂	semidirect
17. C₃₁×#537	C₂	semidirect
18. C₃₁×#535	C₂	semidirect
19. C₃₁×#535	C₂	semidirect
20. C₃₁×#534	C₂	semidirect
21. C₃₁×#525	C₂	semidirect
22. C₃₁×#525	C₂	semidirect
23. C₂×C₃₁×#121	C₂	semidirect
24. C₂×#41×C₃₁	C₂²	semidirect
25. C₂×#41×C₃₁	C₂²	semidirect
26. C₂×#41×C₃₁	C₂²	semidirect
27. C₂×#41×C₃₁	C₂²	semidirect
30. C₂²×D₄×C₃₁	C₂²	semidirect
31. C₂²×D₄×C₃₁	C₂²	semidirect
32. C₂³×C₄×C₃₁	C₂²	semidirect
33. C₃₁×C₄⋊Q₈	C₂²	semidirect
34. C₃₁×#127	C₂²	semidirect
35. C₃₁×#127	C₂²	semidirect
36. C₃₁×#127	C₂²	semidirect
37. C₃₁×#126	C₂²	semidirect
38. C₃₁×#126	C₂²	semidirect
39. C₃₁×#126	C₂²	semidirect
40. C₃₁×#125	C₂²	semidirect
41. C₃₁×#125	C₂²	semidirect
42. C₃₁×#124	C₂²	semidirect
43. C₃₁×#124	C₂²	semidirect
44. C₃₁×#124	C₂²	semidirect
45. C₃₁×#124	C₂²	semidirect
46. C₃₁×#124	C₂²	semidirect
48. C₃₁×#123	C₂²	semidirect
49. C₃₁×#123	C₂²	semidirect
50. C₃₁×#123	C₂²	semidirect
51. C₃₁×#123	C₂²	semidirect
52. C₃₁×#123	C₂²	semidirect
53. C₃₁×#123	C₂²	semidirect
54. C₃₁×#123	C₂²	semidirect
55. C₃₁×#123	C₂²	semidirect
56. C₃₁×#123	C₂²	semidirect
57. C₃₁×#123	C₂²	semidirect
58. C₃₁×#123	C₂²	semidirect
59. C₃₁×C₂²⋊Q₈	C₂²	semidirect
60. C₃₁×C₂²⋊Q₈	C₂²	semidirect
61. C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₃₁×C₂²⋊Q₈	C₂²	semidirect
63. C₃₁×C₂²⋊Q₈	C₂²	semidirect
64. C₃₁×C₂²⋊Q₈	C₂²	semidirect
65. C₃₁×C₂²⋊Q₈	C₂²	semidirect
66. C₃₁×C₂²⋊Q₈	C₂²	semidirect
71. C₃₁×#121	C₂²	semidirect
72. C₃₁×#121	C₂²	semidirect
73. C₃₁×#121	C₂²	semidirect
74. C₃₁×#121	C₂²	semidirect
75. C₃₁×#121	C₂²	semidirect
76. C₃₁×#121	C₂²	semidirect
77. C₃₁×#121	C₂²	semidirect
78. C₃₁×#121	C₂²	semidirect
79. C₃₁×#121	C₂²	semidirect
80. C₃₁×#121	C₂²	semidirect
81. C₃₁×#121	C₂²	semidirect
82. C₃₁×#121	C₂²	semidirect
83. C₃₁×#121	C₂²	semidirect
84. C₃₁×#121	C₂²	semidirect
85. C₃₁×#121	C₂²	semidirect
86. C₃₁×#121	C₂²	semidirect
87. C₃₁×#121	C₂²	semidirect
88. C₃₁×#121	C₂²	semidirect
89. C₃₁×#121	C₂²	semidirect
90. C₃₁×#121	C₂²	semidirect
91. C₃₁×#121	C₂²	semidirect
94. C₃₁×#120	C₂²	semidirect
95. C₃₁×#120	C₂²	semidirect
96. C₃₁×#120	C₂²	semidirect
97. C₃₁×#120	C₂²	semidirect
98. C₃₁×#120	C₂²	semidirect
99. C₃₁×#120	C₂²	semidirect
100. C₃₁×#120	C₂²	semidirect
101. C₄×Q₈×C₃₁	C₂²	semidirect
103. C₄×D₄×C₃₁	C₂²	semidirect
104. C₄×D₄×C₃₁	C₂²	semidirect
105. C₄×D₄×C₃₁	C₂²	semidirect
106. C₄×D₄×C₃₁	C₂²	semidirect
107. C₄×D₄×C₃₁	C₂²	semidirect
108. C₄×D₄×C₃₁	C₂²	semidirect
109. C₄×D₄×C₃₁	C₂²	semidirect
110. C₄×D₄×C₃₁	C₂²	semidirect
111. C₄×D₄×C₃₁	C₂²	semidirect
112. C₄×D₄×C₃₁	C₂²	semidirect
113. C₃₁×#117	C₂²	semidirect
114. C₃₁×#117	C₂²	semidirect
115. C₃₁×#117	C₂²	semidirect
116. C₃₁×#117	C₂²	semidirect
117. C₃₁×#117	C₂²	semidirect
118. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
119. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
120. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
306. #3542	C₃₁	direct (N × H)
350. #562	C₂×C₃₁	semidirect
351. #560	C₂×C₃₁	semidirect
352. #555	C₂×C₃₁	semidirect
353. #553	C₂×C₃₁	semidirect
354. #552	C₂×C₃₁	semidirect
355. #551	C₂×C₃₁	semidirect
356. #550	C₂×C₃₁	semidirect
357. #547	C₂×C₃₁	semidirect
358. #546	C₂×C₃₁	semidirect
359. #546	C₂×C₃₁	semidirect
360. #546	C₂×C₃₁	semidirect
361. D₄²	C₂×C₃₁	semidirect
362. #542	C₂×C₃₁	semidirect
363. #540	C₂×C₃₁	semidirect
364. #540	C₂×C₃₁	semidirect
365. #538	C₂×C₃₁	semidirect
366. #537	C₂×C₃₁	semidirect
367. #535	C₂×C₃₁	semidirect
368. #535	C₂×C₃₁	semidirect
369. #534	C₂×C₃₁	semidirect
370. #525	C₂×C₃₁	semidirect
371. #525	C₂×C₃₁	semidirect
372. C₂×#121	C₂×C₃₁	semidirect
384. C₂×#41	C₂²×C₃₁	semidirect
385. C₂×#41	C₂²×C₃₁	semidirect
386. C₂×#41	C₂²×C₃₁	semidirect
387. C₂×#41	C₂²×C₃₁	semidirect
390. C₂²×D₄	C₂²×C₃₁	semidirect
391. C₂²×D₄	C₂²×C₃₁	semidirect
392. C₂³×C₄	C₂²×C₃₁	semidirect
393. C₄⋊Q₈	C₂²×C₃₁	semidirect
394. #127	C₂²×C₃₁	semidirect
395. #127	C₂²×C₃₁	semidirect
396. #127	C₂²×C₃₁	semidirect
397. #126	C₂²×C₃₁	semidirect
398. #126	C₂²×C₃₁	semidirect
399. #126	C₂²×C₃₁	semidirect
400. #125	C₂²×C₃₁	semidirect
401. #125	C₂²×C₃₁	semidirect
402. #124	C₂²×C₃₁	semidirect
403. #124	C₂²×C₃₁	semidirect
404. #124	C₂²×C₃₁	semidirect
405. #124	C₂²×C₃₁	semidirect
406. #124	C₂²×C₃₁	semidirect
408. #123	C₂²×C₃₁	semidirect
409. #123	C₂²×C₃₁	semidirect
410. #123	C₂²×C₃₁	semidirect
411. #123	C₂²×C₃₁	semidirect
412. #123	C₂²×C₃₁	semidirect
413. #123	C₂²×C₃₁	semidirect
414. #123	C₂²×C₃₁	semidirect
415. #123	C₂²×C₃₁	semidirect
416. #123	C₂²×C₃₁	semidirect
417. #123	C₂²×C₃₁	semidirect
418. #123	C₂²×C₃₁	semidirect
419. C₂²⋊Q₈	C₂²×C₃₁	semidirect
420. C₂²⋊Q₈	C₂²×C₃₁	semidirect
421. C₂²⋊Q₈	C₂²×C₃₁	semidirect
422. C₂²⋊Q₈	C₂²×C₃₁	semidirect
423. C₂²⋊Q₈	C₂²×C₃₁	semidirect
424. C₂²⋊Q₈	C₂²×C₃₁	semidirect
425. C₂²⋊Q₈	C₂²×C₃₁	semidirect
426. C₂²⋊Q₈	C₂²×C₃₁	semidirect
431. #121	C₂²×C₃₁	semidirect
432. #121	C₂²×C₃₁	semidirect
433. #121	C₂²×C₃₁	semidirect
434. #121	C₂²×C₃₁	semidirect
435. #121	C₂²×C₃₁	semidirect
436. #121	C₂²×C₃₁	semidirect
437. #121	C₂²×C₃₁	semidirect
438. #121	C₂²×C₃₁	semidirect
439. #121	C₂²×C₃₁	semidirect
440. #121	C₂²×C₃₁	semidirect
441. #121	C₂²×C₃₁	semidirect
442. #121	C₂²×C₃₁	semidirect
443. #121	C₂²×C₃₁	semidirect
444. #121	C₂²×C₃₁	semidirect
445. #121	C₂²×C₃₁	semidirect
446. #121	C₂²×C₃₁	semidirect
447. #121	C₂²×C₃₁	semidirect
448. #121	C₂²×C₃₁	semidirect
449. #121	C₂²×C₃₁	semidirect
450. #121	C₂²×C₃₁	semidirect
451. #121	C₂²×C₃₁	semidirect
454. #120	C₂²×C₃₁	semidirect
455. #120	C₂²×C₃₁	semidirect
456. #120	C₂²×C₃₁	semidirect
457. #120	C₂²×C₃₁	semidirect
458. #120	C₂²×C₃₁	semidirect
459. #120	C₂²×C₃₁	semidirect
460. #120	C₂²×C₃₁	semidirect
461. C₄×Q₈	C₂²×C₃₁	semidirect
463. C₄×D₄	C₂²×C₃₁	semidirect
464. C₄×D₄	C₂²×C₃₁	semidirect
465. C₄×D₄	C₂²×C₃₁	semidirect
466. C₄×D₄	C₂²×C₃₁	semidirect
467. C₄×D₄	C₂²×C₃₁	semidirect
468. C₄×D₄	C₂²×C₃₁	semidirect
469. C₄×D₄	C₂²×C₃₁	semidirect
470. C₄×D₄	C₂²×C₃₁	semidirect
471. C₄×D₄	C₂²×C₃₁	semidirect
472. C₄×D₄	C₂²×C₃₁	semidirect
473. #117	C₂²×C₃₁	semidirect
474. #117	C₂²×C₃₁	semidirect
475. #117	C₂²×C₃₁	semidirect
476. #117	C₂²×C₃₁	semidirect
477. #117	C₂²×C₃₁	semidirect
478. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
479. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
480. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
481. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
482. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
483. C₃₁	#3542	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×#562	2
C₃₁×#560	2
C₃₁×#555	2
C₃₁×#553	2
C₃₁×#552	2
C₃₁×#551	2
C₃₁×#550	2
C₃₁×#547	2
C₃₁×#546	2
D₄²×C₃₁	2
C₃₁×#542	2
C₃₁×#540	2
C₃₁×#538	2
C₃₁×#537	2
C₃₁×#535	2
C₃₁×#534	2
C₃₁×#525	2
C₂×C₃₁×#121	2
#3542	31

Subgroups — C31×#3542 #16843475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3542 #16843475