Subgroups — C₄×C₃₁×#554 #21490926

Order 7936.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2370	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2368	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2349	C₂	1	2	yes	maximal
8	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2345	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₃₁×#125	C₂	1	2	yes	maximal, complemented
12	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
14	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
16	C₄²×D₄×C₃₁	C₂	1	2	yes	maximal
17	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
18	C₃₁×#554	C₄	1	16	yes	direct product factor
19	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#125	C₂²	1	2	yes	—
21	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
35	C₂²×C₄²×C₃₁	C₂²	1	4	yes	—
36	C₃₁×#391	C₂²	1	2	yes	—
37	C₃₁×#391	C₂²	1	2	yes	—
38	C₃₁×#391	C₂²	1	4	yes	—
39	C₃₁×#389	C₂²	1	2	yes	—
40	C₃₁×#389	C₂²	1	2	yes	—
41	C₃₁×#389	C₂²	1	2	yes	—
42	C₃₁×#389	C₂²	1	2	yes	—
43	C₃₁×#389	C₂²	1	2	yes	—
44	C₃₁×#389	C₂²	1	4	yes	—
45	C₃₁×#387	C₂²	1	4	yes	—
46	C₃₁×#387	C₂²	1	4	yes	—
47	C₃₁×#387	C₂²	1	4	yes	—
48	C₃₁×#387	C₂²	1	4	yes	—
49	C₃₁×#387	C₂²	1	4	yes	—
50	C₃₁×#385	C₂²	1	4	yes	—
51	C₃₁×#385	C₂²	1	4	yes	—
52	C₃₁×#385	C₂²	1	4	yes	—
53	C₃₁×#384	C₂²	1	1	yes	characteristic
54	C₃₁×#382	C₂²	1	2	yes	—
55	C₃₁×#380	C₂²	1	2	yes	—
56	C₃₁×#380	C₂²	1	4	yes	—
57	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
72	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
81	C₂×C₃₁×#95	C₂²	1	4	yes	—
82	C₄³×C₃₁	C₂²	1	1	yes	characteristic
83	C₄³×C₃₁	C₂²	1	2	yes	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
88	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
92	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
93	C₃₁×#125	C₂×C₄	1	16	yes	complemented
94	C₃₁×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
95	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
96	C₄×Q₈×C₃₁	—	2	4	no	—
97	C₄×Q₈×C₃₁	—	2	4	no	—
98	C₄×Q₈×C₃₁	—	4	4	no	—
99	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₃₁	—	2	8	no	—
101	C₄×D₄×C₃₁	—	2	4	no	—
102	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	—
103	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
104	C₄×D₄×C₃₁	Q₈	1	8	yes	complemented
105	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
106	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄²×C₃₁	—	2	8	no	—
132	C₂×C₄²×C₃₁	—	4	8	no	—
133	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
146	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
152	C₃₁×#95	C₂³	1	2	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	4	yes	—
155	C₃₁×#95	C₂³	1	4	yes	—
156	C₃₁×#95	C₂³	1	2	yes	—
157	C₃₁×#95	C₂³	1	2	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	2	yes	—
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₃₁×#95	C₂³	1	2	yes	—
164	C₃₁×#95	C₂³	1	4	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
167	C₂×Q₈×C₃₁	—	2	2	no	—
168	C₂×Q₈×C₃₁	—	2	2	no	—
169	C₂×Q₈×C₃₁	—	4	2	no	—
170	C₂×Q₈×C₃₁	—	4	2	no	—
171	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
172	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
174	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
175	C₂×D₄×C₃₁	#41	1	4	yes	—
176	C₂²×C₄×C₃₁	—	2	4	no	—
177	C₂²×C₄×C₃₁	—	2	4	no	—
178	C₂²×C₄×C₃₁	—	2	4	no	—
179	C₂²×C₄×C₃₁	—	2	4	no	—
180	C₂²×C₄×C₃₁	—	2	8	no	—
181	C₂²×C₄×C₃₁	—	2	4	no	—
182	C₂²×C₄×C₃₁	—	2	4	no	—
183	C₂²×C₄×C₃₁	—	2	8	no	—
184	C₂²×C₄×C₃₁	—	4	4	no	—
185	C₂²×C₄×C₃₁	—	4	4	no	—
186	C₂²×C₄×C₃₁	—	4	4	no	—
187	C₂²×C₄×C₃₁	—	4	2	no	—
188	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
189	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	—
190	C₂²×C₄×C₃₁	C₂×Q₈	1	8	yes	—
191	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₃₁	—	2	8	no	—
208	C₄⋊C₄×C₃₁	—	2	4	no	—
209	C₄⋊C₄×C₃₁	—	2	2	no	—
210	C₄⋊C₄×C₃₁	—	2	4	no	—
211	C₄⋊C₄×C₃₁	—	2	4	no	—
212	C₄⋊C₄×C₃₁	—	2	4	no	—
213	C₄⋊C₄×C₃₁	—	2	2	no	—
214	C₄⋊C₄×C₃₁	—	4	4	no	—
215	C₄⋊C₄×C₃₁	—	4	4	no	—
216	C₄⋊C₄×C₃₁	—	4	2	no	—
217	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
218	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
219	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
222	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
223	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
224	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
225	C₄⋊C₄×C₃₁	#41	1	4	yes	—
226	C₂²⋊C₄×C₃₁	—	2	8	no	—
227	C₂²⋊C₄×C₃₁	—	2	4	no	—
228	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
229	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₃₁	C₂×Q₈	1	8	yes	—
231	C₄²×C₃₁	—	2	4	no	—
232	C₄²×C₃₁	—	2	4	no	—
233	C₄²×C₃₁	—	2	4	no	—
234	C₄²×C₃₁	—	2	2	no	—
235	C₄²×C₃₁	—	2	4	no	—
236	C₄²×C₃₁	—	2	4	no	—
237	C₄²×C₃₁	—	2	2	no	—
238	C₄²×C₃₁	—	2	4	no	—
239	C₄²×C₃₁	—	2	4	no	—
240	C₄²×C₃₁	—	2	8	no	—
241	C₄²×C₃₁	—	2	2	no	—
242	C₄²×C₃₁	—	4	4	no	—
243	C₄²×C₃₁	—	4	4	no	—
244	C₄²×C₃₁	—	4	1	no	—
245	C₄²×C₃₁	—	4	2	no	—
246	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
247	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
248	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
249	C₄²×C₃₁	#41	1	4	yes	—
250	C₄×#554	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂³×C₃₁	—	2	2	no	—
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	2	no	—
254	C₂³×C₃₁	—	2	2	no	—
255	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
256	C₂³×C₃₁	C₂²×Q₈	1	4	yes	—
257	C₂³×C₃₁	C₂×#41	1	4	yes	—
258	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
259	Q₈×C₃₁	—	2	8	no	—
260	Q₈×C₃₁	—	4	8	no	—
261	D₄×C₃₁	C₄×Q₈	1	16	yes	complemented
262	C₂×C₄×C₃₁	—	2	1	no	—
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	2	2	no	—
265	C₂×C₄×C₃₁	—	2	2	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	1	no	—
268	C₂×C₄×C₃₁	—	2	2	no	—
269	C₂×C₄×C₃₁	—	2	2	no	—
270	C₂×C₄×C₃₁	—	2	2	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	4	no	—
273	C₂×C₄×C₃₁	—	2	1	no	—
274	C₂×C₄×C₃₁	—	2	2	no	—
275	C₂×C₄×C₃₁	—	2	1	no	—
276	C₂×C₄×C₃₁	—	2	2	no	—
277	C₂×C₄×C₃₁	—	2	1	no	—
278	C₂×C₄×C₃₁	—	2	1	no	—
279	C₂×C₄×C₃₁	—	2	4	no	—
280	C₂×C₄×C₃₁	—	2	16	no	—
281	C₂×C₄×C₃₁	—	2	16	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	2	no	—
284	C₂×C₄×C₃₁	—	2	1	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	1	no	—
287	C₂×C₄×C₃₁	—	2	2	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	2	4	no	—
290	C₂×C₄×C₃₁	—	2	4	no	—
291	C₂×C₄×C₃₁	—	2	1	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	4	16	no	—
295	C₂×C₄×C₃₁	—	4	8	no	—
296	C₂×C₄×C₃₁	—	4	16	no	—
297	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
298	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
301	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
302	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
305	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
306	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
309	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
310	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
311	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
312	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
313	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
314	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
315	C₂×#554	C₂×C₃₁	1	1	yes	characteristic
316	#2370	C₂×C₃₁	1	2	yes	complemented
317	#2369	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#2368	C₂×C₃₁	1	4	yes	complemented
319	#2360	C₂×C₃₁	1	2	yes	complemented
320	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
321	#2349	C₂×C₃₁	1	2	yes	—
322	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
323	#2345	C₂×C₃₁	1	2	yes	complemented
324	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
325	C₄×#125	C₂×C₃₁	1	2	yes	complemented
326	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
327	C₄×C₂²⋊Q₈	C₂×C₃₁	1	4	yes	complemented
328	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
329	C₄²×D₄	C₂×C₃₁	1	2	yes	—
330	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic
331	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
332	C₂²×C₃₁	—	2	4	no	—
333	C₂²×C₃₁	—	2	4	no	—
334	C₂²×C₃₁	—	2	4	no	—
335	C₂²×C₃₁	—	2	4	no	—
336	C₂²×C₃₁	—	2	4	no	—
337	C₂²×C₃₁	—	2	4	no	—
338	C₂²×C₃₁	C₂×C₄×Q₈	1	8	yes	—
339	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
340	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
341	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
344	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₃₁	#585	1	1	yes	characteristic
346	C₄×C₃₁	—	2	4	no	—
347	C₄×C₃₁	—	2	4	no	—
348	C₄×C₃₁	—	2	4	no	—
349	C₄×C₃₁	—	2	8	no	—
350	C₄×C₃₁	—	2	2	no	—
351	C₄×C₃₁	—	2	4	no	—
352	C₄×C₃₁	—	2	2	no	—
353	C₄×C₃₁	—	2	2	no	—
354	C₄×C₃₁	—	2	4	no	—
355	C₄×C₃₁	—	4	2	no	—
356	C₄×C₃₁	—	4	2	no	—
357	C₄×C₃₁	—	4	1	no	—
358	C₄×C₃₁	—	4	4	no	—
359	C₄×C₃₁	C₂×C₄×Q₈	1	4	yes	—
360	C₄×C₃₁	C₄×#41	1	4	yes	—
361	C₄×C₃₁	#554	1	4	yes	direct product factor
362	#554	C₄×C₃₁	1	16	yes	direct product factor
363	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
364	C₂×#125	C₂²×C₃₁	1	2	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
367	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
377	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
378	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
379	C₂²×C₄²	C₂²×C₃₁	1	4	yes	—
380	#391	C₂²×C₃₁	1	2	yes	—
381	#391	C₂²×C₃₁	1	2	yes	—
382	#391	C₂²×C₃₁	1	4	yes	—
383	#389	C₂²×C₃₁	1	2	yes	—
384	#389	C₂²×C₃₁	1	2	yes	—
385	#389	C₂²×C₃₁	1	2	yes	—
386	#389	C₂²×C₃₁	1	2	yes	—
387	#389	C₂²×C₃₁	1	2	yes	—
388	#389	C₂²×C₃₁	1	4	yes	—
389	#387	C₂²×C₃₁	1	4	yes	—
390	#387	C₂²×C₃₁	1	4	yes	—
391	#387	C₂²×C₃₁	1	4	yes	—
392	#387	C₂²×C₃₁	1	4	yes	—
393	#387	C₂²×C₃₁	1	4	yes	—
394	#385	C₂²×C₃₁	1	4	yes	—
395	#385	C₂²×C₃₁	1	4	yes	—
396	#385	C₂²×C₃₁	1	4	yes	—
397	#384	C₂²×C₃₁	1	1	yes	characteristic
398	#382	C₂²×C₃₁	1	2	yes	—
399	#380	C₂²×C₃₁	1	2	yes	—
400	#380	C₂²×C₃₁	1	4	yes	—
401	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
403	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
404	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
405	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
415	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
425	C₂×#95	C₂²×C₃₁	1	4	yes	—
426	C₄³	C₂²×C₃₁	1	2	yes	—
427	C₄³	C₂²×C₃₁	1	1	yes	characteristic
428	C₂×C₃₁	—	2	8	no	—
429	C₂×C₃₁	C₂²×C₄×Q₈	1	1	yes	characteristic
430	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
431	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₃₁	C₂×#554	1	1	yes	characteristic
433	C₂×C₃₁	#3475	1	1	yes	characteristic
434	C₂×C₃₁	Q₈×#41	1	1	yes	characteristic
435	C₂×C₃₁	#3481	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
438	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
440	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
441	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
442	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
443	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
444	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
445	#125	C₂×C₄×C₃₁	1	16	yes	complemented
446	C₂²⋊Q₈	C₂×C₄×C₃₁	1	32	yes	complemented
447	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
448	C₄×Q₈	—	2	4	no	—
449	C₄×Q₈	—	2	4	no	—
450	C₄×Q₈	—	4	4	no	—
451	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
452	C₄×D₄	—	2	8	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	—
455	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
456	C₄×D₄	Q₈×C₃₁	1	8	yes	complemented
457	C₂×C₄⋊C₄	—	2	8	no	—
458	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
459	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
483	C₂×C₄²	—	2	8	no	—
484	C₂×C₄²	—	4	8	no	—
485	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
486	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
492	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
493	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
494	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
495	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
496	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
497	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
499	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
500	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
501	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
504	#95	C₂³×C₃₁	1	2	yes	—
505	#95	C₂³×C₃₁	1	4	yes	—
506	#95	C₂³×C₃₁	1	4	yes	—
507	#95	C₂³×C₃₁	1	4	yes	—
508	#95	C₂³×C₃₁	1	2	yes	—
509	#95	C₂³×C₃₁	1	2	yes	—
510	#95	C₂³×C₃₁	1	4	yes	—
511	#95	C₂³×C₃₁	1	4	yes	—
512	#95	C₂³×C₃₁	1	4	yes	—
513	#95	C₂³×C₃₁	1	2	yes	—
514	#95	C₂³×C₃₁	1	2	yes	—
515	#95	C₂³×C₃₁	1	2	yes	—
516	#95	C₂³×C₃₁	1	4	yes	—
517	#95	C₂³×C₃₁	1	4	yes	—
518	C₃₁	C₄×#554	1	1	yes	characteristic, direct product factor, Sylow
519	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	4	2	no	—
523	C₂×Q₈	—	4	2	no	—
524	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
525	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
526	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
527	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
528	C₂×D₄	#41×C₃₁	1	4	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	8	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	8	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
542	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	—
543	C₂²×C₄	C₂×Q₈×C₃₁	1	8	yes	—
544	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	4	4	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
571	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
572	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
573	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
575	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
576	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
577	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
578	C₄⋊C₄	#41×C₃₁	1	4	yes	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
583	C₂²⋊C₄	C₂×Q₈×C₃₁	1	8	yes	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	4	no	—
593	C₄²	—	2	8	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	4	no	—
597	C₄²	—	4	1	no	—
598	C₄²	—	4	2	no	—
599	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
600	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
601	C₄²	C₂×Q₈×C₃₁	1	4	yes	—
602	C₄²	#41×C₃₁	1	4	yes	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
608	C₂³	C₂²×Q₈×C₃₁	1	4	yes	—
609	C₂³	C₂×#41×C₃₁	1	4	yes	—
610	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
611	Q₈	—	2	8	no	—
612	Q₈	—	4	8	no	—
613	D₄	C₄×Q₈×C₃₁	1	16	yes	complemented
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	16	no	—
633	C₂×C₄	—	2	16	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	4	16	no	—
647	C₂×C₄	—	4	8	no	—
648	C₂×C₄	—	4	16	no	—
649	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
650	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
652	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
654	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
655	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
656	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
657	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
658	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
659	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
660	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
661	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
662	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
663	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
664	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
665	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
666	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	C₂×C₄×Q₈×C₃₁	1	8	yes	—
674	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
675	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
676	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
677	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
678	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
679	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂²	C₃₁×#585	1	1	yes	characteristic
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	8	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	4	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	4	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	1	no	—
694	C₄	C₂×C₄×Q₈×C₃₁	1	4	yes	—
695	C₄	C₄×#41×C₃₁	1	4	yes	—
696	C₄	C₃₁×#554	1	4	yes	direct product factor
697	C₂	—	2	8	no	—
698	C₂	C₂²×C₄×Q₈×C₃₁	1	1	yes	characteristic
699	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
700	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂	C₂×C₃₁×#554	1	1	yes	characteristic
702	C₂	C₃₁×#3475	1	1	yes	characteristic
703	C₂	Q₈×#41×C₃₁	1	1	yes	characteristic
704	C₂	C₃₁×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2370	C₂	semidirect
3. C₃₁×#2369	C₂	semidirect
4. C₃₁×#2368	C₂	semidirect
5. C₃₁×#2360	C₂	semidirect
6. C₃₁×#2355	C₂	semidirect
9. C₃₁×#2345	C₂	semidirect
10. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
11. C₄×C₃₁×#125	C₂	semidirect
12. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
13. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
14. C₄²×Q₈×C₃₁	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
18. C₃₁×#554	C₄	direct (N × H)
92. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
93. C₃₁×#125	C₂×C₄	semidirect
94. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
95. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₄×Q₈×C₃₁	C₂×C₄	semidirect
104. C₄×D₄×C₃₁	Q₈	semidirect
106. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
250. C₄×#554	C₃₁	direct (N × H)
261. D₄×C₃₁	C₄×Q₈	semidirect
316. #2370	C₂×C₃₁	semidirect
317. #2369	C₂×C₃₁	semidirect
318. #2368	C₂×C₃₁	semidirect
319. #2360	C₂×C₃₁	semidirect
320. #2355	C₂×C₃₁	semidirect
323. #2345	C₂×C₃₁	semidirect
324. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
325. C₄×#125	C₂×C₃₁	semidirect
326. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
327. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
328. C₄²×Q₈	C₂×C₃₁	semidirect
331. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
361. C₄×C₃₁	#554	direct (N × H)
362. #554	C₄×C₃₁	direct (N × H)
444. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
445. #125	C₂×C₄×C₃₁	semidirect
446. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
447. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
451. C₄×Q₈	C₂×C₄×C₃₁	semidirect
456. C₄×D₄	Q₈×C₃₁	semidirect
458. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
518. C₃₁	C₄×#554	direct (N × H)
613. D₄	C₄×Q₈×C₃₁	semidirect
696. C₄	C₃₁×#554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#554	2
C₃₁×#2370	2
C₃₁×#2369	2
C₃₁×#2368	2
C₃₁×#2360	2
C₃₁×#2355	2
C₃₁×#2349	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2345	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#125	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄²×Q₈×C₃₁	2
C₄²×D₄×C₃₁	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₄×#554	31

Subgroups — C4×C31×#554 #21490926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#554 #21490926