Subgroups — D₄×C₃₁×#117 #21490881

Order 7936.

3562 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#117	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2354	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2352	C₂	1	4	yes	maximal, complemented
5	D₄×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2344	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2342	C₂	1	4	yes	maximal, complemented
8	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal
9	C₃₁×#2293	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2290	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2280	C₂	1	2	yes	maximal, complemented
13	C₄²×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₃₁	C₄	1	16	yes	complemented
18	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#117	—	2	16	no	—
26	C₂×C₃₁×#117	C₂²	1	4	yes	—
27	C₂×C₃₁×#117	C₂²	1	2	yes	—
28	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
31	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₃₁	C₂²	1	4	yes	complemented
38	C₃₁×#390	C₂²	1	4	yes	—
39	C₃₁×#389	C₂²	1	4	yes	complemented
40	C₃₁×#388	C₂²	1	8	yes	complemented
41	C₃₁×#388	C₂²	1	8	yes	complemented
42	C₃₁×#387	C₂²	1	8	yes	complemented
43	C₃₁×#386	C₂²	1	8	yes	—
44	C₃₁×#385	C₂²	1	8	yes	complemented
45	C₃₁×#384	C₂²	1	2	yes	complemented
46	C₃₁×#382	C₂²	1	2	yes	complemented
47	C₃₁×#381	C₂²	1	4	yes	—
48	C₃₁×#380	C₂²	1	2	yes	—
49	C₃₁×#380	C₂²	1	2	yes	—
50	C₃₁×#380	C₂²	1	4	yes	complemented
51	C₃₁×#380	C₂²	1	4	yes	complemented
52	C₃₁×#379	C₂²	1	4	yes	—
53	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
54	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
55	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
56	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
57	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
59	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
61	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
62	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
63	C₃₁×#376	C₂²	1	2	yes	complemented
64	C₄³×C₃₁	C₂²	1	2	yes	complemented
65	C₂⁵×C₃₁	C₂³	1	2	yes	—
66	C₂²×D₄×C₃₁	—	2	8	no	—
67	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
68	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₃₁	—	2	8	no	—
72	C₂³×C₄×C₃₁	—	2	8	no	—
73	C₂³×C₄×C₃₁	C₂×C₄	1	16	yes	complemented
74	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
75	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
77	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
78	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
79	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₃₁	—	2	16	no	—
84	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
85	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
86	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
87	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
88	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
89	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
90	C₃₁×#117	—	2	8	no	—
91	C₃₁×#117	—	2	4	no	—
92	C₃₁×#117	—	2	16	no	—
93	C₃₁×#117	—	2	16	no	—
94	C₃₁×#117	—	2	16	no	—
95	C₃₁×#117	D₄	1	8	yes	direct product factor
96	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
97	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
98	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
100	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
108	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
109	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄²×C₃₁	—	2	16	no	—
120	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	complemented
121	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
122	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
123	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
131	C₃₁×#95	C₂³	1	4	yes	—
132	C₃₁×#95	C₂³	1	4	yes	—
133	C₃₁×#95	C₂³	1	4	yes	—
134	C₃₁×#95	C₂³	1	8	yes	—
135	C₃₁×#95	C₂³	1	8	yes	—
136	C₃₁×#95	C₂³	1	4	yes	—
137	C₂⁴×C₃₁	—	2	4	no	—
138	C₂⁴×C₃₁	—	2	4	no	—
139	C₂⁴×C₃₁	—	2	8	no	—
140	C₂⁴×C₃₁	—	4	4	no	—
141	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
142	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
143	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
144	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
145	C₂×D₄×C₃₁	—	2	8	no	—
146	C₂×D₄×C₃₁	—	2	32	no	—
147	C₂×D₄×C₃₁	—	2	4	no	—
148	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
149	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
150	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
151	C₂×D₄×C₃₁	#41	1	8	yes	—
152	C₂²×C₄×C₃₁	—	2	4	no	—
153	C₂²×C₄×C₃₁	—	2	4	no	—
154	C₂²×C₄×C₃₁	—	2	64	no	—
155	C₂²×C₄×C₃₁	—	2	4	no	—
156	C₂²×C₄×C₃₁	—	2	4	no	—
157	C₂²×C₄×C₃₁	—	2	4	no	—
158	C₂²×C₄×C₃₁	—	2	4	no	—
159	C₂²×C₄×C₃₁	—	2	4	no	—
160	C₂²×C₄×C₃₁	—	2	4	no	—
161	C₂²×C₄×C₃₁	—	2	4	no	—
162	C₂²×C₄×C₃₁	—	2	4	no	—
163	C₂²×C₄×C₃₁	—	2	4	no	—
164	C₂²×C₄×C₃₁	—	2	16	no	—
165	C₂²×C₄×C₃₁	—	2	16	no	—
166	C₂²×C₄×C₃₁	—	4	2	no	—
167	C₂²×C₄×C₃₁	—	4	8	no	—
168	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
170	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
171	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
172	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
174	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₃₁	#41	1	4	yes	—
178	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₃₁	—	2	16	no	—
190	C₄⋊C₄×C₃₁	—	2	8	no	—
191	C₄⋊C₄×C₃₁	—	2	4	no	—
192	C₄⋊C₄×C₃₁	—	2	8	no	—
193	C₄⋊C₄×C₃₁	—	4	4	no	—
194	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
195	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
196	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
197	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	complemented
198	C₂²⋊C₄×C₃₁	—	2	8	no	—
199	C₂²⋊C₄×C₃₁	—	2	4	no	—
200	C₂²⋊C₄×C₃₁	—	2	16	no	—
201	C₂²⋊C₄×C₃₁	—	2	16	no	—
202	C₂²⋊C₄×C₃₁	—	4	8	no	—
203	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
204	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
205	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
206	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
207	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
208	C₄²×C₃₁	—	2	16	no	—
209	C₄²×C₃₁	—	2	8	no	—
210	C₄²×C₃₁	—	2	4	no	—
211	C₄²×C₃₁	—	2	8	no	—
212	C₄²×C₃₁	—	4	4	no	—
213	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
214	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
215	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
216	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
217	C₄²×C₃₁	C₂×D₄	1	8	yes	complemented
218	D₄×#117	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₃₁	—	2	2	no	—
220	C₂³×C₃₁	—	2	2	no	—
221	C₂³×C₃₁	—	2	2	no	—
222	C₂³×C₃₁	—	2	4	no	—
223	C₂³×C₃₁	—	2	2	no	—
224	C₂³×C₃₁	—	2	16	no	—
225	C₂³×C₃₁	—	2	16	no	—
226	C₂³×C₃₁	—	2	2	no	—
227	C₂³×C₃₁	—	2	2	no	—
228	C₂³×C₃₁	—	2	4	no	—
229	C₂³×C₃₁	—	2	4	no	—
230	C₂³×C₃₁	—	4	8	no	—
231	C₂³×C₃₁	—	4	16	no	—
232	C₂³×C₃₁	—	4	16	no	—
233	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
234	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
235	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
236	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
237	C₂³×C₃₁	C₂×#41	1	8	yes	—
238	C₂³×C₃₁	C₂×#41	1	2	yes	—
239	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
240	D₄×C₃₁	—	2	16	no	—
241	D₄×C₃₁	—	2	8	no	—
242	D₄×C₃₁	#117	1	16	yes	direct product factor
243	C₂×C₄×C₃₁	—	2	16	no	—
244	C₂×C₄×C₃₁	—	2	2	no	—
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	4	no	—
247	C₂×C₄×C₃₁	—	2	2	no	—
248	C₂×C₄×C₃₁	—	2	2	no	—
249	C₂×C₄×C₃₁	—	2	2	no	—
250	C₂×C₄×C₃₁	—	2	2	no	—
251	C₂×C₄×C₃₁	—	2	4	no	—
252	C₂×C₄×C₃₁	—	2	2	no	—
253	C₂×C₄×C₃₁	—	2	8	no	—
254	C₂×C₄×C₃₁	—	2	16	no	—
255	C₂×C₄×C₃₁	—	2	16	no	—
256	C₂×C₄×C₃₁	—	2	16	no	—
257	C₂×C₄×C₃₁	—	2	16	no	—
258	C₂×C₄×C₃₁	—	2	8	no	—
259	C₂×C₄×C₃₁	—	2	4	no	—
260	C₂×C₄×C₃₁	—	2	4	no	—
261	C₂×C₄×C₃₁	—	2	8	no	—
262	C₂×C₄×C₃₁	—	2	4	no	—
263	C₂×C₄×C₃₁	—	2	8	no	—
264	C₂×C₄×C₃₁	—	4	4	no	—
265	C₂×C₄×C₃₁	—	4	32	no	—
266	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	complemented
267	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
276	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
279	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
280	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
281	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic
282	C₂²×#117	C₂×C₃₁	1	2	yes	complemented
283	#2354	C₂×C₃₁	1	2	yes	complemented
284	#2352	C₂×C₃₁	1	4	yes	complemented
285	D₄×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
286	#2344	C₂×C₃₁	1	2	yes	complemented
287	#2342	C₂×C₃₁	1	4	yes	complemented
288	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	—
289	#2293	C₂×C₃₁	1	2	yes	complemented
290	#2290	C₂×C₃₁	1	4	yes	complemented
291	#2285	C₂×C₃₁	1	1	yes	characteristic, complemented
292	#2280	C₂×C₃₁	1	2	yes	complemented
293	C₄²×D₄	C₂×C₃₁	1	2	yes	complemented
294	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
295	C₂²×C₃₁	—	2	2	no	—
296	C₂²×C₃₁	—	2	4	no	—
297	C₂²×C₃₁	—	2	2	no	—
298	C₂²×C₃₁	—	2	4	no	—
299	C₂²×C₃₁	—	2	8	no	—
300	C₂²×C₃₁	—	2	4	no	—
301	C₂²×C₃₁	—	2	4	no	—
302	C₂²×C₃₁	—	2	8	no	—
303	C₂²×C₃₁	—	2	4	no	—
304	C₂²×C₃₁	—	2	4	no	—
305	C₂²×C₃₁	—	2	4	no	—
306	C₂²×C₃₁	—	4	32	no	—
307	C₂²×C₃₁	—	4	4	no	—
308	C₂²×C₃₁	—	4	4	no	—
309	C₂²×C₃₁	C₂×#117	1	8	yes	complemented
310	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
311	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
312	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₃₁	C₂²×#41	1	2	yes	—
314	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
315	C₂²×C₃₁	#585	1	2	yes	—
316	C₄×C₃₁	—	2	2	no	—
317	C₄×C₃₁	—	2	4	no	—
318	C₄×C₃₁	—	2	4	no	—
319	C₄×C₃₁	—	2	2	no	—
320	C₄×C₃₁	—	2	2	no	—
321	C₄×C₃₁	—	2	8	no	—
322	C₄×C₃₁	—	4	8	no	—
323	C₄×C₃₁	—	4	4	no	—
324	C₄×C₃₁	C₂×#117	1	4	yes	complemented
325	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
326	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
327	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
328	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
329	C₂×C₄×D₄	C₄×C₃₁	1	16	yes	complemented
330	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
331	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
334	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
335	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
336	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
337	C₂×#117	—	2	16	no	—
338	C₂×#117	C₂²×C₃₁	1	4	yes	—
339	C₂×#117	C₂²×C₃₁	1	2	yes	—
340	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
341	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
342	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
343	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
344	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
346	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
347	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
348	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
349	C₂²×C₄²	C₂²×C₃₁	1	4	yes	complemented
350	#390	C₂²×C₃₁	1	4	yes	—
351	#389	C₂²×C₃₁	1	4	yes	complemented
352	#388	C₂²×C₃₁	1	8	yes	complemented
353	#388	C₂²×C₃₁	1	8	yes	complemented
354	#387	C₂²×C₃₁	1	8	yes	complemented
355	#386	C₂²×C₃₁	1	8	yes	—
356	#385	C₂²×C₃₁	1	8	yes	complemented
357	#384	C₂²×C₃₁	1	2	yes	complemented
358	#382	C₂²×C₃₁	1	2	yes	complemented
359	#381	C₂²×C₃₁	1	4	yes	—
360	#380	C₂²×C₃₁	1	2	yes	—
361	#380	C₂²×C₃₁	1	2	yes	—
362	#380	C₂²×C₃₁	1	4	yes	complemented
363	#380	C₂²×C₃₁	1	4	yes	complemented
364	#379	C₂²×C₃₁	1	4	yes	—
365	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
366	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
367	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
368	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
369	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
370	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
373	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
374	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
375	#376	C₂²×C₃₁	1	2	yes	complemented
376	C₄³	C₂²×C₃₁	1	2	yes	complemented
377	C₂×C₃₁	—	2	4	no	—
378	C₂×C₃₁	—	2	8	no	—
379	C₂×C₃₁	—	4	4	no	—
380	C₂×C₃₁	C₂²×#117	1	1	yes	characteristic
381	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
382	C₂×C₃₁	#3428	1	1	yes	characteristic
383	C₂×C₃₁	D₄×#41	1	2	yes	—
384	C₂×C₃₁	#3475	1	2	yes	—
385	C₂⁵	C₂³×C₃₁	1	2	yes	—
386	C₂²×D₄	—	2	8	no	—
387	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
388	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
389	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
391	C₂³×C₄	—	2	8	no	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	C₂×C₄×C₃₁	1	16	yes	complemented
394	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
395	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
396	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
398	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
399	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
400	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
401	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
403	C₄×D₄	—	2	16	no	—
404	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
405	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
406	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
407	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
408	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
409	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
410	#117	—	2	8	no	—
411	#117	—	2	4	no	—
412	#117	—	2	16	no	—
413	#117	—	2	16	no	—
414	#117	—	2	16	no	—
415	#117	D₄×C₃₁	1	8	yes	direct product factor
416	C₂×C₄⋊C₄	—	2	16	no	—
417	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
418	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
427	C₂×C₂²⋊C₄	—	2	16	no	—
428	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
429	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
439	C₂×C₄²	—	2	16	no	—
440	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	complemented
441	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
442	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
443	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
444	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
445	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
446	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
451	#95	C₂³×C₃₁	1	4	yes	—
452	#95	C₂³×C₃₁	1	4	yes	—
453	#95	C₂³×C₃₁	1	4	yes	—
454	#95	C₂³×C₃₁	1	8	yes	—
455	#95	C₂³×C₃₁	1	8	yes	—
456	#95	C₂³×C₃₁	1	4	yes	—
457	C₃₁	D₄×#117	1	1	yes	characteristic, direct product factor, Sylow
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	—	2	8	no	—
461	C₂⁴	—	4	4	no	—
462	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
463	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
464	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
465	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	32	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
470	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
471	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
472	C₂×D₄	#41×C₃₁	1	8	yes	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	64	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	16	no	—
486	C₂²×C₄	—	2	16	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
490	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
491	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
492	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
493	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
494	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
495	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
497	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
498	C₂²×C₄	#41×C₃₁	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
501	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
510	C₄⋊C₄	—	2	16	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	4	4	no	—
515	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
516	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
517	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
518	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	complemented
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	16	no	—
523	C₂²⋊C₄	—	4	8	no	—
524	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
525	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
526	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
527	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
528	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
529	C₄²	—	2	16	no	—
530	C₄²	—	2	8	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	8	no	—
533	C₄²	—	4	4	no	—
534	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
535	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
536	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
537	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
538	C₄²	C₂×D₄×C₃₁	1	8	yes	complemented
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	16	no	—
545	C₂³	—	2	16	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	16	no	—
552	C₂³	—	4	16	no	—
553	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
554	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
555	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
556	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
557	C₂³	C₂×#41×C₃₁	1	8	yes	—
558	C₂³	C₂×#41×C₃₁	1	2	yes	—
559	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
560	D₄	—	2	16	no	—
561	D₄	—	2	8	no	—
562	D₄	C₃₁×#117	1	16	yes	direct product factor
563	C₂×C₄	—	2	16	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	16	no	—
575	C₂×C₄	—	2	16	no	—
576	C₂×C₄	—	2	16	no	—
577	C₂×C₄	—	2	16	no	—
578	C₂×C₄	—	2	8	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	8	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	32	no	—
586	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	complemented
587	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
588	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
589	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
590	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
591	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
592	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
593	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
594	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
596	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
598	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
599	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
600	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	8	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	4	32	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	4	no	—
615	C₂²	C₂×C₃₁×#117	1	8	yes	complemented
616	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
617	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
618	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₃₁	1	2	yes	—
620	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
621	C₂²	C₃₁×#585	1	2	yes	—
622	C₄	—	2	2	no	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	8	no	—
628	C₄	—	4	8	no	—
629	C₄	—	4	4	no	—
630	C₄	C₂×C₃₁×#117	1	4	yes	complemented
631	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
632	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
633	C₂	—	2	4	no	—
634	C₂	—	2	8	no	—
635	C₂	—	4	4	no	—
636	C₂	C₂²×C₃₁×#117	1	1	yes	characteristic
637	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
638	C₂	C₃₁×#3428	1	1	yes	characteristic
639	C₂	D₄×#41×C₃₁	1	2	yes	—
640	C₂	C₃₁×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂³×D₄×C₃₁	C₂²
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. C₂²×C₃₁×#117	C₂	semidirect
3. C₃₁×#2354	C₂	semidirect
4. C₃₁×#2352	C₂	semidirect
5. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
6. C₃₁×#2344	C₂	semidirect
7. C₃₁×#2342	C₂	semidirect
9. C₃₁×#2293	C₂	semidirect
10. C₃₁×#2290	C₂	semidirect
11. C₃₁×#2285	C₂	semidirect
12. C₃₁×#2280	C₂	semidirect
13. C₄²×D₄×C₃₁	C₂	semidirect
14. C₄×C₃₁×#117	C₂	semidirect
17. C₂×C₄×D₄×C₃₁	C₄	semidirect
30. C₂×C₃₁×#117	C₂²	semidirect
31. C₂×C₃₁×#117	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
37. C₂²×C₄²×C₃₁	C₂²	semidirect
39. C₃₁×#389	C₂²	semidirect
40. C₃₁×#388	C₂²	semidirect
41. C₃₁×#388	C₂²	semidirect
42. C₃₁×#387	C₂²	semidirect
44. C₃₁×#385	C₂²	semidirect
45. C₃₁×#384	C₂²	semidirect
46. C₃₁×#382	C₂²	semidirect
50. C₃₁×#380	C₂²	semidirect
51. C₃₁×#380	C₂²	semidirect
53. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
54. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
55. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
56. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
57. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
63. C₃₁×#376	C₂²	semidirect
64. C₄³×C₃₁	C₂²	semidirect
73. C₂³×C₄×C₃₁	C₂×C₄	semidirect
86. C₄×D₄×C₃₁	C₂×C₄	semidirect
87. C₄×D₄×C₃₁	C₂×C₄	semidirect
88. C₄×D₄×C₃₁	C₂×C₄	semidirect
89. C₄×D₄×C₃₁	C₂×C₄	semidirect
95. C₃₁×#117	D₄	direct (N × H)
97. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
108. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
120. C₂×C₄²×C₃₁	C₂×C₄	semidirect
197. C₄⋊C₄×C₃₁	C₂×D₄	semidirect
217. C₄²×C₃₁	C₂×D₄	semidirect
218. D₄×#117	C₃₁	direct (N × H)
242. D₄×C₃₁	#117	direct (N × H)
266. C₂×C₄×C₃₁	C₄×D₄	semidirect
282. C₂²×#117	C₂×C₃₁	semidirect
283. #2354	C₂×C₃₁	semidirect
284. #2352	C₂×C₃₁	semidirect
285. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
286. #2344	C₂×C₃₁	semidirect
287. #2342	C₂×C₃₁	semidirect
289. #2293	C₂×C₃₁	semidirect
290. #2290	C₂×C₃₁	semidirect
291. #2285	C₂×C₃₁	semidirect
292. #2280	C₂×C₃₁	semidirect
293. C₄²×D₄	C₂×C₃₁	semidirect
294. C₄×#117	C₂×C₃₁	semidirect
309. C₂²×C₃₁	C₂×#117	semidirect
324. C₄×C₃₁	C₂×#117	semidirect
329. C₂×C₄×D₄	C₄×C₃₁	semidirect
342. C₂×#117	C₂²×C₃₁	semidirect
343. C₂×#117	C₂²×C₃₁	semidirect
345. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
349. C₂²×C₄²	C₂²×C₃₁	semidirect
351. #389	C₂²×C₃₁	semidirect
352. #388	C₂²×C₃₁	semidirect
353. #388	C₂²×C₃₁	semidirect
354. #387	C₂²×C₃₁	semidirect
356. #385	C₂²×C₃₁	semidirect
357. #384	C₂²×C₃₁	semidirect
358. #382	C₂²×C₃₁	semidirect
362. #380	C₂²×C₃₁	semidirect
363. #380	C₂²×C₃₁	semidirect
365. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
366. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
367. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
368. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
369. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
373. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
374. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
375. #376	C₂²×C₃₁	semidirect
376. C₄³	C₂²×C₃₁	semidirect
393. C₂³×C₄	C₂×C₄×C₃₁	semidirect
406. C₄×D₄	C₂×C₄×C₃₁	semidirect
407. C₄×D₄	C₂×C₄×C₃₁	semidirect
408. C₄×D₄	C₂×C₄×C₃₁	semidirect
409. C₄×D₄	C₂×C₄×C₃₁	semidirect
415. #117	D₄×C₃₁	direct (N × H)
417. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
428. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
440. C₂×C₄²	C₂×C₄×C₃₁	semidirect
457. C₃₁	D₄×#117	direct (N × H)
518. C₄⋊C₄	C₂×D₄×C₃₁	semidirect
538. C₄²	C₂×D₄×C₃₁	semidirect
562. D₄	C₃₁×#117	direct (N × H)
586. C₂×C₄	C₄×D₄×C₃₁	semidirect
615. C₂²	C₂×C₃₁×#117	semidirect
630. C₄	C₂×C₃₁×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₃₁	2
C₂²×C₃₁×#117	2
C₃₁×#2354	2
C₃₁×#2352	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2344	2
C₃₁×#2342	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2293	2
C₃₁×#2290	2
C₃₁×#2285	2
C₃₁×#2280	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
D₄×#117	31

Subgroups — D4×C31×#117 #21490881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₃₁×#117 #21490881