Subgroups — C₃×C₄×C₅×C₂²⋊Q₈ #14275336

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#385	C₂	1	2	yes	maximal
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
12	C₄×C₅×C₂²⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	direct product factor
18	C₃×C₄×C₅×Q₈	—	2	4	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	—	2	4	no	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
32	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×C₄×C₂²⋊Q₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
43	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#387	C₂×C₃	1	2	yes	complemented
46	C₅×#385	C₂×C₃	1	2	yes	—
47	C₅×#380	C₂×C₃	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
50	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
51	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	—	2	2	no	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
63	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	—	2	4	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	—	2	4	no	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
79	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
80	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
81	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
82	C₃×C₄²×C₅	—	2	2	no	—
83	C₃×C₄²×C₅	—	2	2	no	—
84	C₃×C₄²×C₅	—	2	2	no	—
85	C₃×C₄²×C₅	—	2	4	no	—
86	C₃×C₄²×C₅	—	2	4	no	—
87	C₃×C₄²×C₅	D₄	1	4	yes	—
88	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
89	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
91	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#387	C₂×C₅	1	2	yes	complemented
94	C₃×#385	C₂×C₅	1	2	yes	—
95	C₃×#380	C₂×C₅	1	1	yes	characteristic
96	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
97	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
99	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
101	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
102	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
103	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	direct product factor
104	C₄×C₅×Q₈	—	2	4	no	—
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
113	C₂×C₄²×C₅	—	2	4	no	—
114	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
115	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
116	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
120	C₅×#95	C₂²×C₃	1	2	yes	—
121	C₅×#95	C₂²×C₃	1	2	yes	—
122	C₅×#95	C₂²×C₃	1	2	yes	—
123	C₅×#95	C₂²×C₃	1	2	yes	—
124	C₅×#95	C₂²×C₃	1	2	yes	—
125	C₄×C₂²⋊Q₈	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	—	2	1	no	—
129	C₂³×C₃×C₅	—	2	1	no	—
130	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
131	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
132	C₂³×C₃×C₅	#41	1	2	yes	—
133	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
134	C₃×C₅×Q₈	—	2	8	no	—
135	C₂×C₃×C₄×C₅	—	2	8	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	8	no	—
149	C₂×C₃×C₄×C₅	—	2	8	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
157	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
158	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
165	C₂×C₃×C₄×C₅	#41	1	2	yes	—
166	C₂×C₃×C₄×C₅	#41	1	2	yes	—
167	C₂×C₃×C₄×C₅	#41	1	2	yes	—
168	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	direct product factor
173	C₃×C₄×Q₈	—	2	4	no	—
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
182	C₂×C₃×C₄²	—	2	4	no	—
183	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
184	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
189	C₃×#95	C₂²×C₅	1	2	yes	—
190	C₃×#95	C₂²×C₅	1	2	yes	—
191	C₃×#95	C₂²×C₅	1	2	yes	—
192	C₃×#95	C₂²×C₅	1	2	yes	—
193	C₃×#95	C₂²×C₅	1	2	yes	—
194	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×Q₈	—	2	2	no	—
196	C₂×C₅×Q₈	—	2	2	no	—
197	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
198	C₂²×C₄×C₅	—	2	2	no	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	2	no	—
202	C₂²×C₄×C₅	—	2	2	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	—	2	2	no	—
205	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
206	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
207	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
208	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
211	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
212	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
217	C₅×C₄⋊C₄	—	2	4	no	—
218	C₅×C₄⋊C₄	—	2	2	no	—
219	C₅×C₄⋊C₄	—	2	4	no	—
220	C₅×C₄⋊C₄	—	2	2	no	—
221	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
222	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
223	C₅×C₂²⋊C₄	—	2	4	no	—
224	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
225	C₄²×C₅	—	2	2	no	—
226	C₄²×C₅	—	2	2	no	—
227	C₄²×C₅	—	2	2	no	—
228	C₄²×C₅	—	2	4	no	—
229	C₄²×C₅	—	2	4	no	—
230	C₄²×C₅	C₃×D₄	1	4	yes	—
231	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic
234	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#387	C₂×C₃×C₅	1	2	yes	complemented
237	#385	C₂×C₃×C₅	1	2	yes	—
238	#380	C₂×C₃×C₅	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
240	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	2	2	no	—
246	C₂²×C₃×C₅	—	2	2	no	—
247	C₂²×C₃×C₅	—	2	2	no	—
248	C₂²×C₃×C₅	C₄×Q₈	1	4	yes	complemented
249	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
252	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
253	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
254	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
255	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	4	no	—
258	C₃×C₄×C₅	—	2	4	no	—
259	C₃×C₄×C₅	—	2	2	no	—
260	C₃×C₄×C₅	—	2	2	no	—
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	4	2	no	—
263	C₃×C₄×C₅	—	4	2	no	—
264	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
265	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	direct product factor
266	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₃×Q₈	—	2	2	no	—
268	C₂×C₃×Q₈	—	2	2	no	—
269	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
270	C₂²×C₃×C₄	—	2	2	no	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	—	2	2	no	—
274	C₂²×C₃×C₄	—	2	2	no	—
275	C₂²×C₃×C₄	—	2	2	no	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
278	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
283	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
284	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	—	2	4	no	—
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	2	4	no	—
292	C₃×C₄⋊C₄	—	2	2	no	—
293	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
294	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
295	C₃×C₂²⋊C₄	—	2	4	no	—
296	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
297	C₃×C₄²	—	2	2	no	—
298	C₃×C₄²	—	2	2	no	—
299	C₃×C₄²	—	2	2	no	—
300	C₃×C₄²	—	2	4	no	—
301	C₃×C₄²	—	2	4	no	—
302	C₃×C₄²	C₅×D₄	1	4	yes	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
308	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
309	C₂³×C₅	C₃×#41	1	2	yes	—
310	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₅×Q₈	—	2	8	no	—
312	C₂×C₄×C₅	—	2	8	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	8	no	—
326	C₂×C₄×C₅	—	2	8	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
334	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
335	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
336	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
337	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
338	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
339	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
340	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
341	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
342	C₂×C₄×C₅	C₃×#41	1	2	yes	—
343	C₂×C₄×C₅	C₃×#41	1	2	yes	—
344	C₂×C₄×C₅	C₃×#41	1	2	yes	—
345	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
347	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
348	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
349	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	direct product factor
350	C₄×Q₈	—	2	4	no	—
351	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
353	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
355	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
356	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
359	C₂×C₄²	—	2	4	no	—
360	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
361	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
362	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
363	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
364	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
365	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
366	#95	C₂²×C₃×C₅	1	2	yes	—
367	#95	C₂²×C₃×C₅	1	2	yes	—
368	#95	C₂²×C₃×C₅	1	2	yes	—
369	#95	C₂²×C₃×C₅	1	2	yes	—
370	#95	C₂²×C₃×C₅	1	2	yes	—
371	C₂×C₃×C₅	—	2	4	no	—
372	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
374	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
376	C₂×C₃×C₅	#525	1	1	yes	characteristic
377	C₂×C₃×C₅	#529	1	1	yes	characteristic
378	C₂×C₃×C₅	#533	1	1	yes	characteristic
379	C₂³×C₃	—	2	1	no	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
384	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
385	C₂³×C₃	C₅×#41	1	2	yes	—
386	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
387	C₃×Q₈	—	2	8	no	—
388	C₂×C₃×C₄	—	2	8	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	8	no	—
402	C₂×C₃×C₄	—	2	8	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
410	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
411	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
412	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
413	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
414	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
415	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
416	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
417	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
418	C₂×C₃×C₄	C₅×#41	1	2	yes	—
419	C₂×C₃×C₄	C₅×#41	1	2	yes	—
420	C₂×C₃×C₄	C₅×#41	1	2	yes	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	C₃×C₄×Q₈	1	4	yes	complemented
428	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
429	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
430	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
431	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
432	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
433	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
434	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	2	4	no	—
437	C₄×C₅	—	2	4	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	2	2	no	—
441	C₄×C₅	—	4	2	no	—
442	C₄×C₅	—	4	2	no	—
443	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
444	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	direct product factor
445	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
457	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
458	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
459	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
460	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
461	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
462	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
463	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
464	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
465	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
466	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
467	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
473	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	2	4	no	—
481	C₄²	C₃×C₅×D₄	1	4	yes	—
482	C₃×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Hall
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	2	2	no	—
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	2	2	no	—
488	C₂²×C₃	—	2	2	no	—
489	C₂²×C₃	C₄×C₅×Q₈	1	4	yes	complemented
490	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
491	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
492	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
493	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
494	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
495	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
496	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
497	C₃×C₄	—	2	2	no	—
498	C₃×C₄	—	2	4	no	—
499	C₃×C₄	—	2	4	no	—
500	C₃×C₄	—	2	2	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	4	2	no	—
504	C₃×C₄	—	4	2	no	—
505	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
506	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	direct product factor
507	C₂×C₅	—	2	4	no	—
508	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
509	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
510	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
511	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
512	C₂×C₅	C₃×#525	1	1	yes	characteristic
513	C₂×C₅	C₃×#529	1	1	yes	characteristic
514	C₂×C₅	C₃×#533	1	1	yes	characteristic
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
520	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
521	C₂³	C₃×C₅×#41	1	2	yes	—
522	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
523	Q₈	—	2	8	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
546	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
547	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
548	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
549	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
550	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
551	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
552	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
553	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
554	C₂×C₄	C₃×C₅×#41	1	2	yes	—
555	C₂×C₄	C₃×C₅×#41	1	2	yes	—
556	C₂×C₄	C₃×C₅×#41	1	2	yes	—
557	C₂×C₃	—	2	4	no	—
558	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
559	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
560	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
561	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
562	C₂×C₃	C₅×#525	1	1	yes	characteristic
563	C₂×C₃	C₅×#529	1	1	yes	characteristic
564	C₂×C₃	C₅×#533	1	1	yes	characteristic
565	C₅	C₃×C₄×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	C₃×C₄×C₅×Q₈	1	4	yes	complemented
573	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
574	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
575	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
576	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
577	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
578	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
579	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	4	no	—
582	C₄	—	2	4	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
589	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	direct product factor
590	C₃	C₄×C₅×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
591	C₂	—	2	4	no	—
592	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
593	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
594	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
595	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
596	C₂	C₃×C₅×#525	1	1	yes	characteristic
597	C₂	C₃×C₅×#529	1	1	yes	characteristic
598	C₂	C₃×C₅×#533	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
9. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₄×C₅×C₂²⋊Q₈	C₃	direct (N × H)
17. C₃×C₅×C₂²⋊Q₈	C₄	direct (N × H)
39. C₃×C₄×C₂²⋊Q₈	C₅	direct (N × H)
41. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
43. C₅×#391	C₂×C₃	semidirect
44. C₅×#389	C₂×C₃	semidirect
45. C₅×#387	C₂×C₃	semidirect
48. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
49. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
54. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
63. C₂²×C₃×C₄×C₅	Q₈	semidirect
78. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
79. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
89. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
91. C₃×#391	C₂×C₅	semidirect
92. C₃×#389	C₂×C₅	semidirect
93. C₃×#387	C₂×C₅	semidirect
96. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
97. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
103. C₅×C₂²⋊Q₈	C₃×C₄	direct (N × H)
125. C₄×C₂²⋊Q₈	C₃×C₅	direct (N × H)
172. C₃×C₂²⋊Q₈	C₄×C₅	direct (N × H)
197. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
206. C₂²×C₄×C₅	C₃×Q₈	semidirect
221. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
222. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
232. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
234. #391	C₂×C₃×C₅	semidirect
235. #389	C₂×C₃×C₅	semidirect
236. #387	C₂×C₃×C₅	semidirect
239. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
240. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
248. C₂²×C₃×C₅	C₄×Q₈	semidirect
265. C₃×C₄×C₅	C₂²⋊Q₈	direct (N × H)
269. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
278. C₂²×C₃×C₄	C₅×Q₈	semidirect
293. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
294. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
349. C₂²⋊Q₈	C₃×C₄×C₅	direct (N × H)
427. C₂²×C₅	C₃×C₄×Q₈	semidirect
444. C₄×C₅	C₃×C₂²⋊Q₈	direct (N × H)
448. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
457. C₂²×C₄	C₃×C₅×Q₈	semidirect
472. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
473. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
482. C₃×C₅	C₄×C₂²⋊Q₈	direct (N × H)
489. C₂²×C₃	C₄×C₅×Q₈	semidirect
506. C₃×C₄	C₅×C₂²⋊Q₈	direct (N × H)
565. C₅	C₃×C₄×C₂²⋊Q₈	direct (N × H)
572. C₂²	C₃×C₄×C₅×Q₈	semidirect
589. C₄	C₃×C₅×C₂²⋊Q₈	direct (N × H)
590. C₃	C₄×C₅×C₂²⋊Q₈	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×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₄×C₅×C₂²⋊Q₈	3
C₃×C₄×C₂²⋊Q₈	5

Subgroups — C3×C4×C5×C22⋊Q8 #14275336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×C₂²⋊Q₈ #14275336