Subgroups — D₇₅⋊Q₈ #11924913

Order 1200.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₇₅	C₂	1	1	yes	maximal, characteristic
2	Dic₆×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₅₀	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597028	C₂	1	2	yes	maximal
5	#10597026	C₂	1	2	yes	maximal, complemented
6	Q₈×D₂₅	—	3	1	no	maximal, Hall
7	C₂×D₇₅	C₂²	1	1	yes	characteristic
8	C₃×C₄×C₂₅	C₂²	1	1	yes	characteristic
9	Dic₇₅	C₂²	1	1	yes	characteristic
10	C₃×Dic₂₅	C₂²	1	2	yes	—
11	Dic₃×C₂₅	C₂²	1	2	yes	—
12	D₁₅⋊Q₈	—	5	1	no	maximal
13	Q₈×C₂₅	—	3	1	no	—
14	C₄×D₂₅	—	3	1	no	—
15	C₄×D₂₅	—	3	2	no	—
16	Dic₅₀	—	3	2	no	—
17	Dic₅₀	D₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₂₅	C₂³	1	1	yes	characteristic
19	D₇₅	Q₈	1	2	yes	complemented
20	C₄×D₁₅	—	5	1	no	—
21	C₅×Dic₆	D₅	1	1	yes	characteristic
22	C₃×Dic₁₀	—	5	1	no	—
23	#1204	—	5	2	no	—
24	#1200	—	5	2	no	—
25	C₂×D₂₅	—	3	1	no	—
26	C₄×C₂₅	—	3	2	no	—
27	C₄×C₂₅	C₂×D₃	1	1	yes	characteristic
28	Dic₂₅	—	3	1	no	—
29	Dic₂₅	C₂×D₃	1	2	yes	—
30	Q₈×D₅	—	15	1	no	—
31	C₃×C₂₅	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
32	C₂×D₁₅	—	5	1	no	—
33	C₃×C₄×C₅	C₂×D₅	1	1	yes	characteristic
34	Dic₁₅	—	5	1	no	—
35	C₃×Dic₅	—	5	2	no	—
36	C₅×Dic₃	C₂×D₅	1	2	yes	—
37	C₂×C₂₅	C₂²×D₃	1	1	yes	characteristic
38	D₂₅	—	3	2	no	—
39	D₃×Q₈	—	25	1	no	Hall
40	C₅×Q₈	—	3	1	no	—
41	C₄×D₅	—	15	2	no	—
42	C₄×D₅	—	15	1	no	—
43	Dic₁₀	—	5	1	no	—
44	Dic₁₀	—	15	2	no	—
45	C₂×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
46	D₁₅	—	5	2	no	—
47	C₂₅	D₃×Q₈	1	1	yes	characteristic, complemented, Sylow
48	C₃×Q₈	—	25	1	no	—
49	C₄×D₃	—	25	1	no	—
50	C₄×D₃	—	25	2	no	—
51	Dic₆	—	25	2	no	—
52	Dic₆	D₂₅	1	1	yes	characteristic, complemented
53	C₂×D₅	—	15	1	no	—
54	C₄×C₅	—	3	2	no	—
55	C₄×C₅	D₃×D₅	1	1	yes	characteristic
56	Dic₅	—	5	2	no	—
57	Dic₅	—	15	1	no	—
58	C₂×Q₈	—	75	1	no	Sylow
59	C₃×C₅	Q₈×D₅	1	1	yes	characteristic
60	C₂×D₃	—	25	1	no	—
61	C₃×C₄	—	25	2	no	—
62	C₃×C₄	C₂×D₂₅	1	1	yes	characteristic
63	Dic₃	—	25	1	no	—
64	Dic₃	C₂×D₂₅	1	2	yes	—
65	C₂×C₅	C₂×D₃×D₅	1	1	yes	characteristic
66	D₅	—	15	2	no	—
67	Q₈	—	3	1	no	—
68	Q₈	—	25	1	no	—
69	Q₈	—	75	2	no	—
70	C₂×C₄	—	75	2	no	—
71	C₂×C₄	—	75	1	no	—
72	C₂×C₃	C₂²×D₂₅	1	1	yes	characteristic
73	D₃	—	25	2	no	—
74	C₅	D₁₅⋊Q₈	1	1	yes	characteristic
75	C₂²	—	75	1	no	—
76	C₄	—	3	2	no	—
77	C₄	—	25	2	no	—
78	C₄	—	75	1	no	—
79	C₄	D₃×D₂₅	1	1	yes	characteristic
80	C₃	Q₈×D₂₅	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	75	2	no	—
82	C₂	C₂×D₃×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃×D₂₅
commutator, cosocle	C₂×C₃×C₂₅	C₂³
Frattini	C₂×C₅	C₂×D₃×D₅
Fitting	C₃×C₄×C₂₅	C₂²
socle	C₂×C₃×C₅	C₂²×D₅
prime radical	C₂×D₇₅	C₂²
hypercenter	C₄	D₃×D₂₅
hypocenter	C₃×C₂₅	C₂×Q₈
LCS	G ▷ C₂×C₃×C₂₅ ▷ C₃×C₂₅
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. Dic₆×C₂₅	C₂	semidirect
3. C₃×Dic₅₀	C₂	semidirect
5. #10597026	C₂	semidirect
17. Dic₅₀	D₃	semidirect
19. D₇₅	Q₈	semidirect
31. C₃×C₂₅	C₂×Q₈	semidirect
47. C₂₅	D₃×Q₈	semidirect
52. Dic₆	D₂₅	semidirect
80. C₃	Q₈×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₇₅	2
Dic₆×C₂₅	2
C₃×Dic₅₀	2
#10597028	2
#10597026	2
Q₈×D₂₅	3
D₁₅⋊Q₈	5

Subgroups — D75⋊Q8 #11924913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₅⋊Q₈ #11924913