Subgroups — C₅×Q₈×D₁₅ #11925711

Order 1200.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×D₁₅	C₂	1	3	yes	maximal
3	C₅×Dic₃₀	C₂	1	3	yes	maximal, complemented
4	C₅×Q₈×D₅	—	3	1	no	maximal, Hall
5	C₂×C₅×D₁₅	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₅²	C₂²	1	3	yes	—
7	C₅×Dic₁₅	C₂²	1	3	yes	—
8	Q₈×D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₅×D₃×Q₈	—	5	1	no	maximal
10	C₅²×Q₈	D₃	1	1	yes	characteristic, complemented
11	C₄×C₅×D₅	—	3	3	no	—
12	C₅×Dic₁₀	—	3	3	no	—
13	C₂×C₃×C₅²	C₂³	1	1	yes	characteristic
14	C₅×D₁₅	Q₈	1	2	yes	direct product factor
15	C₃×C₅×Q₈	—	2	2	no	—
16	C₃×C₅×Q₈	D₅	1	1	yes	characteristic, complemented
17	C₃×C₅×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
18	C₄×D₁₅	C₂×C₅	1	3	yes	—
19	Dic₃₀	C₂×C₅	1	3	yes	complemented
20	C₄×C₅×D₃	—	5	3	no	—
21	C₅×Dic₆	—	5	3	no	—
22	C₂×C₅×D₅	—	3	1	no	—
23	C₄×C₅²	C₂×D₃	1	3	yes	—
24	C₅×Dic₅	—	3	3	no	—
25	C₂×C₅×Q₈	—	15	1	no	—
26	Q₈×D₅	—	3	1	no	—
27	C₃×C₅²	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₅	C₂²×C₅	1	1	yes	characteristic
29	C₂×C₅×D₃	—	5	1	no	—
30	C₃×C₄×C₅	—	2	6	no	—
31	C₃×C₄×C₅	C₂×D₅	1	3	yes	—
32	C₃×C₄×C₅	C₂²×C₅	1	3	yes	—
33	Dic₁₅	C₂²×C₅	1	3	yes	—
34	C₅×Dic₃	—	5	3	no	—
35	C₂×C₅²	C₂²×D₃	1	1	yes	characteristic
36	C₅×D₅	—	3	2	no	—
37	D₃×Q₈	—	5	1	no	Hall
38	C₅×Q₈	—	2	2	no	—
39	C₅×Q₈	—	15	3	no	—
40	C₅×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
41	C₅×Q₈	D₁₅	1	1	yes	characteristic, direct product factor
42	C₂×C₄×C₅	—	15	3	no	—
43	C₄×D₅	—	3	3	no	—
44	Dic₁₀	—	3	3	no	—
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
47	C₂×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
48	D₁₅	C₅×Q₈	1	2	yes	direct product factor
49	C₅×D₃	—	5	2	no	—
50	C₅²	D₃×Q₈	1	1	yes	characteristic, complemented, Sylow
51	C₃×Q₈	C₅×D₅	1	1	yes	characteristic, complemented
52	C₄×D₃	—	5	3	no	—
53	Dic₆	—	5	3	no	—
54	C₂²×C₅	—	15	1	no	—
55	C₂×D₅	—	3	1	no	—
56	C₄×C₅	—	2	6	no	—
57	C₄×C₅	—	15	3	no	—
58	C₄×C₅	C₂×C₅×D₃	1	3	yes	—
59	C₄×C₅	C₂×D₁₅	1	3	yes	—
60	Dic₅	—	3	3	no	—
61	C₂×Q₈	—	15	1	no	Sylow
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	Q₈×D₅	1	1	yes	characteristic, complemented
64	C₃×C₅	C₂×C₅×Q₈	1	1	yes	characteristic, complemented
65	C₂×D₃	—	5	1	no	—
66	C₃×C₄	C₂×C₅×D₅	1	3	yes	—
67	Dic₃	—	5	3	no	—
68	C₂×C₅	—	2	2	no	—
69	C₂×C₅	—	15	2	no	—
70	C₂×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
71	C₂×C₅	C₂²×D₁₅	1	1	yes	characteristic
72	D₅	—	3	2	no	—
73	Q₈	—	15	3	no	—
74	Q₈	C₅×D₁₅	1	1	yes	characteristic, direct product factor
75	C₂×C₄	—	15	3	no	—
76	C₂×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
77	D₃	—	5	2	no	—
78	C₅	—	2	2	no	—
79	C₅	C₅×D₃×Q₈	1	1	yes	characteristic, complemented
80	C₅	Q₈×D₁₅	1	1	yes	characteristic, direct product factor
81	C₂²	—	15	1	no	—
82	C₄	—	15	3	no	—
83	C₄	C₂×C₅×D₁₅	1	3	yes	—
84	C₃	C₅×Q₈×D₅	1	1	yes	characteristic, complemented, Sylow
85	C₂	—	15	2	no	—
86	C₂	C₂²×C₅×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₁₅
commutator, cosocle	C₂×C₃×C₅	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₁₅
Fitting	C₃×C₅²×Q₈	C₂
socle	C₂×C₃×C₅²	C₂³
prime radical	C₂×C₅×D₁₅	C₂²
hypercenter	C₅×Q₈	D₁₅
hypocenter	C₃×C₅	C₂×C₅×Q₈
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×Q₈	C₂	semidirect
3. C₅×Dic₃₀	C₂	semidirect
8. Q₈×D₁₅	C₅	direct (N × H)
10. C₅²×Q₈	D₃	semidirect
14. C₅×D₁₅	Q₈	direct (N × H)
16. C₃×C₅×Q₈	D₅	semidirect
17. C₃×C₅×Q₈	C₂×C₅	semidirect
19. Dic₃₀	C₂×C₅	semidirect
27. C₃×C₅²	C₂×Q₈	semidirect
40. C₅×Q₈	C₅×D₃	semidirect
41. C₅×Q₈	D₁₅	direct (N × H)
48. D₁₅	C₅×Q₈	direct (N × H)
50. C₅²	D₃×Q₈	semidirect
51. C₃×Q₈	C₅×D₅	semidirect
63. C₃×C₅	Q₈×D₅	semidirect
64. C₃×C₅	C₂×C₅×Q₈	semidirect
74. Q₈	C₅×D₁₅	direct (N × H)
79. C₅	C₅×D₃×Q₈	semidirect
80. C₅	Q₈×D₁₅	direct (N × H)
84. C₃	C₅×Q₈×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×Q₈	2
C₄×C₅×D₁₅	2
C₅×Dic₃₀	2
C₅×Q₈×D₅	3
Q₈×D₁₅	5
C₅×D₃×Q₈	5

Subgroups — C5×Q8×D15 #11925711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Q₈×D₁₅ #11925711