Subgroups — C₅×D₁₅⋊D₄₃ #27166459

Order 12900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₁₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₂₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₄₃	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅⋊D₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×D₃×D₄₃	—	5	1	no	maximal
8	C₅×D₂₁₅	D₃	1	1	yes	characteristic, complemented
9	C₅×D₅×C₄₃	—	3	1	no	—
10	C₅²×D₄₃	—	3	1	no	—
11	D₁₅×C₄₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×D₁₂₉	—	2	2	no	—
13	C₅×D₁₂₉	D₅	1	1	yes	characteristic, complemented
14	C₅×D₁₂₉	C₂×C₅	1	1	yes	characteristic, complemented
15	C₅×D₃×C₄₃	—	5	1	no	—
16	C₃×D₂₁₅	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×C₅×D₄₃	—	5	1	no	—
18	C₅²×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₄₃	—	15	1	no	—
20	D₅×D₄₃	—	3	1	no	—
21	C₃×C₅×C₄₃	—	2	2	no	—
22	C₃×C₅×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₄₃	C₂²×C₅	1	1	yes	characteristic, complemented
24	D₃×D₄₃	—	5	1	no	Hall
25	C₂×C₅×C₄₃	—	15	1	no	—
26	D₂₁₅	C₅×D₃	1	1	yes	characteristic, complemented
27	C₅×D₄₃	—	3	1	no	—
28	C₅×D₄₃	—	3	1	no	—
29	C₅×D₄₃	—	5	1	no	—
30	C₅×D₄₃	—	6	2	no	—
31	D₅×C₄₃	—	3	1	no	—
32	C₅×D₃×D₅	—	43	1	no	maximal, Hall
33	D₁₂₉	C₅×D₅	1	1	yes	characteristic, complemented
34	C₃×D₄₃	—	5	1	no	—
35	D₃×C₄₃	—	5	1	no	—
36	C₅×C₄₃	—	2	2	no	—
37	C₅×C₄₃	D₃×D₅	1	1	yes	characteristic, complemented
38	C₅×C₄₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
39	C₂×D₄₃	—	15	1	no	Hall
40	C₅×D₁₅	D₄₃	1	1	yes	characteristic, complemented
41	C₅²×D₃	—	43	1	no	—
42	C₃×C₅×D₅	—	43	1	no	—
43	C₃×C₄₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
44	C₂×C₅×D₅	—	129	1	no	Hall
45	C₂×C₄₃	—	15	1	no	—
46	D₄₃	—	3	1	no	—
47	D₄₃	—	5	1	no	—
48	C₃×C₅²	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₅×D₃	—	215	1	no	—
50	D₃×D₅	—	43	1	no	—
51	C₂×C₅²	—	129	1	no	—
52	C₅×D₅	—	3	1	no	—
53	C₅×D₅	—	43	1	no	—
54	C₄₃	C₅×D₃×D₅	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₅	—	215	1	no	—
56	D₁₅	C₅×D₄₃	1	1	yes	characteristic, complemented
57	C₃×D₅	—	43	1	no	—
58	C₅×D₃	—	5	1	no	—
59	C₅×D₃	—	43	1	no	—
60	C₅×D₃	—	43	1	no	—
61	C₅×D₃	—	86	2	no	—
62	C₅²	D₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₅	—	645	1	no	—
64	C₂×D₅	—	129	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₄₃	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×C₅×D₄₃	1	1	yes	characteristic, complemented
68	C₂×D₃	—	215	1	no	Hall
69	C₂×C₅	—	258	2	no	—
70	C₂×C₅	—	15	1	no	—
71	C₂×C₅	—	129	1	no	—
72	C₂×C₅	—	129	1	no	—
73	C₂×C₅	—	215	1	no	—
74	D₅	—	3	1	no	—
75	D₅	—	43	1	no	—
76	C₂×C₃	—	215	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	43	1	no	—
79	C₅	—	2	2	no	—
80	C₅	C₅×D₃×D₄₃	1	1	yes	characteristic, complemented
81	C₅	D₁₅⋊D₄₃	1	1	yes	characteristic, direct product factor
82	C₂²	—	645	1	no	Sylow
83	C₃	C₅×D₅×D₄₃	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	15	1	no	—
85	C₂	—	129	1	no	—
86	C₂	—	215	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₅⋊D₄₃
commutator, cosocle, hypocenter	C₃×C₅×C₄₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₄₃	C₂²
LCS	G ▷ C₃×C₅×C₄₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅×C₄₃	C₂	semidirect
2. C₅²×D₁₂₉	C₂	semidirect
3. C₃×C₅×D₂₁₅	C₂	semidirect
5. C₃×C₅²×C₄₃	C₂²	semidirect
6. D₁₅⋊D₄₃	C₅	direct (N × H)
8. C₅×D₂₁₅	D₃	semidirect
11. D₁₅×C₄₃	C₂×C₅	semidirect
13. C₅×D₁₂₉	D₅	semidirect
14. C₅×D₁₂₉	C₂×C₅	semidirect
16. C₃×D₂₁₅	C₂×C₅	semidirect
18. C₅²×C₄₃	C₂×D₃	semidirect
22. C₃×C₅×C₄₃	C₂×D₅	semidirect
23. C₃×C₅×C₄₃	C₂²×C₅	semidirect
26. D₂₁₅	C₅×D₃	semidirect
33. D₁₂₉	C₅×D₅	semidirect
37. C₅×C₄₃	D₃×D₅	semidirect
38. C₅×C₄₃	C₂×C₅×D₃	semidirect
40. C₅×D₁₅	D₄₃	semidirect
43. C₃×C₄₃	C₂×C₅×D₅	semidirect
48. C₃×C₅²	C₂×D₄₃	semidirect
54. C₄₃	C₅×D₃×D₅	semidirect
56. D₁₅	C₅×D₄₃	semidirect
62. C₅²	D₃×D₄₃	semidirect
66. C₃×C₅	D₅×D₄₃	semidirect
67. C₃×C₅	C₂×C₅×D₄₃	semidirect
80. C₅	C₅×D₃×D₄₃	semidirect
81. C₅	D₁₅⋊D₄₃	direct (N × H)
83. C₃	C₅×D₅×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₅×C₄₃	2
C₅²×D₁₂₉	2
C₃×C₅×D₂₁₅	2
C₅×D₅×D₄₃	3
D₁₅⋊D₄₃	5
C₅×D₃×D₄₃	5
C₅×D₃×D₅	43

Subgroups — C5×D15⋊D43 #27166459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₅⋊D₄₃ #27166459