Subgroups — C₅×Dic₅×C₄₃⋊C₃ #27166375

Order 12900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×C₅×C₄₃⋊C₃	—	5	1	no	maximal
5	Dic₅×C₄₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅²×C₄₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₅×C₄₃⋊C₃	—	2	2	no	—
8	C₂×C₅×C₄₃⋊C₃	D₅	1	1	yes	characteristic
9	C₂×C₅×C₄₃⋊C₃	C₂×C₅	1	1	yes	characteristic
10	C₅²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
11	C₄×C₅×C₄₃	—	5	1	no	—
12	Dic₅×C₄₃	C₃×C₅	1	1	yes	characteristic, complemented
13	C₅×C₄₃⋊C₃	—	2	2	no	—
14	C₅×C₄₃⋊C₃	Dic₅	1	1	yes	characteristic, direct product factor
15	C₅×C₄₃⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented
16	C₄×C₄₃⋊C₃	—	5	1	no	Hall
17	C₂×C₅×C₄₃	—	2	2	no	—
18	C₂×C₅×C₄₃	C₃×D₅	1	1	yes	characteristic
19	C₂×C₅×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic
20	C₃×C₅×Dic₅	—	43	1	no	maximal, Hall
21	C₂×C₄₃⋊C₃	C₅×D₅	1	1	yes	characteristic
22	C₅×C₄₃	—	2	2	no	—
23	C₅×C₄₃	C₃×Dic₅	1	1	yes	characteristic, complemented
24	C₅×C₄₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented
25	C₄×C₄₃	—	5	1	no	Hall
26	C₂×C₃×C₅²	—	43	1	no	—
27	C₄₃⋊C₃	C₅×Dic₅	1	1	yes	characteristic, direct product factor, Hall
28	C₅×Dic₅	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₄₃	C₃×C₅×D₅	1	1	yes	characteristic
30	C₃×C₅²	—	43	1	no	Hall
31	C₃×C₄×C₅	—	215	1	no	—
32	C₃×Dic₅	—	43	1	no	—
33	C₂×C₅²	C₂×C₄₃⋊C₃	1	1	yes	characteristic
34	C₄₃	C₃×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₅	—	43	1	no	—
36	C₂×C₃×C₅	—	43	1	no	—
37	C₂×C₃×C₅	—	86	2	no	—
38	C₅²	C₄×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
39	C₄×C₅	—	5	1	no	—
40	Dic₅	C₅×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
41	C₃×C₅	—	43	1	no	—
42	C₃×C₅	—	43	1	no	—
43	C₃×C₅	—	86	2	no	—
44	C₃×C₄	—	215	1	no	Hall
45	C₂×C₅	—	2	2	no	—
46	C₂×C₅	D₅×C₄₃⋊C₃	1	1	yes	characteristic
47	C₂×C₅	C₂×C₅×C₄₃⋊C₃	1	1	yes	characteristic
48	C₂×C₃	—	43	1	no	—
49	C₅	—	2	2	no	—
50	C₅	Dic₅×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
51	C₅	C₄×C₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented
52	C₄	—	5	1	no	Sylow
53	C₃	—	43	1	no	Sylow
54	C₂	C₅×D₅×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₅×C₄₃⋊C₃
commutator, hypocenter	C₅×C₄₃	C₃×C₄×C₅
Frattini	C₂	C₅×D₅×C₄₃⋊C₃
Fitting, socle	C₂×C₅²×C₄₃	C₂×C₃
prime radical	C₂×C₅²×C₄₃⋊C₃	C₂
cosocle	C₂×C₅×C₄₃	C₂×C₃×C₅
LCS	G ▷ C₅×C₄₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₅×C₄₃	C₃	semidirect
3. C₅²×C₄₃⋊C₃	C₄	semidirect
5. Dic₅×C₄₃⋊C₃	C₅	direct (N × H)
10. C₅²×C₄₃	C₃×C₄	semidirect
12. Dic₅×C₄₃	C₃×C₅	semidirect
14. C₅×C₄₃⋊C₃	Dic₅	direct (N × H)
15. C₅×C₄₃⋊C₃	C₄×C₅	semidirect
23. C₅×C₄₃	C₃×Dic₅	semidirect
24. C₅×C₄₃	C₃×C₄×C₅	semidirect
27. C₄₃⋊C₃	C₅×Dic₅	direct (N × H)
28. C₅×Dic₅	C₄₃⋊C₃	direct (N × H)
34. C₄₃	C₃×C₅×Dic₅	semidirect
38. C₅²	C₄×C₄₃⋊C₃	semidirect
40. Dic₅	C₅×C₄₃⋊C₃	direct (N × H)
50. C₅	Dic₅×C₄₃⋊C₃	direct (N × H)
51. C₅	C₄×C₅×C₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₄₃⋊C₃	2
C₅×Dic₅×C₄₃	3
C₄×C₅×C₄₃⋊C₃	5
Dic₅×C₄₃⋊C₃	5
C₃×C₅×Dic₅	43

Subgroups — C5×Dic5×C43⋊C3 #27166375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₅×C₄₃⋊C₃ #27166375