Subgroups — C₁₃×D₁₅×C₇₃ #43249698

Order 28470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₃×C₇₃	—	3	1	no	maximal, Hall
3	D₃×C₁₃×C₇₃	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₇₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₅×C₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₇₃	—	15	1	no	Hall
8	C₃×C₅×C₇₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₇₃	D₁₅	1	1	yes	characteristic, direct product factor, Hall
10	D₅×C₇₃	—	3	1	no	Hall
11	D₃×C₇₃	—	5	1	no	Hall
12	C₁₃×D₁₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₇₃	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇₃	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₃	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₃	—	15	1	no	Hall
17	D₅×C₁₃	—	3	1	no	Hall
18	D₃×C₁₃	—	5	1	no	Hall
19	C₇₃	C₁₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×C₁₃	D₃×C₇₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₃	D₅×C₇₃	1	1	yes	characteristic, complemented, Hall
22	D₁₅	C₁₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₃	—	15	1	no	Hall
24	C₃×C₅	C₂×C₁₃×C₇₃	1	1	yes	characteristic, complemented, Hall
25	C₁₃	D₁₅×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	3	1	no	Hall
27	D₃	—	5	1	no	Hall
28	C₅	D₃×C₁₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₁₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₇₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₁₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₇₃	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₁₃×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₇₃	C₂	semidirect
4. C₅×C₁₃×C₇₃	D₃	semidirect
5. C₃×C₁₃×C₇₃	D₅	semidirect
6. D₁₅×C₇₃	C₁₃	direct (N × H)
8. C₃×C₅×C₇₃	C₂×C₁₃	semidirect
9. C₁₃×C₇₃	D₁₅	direct (N × H)
12. C₁₃×D₁₅	C₇₃	direct (N × H)
13. C₅×C₇₃	D₃×C₁₃	semidirect
14. C₃×C₇₃	D₅×C₁₃	semidirect
15. C₃×C₅×C₁₃	C₂×C₇₃	semidirect
19. C₇₃	C₁₃×D₁₅	direct (N × H)
20. C₅×C₁₃	D₃×C₇₃	semidirect
21. C₃×C₁₃	D₅×C₇₃	semidirect
22. D₁₅	C₁₃×C₇₃	direct (N × H)
24. C₃×C₅	C₂×C₁₃×C₇₃	semidirect
25. C₁₃	D₁₅×C₇₃	direct (N × H)
28. C₅	D₃×C₁₃×C₇₃	semidirect
29. C₃	D₅×C₁₃×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×C₇₃	2
D₅×C₁₃×C₇₃	3
D₃×C₁₃×C₇₃	5
D₁₅×C₇₃	13
C₁₃×D₁₅	73

Subgroups — C13×D15×C73 #43249698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₁₅×C₇₃ #43249698