Subgroups — C₅×#19151043 #43249708

Order 28470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15667864	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₃×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#19151043	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#15667864	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×C₇₃⋊C₃	—	13	1	no	maximal, Hall
7	D₁₃×C₇₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇₃⋊C₃	—	13	1	no	Hall
9	C₁₃×C₇₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇₃	—	13	1	no	Hall
11	C₂×C₇₃⋊C₃	—	13	1	no	Hall
12	C₅×D₁₃⋊C₃	—	73	1	no	maximal, Hall
13	C₅×C₇₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₇₃⋊C₃	—	13	1	no	Hall
15	C₅×C₁₃⋊C₃	—	73	1	no	Hall
16	C₂×C₇₃	—	13	1	no	Hall
17	C₅×D₁₃	C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	D₁₃⋊C₃	—	73	1	no	Hall
19	C₇₃	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₁₃	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃⋊C₃	—	73	1	no	Hall
22	C₂×C₃×C₅	—	949	1	no	Hall
23	D₁₃	C₅×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	949	1	no	Hall
25	C₁₃	C₂×C₅×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	13	1	no	Hall
27	C₂×C₃	—	949	1	no	Hall
28	C₅	#19151043	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	949	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#19151043
commutator, cosocle, hypocenter	C₁₃×C₇₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₇₃	C₂×C₃
LCS	G ▷ C₁₃×C₇₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15667864	C₂	semidirect
2. C₅×D₁₃×C₇₃	C₃	semidirect
3. #19151043	C₅	direct (N × H)
4. C₅×C₁₃×C₇₃	C₂×C₃	semidirect
5. #15667864	C₂×C₅	semidirect
7. D₁₃×C₇₃	C₃×C₅	semidirect
9. C₁₃×C₇₃	C₂×C₃×C₅	semidirect
13. C₅×C₇₃	D₁₃⋊C₃	semidirect
17. C₅×D₁₃	C₇₃⋊C₃	semidirect
19. C₇₃	C₅×D₁₃⋊C₃	semidirect
20. C₅×C₁₃	C₂×C₇₃⋊C₃	semidirect
23. D₁₃	C₅×C₇₃⋊C₃	semidirect
25. C₁₃	C₂×C₅×C₇₃⋊C₃	semidirect
28. C₅	#19151043	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#15667864	2
C₅×D₁₃×C₇₃	3
#19151043	5
C₂×C₅×C₇₃⋊C₃	13
C₅×D₁₃⋊C₃	73

Subgroups — C5×#19151043 #43249708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19151043 #43249708