Subgroups — C₅×#19151040 #43249705

Order 28470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15667865	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃×D₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#19151040	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#15667865	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₇₃⋊C₃	—	13	1	no	maximal, Hall
7	C₁₃×D₇₃	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	C₅×D₇₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	D₇₃⋊C₃	—	13	1	no	Hall
12	C₂×C₅×C₁₃⋊C₃	—	73	1	no	maximal, Hall
13	C₅×C₇₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₇₃⋊C₃	—	13	1	no	Hall
15	C₅×C₁₃⋊C₃	—	73	1	no	Hall
16	D₇₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₃	—	73	1	no	Hall
18	C₂×C₁₃⋊C₃	—	73	1	no	Hall
19	C₇₃	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₁₃	D₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃⋊C₃	—	73	1	no	Hall
22	C₂×C₃×C₅	—	949	1	no	Hall
23	C₂×C₁₃	—	73	1	no	Hall
24	C₃×C₅	—	949	1	no	Hall
25	C₁₃	C₅×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	73	1	no	Hall
27	C₂×C₃	—	949	1	no	Hall
28	C₅	#19151040	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	949	1	no	Sylow
30	C₂	—	73	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#19151040
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×#15667865	C₂	semidirect
2. C₅×C₁₃×D₇₃	C₃	semidirect
3. #19151040	C₅	direct (N × H)
4. C₅×C₁₃×C₇₃	C₂×C₃	semidirect
5. #15667865	C₂×C₅	semidirect
7. C₁₃×D₇₃	C₃×C₅	semidirect
9. C₁₃×C₇₃	C₂×C₃×C₅	semidirect
10. C₅×D₇₃	C₁₃⋊C₃	semidirect
13. C₅×C₇₃	C₂×C₁₃⋊C₃	semidirect
16. D₇₃	C₅×C₁₃⋊C₃	semidirect
19. C₇₃	C₂×C₅×C₁₃⋊C₃	semidirect
20. C₅×C₁₃	D₇₃⋊C₃	semidirect
25. C₁₃	C₅×D₇₃⋊C₃	semidirect
28. C₅	#19151040	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×#15667865	2
C₅×C₁₃×D₇₃	3
#19151040	5
C₅×D₇₃⋊C₃	13
C₂×C₅×C₁₃⋊C₃	73

Subgroups — C5×#19151040 #43249705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19151040 #43249705