Subgroups — C₅×#16809814 #30680804

Order 16770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#13131975	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₃×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16809814	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#13131975	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×C₄₃⋊C₃	—	13	1	no	maximal, Hall
7	D₁₃×C₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₄₃⋊C₃	—	13	1	no	Hall
9	C₁₃×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₄₃	—	13	1	no	Hall
11	C₅×D₁₃⋊C₃	—	43	1	no	maximal, Hall
12	C₂×C₄₃⋊C₃	—	13	1	no	Hall
13	C₅×C₄₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₃⋊C₃	—	43	1	no	Hall
15	C₅×D₁₃	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₄₃⋊C₃	—	13	1	no	Hall
17	C₂×C₄₃	—	13	1	no	Hall
18	D₁₃⋊C₃	—	43	1	no	Hall
19	C₅×C₁₃	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₄₃	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₁₃⋊C₃	—	43	1	no	Hall
22	C₂×C₃×C₅	—	559	1	no	Hall
23	D₁₃	C₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	559	1	no	Hall
25	C₁₃	C₂×C₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	13	1	no	Hall
27	C₂×C₃	—	559	1	no	Hall
28	C₅	#16809814	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	559	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#16809814
commutator, cosocle, hypocenter	C₁₃×C₄₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₁₃×C₄₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#13131975	C₂	semidirect
2. C₅×D₁₃×C₄₃	C₃	semidirect
3. #16809814	C₅	direct (N × H)
4. C₅×C₁₃×C₄₃	C₂×C₃	semidirect
5. #13131975	C₂×C₅	semidirect
7. D₁₃×C₄₃	C₃×C₅	semidirect
9. C₁₃×C₄₃	C₂×C₃×C₅	semidirect
13. C₅×C₄₃	D₁₃⋊C₃	semidirect
15. C₅×D₁₃	C₄₃⋊C₃	semidirect
19. C₅×C₁₃	C₂×C₄₃⋊C₃	semidirect
20. C₄₃	C₅×D₁₃⋊C₃	semidirect
23. D₁₃	C₅×C₄₃⋊C₃	semidirect
25. C₁₃	C₂×C₅×C₄₃⋊C₃	semidirect
28. C₅	#16809814	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×#13131975	2
C₅×D₁₃×C₄₃	3
#16809814	5
C₂×C₅×C₄₃⋊C₃	13
C₅×D₁₃⋊C₃	43

Subgroups — C5×#16809814 #30680804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#16809814 #30680804