Subgroups — C₁₃×D₉₀₃ #37553443

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₀₁	—	3	1	no	maximal, Hall
3	C₇×C₁₃×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₂₉	—	7	1	no	maximal, Hall
5	D₉₀₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₄₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₄₃	—	21	1	no	Hall
8	C₃×C₇×C₄₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	D₃₀₁	—	3	1	no	Hall
10	C₁₃×C₄₃	D₂₁	1	1	yes	characteristic, complemented, Hall
11	C₁₃×D₂₁	—	43	1	no	maximal, Hall
12	C₇×C₄₃	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×C₁₃	D₄₃	1	1	yes	characteristic, complemented, Hall
14	D₁₂₉	—	7	1	no	Hall
15	C₁₃×D₇	—	129	1	no	Hall
16	C₃×C₄₃	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₃	D₁₂₉	1	1	yes	characteristic, complemented, Hall
18	D₄₃	—	21	1	no	Hall
19	D₃×C₁₃	—	301	1	no	Hall
20	C₄₃	C₁₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
21	D₂₁	—	43	1	no	Hall
22	C₃×C₁₃	D₃₀₁	1	1	yes	characteristic, complemented, Hall
23	C₂×C₁₃	—	903	1	no	Hall
24	C₃×C₇	C₁₃×D₄₃	1	1	yes	characteristic, complemented, Hall
25	D₇	—	129	1	no	Hall
26	C₁₃	D₉₀₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₁₃×D₁₂₉	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	301	1	no	Hall
29	C₃	C₁₃×D₃₀₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	903	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₉₀₃
commutator, cosocle, hypocenter	C₃×C₇×C₄₃	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₄₃	C₂
LCS	G ▷ C₃×C₇×C₄₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₄₃	C₂	semidirect
3. C₇×C₁₃×C₄₃	D₃	semidirect
5. D₉₀₃	C₁₃	direct (N × H)
6. C₃×C₁₃×C₄₃	D₇	semidirect
8. C₃×C₇×C₄₃	C₂×C₁₃	semidirect
10. C₁₃×C₄₃	D₂₁	semidirect
12. C₇×C₄₃	D₃×C₁₃	semidirect
13. C₃×C₇×C₁₃	D₄₃	semidirect
16. C₃×C₄₃	C₁₃×D₇	semidirect
17. C₇×C₁₃	D₁₂₉	semidirect
20. C₄₃	C₁₃×D₂₁	semidirect
22. C₃×C₁₃	D₃₀₁	semidirect
24. C₃×C₇	C₁₃×D₄₃	semidirect
26. C₁₃	D₉₀₃	direct (N × H)
27. C₇	C₁₃×D₁₂₉	semidirect
29. C₃	C₁₃×D₃₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₄₃	2
C₁₃×D₃₀₁	3
C₁₃×D₁₂₉	7
D₉₀₃	13
C₁₃×D₂₁	43

Subgroups — C13×D903 #37553443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₉₀₃ #37553443