Subgroups — C₃×C₅×D₁₀₄₃ #44530969

Order 31290.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₀₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×D₁₄₉	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₄₉	D₇	1	1	yes	characteristic, complemented, Hall
8	D₁₀₄₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅×D₁₄₉	—	7	1	no	Hall
10	C₇×C₁₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₄₉	—	7	1	no	Hall
12	C₅×C₁₄₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₄₉	C₅×D₇	1	1	yes	characteristic, complemented, Hall
14	D₁₄₉	—	7	1	no	Hall
15	C₃×C₅×D₇	—	149	1	no	maximal, Hall
16	C₁₄₉	C₃×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₄₉	1	1	yes	characteristic, complemented, Hall
18	C₅×D₇	—	149	1	no	Hall
19	C₃×D₇	—	149	1	no	Hall
20	C₅×C₇	C₃×D₁₄₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅	—	1043	1	no	Hall
22	C₃×C₇	C₅×D₁₄₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₁₀₄₃	1	1	yes	characteristic, direct product factor, Hall
24	D₇	—	149	1	no	Hall
25	C₂×C₅	—	1043	1	no	Hall
26	C₇	C₃×C₅×D₁₄₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	1043	1	no	Hall
28	C₅	C₃×D₁₀₄₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₁₀₄₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	1043	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₁₀₄₃
commutator, cosocle, hypocenter	C₇×C₁₄₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₄₉	C₂
LCS	G ▷ C₇×C₁₄₉
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₄₉	C₂	semidirect
2. C₅×D₁₀₄₃	C₃	direct (N × H)
3. C₃×D₁₀₄₃	C₅	direct (N × H)
4. C₅×C₇×C₁₄₉	C₂×C₃	semidirect
6. C₃×C₇×C₁₄₉	C₂×C₅	semidirect
7. C₃×C₅×C₁₄₉	D₇	semidirect
8. D₁₀₄₃	C₃×C₅	direct (N × H)
10. C₇×C₁₄₉	C₂×C₃×C₅	semidirect
12. C₅×C₁₄₉	C₃×D₇	semidirect
13. C₃×C₁₄₉	C₅×D₇	semidirect
16. C₁₄₉	C₃×C₅×D₇	semidirect
17. C₃×C₅×C₇	D₁₄₉	semidirect
20. C₅×C₇	C₃×D₁₄₉	semidirect
22. C₃×C₇	C₅×D₁₄₉	semidirect
23. C₃×C₅	D₁₀₄₃	direct (N × H)
26. C₇	C₃×C₅×D₁₄₉	semidirect
28. C₅	C₃×D₁₀₄₃	direct (N × H)
29. C₃	C₅×D₁₀₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₄₉	2
C₅×D₁₀₄₃	3
C₃×D₁₀₄₃	5
C₃×C₅×D₁₄₉	7
C₃×C₅×D₇	149

Subgroups — C3×C5×D1043 #44530969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₀₄₃ #44530969