Subgroups — C₃×C₅×D₁₀₄₁ #44530295

Order 31230.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₃₄₇	—	3	1	no	maximal
4	C₃×D₁₀₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₃₄₇	—	2	1	no	—
6	C₃×C₅×C₃₄₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₃₄₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₃₄₇	—	3	1	no	Hall
9	C₃²×C₃₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₁₀₄₁	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₃×D₃₄₇	—	3	1	no	—
12	C₅×C₃₄₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₃₄₇	—	2	1	no	—
14	C₃×C₃₄₇	C₅×D₃	1	1	yes	characteristic, complemented
15	C₃×C₃₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	D₃₄₇	—	3	1	no	Hall
17	C₃₄₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×D₃	—	347	1	no	maximal, Hall
19	C₃²×C₅	D₃₄₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅	—	1041	1	no	—
21	C₅×D₃	—	347	1	no	—
22	C₃×D₃	—	347	1	no	Hall
23	C₃×C₅	—	2	1	no	—
24	C₃×C₅	C₃×D₃₄₇	1	1	yes	characteristic, complemented
25	C₃×C₅	D₁₀₄₁	1	1	yes	characteristic, direct product factor
26	C₂×C₅	—	1041	1	no	Hall
27	C₃²	C₅×D₃₄₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	1041	1	no	—
29	D₃	—	347	1	no	—
30	C₅	C₃×D₁₀₄₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₃	—	2	1	no	—
32	C₃	C₃×C₅×D₃₄₇	1	1	yes	characteristic, complemented
33	C₃	C₅×D₁₀₄₁	1	1	yes	characteristic, direct product factor
34	C₂	—	1041	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₁₀₄₁
commutator, cosocle, hypocenter	C₃×C₃₄₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₄₇	C₂
LCS	G ▷ C₃×C₃₄₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₃₄₇	C₂	semidirect
2. C₅×D₁₀₄₁	C₃	direct (N × H)
4. C₃×D₁₀₄₁	C₅	direct (N × H)
6. C₃×C₅×C₃₄₇	D₃	semidirect
7. C₃×C₅×C₃₄₇	C₂×C₃	semidirect
9. C₃²×C₃₄₇	C₂×C₅	semidirect
10. D₁₀₄₁	C₃×C₅	direct (N × H)
12. C₅×C₃₄₇	C₃×D₃	semidirect
14. C₃×C₃₄₇	C₅×D₃	semidirect
15. C₃×C₃₄₇	C₂×C₃×C₅	semidirect
17. C₃₄₇	C₃×C₅×D₃	semidirect
19. C₃²×C₅	D₃₄₇	semidirect
24. C₃×C₅	C₃×D₃₄₇	semidirect
25. C₃×C₅	D₁₀₄₁	direct (N × H)
27. C₃²	C₅×D₃₄₇	semidirect
30. C₅	C₃×D₁₀₄₁	direct (N × H)
32. C₃	C₃×C₅×D₃₄₇	semidirect
33. C₃	C₅×D₁₀₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₃₄₇	2
C₅×D₁₀₄₁	3
C₃×C₅×D₃₄₇	3
C₃×D₁₀₄₁	5
C₃×C₅×D₃	347

Subgroups — C3×C5×D1041 #44530295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₀₄₁ #44530295