Subgroups — C₅×D₃×C₃₄₉⋊C₃ #44536116

Order 31410.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₃₄₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₃₄₉⋊C₃	—	3	1	no	maximal
4	D₃×C₃₄₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₃₄₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₃₄₉⋊C₃	—	2	1	no	—
7	C₅×C₃₄₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₅×C₃₄₉	—	3	1	no	Hall
9	C₃×C₃₄₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₃×C₃₄₉	C₃×C₅	1	1	yes	characteristic, complemented
11	C₂×C₃₄₉⋊C₃	—	3	1	no	—
12	C₅×C₃₄₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₃₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	C₃₄₉⋊C₃	—	2	1	no	—
15	C₃₄₉⋊C₃	C₅×D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃₄₉	—	3	1	no	Hall
17	C₃₄₉	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×D₃	—	349	1	no	maximal, Hall
19	C₃²×C₅	—	349	1	no	Hall
20	C₂×C₃×C₅	—	1047	1	no	—
21	C₅×D₃	C₃₄₉⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃×D₃	—	349	1	no	Hall
23	C₃×C₅	—	349	1	no	—
24	C₃×C₅	—	698	1	no	—
25	C₃×C₅	C₂×C₃₄₉⋊C₃	1	1	yes	characteristic, complemented
26	C₂×C₅	—	3	1	no	Hall
27	C₃²	—	349	1	no	Sylow
28	C₂×C₃	—	1047	1	no	—
29	D₃	C₅×C₃₄₉⋊C₃	1	1	yes	characteristic, direct product factor
30	C₅	D₃×C₃₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₃	—	349	1	no	—
32	C₃	—	698	1	no	—
33	C₃	C₂×C₅×C₃₄₉⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃×C₃₄₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₃₄₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₄₉	C₂×C₃
LCS	G ▷ C₃×C₃₄₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₃₄₉⋊C₃	C₂	semidirect
2. C₅×D₃×C₃₄₉	C₃	semidirect
4. D₃×C₃₄₉⋊C₃	C₅	direct (N × H)
5. C₃×C₅×C₃₄₉	C₂×C₃	semidirect
7. C₅×C₃₄₉⋊C₃	D₃	direct (N × H)
9. C₃×C₃₄₉⋊C₃	C₂×C₅	semidirect
10. D₃×C₃₄₉	C₃×C₅	semidirect
12. C₅×C₃₄₉	C₃×D₃	semidirect
13. C₃×C₃₄₉	C₂×C₃×C₅	semidirect
15. C₃₄₉⋊C₃	C₅×D₃	direct (N × H)
17. C₃₄₉	C₃×C₅×D₃	semidirect
21. C₅×D₃	C₃₄₉⋊C₃	direct (N × H)
25. C₃×C₅	C₂×C₃₄₉⋊C₃	semidirect
29. D₃	C₅×C₃₄₉⋊C₃	direct (N × H)
30. C₅	D₃×C₃₄₉⋊C₃	direct (N × H)
33. C₃	C₂×C₅×C₃₄₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₃₄₉⋊C₃	2
C₅×D₃×C₃₄₉	3
C₂×C₅×C₃₄₉⋊C₃	3
D₃×C₃₄₉⋊C₃	5
C₃×C₅×D₃	349

Subgroups — C5×D3×C349⋊C3 #44536116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₃₄₉⋊C₃ #44536116