Subgroups — C₃×C₅×D₃₄₉⋊C₃ #44536112

Order 31410.

48 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×D₃₄₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅×D₃₄₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃₄₉⋊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	C₂×C₃	1	3	yes	complemented
7	C₅×D₃₄₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₃₄₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃₄₉	C₃×C₅	1	1	yes	characteristic, complemented
10	D₃₄₉⋊C₃	C₃×C₅	1	3	yes	direct product factor
11	C₅×C₃₄₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₃₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
13	C₃₄₉⋊C₃	C₂×C₃×C₅	1	3	yes	complemented
14	D₃₄₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₃₄₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃²×C₅	—	349	1	no	maximal, Hall
17	C₃²×C₅	—	349	1	no	Hall
18	C₂×C₃×C₅	—	349	3	no	—
19	C₂×C₃×C₅	—	349	1	no	—
20	C₂×C₃²	—	349	1	no	Hall
21	C₃×C₅	—	349	3	no	—
22	C₃×C₅	D₃₄₉⋊C₃	1	1	yes	characteristic, direct product factor
23	C₂×C₅	—	349	1	no	Hall
24	C₃²	—	349	1	no	Sylow
25	C₂×C₃	—	349	3	no	—
26	C₂×C₃	—	349	1	no	—
27	C₅	C₃×D₃₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₃	—	349	3	no	—
29	C₃	C₅×D₃₄₉⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	349	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₃₄₉⋊C₃
commutator, cosocle, hypocenter	C₃₄₉	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₄₉	C₂×C₃
LCS	G ▷ C₃₄₉
UCS	C₁ ◁ C₃×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×D₃₄₉⋊C₃	C₃	direct (N × H)
3. C₃×C₅×D₃₄₉	C₃	semidirect
4. C₃×D₃₄₉⋊C₃	C₅	direct (N × H)
5. C₃×C₅×C₃₄₉	C₂×C₃	semidirect
6. C₅×C₃₄₉⋊C₃	C₂×C₃	semidirect
7. C₅×D₃₄₉	C₃²	semidirect
8. C₃×C₃₄₉⋊C₃	C₂×C₅	semidirect
9. C₃×D₃₄₉	C₃×C₅	semidirect
10. D₃₄₉⋊C₃	C₃×C₅	direct (N × H)
11. C₅×C₃₄₉	C₂×C₃²	semidirect
12. C₃×C₃₄₉	C₂×C₃×C₅	semidirect
13. C₃₄₉⋊C₃	C₂×C₃×C₅	semidirect
14. D₃₄₉	C₃²×C₅	semidirect
15. C₃₄₉	C₂×C₃²×C₅	semidirect
22. C₃×C₅	D₃₄₉⋊C₃	direct (N × H)
27. C₅	C₃×D₃₄₉⋊C₃	direct (N × H)
29. C₃	C₅×D₃₄₉⋊C₃	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×C₃₄₉⋊C₃	2
C₅×D₃₄₉⋊C₃	3
C₃×C₅×D₃₄₉	3
C₃×D₃₄₉⋊C₃	5
C₂×C₃²×C₅	349

Subgroups — C3×C5×D349⋊C3 #44536112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃₄₉⋊C₃ #44536112