Subgroups — C₃×C₅⋊(D₃₄₉⋊C₃) #44536113

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×D₁₇₄₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃₄₉⋊C₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₃₄₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₃₄₉⋊C₃	C₂×C₃	1	3	yes	complemented
7	D₁₇₄₅	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₃₄₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃₄₉	—	5	1	no	—
10	D₃₄₉⋊C₃	—	5	3	no	—
11	C₅×C₃₄₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₃₄₉	C₃×D₅	1	1	yes	characteristic, complemented
13	C₃₄₉⋊C₃	C₃×D₅	1	3	yes	complemented
14	D₃₄₉	—	5	1	no	Hall
15	C₃₄₉	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₃²×D₅	—	349	1	no	maximal, Hall
17	C₃²×C₅	—	349	1	no	Hall
18	C₃×D₅	—	349	3	no	—
19	C₃×D₅	—	349	1	no	—
20	C₂×C₃²	—	1745	1	no	Hall
21	C₃×C₅	—	349	3	no	—
22	C₃×C₅	D₃₄₉⋊C₃	1	1	yes	characteristic, complemented
23	D₅	—	349	1	no	Hall
24	C₃²	—	349	1	no	Sylow
25	C₂×C₃	—	1745	3	no	—
26	C₂×C₃	—	1745	1	no	—
27	C₅	C₃×D₃₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₃	—	349	3	no	—
29	C₃	C₅⋊(D₃₄₉⋊C₃)	1	1	yes	characteristic, direct product factor
30	C₂	—	1745	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊(D₃₄₉⋊C₃)
commutator, cosocle, hypocenter	C₅×C₃₄₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₄₉	C₂×C₃
LCS	G ▷ C₅×C₃₄₉
UCS	C₁ ◁ C₃

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

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