Subgroups — C₃×(C₁₃⋊C₃)⋊D₁₀₉ #38784113

Order 25506.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₃⋊C₃)⋊D₁₀₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₄₁₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₁₀₉	C₂×C₃	1	3	yes	complemented
6	D₁₄₁₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃²×D₁₀₉	—	13	1	no	maximal, Hall
8	C₁₃×C₁₀₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₁₀₉	—	13	1	no	Hall
10	C₃×D₁₀₉	—	13	3	no	—
11	C₃×D₁₀₉	—	39	1	no	—
12	C₃×C₁₀₉	—	13	3	no	—
13	C₃×C₁₀₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
14	C₃×D₁₃⋊C₃	—	109	1	no	maximal, Hall
15	D₁₀₉	—	39	1	no	Hall
16	C₃×C₁₃⋊C₃	D₁₀₉	1	1	yes	characteristic, complemented, Hall
17	C₁₀₉	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₁₃	—	109	1	no	—
19	D₁₃⋊C₃	—	109	3	no	—
20	C₃×C₁₃	C₃×D₁₀₉	1	1	yes	characteristic, complemented
21	C₁₃⋊C₃	C₃×D₁₀₉	1	3	yes	complemented
22	D₁₃	—	109	1	no	Hall
23	C₂×C₃²	—	1417	1	no	Hall
24	C₁₃	C₃²×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	13	1	no	Sylow
26	C₂×C₃	—	1417	3	no	—
27	C₂×C₃	—	4251	1	no	—
28	C₃	—	13	3	no	—
29	C₃	(C₁₃⋊C₃)⋊D₁₀₉	1	1	yes	characteristic, direct product factor
30	C₂	—	4251	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	(C₁₃⋊C₃)⋊D₁₀₉
commutator, cosocle, hypocenter	C₁₃×C₁₀₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₀₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₀₉
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.