Subgroups — C₂×C₂₉⋊(D₁₀₉⋊C₃) #49181908

Order 37932.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉⋊(D₁₀₉⋊C₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₉×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₁₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₉×C₁₀₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₉×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
6	D₃₁₆₁	C₂×C₃	1	2	yes	complemented
7	C₂₉×C₁₀₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₀₉⋊C₃	—	29	1	no	maximal, Hall
9	C₂×C₁₀₉⋊C₃	D₂₉	1	1	yes	characteristic, complemented
10	D₁₀₉⋊C₃	—	29	2	no	—
11	C₂×D₁₀₉	—	29	1	no	Hall
12	C₂×C₃×D₂₉	—	109	1	no	maximal, Hall
13	C₁₀₉⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₀₉	C₃×D₂₉	1	1	yes	characteristic, complemented
15	D₁₀₉	—	29	2	no	—
16	C₂×C₃×C₂₉	—	109	1	no	—
17	C₃×D₂₉	—	109	2	no	—
18	C₂×D₂₉	—	109	1	no	Hall
19	C₁₀₉	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₂₉	—	109	1	no	Hall
21	C₂×C₂₉	D₁₀₉⋊C₃	1	1	yes	characteristic, complemented
22	D₂₉	—	109	2	no	—
23	C₂₉	C₂×D₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	3161	1	no	Hall
25	C₂×C₃	—	3161	2	no	—
26	C₂×C₃	—	109	1	no	—
27	C₂²	—	3161	1	no	Sylow
28	C₃	—	109	1	no	Sylow
29	C₂	—	3161	2	no	—
30	C₂	C₂₉⋊(D₁₀₉⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₂₉⋊(D₁₀₉⋊C₃)
commutator, cosocle, hypocenter	C₂₉×C₁₀₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₂₉×C₁₀₉	C₂×C₃
LCS	G ▷ C₂₉×C₁₀₉
UCS	C₁ ◁ C₂

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.