Subgroups — C₅²×C₂²⋊(C₁₀₃⋊C₃) #44525544

Order 30900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₁₀₃⋊C₃	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊(C₁₀₃⋊C₃)	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₁₀₃	—	3	1	no	—
5	C₅²×C₁₀₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₁₀₃	C₃×C₅	1	6	yes	complemented
7	C₅×C₁₀₃⋊C₃	—	4	6	no	—
8	C₂²⋊(C₁₀₃⋊C₃)	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₁₀₃	—	3	6	no	—
10	C₅×C₁₀₃	C₅×A₄	1	6	yes	complemented
11	C₂²×C₁₀₃	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
12	C₁₀₃⋊C₃	—	4	1	no	Hall
13	C₅²×A₄	—	103	1	no	maximal, Hall
14	C₂×C₁₀₃	—	3	1	no	—
15	C₁₀₃	C₅²×A₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅²	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅²	—	412	1	no	Hall
18	C₅×A₄	—	103	6	no	—
19	C₂×C₅²	—	3	1	no	—
20	C₅²	C₂²⋊(C₁₀₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₅	C₅×C₁₀₃⋊C₃	1	6	yes	complemented
22	C₃×C₅	—	412	6	no	—
23	A₄	—	103	1	no	Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×C₂²⋊(C₁₀₃⋊C₃)	1	6	yes	direct product factor
26	C₂²	C₅²×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	412	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	C₂²⋊(C₁₀₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₀₃	C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₁₀₃	C₃
LCS	G ▷ C₂²×C₁₀₃
UCS	C₁ ◁ C₅²

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.