Subgroups — C₅²×D₄₄₇ #36375324

Order 22350.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₁₄₉	—	3	1	no	maximal, Hall
3	C₅×D₄₄₇	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₁₄₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₄₉	C₂×C₅	1	6	yes	complemented
6	C₅×D₁₄₉	—	3	6	no	—
7	D₄₄₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₄₉	C₅×D₃	1	6	yes	complemented
9	C₃×C₁₄₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	D₁₄₉	—	3	1	no	Hall
11	C₅²×D₃	—	149	1	no	maximal, Hall
12	C₁₄₉	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₅²	D₁₄₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅²	—	447	1	no	Hall
15	C₅×D₃	—	149	6	no	—
16	C₅²	D₄₄₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₅×D₁₄₉	1	6	yes	complemented
18	C₂×C₅	—	447	6	no	—
19	D₃	—	149	1	no	Hall
20	C₅	C₅×D₄₄₇	1	6	yes	direct product factor
21	C₃	C₅²×D₁₄₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	447	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₄₄₇
commutator, cosocle, hypocenter	C₃×C₁₄₉	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₄₉	C₂
LCS	G ▷ C₃×C₁₄₉
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.