Subgroups — C₅²×D₆₈₉ #46828014

Order 34450.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₈₉	C₅	1	6	yes	maximal, direct product factor
3	C₅×C₁₃×C₅₃	C₂×C₅	1	6	yes	complemented
4	C₅²×D₅₃	—	13	1	no	maximal, Hall
5	D₆₈₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₅²×C₅₃	D₁₃	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₅₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
8	C₅²×D₁₃	—	53	1	no	maximal, Hall
9	C₅×D₅₃	—	13	6	no	—
10	C₅²×C₁₃	D₅₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₅₃	C₅×D₁₃	1	6	yes	complemented
12	C₅×D₁₃	—	53	6	no	—
13	D₅₃	—	13	1	no	Hall
14	C₅×C₁₃	C₅×D₅₃	1	6	yes	complemented
15	C₅₃	C₅²×D₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅²	—	689	1	no	Hall
17	D₁₃	—	53	1	no	Hall
18	C₅²	D₆₈₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	C₅²×D₅₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	689	6	no	—
21	C₅	C₅×D₆₈₉	1	6	yes	direct product factor
22	C₂	—	689	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₆₈₉
commutator, cosocle, hypocenter	C₁₃×C₅₃	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₅₃	C₂
LCS	G ▷ C₁₃×C₅₃
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.