Subgroups — C₅²⋊C₃×#67063 #40998913

Order 26700.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×#67063	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²⋊C₃×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅²×D₈₉	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₈₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₅×#67063	—	3	2	no	—
7	C₃×#67063	—	25	1	no	maximal, Hall
8	C₅×D₈₉	—	3	2	no	—
9	C₃×D₈₉	—	25	1	no	—
10	C₅×C₈₉	—	3	2	no	—
11	#67063	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₅²⋊C₃	—	89	1	no	maximal, Hall
13	C₃×C₈₉	—	25	1	no	Hall
14	D₈₉	C₂×C₅²⋊C₃	1	1	yes	characteristic
15	C₂×C₅²⋊C₃	—	89	1	no	—
16	C₄×C₅²	—	89	1	no	Hall
17	C₈₉	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₅²⋊C₃	#67063	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅²	—	89	1	no	—
20	C₅²	C₃×#67063	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₅	—	267	2	no	—
22	C₃×C₄	—	2225	1	no	Hall
23	C₂×C₅	—	267	2	no	—
24	C₂×C₃	—	2225	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	89	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	—	89	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₈₉	C₃×C₄
prime radical	C₅²⋊C₃×D₈₉	C₂
cosocle	C₅²×D₈₉	C₂×C₃
LCS	G ▷ C₅²×C₈₉
UCS	C₁

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.