Subgroups — C₅²⋊#89205 #26010607

Order 11025.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇²	C₃	1	1	yes	maximal, characteristic
2	C₇⋊(C₅²⋊C₉)	—	7	2	no	maximal
3	C₅²×C₇²	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₇²	—	3	2	no	—
5	C₃×C₅²×C₇	—	3	2	no	—
6	C₃×C₅²×C₇	ΓL(1,𝔽₈)	1	2	yes	—
7	#89205	—	25	1	no	maximal, Hall
8	C₅×C₇²	—	3	2	no	—
9	C₅²⋊C₉	—	49	1	no	Hall
10	C₅²×C₇	—	3	2	no	—
11	C₅²×C₇	C₇⋊C₉	1	2	yes	complemented
12	C₃×C₇²	C₅²⋊C₃	1	1	yes	characteristic
13	C₃×C₅×C₇	—	3	12	no	—
14	C₃×C₅×C₇	—	3	4	no	—
15	C₃×C₅²	#3862	1	1	yes	characteristic
16	C₇⋊C₉	—	175	2	no	—
17	C₇²	C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₅×C₇	—	3	12	no	—
19	C₅×C₇	—	3	4	no	—
20	C₅²	#89205	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₇	—	3	2	no	—
22	C₃×C₇	C₇⋊(C₅²⋊C₃)	1	2	yes	—
23	C₃×C₅	—	3	2	no	—
24	C₉	—	1225	1	no	Sylow
25	C₇	—	3	2	no	—
26	C₇	C₇⋊(C₅²⋊C₉)	1	2	yes	complemented
27	C₅	—	3	2	no	—
28	C₃	C₅²⋊#3862	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅²⋊#3862
commutator, hypocenter	C₅²×C₇²	C₉
Fitting, socle, prime radical, cosocle	C₃×C₅²×C₇²	C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁ ◁ C₃

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.