Subgroups — #4223×C₅²⋊C₉ #49146809

Order 36900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₁×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅²×#4223	C₃	1	1	yes	maximal, characteristic
3	C₄₁×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅²×D₄₁	C₂×C₃	1	1	yes	characteristic
5	C₅²×#4223	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₄₁	C₃×C₄	1	1	yes	characteristic
7	C₃×C₅×#4223	—	3	2	no	—
8	C₅²×D₄₁	C₂×C₉	1	1	yes	characteristic
9	C₉×#4223	—	25	1	no	maximal, Hall
10	C₃×C₅×D₄₁	—	3	2	no	—
11	C₅²×C₄₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₄×C₅²⋊C₉	—	41	1	no	maximal, Hall
13	C₅×#4223	—	3	2	no	—
14	C₉×D₄₁	—	25	1	no	—
15	C₃×C₅×C₄₁	—	3	2	no	—
16	C₃×#4223	C₅²⋊C₃	1	1	yes	characteristic
17	C₂×C₅²⋊C₉	—	41	1	no	—
18	C₅×D₄₁	—	3	2	no	—
19	C₉×C₄₁	—	25	1	no	Hall
20	C₃×C₄×C₅²	—	41	1	no	—
21	C₃×D₄₁	C₂×C₅²⋊C₃	1	1	yes	characteristic
22	C₅²⋊C₉	#4223	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₄₁	—	3	2	no	—
24	#4223	C₅²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅²	—	41	1	no	—
26	C₃×C₄₁	C₄×C₅²⋊C₃	1	1	yes	characteristic
27	C₄×C₅²	—	41	1	no	Hall
28	D₄₁	C₂×C₅²⋊C₉	1	1	yes	characteristic
29	C₃×C₅²	C₃×#4223	1	1	yes	characteristic
30	C₃×C₄×C₅	—	123	2	no	—
31	C₂×C₅²	—	41	1	no	—
32	C₄₁	C₄×C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
33	C₄×C₉	—	1025	1	no	Hall
34	C₂×C₃×C₅	—	123	2	no	—
35	C₅²	C₉×#4223	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₅	—	123	2	no	—
37	C₂×C₉	—	1025	1	no	—
38	C₃×C₅	—	3	2	no	—
39	C₃×C₄	—	41	1	no	—
40	C₂×C₅	—	123	2	no	—
41	C₉	—	25	1	no	Sylow
42	C₂×C₃	—	41	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	41	1	no	Sylow
45	C₃	C₅²⋊C₃×#4223	1	1	yes	characteristic
46	C₂	—	41	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅²⋊C₃×#4223
commutator, hypocenter	C₅²×C₄₁	C₄×C₉
Fitting, socle	C₃×C₅²×C₄₁	C₃×C₄
prime radical, cosocle	C₃×C₅²×D₄₁	C₂×C₃
LCS	G ▷ C₅²×C₄₁
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₄₁×C₅²⋊C₉	C₄	semidirect
5. C₅²×#4223	C₉	semidirect
11. C₅²×C₄₁	C₄×C₉	semidirect
22. C₅²⋊C₉	#4223	direct (N × H)
24. #4223	C₅²⋊C₉	direct (N × H)
32. C₄₁	C₄×C₅²⋊C₉	semidirect
35. C₅²	C₉×#4223	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄₁×C₅²⋊C₉	2
C₃×C₅²×#4223	3
C₉×#4223	25
C₄×C₅²⋊C₉	41

Subgroups — #4223×C52⋊C9 #49146809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4223×C₅²⋊C₉ #49146809