Subgroups — C₅×C₉⋊#10621721 #44477441

Order 30420.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×D₁₆₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#10621721	—	3	1	no	maximal
3	C₅×C₉×C₁₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10621721	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×D₁₆₉	D₃	1	1	yes	characteristic
6	C₅×#10621721	—	9	1	no	Hall
7	C₉×D₁₆₉	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₆₉	Dic₃	1	1	yes	characteristic
9	C₅×C₉⋊#261	—	13	1	no	maximal
10	C₃⋊#10621721	—	3	1	no	—
11	C₅×D₁₆₉	D₉	1	1	yes	characteristic
12	C₉×C₁₆₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₉×D₁₃	—	13	1	no	—
14	C₃×D₁₆₉	C₅×D₃	1	1	yes	characteristic
15	C₅×C₁₆₉	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₅×C₃⋊#261	—	39	1	no	—
17	#10621721	—	9	1	no	Hall
18	C₅×C₉×C₁₃	#261	1	1	yes	characteristic
19	C₃×C₁₆₉	C₅×Dic₃	1	1	yes	characteristic
20	C₉⋊#261	—	13	1	no	—
21	C₃×C₅×D₁₃	—	13	1	no	—
22	D₁₆₉	C₅×D₉	1	1	yes	characteristic
23	C₅×#261	—	117	1	no	—
24	C₉×D₁₃	—	13	1	no	—
25	C₃×C₅×C₁₃	C₃⋊#261	1	1	yes	characteristic
26	C₅×Dic₉	—	169	1	no	Hall
27	C₁₆₉	C₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
28	C₃⋊#261	—	39	1	no	—
29	C₅×D₁₃	—	13	1	no	—
30	C₉×C₁₃	C₅×#261	1	1	yes	characteristic
31	C₂×C₅×C₉	—	169	1	no	—
32	C₃×D₁₃	—	13	1	no	—
33	C₅×C₁₃	C₉⋊#261	1	1	yes	characteristic
34	C₅×Dic₃	—	507	1	no	—
35	#261	—	117	1	no	—
36	C₅×C₉	#10621721	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₃	C₅×C₃⋊#261	1	1	yes	characteristic
38	Dic₉	—	169	1	no	Hall
39	C₂×C₃×C₅	—	169	1	no	—
40	D₁₃	—	13	1	no	—
41	C₄×C₅	—	1521	1	no	Hall
42	C₂×C₉	—	169	1	no	—
43	C₃×C₅	C₃⋊#10621721	1	1	yes	characteristic
44	C₁₃	C₅×C₉⋊#261	1	1	yes	characteristic
45	Dic₃	—	507	1	no	—
46	C₂×C₅	—	169	1	no	—
47	C₉	C₅×#10621721	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	169	1	no	—
49	C₅	C₉⋊#10621721	1	1	yes	characteristic, direct product factor, Sylow
50	C₄	—	1521	1	no	Sylow
51	C₃	C₅×C₃⋊#10621721	1	1	yes	characteristic
52	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₉⋊#10621721
commutator, hypocenter	C₉×C₁₆₉	C₄×C₅
Frattini	C₃×C₁₃	C₅×C₃⋊#261
Fitting	C₅×C₉×C₁₆₉	C₄
socle	C₃×C₅×C₁₃	C₃⋊#261
prime radical	C₃×C₅×D₁₆₉	D₃
cosocle	C₉×D₁₆₉	C₂×C₅
LCS	G ▷ C₉×C₁₆₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₆₉	C₄	semidirect
4. C₉⋊#10621721	C₅	direct (N × H)
12. C₉×C₁₆₉	C₄×C₅	semidirect
15. C₅×C₁₆₉	Dic₉	semidirect
27. C₁₆₉	C₅×Dic₉	semidirect
36. C₅×C₉	#10621721	semidirect
47. C₉	C₅×#10621721	semidirect
49. C₅	C₉⋊#10621721	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₉×D₁₆₉	2
C₅×C₃⋊#10621721	3
C₉⋊#10621721	5
C₅×C₉⋊#261	13

Subgroups — C5×C9⋊#10621721 #44477441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉⋊#10621721 #44477441