Subgroups — C₉×#16809991 #44477604

Order 30420.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₃²	C₂	1	1	yes	maximal, characteristic
2	C₃×#16809991	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×#10621725	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	#16809991	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₃²	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic
9	C₉×Dic₆₅	—	13	14	no	maximal
10	C₃×#10621725	—	5	1	no	—
11	C₂×C₅×C₁₃²	C₂×C₉	1	1	yes	characteristic
12	C₉×C₁₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₉×C₁₃	D₁₃	1	14	yes	—
14	C₂×C₃×C₁₃²	C₃×D₅	1	1	yes	characteristic
15	C₅×C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₃×Dic₆₅	—	13	14	no	—
17	#10621725	—	5	1	no	Hall
18	C₅×C₉×C₁₃	Dic₁₃	1	14	yes	complemented
19	C₃×C₁₃²	C₃×Dic₅	1	1	yes	characteristic
20	C₉×Dic₁₃	—	65	14	no	—
21	C₂×C₃×C₅×C₁₃	C₃×D₁₃	1	14	yes	—
22	C₂×C₁₃²	C₉×D₅	1	1	yes	characteristic
23	Dic₆₅	—	13	14	no	—
24	C₂×C₉×C₁₃	D₆₅	1	14	yes	—
25	C₃×C₅×C₁₃	C₃×Dic₁₃	1	14	yes	—
26	C₉×Dic₅	—	169	1	no	Hall
27	C₁₃²	C₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
28	C₃×Dic₁₃	—	65	14	no	—
29	C₂×C₅×C₁₃	C₉×D₁₃	1	14	yes	—
30	C₉×C₁₃	Dic₆₅	1	14	yes	complemented
31	C₂×C₅×C₉	C₁₃⋊D₁₃	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₃×D₆₅	1	14	yes	—
33	C₅×C₁₃	C₉×Dic₁₃	1	14	yes	complemented
34	C₃×Dic₅	—	169	1	no	—
35	Dic₁₃	—	65	14	no	—
36	C₅×C₉	#10621725	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₃	C₃×Dic₆₅	1	14	yes	—
38	C₄×C₉	—	845	1	no	Hall
39	C₂×C₃×C₅	C₃×C₁₃⋊D₁₃	1	1	yes	characteristic
40	C₂×C₁₃	C₉×D₆₅	1	14	yes	—
41	Dic₅	—	169	1	no	Hall
42	C₂×C₉	C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
43	C₃×C₅	C₃×#10621725	1	1	yes	characteristic
44	C₁₃	C₉×Dic₆₅	1	14	yes	complemented
45	C₃×C₄	—	845	1	no	—
46	C₂×C₅	C₉×C₁₃⋊D₁₃	1	1	yes	characteristic
47	C₉	#16809991	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	C₃×C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
49	C₅	C₉×#10621725	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	845	1	no	Sylow
51	C₃	C₃×#16809991	1	1	yes	characteristic
52	C₂	C₉×C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	C₅⋊(C₁₃⋊D₁₃)
commutator, hypocenter	C₅×C₁₃²	C₄×C₉
Frattini	C₂×C₃	C₃×C₅⋊(C₁₃⋊D₁₃)
Fitting	C₂×C₅×C₉×C₁₃²	C₂
socle, prime radical, cosocle	C₂×C₃×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃²	C₄	semidirect
6. #16809991	C₉	direct (N × H)
12. C₉×C₁₃²	Dic₅	semidirect
15. C₅×C₁₃²	C₄×C₉	semidirect
18. C₅×C₉×C₁₃	Dic₁₃	semidirect
27. C₁₃²	C₉×Dic₅	semidirect
30. C₉×C₁₃	Dic₆₅	semidirect
33. C₅×C₁₃	C₉×Dic₁₃	semidirect
36. C₅×C₉	#10621725	semidirect
44. C₁₃	C₉×Dic₆₅	semidirect
47. C₉	#16809991	direct (N × H)
49. C₅	C₉×#10621725	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×C₁₃²	2
C₃×#16809991	3
C₉×#10621725	5
C₉×Dic₆₅	13

Subgroups — C9×#16809991 #44477604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#16809991 #44477604