Subgroups — C₅×C₉⋊#10621725 #44477607

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	C₅×C₃⋊#10621725	—	3	1	no	maximal
3	C₅×C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10621725	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₃²	D₃	1	1	yes	characteristic
6	C₅×#10621725	—	9	1	no	Hall
7	C₂×C₉×C₁₃²	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₃²	Dic₃	1	1	yes	characteristic
9	C₅×Dic₁₁₇	—	13	14	no	maximal
10	C₃⋊#10621725	—	3	1	no	—
11	C₂×C₅×C₁₃²	D₉	1	1	yes	characteristic
12	C₉×C₁₃²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₉×C₁₃	D₁₃	1	14	yes	—
14	C₂×C₃×C₁₃²	C₅×D₃	1	1	yes	characteristic
15	C₅×C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₅×Dic₃₉	—	39	14	no	—
17	#10621725	—	9	1	no	Hall
18	C₅×C₉×C₁₃	Dic₁₃	1	14	yes	complemented
19	C₃×C₁₃²	C₅×Dic₃	1	1	yes	characteristic
20	Dic₁₁₇	—	13	14	no	—
21	C₂×C₃×C₅×C₁₃	D₃₉	1	14	yes	—
22	C₂×C₁₃²	C₅×D₉	1	1	yes	characteristic
23	C₅×Dic₁₃	—	117	14	no	—
24	C₂×C₉×C₁₃	C₅×D₁₃	1	14	yes	—
25	C₃×C₅×C₁₃	Dic₃₉	1	14	yes	—
26	C₅×Dic₉	—	169	1	no	Hall
27	C₁₃²	C₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
28	Dic₃₉	—	39	14	no	—
29	C₂×C₅×C₁₃	D₁₁₇	1	14	yes	—
30	C₉×C₁₃	C₅×Dic₁₃	1	14	yes	complemented
31	C₂×C₅×C₉	C₁₃⋊D₁₃	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₅×D₃₉	1	14	yes	—
33	C₅×C₁₃	Dic₁₁₇	1	14	yes	complemented
34	C₅×Dic₃	—	507	1	no	—
35	Dic₁₃	—	117	14	no	—
36	C₅×C₉	#10621725	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₃	C₅×Dic₃₉	1	14	yes	—
38	Dic₉	—	169	1	no	Hall
39	C₂×C₃×C₅	C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
40	C₂×C₁₃	C₅×D₁₁₇	1	14	yes	—
41	C₄×C₅	—	1521	1	no	Hall
42	C₂×C₉	C₅×C₁₃⋊D₁₃	1	1	yes	characteristic
43	C₃×C₅	C₃⋊#10621725	1	1	yes	characteristic
44	C₁₃	C₅×Dic₁₁₇	1	14	yes	complemented
45	Dic₃	—	507	1	no	—
46	C₂×C₅	C₉⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
47	C₉	C₅×#10621725	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₅×C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
49	C₅	C₉⋊#10621725	1	1	yes	characteristic, direct product factor, Sylow
50	C₄	—	1521	1	no	Sylow
51	C₃	C₅×C₃⋊#10621725	1	1	yes	characteristic
52	C₂	C₅×C₉⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₉⋊(C₁₃⋊D₁₃)
commutator, hypocenter	C₉×C₁₃²	C₄×C₅
Frattini	C₂×C₃	C₅×C₃⋊(C₁₃⋊D₁₃)
Fitting	C₂×C₅×C₉×C₁₃²	C₂
socle, prime radical	C₂×C₃×C₅×C₁₃²	D₃
cosocle	C₂×C₉×C₁₃²	C₂×C₅
LCS	G ▷ C₉×C₁₃²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃²	C₄	semidirect
4. C₉⋊#10621725	C₅	direct (N × H)
12. C₉×C₁₃²	C₄×C₅	semidirect
15. C₅×C₁₃²	Dic₉	semidirect
18. C₅×C₉×C₁₃	Dic₁₃	semidirect
27. C₁₃²	C₅×Dic₉	semidirect
30. C₉×C₁₃	C₅×Dic₁₃	semidirect
33. C₅×C₁₃	Dic₁₁₇	semidirect
36. C₅×C₉	#10621725	semidirect
44. C₁₃	C₅×Dic₁₁₇	semidirect
47. C₉	C₅×#10621725	semidirect
49. C₅	C₉⋊#10621725	direct (N × H)

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
C₅×C₃⋊#10621725	3
C₉⋊#10621725	5
C₅×Dic₁₁₇	13

Subgroups — C5×C9⋊#10621725 #44477607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉⋊#10621725 #44477607