Subgroups — #44478203

Order 30420.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₅⋊(C₁₃⋊D₁₃)))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20258973	—	5	1	no	maximal, Hall
4	C₃⋊(C₅⋊(C₁₃⋊D₁₃))	—	6	2	no	—
5	#16810003	—	9	1	no	maximal, Hall
6	C₃⋊(C₃⋊(C₁₃⋊D₁₃))	—	5	1	no	—
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	#14556843	—	13	14	no	maximal
9	C₅⋊(C₁₃⋊D₁₃)	—	9	1	no	—
10	C₃²×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃⋊D₁₉₅	—	13	14	no	—
12	C₃⋊(C₁₃⋊D₁₃)	—	30	2	no	—
13	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
14	#10621728	—	45	1	no	Hall
15	C₃²×C₅×C₁₃	#261	1	14	yes	complemented
16	C₃×C₁₃²	—	2	2	no	—
17	#90866	—	65	14	no	—
18	D₁₉₅	—	78	28	no	—
19	C₁₃⋊D₁₃	—	45	1	no	—
20	#63121	—	117	14	no	—
21	C₃⋊D₃₉	—	65	14	no	—
22	C₃×C₅×C₁₃	—	2	28	no	—
23	#4380	—	169	1	no	Hall
24	C₁₃²	#4380	1	1	yes	characteristic, complemented, Sylow
25	D₆₅	—	117	14	no	—
26	C₃²×C₁₃	#63121	1	14	yes	complemented
27	C₃⋊D₁₅	—	169	1	no	—
28	D₃₉	—	390	28	no	—
29	C₅×C₁₃	#90866	1	14	yes	complemented
30	#261	—	585	14	no	—
31	C₃²×C₅	#10621728	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	—	2	28	no	—
33	#157	—	845	1	no	Hall
34	D₁₅	—	1014	2	no	—
35	D₁₃	—	585	14	no	—
36	AGL(1,𝔽₅)	—	1521	1	no	Hall
37	C₃⋊D₃	—	845	1	no	—
38	C₃×C₅	—	2	2	no	—
39	C₁₃	#14556843	1	14	yes	complemented
40	D₅	—	1521	1	no	—
41	C₃²	#16810003	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	5070	2	no	—
43	C₅	#20258973	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	7605	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	7605	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₃²	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₅⋊(C₁₃⋊D₁₃)))	C₂
LCS	G ▷ C₃²×C₅×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₃²	C₄	semidirect
10. C₃²×C₁₃²	AGL(1,𝔽₅)	semidirect
13. C₅×C₁₃²	#157	semidirect
15. C₃²×C₅×C₁₃	#261	semidirect
24. C₁₃²	#4380	semidirect
26. C₃²×C₁₃	#63121	semidirect
29. C₅×C₁₃	#90866	semidirect
31. C₃²×C₅	#10621728	semidirect
39. C₁₃	#14556843	semidirect
41. C₃²	#16810003	semidirect
43. C₅	#20258973	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃⋊(C₅⋊(C₁₃⋊D₁₃)))	2
#20258973	5
#16810003	9
#14556843	13