Subgroups — C₅×#20258976 #44478191

Order 30420.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20258976	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃×C₁₃²	—	6	2	no	—
5	C₅×#10621725	—	9	1	no	maximal, Hall
6	C₁₃²×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	C₅×#90865	—	13	14	no	maximal
9	C₂×C₅×C₁₃²	—	9	1	no	—
10	C₃²×C₁₃²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₃×C₃⋊D₃	D₁₃	1	14	yes	—
12	D₃×C₁₃²	—	6	2	no	—
13	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
14	#10621725	—	9	1	no	Hall
15	C₃²×C₅×C₁₃	Dic₁₃	1	14	yes	complemented
16	C₃×C₁₃²	—	2	2	no	—
17	#90865	—	13	14	no	—
18	C₅×D₃×C₁₃	—	6	28	no	—
19	C₂×C₁₃²	—	9	1	no	—
20	C₅×Dic₁₃	—	117	14	no	—
21	C₁₃×C₃⋊D₃	C₅×D₁₃	1	14	yes	—
22	C₃×C₅×C₁₃	—	2	28	no	—
23	C₅×#157	—	169	1	no	Hall
24	C₁₃²	C₅×#157	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅×C₁₃	—	9	14	no	—
26	C₃²×C₁₃	C₅×Dic₁₃	1	14	yes	complemented
27	C₅×C₃⋊D₃	C₁₃⋊D₁₃	1	1	yes	characteristic
28	D₃×C₁₃	—	6	28	no	—
29	C₅×C₁₃	#90865	1	14	yes	complemented
30	Dic₁₃	—	117	14	no	—
31	C₃²×C₅	#10621725	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	—	2	28	no	—
33	#157	—	169	1	no	Hall
34	C₅×D₃	—	6	2	no	—
35	C₂×C₁₃	—	9	14	no	—
36	C₄×C₅	—	1521	1	no	Hall
37	C₃⋊D₃	C₅×C₁₃⋊D₁₃	1	1	yes	characteristic
38	C₃×C₅	—	2	2	no	—
39	C₁₃	C₅×#90865	1	14	yes	complemented
40	C₂×C₅	—	9	1	no	—
41	C₃²	C₅×#10621725	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	#20258976	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	1521	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#20258976
commutator, hypocenter	C₃²×C₁₃²	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₄
prime radical	C₅×C₁₃²×C₃⋊D₃	C₂
cosocle	C₁₃²×C₃⋊D₃	C₂×C₅
LCS	G ▷ C₃²×C₁₃²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₃²	C₄	semidirect
3. #20258976	C₅	direct (N × H)
10. C₃²×C₁₃²	C₄×C₅	semidirect
13. C₅×C₁₃²	#157	semidirect
15. C₃²×C₅×C₁₃	Dic₁₃	semidirect
24. C₁₃²	C₅×#157	semidirect
26. C₃²×C₁₃	C₅×Dic₁₃	semidirect
29. C₅×C₁₃	#90865	semidirect
31. C₃²×C₅	#10621725	semidirect
39. C₁₃	C₅×#90865	semidirect
41. C₃²	C₅×#10621725	semidirect
43. C₅	#20258976	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×C₁₃²×C₃⋊D₃	2
#20258976	5
C₅×#10621725	9
C₅×#90865	13

Subgroups — C5×#20258976 #44478191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20258976 #44478191