Subgroups — C₁₃²×#4380 #44478194

Order 30420.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃²×#157	—	5	1	no	maximal, Hall
4	C₁₃²×D₁₅	—	6	2	no	—
5	C₁₃²×AGL(1,𝔽₅)	—	9	1	no	maximal, Hall
6	C₁₃²×C₃⋊D₃	—	5	1	no	—
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	C₁₃×#4380	C₁₃	1	14	yes	maximal, direct product factor
9	D₅×C₁₃²	—	9	1	no	—
10	C₃²×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₃⋊D₁₅	C₂×C₁₃	1	14	yes	—
12	D₃×C₁₃²	—	30	2	no	—
13	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₃²	—	45	1	no	Hall
15	C₃²×C₅×C₁₃	C₄×C₁₃	1	14	yes	complemented
16	C₃×C₁₃²	—	2	2	no	—
17	C₁₃×#157	—	5	14	no	—
18	C₁₃×D₁₅	—	6	28	no	—
19	C₂×C₁₃²	—	45	1	no	—
20	C₁₃×AGL(1,𝔽₅)	—	9	14	no	—
21	C₁₃×C₃⋊D₃	—	5	14	no	—
22	C₃×C₅×C₁₃	—	2	28	no	—
23	#4380	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
24	C₁₃²	#4380	1	1	yes	characteristic, direct product factor, Sylow
25	D₅×C₁₃	—	9	14	no	—
26	C₃²×C₁₃	C₁₃×AGL(1,𝔽₅)	1	14	yes	complemented
27	C₃⋊D₁₅	C₂×C₁₃²	1	1	yes	characteristic
28	D₃×C₁₃	—	30	28	no	—
29	C₅×C₁₃	C₁₃×#157	1	14	yes	complemented
30	C₄×C₁₃	—	45	14	no	—
31	C₃²×C₅	C₄×C₁₃²	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	—	2	28	no	—
33	#157	—	5	1	no	Hall
34	D₁₅	—	6	2	no	—
35	C₂×C₁₃	—	45	14	no	—
36	AGL(1,𝔽₅)	—	9	1	no	Hall
37	C₃⋊D₃	—	5	1	no	—
38	C₃×C₅	—	2	2	no	—
39	C₁₃	C₁₃×#4380	1	14	yes	direct product factor
40	D₅	—	9	1	no	—
41	C₃²	C₁₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	30	2	no	—
43	C₅	C₁₃²×#157	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	45	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃²	#4380
commutator, hypocenter	C₃²×C₅	C₄×C₁₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₄
prime radical	C₁₃²×C₃⋊D₁₅	C₂
cosocle	C₃⋊D₁₅	C₂×C₁₃²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₁₃²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₃²	C₄	semidirect
8. C₁₃×#4380	C₁₃	direct (N × H)
10. C₃²×C₁₃²	AGL(1,𝔽₅)	semidirect
13. C₅×C₁₃²	#157	semidirect
15. C₃²×C₅×C₁₃	C₄×C₁₃	semidirect
23. #4380	C₁₃²	direct (N × H)
24. C₁₃²	#4380	direct (N × H)
26. C₃²×C₁₃	C₁₃×AGL(1,𝔽₅)	semidirect
29. C₅×C₁₃	C₁₃×#157	semidirect
31. C₃²×C₅	C₄×C₁₃²	semidirect
39. C₁₃	C₁₃×#4380	direct (N × H)
41. C₃²	C₁₃²×AGL(1,𝔽₅)	semidirect
43. C₅	C₁₃²×#157	semidirect

Maximal subgroups

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

subgroup	index
C₁₃²×C₃⋊D₁₅	2
C₁₃²×#157	5
C₁₃²×AGL(1,𝔽₅)	9
C₁₃×#4380	13

Subgroups — C132×#4380 #44478194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃²×#4380 #44478194