Subgroups — C₁₃⋊C₉×#63121 #44477663

Order 30420.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₉×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#63121	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	#261×C₁₃⋊C₉	—	5	1	no	maximal, Hall
5	C₃×C₁₃×D₆₅	C₂×C₃	1	1	yes	characteristic
6	C₁₃×#63121	C₉	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₁₃⋊C₉	—	5	1	no	—
8	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic
9	C₉×#63121	—	13	1	no	maximal
10	AGL(1,𝔽₅)×C₁₃⋊C₉	—	13	1	no	maximal
11	C₃×C₁₃×#261	—	5	1	no	—
12	C₁₃×D₆₅	C₂×C₉	1	1	yes	characteristic
13	C₁₃×C₁₃⋊C₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
14	C₉×D₆₅	—	13	1	no	—
15	D₅×C₁₃⋊C₉	—	13	1	no	—
16	C₃×C₁₃×D₁₃	—	5	1	no	—
17	C₅×C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃×#63121	C₁₃⋊C₃	1	1	yes	characteristic
19	C₃×C₁₃×AGL(1,𝔽₅)	—	13	1	no	—
20	C₁₃×#261	—	5	1	no	Hall
21	C₅×C₉×C₁₃	—	13	1	no	—
22	C₅×C₁₃⋊C₉	#261	1	1	yes	characteristic, complemented
23	C₃×C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₉×#261	—	65	1	no	—
25	C₄×C₁₃⋊C₉	—	65	1	no	—
26	C₃×D₆₅	C₂×C₁₃⋊C₃	1	1	yes	characteristic
27	C₃×D₅×C₁₃	—	13	1	no	—
28	C₁₃×D₁₃	—	5	1	no	—
29	#63121	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor
30	C₁₃×AGL(1,𝔽₅)	—	13	1	no	—
31	C₉×D₁₃	—	65	1	no	—
32	C₂×C₁₃⋊C₉	—	65	1	no	—
33	C₃×C₅×C₁₃	—	12	1	no	—
34	C₃×C₅×C₁₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic
35	C₃×C₅×C₁₃	C₃×#261	1	1	yes	characteristic
36	C₉×AGL(1,𝔽₅)	—	169	1	no	Hall
37	C₁₃²	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
38	C₃×#261	—	5	1	no	—
39	C₃×C₄×C₁₃	—	65	1	no	—
40	D₆₅	C₂×C₁₃⋊C₉	1	1	yes	characteristic
41	D₅×C₁₃	—	13	1	no	—
42	C₉×C₁₃	—	13	1	no	—
43	C₁₃⋊C₉	#63121	1	1	yes	characteristic, direct product factor
44	C₉×D₅	—	169	1	no	—
45	C₂×C₃×C₁₃	—	65	1	no	—
46	C₃×D₁₃	—	5	1	no	—
47	C₅×C₁₃	—	12	1	no	—
48	C₅×C₁₃	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented
49	C₅×C₁₃	C₉×#261	1	1	yes	characteristic, complemented
50	C₃×AGL(1,𝔽₅)	—	13	1	no	—
51	#261	—	5	1	no	—
52	C₄×C₁₃	—	65	1	no	—
53	C₅×C₉	—	13	1	no	Hall
54	C₃×C₁₃	—	12	1	no	—
55	C₃×C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	1	1	yes	characteristic
56	C₃×C₁₃	C₃×#63121	1	1	yes	characteristic
57	C₄×C₉	—	845	1	no	Hall
58	C₃×D₅	—	13	1	no	—
59	C₂×C₁₃	—	65	1	no	—
60	D₁₃	—	5	1	no	—
61	AGL(1,𝔽₅)	—	13	1	no	Hall
62	C₂×C₉	—	845	1	no	—
63	C₃×C₅	C₁₃⋊C₃×#261	1	1	yes	characteristic
64	C₁₃	—	12	1	no	—
65	C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₉	1	1	yes	characteristic, complemented
66	C₁₃	C₉×#63121	1	1	yes	characteristic, complemented
67	C₃×C₄	—	65	1	no	—
68	D₅	—	13	1	no	—
69	C₉	—	13	1	no	Sylow
70	C₂×C₃	—	65	1	no	—
71	C₅	#261×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
72	C₄	—	65	1	no	Sylow
73	C₃	C₁₃⋊C₃×#63121	1	1	yes	characteristic
74	C₂	—	65	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₃⋊C₃×#63121
commutator, hypocenter	C₅×C₁₃²	C₄×C₉
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical, cosocle	C₃×C₁₃×D₆₅	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₃×C₁₃⋊C₉	C₄	semidirect
6. C₁₃×#63121	C₉	semidirect
13. C₁₃×C₁₃⋊C₉	AGL(1,𝔽₅)	semidirect
17. C₅×C₁₃²	C₄×C₉	semidirect
22. C₅×C₁₃⋊C₉	#261	semidirect
29. #63121	C₁₃⋊C₉	direct (N × H)
37. C₁₃²	C₉×AGL(1,𝔽₅)	semidirect
43. C₁₃⋊C₉	#63121	direct (N × H)
48. C₅×C₁₃	C₄×C₁₃⋊C₉	semidirect
49. C₅×C₁₃	C₉×#261	semidirect
65. C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₉	semidirect
66. C₁₃	C₉×#63121	semidirect
71. C₅	#261×C₁₃⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊C₉×D₆₅	2
C₃×C₁₃×#63121	3
#261×C₁₃⋊C₉	5
C₉×#63121	13
AGL(1,𝔽₅)×C₁₃⋊C₉	13

Subgroups — C13⋊C9×#63121 #44477663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₉×#63121 #44477663