Subgroups — C₁₃⋊C₉×#63120 #44477666

Order 30420.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₃×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#63120	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₃×C₁₃⋊C₉	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	C₁₃×#63120	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₃×C₁₃⋊C₉	—	5	1	no	—
8	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic
9	C₉×#63120	—	13	1	no	maximal
10	AGL(1,𝔽₅)×C₁₃⋊C₉	—	13	1	no	maximal
11	C₃×C₁₃×Dic₁₃	—	5	1	no	—
12	D₅×C₁₃²	C₂×C₉	1	1	yes	characteristic
13	C₁₃×C₁₃⋊C₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
14	C₉×D₅×C₁₃	—	13	1	no	—
15	D₅×C₁₃⋊C₉	D₁₃	1	1	yes	characteristic
16	C₂×C₃×C₁₃²	—	5	1	no	—
17	C₅×C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃×#63120	C₁₃⋊C₃	1	1	yes	characteristic
19	C₃×C₁₃×AGL(1,𝔽₅)	—	13	1	no	—
20	C₁₃×Dic₁₃	—	5	1	no	Hall
21	C₅×C₉×C₁₃	—	13	1	no	—
22	C₅×C₁₃⋊C₉	Dic₁₃	1	1	yes	characteristic, complemented
23	C₃×C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₉×Dic₁₃	—	65	1	no	—
25	C₄×C₁₃⋊C₉	—	65	1	no	—
26	C₃×D₅×C₁₃	—	6	2	no	—
27	C₃×D₅×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
28	C₃×D₅×C₁₃	C₃×D₁₃	1	1	yes	characteristic
29	C₂×C₁₃²	—	5	1	no	—
30	#63120	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor
31	C₁₃×AGL(1,𝔽₅)	—	13	1	no	—
32	C₂×C₉×C₁₃	—	65	1	no	—
33	C₂×C₁₃⋊C₉	—	5	1	no	—
34	C₃×C₅×C₁₃	—	6	2	no	—
35	C₃×C₅×C₁₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic
36	C₃×C₅×C₁₃	C₃×Dic₁₃	1	1	yes	characteristic
37	C₉×AGL(1,𝔽₅)	—	169	1	no	Hall
38	C₁₃²	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₄×C₁₃	—	65	1	no	—
40	C₃×Dic₁₃	—	5	1	no	—
41	D₅×C₁₃	—	6	2	no	—
42	D₅×C₁₃	C₂×C₁₃⋊C₉	1	1	yes	characteristic
43	D₅×C₁₃	C₉×D₁₃	1	1	yes	characteristic
44	C₉×C₁₃	—	13	1	no	—
45	C₁₃⋊C₉	#63120	1	1	yes	characteristic, direct product factor
46	C₉×D₅	—	13	1	no	—
47	C₂×C₃×C₁₃	—	5	1	no	—
48	C₂×C₃×C₁₃	—	5	1	no	—
49	C₂×C₃×C₁₃	—	30	2	no	—
50	C₅×C₁₃	—	6	2	no	—
51	C₅×C₁₃	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented
52	C₅×C₁₃	C₉×Dic₁₃	1	1	yes	characteristic, complemented
53	C₃×AGL(1,𝔽₅)	—	13	1	no	—
54	C₄×C₁₃	—	65	1	no	—
55	Dic₁₃	—	5	1	no	—
56	C₅×C₉	—	13	1	no	Hall
57	C₃×C₁₃	—	6	2	no	—
58	C₃×C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	1	1	yes	characteristic
59	C₃×C₁₃	C₃×#63120	1	1	yes	characteristic
60	C₄×C₉	—	845	1	no	Hall
61	C₃×D₅	D₁₃×C₁₃⋊C₃	1	1	yes	characteristic
62	C₂×C₁₃	—	5	1	no	—
63	C₂×C₁₃	—	5	1	no	—
64	C₂×C₁₃	—	30	2	no	—
65	AGL(1,𝔽₅)	—	13	1	no	Hall
66	C₂×C₉	—	65	1	no	—
67	C₃×C₅	C₁₃⋊C₃×Dic₁₃	1	1	yes	characteristic
68	C₁₃	—	6	2	no	—
69	C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₉	1	1	yes	characteristic, complemented
70	C₁₃	C₉×#63120	1	1	yes	characteristic, complemented
71	C₃×C₄	—	65	1	no	—
72	D₅	D₁₃×C₁₃⋊C₉	1	1	yes	characteristic
73	C₉	—	13	1	no	Sylow
74	C₂×C₃	—	5	1	no	—
75	C₅	Dic₁₃×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
76	C₄	—	65	1	no	Sylow
77	C₃	C₁₃⋊C₃×#63120	1	1	yes	characteristic
78	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₃⋊C₃×#63120
commutator, hypocenter	C₅×C₁₃²	C₄×C₉
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical, cosocle	C₃×D₅×C₁₃²	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×#63120	C₉	semidirect
13. C₁₃×C₁₃⋊C₉	AGL(1,𝔽₅)	semidirect
17. C₅×C₁₃²	C₄×C₉	semidirect
22. C₅×C₁₃⋊C₉	Dic₁₃	semidirect
30. #63120	C₁₃⋊C₉	direct (N × H)
38. C₁₃²	C₉×AGL(1,𝔽₅)	semidirect
45. C₁₃⋊C₉	#63120	direct (N × H)
51. C₅×C₁₃	C₄×C₁₃⋊C₉	semidirect
52. C₅×C₁₃	C₉×Dic₁₃	semidirect
69. C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₉	semidirect
70. C₁₃	C₉×#63120	semidirect
75. C₅	Dic₁₃×C₁₃⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₁₃×C₁₃⋊C₉	2
C₃×C₁₃×#63120	3
Dic₁₃×C₁₃⋊C₉	5
C₉×#63120	13
AGL(1,𝔽₅)×C₁₃⋊C₉	13

Subgroups — C13⋊C9×#63120 #44477666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₉×#63120 #44477666