Subgroups — C₁₃×#63118⋊C₉ #44477669

Order 30420.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×D₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#63118	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×#261⋊C₉	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₃×D₁₃	C₂×C₃	1	1	yes	characteristic
6	C₁₃×#63118	C₉	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₁₃⋊C₉	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic
9	#63118⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
10	C₉×C₁₃×Dic₅	—	13	1	no	maximal
11	C₃×C₁₃×#261	—	5	1	no	—
12	C₅×C₁₃×D₁₃	C₂×C₉	1	1	yes	characteristic
13	C₁₃×C₁₃⋊C₉	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₉×C₁₃	—	13	1	no	—
15	C₅×D₁₃⋊C₉	C₂×C₁₃	1	1	yes	characteristic
16	C₃×C₁₃×D₁₃	C₃×D₅	1	1	yes	characteristic
17	C₅×C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃×#63118	C₃×C₁₃	1	1	yes	characteristic
19	C₃×C₁₃×Dic₅	—	39	1	no	—
20	C₁₃×#261	—	5	1	no	Hall
21	C₅×C₉×C₁₃	—	13	1	no	—
22	C₅×C₁₃⋊C₉	C₄×C₁₃	1	1	yes	characteristic, complemented
23	C₃×C₁₃²	C₃×Dic₅	1	1	yes	characteristic
24	#261⋊C₉	—	5	1	no	—
25	C₄×C₉×C₁₃	—	65	1	no	—
26	C₂×C₃×C₅×C₁₃	—	39	1	no	—
27	C₃×C₅×D₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic
28	C₁₃×D₁₃	C₉×D₅	1	1	yes	characteristic
29	#63118	C₉×C₁₃	1	1	yes	characteristic, complemented
30	C₁₃×Dic₅	—	39	1	no	—
31	C₂×C₉×C₁₃	—	13	1	no	—
32	D₁₃⋊C₉	D₅×C₁₃	1	1	yes	characteristic
33	C₃×C₅×C₁₃	—	12	1	no	—
34	C₃×C₅×C₁₃	C₃×C₄×C₁₃	1	1	yes	characteristic
35	C₃×C₅×C₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic
36	C₉×Dic₅	—	13	1	no	Hall
37	C₁₃²	C₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
38	C₃×#261	—	5	1	no	—
39	C₃×C₄×C₁₃	—	195	1	no	—
40	C₂×C₅×C₁₃	—	39	1	no	—
41	C₅×D₁₃	C₂×C₉×C₁₃	1	1	yes	characteristic
42	C₉×C₁₃	—	13	1	no	—
43	C₁₃⋊C₉	C₁₃×Dic₅	1	1	yes	characteristic, complemented
44	C₂×C₅×C₉	—	13	1	no	—
45	C₂×C₃×C₁₃	—	39	1	no	—
46	C₃×D₁₃	C₃×D₅×C₁₃	1	1	yes	characteristic
47	C₅×C₁₃	—	12	1	no	—
48	C₅×C₁₃	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented
49	C₅×C₁₃	#261⋊C₉	1	1	yes	characteristic, complemented
50	C₃×Dic₅	—	39	1	no	—
51	#261	—	5	1	no	—
52	C₄×C₁₃	—	195	1	no	—
53	C₅×C₉	—	13	1	no	Hall
54	C₃×C₁₃	—	12	1	no	—
55	C₃×C₁₃	C₃×C₁₃×Dic₅	1	1	yes	characteristic
56	C₃×C₁₃	#63118⋊C₃	1	1	yes	characteristic
57	C₄×C₉	—	65	1	no	Hall
58	C₂×C₃×C₅	—	39	1	no	—
59	C₂×C₁₃	—	39	1	no	—
60	D₁₃	C₉×D₅×C₁₃	1	1	yes	characteristic
61	Dic₅	—	39	1	no	Hall
62	C₂×C₉	—	13	1	no	—
63	C₃×C₅	C₁₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic
64	C₁₃	—	12	1	no	—
65	C₁₃	C₉×C₁₃×Dic₅	1	1	yes	characteristic, complemented
66	C₁₃	#63118⋊C₉	1	1	yes	characteristic, direct product factor
67	C₃×C₄	—	195	1	no	—
68	C₂×C₅	—	39	1	no	—
69	C₉	—	13	1	no	Sylow
70	C₂×C₃	—	39	1	no	—
71	C₅	C₁₃×#261⋊C₉	1	1	yes	characteristic, complemented, Sylow
72	C₄	—	195	1	no	Sylow
73	C₃	C₁₃×#63118⋊C₃	1	1	yes	characteristic
74	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	#63118⋊C₃
commutator, hypocenter	C₅×C₁₃	C₄×C₉×C₁₃
Frattini	C₃	C₁₃×#63118⋊C₃
Fitting, socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical	C₃×C₅×C₁₃×D₁₃	C₂×C₃
cosocle	C₃×C₅×D₁₃	C₂×C₃×C₁₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₁₃

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×#63118	C₉	semidirect
9. #63118⋊C₉	C₁₃	direct (N × H)
13. C₁₃×C₁₃⋊C₉	Dic₅	semidirect
17. C₅×C₁₃²	C₄×C₉	semidirect
22. C₅×C₁₃⋊C₉	C₄×C₁₃	semidirect
29. #63118	C₉×C₁₃	semidirect
37. C₁₃²	C₉×Dic₅	semidirect
43. C₁₃⋊C₉	C₁₃×Dic₅	semidirect
48. C₅×C₁₃	C₄×C₉×C₁₃	semidirect
49. C₅×C₁₃	#261⋊C₉	semidirect
65. C₁₃	C₉×C₁₃×Dic₅	semidirect
66. C₁₃	#63118⋊C₉	direct (N × H)
71. C₅	C₁₃×#261⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×D₁₃⋊C₉	2
C₃×C₁₃×#63118	3
C₁₃×#261⋊C₉	5
#63118⋊C₉	13
C₉×C₁₃×Dic₅	13

Subgroups — C13×#63118⋊C9 #44477669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#63118⋊C₉ #44477669