Subgroups — C₅×(C₇⋊C₉)⋊#261 #30655005

Order 16380.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₃×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₇⋊#261	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₃×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₇⋊C₉)⋊#261	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×D₁₃	C₂×C₃	1	1	yes	characteristic
6	C₅×C₉×#261	—	7	1	no	maximal, Hall
7	C₅×C₇⋊#261	C₉	1	1	yes	characteristic, complemented, Hall
8	D₁₃×C₇⋊C₉	C₂×C₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₁₃	C₃×C₄	1	1	yes	characteristic
10	C₅×Dic₇⋊C₉	—	13	1	no	maximal, Hall
11	C₅×C₉×D₁₃	—	7	1	no	—
12	C₃×C₇⋊#261	C₃×C₅	1	1	yes	characteristic
13	C₅×C₇×D₁₃	C₂×C₉	1	1	yes	characteristic
14	C₁₃×C₇⋊C₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×#261	—	21	1	no	—
16	C₂×C₅×C₇⋊C₉	—	13	1	no	—
17	C₅×C₉×C₁₃	—	7	1	no	Hall
18	C₃×C₇×D₁₃	C₂×C₃×C₅	1	1	yes	characteristic
19	C₉×#261	—	7	1	no	Hall
20	C₅×C₇×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×Dic₇	—	13	1	no	—
22	C₃×C₅×D₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
23	C₇⋊#261	C₅×C₉	1	1	yes	characteristic, complemented, Hall
24	C₅×C₇⋊C₉	#261	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇×C₁₃	C₃×C₄×C₅	1	1	yes	characteristic
26	C₅×#261	—	21	1	no	Hall
27	Dic₇⋊C₉	—	13	1	no	Hall
28	C₉×D₁₃	—	7	1	no	—
29	C₂×C₃×C₅×C₇	—	13	1	no	—
30	C₃×C₅×C₁₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
31	C₇×D₁₃	C₂×C₅×C₉	1	1	yes	characteristic
32	C₄×C₅×C₉	—	91	1	no	Hall
33	C₃×#261	—	21	1	no	—
34	C₅×Dic₇	—	13	1	no	Hall
35	C₅×D₁₃	D₇⋊C₉	1	1	yes	characteristic
36	C₂×C₇⋊C₉	—	13	1	no	—
37	C₉×C₁₃	—	7	1	no	Hall
38	C₃×C₅×C₇	C₃×#261	1	1	yes	characteristic
39	C₇×C₁₃	C₄×C₅×C₉	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅×C₉	—	91	1	no	—
41	C₃×Dic₇	—	13	1	no	—
42	C₃×D₁₃	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic
43	C₂×C₅×C₇	—	13	1	no	—
44	C₅×C₁₃	Dic₇⋊C₉	1	1	yes	characteristic, complemented, Hall
45	C₇⋊C₉	C₅×#261	1	1	yes	characteristic, complemented, Hall
46	C₃×C₄×C₅	—	273	1	no	—
47	#261	—	21	1	no	Hall
48	C₅×C₉	—	7	1	no	Hall
49	C₂×C₃×C₇	—	13	1	no	—
50	C₃×C₁₃	C₅×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
51	C₄×C₉	—	91	1	no	Hall
52	C₅×C₇	C₉×#261	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×C₅	—	13	1	no	—
54	Dic₇	—	13	1	no	Hall
55	D₁₃	C₅×D₇⋊C₉	1	1	yes	characteristic
56	C₃×C₇	C₃×C₅×#261	1	1	yes	characteristic
57	C₄×C₅	—	273	1	no	Hall
58	C₂×C₉	—	91	1	no	—
59	C₃×C₅	ΓL(1,𝔽₈)⋊#261	1	1	yes	characteristic
60	C₂×C₇	—	13	1	no	—
61	C₁₃	C₅×Dic₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
62	C₃×C₄	—	273	1	no	—
63	C₂×C₅	—	13	1	no	—
64	C₉	—	7	1	no	Sylow
65	C₇	C₅×C₉×#261	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	13	1	no	—
67	C₅	(C₇⋊C₉)⋊#261	1	1	yes	characteristic, direct product factor, Sylow
68	C₄	—	273	1	no	Sylow
69	C₃	C₅×ΓL(1,𝔽₈)⋊#261	1	1	yes	characteristic
70	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	ΓL(1,𝔽₈)⋊#261
commutator, hypocenter	C₇×C₁₃	C₄×C₅×C₉
Frattini	C₃	C₅×ΓL(1,𝔽₈)⋊#261
Fitting, socle	C₃×C₅×C₇×C₁₃	C₃×C₄
prime radical	C₃×C₅×C₇×D₁₃	C₂×C₃
cosocle	C₃×C₇×D₁₃	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₃×C₇⋊C₉	C₄	semidirect
4. (C₇⋊C₉)⋊#261	C₅	direct (N × H)
7. C₅×C₇⋊#261	C₉	semidirect
14. C₁₃×C₇⋊C₉	C₄×C₅	semidirect
20. C₅×C₇×C₁₃	C₄×C₉	semidirect
23. C₇⋊#261	C₅×C₉	semidirect
24. C₅×C₇⋊C₉	#261	semidirect
39. C₇×C₁₃	C₄×C₅×C₉	semidirect
44. C₅×C₁₃	Dic₇⋊C₉	semidirect
45. C₇⋊C₉	C₅×#261	semidirect
52. C₅×C₇	C₉×#261	semidirect
61. C₁₃	C₅×Dic₇⋊C₉	semidirect
65. C₇	C₅×C₉×#261	semidirect
67. C₅	(C₇⋊C₉)⋊#261	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×D₁₃×C₇⋊C₉	2
C₃×C₅×C₇⋊#261	3
(C₇⋊C₉)⋊#261	5
C₅×C₉×#261	7
C₅×Dic₇⋊C₉	13

Subgroups — C5×(C7⋊C9)⋊#261 #30655005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×(C₇⋊C₉)⋊#261 #30655005