Subgroups — C₃⋊(#15668527⋊C₃) #39908057

Order 26100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668527	C₃	1	1	yes	maximal, characteristic, complemented
3	#15668527⋊C₃	—	3	1	no	maximal
4	C₃×C₂₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₂₉×(C₅⋊D₅)⋊C₃	—	2	1	no	—
7	C₂₉×(C₅⋊D₅)⋊C₃	D₃	1	1	yes	characteristic
8	#15668527	—	3	1	no	Hall
9	C₂₉×C₅²⋊C₃	—	2	1	no	—
10	C₂₉×C₅²⋊C₃	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃⋊#10596816	—	15	2	no	—
13	C₂₉×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
14	C₃×Dic₈₇	—	25	1	no	maximal, Hall
15	C₃⋊(#1043⋊C₃)	—	29	1	no	maximal, Hall
16	C₃×D₅×C₂₉	—	15	2	no	—
17	C₅²×C₂₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	#10596816	—	45	2	no	—
19	C₂×C₃²×C₂₉	—	25	1	no	—
20	C₃×(C₅⋊D₅)⋊C₃	D₂₉	1	1	yes	characteristic
21	C₃×C₅×C₂₉	—	3	2	no	—
22	Dic₈₇	—	25	1	no	—
23	C₃×Dic₂₉	—	75	1	no	—
24	C₃⋊#1043	—	29	1	no	—
25	#1043⋊C₃	—	87	1	no	—
26	D₅×C₂₉	—	15	2	no	—
27	C₃²×C₂₉	—	100	1	no	Hall
28	C₃×C₅²⋊C₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₂₉	—	25	1	no	—
30	C₂×C₃×C₂₉	—	25	1	no	—
31	C₂×C₃×C₂₉	—	50	1	no	—
32	C₃×C₅⋊D₅	C₃×D₂₉	1	1	yes	characteristic
33	(C₅⋊D₅)⋊C₃	—	2	1	no	—
34	(C₅⋊D₅)⋊C₃	D₈₇	1	1	yes	characteristic
35	C₅×C₂₉	—	3	2	no	—
36	Dic₂₉	—	75	1	no	Hall
37	#1043	—	87	1	no	Hall
38	C₃×C₂₉	—	100	1	no	—
39	C₃×C₂₉	—	100	1	no	—
40	C₃×C₂₉	#1043⋊C₃	1	1	yes	characteristic, complemented
41	C₃×C₅²	C₃×Dic₂₉	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	2	1	no	—
43	C₅²⋊C₃	Dic₈₇	1	1	yes	characteristic, complemented
44	ΓL(1,𝔽₁₆)	—	435	2	no	—
45	C₂×C₂₉	—	25	1	no	—
46	C₅⋊D₅	C₃×D₈₇	1	1	yes	characteristic
47	C₃×Dic₃	—	725	1	no	Hall
48	C₃×D₅	—	15	2	no	—
49	C₂₉	C₃⋊(#1043⋊C₃)	1	1	yes	characteristic, complemented, Sylow
50	C₅²	C₃×Dic₈₇	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	1305	2	no	—
52	C₂×C₃²	—	25	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	2175	1	no	—
55	Dic₃	—	725	1	no	—
56	D₅	—	15	2	no	—
57	C₃²	—	100	1	no	Sylow
58	C₂×C₃	—	25	1	no	—
59	C₂×C₃	—	25	1	no	—
60	C₂×C₃	—	50	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	2175	1	no	Sylow
63	C₃	—	100	1	no	—
64	C₃	—	100	1	no	—
65	C₃	#15668527⋊C₃	1	1	yes	characteristic, complemented
66	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₂₉	C₃×C₄
prime radical	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₃×C₂₉×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊#15668527	C₃	semidirect
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
10. C₂₉×C₅²⋊C₃	Dic₃	semidirect
11. C₃×C₅²×C₂₉	C₃×C₄	semidirect
17. C₅²×C₂₉	C₃×Dic₃	semidirect
28. C₃×C₅²⋊C₃	Dic₂₉	semidirect
40. C₃×C₂₉	#1043⋊C₃	semidirect
41. C₃×C₅²	C₃×Dic₂₉	semidirect
43. C₅²⋊C₃	Dic₈₇	semidirect
49. C₂₉	C₃⋊(#1043⋊C₃)	semidirect
50. C₅²	C₃×Dic₈₇	semidirect
65. C₃	#15668527⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂₉×(C₅⋊D₅)⋊C₃	2
C₃⋊#15668527	3
#15668527⋊C₃	3
C₃×Dic₈₇	25
C₃⋊(#1043⋊C₃)	29

Subgroups — C3⋊(#15668527⋊C3) #39908057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#15668527⋊C₃) #39908057