Subgroups — C₅×C₃⋊(C₇⋊#1181) #27131774

Order 12180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇⋊#1181	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₇⋊#1181)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×D₂₉	D₃	1	1	yes	characteristic
6	C₅×C₃⋊#1181	—	7	1	no	maximal, Hall
7	C₃×C₇×D₂₉	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₂₉	D₇	1	1	yes	characteristic
10	C₇⋊#1181	—	3	1	no	Hall
11	C₃×C₇×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×#1181	—	21	1	no	Hall
13	C₃×C₅×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₅×Dic₂₁	—	29	1	no	maximal, Hall
15	C₇×D₂₉	C₅×D₃	1	1	yes	characteristic
16	C₃⋊#1181	—	7	1	no	Hall
17	C₅×D₂₉	D₂₁	1	1	yes	characteristic
18	C₂×C₃×C₅×C₇	—	29	1	no	—
19	C₇×C₂₉	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₃×D₂₉	C₅×D₇	1	1	yes	characteristic
21	C₅×C₂₉	Dic₂₁	1	1	yes	characteristic, complemented, Hall
22	C₅×Dic₇	—	87	1	no	Hall
23	#1181	—	21	1	no	Hall
24	C₃×C₅×C₇	#1181	1	1	yes	characteristic, complemented, Hall
25	C₃×C₂₉	C₅×Dic₇	1	1	yes	characteristic, complemented, Hall
26	Dic₂₁	—	29	1	no	Hall
27	C₂×C₅×C₇	—	29	1	no	—
28	C₅×Dic₃	—	203	1	no	Hall
29	D₂₉	C₅×D₂₁	1	1	yes	characteristic
30	C₂×C₃×C₇	—	29	1	no	—
31	C₅×C₇	C₃⋊#1181	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₅	—	29	1	no	—
33	C₂₉	C₅×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
34	Dic₇	—	87	1	no	Hall
35	C₃×C₇	C₅×#1181	1	1	yes	characteristic, complemented, Hall
36	C₄×C₅	—	609	1	no	Hall
37	C₃×C₅	C₇⋊#1181	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	29	1	no	—
39	Dic₃	—	203	1	no	Hall
40	C₂×C₅	—	29	1	no	—
41	C₇	C₅×C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	29	1	no	—
43	C₅	C₃⋊(C₇⋊#1181)	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	609	1	no	Sylow
45	C₃	C₅×C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₇⋊#1181)
commutator, hypocenter	C₃×C₇×C₂₉	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₄
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₂₉	C₄	semidirect
4. C₃⋊(C₇⋊#1181)	C₅	direct (N × H)
8. C₅×C₇×C₂₉	Dic₃	semidirect
11. C₃×C₇×C₂₉	C₄×C₅	semidirect
13. C₃×C₅×C₂₉	Dic₇	semidirect
19. C₇×C₂₉	C₅×Dic₃	semidirect
21. C₅×C₂₉	Dic₂₁	semidirect
24. C₃×C₅×C₇	#1181	semidirect
25. C₃×C₂₉	C₅×Dic₇	semidirect
31. C₅×C₇	C₃⋊#1181	semidirect
33. C₂₉	C₅×Dic₂₁	semidirect
35. C₃×C₇	C₅×#1181	semidirect
37. C₃×C₅	C₇⋊#1181	semidirect
41. C₇	C₅×C₃⋊#1181	semidirect
43. C₅	C₃⋊(C₇⋊#1181)	direct (N × H)
45. C₃	C₅×C₇⋊#1181	semidirect

Subgroups — C5×C3⋊(C7⋊#1181) #27131774

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊(C₇⋊#1181) #27131774