Subgroups — C₃×C₇⋊#10596817 #27131766

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	C₇⋊#10596817	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇⋊#1181	—	5	1	no	maximal, Hall
5	C₅×C₇×D₂₉	C₂×C₃	1	1	yes	characteristic
6	C₃×#10596817	—	7	1	no	maximal, Hall
7	C₃×C₇×D₂₉	D₅	1	1	yes	characteristic
8	C₅×C₇×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₂₉	D₇	1	1	yes	characteristic
10	C₇⋊#1181	—	5	1	no	Hall
11	C₃×C₇×C₂₉	Dic₅	1	1	yes	characteristic, complemented, Hall
12	#10596817	—	7	1	no	Hall
13	C₃×C₅×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₃×Dic₃₅	—	29	1	no	maximal, Hall
15	C₇×D₂₉	C₃×D₅	1	1	yes	characteristic
16	C₃×#1181	—	35	1	no	Hall
17	C₅×D₂₉	C₃×D₇	1	1	yes	characteristic
18	C₂×C₃×C₅×C₇	—	29	1	no	—
19	C₇×C₂₉	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
20	C₃×D₂₉	D₃₅	1	1	yes	characteristic
21	C₅×C₂₉	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
22	Dic₃₅	—	29	1	no	Hall
23	#1181	—	35	1	no	Hall
24	C₃×C₅×C₇	#1181	1	1	yes	characteristic, complemented, Hall
25	C₃×C₂₉	Dic₃₅	1	1	yes	characteristic, complemented, Hall
26	C₃×Dic₇	—	145	1	no	Hall
27	C₂×C₅×C₇	—	29	1	no	—
28	C₃×Dic₅	—	203	1	no	Hall
29	D₂₉	C₃×D₃₅	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	C₃×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
34	Dic₇	—	145	1	no	Hall
35	C₃×C₇	#10596817	1	1	yes	characteristic, complemented, Hall
36	Dic₅	—	203	1	no	Hall
37	C₃×C₅	C₇⋊#1181	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	29	1	no	—
39	C₃×C₄	—	1015	1	no	Hall
40	C₂×C₅	—	29	1	no	—
41	C₇	C₃×#10596817	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	29	1	no	—
43	C₅	C₃×C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	1015	1	no	Sylow
45	C₃	C₇⋊#10596817	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₇⋊#10596817
commutator, hypocenter	C₅×C₇×C₂₉	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₄
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₇⋊#10596817	C₃	direct (N × H)
3. C₃×C₅×C₇×C₂₉	C₄	semidirect
8. C₅×C₇×C₂₉	C₃×C₄	semidirect
11. C₃×C₇×C₂₉	Dic₅	semidirect
13. C₃×C₅×C₂₉	Dic₇	semidirect
19. C₇×C₂₉	C₃×Dic₅	semidirect
21. C₅×C₂₉	C₃×Dic₇	semidirect
24. C₃×C₅×C₇	#1181	semidirect
25. C₃×C₂₉	Dic₃₅	semidirect
31. C₅×C₇	C₃×#1181	semidirect
33. C₂₉	C₃×Dic₃₅	semidirect
35. C₃×C₇	#10596817	semidirect
37. C₃×C₅	C₇⋊#1181	semidirect
41. C₇	C₃×#10596817	semidirect
43. C₅	C₃×C₇⋊#1181	semidirect
45. C₃	C₇⋊#10596817	direct (N × H)

Subgroups — C3×C7⋊#10596817 #27131766

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇⋊#10596817 #27131766