Subgroups — C₃×C₅×#14523823 #44544396

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₅×#14523823	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14523823	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×D₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic
6	C₃×D₁₃×C₄₁	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×Dic₄₁	—	13	1	no	maximal, Hall
9	#14523823	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₁	—	13	1	no	—
12	D₁₃×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×Dic₄₁	—	13	1	no	Hall
14	C₃×C₅×#261	—	41	1	no	maximal, Hall
15	C₃×C₅×C₄₁	#261	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×Dic₄₁	—	13	1	no	Hall
18	C₂×C₅×C₄₁	—	13	1	no	—
19	C₃×C₅×D₁₃	D₄₁	1	1	yes	characteristic
20	C₅×#261	—	41	1	no	Hall
21	C₂×C₃×C₄₁	—	13	1	no	—
22	C₅×C₄₁	C₃×#261	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	Dic₄₁	1	1	yes	characteristic, complemented, Hall
24	Dic₄₁	—	13	1	no	Hall
25	C₃×#261	—	41	1	no	Hall
26	C₅×D₁₃	C₃×D₄₁	1	1	yes	characteristic
27	C₃×C₄₁	C₅×#261	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₁	—	13	1	no	—
29	C₃×D₁₃	C₅×D₄₁	1	1	yes	characteristic
30	C₅×C₁₃	C₃×Dic₄₁	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄×C₅	—	533	1	no	Hall
32	#261	—	41	1	no	Hall
33	C₄₁	C₃×C₅×#261	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	C₅×Dic₄₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	13	1	no	—
36	D₁₃	C₃×C₅×D₄₁	1	1	yes	characteristic
37	C₄×C₅	—	533	1	no	Hall
38	C₃×C₅	#14523823	1	1	yes	characteristic, direct product factor, Hall
39	C₁₃	C₃×C₅×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	533	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₃×#14523823	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	533	1	no	Sylow
45	C₃	C₅×#14523823	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	#14523823
commutator, hypocenter	C₁₃×C₄₁	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₁	C₄
prime radical	C₃×C₅×D₁₃×C₄₁	C₂
cosocle	D₁₃×C₄₁	C₂×C₃×C₅
LCS	G ▷ C₁₃×C₄₁
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#14523823	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₄₁	C₄	semidirect
4. C₃×#14523823	C₅	direct (N × H)
7. C₅×C₁₃×C₄₁	C₃×C₄	semidirect
9. #14523823	C₃×C₅	direct (N × H)
10. C₃×C₁₃×C₄₁	C₄×C₅	semidirect
15. C₃×C₅×C₄₁	#261	semidirect
16. C₁₃×C₄₁	C₃×C₄×C₅	semidirect
22. C₅×C₄₁	C₃×#261	semidirect
23. C₃×C₅×C₁₃	Dic₄₁	semidirect
27. C₃×C₄₁	C₅×#261	semidirect
30. C₅×C₁₃	C₃×Dic₄₁	semidirect
33. C₄₁	C₃×C₅×#261	semidirect
34. C₃×C₁₃	C₅×Dic₄₁	semidirect
38. C₃×C₅	#14523823	direct (N × H)
39. C₁₃	C₃×C₅×Dic₄₁	semidirect
43. C₅	C₃×#14523823	direct (N × H)
45. C₃	C₅×#14523823	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×D₁₃×C₄₁	2
C₅×#14523823	3
C₃×#14523823	5
C₃×C₅×Dic₄₁	13
C₃×C₅×#261	41

Subgroups — C3×C5×#14523823 #44544396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#14523823 #44544396