Subgroups — C₃×C₁₃×#4223⋊C₅ #44544320

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#4223⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×#4223	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₃×D₄₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₃×D₄₁	C₂×C₅	1	1	yes	characteristic
7	C₁₃×C₄₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#4223⋊C₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃×#4223	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₃×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₄₁⋊C₅	C₂×C₁₃	1	1	yes	characteristic
12	C₁₃×D₄₁	C₂×C₃×C₅	1	1	yes	characteristic
13	#4223⋊C₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₄×C₅×C₁₃	—	41	1	no	maximal, Hall
15	C₃×C₄₁⋊C₅	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×#4223	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
18	D₄₁⋊C₅	C₂×C₃×C₁₃	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₃	—	41	1	no	—
20	C₄×C₅×C₁₃	—	41	1	no	Hall
21	C₃×D₄₁	C₂×C₅×C₁₃	1	1	yes	characteristic
22	C₄₁⋊C₅	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	—	41	1	no	Hall
24	#4223	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄×C₁₃	—	41	1	no	Hall
26	C₂×C₅×C₁₃	—	41	1	no	—
27	C₃×C₄₁	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
28	D₄₁	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
29	C₂×C₃×C₁₃	—	41	1	no	—
30	C₅×C₁₃	—	41	1	no	Hall
31	C₃×C₄×C₅	—	41	1	no	Hall
32	C₄×C₁₃	—	41	1	no	Hall
33	C₄₁	C₃×C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	#4223⋊C₅	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₃×C₅	—	41	1	no	—
36	C₂×C₁₃	—	41	1	no	—
37	C₄×C₅	—	41	1	no	Hall
38	C₃×C₅	—	41	1	no	Hall
39	C₁₃	C₃×#4223⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	—	41	1	no	Hall
41	C₂×C₅	—	41	1	no	—
42	C₂×C₃	—	41	1	no	—
43	C₅	—	41	1	no	Sylow
44	C₄	—	41	1	no	Sylow
45	C₃	C₁₃×#4223⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	41	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	#4223⋊C₅
commutator, hypocenter	C₄₁	C₃×C₄×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₄₁	C₄×C₅
prime radical	C₃×C₁₃×D₄₁⋊C₅	C₂
cosocle	D₄₁	C₂×C₃×C₅×C₁₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×#4223⋊C₅	C₃	direct (N × H)
3. C₃×C₁₃×C₄₁⋊C₅	C₄	semidirect
4. C₃×C₁₃×#4223	C₅	semidirect
7. C₁₃×C₄₁⋊C₅	C₃×C₄	semidirect
8. C₃×#4223⋊C₅	C₁₃	direct (N × H)
9. C₁₃×#4223	C₃×C₅	semidirect
10. C₃×C₁₃×C₄₁	C₄×C₅	semidirect
13. #4223⋊C₅	C₃×C₁₃	direct (N × H)
15. C₃×C₄₁⋊C₅	C₄×C₁₃	semidirect
16. C₁₃×C₄₁	C₃×C₄×C₅	semidirect
17. C₃×#4223	C₅×C₁₃	semidirect
22. C₄₁⋊C₅	C₃×C₄×C₁₃	semidirect
24. #4223	C₃×C₅×C₁₃	semidirect
27. C₃×C₄₁	C₄×C₅×C₁₃	semidirect
33. C₄₁	C₃×C₄×C₅×C₁₃	semidirect
34. C₃×C₁₃	#4223⋊C₅	direct (N × H)
39. C₁₃	C₃×#4223⋊C₅	direct (N × H)
45. C₃	C₁₃×#4223⋊C₅	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×C₁₃×D₄₁⋊C₅	2
C₁₃×#4223⋊C₅	3
C₃×C₁₃×#4223	5
C₃×#4223⋊C₅	13
C₃×C₄×C₅×C₁₃	41

Subgroups — C3×C13×#4223⋊C5 #44544320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×#4223⋊C₅ #44544320