Subgroups — C₃×C₅×C₂²⋊#92788 #44478332

Order 30420.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊#92788	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#92788	—	4	1	no	maximal, Hall
4	C₃×C₂²⋊#92788	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₃²	—	3	1	no	—
6	C₂²×C₅×C₁₃²	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₅×#92788	—	4	3	no	—
8	C₃×C₅×C₁₃²	A₄	1	1	yes	characteristic, complemented
9	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	—	13	14	no	maximal
10	C₂²⋊#92788	C₃×C₅	1	3	yes	direct product factor
11	C₂²×C₃×C₁₃²	C₃×C₅	1	1	yes	characteristic, complemented
12	C₂×C₅×C₁₃²	—	3	1	no	—
13	C₃×#92788	—	4	1	no	Hall
14	C₂×C₃×C₁₃²	—	3	1	no	—
15	C₅×C₁₃²	C₃×A₄	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃×C₅×C₁₃	C₁₃⋊C₃	1	14	yes	complemented
17	C₅×C₂²⋊(C₁₃⋊C₃)	—	13	42	no	—
18	C₂²×C₁₃²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×C₁₃⋊C₃	—	52	14	no	—
20	C₃×C₁₃²	C₅×A₄	1	1	yes	characteristic, complemented
21	#92788	—	4	3	no	—
22	C₃×C₂²⋊(C₁₃⋊C₃)	—	13	14	no	—
23	C₂×C₃×C₅×C₁₃	—	3	14	no	—
24	C₂×C₁₃²	—	3	1	no	—
25	C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	1	14	yes	complemented
26	C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)	1	14	yes	complemented
27	C₅×C₁₃⋊C₃	—	52	42	no	—
28	C₃×C₅×A₄	—	169	1	no	Hall
29	C₁₃²	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃×C₁₃	C₅×C₁₃⋊C₃	1	14	yes	complemented
31	C₂²⋊(C₁₃⋊C₃)	—	13	42	no	—
32	C₂×C₅×C₁₃	—	3	14	no	—
33	C₃×C₁₃⋊C₃	—	52	14	no	—
34	C₂×C₃×C₁₃	—	3	14	no	—
35	C₅×C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	14	yes	complemented
36	C₂²×C₃×C₅	#92788	1	1	yes	characteristic, complemented
37	C₅×A₄	—	169	3	no	—
38	C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	1	14	yes	complemented
39	C₃²×C₅	—	676	1	no	Hall
40	C₃×C₁₃	C₅×C₂²⋊(C₁₃⋊C₃)	1	14	yes	complemented
41	C₁₃⋊C₃	—	52	42	no	—
42	C₃×A₄	—	169	1	no	Hall
43	C₂×C₃×C₅	—	3	1	no	—
44	C₂×C₁₃	—	3	14	no	—
45	C₂²×C₅	C₃×#92788	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅	—	676	3	no	—
47	C₃×C₅	C₂²⋊#92788	1	1	yes	characteristic, direct product factor
48	C₁₃	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	1	14	yes	complemented
49	C₂²×C₃	C₅×#92788	1	1	yes	characteristic, complemented
50	A₄	—	169	3	no	—
51	C₂×C₅	—	3	1	no	—
52	C₃²	—	676	1	no	Sylow
53	C₂×C₃	—	3	1	no	—
54	C₅	C₃×C₂²⋊#92788	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²	C₃×C₅×#92788	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	676	3	no	—
57	C₃	C₅×C₂²⋊#92788	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	C₂²⋊#92788
commutator, cosocle, hypocenter	C₂²×C₁₃²	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₁₃²	C₃
LCS	G ▷ C₂²×C₁₃²
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂²⋊#92788	C₃	direct (N × H)
2. C₂²×C₃×C₅×C₁₃²	C₃	semidirect
4. C₃×C₂²⋊#92788	C₅	direct (N × H)
6. C₂²×C₅×C₁₃²	C₃²	semidirect
8. C₃×C₅×C₁₃²	A₄	semidirect
10. C₂²⋊#92788	C₃×C₅	direct (N × H)
11. C₂²×C₃×C₁₃²	C₃×C₅	semidirect
15. C₅×C₁₃²	C₃×A₄	semidirect
16. C₂²×C₃×C₅×C₁₃	C₁₃⋊C₃	semidirect
18. C₂²×C₁₃²	C₃²×C₅	semidirect
20. C₃×C₁₃²	C₅×A₄	semidirect
25. C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	semidirect
26. C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)	semidirect
29. C₁₃²	C₃×C₅×A₄	semidirect
30. C₂²×C₃×C₁₃	C₅×C₁₃⋊C₃	semidirect
35. C₅×C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	semidirect
36. C₂²×C₃×C₅	#92788	semidirect
38. C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	semidirect
40. C₃×C₁₃	C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
45. C₂²×C₅	C₃×#92788	semidirect
47. C₃×C₅	C₂²⋊#92788	direct (N × H)
48. C₁₃	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
49. C₂²×C₃	C₅×#92788	semidirect
54. C₅	C₃×C₂²⋊#92788	direct (N × H)
55. C₂²	C₃×C₅×#92788	semidirect
57. C₃	C₅×C₂²⋊#92788	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂²⋊#92788	3
C₂²×C₃×C₅×C₁₃²	3
C₃×C₅×#92788	4
C₃×C₂²⋊#92788	5
C₃×C₅×C₂²⋊(C₁₃⋊C₃)	13

Subgroups — C3×C5×C22⋊#92788 #44478332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₂²⋊#92788 #44478332