Subgroups — C₃×C₅×C₂²⋊#92789 #44478333

Order 30420.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊#92789	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#92789	—	4	1	no	maximal, Hall
4	C₃×C₂²⋊#92789	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×#92789	—	4	3	no	—
8	C₃×C₅×C₁₃²	A₄	1	1	yes	characteristic, complemented
9	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	—	13	2	no	maximal
10	C₂²⋊#92789	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×#92789	—	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	—	3	4	no	—
17	C₂²×C₃×C₅×C₁₃	C₁₃⋊C₃	1	2	yes	complemented
18	C₅×C₂²⋊(C₁₃⋊C₃)	—	13	6	no	—
19	C₂²×C₁₃²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅×C₁₃⋊C₃	—	52	2	no	—
21	C₃×C₁₃²	C₅×A₄	1	1	yes	characteristic, complemented
22	#92789	—	4	3	no	—
23	C₃×C₂²⋊(C₁₃⋊C₃)	—	13	2	no	—
24	C₂×C₃×C₅×C₁₃	—	3	12	no	—
25	C₂×C₃×C₅×C₁₃	—	3	2	no	—
26	C₂×C₁₃²	—	3	1	no	—
27	C₂²×C₅×C₁₃	—	3	4	no	—
28	C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	1	2	yes	complemented
29	C₃×C₅×C₁₃	—	3	4	no	—
30	C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
31	C₅×C₁₃⋊C₃	—	52	6	no	—
32	C₃×C₅×A₄	—	169	1	no	Hall
33	C₁₃²	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₃×C₁₃	—	3	4	no	—
35	C₂²×C₃×C₁₃	C₅×C₁₃⋊C₃	1	2	yes	complemented
36	C₂²⋊(C₁₃⋊C₃)	—	13	6	no	—
37	C₂×C₅×C₁₃	—	3	12	no	—
38	C₂×C₅×C₁₃	—	3	2	no	—
39	C₃×C₁₃⋊C₃	—	52	2	no	—
40	C₂×C₃×C₁₃	—	3	12	no	—
41	C₂×C₃×C₁₃	—	3	2	no	—
42	C₅×C₁₃	—	3	4	no	—
43	C₅×C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
44	C₂²×C₃×C₅	#92789	1	1	yes	characteristic, complemented
45	C₅×A₄	—	169	3	no	—
46	C₂²×C₁₃	—	3	4	no	—
47	C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	1	2	yes	complemented
48	C₃²×C₅	—	676	1	no	Hall
49	C₃×C₁₃	—	3	4	no	—
50	C₃×C₁₃	C₅×C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
51	C₁₃⋊C₃	—	52	6	no	—
52	C₃×A₄	—	169	1	no	Hall
53	C₂×C₃×C₅	—	3	1	no	—
54	C₂×C₁₃	—	3	12	no	—
55	C₂×C₁₃	—	3	2	no	—
56	C₂²×C₅	C₃×#92789	1	1	yes	characteristic, complemented, Hall
57	C₃×C₅	—	676	3	no	—
58	C₃×C₅	C₂²⋊#92789	1	1	yes	characteristic, direct product factor
59	C₁₃	—	3	4	no	—
60	C₁₃	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	1	2	yes	complemented
61	C₂²×C₃	C₅×#92789	1	1	yes	characteristic, complemented
62	A₄	—	169	3	no	—
63	C₂×C₅	—	3	1	no	—
64	C₃²	—	676	1	no	Sylow
65	C₂×C₃	—	3	1	no	—
66	C₅	C₃×C₂²⋊#92789	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	C₃×C₅×#92789	1	1	yes	characteristic, complemented, Sylow
68	C₃	—	676	3	no	—
69	C₃	C₅×C₂²⋊#92789	1	1	yes	characteristic, direct product factor
70	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	C₂²⋊#92789
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⋊#92789	C₃	direct (N × H)
2. C₂²×C₃×C₅×C₁₃²	C₃	semidirect
4. C₃×C₂²⋊#92789	C₅	direct (N × H)
6. C₂²×C₅×C₁₃²	C₃²	semidirect
8. C₃×C₅×C₁₃²	A₄	semidirect
10. C₂²⋊#92789	C₃×C₅	direct (N × H)
11. C₂²×C₃×C₁₃²	C₃×C₅	semidirect
15. C₅×C₁₃²	C₃×A₄	semidirect
17. C₂²×C₃×C₅×C₁₃	C₁₃⋊C₃	semidirect
19. C₂²×C₁₃²	C₃²×C₅	semidirect
21. C₃×C₁₃²	C₅×A₄	semidirect
28. C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	semidirect
30. C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)	semidirect
33. C₁₃²	C₃×C₅×A₄	semidirect
35. C₂²×C₃×C₁₃	C₅×C₁₃⋊C₃	semidirect
43. C₅×C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	semidirect
44. C₂²×C₃×C₅	#92789	semidirect
47. C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	semidirect
50. C₃×C₁₃	C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
56. C₂²×C₅	C₃×#92789	semidirect
58. C₃×C₅	C₂²⋊#92789	direct (N × H)
60. C₁₃	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
61. C₂²×C₃	C₅×#92789	semidirect
66. C₅	C₃×C₂²⋊#92789	direct (N × H)
67. C₂²	C₃×C₅×#92789	semidirect
69. C₃	C₅×C₂²⋊#92789	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⋊#92789	3
C₂²×C₃×C₅×C₁₃²	3
C₃×C₅×#92789	4
C₃×C₂²⋊#92789	5
C₃×C₅×C₂²⋊(C₁₃⋊C₃)	13

Subgroups — C3×C5×C22⋊#92789 #44478333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₂²⋊#92789 #44478333