Subgroups — #20258902

Order 6084.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊#11759818	C₂	1	2	yes	maximal, complemented
2	C₃×#11759816	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₉⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	#11759818⋊C₂	—	3	1	no	maximal
5	C₃×#92789	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₃₉	C₂×C₃	1	2	yes	complemented
7	C₃×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	#11759818	—	3	2	no	—
9	#11759816	—	2	1	no	—
10	#11759816	D₃	1	1	yes	characteristic, complemented
11	D₁₃²	—	3	1	no	Hall
12	C₃×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
13	#92789	—	2	1	no	—
14	#92789	C₂×D₃	1	1	yes	characteristic, complemented
15	D₃×D₁₃⋊C₃	—	13	2	no	maximal
16	C₁₃⋊D₁₃	C₃×D₃	1	1	yes	characteristic, complemented
17	C₁₃×D₁₃	—	3	2	no	—
18	C₃⋊(D₁₃⋊C₃)	—	13	2	no	—
19	D₃×C₁₃⋊C₃	—	13	2	no	—
20	C₃×D₁₃⋊C₃	—	13	2	no	—
21	C₁₃²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
22	D₃×D₁₃	—	13	2	no	—
23	C₂×D₁₃⋊C₃	—	39	2	no	—
24	C₃×C₁₃⋊C₃	—	13	2	no	—
25	D₃₉	D₁₃⋊C₃	1	2	yes	complemented
26	C₃×D₁₃	—	13	2	no	—
27	C₃×D₁₃	—	78	2	no	—
28	D₃×C₁₃	—	13	2	no	—
29	C₂×C₁₃⋊C₃	—	39	2	no	—
30	D₁₃⋊C₃	—	13	2	no	—
31	D₁₃⋊C₃	—	26	2	no	—
32	D₁₃⋊C₃	—	39	2	no	—
33	C₂×D₁₃	—	39	2	no	—
34	C₃×C₁₃	—	6	2	no	—
35	C₃×C₁₃	C₂×D₁₃⋊C₃	1	2	yes	complemented
36	C₁₃⋊C₃	—	13	2	no	—
37	C₁₃⋊C₃	—	26	2	no	—
38	C₂×C₃×D₃	—	169	1	no	Hall
39	C₂×C₁₃	—	39	2	no	—
40	D₁₃	—	3	2	no	—
41	D₁₃	—	13	2	no	—
42	D₁₃	—	78	2	no	—
43	C₂×C₃²	—	169	1	no	—
44	C₃×D₃	—	169	2	no	—
45	C₁₃	—	6	2	no	—
46	C₁₃	D₃×D₁₃⋊C₃	1	2	yes	complemented
47	C₂²×C₃	—	507	1	no	—
48	C₂×D₃	—	169	1	no	—
49	C₃²	—	169	1	no	Sylow
50	C₂×C₃	—	338	1	no	—
51	C₂×C₃	—	169	1	no	—
52	C₂×C₃	—	169	1	no	—
53	C₂×C₃	—	507	2	no	—
54	D₃	—	13	2	no	—
55	C₂²	—	507	1	no	Sylow
56	C₃	—	338	1	no	—
57	C₃	—	169	1	no	—
58	C₃	#11759818⋊C₂	1	1	yes	characteristic, complemented
59	C₂	—	39	2	no	—
60	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃²	C₂²×C₃
LCS	G ▷ C₃×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊#11759818	C₂	semidirect
2. C₃×#11759816	C₂	semidirect
3. D₃₉⋊D₁₃	C₃	semidirect
5. C₃×#92789	C₂²	semidirect
6. C₁₃×D₃₉	C₂×C₃	semidirect
7. C₃×C₁₃⋊D₁₃	C₂×C₃	semidirect
10. #11759816	D₃	semidirect
12. C₃×C₁₃²	C₂²×C₃	semidirect
14. #92789	C₂×D₃	semidirect
16. C₁₃⋊D₁₃	C₃×D₃	semidirect
21. C₁₃²	C₂×C₃×D₃	semidirect
25. D₃₉	D₁₃⋊C₃	semidirect
35. C₃×C₁₃	C₂×D₁₃⋊C₃	semidirect
46. C₁₃	D₃×D₁₃⋊C₃	semidirect
58. C₃	#11759818⋊C₂	semidirect