Subgroups — C₃×#6129 #10597772

Order 624.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×Dic₁₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#6129	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×D₁₃	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₃×Dic₁₃	C₂²	1	2	yes	—
11	C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	D₄×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²⋊D₁₃	C₂×C₃	1	2	yes	complemented
14	C₂×Dic₁₃	C₂×C₃	1	2	yes	complemented
15	C₄×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
16	Dic₂₆	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×C₃×C₁₃	—	2	2	no	—
18	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×D₁₃	—	2	1	no	—
20	C₂²×C₁₃	C₂²×C₃	1	2	yes	—
21	C₂×D₁₃	C₂²×C₃	1	1	yes	characteristic
22	C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
23	Dic₁₃	C₂²×C₃	1	2	yes	—
24	Dic₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₃×#41	—	13	1	no	maximal, Hall
26	C₃×C₁₃	#41	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₃	—	2	2	no	—
28	C₂×C₁₃	C₂³×C₃	1	1	yes	characteristic
29	D₁₃	—	2	1	no	—
30	C₃×Q₈	—	13	1	no	—
31	C₃×D₄	—	13	2	no	—
32	C₃×D₄	D₁₃	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄	—	13	2	no	—
34	C₂×C₃×C₄	—	13	1	no	—
35	#41	—	13	1	no	Sylow
36	C₁₃	C₃×#41	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	13	1	no	—
38	C₂²×C₃	C₂×D₁₃	1	2	yes	—
39	C₃×C₄	—	13	1	no	—
40	C₃×C₄	—	13	2	no	—
41	C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
42	Q₈	—	13	1	no	—
43	D₄	—	13	2	no	—
44	D₄	C₃×D₁₃	1	1	yes	characteristic, complemented
45	C₂×C₄	—	13	2	no	—
46	C₂×C₄	—	13	1	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	—	26	1	no	—
49	C₂×C₃	C₂²×D₁₃	1	1	yes	characteristic
50	C₂²	—	13	1	no	—
51	C₂²	C₂×C₃×D₁₃	1	2	yes	—
52	C₄	—	13	1	no	—
53	C₄	—	13	2	no	—
54	C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
55	C₃	#6129	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	2	2	no	—
57	C₂	—	26	1	no	—
58	C₂	C₂²×C₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₁₃
commutator, cosocle	C₂×C₁₃	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₁₃
Fitting	C₃×D₄×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂³
hypercenter	C₃×D₄	D₁₃
hypocenter	C₁₃	C₃×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₁₃	C₂	semidirect
2. C₃×C₂²⋊D₁₃	C₂	semidirect
3. C₂×C₃×Dic₁₃	C₂	semidirect
4. C₃×C₄×D₁₃	C₂	semidirect
5. C₃×Dic₂₆	C₂	semidirect
6. #6129	C₃	direct (N × H)
12. D₄×C₁₃	C₂×C₃	semidirect
13. C₂²⋊D₁₃	C₂×C₃	semidirect
14. C₂×Dic₁₃	C₂×C₃	semidirect
15. C₄×D₁₃	C₂×C₃	semidirect
16. Dic₂₆	C₂×C₃	semidirect
26. C₃×C₁₃	#41	semidirect
32. C₃×D₄	D₁₃	semidirect
36. C₁₃	C₃×#41	semidirect
44. D₄	C₃×D₁₃	semidirect
55. C₃	#6129	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×D₄×C₁₃	2
C₃×C₂²⋊D₁₃	2
C₂×C₃×Dic₁₃	2
C₃×C₄×D₁₃	2
C₃×Dic₂₆	2
#6129	3
C₃×#41	13

Subgroups — C3×#6129 #10597772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#6129 #10597772