Subgroups — C₂×Dic₃×D₁₃ #10597744

Order 624.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×D₁₃	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₁₃	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×D₁₃	C₄	1	4	yes	complemented
8	C₂×C₃×D₁₃	C₂²	1	2	yes	—
9	Dic₃₉	C₂²	1	2	yes	complemented
10	Dic₃×C₁₃	C₂²	1	2	yes	complemented
11	C₂²×D₁₃	D₃	1	1	yes	characteristic
12	C₂×C₄×C₁₃	—	3	1	no	—
13	C₂×Dic₁₃	—	3	1	no	—
14	C₄×D₁₃	—	3	4	no	—
15	C₂×C₃×C₁₃	C₂×C₄	1	2	yes	complemented
16	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₃×D₁₃	C₂×C₄	1	4	yes	complemented
18	C₂²×C₁₃	C₂×D₃	1	1	yes	characteristic
19	C₂×D₁₃	Dic₃	1	4	yes	direct product factor
20	C₂×D₁₃	C₂×D₃	1	2	yes	—
21	C₄×C₁₃	—	3	2	no	—
22	Dic₁₃	—	3	2	no	—
23	C₂²×Dic₃	—	13	1	no	maximal, Hall
24	C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₃	C₂×Dic₃	1	2	yes	complemented
26	C₂×C₁₃	C₂²×D₃	1	1	yes	characteristic
27	D₁₃	C₂×Dic₃	1	4	yes	direct product factor
28	C₂³×C₃	—	13	1	no	—
29	C₂×Dic₃	—	13	1	no	—
30	C₂×Dic₃	—	13	4	no	—
31	C₂×Dic₃	D₁₃	1	1	yes	characteristic, direct product factor
32	C₂²×C₄	—	39	1	no	Sylow
33	C₁₃	C₂²×Dic₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₃	—	13	4	no	—
35	C₂²×C₃	—	13	2	no	—
36	C₂²×C₃	C₂×D₁₃	1	1	yes	characteristic
37	Dic₃	—	13	2	no	—
38	Dic₃	C₂×D₁₃	1	2	yes	direct product factor
39	C₂³	—	13	1	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	39	4	no	—
42	C₂×C₄	—	39	1	no	—
43	C₂×C₃	—	13	4	no	—
44	C₂×C₃	C₄×D₁₃	1	2	yes	complemented
45	C₂×C₃	C₂²×D₁₃	1	1	yes	characteristic
46	C₂²	—	13	4	no	—
47	C₂²	—	13	2	no	—
48	C₂²	D₃×D₁₃	1	1	yes	characteristic
49	C₄	—	3	2	no	—
50	C₄	—	39	2	no	—
51	C₃	C₂×C₄×D₁₃	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	13	4	no	—
53	C₂	Dic₃×D₁₃	1	2	yes	direct product factor
54	C₂	C₂×D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂²×C₄
Frattini	C₂	C₂×D₃×D₁₃
Fitting, socle	C₂²×C₃×C₁₃	C₂²
prime radical	C₂²×C₃×D₁₃	C₂
cosocle	C₂×C₃×C₁₃	C₂³
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₉	C₂	semidirect
3. C₂×Dic₃×C₁₃	C₂	semidirect
4. Dic₃×D₁₃	C₂	direct (N × H)
7. C₂×C₃×D₁₃	C₄	semidirect
9. Dic₃₉	C₂²	semidirect
10. Dic₃×C₁₃	C₂²	semidirect
15. C₂×C₃×C₁₃	C₂×C₄	semidirect
17. C₃×D₁₃	C₂×C₄	semidirect
19. C₂×D₁₃	Dic₃	direct (N × H)
24. C₃×C₁₃	C₂²×C₄	semidirect
25. C₂×C₁₃	C₂×Dic₃	semidirect
27. D₁₃	C₂×Dic₃	direct (N × H)
31. C₂×Dic₃	D₁₃	direct (N × H)
33. C₁₃	C₂²×Dic₃	semidirect
38. Dic₃	C₂×D₁₃	direct (N × H)
44. C₂×C₃	C₄×D₁₃	semidirect
51. C₃	C₂×C₄×D₁₃	semidirect
53. C₂	Dic₃×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₁₃	2
C₂×Dic₃₉	2
C₂×Dic₃×C₁₃	2
Dic₃×D₁₃	2
C₂×C₄×D₁₃	3
C₂²×Dic₃	13

Subgroups — C2×Dic3×D13 #10597744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃×D₁₃ #10597744