Subgroups — C₂×C₁₃×Dic₁₄ #13089892

Order 1456.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×Dic₇	C₂	1	2	yes	maximal
3	C₁₃×Dic₁₄	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₁₃	C₂²	1	2	yes	—
6	C₁₃×Dic₇	C₂²	1	4	yes	—
7	C₂×Q₈×C₁₃	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃	Q₈	1	2	yes	complemented
9	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
10	C₂×Dic₁₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	Q₈×C₁₃	—	7	4	no	—
12	C₂×C₄×C₁₃	—	7	2	no	—
13	C₂×C₄×C₁₃	D₇	1	1	yes	characteristic
14	C₇×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
15	C₂×C₄×C₇	C₂×C₁₃	1	1	yes	characteristic
16	C₂×Dic₇	C₂×C₁₃	1	2	yes	—
17	Dic₁₄	C₂×C₁₃	1	4	yes	direct product factor
18	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
19	C₄×C₁₃	—	7	4	no	—
20	C₄×C₁₃	C₂×D₇	1	2	yes	—
21	C₂²×C₇	C₂²×C₁₃	1	1	yes	characteristic
22	C₄×C₇	C₂²×C₁₃	1	2	yes	—
23	Dic₇	C₂²×C₁₃	1	4	yes	—
24	C₂×C₁₃	Dic₁₄	1	2	yes	direct product factor
25	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
26	C₂×Q₈	—	7	1	no	Sylow
27	C₂×C₇	Q₈×C₁₃	1	2	yes	complemented
28	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
29	C₁₃	C₂×Dic₁₄	1	1	yes	characteristic, direct product factor, Sylow
30	Q₈	—	7	4	no	—
31	C₂×C₄	—	7	2	no	—
32	C₂×C₄	C₁₃×D₇	1	1	yes	characteristic
33	C₇	C₂×Q₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²	C₂×C₁₃×D₇	1	1	yes	characteristic
35	C₄	—	7	4	no	—
36	C₄	C₂×C₁₃×D₇	1	2	yes	—
37	C₂	C₁₃×Dic₁₄	1	2	yes	direct product factor
38	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂×D₇
commutator, cosocle	C₂×C₇	C₂³×C₁₃
Frattini	C₂	C₂²×C₁₃×D₇
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle, prime radical	C₂²×C₇×C₁₃	C₂²
hypercenter	C₂×C₄×C₁₃	D₇
hypocenter	C₇	C₂×Q₈×C₁₃
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₁₃×Dic₁₄	C₂	direct (N × H)
8. C₂×C₇×C₁₃	Q₈	semidirect
10. C₂×Dic₁₄	C₁₃	direct (N × H)
14. C₇×C₁₃	C₂×Q₈	semidirect
17. Dic₁₄	C₂×C₁₃	direct (N × H)
24. C₂×C₁₃	Dic₁₄	direct (N × H)
27. C₂×C₇	Q₈×C₁₃	semidirect
29. C₁₃	C₂×Dic₁₄	direct (N × H)
33. C₇	C₂×Q₈×C₁₃	semidirect
37. C₂	C₁₃×Dic₁₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₇×C₁₃	2
C₂×C₁₃×Dic₇	2
C₁₃×Dic₁₄	2
C₂×Q₈×C₁₃	7
C₂×Dic₁₄	13

Subgroups — C2×C13×Dic14 #13089892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×Dic₁₄ #13089892