Subgroups — C₇×Q₈×D₁₃ #13089888

Order 1456.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₇×D₁₃	C₂	1	3	yes	maximal
3	C₇×Dic₂₆	C₂	1	3	yes	maximal, complemented
4	C₂×C₇×D₁₃	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₁₃	C₂²	1	3	yes	—
6	C₇×Dic₁₃	C₂²	1	3	yes	—
7	Q₈×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
9	C₇×D₁₃	Q₈	1	2	yes	direct product factor
10	C₂×C₇×Q₈	—	13	1	no	maximal, Hall
11	Q₈×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₄×D₁₃	C₂×C₇	1	3	yes	—
13	Dic₂₆	C₂×C₇	1	3	yes	complemented
14	C₇×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
15	C₇×Q₈	—	13	3	no	—
16	C₇×Q₈	D₁₃	1	1	yes	characteristic, direct product factor
17	C₂×C₄×C₇	—	13	3	no	—
18	C₂×D₁₃	C₂²×C₇	1	1	yes	characteristic
19	C₄×C₁₃	C₂²×C₇	1	3	yes	—
20	Dic₁₃	C₂²×C₇	1	3	yes	—
21	C₂²×C₇	—	13	1	no	—
22	C₄×C₇	—	13	3	no	—
23	C₄×C₇	C₂×D₁₃	1	3	yes	—
24	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
25	D₁₃	C₇×Q₈	1	2	yes	direct product factor
26	C₂×Q₈	—	13	1	no	Sylow
27	C₂×C₇	—	13	2	no	—
28	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
29	C₁₃	C₂×C₇×Q₈	1	1	yes	characteristic, complemented, Sylow
30	Q₈	—	13	3	no	—
31	Q₈	C₇×D₁₃	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	13	3	no	—
33	C₇	Q₈×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	13	1	no	—
35	C₄	—	13	3	no	—
36	C₄	C₂×C₇×D₁₃	1	3	yes	—
37	C₂	—	13	2	no	—
38	C₂	C₂²×C₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂²×D₁₃
commutator, cosocle	C₂×C₁₃	C₂³×C₇
Frattini	C₂	C₂²×C₇×D₁₃
Fitting	C₇×Q₈×C₁₃	C₂
socle	C₂×C₇×C₁₃	C₂³
prime radical	C₂×C₇×D₁₃	C₂²
hypercenter	C₇×Q₈	D₁₃
hypocenter	C₁₃	C₂×C₇×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₇ ◁ C₇×Q₈

Complements

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

N	H ≅ G/N	type
1. C₇×Q₈×C₁₃	C₂	semidirect
3. C₇×Dic₂₆	C₂	semidirect
7. Q₈×D₁₃	C₇	direct (N × H)
9. C₇×D₁₃	Q₈	direct (N × H)
11. Q₈×C₁₃	C₂×C₇	semidirect
13. Dic₂₆	C₂×C₇	semidirect
14. C₇×C₁₃	C₂×Q₈	semidirect
16. C₇×Q₈	D₁₃	direct (N × H)
25. D₁₃	C₇×Q₈	direct (N × H)
29. C₁₃	C₂×C₇×Q₈	semidirect
31. Q₈	C₇×D₁₃	direct (N × H)
33. C₇	Q₈×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
C₇×Q₈×C₁₃	2
C₄×C₇×D₁₃	2
C₇×Dic₂₆	2
Q₈×D₁₃	7
C₂×C₇×Q₈	13

Subgroups — C7×Q8×D13 #13089888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Q₈×D₁₃ #13089888