Subgroups — C₃×Q₈×D₁₃ #10597773

Order 624.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₁₃	C₂	1	3	yes	maximal
3	C₃×Dic₂₆	C₂	1	3	yes	maximal, complemented
4	Q₈×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×D₁₃	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₃×Dic₁₃	C₂²	1	3	yes	—
8	Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₄×D₁₃	C₂×C₃	1	3	yes	—
10	Dic₂₆	C₂×C₃	1	3	yes	complemented
11	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	C₃×D₁₃	Q₈	1	2	yes	direct product factor
13	C₂×D₁₃	C₂²×C₃	1	1	yes	characteristic
14	C₄×C₁₃	C₂²×C₃	1	3	yes	—
15	Dic₁₃	C₂²×C₃	1	3	yes	—
16	C₂×C₃×Q₈	—	13	1	no	maximal, Hall
17	C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃	C₂³×C₃	1	1	yes	characteristic
19	D₁₃	C₃×Q₈	1	2	yes	direct product factor
20	C₃×Q₈	—	13	3	no	—
21	C₃×Q₈	D₁₃	1	1	yes	characteristic, direct product factor
22	C₂×C₃×C₄	—	13	3	no	—
23	C₂×Q₈	—	13	1	no	Sylow
24	C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₃	—	13	1	no	—
26	C₃×C₄	—	13	3	no	—
27	C₃×C₄	C₂×D₁₃	1	3	yes	—
28	Q₈	—	13	3	no	—
29	Q₈	C₃×D₁₃	1	1	yes	characteristic, direct product factor
30	C₂×C₄	—	13	3	no	—
31	C₂×C₃	—	13	2	no	—
32	C₂×C₃	C₂²×D₁₃	1	1	yes	characteristic
33	C₂²	—	13	1	no	—
34	C₄	—	13	3	no	—
35	C₄	C₂×C₃×D₁₃	1	3	yes	—
36	C₃	Q₈×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	13	2	no	—
38	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×Q₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂³
prime radical	C₂×C₃×D₁₃	C₂²
hypercenter	C₃×Q₈	D₁₃
hypocenter	C₁₃	C₂×C₃×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₁₃	C₂	semidirect
3. C₃×Dic₂₆	C₂	semidirect
4. Q₈×D₁₃	C₃	direct (N × H)
8. Q₈×C₁₃	C₂×C₃	semidirect
10. Dic₂₆	C₂×C₃	semidirect
12. C₃×D₁₃	Q₈	direct (N × H)
17. C₃×C₁₃	C₂×Q₈	semidirect
19. D₁₃	C₃×Q₈	direct (N × H)
21. C₃×Q₈	D₁₃	direct (N × H)
24. C₁₃	C₂×C₃×Q₈	semidirect
29. Q₈	C₃×D₁₃	direct (N × H)
36. C₃	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
C₃×Q₈×C₁₃	2
C₃×C₄×D₁₃	2
C₃×Dic₂₆	2
Q₈×D₁₃	3
C₂×C₃×Q₈	13

Subgroups — C3×Q8×D13 #10597773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×D₁₃ #10597773