Subgroups — C₂×Q₁₆×C₁₃⋊C₃ #11928739

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃⋊C₃	C₂	1	2	yes	maximal
2	Q₁₆×C₁₃⋊C₃	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₁₆	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	Q₈×C₁₃⋊C₃	—	2	2	no	—
6	Q₈×C₁₃⋊C₃	C₂²	1	4	yes	—
7	C₂×C₄×C₁₃⋊C₃	—	2	2	no	—
8	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
9	C₈×C₁₃⋊C₃	C₂²	1	2	yes	—
10	C₂×Q₈×C₁₃	C₂×C₃	1	2	yes	—
11	C₁₃×Q₁₆	C₂×C₃	1	4	yes	complemented
12	C₂×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₁₃⋊C₃	D₄	1	1	yes	characteristic
14	C₄×C₁₃⋊C₃	—	2	4	no	—
15	C₄×C₁₃⋊C₃	D₄	1	1	yes	characteristic
16	C₄×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
17	Q₈×C₁₃	—	2	2	no	—
18	Q₈×C₁₃	C₂²×C₃	1	4	yes	—
19	C₂×C₄×C₁₃	—	2	2	no	—
20	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
21	C₈×C₁₃	C₂²×C₃	1	2	yes	—
22	C₂×C₃×Q₁₆	—	13	1	no	maximal, Hall
23	C₂×C₁₃⋊C₃	Q₁₆	1	2	yes	direct product factor
24	C₂×C₁₃⋊C₃	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
26	C₄×C₁₃	—	2	4	no	—
27	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
28	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
29	C₂×C₃×Q₈	—	13	2	no	—
30	C₃×Q₁₆	—	13	4	no	—
31	C₂×C₃×C₈	—	13	1	no	—
32	C₁₃⋊C₃	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Hall
33	C₂×Q₁₆	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₃	C₃×Q₁₆	1	2	yes	complemented
35	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
36	C₃×Q₈	—	13	4	no	—
37	C₃×Q₈	—	26	2	no	—
38	C₂×C₃×C₄	—	13	1	no	—
39	C₂×C₃×C₄	—	26	2	no	—
40	C₃×C₈	—	13	2	no	—
41	C₂×Q₈	C₂×C₁₃⋊C₃	1	2	yes	—
42	Q₁₆	C₂×C₁₃⋊C₃	1	4	yes	direct product factor
43	C₂×C₈	C₂×C₁₃⋊C₃	1	1	yes	characteristic
44	C₁₃	C₂×C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₃	—	13	1	no	—
46	C₃×C₄	—	13	1	no	—
47	C₃×C₄	—	13	1	no	—
48	C₃×C₄	—	26	4	no	—
49	Q₈	—	2	2	no	—
50	Q₈	C₂²×C₁₃⋊C₃	1	4	yes	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
53	C₈	C₂²×C₁₃⋊C₃	1	2	yes	—
54	C₂×C₃	—	13	1	no	—
55	C₂×C₃	—	13	2	no	—
56	C₂²	D₄×C₁₃⋊C₃	1	1	yes	characteristic
57	C₄	—	2	4	no	—
58	C₄	D₄×C₁₃⋊C₃	1	1	yes	characteristic
59	C₄	C₂³×C₁₃⋊C₃	1	1	yes	characteristic
60	C₃	—	13	1	no	Sylow
61	C₂	Q₁₆×C₁₃⋊C₃	1	2	yes	direct product factor
62	C₂	C₂×D₄×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₁₃⋊C₃
commutator, cosocle	C₄×C₁₃	C₂³×C₃
Frattini	C₄	C₂³×C₁₃⋊C₃
Fitting	C₂×C₁₃×Q₁₆	C₃
socle	C₂²×C₁₃	C₃×D₄
prime radical	C₂²×C₁₃⋊C₃	D₄
hypercenter	C₂×Q₁₆	C₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×Q₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₁₆×C₁₃⋊C₃	C₂	direct (N × H)
4. C₂×C₁₃×Q₁₆	C₃	semidirect
11. C₁₃×Q₁₆	C₂×C₃	semidirect
23. C₂×C₁₃⋊C₃	Q₁₆	direct (N × H)
32. C₁₃⋊C₃	C₂×Q₁₆	direct (N × H)
33. C₂×Q₁₆	C₁₃⋊C₃	direct (N × H)
34. C₂×C₁₃	C₃×Q₁₆	semidirect
42. Q₁₆	C₂×C₁₃⋊C₃	direct (N × H)
44. C₁₃	C₂×C₃×Q₁₆	semidirect
61. C₂	Q₁₆×C₁₃⋊C₃	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×Q₈×C₁₃⋊C₃	2
Q₁₆×C₁₃⋊C₃	2
C₂×C₈×C₁₃⋊C₃	2
C₂×C₁₃×Q₁₆	3
C₂×C₃×Q₁₆	13

Subgroups — C2×Q16×C13⋊C3 #11928739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₁₆×C₁₃⋊C₃ #11928739