Subgroups — C₃×Q₁₆×D₁₃ #11928807

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×D₁₃	C₂	1	2	yes	maximal
2	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6107	C₂	1	2	yes	maximal, complemented
4	C₃×Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
6	Q₁₆×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₃×C₄×D₁₃	—	2	2	no	—
9	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
10	C₃×Dic₂₆	—	2	2	no	—
11	C₃×Dic₂₆	C₂²	1	2	yes	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₃×#1055	C₂²	1	1	yes	characteristic
14	Q₈×D₁₃	C₂×C₃	1	2	yes	—
15	C₁₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
16	#6107	C₂×C₃	1	2	yes	complemented
17	Dic₅₂	C₂×C₃	1	1	yes	characteristic, complemented
18	C₈×D₁₃	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×D₁₃	D₄	1	1	yes	characteristic
20	C₃×C₄×C₁₃	—	2	2	no	—
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₃×Dic₁₃	—	2	2	no	—
23	C₃×Dic₁₃	D₄	1	1	yes	characteristic
24	Q₈×C₁₃	C₂²×C₃	1	2	yes	—
25	C₄×D₁₃	—	2	2	no	—
26	C₄×D₁₃	C₂²×C₃	1	1	yes	characteristic
27	Dic₂₆	—	2	2	no	—
28	Dic₂₆	C₂²×C₃	1	2	yes	—
29	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
30	#1055	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₃×Q₁₆	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₃×D₁₃	Q₁₆	1	2	yes	direct product factor
34	C₂×D₁₃	C₃×D₄	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
37	Dic₁₃	—	2	2	no	—
38	Dic₁₃	C₃×D₄	1	1	yes	characteristic
39	C₂×C₃×Q₈	—	13	2	no	—
40	C₃×Q₁₆	—	13	2	no	—
41	C₃×Q₁₆	—	13	1	no	—
42	C₃×Q₁₆	D₁₃	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₈	—	13	1	no	—
44	C₃×C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
45	C₂×Q₁₆	—	13	1	no	Sylow
46	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
47	D₁₃	C₃×Q₁₆	1	2	yes	direct product factor
48	C₃×Q₈	—	13	2	no	—
49	C₃×Q₈	—	26	2	no	—
50	C₃×Q₈	C₂×D₁₃	1	2	yes	—
51	C₂×C₃×C₄	—	13	1	no	—
52	C₂×C₃×C₄	—	26	2	no	—
53	C₃×C₈	—	13	1	no	—
54	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
55	C₂×Q₈	—	13	2	no	—
56	Q₁₆	—	13	2	no	—
57	Q₁₆	—	13	1	no	—
58	Q₁₆	C₃×D₁₃	1	1	yes	characteristic, direct product factor
59	C₂×C₈	—	13	1	no	—
60	C₁₃	C₂×C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	—	13	1	no	—
62	C₃×C₄	—	2	2	no	—
63	C₃×C₄	—	13	1	no	—
64	C₃×C₄	—	26	2	no	—
65	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
66	Q₈	—	13	2	no	—
67	Q₈	—	26	2	no	—
68	Q₈	C₂×C₃×D₁₃	1	2	yes	—
69	C₂×C₄	—	13	1	no	—
70	C₂×C₄	—	26	2	no	—
71	C₈	—	13	1	no	—
72	C₈	C₂×C₃×D₁₃	1	1	yes	characteristic
73	C₂×C₃	—	13	2	no	—
74	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
75	C₂²	—	13	1	no	—
76	C₄	—	2	2	no	—
77	C₄	—	13	1	no	—
78	C₄	—	26	2	no	—
79	C₄	C₂²×C₃×D₁₃	1	1	yes	characteristic
80	C₃	Q₁₆×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	—	13	2	no	—
82	C₂	C₃×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₁₃
Fitting	C₃×C₁₃×Q₁₆	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
prime radical	C₂×C₃×D₁₃	D₄
hypercenter	C₃×Q₁₆	D₁₃
hypocenter	C₁₃	C₂×C₃×Q₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×Q₁₆	C₂	semidirect
3. C₃×#6107	C₂	semidirect
4. C₃×Dic₅₂	C₂	semidirect
6. Q₁₆×D₁₃	C₃	direct (N × H)
15. C₁₃×Q₁₆	C₂×C₃	semidirect
16. #6107	C₂×C₃	semidirect
17. Dic₅₂	C₂×C₃	semidirect
33. C₃×D₁₃	Q₁₆	direct (N × H)
42. C₃×Q₁₆	D₁₃	direct (N × H)
44. C₃×C₁₃	C₂×Q₁₆	semidirect
47. D₁₃	C₃×Q₁₆	direct (N × H)
58. Q₁₆	C₃×D₁₃	direct (N × H)
60. C₁₃	C₂×C₃×Q₁₆	semidirect
80. C₃	Q₁₆×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×D₁₃	2
C₃×C₁₃×Q₁₆	2
C₃×#6107	2
C₃×Dic₅₂	2
C₃×C₈×D₁₃	2
Q₁₆×D₁₃	3
C₂×C₃×Q₁₆	13

Subgroups — C3×Q16×D13 #11928807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₁₆×D₁₃ #11928807