Subgroups — C₁₃×#829 #11928100

Order 1248.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×Q₃₂	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₃	—	2	1	no	—
6	C₁₃×Dic₆	—	2	1	no	—
7	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×Q₁₆	—	3	1	no	—
9	C₁₃×Q₁₆	D₃	1	1	yes	characteristic
10	C₁₃×C₁₆	—	3	1	no	—
11	C₃×C₄×C₁₃	—	4	1	no	—
12	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
13	Dic₃×C₁₃	—	4	1	no	—
14	Q₈×C₁₃	—	2	1	no	—
15	Q₈×C₁₃	—	6	1	no	—
16	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
17	#829	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
19	C₄×C₁₃	—	4	1	no	—
20	C₄×C₁₃	—	12	1	no	—
21	C₄×C₁₃	#67	1	1	yes	characteristic
22	C₃×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
23	Dic₁₂	C₂×C₁₃	1	1	yes	characteristic
24	C₃⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
25	C₃×C₁₃	Q₃₂	1	1	yes	characteristic, complemented, Hall
26	Q₃₂	—	3	1	no	Sylow
27	C₂×C₁₃	#213	1	1	yes	characteristic
28	C₃×Q₈	—	2	1	no	—
29	Dic₆	—	2	1	no	—
30	C₃×C₈	C₂²×C₁₃	1	1	yes	characteristic
31	Q₁₆	—	3	1	no	—
32	Q₁₆	D₃×C₁₃	1	1	yes	characteristic
33	C₁₆	—	3	1	no	—
34	C₁₃	#829	1	1	yes	characteristic, direct product factor, Sylow
35	C₃×C₄	—	4	1	no	—
36	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
37	Dic₃	—	4	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	6	1	no	—
40	C₈	C₂×D₃×C₁₃	1	1	yes	characteristic
41	C₂×C₃	C₁₃×D₈	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	—	12	1	no	—
44	C₄	C₁₃×#67	1	1	yes	characteristic
45	C₃	C₁₃×Q₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₁₃×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	#213
commutator, cosocle	C₃×C₈	C₂²×C₁₃
Frattini	C₈	C₂×D₃×C₁₃
Fitting	C₃×C₁₃×Q₁₆	C₂
socle, prime radical	C₂×C₃×C₁₃	D₈
hypercenter	C₁₃×Q₁₆	D₃
hypocenter	C₃	C₁₃×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₈×C₁₃ ◁ C₁₃×Q₁₆

Complements

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

N	H ≅ G/N	type
17. #829	C₁₃	direct (N × H)
25. C₃×C₁₃	Q₃₂	semidirect
34. C₁₃	#829	direct (N × H)
45. C₃	C₁₃×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×Q₁₆	2
C₁₃×Dic₁₂	2
C₁₃×C₃⋊C₁₆	2
C₁₃×Q₃₂	3
#829	13

Subgroups — C13×#829 #11928100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#829 #11928100