Subgroups — C₁₃×#822 #11928093

Order 1248.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#108	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₃×C₈×C₁₃	—	2	1	no	—
7	C₁₃×C₃⋊C₈	—	2	1	no	—
8	C₁₃×C₃⋊C₈	C₄	1	2	yes	—
9	C₁₃×M₁₆	—	3	1	no	—
10	C₁₃×M₁₆	D₃	1	1	yes	characteristic
11	C₂×C₈×C₁₃	—	3	1	no	—
12	C₂²×C₃×C₁₃	Q₈	1	1	yes	characteristic
13	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
16	C₈×C₁₃	—	2	1	no	—
17	C₈×C₁₃	—	3	2	no	—
18	C₈×C₁₃	—	6	1	no	—
19	#822	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃×C₁₃	—	2	1	no	—
21	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₁₃	Dic₆	1	1	yes	characteristic
23	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
24	C₄×C₁₃	#67	1	1	yes	characteristic
25	C₃×M₁₆	C₂×C₁₃	1	1	yes	characteristic
26	#208	C₂×C₁₃	1	1	yes	characteristic
27	C₂×C₃⋊C₈	C₂×C₁₃	1	1	yes	characteristic
28	C₃×C₁₃	#108	1	1	yes	characteristic, complemented, Hall
29	#108	—	3	1	no	Sylow
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	Dic₃⋊C₄	1	1	yes	characteristic
32	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
33	C₃×C₈	—	2	1	no	—
34	C₃⋊C₈	—	2	1	no	—
35	C₃⋊C₈	C₄×C₁₃	1	2	yes	—
36	M₁₆	—	3	1	no	—
37	M₁₆	D₃×C₁₃	1	1	yes	characteristic
38	C₂×C₈	—	3	1	no	—
39	C₁₃	#822	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²×C₃	Q₈×C₁₃	1	1	yes	characteristic
41	C₃×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
42	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
43	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	3	2	no	—
46	C₈	—	6	1	no	—
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₁₃×C₄⋊C₄	1	1	yes	characteristic
49	C₂²	C₁₃×Dic₆	1	1	yes	characteristic
50	C₄	C₄×D₃×C₁₃	1	1	yes	characteristic
51	C₄	C₁₃×#67	1	1	yes	characteristic
52	C₃	C₁₃×#108	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	2	1	no	—
54	C₂	C₁₃×Dic₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#67
commutator	C₃×C₄	C₂×C₄×C₁₃
Frattini	C₂×C₄	C₂×D₃×C₁₃
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₄⋊C₄
prime radical	C₂²×C₃×C₁₃	Q₈
cosocle	C₂×C₃×C₄	C₂²×C₁₃
hypercenter	C₁₃×M₁₆	D₃
hypocenter	C₃	C₁₃×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×M₁₆

Complements

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

N	H ≅ G/N	type
19. #822	C₁₃	direct (N × H)
28. C₃×C₁₃	#108	semidirect
39. C₁₃	#822	direct (N × H)
52. C₃	C₁₃×#108	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×M₁₆	2
C₁₃×#208	2
C₂×C₁₃×C₃⋊C₈	2
C₁₃×#108	3
#822	13

Subgroups — C13×#822 #11928093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#822 #11928093