Subgroups — C₁₃×#869 #11928845

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊Dic₃	C₂	1	4	yes	maximal
4	C₁₃×C₄⋊Q₈	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
7	C₂×Dic₃×C₁₃	C₂²	1	4	yes	—
8	C₁₃×Dic₆	—	2	4	no	—
9	C₂×Q₈×C₁₃	—	3	2	no	—
10	C₁₃×C₄⋊C₄	—	3	4	no	—
11	C₄²×C₁₃	D₃	1	1	yes	characteristic
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₃	D₄	1	2	yes	—
14	C₃×C₄×C₁₃	Q₈	1	4	yes	complemented
15	Dic₃×C₁₃	—	2	4	no	—
16	Q₈×C₁₃	—	6	4	no	—
17	C₂×C₄×C₁₃	—	3	4	no	—
18	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
19	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
20	#869	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	—
23	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
24	C₄×C₁₃	—	6	4	no	—
25	C₄×C₁₃	Dic₆	1	4	yes	complemented
26	C₄×C₁₃	D₁₂	1	2	yes	—
27	C₂×Dic₆	C₂×C₁₃	1	2	yes	—
28	C₃×C₄²	C₂×C₁₃	1	1	yes	characteristic
29	C₄⋊Dic₃	C₂×C₁₃	1	4	yes	—
30	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
31	C₄⋊Q₈	—	3	1	no	Sylow
32	C₂×C₁₃	C₂×Dic₆	1	2	yes	—
33	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
35	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
36	C₂×Dic₃	C₂²×C₁₃	1	4	yes	—
37	Dic₆	—	2	4	no	—
38	C₂×Q₈	—	3	2	no	—
39	C₄⋊C₄	—	3	4	no	—
40	C₄²	D₃×C₁₃	1	1	yes	characteristic
41	C₁₃	#869	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
43	C₃×C₄	D₄×C₁₃	1	2	yes	—
44	C₃×C₄	Q₈×C₁₃	1	4	yes	complemented
45	Dic₃	—	2	4	no	—
46	Q₈	—	6	4	no	—
47	C₂×C₄	—	3	4	no	—
48	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
49	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
50	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
51	C₂×C₃	C₂×Q₈×C₁₃	1	2	yes	—
52	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
53	C₄	—	6	4	no	—
54	C₄	C₁₃×Dic₆	1	4	yes	complemented
55	C₄	C₁₃×D₁₂	1	2	yes	—
56	C₃	C₁₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
57	C₂	C₂×C₁₃×Dic₆	1	2	yes	—
58	C₂	C₂×C₁₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₄²×C₁₃	D₃
hypocenter	C₃	C₁₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃

Complements

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

N	H ≅ G/N	type
14. C₃×C₄×C₁₃	Q₈	semidirect
20. #869	C₁₃	direct (N × H)
25. C₄×C₁₃	Dic₆	semidirect
30. C₃×C₁₃	C₄⋊Q₈	semidirect
41. C₁₃	#869	direct (N × H)
44. C₃×C₄	Q₈×C₁₃	semidirect
54. C₄	C₁₃×Dic₆	semidirect
56. C₃	C₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Dic₆	2
C₃×C₄²×C₁₃	2
C₁₃×C₄⋊Dic₃	2
C₁₃×C₄⋊Q₈	3
#869	13

Subgroups — C13×#869 #11928845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#869 #11928845