Subgroups — C₁₃×#870 #11928846

Order 1248.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₁₃×Dic₃⋊C₄	C₂	1	4	yes	maximal
4	C₁₃×#125	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₃×C₁₃	C₂²	1	4	yes	—
8	C₁₃×C₄⋊C₄	—	3	4	no	—
9	C₁₃×C₄⋊C₄	—	3	2	no	—
10	C₄²×C₁₃	D₃	1	1	yes	characteristic
11	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	C₃×C₄×C₁₃	—	2	2	no	—
13	C₃×C₄×C₁₃	Q₈	1	2	yes	—
14	Dic₃×C₁₃	—	2	4	no	—
15	C₂×C₄×C₁₃	—	3	4	no	—
16	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
17	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
18	#870	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₃×C₁₃	#41	1	2	yes	—
21	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
22	C₄×C₁₃	—	2	2	no	—
23	C₄×C₁₃	—	6	4	no	—
24	C₄×C₁₃	Dic₆	1	2	yes	—
25	C₃×C₄²	C₂×C₁₃	1	1	yes	characteristic
26	C₄⋊Dic₃	C₂×C₁₃	1	2	yes	—
27	Dic₃⋊C₄	C₂×C₁₃	1	4	yes	—
28	C₃×C₁₃	#125	1	1	yes	characteristic, complemented, Hall
29	#125	—	3	1	no	Sylow
30	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
31	C₂×C₁₃	#235	1	2	yes	—
32	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
33	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
34	C₂×Dic₃	C₂²×C₁₃	1	4	yes	—
35	C₄⋊C₄	—	3	4	no	—
36	C₄⋊C₄	—	3	2	no	—
37	C₄²	D₃×C₁₃	1	1	yes	characteristic
38	C₁₃	#870	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
40	C₃×C₄	—	2	2	no	—
41	C₃×C₄	Q₈×C₁₃	1	2	yes	—
42	Dic₃	—	2	4	no	—
43	C₂×C₄	—	3	4	no	—
44	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
45	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
46	C₂×C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic
47	C₂×C₃	C₁₃×#41	1	2	yes	—
48	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	6	4	no	—
51	C₄	C₁₃×Dic₆	1	2	yes	—
52	C₃	C₁₃×#125	1	1	yes	characteristic, complemented, Sylow
53	C₂	C₂×C₁₃×Dic₆	1	1	yes	characteristic
54	C₂	C₁₃×#235	1	2	yes	—

	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×#125
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
18. #870	C₁₃	direct (N × H)
28. C₃×C₁₃	#125	semidirect
38. C₁₃	#870	direct (N × H)
52. C₃	C₁₃×#125	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₃	2
C₁₃×C₄⋊Dic₃	2
C₁₃×Dic₃⋊C₄	2
C₁₃×#125	3
#870	13

Subgroups — C13×#870 #11928846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#870 #11928846