Subgroups — C₁₃×#1357 #13110415

Order 1664.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#364	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×D₈	—	2	2	no	—
4	C₁₃×#127	C₄	1	2	yes	—
5	C₁₃×M₃₂	—	2	2	no	—
6	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₁₃	—	2	2	no	—
8	C₂×D₄×C₁₃	—	4	2	no	—
9	C₁₃×D₈	—	4	2	no	—
10	C₁₃×D₈	—	4	2	no	—
11	C₂×C₈×C₁₃	D₄	1	2	yes	—
12	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₁₆	—	4	2	no	—
14	#1357	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂³×C₁₃	—	4	2	no	—
16	D₄×C₁₃	—	4	4	no	—
17	D₄×C₁₃	—	8	4	no	—
18	C₂×C₄×C₁₃	—	2	1	no	—
19	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₁₃	D₈	1	2	yes	—
21	C₈×C₁₃	SD₁₆	1	2	yes	—
22	#493	C₂×C₁₃	1	1	yes	characteristic
23	#364	C₂×C₁₃	1	2	yes	complemented
24	C₂²×C₁₃	—	8	4	no	—
25	C₂²×C₁₃	—	8	2	no	—
26	C₂²×C₁₃	#100	1	1	yes	characteristic
27	C₄×C₁₃	—	2	2	no	—
28	C₄×C₁₃	#102	1	2	yes	—
29	C₂×D₈	—	2	2	no	—
30	#127	C₄×C₁₃	1	2	yes	—
31	M₃₂	—	2	2	no	—
32	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
33	C₂×C₁₃	—	2	1	no	—
34	C₂×C₁₃	—	16	2	no	—
35	C₂×C₁₃	#331	1	1	yes	characteristic
36	C₂×D₄	—	2	2	no	—
37	C₂×D₄	—	4	2	no	—
38	D₈	—	4	2	no	—
39	D₈	—	4	2	no	—
40	C₂×C₈	D₄×C₁₃	1	2	yes	—
41	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
42	C₁₆	—	4	2	no	—
43	C₁₃	#1357	1	1	yes	characteristic, direct product factor, Sylow
44	C₂³	—	4	2	no	—
45	D₄	—	4	4	no	—
46	D₄	—	8	4	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
49	C₈	C₁₃×D₈	1	2	yes	—
50	C₈	C₁₃×SD₁₆	1	2	yes	—
51	C₂²	—	8	4	no	—
52	C₂²	—	8	2	no	—
53	C₂²	C₁₃×#100	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₁₃×#102	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	16	2	no	—
58	C₂	C₁₃×#331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#331
commutator	C₄²	C₂×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₃
prime radical	C₁₃×#493	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#364	C₂	semidirect
14. #1357	C₁₃	direct (N × H)
23. #364	C₂×C₁₃	semidirect
43. C₁₃	#1357	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#493	2
C₁₃×#364	2
#1357	13

Subgroups — C13×#1357 #13110415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1357 #13110415