Subgroups — C₁₃×#1419 #13110477

Order 1664.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₈	—	2	1	no	—
5	C₁₃×D₁₆	—	2	1	no	—
6	C₁₃×D₁₆	C₄	1	2	yes	—
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#108	—	2	1	no	—
9	C₁₃×C₃₂	—	2	1	no	—
10	C₂×D₄×C₁₃	—	4	1	no	—
11	C₁₃×D₈	—	2	2	no	—
12	C₁₃×D₈	—	4	1	no	—
13	C₁₃×M₁₆	—	4	1	no	—
14	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₃×C₁₆	D₄	1	1	yes	characteristic
17	#1419	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂³×C₁₃	—	8	1	no	—
19	D₄×C₁₃	—	4	2	no	—
20	D₄×C₁₃	—	8	1	no	—
21	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
22	C₈×C₁₃	—	8	1	no	—
23	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
25	C₂×D₁₆	C₂×C₁₃	1	1	yes	characteristic
26	M₆₄	C₂×C₁₃	1	1	yes	characteristic, complemented
27	#368	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₂²×C₁₃	—	8	2	no	—
29	C₂²×C₁₃	—	16	2	no	—
30	C₂²×C₁₃	SD₃₂	1	1	yes	characteristic
31	C₄×C₁₃	#102	1	1	yes	characteristic
32	C₄×C₁₃	D₁₆	1	1	yes	characteristic
33	C₂×D₈	—	2	1	no	—
34	D₁₆	—	2	1	no	—
35	D₁₆	C₄×C₁₃	1	2	yes	—
36	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
37	#108	—	2	1	no	—
38	C₃₂	—	2	1	no	—
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	—	16	2	no	—
41	C₂×C₁₃	#357	1	1	yes	characteristic
42	C₂×D₄	—	4	1	no	—
43	D₈	—	2	2	no	—
44	D₈	—	4	1	no	—
45	M₁₆	—	4	1	no	—
46	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
47	C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
48	C₁₆	D₄×C₁₃	1	1	yes	characteristic
49	C₁₃	#1419	1	1	yes	characteristic, direct product factor, Sylow
50	C₂³	—	8	1	no	—
51	D₄	—	4	2	no	—
52	D₄	—	8	1	no	—
53	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
56	C₈	C₁₃×SD₁₆	1	1	yes	characteristic
57	C₂²	—	8	2	no	—
58	C₂²	—	16	2	no	—
59	C₂²	C₁₃×SD₃₂	1	1	yes	characteristic
60	C₄	C₁₃×#102	1	1	yes	characteristic
61	C₄	C₁₃×D₁₆	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	16	2	no	—
64	C₂	C₁₃×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#357
commutator	C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₃
prime radical	C₂×C₁₃×D₁₆	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₂×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×M₆₄	C₂	semidirect
3. C₁₃×#368	C₂	semidirect
17. #1419	C₁₃	direct (N × H)
26. M₆₄	C₂×C₁₃	semidirect
27. #368	C₂×C₁₃	semidirect
49. C₁₃	#1419	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×D₁₆	2
C₁₃×M₆₄	2
C₁₃×#368	2
#1419	13

Subgroups — C13×#1419 #13110477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1419 #13110477