Subgroups — C₁₃×#1426 #13110484

Order 1664.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#368	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#367	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₁₃×#108	—	2	1	no	—
6	C₁₃×#107	—	2	1	no	—
7	C₁₃×C₃₂	C₄	1	2	yes	complemented
8	C₁₃×M₁₆	—	4	1	no	—
9	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
10	C₁₃×C₄⋊C₄	—	4	1	no	—
11	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₁₃×C₁₆	Q₈	1	1	yes	characteristic
13	#1426	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₄×C₁₃	—	8	1	no	—
15	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
16	C₈×C₁₃	—	8	1	no	—
17	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
19	M₆₄	C₂×C₁₃	1	1	yes	characteristic
20	#368	C₂×C₁₃	1	1	yes	characteristic
21	#367	C₂×C₁₃	1	1	yes	characteristic
22	C₂²×C₁₃	SD₃₂	1	1	yes	characteristic
23	C₄×C₁₃	—	16	1	no	—
24	C₄×C₁₃	#107	1	1	yes	characteristic
25	C₄×C₁₃	SD₃₂	1	1	yes	characteristic
26	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
27	#108	—	2	1	no	—
28	#107	—	2	1	no	—
29	C₃₂	C₄×C₁₃	1	2	yes	complemented
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	#367	1	1	yes	characteristic
32	M₁₆	—	4	1	no	—
33	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
34	C₄⋊C₄	—	4	1	no	—
35	C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
36	C₁₆	Q₈×C₁₃	1	1	yes	characteristic
37	C₁₃	#1426	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₄	—	8	1	no	—
39	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
42	C₈	C₁₃×Q₁₆	1	1	yes	characteristic
43	C₂²	C₁₃×SD₃₂	1	1	yes	characteristic
44	C₄	—	16	1	no	—
45	C₄	C₁₃×#107	1	1	yes	characteristic
46	C₄	C₁₃×SD₃₂	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₁₃×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#367
commutator	C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₃
prime radical	C₂²×C₁₃	SD₃₂
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
7. C₁₃×C₃₂	C₄	semidirect
13. #1426	C₁₃	direct (N × H)
29. C₃₂	C₄×C₁₃	semidirect
37. C₁₃	#1426	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×M₆₄	2
C₁₃×#368	2
C₁₃×#367	2
#1426	13

Subgroups — C13×#1426 #13110484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1426 #13110484