Subgroups — #15750821

Order 3328.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113036	C₂	1	2	yes	maximal
2	C₂×C₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
4	#11718096	—	2	2	no	—
5	C₁₃×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
7	#88058	—	4	2	no	—
8	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₁₃×C₃₂	Q₈	1	1	yes	characteristic
10	#7546	—	13	1	no	maximal, Sylow
11	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
12	C₄⋊Dic₁₃	—	8	2	no	—
13	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
14	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
15	C₂×C₆₄	D₁₃	1	1	yes	characteristic
16	#1423	—	13	2	no	—
17	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
18	C₂×Dic₁₃	—	16	2	no	—
19	C₈×C₁₃	#107	1	1	yes	characteristic
20	C₈×C₁₃	Q₃₂	1	1	yes	characteristic
21	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
22	#366	—	26	2	no	—
23	C₆₄	Dic₁₃	1	2	yes	complemented
24	C₂²×C₁₃	D₃₂	1	1	yes	characteristic
25	C₄×C₁₃	#366	1	1	yes	characteristic
26	C₄×C₁₃	Q₆₄	1	1	yes	characteristic
27	Dic₁₃	—	32	2	no	—
28	C₂×C₁₆	D₅₂	1	1	yes	characteristic
29	#107	—	52	2	no	—
30	C₃₂	Dic₂₆	1	1	yes	characteristic
31	C₃₂	C₂×Dic₁₃	1	1	yes	characteristic
32	C₂×C₁₃	#1423	1	1	yes	characteristic
33	C₂×C₁₃	SD₁₂₈	1	2	yes	—
34	C₂×C₈	D₁₀₄	1	1	yes	characteristic
35	C₄⋊C₄	—	104	2	no	—
36	C₁₆	Dic₅₂	1	1	yes	characteristic
37	C₁₆	C₄⋊Dic₁₃	1	1	yes	characteristic
38	C₁₃	#7546	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄	—	208	2	no	—
40	C₂×C₄	D₂₀₈	1	1	yes	characteristic
41	C₈	Dic₁₀₄	1	1	yes	characteristic
42	C₈	#88058	1	1	yes	characteristic
43	C₂²	D₄₁₆	1	1	yes	characteristic
44	C₄	—	416	2	no	—
45	C₄	Dic₂₀₈	1	1	yes	characteristic
46	C₄	#11718096	1	1	yes	characteristic
47	C₂	#13113036	1	1	yes	characteristic
48	C₂	#13113052	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄₁₆
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₂×C₁₃×C₆₄	C₂
socle, prime radical	C₂²×C₁₃	D₃₂
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₃
hypocenter	C₁₃	#7546
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
5. C₁₃×C₆₄	C₄	semidirect
23. C₆₄	Dic₁₃	semidirect
38. C₁₃	#7546	semidirect

Maximal subgroups

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

subgroup	index
#13113036	2
C₂×C₁₃×C₆₄	2
#7546	13