Subgroups — #13112970

Order 1664.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#88034	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	#88034	C₄	1	4	yes	complemented
7	C₂×C₈×C₁₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₃	C₈	1	1	yes	characteristic
10	C₁₃×C₁₆	C₈	1	2	yes	—
11	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
12	#1397	—	13	1	no	maximal, Sylow
13	C₂×C₄×C₁₃	C₁₆	1	2	yes	—
14	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₃	C₁₆	1	2	yes	—
16	C₈×C₁₃	C₄²	1	1	yes	characteristic
17	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₃₂	—	13	2	no	—
19	C₄×C₁₆	D₁₃	1	1	yes	characteristic
20	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₁₃	—	2	2	no	—
22	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
23	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₁₆	Dic₁₃	1	1	yes	characteristic
25	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
26	C₄×C₈	Dic₁₃	1	1	yes	characteristic
27	C₃₂	—	13	4	no	—
28	C₂×C₁₃	C₄×C₁₆	1	1	yes	characteristic
29	C₂×C₁₃	M₆₄	1	2	yes	—
30	C₂×C₈	#1055	1	1	yes	characteristic
31	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
32	C₄²	#1055	1	1	yes	characteristic
33	C₁₆	#1055	1	2	yes	—
34	C₁₆	C₄×D₁₃	1	2	yes	—
35	C₁₃	#1397	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₄	#6090	1	2	yes	—
37	C₂×C₄	C₂×#1055	1	1	yes	characteristic
38	C₈	#6090	1	2	yes	—
39	C₈	C₂×#1055	1	1	yes	characteristic
40	C₈	C₄×Dic₁₃	1	1	yes	characteristic
41	C₂²	C₂×#6090	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₄×#1055	1	1	yes	characteristic
44	C₄	C₂×#6090	1	1	yes	characteristic
45	C₂	C₄×#6090	1	1	yes	characteristic
46	C₂	#11718091	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₄×C₁₆
Fitting	C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	C₄×C₁₆	D₁₃
hypocenter	C₁₃	#1397
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
6. #88034	C₄	semidirect
35. C₁₃	#1397	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×C₁₆	2
C₂×#88034	2
#1397	13