Subgroups — #13112969

Order 1664.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#88034	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₁₃×C₃₂	C₄	1	2	yes	complemented
8	#88034	C₄	1	2	yes	complemented
9	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₁₃	C₈	1	1	yes	characteristic
11	C₂×#1055	C₈	1	1	yes	characteristic
12	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
14	#6090	C₈	1	2	yes	—
15	#1397	—	13	1	no	maximal, Sylow
16	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₃	C₁₆	1	2	yes	—
18	C₈×C₁₃	C₄²	1	1	yes	characteristic
19	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
20	#1055	C₁₆	1	2	yes	—
21	C₂×C₃₂	—	13	1	no	—
22	C₂×C₃₂	D₁₃	1	1	yes	characteristic
23	C₄×C₁₆	—	13	1	no	—
24	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
25	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
26	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
27	Dic₁₃	—	2	2	no	—
28	C₂×C₁₆	—	13	1	no	—
29	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
30	C₄×C₈	—	13	1	no	—
31	C₃₂	—	13	2	no	—
32	C₃₂	Dic₁₃	1	2	yes	complemented
33	C₂×C₁₃	C₄×C₁₆	1	1	yes	characteristic
34	C₂×C₁₃	M₆₄	1	2	yes	—
35	C₂×C₈	—	13	1	no	—
36	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
37	C₄²	—	13	1	no	—
38	C₁₆	—	13	2	no	—
39	C₁₆	C₄×D₁₃	1	1	yes	characteristic
40	C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
41	C₁₃	#1397	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₄	—	13	2	no	—
43	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
44	C₈	—	13	2	no	—
45	C₈	C₈×D₁₃	1	1	yes	characteristic
46	C₈	C₄×Dic₁₃	1	1	yes	characteristic
47	C₂²	C₁₆×D₁₃	1	1	yes	characteristic
48	C₄	—	26	2	no	—
49	C₄	C₁₆×D₁₃	1	1	yes	characteristic
50	C₄	C₈×Dic₁₃	1	1	yes	characteristic
51	C₂	#11718039	1	2	yes	—
52	C₂	C₁₆×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₄×C₁₆
Fitting	C₂×C₁₃×C₃₂	C₂
socle, prime radical	C₂²×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	#1397
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
7. C₁₃×C₃₂	C₄	semidirect
8. #88034	C₄	semidirect
32. C₃₂	Dic₁₃	semidirect
41. C₁₃	#1397	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×C₃₂	2
C₁₆×Dic₁₃	2
C₂×#88034	2
#1397	13