Subgroups — #13113031

Order 1664.

62 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	—	2	1	no	—
8	#88034	—	2	1	no	—
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	D₄	1	1	yes	characteristic
13	C₁₃×C₁₆	Q₈	1	1	yes	characteristic
14	#6090	—	2	1	no	—
15	C₄⋊C₃₂	—	13	1	no	maximal, Sylow
16	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
18	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
19	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
20	C₈×C₁₃	M₁₆	1	1	yes	characteristic
21	#1055	—	2	1	no	—
22	C₂×C₃₂	—	13	1	no	—
23	C₂×C₃₂	D₁₃	1	1	yes	characteristic
24	C₄×C₁₆	—	13	1	no	—
25	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
26	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₃	M₃₂	1	1	yes	characteristic
28	Dic₁₃	—	2	1	no	—
29	Dic₁₃	C₃₂	1	2	yes	complemented
30	C₂×C₁₆	—	13	1	no	—
31	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
32	C₄×C₈	—	13	1	no	—
33	C₃₂	—	2	1	no	—
34	C₃₂	—	26	1	no	—
35	C₂×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
36	C₂×C₁₃	C₂×C₃₂	1	1	yes	characteristic
37	C₂×C₁₃	M₆₄	1	1	yes	characteristic
38	C₂×C₈	—	13	1	no	—
39	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
40	C₄²	—	13	1	no	—
41	C₁₆	—	26	1	no	—
42	C₁₆	Dic₂₆	1	1	yes	characteristic
43	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
44	C₁₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄	—	13	1	no	—
46	C₂×C₄	—	13	1	no	—
47	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
48	C₈	—	26	1	no	—
49	C₈	#6094	1	1	yes	characteristic
50	C₈	#6101	1	1	yes	characteristic
51	C₂²	C₁₆×D₁₃	1	1	yes	characteristic
52	C₄	—	13	2	no	—
53	C₄	—	26	1	no	—
54	C₄	#88038	1	1	yes	characteristic
55	C₄	#88054	1	1	yes	characteristic
56	C₂	D₁₃×C₃₂	1	1	yes	characteristic
57	C₂	#11718039	1	1	yes	characteristic
58	C₂	#11718093	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₃₂
Fitting	C₂×C₁₃×C₃₂	C₂
socle, prime radical	C₂²×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	C₄⋊C₃₂
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
29. Dic₁₃	C₃₂	semidirect
44. C₁₃	C₄⋊C₃₂	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
C₄⋊C₃₂	13