Subgroups — #13112905

Order 1664.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6090	C₂	1	1	yes	maximal, characteristic
3	C₈×#1055	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₁₆	—	2	1	no	—
5	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6090	—	2	1	no	—
7	C₄×#1055	C₄	1	1	yes	characteristic
8	C₄×#1055	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
11	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×#1055	—	2	1	no	—
13	C₂×#1055	C₈	1	1	yes	characteristic
14	C₂×#1055	C₈	1	1	yes	characteristic
15	C₁₃×C₁₆	—	4	1	no	—
16	#6090	—	4	1	no	—
17	#1370	—	13	1	no	maximal, Sylow
18	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
20	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
21	C₈×C₁₃	—	2	1	no	—
22	C₈×C₁₃	D₈	1	1	yes	characteristic
23	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
24	#1055	—	2	2	no	—
25	#1055	—	2	1	no	—
26	#1055	C₁₆	1	2	yes	complemented
27	C₄⋊C₁₆	—	13	1	no	—
28	C₄⋊C₁₆	D₁₃	1	1	yes	characteristic
29	C₈²	—	13	1	no	—
30	C₂²×C₁₃	C₄⋊C₈	1	1	yes	characteristic
31	C₄×C₁₃	—	2	1	no	—
32	C₄×C₁₃	#107	1	1	yes	characteristic
33	C₄×C₁₃	#108	1	1	yes	characteristic
34	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
35	C₄×C₁₃	M₃₂	1	1	yes	characteristic
36	C₂×C₁₆	—	2	1	no	—
37	C₂×C₁₆	—	26	1	no	—
38	C₄×C₈	—	13	1	no	—
39	C₄×C₈	—	13	1	no	—
40	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
41	C₂×C₁₃	#335	1	1	yes	characteristic
42	C₂×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
43	C₂×C₁₃	#364	1	1	yes	characteristic
44	C₂×C₈	—	13	1	no	—
45	C₂×C₈	—	13	1	no	—
46	C₂×C₈	—	26	1	no	—
47	C₂×C₈	Dic₂₆	1	1	yes	characteristic
48	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
49	C₄²	C₄×D₁₃	1	1	yes	characteristic
50	C₁₆	—	4	1	no	—
51	C₁₆	—	52	1	no	—
52	C₁₃	#1370	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
54	C₂×C₄	#6094	1	1	yes	characteristic
55	C₂×C₄	#6101	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	13	2	no	—
58	C₈	—	26	2	no	—
59	C₈	—	26	1	no	—
60	C₈	#6104	1	1	yes	characteristic
61	C₈	#6107	1	1	yes	characteristic
62	C₂²	#88054	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	C₁₆×D₁₃	1	1	yes	characteristic
65	C₄	#88038	1	1	yes	characteristic
66	C₄	#88047	1	1	yes	characteristic
67	C₄	#88062	1	1	yes	characteristic
68	C₂	#11718071	1	1	yes	characteristic
69	C₂	#11718093	1	1	yes	characteristic
70	C₂	#11718103	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₁₃×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	C₄⋊C₁₆	D₁₃
hypocenter	C₁₃	#1370
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
26. #1055	C₁₆	semidirect
52. C₁₃	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₄⋊C₁₆	2
C₄⋊#6090	2
C₈×#1055	2
#1370	13