Subgroups — #13129952

Order 1664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88038	C₂	1	1	yes	maximal, characteristic
2	#11718249	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×#6090	C₂²	1	1	yes	characteristic
6	#88038	—	2	2	no	—
7	#88036	—	2	2	no	—
8	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×#1055	C₈	1	1	yes	characteristic
11	C₈×D₁₃	—	2	1	no	—
12	C₈×D₁₃	—	2	1	no	—
13	C₁₃×C₁₆	—	2	1	no	—
14	#6090	D₄	1	2	yes	—
15	#1400	—	13	1	no	maximal, Sylow
16	C₂²×D₁₃	C₁₆	1	1	yes	characteristic
17	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
19	C₄×D₁₃	—	2	1	no	—
20	C₄×D₁₃	—	2	1	no	—
21	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₃	M₁₆	1	1	yes	characteristic
23	#1055	—	2	1	no	—
24	C₂×M₃₂	—	13	1	no	—
25	M₆₄	—	13	2	no	—
26	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
27	C₂×D₁₃	—	2	1	no	—
28	C₂×D₁₃	—	4	1	no	—
29	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₁₃	M₃₂	1	1	yes	characteristic
31	Dic₁₃	—	2	1	no	—
32	C₂²×C₈	—	13	1	no	—
33	M₃₂	—	26	2	no	—
34	C₂×C₁₆	—	13	1	no	—
35	C₂×C₁₆	#261	1	1	yes	characteristic
36	C₃₂	—	26	2	no	—
37	C₂×C₁₃	—	2	1	no	—
38	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
39	D₁₃	—	4	1	no	—
40	C₂²×C₄	—	13	1	no	—
41	C₂×C₈	—	13	1	no	—
42	C₂×C₈	—	26	1	no	—
43	C₂×C₈	—	26	1	no	—
44	C₂×C₈	C₂×#261	1	1	yes	characteristic
45	C₁₆	—	2	1	no	—
46	C₁₆	—	13	2	no	—
47	C₁₃	#1400	1	1	yes	characteristic, complemented, Sylow
48	C₂³	—	13	1	no	—
49	C₂×C₄	—	13	1	no	—
50	C₂×C₄	—	26	1	no	—
51	C₂×C₄	—	26	1	no	—
52	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
53	C₈	—	26	1	no	—
54	C₈	#6118	1	1	yes	characteristic
55	C₈	C₂²⋊#261	1	1	yes	characteristic
56	C₂²	—	26	1	no	—
57	C₂²	—	52	1	no	—
58	C₂²	D₁₃⋊C₁₆	1	1	yes	characteristic
59	C₄	—	26	1	no	—
60	C₄	#88098	1	1	yes	characteristic
61	C₄	#88111	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	52	1	no	—
64	C₂	#11718259	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#261
commutator	C₂²×C₁₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	C₂²⋊C₁₆
prime radical	C₂²×D₁₃	C₁₆
cosocle	C₂×#6090	C₂²
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	#1400
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #11718249	C₂	semidirect
47. C₁₃	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88038	2
#11718249	2
#1400	13