Subgroups — #15750730

Order 3328.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113047	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₁₃×M₆₄	—	2	2	no	—
5	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
6	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
7	#11718035	—	2	2	no	—
8	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	—	2	1	no	—
10	C₂×C₁₃×C₁₆	—	2	1	no	—
11	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₃₂	—	2	1	no	—
14	C₁₃×C₃₂	D₄	1	2	yes	—
15	#7513	—	13	1	no	maximal, Sylow
16	C₂²×C₄×C₁₃	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₃	—	2	1	no	—
18	C₂×C₈×C₁₃	—	2	1	no	—
19	C₂×C₈×C₁₃	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
21	C₁₃×C₁₆	—	2	1	no	—
22	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
24	C₂×M₆₄	D₁₃	1	1	yes	characteristic
25	M₁₂₈	—	13	2	no	—
26	C₂³×C₁₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	—	2	1	no	—
29	C₂×C₄×C₁₃	C₃₂	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₁₃	—	2	1	no	—
32	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₈×C₁₃	M₃₂	1	1	yes	characteristic
34	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
35	M₆₄	—	2	2	no	—
36	C₂×C₃₂	Dic₁₃	1	1	yes	characteristic
37	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
38	C₆₄	—	26	2	no	—
39	C₂²×C₁₃	—	2	1	no	—
40	C₂²×C₁₃	—	4	1	no	—
41	C₂²×C₁₃	C₂×C₃₂	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₄×C₁₃	M₆₄	1	1	yes	characteristic
45	C₂²×C₈	#1055	1	1	yes	characteristic
46	C₂×C₁₆	—	2	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	#1055	1	1	yes	characteristic
49	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
50	C₃₂	—	2	1	no	—
51	C₃₂	C₂²⋊D₁₃	1	2	yes	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	—	4	1	no	—
54	C₂×C₁₃	C₂²⋊C₃₂	1	1	yes	characteristic
55	C₂²×C₄	#6090	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	#6090	1	1	yes	characteristic
59	C₂×C₈	C₂×#1055	1	1	yes	characteristic
60	C₁₆	—	2	1	no	—
61	C₁₆	#6099	1	1	yes	characteristic
62	C₁₆	C₂²⋊Dic₁₃	1	1	yes	characteristic
63	C₁₃	#7513	1	1	yes	characteristic, complemented, Sylow
64	C₂³	#88034	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#88034	1	1	yes	characteristic
68	C₂×C₄	C₂×#6090	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	#88052	1	1	yes	characteristic
71	C₈	C₂²⋊#1055	1	1	yes	characteristic
72	C₂²	—	2	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×#88034	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#11718091	1	1	yes	characteristic
77	C₄	C₂²⋊#6090	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	4	1	no	—
80	C₂	C₂²⋊#88034	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊Dic₁₃
commutator	C₂²×C₁₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₂×C₁₃×M₆₄	C₂
socle	C₂×C₁₃	C₂²⋊C₃₂
prime radical	C₂³×C₁₃	C₃₂
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	C₂×M₆₄	D₁₃
hypocenter	C₁₃	#7513
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
1. #13113047	C₂	semidirect
63. C₁₃	#7513	semidirect

Maximal subgroups

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

subgroup	index
#13113047	2
C₂×C₁₃×M₆₄	2
#7513	13