Subgroups — C₂×#13133151 #16810657

Order 3392.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₅₃	C₂	1	2	yes	maximal
2	#13133151	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₅₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₅₃	—	2	2	no	—
6	C₂×C₈×C₅₃	C₄	1	4	yes	complemented
7	C₂×C₈×C₅₃	C₂²	1	2	yes	—
8	C₄⋊Dic₅₃	—	2	2	no	—
9	C₄⋊Dic₅₃	C₂²	1	4	yes	—
10	C₂³×C₅₃	D₄	1	1	yes	characteristic
11	C₂×C₄×C₅₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₅₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₅₃	Q₈	1	2	yes	—
14	C₂×C₄×C₅₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₅₃	—	2	4	no	—
16	C₂×Dic₅₃	—	4	4	no	—
17	C₈×C₅₃	C₂×C₄	1	4	yes	complemented
18	C₂²×C₅₃	C₄⋊C₄	1	2	yes	—
19	C₂²×C₅₃	D₈	1	2	yes	—
20	C₂²×C₅₃	Q₁₆	1	2	yes	—
21	C₂²×C₅₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₅₃	C₄⋊C₄	1	2	yes	—
23	C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
25	Dic₅₃	—	4	4	no	—
26	C₂×C₅₃	#107	1	4	yes	complemented
27	C₂×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₅₃	C₂×D₈	1	1	yes	characteristic
29	C₂×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
30	C₂×#107	—	53	1	no	maximal, Sylow
31	C₅₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₈	D₅₃	1	1	yes	characteristic
33	C₂×C₄⋊C₄	—	53	2	no	—
34	#107	—	53	4	no	—
35	C₂²×C₄	—	106	2	no	—
36	C₂²×C₄	C₂×D₅₃	1	1	yes	characteristic
37	C₂×C₈	Dic₅₃	1	4	yes	complemented
38	C₂×C₈	C₂×D₅₃	1	2	yes	—
39	C₄⋊C₄	—	53	4	no	—
40	C₄⋊C₄	—	106	2	no	—
41	C₂³	D₂₁₂	1	1	yes	characteristic
42	C₂×C₄	—	106	4	no	—
43	C₂×C₄	—	212	4	no	—
44	C₂×C₄	Dic₁₀₆	1	2	yes	—
45	C₂×C₄	D₂₁₂	1	1	yes	characteristic
46	C₂×C₄	C₂×Dic₅₃	1	2	yes	—
47	C₂×C₄	C₂²×D₅₃	1	1	yes	characteristic
48	C₈	C₂×Dic₅₃	1	4	yes	complemented
49	C₂²	D₄₂₄	1	2	yes	—
50	C₂²	Dic₂₁₂	1	2	yes	—
51	C₂²	C₄⋊Dic₅₃	1	2	yes	—
52	C₂²	C₂×D₂₁₂	1	1	yes	characteristic
53	C₄	—	212	4	no	—
54	C₄	C₄⋊Dic₅₃	1	2	yes	—
55	C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
56	C₄	C₂²×Dic₅₃	1	1	yes	characteristic
57	C₂	#13133151	1	4	yes	direct product factor
58	C₂	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
59	C₂	C₂×D₄₂₄	1	1	yes	characteristic
60	C₂	C₂×Dic₂₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₁₂
commutator	C₄×C₅₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₃
Fitting	C₂²×C₈×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	D₄
cosocle	C₂×C₄×C₅₃	C₂³
hypercenter	C₂²×C₈	D₅₃
hypocenter	C₅₃	C₂×#107
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #13133151	C₂	direct (N × H)
6. C₂×C₈×C₅₃	C₄	semidirect
17. C₈×C₅₃	C₂×C₄	semidirect
26. C₂×C₅₃	#107	semidirect
31. C₅₃	C₂×#107	semidirect
37. C₂×C₈	Dic₅₃	semidirect
48. C₈	C₂×Dic₅₃	semidirect
57. C₂	#13133151	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₅₃	2
#13133151	2
C₂²×C₈×C₅₃	2
C₂×#107	53

Subgroups — C2×#13133151 #16810657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13133151 #16810657