Subgroups — C₂×C₅₃×D₁₇₁ #49136236

Order 36252.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₁₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×D₅₇	—	3	1	no	maximal
4	C₉×C₁₉×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅₃×D₅₇	—	3	2	no	—
6	C₂×C₃×C₁₉×C₅₃	D₃	1	1	yes	characteristic
7	C₂×D₁₉×C₅₃	—	9	1	no	Hall
8	C₃×C₁₉×C₅₃	C₂×D₃	1	1	yes	characteristic
9	C₂×C₁₉×C₅₃	D₉	1	1	yes	characteristic, complemented
10	D₁₉×C₅₃	—	9	2	no	—
11	C₂×D₉×C₅₃	—	19	1	no	maximal, Hall
12	C₁₉×C₅₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₅₃	D₁₉	1	1	yes	characteristic, complemented
14	D₉×C₅₃	—	19	2	no	—
15	C₂×D₁₇₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×D₃×C₅₃	—	57	1	no	—
17	C₉×C₅₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₉×C₁₉	C₂×C₅₃	1	1	yes	characteristic, complemented
19	D₁₇₁	C₂×C₅₃	1	2	yes	direct product factor
20	C₂×C₃×C₅₃	D₅₇	1	1	yes	characteristic
21	D₃×C₅₃	—	57	2	no	—
22	C₂×D₅₇	—	3	1	no	—
23	C₂²×C₅₃	—	171	1	no	Hall
24	C₉×C₁₉	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅₃	C₂×D₅₇	1	1	yes	characteristic
26	C₂×C₃×C₁₉	D₃×C₅₃	1	1	yes	characteristic
27	D₅₇	—	3	2	no	—
28	C₂×C₅₃	—	171	2	no	—
29	C₂×C₅₃	D₁₇₁	1	1	yes	characteristic, direct product factor
30	C₂×D₁₉	—	9	1	no	Hall
31	C₃×C₁₉	C₂×D₃×C₅₃	1	1	yes	characteristic
32	C₅₃	C₂×D₁₇₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₁₉	D₉×C₅₃	1	1	yes	characteristic, complemented
34	D₁₉	—	9	2	no	—
35	C₂×D₉	—	19	1	no	Hall
36	C₁₉	C₂×D₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	D₁₉×C₅₃	1	1	yes	characteristic, complemented
38	D₉	—	19	2	no	—
39	C₂×D₃	—	57	1	no	—
40	C₉	C₂×D₁₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₅₃×D₅₇	1	1	yes	characteristic
42	D₃	—	57	2	no	—
43	C₂²	—	171	1	no	Sylow
44	C₃	C₂×C₅₃×D₅₇	1	1	yes	characteristic
45	C₂	—	171	2	no	—
46	C₂	C₅₃×D₁₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅₃	D₁₇₁
commutator, cosocle, hypocenter	C₉×C₁₉	C₂²×C₅₃
Frattini	C₃	C₂×C₅₃×D₅₇
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₁₇₁	C₂	direct (N × H)
2. C₂×C₉×C₁₉×C₅₃	C₂	semidirect
4. C₉×C₁₉×C₅₃	C₂²	semidirect
9. C₂×C₁₉×C₅₃	D₉	semidirect
12. C₁₉×C₅₃	C₂×D₉	semidirect
13. C₂×C₉×C₅₃	D₁₉	semidirect
15. C₂×D₁₇₁	C₅₃	direct (N × H)
17. C₉×C₅₃	C₂×D₁₉	semidirect
18. C₂×C₉×C₁₉	C₂×C₅₃	semidirect
19. D₁₇₁	C₂×C₅₃	direct (N × H)
24. C₉×C₁₉	C₂²×C₅₃	semidirect
29. C₂×C₅₃	D₁₇₁	direct (N × H)
32. C₅₃	C₂×D₁₇₁	direct (N × H)
33. C₂×C₁₉	D₉×C₅₃	semidirect
36. C₁₉	C₂×D₉×C₅₃	semidirect
37. C₂×C₉	D₁₉×C₅₃	semidirect
40. C₉	C₂×D₁₉×C₅₃	semidirect
46. C₂	C₅₃×D₁₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×D₁₇₁	2
C₂×C₉×C₁₉×C₅₃	2
C₂×C₅₃×D₅₇	3
C₂×D₉×C₅₃	19
C₂×D₁₇₁	53

Subgroups — C2×C53×D171 #49136236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×D₁₇₁ #49136236