Subgroups — C₂×C₃×C₅₃×D₄₉ #44528343

Order 31164.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×D₄₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×D₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄₉×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅₃×D₄₉	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₄₉×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₇×C₅₃	—	7	1	no	maximal
8	C₄₉×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₇×C₅₃	—	7	2	no	—
10	C₂×C₃×C₇×C₅₃	D₇	1	1	yes	characteristic
11	C₂×D₇×C₅₃	—	7	1	no	—
12	C₃×C₇×C₅₃	C₂×D₇	1	1	yes	characteristic
13	C₂×C₇×C₅₃	C₃×D₇	1	1	yes	characteristic
14	D₇×C₅₃	—	7	2	no	—
15	C₂²×C₃×C₅₃	—	49	1	no	Hall
16	C₂×C₃×D₄₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₇×C₅₃	C₂×C₃×D₇	1	1	yes	characteristic
18	C₂×C₃×C₅₃	—	49	2	no	—
19	C₂×C₃×C₅₃	D₄₉	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₄₉	C₂×C₅₃	1	1	yes	characteristic, complemented
21	C₃×D₄₉	C₂×C₅₃	1	2	yes	direct product factor
22	C₂²×C₅₃	—	49	1	no	Hall
23	C₂×D₄₉	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅₃	C₂×D₄₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₉	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅₃	—	49	2	no	—
27	C₂×C₅₃	C₃×D₄₉	1	1	yes	characteristic, direct product factor
28	C₂×C₄₉	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented
29	D₄₉	C₂×C₃×C₅₃	1	2	yes	direct product factor
30	C₂×C₃×D₇	—	7	1	no	—
31	C₅₃	C₂×C₃×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₄₉	C₂²×C₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	D₇×C₅₃	1	1	yes	characteristic
34	C₃×D₇	—	7	2	no	—
35	C₂×D₇	—	7	1	no	—
36	C₃×C₇	C₂×D₇×C₅₃	1	1	yes	characteristic
37	C₂×C₇	C₃×D₇×C₅₃	1	1	yes	characteristic
38	D₇	—	7	2	no	—
39	C₂²×C₃	—	49	1	no	Hall
40	C₇	C₂×C₃×D₇×C₅₃	1	1	yes	characteristic
41	C₂×C₃	—	49	2	no	—
42	C₂×C₃	C₅₃×D₄₉	1	1	yes	characteristic, direct product factor
43	C₂²	—	49	1	no	Sylow
44	C₃	C₂×C₅₃×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	49	2	no	—
46	C₂	C₃×C₅₃×D₄₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅₃	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂²×C₃×C₅₃
Frattini	C₇	C₂×C₃×D₇×C₅₃
Fitting	C₂×C₃×C₄₉×C₅₃	C₂
socle	C₂×C₃×C₇×C₅₃	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₃×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₃×D₄₉	C₂	direct (N × H)
2. C₂×C₃×C₄₉×C₅₃	C₂	semidirect
3. C₂×C₅₃×D₄₉	C₃	direct (N × H)
4. C₃×C₄₉×C₅₃	C₂²	semidirect
5. C₅₃×D₄₉	C₂×C₃	direct (N × H)
6. C₂×C₄₉×C₅₃	C₂×C₃	semidirect
8. C₄₉×C₅₃	C₂²×C₃	semidirect
16. C₂×C₃×D₄₉	C₅₃	direct (N × H)
19. C₂×C₃×C₅₃	D₄₉	direct (N × H)
20. C₂×C₃×C₄₉	C₂×C₅₃	semidirect
21. C₃×D₄₉	C₂×C₅₃	direct (N × H)
23. C₂×D₄₉	C₃×C₅₃	direct (N × H)
24. C₃×C₅₃	C₂×D₄₉	direct (N × H)
25. C₃×C₄₉	C₂²×C₅₃	semidirect
27. C₂×C₅₃	C₃×D₄₉	direct (N × H)
28. C₂×C₄₉	C₂×C₃×C₅₃	semidirect
29. D₄₉	C₂×C₃×C₅₃	direct (N × H)
31. C₅₃	C₂×C₃×D₄₉	direct (N × H)
32. C₄₉	C₂²×C₃×C₅₃	semidirect
42. C₂×C₃	C₅₃×D₄₉	direct (N × H)
44. C₃	C₂×C₅₃×D₄₉	direct (N × H)
46. C₂	C₃×C₅₃×D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅₃×D₄₉	2
C₂×C₃×C₄₉×C₅₃	2
C₂×C₅₃×D₄₉	3
C₂×C₃×D₇×C₅₃	7
C₂×C₃×D₄₉	53

Subgroups — C2×C3×C53×D49 #44528343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅₃×D₄₉ #44528343