Subgroups — C₃×C₇×D₅₅₃ #37551173

Order 23226.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₇×D₇₉	—	7	1	no	maximal
6	C₃×C₇×C₇₉	—	2	3	no	—
7	C₃×C₇×C₇₉	D₇	1	1	yes	characteristic, complemented
8	C₃×C₇×C₇₉	C₂×C₇	1	1	yes	characteristic, complemented
9	D₅₅₃	C₃×C₇	1	1	yes	characteristic, direct product factor
10	C₇×D₇₉	—	7	1	no	—
11	C₇×C₇₉	—	2	3	no	—
12	C₇×C₇₉	C₃×D₇	1	1	yes	characteristic, complemented
13	C₇×C₇₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	C₃×D₇₉	—	7	1	no	Hall
15	C₃×C₇×D₇	—	79	1	no	maximal, Hall
16	C₃×C₇₉	C₇×D₇	1	1	yes	characteristic, complemented, Hall
17	D₇₉	—	7	1	no	Hall
18	C₃×C₇²	D₇₉	1	1	yes	characteristic, complemented, Hall
19	C₇×D₇	—	79	1	no	Hall
20	C₇₉	C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
21	C₇²	C₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₇	—	553	1	no	—
23	C₃×D₇	—	79	1	no	—
24	C₃×C₇	—	2	3	no	—
25	C₃×C₇	C₇×D₇₉	1	1	yes	characteristic, complemented
26	C₃×C₇	D₅₅₃	1	1	yes	characteristic, direct product factor
27	C₂×C₇	—	553	1	no	—
28	D₇	—	79	1	no	—
29	C₇	—	2	3	no	—
30	C₇	C₃×C₇×D₇₉	1	1	yes	characteristic, complemented
31	C₇	C₃×D₅₅₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	553	1	no	Hall
33	C₃	C₇×D₅₅₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	553	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₅₅₃
commutator, cosocle, hypocenter	C₇×C₇₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₇₉	C₂
LCS	G ▷ C₇×C₇₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₇₉	C₂	semidirect
2. C₇×D₅₅₃	C₃	direct (N × H)
3. C₇²×C₇₉	C₂×C₃	semidirect
4. C₃×D₅₅₃	C₇	direct (N × H)
7. C₃×C₇×C₇₉	D₇	semidirect
8. C₃×C₇×C₇₉	C₂×C₇	semidirect
9. D₅₅₃	C₃×C₇	direct (N × H)
12. C₇×C₇₉	C₃×D₇	semidirect
13. C₇×C₇₉	C₂×C₃×C₇	semidirect
16. C₃×C₇₉	C₇×D₇	semidirect
18. C₃×C₇²	D₇₉	semidirect
20. C₇₉	C₃×C₇×D₇	semidirect
21. C₇²	C₃×D₇₉	semidirect
25. C₃×C₇	C₇×D₇₉	semidirect
26. C₃×C₇	D₅₅₃	direct (N × H)
30. C₇	C₃×C₇×D₇₉	semidirect
31. C₇	C₃×D₅₅₃	direct (N × H)
33. C₃	C₇×D₅₅₃	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×C₇²×C₇₉	2
C₇×D₅₅₃	3
C₃×D₅₅₃	7
C₃×C₇×D₇₉	7
C₃×C₇×D₇	79

Subgroups — C3×C7×D553 #37551173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₅₅₃ #37551173