Subgroups — C₄×C₅×C₇×C₇₃⋊C₃ #44501239

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₇×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₇×C₇₃⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₇×C₇₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic
6	C₄×C₅×C₇₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇×C₇₃⋊C₃	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₇₃⋊C₃	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇×C₇₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₇×C₇₃⋊C₃	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₅×C₇₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₅×C₇₃⋊C₃	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₇×C₇₃	C₂×C₃×C₅	1	1	yes	characteristic
15	C₄×C₇₃⋊C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₇₃	C₂×C₃×C₇	1	1	yes	characteristic
17	C₇×C₇₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇₃⋊C₃	C₂×C₅×C₇	1	1	yes	characteristic
19	C₃×C₄×C₅×C₇	—	73	1	no	maximal, Hall
20	C₅×C₇₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
21	C₄×C₇₃	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
22	C₇₃⋊C₃	C₄×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅×C₇	—	73	1	no	—
24	C₂×C₇₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic
25	C₄×C₅×C₇	C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₇	—	73	1	no	Hall
27	C₃×C₄×C₇	—	73	1	no	Hall
28	C₇₃	C₃×C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	C₂×C₇₃⋊C₃	1	1	yes	characteristic
30	C₃×C₄×C₅	—	73	1	no	Hall
31	C₂×C₃×C₇	—	73	1	no	—
32	C₅×C₇	C₄×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₅	—	73	1	no	—
34	C₄×C₇	C₅×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₇	—	73	1	no	Hall
36	C₄×C₅	C₇×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅	—	73	1	no	Hall
38	C₂×C₇	C₂×C₅×C₇₃⋊C₃	1	1	yes	characteristic
39	C₃×C₄	—	73	1	no	Hall
40	C₂×C₅	C₂×C₇×C₇₃⋊C₃	1	1	yes	characteristic
41	C₇	C₄×C₅×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	—	73	1	no	—
43	C₅	C₄×C₇×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₅×C₇×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	73	1	no	Sylow
46	C₂	C₂×C₅×C₇×C₇₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅×C₇	C₇₃⋊C₃
commutator, hypocenter	C₇₃	C₃×C₄×C₅×C₇
Frattini	C₂	C₂×C₅×C₇×C₇₃⋊C₃
Fitting	C₄×C₅×C₇×C₇₃	C₃
socle	C₂×C₅×C₇×C₇₃	C₂×C₃
prime radical	C₂×C₅×C₇×C₇₃⋊C₃	C₂
cosocle	C₂×C₇₃	C₂×C₃×C₅×C₇
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₄×C₅×C₇

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₇×C₇₃	C₃	semidirect
3. C₅×C₇×C₇₃⋊C₃	C₄	direct (N × H)
4. C₄×C₇×C₇₃⋊C₃	C₅	direct (N × H)
6. C₄×C₅×C₇₃⋊C₃	C₇	direct (N × H)
8. C₅×C₇×C₇₃	C₃×C₄	semidirect
10. C₄×C₇×C₇₃	C₃×C₅	semidirect
11. C₇×C₇₃⋊C₃	C₄×C₅	direct (N × H)
12. C₄×C₅×C₇₃	C₃×C₇	semidirect
13. C₅×C₇₃⋊C₃	C₄×C₇	direct (N × H)
15. C₄×C₇₃⋊C₃	C₅×C₇	direct (N × H)
17. C₇×C₇₃	C₃×C₄×C₅	semidirect
20. C₅×C₇₃	C₃×C₄×C₇	semidirect
21. C₄×C₇₃	C₃×C₅×C₇	semidirect
22. C₇₃⋊C₃	C₄×C₅×C₇	direct (N × H)
25. C₄×C₅×C₇	C₇₃⋊C₃	direct (N × H)
28. C₇₃	C₃×C₄×C₅×C₇	semidirect
32. C₅×C₇	C₄×C₇₃⋊C₃	direct (N × H)
34. C₄×C₇	C₅×C₇₃⋊C₃	direct (N × H)
36. C₄×C₅	C₇×C₇₃⋊C₃	direct (N × H)
41. C₇	C₄×C₅×C₇₃⋊C₃	direct (N × H)
43. C₅	C₄×C₇×C₇₃⋊C₃	direct (N × H)
44. C₄	C₅×C₇×C₇₃⋊C₃	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×C₅×C₇×C₇₃⋊C₃	2
C₄×C₅×C₇×C₇₃	3
C₄×C₇×C₇₃⋊C₃	5
C₄×C₅×C₇₃⋊C₃	7
C₃×C₄×C₅×C₇	73

Subgroups — C4×C5×C7×C73⋊C3 #44501239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₇×C₇₃⋊C₃ #44501239