Subgroups — C₃×C₇×Dic₇₁⋊C₅ #44447141

Order 29820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₇₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₇₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×Dic₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₇×C₇₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₃×Dic₇₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇×C₇₁	C₂×C₅	1	1	yes	characteristic
8	C₇×C₇₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇₁⋊C₅	C₂×C₇	1	1	yes	characteristic
10	C₇×Dic₇₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	Dic₇₁⋊C₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₇₁⋊C₅	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₃×Dic₇₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₁⋊C₅	C₂×C₃×C₇	1	1	yes	characteristic
17	C₇×C₇₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇₁	C₂×C₅×C₇	1	1	yes	characteristic
19	C₃×C₄×C₅×C₇	—	71	1	no	maximal, Hall
20	C₇₁⋊C₅	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
21	Dic₇₁	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇₁	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	—	71	1	no	—
24	C₂×C₇₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
25	C₄×C₅×C₇	—	71	1	no	Hall
26	C₃×C₅×C₇	—	71	1	no	Hall
27	C₃×C₄×C₇	—	71	1	no	Hall
28	C₇₁	C₃×C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	—	71	1	no	—
30	C₃×C₄×C₅	—	71	1	no	Hall
31	C₂×C₃×C₇	D₇₁⋊C₅	1	1	yes	characteristic
32	C₅×C₇	—	71	1	no	Hall
33	C₂×C₃×C₅	—	71	1	no	—
34	C₄×C₇	—	71	1	no	Hall
35	C₃×C₇	Dic₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
36	C₄×C₅	—	71	1	no	Hall
37	C₃×C₅	—	71	1	no	Hall
38	C₂×C₇	C₃×D₇₁⋊C₅	1	1	yes	characteristic
39	C₃×C₄	—	71	1	no	Hall
40	C₂×C₅	—	71	1	no	—
41	C₇	C₃×Dic₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₇×D₇₁⋊C₅	1	1	yes	characteristic
43	C₅	—	71	1	no	Sylow
44	C₄	—	71	1	no	Sylow
45	C₃	C₇×Dic₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₇×D₇₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₇₁⋊C₅
commutator, hypocenter	C₇₁	C₃×C₄×C₅×C₇
Frattini	C₂	C₃×C₇×D₇₁⋊C₅
Fitting, socle	C₂×C₃×C₇×C₇₁	C₂×C₅
prime radical	C₂×C₃×C₇×C₇₁⋊C₅	C₂
cosocle	C₂×C₇₁	C₂×C₃×C₅×C₇
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₇₁⋊C₅	C₃	direct (N × H)
3. C₃×C₇×C₇₁⋊C₅	C₄	semidirect
4. C₃×C₇×Dic₇₁	C₅	semidirect
6. C₃×Dic₇₁⋊C₅	C₇	direct (N × H)
8. C₇×C₇₁⋊C₅	C₃×C₄	semidirect
10. C₇×Dic₇₁	C₃×C₅	semidirect
11. C₃×C₇×C₇₁	C₄×C₅	semidirect
12. Dic₇₁⋊C₅	C₃×C₇	direct (N × H)
13. C₃×C₇₁⋊C₅	C₄×C₇	semidirect
15. C₃×Dic₇₁	C₅×C₇	semidirect
17. C₇×C₇₁	C₃×C₄×C₅	semidirect
20. C₇₁⋊C₅	C₃×C₄×C₇	semidirect
21. Dic₇₁	C₃×C₅×C₇	semidirect
22. C₃×C₇₁	C₄×C₅×C₇	semidirect
28. C₇₁	C₃×C₄×C₅×C₇	semidirect
35. C₃×C₇	Dic₇₁⋊C₅	direct (N × H)
41. C₇	C₃×Dic₇₁⋊C₅	direct (N × H)
45. C₃	C₇×Dic₇₁⋊C₅	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×C₃×C₇×C₇₁⋊C₅	2
C₇×Dic₇₁⋊C₅	3
C₃×C₇×Dic₇₁	5
C₃×Dic₇₁⋊C₅	7
C₃×C₄×C₅×C₇	71

Subgroups — C3×C7×Dic71⋊C5 #44447141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×Dic₇₁⋊C₅ #44447141