Subgroups — C₃⋊(C₇⋊(Dic₇₁⋊C₅)) #44447147

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)	—	3	1	no	maximal, Hall
3	C₃×C₇×C₇₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₄₉₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₇×C₇₁⋊C₅	D₃	1	1	yes	characteristic
6	C₃⋊(Dic₇₁⋊C₅)	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇×C₇₁	C₂×C₅	1	1	yes	characteristic
8	C₇×C₇₁⋊C₅	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇₁⋊C₅	D₇	1	1	yes	characteristic
10	Dic₄₉₇	—	3	1	no	Hall
11	C₃×C₇×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	Dic₇₁⋊C₅	—	21	1	no	Hall
13	C₃×C₇₁⋊C₅	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₇₁	C₅×D₃	1	1	yes	characteristic
15	Dic₂₁₃	—	7	1	no	Hall
16	C₂×C₇₁⋊C₅	D₂₁	1	1	yes	characteristic
17	C₇×C₇₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇₁	C₅×D₇	1	1	yes	characteristic
19	C₅×Dic₂₁	—	71	1	no	maximal, Hall
20	C₇₁⋊C₅	Dic₂₁	1	1	yes	characteristic, complemented, Hall
21	Dic₇₁	—	21	1	no	Hall
22	C₃×C₇₁	C₅×Dic₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	—	71	1	no	—
24	C₂×C₇₁	C₅×D₂₁	1	1	yes	characteristic
25	C₅×Dic₇	—	213	1	no	Hall
26	C₃×C₅×C₇	—	71	1	no	Hall
27	Dic₂₁	—	355	1	no	Hall
28	C₇₁	C₅×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	—	71	1	no	—
30	C₅×Dic₃	—	497	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	Dic₇	—	1065	1	no	Hall
35	C₃×C₇	Dic₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
36	C₄×C₅	—	1491	1	no	Hall
37	C₃×C₅	—	71	1	no	Hall
38	C₂×C₇	C₃⋊(D₇₁⋊C₅)	1	1	yes	characteristic
39	Dic₃	—	2485	1	no	Hall
40	C₂×C₅	—	71	1	no	—
41	C₇	C₃⋊(Dic₇₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	C₇⋊(D₇₁⋊C₅)	1	1	yes	characteristic
43	C₅	—	71	1	no	Sylow
44	C₄	—	7455	1	no	Sylow
45	C₃	C₇⋊(Dic₇₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₃⋊(C₇⋊(D₇₁⋊C₅))	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₇₁⋊C₅	C₄	semidirect
4. Dic₁₄₉₁	C₅	semidirect
8. C₇×C₇₁⋊C₅	Dic₃	semidirect
11. C₃×C₇×C₇₁	C₄×C₅	semidirect
13. C₃×C₇₁⋊C₅	Dic₇	semidirect
17. C₇×C₇₁	C₅×Dic₃	semidirect
20. C₇₁⋊C₅	Dic₂₁	semidirect
22. C₃×C₇₁	C₅×Dic₇	semidirect
28. C₇₁	C₅×Dic₂₁	semidirect
35. C₃×C₇	Dic₇₁⋊C₅	semidirect
41. C₇	C₃⋊(Dic₇₁⋊C₅)	semidirect
45. C₃	C₇⋊(Dic₇₁⋊C₅)	semidirect

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
Dic₁₄₉₁	5
C₃⋊(Dic₇₁⋊C₅)	7
C₅×Dic₂₁	71

Subgroups — C3⋊(C7⋊(Dic71⋊C5)) #44447147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊(Dic₇₁⋊C₅)) #44447147