Subgroups — C₃×C₇₁⋊((C₅⋊D₅)⋊C₃) #44544070

Order 31950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₃₅₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇₁⋊((C₅⋊D₅)⋊C₃)	C₃	1	3	yes	maximal, direct product factor
4	C₇₁×C₅²⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅⋊D₃₅₅	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃₅₅	—	15	2	no	—
8	C₅²×C₇₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₇₁	—	25	1	no	maximal, Hall
10	C₃×C₅×C₇₁	—	3	2	no	—
11	D₃₅₅	—	15	2	no	—
12	C₃²×C₇₁	—	25	1	no	Hall
13	C₃×(C₅⋊D₅)⋊C₃	—	71	1	no	maximal, Hall
14	C₃×D₇₁	—	25	3	no	—
15	C₃×D₇₁	—	25	1	no	—
16	C₅×C₇₁	—	3	2	no	—
17	C₃×C₅²⋊C₃	D₇₁	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇₁	—	25	3	no	—
19	C₃×C₇₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
20	C₃×C₅⋊D₅	—	71	1	no	—
21	(C₅⋊D₅)⋊C₃	—	71	3	no	—
22	D₇₁	—	25	1	no	Hall
23	C₃×C₅²	C₃×D₇₁	1	1	yes	characteristic, complemented
24	C₅²⋊C₃	C₃×D₇₁	1	3	yes	complemented
25	C₇₁	C₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₅⋊D₅	—	71	1	no	Hall
27	C₃×D₅	—	1065	2	no	—
28	C₅²	C₃²×D₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²	—	1775	1	no	Hall
30	C₃×C₅	—	3	2	no	—
31	D₅	—	1065	2	no	—
32	C₃²	—	25	1	no	Sylow
33	C₂×C₃	—	1775	3	no	—
34	C₂×C₃	—	1775	1	no	—
35	C₅	—	3	2	no	—
36	C₃	—	25	3	no	—
37	C₃	C₇₁⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor
38	C₂	—	1775	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₇₁⋊((C₅⋊D₅)⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₇₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₁	C₂×C₃
LCS	G ▷ C₅²×C₇₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇₁×C₅²⋊C₃	C₂	semidirect
2. C₃×C₅⋊D₃₅₅	C₃	semidirect
3. C₇₁⋊((C₅⋊D₅)⋊C₃)	C₃	direct (N × H)
4. C₇₁×C₅²⋊C₃	C₂×C₃	semidirect
5. C₃×C₅²×C₇₁	C₂×C₃	semidirect
6. C₅⋊D₃₅₅	C₃²	semidirect
8. C₅²×C₇₁	C₂×C₃²	semidirect
17. C₃×C₅²⋊C₃	D₇₁	semidirect
19. C₃×C₇₁	(C₅⋊D₅)⋊C₃	semidirect
23. C₃×C₅²	C₃×D₇₁	semidirect
24. C₅²⋊C₃	C₃×D₇₁	semidirect
25. C₇₁	C₃×(C₅⋊D₅)⋊C₃	semidirect
28. C₅²	C₃²×D₇₁	semidirect
37. C₃	C₇₁⋊((C₅⋊D₅)⋊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
C₃×C₇₁×C₅²⋊C₃	2
C₃×C₅⋊D₃₅₅	3
C₇₁⋊((C₅⋊D₅)⋊C₃)	3
C₃²×D₇₁	25
C₃×(C₅⋊D₅)⋊C₃	71

Subgroups — C3×C71⋊((C5⋊D5)⋊C3) #44544070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇₁⋊((C₅⋊D₅)⋊C₃) #44544070