Subgroups — C₅×C₇×C₃⋊D₂₁ #17984411

Order 4410.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₂₁	—	3	4	no	maximal
3	C₇×C₃⋊D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇²	D₃	1	4	yes	complemented
5	C₅×C₃⋊D₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₅×C₇×C₃⋊D₃	—	7	1	no	maximal
7	C₅×C₇×D₇	—	9	1	no	Hall
8	C₃²×C₇²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₅×C₇	—	2	3	no	—
10	C₃²×C₅×C₇	D₇	1	1	yes	characteristic, complemented
11	C₃²×C₅×C₇	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×D₂₁	—	3	4	no	—
13	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
14	C₅×D₂₁	—	3	4	no	—
15	C₅×D₃×C₇	—	21	4	no	—
16	C₃×C₇²	C₅×D₃	1	4	yes	complemented
17	C₃⋊D₂₁	C₅×C₇	1	1	yes	characteristic, direct product factor
18	C₇×C₃⋊D₃	—	7	1	no	—
19	C₃×C₅×C₇	—	2	12	no	—
20	C₃×C₅×C₇	D₃×C₇	1	4	yes	complemented
21	C₃×C₅×C₇	D₂₁	1	4	yes	complemented
22	C₇×D₇	—	9	1	no	Hall
23	C₅×C₃⋊D₃	—	7	1	no	Hall
24	C₂×C₅×C₇	—	63	1	no	—
25	C₅×D₇	—	9	1	no	—
26	C₃²×C₇	—	2	3	no	—
27	C₃²×C₇	C₅×D₇	1	1	yes	characteristic, complemented
28	C₃²×C₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented
29	C₇²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
30	C₃²×C₅	C₇×D₇	1	1	yes	characteristic, complemented, Hall
31	D₂₁	—	3	4	no	—
32	D₃×C₇	—	21	4	no	—
33	C₅×C₇	—	2	3	no	—
34	C₅×C₇	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
35	C₅×C₇	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
36	C₅×D₃	—	21	4	no	—
37	C₃×C₇	—	2	12	no	—
38	C₃×C₇	C₅×D₃×C₇	1	4	yes	complemented
39	C₃×C₇	C₅×D₂₁	1	4	yes	complemented
40	C₃⋊D₃	—	7	1	no	Hall
41	C₃×C₅	C₇×D₂₁	1	4	yes	complemented
42	C₂×C₇	—	63	1	no	—
43	D₇	—	9	1	no	—
44	C₂×C₅	—	63	1	no	Hall
45	C₃²	C₅×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
46	C₇	—	2	3	no	—
47	C₇	C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
48	C₇	C₅×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
49	D₃	—	21	4	no	—
50	C₅	C₇×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₅×C₇×D₂₁	1	4	yes	complemented
52	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇²	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇²	C₂	semidirect
3. C₇×C₃⋊D₂₁	C₅	direct (N × H)
4. C₃×C₅×C₇²	D₃	semidirect
5. C₅×C₃⋊D₂₁	C₇	direct (N × H)
8. C₃²×C₇²	C₂×C₅	semidirect
10. C₃²×C₅×C₇	D₇	semidirect
11. C₃²×C₅×C₇	C₂×C₇	semidirect
13. C₅×C₇²	C₃⋊D₃	semidirect
16. C₃×C₇²	C₅×D₃	semidirect
17. C₃⋊D₂₁	C₅×C₇	direct (N × H)
20. C₃×C₅×C₇	D₃×C₇	semidirect
21. C₃×C₅×C₇	D₂₁	semidirect
27. C₃²×C₇	C₅×D₇	semidirect
28. C₃²×C₇	C₂×C₅×C₇	semidirect
29. C₇²	C₅×C₃⋊D₃	semidirect
30. C₃²×C₅	C₇×D₇	semidirect
34. C₅×C₇	C₇×C₃⋊D₃	semidirect
35. C₅×C₇	C₃⋊D₂₁	direct (N × H)
38. C₃×C₇	C₅×D₃×C₇	semidirect
39. C₃×C₇	C₅×D₂₁	semidirect
41. C₃×C₅	C₇×D₂₁	semidirect
45. C₃²	C₅×C₇×D₇	semidirect
47. C₇	C₅×C₇×C₃⋊D₃	semidirect
48. C₇	C₅×C₃⋊D₂₁	direct (N × H)
50. C₅	C₇×C₃⋊D₂₁	direct (N × H)
51. C₃	C₅×C₇×D₂₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅×C₇²	2
C₅×C₇×D₂₁	3
C₇×C₃⋊D₂₁	5
C₅×C₃⋊D₂₁	7
C₅×C₇×C₃⋊D₃	7

Subgroups — C5×C7×C3⋊D21 #17984411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₃⋊D₂₁ #17984411