Subgroups — C₂×C₃×C₅⋊D₃₅₅ #36319154

Order 21300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₃₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅⋊D₃₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₃₅₅	—	5	6	no	maximal
6	C₅⋊D₃₅₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₃₅₅	—	5	12	no	—
9	C₂×C₃×C₅×C₇₁	D₅	1	6	yes	complemented
10	C₅²×C₇₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₃₅₅	—	5	6	no	—
12	C₃×C₅×C₇₁	C₂×D₅	1	6	yes	complemented
13	C₂×C₃×D₇₁	—	25	1	no	Hall
14	C₂×C₅×C₇₁	C₃×D₅	1	6	yes	complemented
15	D₃₅₅	—	5	12	no	—
16	C₂×C₃×C₇₁	C₅⋊D₅	1	1	yes	characteristic, complemented
17	C₃×D₇₁	—	25	2	no	—
18	C₅×C₇₁	C₂×C₃×D₅	1	6	yes	complemented
19	C₂×C₃×C₅⋊D₅	—	71	1	no	maximal, Hall
20	C₂×D₇₁	—	25	1	no	Hall
21	C₃×C₇₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅²	D₇₁	1	1	yes	characteristic, complemented
23	C₃×C₅⋊D₅	—	71	2	no	—
24	C₂×C₇₁	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
25	D₇₁	—	25	2	no	—
26	C₂×C₅⋊D₅	—	71	1	no	Hall
27	C₃×C₅²	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
28	C₇₁	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×D₅	—	355	6	no	—
30	C₂×C₅²	C₃×D₇₁	1	1	yes	characteristic, complemented
31	C₅⋊D₅	—	71	2	no	—
32	C₂×C₃×C₅	D₃₅₅	1	6	yes	complemented
33	C₃×D₅	—	355	12	no	—
34	C₅²	C₂×C₃×D₇₁	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	355	6	no	—
36	C₃×C₅	C₂×D₃₅₅	1	6	yes	complemented
37	C₂²×C₃	—	1775	1	no	Hall
38	C₂×C₅	C₃×D₃₅₅	1	6	yes	complemented
39	D₅	—	355	12	no	—
40	C₂×C₃	—	1775	2	no	—
41	C₂×C₃	C₅⋊D₃₅₅	1	1	yes	characteristic, direct product factor
42	C₅	C₂×C₃×D₃₅₅	1	6	yes	complemented
43	C₂²	—	1775	1	no	Sylow
44	C₃	C₂×C₅⋊D₃₅₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	1775	2	no	—
46	C₂	C₃×C₅⋊D₃₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₃₅₅
commutator, cosocle, hypocenter	C₅²×C₇₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₇₁	C₂
LCS	G ▷ C₅²×C₇₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊D₃₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₇₁	C₂	semidirect
3. C₂×C₅⋊D₃₅₅	C₃	direct (N × H)
4. C₃×C₅²×C₇₁	C₂²	semidirect
6. C₅⋊D₃₅₅	C₂×C₃	direct (N × H)
7. C₂×C₅²×C₇₁	C₂×C₃	semidirect
9. C₂×C₃×C₅×C₇₁	D₅	semidirect
10. C₅²×C₇₁	C₂²×C₃	semidirect
12. C₃×C₅×C₇₁	C₂×D₅	semidirect
14. C₂×C₅×C₇₁	C₃×D₅	semidirect
16. C₂×C₃×C₇₁	C₅⋊D₅	semidirect
18. C₅×C₇₁	C₂×C₃×D₅	semidirect
21. C₃×C₇₁	C₂×C₅⋊D₅	semidirect
22. C₂×C₃×C₅²	D₇₁	semidirect
24. C₂×C₇₁	C₃×C₅⋊D₅	semidirect
27. C₃×C₅²	C₂×D₇₁	semidirect
28. C₇₁	C₂×C₃×C₅⋊D₅	semidirect
30. C₂×C₅²	C₃×D₇₁	semidirect
32. C₂×C₃×C₅	D₃₅₅	semidirect
34. C₅²	C₂×C₃×D₇₁	semidirect
36. C₃×C₅	C₂×D₃₅₅	semidirect
38. C₂×C₅	C₃×D₃₅₅	semidirect
41. C₂×C₃	C₅⋊D₃₅₅	direct (N × H)
42. C₅	C₂×C₃×D₃₅₅	semidirect
44. C₃	C₂×C₅⋊D₃₅₅	direct (N × H)
46. C₂	C₃×C₅⋊D₃₅₅	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×C₅⋊D₃₅₅	2
C₂×C₃×C₅²×C₇₁	2
C₂×C₅⋊D₃₅₅	3
C₂×C₃×D₃₅₅	5
C₂×C₃×C₅⋊D₅	71

Subgroups — C2×C3×C5⋊D355 #36319154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅⋊D₃₅₅ #36319154