Subgroups — C₇×C₃⋊D₄₆₅ #34086291

Order 19530.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₆₅	—	3	4	no	maximal
3	C₇×C₃⋊D₉₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₃₁	D₃	1	4	yes	complemented
5	C₃⋊D₄₆₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₁₅₅	—	9	1	no	Hall
7	C₃²×C₇×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₉₃	—	15	4	no	—
10	C₅×C₇×C₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	D₄₆₅	—	3	4	no	—
12	C₃×C₇×C₃₁	D₁₅	1	4	yes	complemented
13	C₇×C₃⋊D₁₅	—	31	1	no	maximal, Hall
14	C₃⋊D₉₃	—	5	1	no	Hall
15	C₃×C₅×C₃₁	D₃×C₇	1	4	yes	complemented
16	C₇×D₃₁	—	45	1	no	Hall
17	C₃²×C₅×C₇	D₃₁	1	1	yes	characteristic, complemented, Hall
18	D₁₅₅	—	9	1	no	Hall
19	C₃²×C₃₁	C₇×D₅	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃₁	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
21	C₇×D₁₅	—	93	4	no	—
22	D₉₃	—	15	4	no	—
23	C₅×C₃₁	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₇×C₃⋊D₃	—	155	1	no	Hall
25	C₃×C₅×C₇	D₉₃	1	4	yes	complemented
26	C₃×C₃₁	C₇×D₁₅	1	4	yes	complemented
27	C₃⋊D₁₅	—	31	1	no	Hall
28	C₇×D₅	—	279	1	no	Hall
29	C₃²×C₇	D₁₅₅	1	1	yes	characteristic, complemented, Hall
30	D₃₁	—	45	1	no	Hall
31	C₃²×C₅	C₇×D₃₁	1	1	yes	characteristic, complemented, Hall
32	D₃×C₇	—	465	4	no	—
33	C₅×C₇	C₃⋊D₉₃	1	1	yes	characteristic, complemented, Hall
34	C₃₁	C₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
35	D₁₅	—	93	4	no	—
36	C₃×C₇	D₄₆₅	1	4	yes	complemented
37	C₃⋊D₃	—	155	1	no	Hall
38	C₃×C₅	C₇×D₉₃	1	4	yes	complemented
39	C₂×C₇	—	1395	1	no	Hall
40	D₅	—	279	1	no	Hall
41	C₃²	C₇×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₃⋊D₄₆₅	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	465	4	no	—
44	C₅	C₇×C₃⋊D₉₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇×D₄₆₅	1	4	yes	complemented
46	C₂	—	1395	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₄₆₅
commutator, cosocle, hypocenter	C₃²×C₅×C₃₁	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₁	C₂
LCS	G ▷ C₃²×C₅×C₃₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₃₁	C₂	semidirect
4. C₃×C₅×C₇×C₃₁	D₃	semidirect
5. C₃⋊D₄₆₅	C₇	direct (N × H)
7. C₃²×C₇×C₃₁	D₅	semidirect
8. C₃²×C₅×C₃₁	C₂×C₇	semidirect
10. C₅×C₇×C₃₁	C₃⋊D₃	semidirect
12. C₃×C₇×C₃₁	D₁₅	semidirect
15. C₃×C₅×C₃₁	D₃×C₇	semidirect
17. C₃²×C₅×C₇	D₃₁	semidirect
19. C₃²×C₃₁	C₇×D₅	semidirect
20. C₇×C₃₁	C₃⋊D₁₅	semidirect
23. C₅×C₃₁	C₇×C₃⋊D₃	semidirect
25. C₃×C₅×C₇	D₉₃	semidirect
26. C₃×C₃₁	C₇×D₁₅	semidirect
29. C₃²×C₇	D₁₅₅	semidirect
31. C₃²×C₅	C₇×D₃₁	semidirect
33. C₅×C₇	C₃⋊D₉₃	semidirect
34. C₃₁	C₇×C₃⋊D₁₅	semidirect
36. C₃×C₇	D₄₆₅	semidirect
38. C₃×C₅	C₇×D₉₃	semidirect
41. C₃²	C₇×D₁₅₅	semidirect
42. C₇	C₃⋊D₄₆₅	direct (N × H)
44. C₅	C₇×C₃⋊D₉₃	semidirect
45. C₃	C₇×D₄₆₅	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₃₁	2
C₇×D₄₆₅	3
C₇×C₃⋊D₉₃	5
C₃⋊D₄₆₅	7
C₇×C₃⋊D₁₅	31

Subgroups — C7×C3⋊D465 #34086291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₄₆₅ #34086291