Subgroups — C₂×C₅⋊((C₇₃⋊C₃)⋊D₇) #44501389

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊((C₇₃⋊C₃)⋊D₇)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₅₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₇×C₇₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×(C₇₃⋊C₃)⋊D₇	—	5	1	no	maximal, Hall
6	D₂₅₅₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅⋊(D₇₃⋊C₃)	—	7	1	no	maximal, Hall
9	(C₇₃⋊C₃)⋊D₇	—	5	2	no	—
10	C₂×C₇×C₇₃⋊C₃	D₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₅⋊(D₇₃⋊C₃)	—	7	2	no	—
13	C₂×C₅×C₇₃⋊C₃	D₇	1	1	yes	characteristic, complemented
14	C₂×D₅₁₁	—	5	1	no	Hall
15	C₇×C₇₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₆₅	—	7	1	no	Hall
17	C₅×C₇₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented
19	D₅₁₁	—	5	2	no	—
20	C₂×D₇₃⋊C₃	—	35	1	no	Hall
21	C₂×C₅×C₇₃	C₃×D₇	1	1	yes	characteristic, complemented
22	D₃₆₅	—	7	2	no	—
23	C₇×C₇₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇₃⋊C₃	D₃₅	1	1	yes	characteristic, complemented
25	D₇₃⋊C₃	—	35	2	no	—
26	C₂×C₃×D₃₅	—	73	1	no	maximal, Hall
27	C₅×C₇₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
28	C₂×D₇₃	—	35	1	no	Hall
29	C₇₃⋊C₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₇	—	73	1	no	—
31	C₃×D₃₅	—	73	2	no	—
32	C₂×C₇₃	C₃×D₃₅	1	1	yes	characteristic, complemented
33	D₇₃	—	35	2	no	—
34	C₂×D₃₅	—	73	1	no	Hall
35	C₃×C₅×C₇	—	73	1	no	Hall
36	C₂×C₃×D₇	—	365	1	no	Hall
37	C₇₃	C₂×C₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented
39	D₃₅	—	73	2	no	—
40	C₂×C₃×D₅	—	511	1	no	Hall
41	C₂×C₃×C₇	—	73	1	no	—
42	C₃×D₇	—	365	2	no	—
43	C₅×C₇	C₂×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	—	73	1	no	—
45	C₃×D₅	—	511	2	no	—
46	C₂×D₇	—	365	1	no	Hall
47	C₃×C₇	—	73	1	no	Hall
48	C₂×D₅	—	511	1	no	Hall
49	C₃×C₅	—	73	1	no	Hall
50	C₂×C₇	C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented
51	D₇	—	365	2	no	—
52	C₂²×C₃	—	2555	1	no	Hall
53	C₂×C₅	(C₇₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
54	D₅	—	511	2	no	—
55	C₇	C₂×C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	73	1	no	—
57	C₂×C₃	—	2555	2	no	—
58	C₅	C₂×(C₇₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2555	1	no	Sylow
60	C₃	—	73	1	no	Sylow
61	C₂	—	2555	2	no	—
62	C₂	C₅⋊((C₇₃⋊C₃)⋊D₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊((C₇₃⋊C₃)⋊D₇)
commutator, cosocle, hypocenter	C₅×C₇×C₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₇₃	C₂×C₃
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊((C₇₃⋊C₃)⋊D₇)	C₂	direct (N × H)
2. C₂×C₅×C₇×C₇₃⋊C₃	C₂	semidirect
3. C₂×D₂₅₅₅	C₃	semidirect
4. C₅×C₇×C₇₃⋊C₃	C₂²	semidirect
6. D₂₅₅₅	C₂×C₃	semidirect
7. C₂×C₅×C₇×C₇₃	C₂×C₃	semidirect
10. C₂×C₇×C₇₃⋊C₃	D₅	semidirect
11. C₅×C₇×C₇₃	C₂²×C₃	semidirect
13. C₂×C₅×C₇₃⋊C₃	D₇	semidirect
15. C₇×C₇₃⋊C₃	C₂×D₅	semidirect
17. C₅×C₇₃⋊C₃	C₂×D₇	semidirect
18. C₂×C₇×C₇₃	C₃×D₅	semidirect
21. C₂×C₅×C₇₃	C₃×D₇	semidirect
23. C₇×C₇₃	C₂×C₃×D₅	semidirect
24. C₂×C₇₃⋊C₃	D₃₅	semidirect
27. C₅×C₇₃	C₂×C₃×D₇	semidirect
29. C₇₃⋊C₃	C₂×D₃₅	semidirect
32. C₂×C₇₃	C₃×D₃₅	semidirect
37. C₇₃	C₂×C₃×D₃₅	semidirect
38. C₂×C₅×C₇	D₇₃⋊C₃	semidirect
43. C₅×C₇	C₂×D₇₃⋊C₃	semidirect
50. C₂×C₇	C₅⋊(D₇₃⋊C₃)	semidirect
53. C₂×C₅	(C₇₃⋊C₃)⋊D₇	semidirect
55. C₇	C₂×C₅⋊(D₇₃⋊C₃)	semidirect
58. C₅	C₂×(C₇₃⋊C₃)⋊D₇	semidirect
62. C₂	C₅⋊((C₇₃⋊C₃)⋊D₇)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅⋊((C₇₃⋊C₃)⋊D₇)	2
C₂×C₅×C₇×C₇₃⋊C₃	2
C₂×D₂₅₅₅	3
C₂×(C₇₃⋊C₃)⋊D₇	5
C₂×C₅⋊(D₇₃⋊C₃)	7
C₂×C₃×D₃₅	73

Subgroups — C2×C5⋊((C73⋊C3)⋊D7) #44501389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊((C₇₃⋊C₃)⋊D₇) #44501389