Subgroups — #15690445⋊D₅ #44501340

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#15690449	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊#15690441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#15690445	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×#13095275	C₂²	1	1	yes	characteristic, complemented, Hall
6	#15690441⋊C₂	—	5	1	no	maximal, Hall
7	D₂₅₅₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₃₆₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₅⋊(D₇₃⋊C₃)	—	7	1	no	maximal, Hall
11	#15690449	—	5	1	no	—
12	#15690445	D₅	1	1	yes	characteristic, complemented
13	#15690441	—	5	1	no	—
14	C₅×C₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₅⋊(D₇₃⋊C₃)	—	7	1	no	—
16	C₅⋊(D₇₃⋊C₃)	—	7	1	no	—
17	C₂×C₅×C₇₃⋊C₃	—	7	1	no	—
18	D₇×D₇₃	—	5	1	no	Hall
19	#13095275	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₆₅	—	7	1	no	Hall
21	C₅×C₇₃⋊C₃	—	7	1	no	Hall
22	D₅₁₁	—	5	1	no	—
23	C₇×D₇₃	—	5	1	no	—
24	D₇×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented
25	C₂×D₇₃⋊C₃	—	35	1	no	Hall
26	C₂×C₅×C₇₃	—	7	1	no	—
27	D₃₆₅	—	7	1	no	—
28	D₃₆₅	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	C₇×C₇₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇₃⋊C₃	—	7	1	no	—
31	D₇₃⋊C₃	—	35	1	no	—
32	D₇₃⋊C₃	—	35	1	no	—
33	D₅×AGL(1,𝔽₇)	—	73	1	no	maximal, Hall
34	C₅×C₇₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₃	—	35	1	no	Hall
36	C₇₃⋊C₃	—	7	1	no	Hall
37	C₅⋊AGL(1,𝔽₇)	—	73	1	no	—
38	D₅×ΓL(1,𝔽₈)	—	73	1	no	—
39	C₅×AGL(1,𝔽₇)	—	73	1	no	—
40	C₂×C₇₃	—	7	1	no	—
41	D₇₃	—	5	1	no	—
42	D₇₃	—	35	1	no	—
43	D₅×D₇	—	73	1	no	Hall
44	C₅×ΓL(1,𝔽₈)	—	73	1	no	Hall
45	C₂×AGL(1,𝔽₇)	—	365	1	no	Hall
46	C₇₃	D₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
47	D₃₅	—	73	1	no	—
48	C₅×D₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented
49	C₇×D₅	—	73	1	no	—
50	C₂×C₃×D₅	—	511	1	no	Hall
51	C₂×ΓL(1,𝔽₈)	—	365	1	no	—
52	AGL(1,𝔽₇)	—	73	1	no	—
53	AGL(1,𝔽₇)	—	365	1	no	—
54	C₅×C₇	C₂×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	511	1	no	—
56	C₃×D₅	—	511	1	no	—
57	C₃×D₅	—	511	1	no	—
58	C₂×D₇	—	365	1	no	Hall
59	ΓL(1,𝔽₈)	—	73	1	no	Hall
60	C₂×D₅	—	511	1	no	Hall
61	C₃×C₅	—	511	1	no	Hall
62	C₂×C₇	—	365	1	no	—
63	D₇	—	365	1	no	—
64	D₇	C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented
65	C₂²×C₃	—	2555	1	no	Hall
66	C₂×C₅	—	7	1	no	—
67	D₅	—	73	1	no	—
68	D₅	—	511	1	no	—
69	C₇	C₂×C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	2555	1	no	—
71	C₂×C₃	—	2555	1	no	—
72	C₂×C₃	—	511	1	no	—
73	C₅	#15690441⋊C₂	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	2555	1	no	Sylow
75	C₃	—	511	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	365	1	no	—
78	C₂	—	2555	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₇₃	C₂²×C₃
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊#15690449	C₂	semidirect
2. C₅⋊#15690441	C₂	semidirect
3. C₅×#15690445	C₂	semidirect
4. D₇×D₃₆₅	C₃	semidirect
5. C₅×#13095275	C₂²	semidirect
7. D₂₅₅₅	C₂×C₃	semidirect
8. C₇×D₃₆₅	C₂×C₃	semidirect
9. C₅×D₇×C₇₃	C₂×C₃	semidirect
12. #15690445	D₅	semidirect
14. C₅×C₇×C₇₃	C₂²×C₃	semidirect
19. #13095275	C₂×D₅	semidirect
24. D₇×C₇₃	C₃×D₅	semidirect
28. D₃₆₅	AGL(1,𝔽₇)	semidirect
29. C₇×C₇₃	C₂×C₃×D₅	semidirect
34. C₅×C₇₃	C₂×AGL(1,𝔽₇)	semidirect
46. C₇₃	D₅×AGL(1,𝔽₇)	semidirect
48. C₅×D₇	D₇₃⋊C₃	semidirect
54. C₅×C₇	C₂×D₇₃⋊C₃	semidirect
64. D₇	C₅⋊(D₇₃⋊C₃)	semidirect
69. C₇	C₂×C₅⋊(D₇₃⋊C₃)	semidirect
73. C₅	#15690441⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊#15690449	2
C₅⋊#15690441	2
C₅×#15690445	2
D₇×D₃₆₅	3
#15690441⋊C₂	5
C₂×C₅⋊(D₇₃⋊C₃)	7
D₅×AGL(1,𝔽₇)	73

Subgroups — #15690445⋊D5 #44501340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #15690445⋊D₅ #44501340