Finite Group Databasebeta

← C3×#19129773 #30655375

Subgroups — C3×#19129773 #30655375

Order 16380.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#10587717C211yesmaximal, characteristic
2C3×C7×#63118C311yesmaximal, characteristic, complemented
3#19129773C313yesmaximal, direct product factor
4C3×C5×#63271C411yescharacteristic, complemented, Hall
5C3×#11763981—51nomaximal, Hall
6C5×#10587717C2×C313yes—
7C3×C5×C7×D13C2×C311yescharacteristic
8C3×#63118⋊C3—71nomaximal, Hall
9C7×#63118C3211yescharacteristic, complemented, Hall
10C3×#10587717D511yescharacteristic
11C3×C5×C7×C13C3×C411yescharacteristic, complemented
12C5×#63271C3×C413yescomplemented
13C3×Dic5×ΓL(1,𝔽8)—131nomaximal, Hall
14C3×C5×D13⋊C3—71no—
15C3×C7×#261—51no—
16#11763981—53no—
17C5×C7×D13C2×C3211yescharacteristic
18C3×#63271Dic511yescharacteristic, complemented, Hall
19C3×#63118ΓL(1,𝔽8)11yescharacteristic, complemented
20#63118⋊C3—73no—
21C2×C3×C5×ΓL(1,𝔽8)—131no—
22C3×C5×C13⋊C3—71noHall
23C3×C7×D13C3×D511yescharacteristic
24#10587717C3×D513yes—
25C3×AGL(1,𝔽13)—351noHall
26C5×C7×C13C32×C411yescharacteristic, complemented, Hall
27C3×C7×Dic5—131no—
28Dic5×ΓL(1,𝔽8)—133no—
29C3×C5×D13C2×ΓL(1,𝔽8)11yescharacteristic
30C5×D13⋊C3—73no—
31C7×#261—51noHall
32C3×C5×ΓL(1,𝔽8)—131noHall
33C3×C7×C13C3×Dic511yescharacteristic, complemented
34#63271C3×Dic513yescomplemented
35#63118C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
36C3×C4×ΓL(1,𝔽8)—651noHall
37C3×D13⋊C3—71no—
38C2×C3×C5×C7—391no—
39C2×C5×ΓL(1,𝔽8)—133no—
40C3×C5×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
41C5×C13⋊C3—73no—
42C7×D13C32×D511yescharacteristic
43C32×Dic5—911noHall
44C3×#261—51no—
45AGL(1,𝔽13)—353no—
46C7×Dic5—131noHall
47C5×D13C2×C3×ΓL(1,𝔽8)11yescharacteristic
48C2×C3×ΓL(1,𝔽8)—131no—
49C3×C13⋊C3—71noHall
50C3×C5×C7AGL(1,𝔽13)11yescharacteristic, complemented
51C5×ΓL(1,𝔽8)—133no—
52C7×C13C32×Dic511yescharacteristic, complemented, Hall
53C2×C32×C5—911no—
54C3×C4×C7—651no—
55C4×ΓL(1,𝔽8)—653no—
56C3×D13D5×ΓL(1,𝔽8)11yescharacteristic
57D13⋊C3—73no—
58C2×C5×C7—391no—
59C5×C13C3×C4×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
60C3×ΓL(1,𝔽8)—131noHall
61C3×Dic5—391no—
62C3×Dic5—913no—
63#261—51noHall
64C32×C5—911noHall
65C2×C3×C7—391no—
66C2×ΓL(1,𝔽8)—133no—
67C3×C13Dic5×ΓL(1,𝔽8)11yescharacteristic, complemented
68C13⋊C3—73no—
69C32×C4—4551noHall
70C5×C7C3×AGL(1,𝔽13)11yescharacteristic, complemented, Hall
71C2×C3×C5—391no—
72C2×C3×C5—913no—
73C4×C7—651noHall
74D13C3×D5×ΓL(1,𝔽8)11yescharacteristic
75C3×C7#63118⋊C311yescharacteristic, complemented
76ΓL(1,𝔽8)—133no—
77Dic5—391noHall
78C2×C32—911no—
79C3×C5—913no—
80C3×C5#1176398111yescharacteristic, complemented
81C2×C7—391no—
82C13C3×Dic5×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
83C3×C4—1951no—
84C3×C4—4553no—
85C2×C5—391no—
86C32—911noSylow
87C7C3×#63118⋊C311yescharacteristic, complemented, Sylow
88C2×C3—391no—
89C2×C3—913no—
90C5C3×#1176398111yescharacteristic, complemented, Sylow
91C4—1951noSylow
92C3—913no—
93C3#1912977311yescharacteristic, direct product factor
94C2—391no—
subgroupG/H
center, hypercenterC3#19129773
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×#10587717C2
cosocleC5×C7×D13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3×C7×#63118C3semidirect
3. #19129773C3direct (N × H)
4. C3×C5×#63271C4semidirect
9. C7×#63118C32semidirect
11. C3×C5×C7×C13C3×C4semidirect
12. C5×#63271C3×C4semidirect
18. C3×#63271Dic5semidirect
19. C3×#63118ΓL(1,𝔽8)semidirect
26. C5×C7×C13C32×C4semidirect
33. C3×C7×C13C3×Dic5semidirect
34. #63271C3×Dic5semidirect
35. #63118C3×ΓL(1,𝔽8)semidirect
40. C3×C5×C13C4×ΓL(1,𝔽8)semidirect
50. C3×C5×C7AGL(1,𝔽13)semidirect
52. C7×C13C32×Dic5semidirect
59. C5×C13C3×C4×ΓL(1,𝔽8)semidirect
67. C3×C13Dic5×ΓL(1,𝔽8)semidirect
70. C5×C7C3×AGL(1,𝔽13)semidirect
75. C3×C7#63118⋊C3semidirect
80. C3×C5#11763981semidirect
82. C13C3×Dic5×ΓL(1,𝔽8)semidirect
87. C7C3×#63118⋊C3semidirect
90. C5C3×#11763981semidirect
93. C3#19129773direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#105877172
C3×C7×#631183
#191297733
C3×#117639815
C3×#63118⋊C37
C3×Dic5×ΓL(1,𝔽8)13