Finite Group Databasebeta

← C3×C31×C3⋊#1044 #42124921

Subgroups — C3×C31×C3⋊#1044 #42124921

Order 27900.

160 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C31×C5⋊D5C211yesmaximal, characteristic
2C31×C3⋊#1044C311yesmaximal, characteristic, direct product factor
3C3×C31×#1044—31nomaximal
4C32×C52×C31C411yescharacteristic, complemented, Hall
5C3×C31×ΓL(1,𝔽16)—52nomaximal
6C3×C31×C5⋊D5—21no—
7C3×C31×C5⋊D5D311yescharacteristic
8C3×C31×C5⋊D5C2×C311yescharacteristic
9C31×#1044—31noHall
10C32×D5×C31—52no—
11C32×D5×C31—102no—
12C3×C52×C31—21no—
13C3×C52×C31Dic311yescharacteristic, complemented
14C3×C52×C31C3×C411yescharacteristic, complemented
15C31×ΓL(1,𝔽16)—52no—
16C3×AGL(1,𝔽5)×C31—152no—
17C31×C5⋊D5C3×D311yescharacteristic
18C32×C5×C31—22no—
19C32×C5×C31AGL(1,𝔽5)12yescomplemented
20C3×Dic3×C31—251noHall
21C3×D5×C31—52no—
22C3×D5×C31—52no—
23C3×D5×C31—102no—
24C3×D5×C31—102no—
25C3×D5×C31—102no—
26C3×D5×C31—104no—
27C3×C3⋊#1044C3111yesmaximal, characteristic, direct product factor, Hall
28C52×C31C3×Dic311yescharacteristic, complemented, Hall
29AGL(1,𝔽5)×C31—152no—
30C2×C32×C31—251no—
31C3×C5×C31—24no—
32C3×C5×C31—22no—
33C3×C5×C31—22no—
34C3×C5×C31—22no—
35C3×C5×C31C3×AGL(1,𝔽5)12yescomplemented
36C3×C5×C31ΓL(1,𝔽16)12yescomplemented
37C32×C5⋊D5C2×C3111yescharacteristic
38C3×C4×C31—751no—
39Dic3×C31—251no—
40D5×C31—52no—
41D5×C31—102no—
42C3⋊#1044C3×C3111yescharacteristic, direct product factor
43C3×#1044—31no—
44C32×C31#104411yescharacteristic, complemented, Hall
45C32×C52C4×C3111yescharacteristic, complemented, Hall
46C2×C3×C31—251no—
47C2×C3×C31—251no—
48C2×C3×C31—501no—
49C3×ΓL(1,𝔽16)—52no—
50C5×C31—22no—
51C5×C31C3×ΓL(1,𝔽16)12yescomplemented
52C3×C5⋊D5—21no—
53C3×C5⋊D5D3×C3111yescharacteristic
54C3×C5⋊D5C2×C3×C3111yescharacteristic
55C4×C31—751noHall
56#1044—31noHall
57C3×C31—21no—
58C3×C31C3×#104411yescharacteristic, complemented
59C3×C31C3⋊#104411yescharacteristic, direct product factor
60C32×D5—52no—
61C32×D5—102no—
62C3×C52—21no—
63C3×C52Dic3×C3111yescharacteristic, complemented
64C3×C52C3×C4×C3111yescharacteristic, complemented
65C2×C31—251no—
66ΓL(1,𝔽16)—52no—
67C3×AGL(1,𝔽5)—152no—
68C5⋊D5C3×D3×C3111yescharacteristic
69C32×C5—22no—
70C32×C5AGL(1,𝔽5)×C3112yescomplemented
71C3×Dic3—251noHall
72C31C3×C3⋊#104411yescharacteristic, direct product factor, Sylow
73C3×D5—52no—
74C3×D5—52no—
75C3×D5—102no—
76C3×D5—102no—
77C3×D5—102no—
78C3×D5—104no—
79C52C3×Dic3×C3111yescharacteristic, complemented, Sylow
80AGL(1,𝔽5)—152no—
81C2×C32—251no—
82C3×C5—24no—
83C3×C5—22no—
84C3×C5—22no—
85C3×C5—22no—
86C3×C5C3×AGL(1,𝔽5)×C3112yescomplemented
87C3×C5C31×ΓL(1,𝔽16)12yescomplemented
88C3×C4—751no—
89Dic3—251no—
90D5—52no—
91D5—102no—
92C32C31×#104411yescharacteristic, complemented, Sylow
93C2×C3—251no—
94C2×C3—251no—
95C2×C3—501no—
96C5—22no—
97C5C3×C31×ΓL(1,𝔽16)12yescomplemented
98C4—751noSylow
99C3—21no—
100C3C3×C31×#104411yescharacteristic, complemented
101C3C31×C3⋊#104411yescharacteristic, direct product factor
102C2—251no—
subgroupG/H
center, hypercenterC3×C31C3⋊#1044
commutator, hypocenterC3×C52C3×C4×C31
FrattiniC1G
Fitting, socleC32×C52×C31C4
prime radicalC32×C31×C5⋊D5C2
cosocleC3×C5⋊D5C2×C3×C31
LCSG ▷ C3×C52
UCSC1 ◁ C3×C31

Complements

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

NH ≅ G/Ntype
2. C31×C3⋊#1044C3direct (N × H)
4. C32×C52×C31C4semidirect
13. C3×C52×C31Dic3semidirect
14. C3×C52×C31C3×C4semidirect
19. C32×C5×C31AGL(1,𝔽5)semidirect
27. C3×C3⋊#1044C31direct (N × H)
28. C52×C31C3×Dic3semidirect
35. C3×C5×C31C3×AGL(1,𝔽5)semidirect
36. C3×C5×C31ΓL(1,𝔽16)semidirect
42. C3⋊#1044C3×C31direct (N × H)
44. C32×C31#1044semidirect
45. C32×C52C4×C31semidirect
51. C5×C31C3×ΓL(1,𝔽16)semidirect
58. C3×C31C3×#1044semidirect
59. C3×C31C3⋊#1044direct (N × H)
63. C3×C52Dic3×C31semidirect
64. C3×C52C3×C4×C31semidirect
70. C32×C5AGL(1,𝔽5)×C31semidirect
72. C31C3×C3⋊#1044direct (N × H)
79. C52C3×Dic3×C31semidirect
86. C3×C5C3×AGL(1,𝔽5)×C31semidirect
87. C3×C5C31×ΓL(1,𝔽16)semidirect
92. C32C31×#1044semidirect
97. C5C3×C31×ΓL(1,𝔽16)semidirect
100. C3C3×C31×#1044semidirect
101. C3C31×C3⋊#1044direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C31×C5⋊D52
C31×C3⋊#10443
C3×C31×#10443
C3×C31×ΓL(1,𝔽16)5
C3×C3⋊#104431