Finite Group Databasebeta

← C5×#2030⋊C3 #14510693

Subgroups — C5×#2030⋊C3 #14510693

Order 1920.

170 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 28 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
1C5×#543⋊C3C211yesmaximal, characteristic
2C5×#2030C311yesmaximal, characteristic, complemented, Hall
3C2×C4×C5×A4—41nomaximal
4#2030⋊C3C511yesmaximal, characteristic, direct product factor, Hall
5C5×#543C2×C311yescharacteristic
6C5×#381—31no—
7C5×#342—31no—
8C22×C5×A4—41no—
9C2×C5×SL(2,𝔽3)—82no—
10C4×C5×A4—42no—
11#543⋊C3C2×C511yescharacteristic
12C23×C4×C5A411yescharacteristic
13C5×C22⋊Q8—62no—
14C2×C5×C22⋊C4—31no—
15C2×C5×C22⋊C4—31no—
16C5×#95—62no—
17#2030C3×C511yescharacteristic, complemented, Sylow
18C2×C5×A4—42no—
19C2×C5×A4—41no—
20C2×C3×C4×C5—161no—
21C5×SL(2,𝔽3)—82no—
22C2×C4×A4—41no—
23C24×C5C2×A411yescharacteristic
24C2×C5×Q8—22no—
25C22×C4×C5—32no—
26C22×C4×C5—61no—
27C22×C4×C5—61no—
28C22×C4×C5—61no—
29C22×C4×C5SL(2,𝔽3)12yescomplemented
30C5×C4⋊C4—62no—
31C5×C22⋊C4—62no—
32C5×C22⋊C4—62no—
33#543C2×C3×C511yescharacteristic
34#381—31no—
35#342—31no—
36C22×C3×C5—161no—
37C5×A4—41no—
38C3×C4×C5—162no—
39C22×A4—41no—
40C2×SL(2,𝔽3)—82no—
41C4×A4—42no—
42C23×C5—31no—
43C23×C5—31no—
44C23×C5—42no—
45C23×C5C2×SL(2,𝔽3)11yescharacteristic
46C5×Q8—82no—
47C2×C4×C5—41no—
48C2×C4×C5—62no—
49C2×C4×C5—62no—
50C2×C4×C5—121no—
51C2×C4×C5—122no—
52C2×C4×C5—121no—
53C2×C4×C5—122no—
54C23×C4C5×A411yescharacteristic
55C22⋊Q8—62no—
56C2×C22⋊C4—31no—
57C2×C22⋊C4—31no—
58#95—62no—
59C2×C3×C5—161no—
60C2×C3×C5—162no—
61C2×A4—42no—
62C2×A4—41no—
63C2×C3×C4—161no—
64SL(2,𝔽3)—82no—
65C22×C5—31no—
66C22×C5—31no—
67C22×C5—41no—
68C22×C5—62no—
69C22×C5—121no—
70C22×C5#120⋊C311yescharacteristic
71C4×C5—42no—
72C4×C5—122no—
73C4×C5—241no—
74C24C2×C5×A411yescharacteristic
75C2×Q8—22no—
76C22×C4—32no—
77C22×C4—61no—
78C22×C4—61no—
79C22×C4—61no—
80C22×C4C5×SL(2,𝔽3)12yescomplemented
81C4⋊C4—62no—
82C22⋊C4—62no—
83C22⋊C4—62no—
84C3×C5—161noHall
85C22×C3—161no—
86A4—41no—
87C3×C4—162no—
88C2×C5—61no—
89C2×C5—61no—
90C2×C5#393⋊C311yescharacteristic
91C2×C5#458⋊C312yes—
92C23—31no—
93C23—31no—
94C23—42no—
95C23C2×C5×SL(2,𝔽3)11yescharacteristic
96Q8—82no—
97C2×C4—41no—
98C2×C4—62no—
99C2×C4—62no—
100C2×C4—121no—
101C2×C4—122no—
102C2×C4—121no—
103C2×C4—122no—
104C2×C3—161no—
105C2×C3—162no—
106C5#2030⋊C311yescharacteristic, direct product factor, Sylow
107C22—31no—
108C22—31no—
109C22—41no—
110C22—62no—
111C22—121no—
112C22C5×#120⋊C311yescharacteristic
113C4—42no—
114C4—122no—
115C4—241no—
116C3—161noSylow
117C2—61no—
118C2—61no—
119C2C5×#393⋊C311yescharacteristic
120C2C5×#458⋊C312yes—
subgroupG/H
center, socle, hypercenterC22×C5#120⋊C3
commutator, cosocle, hypocenter#543C2×C3×C5
FrattiniC24C2×C5×A4
FittingC5×#2030C3
prime radicalC5×#543⋊C3C2
LCSG ▷ #543
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
2. C5×#2030C3semidirect
4. #2030⋊C3C5direct (N × H)
17. #2030C3×C5semidirect
29. C22×C4×C5SL(2,𝔽3)semidirect
80. C22×C4C5×SL(2,𝔽3)semidirect
106. C5#2030⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#543⋊C32
C5×#20303
C2×C4×C5×A44
#2030⋊C35