Finite Group Databasebeta

← C3×#91143 #13085367

Subgroups — C3×#91143 #13085367

Order 1440.

104 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 16 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
1C2×C3×SL(2,𝔽5)C211yesmaximal, characteristic
2#91143C311yesmaximal, characteristic, direct product factor
3C3×SL(2,𝔽5)C411yescharacteristic, complemented
4C3×#859—51nomaximal, Hall
5C2×C3×#170—61nomaximal
6C2×SL(2,𝔽5)C2×C311yescharacteristic
7C2×C3×SL(2,𝔽3)—51no—
8C3×Dic3⋊C4—101nomaximal
9C2×C3×Dic5—61no—
10C3×#170—62no—
11SL(2,𝔽5)C3×C411yescharacteristic, complemented
12#859—51no—
13C3×#103—151no—
14C2×#170—61no—
15C2×C32×C4—101no—
16C2×C3×Dic3—101no—
17C2×C3×Dic3—101no—
18C3×SL(2,𝔽3)—51no—
19C22×C3×C5—61no—
20C3×Dic5—61no—
21C3×Dic5—61no—
22C2×C3×Q8—51no—
23C2×SL(2,𝔽3)—51no—
24C2×SL(2,𝔽3)—101no—
25C2×C3×C8—151no—
26C3×C4⋊C4—151no—
27Dic3⋊C4—101no—
28C2×Dic5—61no—
29#170—62no—
30C22×C32—101no—
31C32×C4—201no—
32C3×Dic3—101no—
33C3×Dic3—101no—
34C3×Dic3—201no—
35#103—151noSylow
36C2×C3×C5—61no—
37C2×C3×C5—61no—
38C2×C3×C5—61no—
39C3×Q8—51no—
40C3×Q8—151no—
41C2×C3×C4—101no—
42C2×C3×C4—101no—
43C2×C3×C4—151no—
44C2×C3×C4—201no—
45C2×Dic3—101no—
46C2×Dic3—101no—
47SL(2,𝔽3)—51no—
48SL(2,𝔽3)—101no—
49C3×C8—301no—
50C22×C5—61no—
51Dic5—61no—
52Dic5—61no—
53C2×C32—101no—
54C2×C32—101no—
55C2×C32—101no—
56C2×Q8—51no—
57C2×C8—151no—
58C4⋊C4—151no—
59C3×C5—61no—
60C22×C3—101no—
61C22×C3—201no—
62C22×C3S511yescharacteristic
63C3×C4—151no—
64C3×C4—151no—
65C3×C4—201no—
66C3×C4—202no—
67C3×C4—201no—
68Dic3—101no—
69Dic3—101no—
70Dic3—201no—
71C2×C5—61no—
72C2×C5—61no—
73C2×C5—61no—
74C32—101noSylow
75Q8—51no—
76Q8—151no—
77C2×C4—101no—
78C2×C4—151no—
79C8—301no—
80C2×C3—101no—
81C2×C3—101no—
82C2×C3—101no—
83C2×C3—201no—
84C2×C3—201no—
85C2×C3—201no—
86C2×C3#672811yescharacteristic
87C2×C3#672911yescharacteristic
88C2×C3A5⋊C411yescharacteristic
89C5—61noSylow
90C22C3×S511yescharacteristic
91C4—151no—
92C4—151no—
93C4—201no—
94C3—101no—
95C3—201no—
96C3#9114311yescharacteristic, direct product factor
97C2C3×#672811yescharacteristic
98C2C3×#672911yescharacteristic
99C2C3×A5⋊C411yescharacteristic
subgroupG/H
center, Fitting, socle, hypercenterC22×C3S5
commutator, hypocenterSL(2,𝔽5)C3×C4
FrattiniC22C3×S5
prime radicalC2×C3×SL(2,𝔽5)C2
cosocleC2×SL(2,𝔽5)C2×C3
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. #91143C3direct (N × H)
3. C3×SL(2,𝔽5)C4semidirect
11. SL(2,𝔽5)C3×C4semidirect
96. C3#91143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×SL(2,𝔽5)2
#911433
C3×#8595
C2×C3×#1706
C3×Dic3⋊C410