Finite Group Databasebeta

← C3×#91948 #13089056

Subgroups — C3×#91948 #13089056

Order 1440.

180 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C3×C4×C5×A4C211yesmaximal, characteristic
2C3×A4⋊Dic5C212yesmaximal
3#91948C311yesmaximal, characteristic, direct product factor
4C3×#4070—31nomaximal
5C2×C3×C5×A4C2211yescharacteristic
6C3×Dic30—41nomaximal
7C3×A4⋊Q8—51nomaximal, Hall
8C22×C3×C4×C5D311yescharacteristic
9C2×C3×Dic10—31no—
10C4×C5×A4—21no—
11C4×C5×A4C2×C311yescharacteristic
12A4⋊Dic5C2×C312yes—
13C3×C22⋊Dic5—32no—
14C3×C4⋊Dic5—31no—
15C3×#683—32no—
16C3×C5×A4Q811yescharacteristic, complemented
17C32×C4×C5—41no—
18C3×Dic15—42no—
19#4070—31noHall
20C3×C4×A4D511yescharacteristic
21C3×SL(2,ℤ/4)—52no—
22C23×C3×C5C2×D311yescharacteristic
23C2×C5×A4—21no—
24C2×C5×A4C22×C311yescharacteristic
25C2×C3×C4×C5—31no—
26C2×C3×C4×C5—31no—
27Dic30—41no—
28C2×C3×Dic5—32no—
29C2×C3×Dic5—32no—
30C3×Dic10—61no—
31C3×Dic10—61no—
32A4⋊Q8—51no—
33C3×C22⋊Q8—151no—
34C2×C32×C5—41no—
35C22×C4×C5C3×D311yescharacteristic
36C2×Dic10—31no—
37C22⋊Dic5—32no—
38C4⋊Dic5—31no—
39#683—32no—
40C2×C3×A4C2×D511yescharacteristic
41C3×Dic6—201no—
42C22×C3×C5—31no—
43C22×C3×C5—31no—
44C22×C3×C5Dic611yescharacteristic, complemented
45C5×A4—21no—
46C5×A4C3×Q811yescharacteristic, complemented
47C3×C4×C5—31no—
48C3×C4×C5—41no—
49C3×C4×C5—81no—
50C3×C4×C5S411yescharacteristic
51Dic15—42no—
52C3×Dic5—62no—
53C3×Dic5—62no—
54C2×C3×Q8—151no—
55C22×C3×C4D1511yescharacteristic
56C4×A4—21no—
57C4×A4C3×D511yescharacteristic
58SL(2,ℤ/4)—52no—
59C3×C4⋊C4—152no—
60C3×C4⋊C4—151no—
61C3×C22⋊C4—152no—
62C32×C5—41noHall
63C23×C5C2×C3×D311yescharacteristic
64C2×C4×C5—31no—
65C2×C4×C5—31no—
66C2×Dic5—32no—
67C2×Dic5—32no—
68Dic10—61no—
69Dic10—61no—
70C3×A4Dic1011yescharacteristic, complemented
71C32×C4—41no—
72C3×Dic3—202no—
73C22⋊Q8—151noSylow
74C2×C3×C5—31no—
75C2×C3×C5—31no—
76C2×C3×C5—41no—
77C2×C3×C5—81no—
78C2×C3×C5C2×S411yescharacteristic
79C23×C3C2×D1511yescharacteristic
80C2×A4—21no—
81C2×A4C2×C3×D511yescharacteristic
82C3×Q8—301no—
83C3×Q8—301no—
84C2×C3×C4—31no—
85C2×C3×C4—31no—
86C2×C3×C4—152no—
87C2×C3×C4—152no—
88Dic6—201no—
89C22×C5—31no—
90C22×C5—31no—
91C22×C5C3×Dic611yescharacteristic, complemented
92C4×C5—31no—
93C4×C5C3×S411yescharacteristic
94Dic5—62no—
95Dic5—62no—
96C2×C32—41no—
97C2×Q8—151no—
98C22×C4C3×D1511yescharacteristic
99C4⋊C4—152no—
100C4⋊C4—151no—
101C22⋊C4—152no—
102C3×C5—41no—
103C3×C5—81no—
104C3×C5A4⋊Q811yescharacteristic, complemented
105C22×C3—31no—
106C22×C3—31no—
107C22×C3Dic3011yescharacteristic, complemented
108A4—21no—
109A4C3×Dic1011yescharacteristic, complemented
110C3×C4—31no—
111C3×C4—41no—
112C3×C4—81no—
113C3×C4—302no—
114C3×C4—302no—
115C3×C4C5⋊S411yescharacteristic
116Dic3—202no—
117C2×C5—31no—
118C2×C5—31no—
119C2×C5C2×C3×S411yescharacteristic
120C32—41noSylow
121C23C2×C3×D1511yescharacteristic
122Q8—301no—
123Q8—301no—
124C2×C4—31no—
125C2×C4—31no—
126C2×C4—152no—
127C2×C4—152no—
128C2×C3—31no—
129C2×C3—31no—
130C2×C3—41no—
131C2×C3—81no—
132C2×C3C2×C5⋊S411yescharacteristic
133C5C3×A4⋊Q811yescharacteristic, complemented, Sylow
134C22—31no—
135C22—31no—
136C22C3×Dic3011yescharacteristic, complemented
137C4—31no—
138C4—302no—
139C4—302no—
140C4C3×C5⋊S411yescharacteristic
141C3—41no—
142C3—81no—
143C3#9194811yescharacteristic, direct product factor
144C2—31no—
145C2—31no—
146C2C2×C3×C5⋊S411yescharacteristic
subgroupG/H
centerC2×C3C2×C5⋊S4
commutator, cosocleC2×C5×A4C22×C3
FrattiniC2C2×C3×C5⋊S4
FittingC22×C3×C4×C5D3
socleC23×C3×C5C2×D3
prime radicalC2×C3×C5×A4C22
hypercenterC3×C4C5⋊S4
hypocenterC5×A4C3×Q8
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
3. #91948C3direct (N × H)
16. C3×C5×A4Q8semidirect
44. C22×C3×C5Dic6semidirect
46. C5×A4C3×Q8semidirect
70. C3×A4Dic10semidirect
91. C22×C5C3×Dic6semidirect
104. C3×C5A4⋊Q8semidirect
107. C22×C3Dic30semidirect
109. A4C3×Dic10semidirect
133. C5C3×A4⋊Q8semidirect
136. C22C3×Dic30semidirect
143. C3#91948direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C5×A42
C3×A4⋊Dic52
#919483
C3×#40703
C3×Dic304
C3×A4⋊Q85