Finite Group Databasebeta

← #14279535

Subgroups — #14279535

Order 1920.

168 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 47 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×C5×#488C211yesmaximal, characteristic
2#11746363C211yesmaximal, characteristic
3#11746362C211yesmaximal, characteristic
4#10598273—31nomaximal, Hall
5C3×C5×#125C411yescharacteristic, complemented
6C3×C5×#124C2211yescharacteristic
7C3×C5×#103—21no—
8C3×C5×#102—21no—
9C3×C4×C5×C8C411yescharacteristic, complemented
10#91120—21no—
11#91118—21no—
12#67782—51nomaximal, Hall
13C5×#488D311yescharacteristic
14#64762—31no—
15#64761—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×C8—21no—
19C3×C5×C4⋊C4—21no—
20C3×C5×C4⋊C4—41no—
21C3×C5×C22⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23#6719—41no—
24#6710—41no—
25C3×#488D511yescharacteristic
26#4542—51no—
27#4541—51no—
28C5×#125Dic311yescharacteristic, complemented
29C5×#124C2×D311yescharacteristic
30C5×#103—21no—
31C5×#102—21no—
32C4×C5×C8Dic311yescharacteristic, complemented
33#3968—61no—
34#3966—61no—
35#1414—151noSylow
36C23×C3×C5—21no—
37C3×C5×Q8—41no—
38C3×C5×D4—41no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C2×Dic15—81no—
44C3×C5×C8—41no—
45C3⋊#168—81no—
46C3×#125Dic511yescharacteristic, complemented
47C3×#124C2×D511yescharacteristic
48C3×#103—21no—
49C3×#102—21no—
50C3×C4×C8Dic511yescharacteristic, complemented
51#836—101no—
52#834—101no—
53C2×C5×Q8#6711yescharacteristic
54C2×C5×D4#6711yescharacteristic
55C2×C5×C8—21no—
56C5×C4⋊C4—21no—
57C5×C4⋊C4—41no—
58C5×C22⋊C4—41no—
59C42×C5C2×Dic311yescharacteristic
60C22⋊Dic5—121no—
61#681—121no—
62#488D1511yescharacteristic
63#355—151no—
64#354—151no—
65C22×C3×C5—41no—
66C22×C3×C5—81no—
67C22×C3×C5#9911yescharacteristic
68C3×C4×C5—21no—
69C3×C4×C5—41no—
70C3×C4×C5—41no—
71C3×C4×C5—81no—
72Dic15—161no—
73C2×C3×Q8C22⋊D511yescharacteristic
74C2×C3×D4C22⋊D511yescharacteristic
75C2×C3×C8—21no—
76C3×C4⋊C4—21no—
77C3×C4⋊C4—41no—
78C3×C22⋊C4—41no—
79C3×C42C2×Dic511yescharacteristic
80#217—201no—
81#208—201no—
82C23×C5—21no—
83C5×Q8—41no—
84C5×D4—41no—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—41no—
88C2×C4×C5#21711yescharacteristic
89C2×Dic5—241no—
90C5×C8—41no—
91#168—241no—
92#125Dic1511yescharacteristic, complemented
93#124C2×D1511yescharacteristic
94#103—21no—
95#102—21no—
96#101—301no—
97#99—301no—
98C4×C8Dic1511yescharacteristic, complemented
99C2×C3×C5—21no—
100C2×C3×C5—81no—
101C2×C3×C5#35411yescharacteristic
102C23×C3—21no—
103C3×Q8—41no—
104C3×D4—41no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—41no—
108C2×C3×C4C22⋊Dic511yescharacteristic
109C2×Dic3—401no—
110C3×C8—41no—
111C3⋊C8—401no—
112C22×C5—41no—
113C22×C5—81no—
114C22×C5#83411yescharacteristic
115C4×C5—21no—
116C4×C5—41no—
117C4×C5—41no—
118C4×C5—81no—
119Dic5—481no—
120C2×Q8#122011yescharacteristic
121C2×D4#122011yescharacteristic
122M16—601no—
123C2×C8—21no—
124C4⋊C4—21no—
125C4⋊C4—41no—
126C22⋊C4—41no—
127C22⋊C4—601no—
128C42C2×Dic1511yescharacteristic
129C3×C5#141411yescharacteristic, complemented, Hall
130C22×C3—41no—
131C22×C3—81no—
132C22×C3#396611yescharacteristic
133C3×C4—21no—
134C3×C4—41no—
135C3×C4—41no—
136C3×C4—81no—
137Dic3—801no—
138C2×C5—21no—
139C2×C5—81no—
140C2×C5#454111yescharacteristic
141C23—21no—
142Q8—41no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—1201no—
148C2×C4#671911yescharacteristic
149C8—41no—
150C8—1201no—
151C2×C3—21no—
152C2×C3—81no—
153C2×C3#6476111yescharacteristic
154C5#6778211yescharacteristic, complemented, Sylow
155C22—41no—
156C22—81no—
157C22#9111811yescharacteristic
158C4—21no—
159C4—41no—
160C4—41no—
161C4—81no—
162C4—2401no—
163C3#1059827311yescharacteristic, complemented, Sylow
164C2—21no—
165C2—81no—
166C2#1174636211yescharacteristic
subgroupG/H
centerC2#11746362
commutatorC3×C42×C5C2×C4
Frattini#124C2×D15
FittingC3×C5×#488C2
socleC2×C3×C5#354
prime radicalC2×C3×C5×D4D4
cosocleC3×C5×#124C22
hypercenter#488D15
hypocenterC3×C5#1414
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
5. C3×C5×#125C4semidirect
9. C3×C4×C5×C8C4semidirect
28. C5×#125Dic3semidirect
32. C4×C5×C8Dic3semidirect
46. C3×#125Dic5semidirect
50. C3×C4×C8Dic5semidirect
92. #125Dic15semidirect
98. C4×C8Dic15semidirect
129. C3×C5#1414semidirect
154. C5#67782semidirect
163. C3#10598273semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4882
#117463632
#117463622
#105982733
#677825