Finite Group Databasebeta

← #14279551

Subgroups — #14279551

Order 1920.

168 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 40 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
1#11751157C211yesmaximal, characteristic
2C5×#4542C211yesmaximal, characteristic
3C3×#64761C211yesmaximal, characteristic
4#10598038—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6#91759C411yescharacteristic, complemented
7#91119—21no—
8#91116—21no—
9C4×C3⋊#168C411yescharacteristic, complemented
10C5×#836—21no—
11C3×#3966—21no—
12#67543—51nomaximal, Hall
13#65345—31no—
14C5×#355—31no—
15#64761D311yescharacteristic
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C3×C5×C22⋊C4—41no—
19C3×C42×C5C2×C411yescharacteristic
20C4⋊Dic15—21no—
21#6712—41no—
22C2×C3⋊#168—21no—
23C5×#208—41no—
24C3×C22⋊Dic5—41no—
25#5056—51no—
26C3×#354—51no—
27#4542D511yescharacteristic
28C5×#124C2×D311yescharacteristic
29#4016—31no—
30C5×#101—61no—
31#3967—61no—
32#3966—21no—
33#3964—61no—
34C4×#168—31no—
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×C5C22⋊C411yescharacteristic
42C2×Dic15—41no—
43C2×C3×Dic5—81no—
44C3⋊#168—41no—
45C5×C3⋊C8—81no—
46C3×#124C2×D511yescharacteristic
47#870—51no—
48C3×#99—101no—
49#836—21no—
50#835—101no—
51#832—101no—
52C4×C3⋊C8—51no—
53C2×C5×Q8D1211yescharacteristic
54C2×C5×D4#6711yescharacteristic
55C5×M16—121no—
56C5×C22⋊C4—41no—
57C42×C5C4×D311yescharacteristic
58C22⋊Dic5—41no—
59C4⋊Dic5—61no—
60#683—121no—
61C2×#168—61no—
62#488—151no—
63#355—31no—
64#354—51no—
65C22×C3×C5—41no—
66C22×C3×C5—81no—
67C22×C3×C5#9911yescharacteristic
68C3×C4×C5—21no—
69C3×C4×C5—41no—
70C3×C4×C5—41no—
71Dic15—81no—
72C3×Dic5—161no—
73C2×C3×Q8C22⋊D511yescharacteristic
74C2×C3×D4D2011yescharacteristic
75C3×C22⋊C4—41no—
76C3×C22⋊C4—201no—
77C3×C42C4×D511yescharacteristic
78C4⋊Dic3—101no—
79Dic3⋊C4—201no—
80#208—41no—
81C2×C3⋊C8—101no—
82C23×C5—21no—
83C5×Q8—41no—
84C5×D4—41no—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5(C2×D3)⋊C411yescharacteristic
88C2×Dic5—81no—
89C2×Dic5—121no—
90C5×C8—241no—
91#168—121no—
92#125—151no—
93#124D3×D511yescharacteristic
94#103—301no—
95#102—301no—
96#101—61no—
97#99—101no—
98C4×C8—151no—
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—401no—
108C2×C3×C4#68511yescharacteristic
109C2×Dic3—201no—
110C3⋊C8—81no—
111C3⋊C8—201no—
112C22×C5—41no—
113C22×C5—81no—
114C22×C5#80611yescharacteristic
115C4×C5—21no—
116C4×C5—41no—
117C4×C5—41no—
118Dic5—161no—
119Dic5—241no—
120C2×Q8#120311yescharacteristic
121C2×D4#120211yescharacteristic
122M16—121no—
123C2×C8—301no—
124C4⋊C4—301no—
125C4⋊C4—601no—
126C22⋊C4—41no—
127C22⋊C4—201no—
128C42#120011yescharacteristic
129C3×C5#141411yescharacteristic, complemented, Hall
130C22×C3—41no—
131C22×C3—81no—
132C22×C3#393811yescharacteristic
133C3×C4—21no—
134C3×C4—41no—
135C3×C4—41no—
136C3×C4—801no—
137Dic3—401no—
138C2×C5—21no—
139C2×C5—81no—
140C2×C5#447311yescharacteristic
141C23—21no—
142Q8—41no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—401no—
147C2×C4—601no—
148C2×C4#666711yescharacteristic
149C8—241no—
150C8—601no—
151C2×C3—21no—
152C2×C3—81no—
153C2×C3#6469311yescharacteristic
154C5#6754311yescharacteristic, complemented, Sylow
155C22—41no—
156C22—81no—
157C22#9099711yescharacteristic
158C4—21no—
159C4—41no—
160C4—41no—
161C4—801no—
162C4—1201no—
163C3#1059803811yescharacteristic, complemented, Sylow
164C2—21no—
165C2—81no—
166C2#1174601111yescharacteristic
subgroupG/H
centerC2#11746011
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5#354
prime radicalC2×C3×C5×D4D4
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

Complements

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

NH ≅ G/Ntype
6. #91759C4semidirect
9. C4×C3⋊#168C4semidirect
129. C3×C5#1414semidirect
154. C5#67543semidirect
163. C3#10598038semidirect

Maximal subgroups

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

subgroupindex
#117511572
C5×#45422
C3×#647612
#105980383
#675435