Finite Group Databasebeta

← #14279557

Subgroups — #14279557

Order 1920.

168 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 34 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#11746896C211yesmaximal, characteristic
2#11746727C211yesmaximal, characteristic
3C3×#64854C211yesmaximal, characteristic
4#10598741—31nomaximal, Hall
5C5×#870C411yescharacteristic, complemented
6C3×#4021C2211yescharacteristic
7#91234—21no—
8C3×#3999—21no—
9C4×C3⋊#168C411yescharacteristic, complemented
10#90970—21no—
11#90964—21no—
12#67543—51nomaximal, Hall
13#65357—31no—
14#64856—31no—
15#64854D311yescharacteristic
16C2×C3×D20D411yescharacteristic
17C2×C3×Dic10D411yescharacteristic
18#6762—41no—
19C3×C22⋊AGL(1,𝔽5)—41no—
20C3×C42×C5C2×C411yescharacteristic
21C2×C3⋊#168—21no—
22C5×C4⋊Dic3—21no—
23C5×Dic3⋊C4—41no—
24C3×#685—41no—
25#5056—51no—
26C3×#354—51no—
27#4542—51no—
28C5×#125—31no—
29#4021C2×D311yescharacteristic
30#4005—61no—
31#3999—21no—
32#3942—61no—
33#3941—61no—
34C4×#168—31no—
35#1414—151noSylow
36C22×C3×D5—21no—
37C2×C3×AGL(1,𝔽5)—81no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5C22⋊C411yescharacteristic
40C2×C5×Dic3—41no—
41C2×C3×Dic5—21no—
42C3×D20—41no—
43C3×Dic10—41no—
44C3⋊#170—81no—
45C3⋊#168—41no—
46C3×#124—51no—
47#870AGL(1,𝔽5)11yescharacteristic, complemented
48C3×#99—101no—
49#836—101no—
50#835—101no—
51#832—101no—
52C4×C3⋊C8—51no—
53C2×D20#6711yescharacteristic
54C2×Dic10D1211yescharacteristic
55C22⋊AGL(1,𝔽5)—41no—
56#704—121no—
57C5×C4⋊C4—61no—
58C5×C4⋊C4—121no—
59C42×C5C4×D311yescharacteristic
60#685—41no—
61C2×#168—61no—
62#488—151no—
63#355—151no—
64#354—51no—
65C22×C3×C5#9911yescharacteristic
66C2×C3×D5—41no—
67C2×C3×D5—81no—
68C3×AGL(1,𝔽5)—161no—
69C3×C4×C5—21no—
70C3×C4×C5—41no—
71C3×Dic5—41no—
72C5×Dic3—81no—
73C2×C3×Q8—51no—
74C2×C3×D4—51no—
75C3×C22⋊C4—201no—
76C3×C22⋊C4—201no—
77C3×C42C2×AGL(1,𝔽5)11yescharacteristic
78C4⋊Dic3—21no—
79Dic3⋊C4—41no—
80#208—201no—
81C2×C3⋊C8—101no—
82C22×D5—21no—
83C2×AGL(1,𝔽5)—81no—
84C2×C4×C5—21no—
85C2×C4×C5—121no—
86C2×C4×C5(C2×D3)⋊C411yescharacteristic
87C2×Dic5—21no—
88D20—41no—
89Dic10—41no—
90#170—241no—
91#168—121no—
92#125—31no—
93#124—51no—
94#103—301no—
95#102—301no—
96#101—301no—
97#99—101no—
98C4×C8—151no—
99C2×C3×C5—21no—
100C2×C3×C5#35411yescharacteristic
101C3×D5—81no—
102C23×C3—101no—
103C3×Q8—201no—
104C3×D4—201no—
105C2×C3×C4—21no—
106C2×C3×C4—101no—
107C2×C3×C4—401no—
108C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
109C2×Dic3—41no—
110C3⋊C8—201no—
111C3⋊C8—401no—
112C22×C5#80611yescharacteristic
113C2×D5—41no—
114C2×D5—81no—
115AGL(1,𝔽5)—161no—
116C4×C5—21no—
117C4×C5—41no—
118C4×C5—241no—
119Dic5—41no—
120C2×Q8—51no—
121C2×D4—51no—
122M16—601no—
123C2×C8—301no—
124C4⋊C4—61no—
125C4⋊C4—121no—
126C22⋊C4—201no—
127C22⋊C4—201no—
128C42D3×AGL(1,𝔽5)11yescharacteristic
129C3×C5#141411yescharacteristic, complemented, Hall
130C22×C3—201no—
131C22×C3—401no—
132C22×C3#401111yescharacteristic
133C3×C4—21no—
134C3×C4—41no—
135C3×C4—201no—
136C3×C4—801no—
137Dic3—81no—
138C2×C5—21no—
139C2×C5#447311yescharacteristic
140D5—81no—
141C23—101no—
142Q8—201no—
143D4—201no—
144C2×C4—21no—
145C2×C4—101no—
146C2×C4—121no—
147C2×C4—401no—
148C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
149C8—601no—
150C8—1201no—
151C2×C3—21no—
152C2×C3—401no—
153C2×C3#6492811yescharacteristic
154C5#6754311yescharacteristic, complemented, Sylow
155C22—201no—
156C22—401no—
157C22#9117211yescharacteristic
158C4—21no—
159C4—41no—
160C4—201no—
161C4—241no—
162C4—801no—
163C3#1059874111yescharacteristic, complemented, Sylow
164C2—21no—
165C2—401no—
166C2#1174655611yescharacteristic
subgroupG/H
centerC2#11746556
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#354
prime radicalC2×C3×D20D4
cosocleC3×#4021C22
hypocenterC3×C5#1414
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
5. C5×#870C4semidirect
9. C4×C3⋊#168C4semidirect
47. #870AGL(1,𝔽5)semidirect
129. C3×C5#1414semidirect
154. C5#67543semidirect
163. C3#10598741semidirect

Maximal subgroups

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

subgroupindex
#117468962
#117467272
C3×#648542
#105987413
#675435