Finite Group Databasebeta

← #14279509

Subgroups — #14279509

Order 1920.

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

normal subgroups only

This group has 188 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#11746897C211yesmaximal, characteristic
2#11746724C211yesmaximal, characteristic
3C3×#64853C211yesmaximal, characteristic
4#10598739—31nomaximal, Hall
5C5×#870C411yescharacteristic, complemented
6C3×#4020C2211yescharacteristic
7#91228—21no—
8C3×#3999—21no—
9#91087C411yescharacteristic, complemented
10#90964—21no—
11#90964—21no—
12#67539—51nomaximal, Hall
13#65356—31no—
14#64853—31no—
15#64853D311yescharacteristic
16C2×C3×D20—41no—
17C2×C3×D20D411yescharacteristic
18C2×C3×D20D411yescharacteristic
19#6763—41no—
20C3×C22⋊AGL(1,𝔽5)—41no—
21C3×C42×C5C2×C411yescharacteristic
22C2×C3⋊#168—21no—
23C5×C4⋊Dic3—21no—
24C5×Dic3⋊C4—41no—
25#5071—51no—
26C3×#353—51no—
27#4545—51no—
28C5×#125—31no—
29#4020C2×D311yescharacteristic
30#3999—21no—
31#3999—61no—
32#3941—61no—
33#3941—61no—
34#3935—31no—
35#1412—151noSylow
36C22×C3×D5—21no—
37C22×C3×D5—21no—
38C2×ΓL(1,𝔽16)—81no—
39C2×C3×AGL(1,𝔽5)—81no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5C22⋊C411yescharacteristic
42C2×C5×Dic3—41no—
43C3×D20—41no—
44C3×D20—41no—
45C3×D20—82no—
46C3⋊#168—41no—
47C3×#127—51no—
48#870AGL(1,𝔽5)11yescharacteristic, complemented
49C3×#99—101no—
50#834—101no—
51#832—101no—
52#832—101no—
53#803—51no—
54C2×D20—41no—
55C2×D20D1211yescharacteristic
56C2×D20#6711yescharacteristic
57C22⋊AGL(1,𝔽5)—41no—
58C22⋊AGL(1,𝔽5)—121no—
59C5×C4⋊C4—61no—
60C5×C4⋊C4—121no—
61C42×C5C4×D311yescharacteristic
62C2×#168—61no—
63#490—151no—
64#353—51no—
65#353—151no—
66C22×C3×C5#9911yescharacteristic
67C2×C3×D5—41no—
68C2×C3×D5—41no—
69C2×C3×D5—81no—
70C2×C3×D5—81no—
71ΓL(1,𝔽16)—161no—
72C3×AGL(1,𝔽5)—161no—
73C3×C4×C5—21no—
74C3×C4×C5—41no—
75C5×Dic3—81no—
76C2×C3×D4—51no—
77C2×C3×D4—51no—
78C2×C3×D4—201no—
79C3×C22⋊C4—201no—
80C3×C42C2×AGL(1,𝔽5)11yescharacteristic
81#217—201no—
82C4⋊Dic3—21no—
83Dic3⋊C4—41no—
84C2×C3⋊C8—101no—
85C22×D5—21no—
86C22×D5—21no—
87C2×AGL(1,𝔽5)—81no—
88C2×AGL(1,𝔽5)—241no—
89C2×C4×C5—21no—
90C2×C4×C5—121no—
91C2×C4×C5(C2×D3)⋊C411yescharacteristic
92D20—41no—
93D20—41no—
94D20—82no—
95#168—121no—
96#127—51no—
97#125—31no—
98#102—301no—
99#102—301no—
100#99—101no—
101#99—301no—
102#97—151no—
103C2×C3×C5—21no—
104C2×C3×C5#35411yescharacteristic
105C3×D5—81no—
106C3×D5—81no—
107C23×C3—101no—
108C23×C3—101no—
109C3×D4—201no—
110C3×D4—201no—
111C3×D4—402no—
112C2×C3×C4—21no—
113C2×C3×C4—401no—
114C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
115C2×Dic3—41no—
116C2×Dic3—401no—
117C3⋊C8—201no—
118C22×C5#80611yescharacteristic
119C2×D5—41no—
120C2×D5—41no—
121C2×D5—81no—
122C2×D5—81no—
123AGL(1,𝔽5)—161no—
124AGL(1,𝔽5)—481no—
125C4×C5—21no—
126C4×C5—41no—
127C4×C5—241no—
128C2×D4—51no—
129C2×D4—51no—
130C2×D4—201no—
131C2×C8—301no—
132C4⋊C4—61no—
133C4⋊C4—121no—
134C22⋊C4—201no—
135C22⋊C4—601no—
136C42D3×AGL(1,𝔽5)11yescharacteristic
137C3×C5#141211yescharacteristic, complemented, Hall
138C22×C3—201no—
139C22×C3—201no—
140C22×C3—401no—
141C22×C3—401no—
142C22×C3#401111yescharacteristic
143C3×C4—21no—
144C3×C4—41no—
145C3×C4—801no—
146Dic3—81no—
147Dic3—801no—
148C2×C5—21no—
149C2×C5#447311yescharacteristic
150D5—81no—
151D5—81no—
152C23—101no—
153C23—101no—
154D4—201no—
155D4—201no—
156D4—402no—
157C2×C4—21no—
158C2×C4—121no—
159C2×C4—401no—
160C2×C4—1201no—
161C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
162C8—601no—
163C2×C3—21no—
164C2×C3—401no—
165C2×C3—401no—
166C2×C3#6492811yescharacteristic
167C5#6753911yescharacteristic, complemented, Sylow
168C22—201no—
169C22—201no—
170C22—401no—
171C22—401no—
172C22#9117211yescharacteristic
173C4—21no—
174C4—41no—
175C4—241no—
176C4—801no—
177C4—2401no—
178C3#1059873911yescharacteristic, complemented, Sylow
179C2—21no—
180C2—401no—
181C2—401no—
182C2#1174655611yescharacteristic
subgroupG/H
centerC2#11746556
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#354
prime radical, cosocleC3×#4020C22
hypocenterC3×C5#1412
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. #91087C4semidirect
48. #870AGL(1,𝔽5)semidirect
137. C3×C5#1412semidirect
167. C5#67539semidirect
178. C3#10598739semidirect

Maximal subgroups

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

subgroupindex
#117468972
#117467242
C3×#648532
#105987393
#675395