Finite Group Databasebeta

← C5⋊#85548 #14513950

Subgroups — C5⋊#85548 #14513950

Order 1920.

212 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 23 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
1C5×#543⋊C3C211yesmaximal, characteristic
2#10602683—31nomaximal, Hall
3C2×A4⋊Dic5—41nomaximal
4#91184—42nomaximal
5#85548—51nomaximal, Hall
6C5×#543D311yescharacteristic
7#65332—32no—
8#65242—31no—
9#64758—32no—
10#64745—31no—
11C22×C5×A4—41no—
12C2×C5×SL(2,𝔽3)—42no—
13C2×C5×SL(2,𝔽3)—81no—
14A4⋊Dic5—42no—
15#543⋊C3D511yescharacteristic
16C5×C22⋊Q8—32no—
17C5×C22⋊Q8—61no—
18C2×C5×C22⋊C4—31no—
19C2×C22⋊Dic5—61no—
20C2×C4⋊Dic5—31no—
21#3967—62no—
22#3963—31no—
23#3963—61no—
24C22⋊#168—32no—
25#3940—62no—
26#1608—151noSylow
27C2×C5×A4—41no—
28C2×C5×A4—41no—
29C2×C5×A4—41no—
30C2×Dic15—161no—
31C5×SL(2,𝔽3)—42no—
32C5×SL(2,𝔽3)—81no—
33C2×SL(2,ℤ/4)—201no—
34#859—202no—
35C24×C5S411yescharacteristic
36C2×C5×Q8—21no—
37C2×C5×Q8S412yes—
38C22×C4×C5—31no—
39C22×C4×C5—31no—
40C22×Dic5—61no—
41C22×Dic5—61no—
42C5×C4⋊C4—32no—
43C5×C4⋊C4—61no—
44C5×C22⋊C4—62no—
45C22⋊Dic5—121no—
46C22⋊Dic5—121no—
47C4⋊Dic5—62no—
48C2×#168—62no—
49#543D1511yescharacteristic
50#483—152no—
51#397—151no—
52#328—152no—
53#323—151no—
54C22×C3×C5—161no—
55C5×A4—41no—
56Dic15—162no—
57C22×A4—41no—
58C2×SL(2,𝔽3)—42no—
59C2×SL(2,𝔽3)—81no—
60SL(2,ℤ/4)—202no—
61C23×C5—31no—
62C23×C5—31no—
63C23×C5—41no—
64C23×C5—41no—
65C23×C5GL(2,𝔽3)11yescharacteristic
66C5×Q8—42no—
67C5×Q8—81no—
68C2×C4×C5—32no—
69C2×C4×C5—61no—
70C2×C4×C5—121no—
71C2×C4×C5—121no—
72C2×Dic5—121no—
73C2×Dic5—121no—
74C2×Dic5—121no—
75C2×Dic5—121no—
76C2×Dic5—121no—
77C2×Dic5—121no—
78#168—122no—
79C22⋊Q8—32no—
80C22⋊Q8—61no—
81C2×C4⋊C4—151no—
82C2×C22⋊C4—31no—
83C2×C22⋊C4—301no—
84#106—302no—
85#103—302no—
86C22⋊C8—152no—
87#95—151no—
88#95—301no—
89C2×C3×C5—161no—
90C2×C3×C5—161no—
91C2×C3×C5—161no—
92C2×A4—41no—
93C2×A4—41no—
94C2×A4—41no—
95C2×Dic3—801no—
96SL(2,𝔽3)—42no—
97SL(2,𝔽3)—81no—
98C22×C5—31no—
99C22×C5—31no—
100C22×C5—41no—
101C22×C5—61no—
102C22×C5—61no—
103C22×C5—121no—
104C22×C5#102011yescharacteristic
105C4×C5—62no—
106C4×C5—121no—
107Dic5—241no—
108Dic5—241no—
109C24C5⋊S411yescharacteristic
110C2×Q8—21no—
111C2×Q8C5⋊S412yes—
112C22×C4—31no—
113C22×C4—31no—
114C22×C4—301no—
115C22×C4—301no—
116C2×C8—302no—
117C4⋊C4—32no—
118C4⋊C4—61no—
119C4⋊C4—302no—
120C22⋊C4—62no—
121C22⋊C4—601no—
122C22⋊C4—601no—
123C3×C5—161noHall
124C22×C3—161no—
125A4—41no—
126Dic3—802no—
127C2×C5—61no—
128C2×C5—61no—
129C2×C5#593111yescharacteristic
130C2×C5#593211yescharacteristic
131C2×C5#593311yescharacteristic
132C23—31no—
133C23—31no—
134C23—41no—
135C23—41no—
136C23C5⋊GL(2,𝔽3)11yescharacteristic
137Q8—42no—
138Q8—81no—
139C2×C4—32no—
140C2×C4—61no—
141C2×C4—121no—
142C2×C4—121no—
143C2×C4—601no—
144C2×C4—601no—
145C2×C4—601no—
146C2×C4—601no—
147C2×C4—601no—
148C2×C4—601no—
149C8—602no—
150C2×C3—161no—
151C2×C3—161no—
152C2×C3—161no—
153C5#8554811yescharacteristic, complemented, Sylow
154C22—31no—
155C22—31no—
156C22—41no—
157C22—61no—
158C22—61no—
159C22—121no—
160C22C5⋊#102011yescharacteristic
161C4—62no—
162C4—121no—
163C4—1201no—
164C4—1201no—
165C3—161noSylow
166C2—61no—
167C2—61no—
168C2C5⋊#593111yescharacteristic
169C2C5⋊#593211yescharacteristic
170C2C5⋊#593311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22C5⋊#1020
commutator, prime radical, cosocle, hypocenterC5×#543⋊C3C2
FittingC5×#543D3
socleC22×C5#1020
LCSG ▷ C5×#543⋊C3
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
153. C5#85548semidirect

Maximal subgroups

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

subgroupindex
C5×#543⋊C32
#106026833
C2×A4⋊Dic54
#911844
#855485