Finite Group Databasebeta

← #14512005

Subgroups — #14512005

Order 1920.

222 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 37 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×C4⋊(#41⋊C3)C211yesmaximal, characteristic
2#11752105C211yesmaximal, characteristic, complemented
3SL(2,𝔽3)⋊#168C211yesmaximal, characteristic, complemented
4#10602714—31nomaximal, Hall
5C2×C5×#41⋊C3—21no—
6C4×C5×SL(2,𝔽3)C2211yescharacteristic
7#91184—21no—
8#91094—41nomaximal
9#73091—51nomaximal, Hall
10C5×#550D311yescharacteristic
11#65359—31no—
12#65309—31no—
13#65308—31no—
14#64764—31no—
15Q8⋊#168—31no—
16D4⋊#168—31no—
17C2×Dic30—41no—
18C5×#41⋊C3—41no—
19C2×C5×SL(2,𝔽3)D411yescharacteristic
20C3×C5×C4⋊C4—41no—
21C2×C3⋊#168—41no—
22C4⋊(#41⋊C3)D511yescharacteristic
23#5386—51no—
24SL(2,𝔽3)⋊C8—51no—
25C2×C5×#41—21no—
26C5×#127—31no—
27C5×#121—61no—
28C4×C5×Q8C2×D311yescharacteristic
29C4×C5×D4—31no—
30C2×#687—61no—
31#4015—31no—
32#3967—61no—
33#3964—62no—
34#3942—61no—
35#3940—61no—
36C4⋊#168—31no—
37C4⋊#168—31no—
38C4×#168—31no—
39#1642—151noSylow
40C2×C3×C4×C5—41no—
41C2×C3×C4×C5—81no—
42C2×Dic15—81no—
43Dic30—42no—
44Dic30—81no—
45C5×SL(2,𝔽3)SD1611yescharacteristic, complemented
46C3⋊#168—81no—
47C2×#41⋊C3—21no—
48C4×SL(2,𝔽3)C2×D511yescharacteristic
49#859—101no—
50#810—201no—
51C5×#41—41no—
52C5×#41—121no—
53C2×C5×Q8#6711yescharacteristic
54C2×C5×D4—32no—
55C2×C5×D4—31no—
56C2×C5×D4—61no—
57C22×C4×C5—61no—
58C2×Dic10—61no—
59C5×C4⋊C4—31no—
60C5×C4⋊C4S411yescharacteristic
61C5×C22⋊C4—61no—
62C42×C5—31no—
63#687—122no—
64C4⋊Dic5—61no—
65C4⋊Dic5—61no—
66C2×#168—61no—
67C2×#168—61no—
68C2×#168—61no—
69#550D1511yescharacteristic
70#486—151no—
71#475—151no—
72#461—151no—
73#331—151no—
74Q8⋊C8—151no—
75D4⋊C8—151no—
76C22×C3×C5—41no—
77C3×C4×C5—41no—
78C3×C4×C5—41no—
79C3×C4×C5—161no—
80Dic15—82no—
81C2×Dic6—201no—
82#41⋊C3—41no—
83C2×SL(2,𝔽3)C22⋊D511yescharacteristic
84C3×C4⋊C4—41no—
85C2×C3⋊C8—201no—
86C23×C5—61no—
87C5×Q8—31no—
88C5×Q8#21411yescharacteristic
89C5×D4—61no—
90C5×D4—61no—
91C5×D4—121no—
92C5×D4—121no—
93C5×D4—122no—
94C2×C4×C5—21no—
95C2×C4×C5—31no—
96C2×C4×C5—31no—
97C2×C4×C5—121no—
98C2×C4×C5—121no—
99C2×C4×C5C2×S411yescharacteristic
100C2×Dic5—121no—
101Dic10—121no—
102Dic10—121no—
103#168—121no—
104#168—121no—
105#168—121no—
106C2×#41—21no—
107C2×SD16—301no—
108C4⋊Q8—151no—
109#127—31no—
110#121—61no—
111C4×Q8C2×D1511yescharacteristic
112C4×D4—31no—
113#106—301no—
114C4⋊C8—151no—
115C4⋊C8—151no—
116#103—301no—
117#103—301no—
118#102—302no—
119C4×C8—151no—
120C2×C3×C5—41no—
121C2×C3×C5—41no—
122C2×C3×C5—41no—
123C2×C3×C4—41no—
124C2×C3×C4—81no—
125C2×Dic3—401no—
126Dic6—202no—
127Dic6—401no—
128SL(2,𝔽3)#68711yescharacteristic, complemented
129C3⋊C8—401no—
130C22×C5—121no—
131C22×C5—121no—
132C22×C5—121no—
133C22×C5GL(2,ℤ/4)11yescharacteristic
134C4×C5—31no—
135C4×C5—31no—
136C4×C5—41no—
137C4×C5—61no—
138C4×C5#98511yescharacteristic
139C4×C5#98611yescharacteristic
140Dic5—241no—
141#41—41no—
142#41—121no—
143C2×Q8—301no—
144C2×Q8#122011yescharacteristic
145C2×D4—32no—
146C2×D4—31no—
147C2×D4—61no—
148C22×C4—61no—
149SD16—602no—
150C2×C8—301no—
151C2×C8—301no—
152C2×C8—301no—
153C4⋊C4—31no—
154C4⋊C4—301no—
155C4⋊C4—301no—
156C4⋊C4C5⋊S411yescharacteristic
157C22⋊C4—61no—
158C42—31no—
159C3×C5—41noHall
160C22×C3—41no—
161C3×C4—41no—
162C3×C4—41no—
163C3×C4—161no—
164Dic3—402no—
165C2×C5—241no—
166C2×C5#541411yescharacteristic
167C2×C5#542711yescharacteristic
168C2×C5#542811yescharacteristic
169C23—61no—
170Q8—31no—
171Q8—601no—
172Q8—601no—
173Q8#671611yescharacteristic
174D4—61no—
175D4—61no—
176D4—121no—
177D4—121no—
178D4—122no—
179C2×C4—21no—
180C2×C4—31no—
181C2×C4—31no—
182C2×C4—121no—
183C2×C4—121no—
184C2×C4—601no—
185C2×C4C2×C5⋊S411yescharacteristic
186C8—601no—
187C8—601no—
188C8—601no—
189C2×C3—41no—
190C2×C3—41no—
191C2×C3—41no—
192C5#7309111yescharacteristic, complemented, Sylow
193C22—121no—
194C22—121no—
195C22—121no—
196C22#9195811yescharacteristic
197C4—31no—
198C4—31no—
199C4—41no—
200C4—61no—
201C4—1201no—
202C4#9195511yescharacteristic
203C4#9195611yescharacteristic
204C3—41noSylow
205C2—241no—
206C2#1175213311yescharacteristic
207C2#1175214611yescharacteristic
208C2#1175214711yescharacteristic
subgroupG/H
centerC22#91958
commutator, cosocleC4×C5×SL(2,𝔽3)C22
FrattiniC2×C4C2×C5⋊S4
FittingC5×#550D3
socleC22×C5GL(2,ℤ/4)
prime radicalC5×C4⋊(#41⋊C3)C2
hypercenterC4⋊C4C5⋊S4
hypocenterC5×SL(2,𝔽3)SD16
LCSG ▷ C4×C5×SL(2,𝔽3) ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752105C2semidirect
3. SL(2,𝔽3)⋊#168C2semidirect
45. C5×SL(2,𝔽3)SD16semidirect
128. SL(2,𝔽3)#687semidirect
192. C5#73091semidirect

Maximal subgroups

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

subgroupindex
C5×C4⋊(#41⋊C3)2
#117521052
SL(2,𝔽3)⋊#1682
#106027143
#910944
#730915