Finite Group Databasebeta

← #14512440

Subgroups — #14512440

Order 1920.

302 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C2×#91885C212yesmaximal
2C4×C5⋊(#41⋊C3)C211yesmaximal, characteristic
3#10604450—31nomaximal, Hall
4C2×C5⋊(#41⋊C3)C2211yescharacteristic
5#91885C414yescomplemented
6C4×C5×SL(2,𝔽3)C411yescharacteristic, complemented
7#91231—41nomaximal
8Dic5×SL(2,𝔽3)C411yescharacteristic, complemented
9#73067—51nomaximal, Hall
10C4×#713D311yescharacteristic
11C2×#4010—32no—
12#65686—31no—
13C4×#700—31no—
14#64875—32no—
15C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
16C2×C3⋊#170—42no—
17C5⋊(#41⋊C3)C2×C412yes—
18C3×C4×Dic5—41no—
19C4×#41⋊C3—51no—
20C2×GU(2,𝔽3)—52no—
21C2×#713C2×D311yescharacteristic
22C2×C4×AGL(1,𝔽5)—32no—
23C2×#700—32no—
24C4×C5×Q8Dic311yescharacteristic
25Q8×Dic5Dic311yescharacteristic
26#4039—31no—
27#4038—31no—
28C4×D20—31no—
29C42×D5—31no—
30#4010—34no—
31#4010—34no—
32(C2×AGL(1,𝔽5))⋊C4—61no—
33(C2×AGL(1,𝔽5))⋊C4—61no—
34#4002—61no—
35C4×#170—61no—
36#1759—151noSylow
37C2×C3×C4×C5—41no—
38C2×C3×Dic5—41no—
39C2×C3×Dic5—41no—
40C5×SL(2,𝔽3)C4211yescharacteristic
41C3⋊#170—44no—
42C2×#41⋊C3—51no—
43C4×SL(2,𝔽3)—51no—
44C4×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic, complemented
45GU(2,𝔽3)—54no—
46#803—201no—
47C22×AGL(1,𝔽5)—62no—
48C2×C5×Q8C2×Dic311yescharacteristic
49#713—32no—
50#713C4×D312yes—
51C2×D20—31no—
52C2×C4×D5—31no—
53C2×C4×D5—31no—
54C2×C4×D5—31no—
55C2×#170—62no—
56C4×AGL(1,𝔽5)—34no—
57C4×AGL(1,𝔽5)—62no—
58#700—34no—
59#700—62no—
60C5×C4⋊C4—31no—
61C42×C5—31no—
62#685—61no—
63C4⋊Dic5—31no—
64C4×Dic5—31no—
65C4×Dic5—31no—
66C4×Dic5S411yescharacteristic
67C4×#41—51no—
68C2×#104—152no—
69C4×M16—151no—
70#376—151no—
71#339—152no—
72C22×C3×C5—41no—
73C3×C4×C5—81no—
74C3×Dic5—42no—
75C3×Dic5—81no—
76#41⋊C3—52no—
77C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
78C3×C42—201no—
79C2×C3⋊C8—202no—
80C22×D5—31no—
81C2×AGL(1,𝔽5)—64no—
82C2×AGL(1,𝔽5)—122no—
83C2×AGL(1,𝔽5)—122no—
84C5×Q8—31no—
85C5×Q8C4×Dic311yescharacteristic
86C2×C4×C5—31no—
87C2×C4×C5—31no—
88C2×C4×C5SL(2,ℤ/4)11yescharacteristic
89C2×Dic5—31no—
90C2×Dic5SL(2,ℤ/4)11yescharacteristic
91C2×Dic5C2×S411yescharacteristic
92D20—32no—
93D20—61no—
94C4×D5—32no—
95C4×D5—32no—
96C4×D5—121no—
97C4×D5—121no—
98#170—64no—
99C2×#41—51no—
100C2×M16—152no—
101C4×Q8—51no—
102C4×Q8ΓL(1,𝔽16)11yescharacteristic
103C4×D4—151no—
104C4×D4—151no—
105#117—151no—
106C2×C42—151no—
107C2×C42—152no—
108#104—154no—
109#104—154no—
110#97—301no—
111C4×C8—301no—
112#95—301no—
113#95—301no—
114C2×C3×C5—41no—
115C2×C3×C5—41no—
116C2×C3×C5—41no—
117C2×C3×C4—41no—
118C2×C3×C4—201no—
119C2×C3×C4—201no—
120SL(2,𝔽3)C4×AGL(1,𝔽5)11yescharacteristic
121C3⋊C8—204no—
122C22×C5C2×SL(2,ℤ/4)11yescharacteristic
123C2×D5—32no—
124C2×D5—61no—
125C2×D5—61no—
126AGL(1,𝔽5)—124no—
127C4×C5—21no—
128C4×C5—31no—
129C4×C5—31no—
130C4×C5—61no—
131Dic5—21no—
132Dic5—61no—
133Dic5C4×S412yes—
134#41—52no—
135#41—152no—
136C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
137C2×D4—151no—
138C22×C4—151no—
139C22×C4—151no—
140C22×C4—151no—
141C22×C4—302no—
142M16—154no—
143M16—302no—
144C2×C8—302no—
145C4⋊C4—31no—
146C4⋊C4—151no—
147C22⋊C4—301no—
148C42—31no—
149C42—51no—
150C42—151no—
151C42—151no—
152C42—154no—
153C42—302no—
154C3×C5—41noHall
155C22×C3—41no—
156C3×C4—81no—
157C3×C4—202no—
158C3×C4—401no—
159C2×C5C4×SL(2,ℤ/4)11yescharacteristic
160C2×C5#542311yescharacteristic
161C2×C5#542311yescharacteristic
162D5—62no—
163C23—151no—
164Q8—31no—
165Q8C4×ΓL(1,𝔽16)11yescharacteristic
166D4—152no—
167D4—301no—
168C2×C4—31no—
169C2×C4—31no—
170C2×C4—51no—
171C2×C4—51no—
172C2×C4—152no—
173C2×C4—152no—
174C2×C4—151no—
175C2×C4—304no—
176C2×C4—601no—
177C2×C4—601no—
178C2×C4—602no—
179C2×C4—602no—
180C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
181C8—304no—
182C2×C3—41no—
183C2×C3—41no—
184C2×C3—41no—
185C5#7306711yescharacteristic, complemented, Sylow
186C22—152no—
187C22—301no—
188C22—301no—
189C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
190C4—21no—
191C4—31no—
192C4—31no—
193C4—52no—
194C4—61no—
195C4—101no—
196C4—301no—
197C4—604no—
198C3—41noSylow
199C2—302no—
200C2C4×A4⋊AGL(1,𝔽5)11yescharacteristic
201C2#1175672011yescharacteristic
202C2#1175672411yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C42
FittingC4×C5×Q8Dic3
socleC22×C5C2×SL(2,ℤ/4)
prime radical, cosocleC2×C5⋊(#41⋊C3)C22
hypercenterC2×C4A4⋊AGL(1,𝔽5)
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
5. #91885C4semidirect
6. C4×C5×SL(2,𝔽3)C4semidirect
8. Dic5×SL(2,𝔽3)C4semidirect
44. C4×SL(2,𝔽3)AGL(1,𝔽5)semidirect
185. C5#73067semidirect

Maximal subgroups

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

subgroupindex
C2×#918852
C4×C5⋊(#41⋊C3)2
#106044503
#912314
#730675