Finite Group Databasebeta

← C22×#91956 #14514604

Subgroups — C22×#91956 #14514604

Order 1920.

1822 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 1822 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2C2×#91956C2112yesmaximal, direct product factor
3C22×C5⋊GL(2,𝔽3)C212yesmaximal, complemented
4C22×#4095—31nomaximal, Hall
5C22×D60—41nomaximal
6C2×C5×#41⋊C3C2216yescomplemented
7C22×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
8#91956C22116yesdirect product factor
9C2×C5⋊GL(2,𝔽3)C22112yescomplemented
10C22×#986—51nomaximal, Hall
11C22×C5×#41D311yescharacteristic, complemented
12C23×D20—31no—
13C2×#4095—312no—
14C2×#4095—312no—
15C22×#688—32no—
16C22×#686—32no—
17C22×#681—31no—
18C23×D15—42no—
19C22×C3×C4×C5—41no—
20C2×D60—412no—
21C5×#41⋊C3C2314yescomplemented
22C2×C5×SL(2,𝔽3)C2313yescomplemented
23C5⋊GL(2,𝔽3)C2318yescomplemented
24C22×#41⋊C3D511yescharacteristic, complemented
25C2×#986—512no—
26C22×GL(2,𝔽3)—52no—
27C24×D5—61no—
28C2×C5×#41—36no—
29C2×C5×#41C2×D316yescomplemented
30C22×C5×Q8C2×D311yescharacteristic
31C22×C5×D4—31no—
32C23×C4×C5—31no—
33C22×D20—32no—
34C22×D20—312no—
35C22×D20—66no—
36C22×D20—61no—
37#4095—348no—
38#4095—316no—
39C2×#688—312no—
40C2×#688—312no—
41C2×#686—324no—
42C2×#681—312no—
43C22×#168—32no—
44C22×AGL(1,ℤ/8)—151noSylow
45C23×C3×C5—41no—
46C22×D15—412no—
47C22×D15—88no—
48C2×C3×C4×C5—46no—
49D60—416no—
50C5×SL(2,𝔽3)C2411yescharacteristic, complemented
51C22×D12—201no—
52C2×#41⋊C3C2×D516yescomplemented
53C22×SL(2,𝔽3)C2×D511yescharacteristic, complemented
54#986—516no—
55C2×GL(2,𝔽3)—512no—
56C24×C5—31no—
57C23×D5—612no—
58C23×D5—62no—
59C23×D5—128no—
60C5×#41—312no—
61C5×#41—64no—
62C5×#41C22×D314yescomplemented
63C2×C5×Q8—33no—
64C2×C5×Q8C22×D313yes—
65C2×C5×D4—36no—
66C2×C5×D4—63no—
67C22×C4×C5—31no—
68C22×C4×C5—36no—
69C22×C4×C5—36no—
70C22×C4×C5S411yescharacteristic
71C2×D20—312no—
72C2×D20—316no—
73C2×D20—66no—
74C2×D20—624no—
75C2×D20—612no—
76#688—324no—
77#688—38no—
78#686—332no—
79#681—316no—
80C2×#168—312no—
81C22×#41D1511yescharacteristic, complemented
82C23×D4—151no—
83C2×AGL(1,ℤ/8)—1512no—
84C2×AGL(1,ℤ/8)—1512no—
85C22×SD16—152no—
86C22×D8—152no—
87C22×M16—151no—
88C22×C3×C5—44no—
89C22×C3×C5—43no—
90C2×D15—48no—
91C2×D15—824no—
92C3×C4×C5—44no—
93C23×D3—202no—
94C22×C3×C4—41no—
95C2×D12—2012no—
96#41⋊C3C22×D514yescomplemented
97C2×SL(2,𝔽3)C22×D513yescomplemented
98GL(2,𝔽3)—58no—
99C23×C5—36no—
100C23×C5—64no—
101C23×C5C2×S411yescharacteristic
102C22×D5—616no—
103C22×D5—612no—
104C22×D5—1248no—
105C22×D5—128no—
106C5×Q8—33no—
107C5×Q8—61no—
108C5×Q8C23×D311yescharacteristic
109C5×D4—34no—
110C5×D4—66no—
111C2×C4×C5—33no—
112C2×C4×C5—33no—
113C2×C4×C5—34no—
114C2×C4×C5—312no—
115C2×C4×C5C2×S416yes—
116D20—38no—
117D20—612no—
118D20—616no—
119#168—38no—
120C25—301no—
121C2×#41—36no—
122C2×#41C2×D1516yescomplemented
123C22×Q8C2×D1511yescharacteristic
124C22×D4—31no—
125C22×D4—152no—
126C22×D4—1512no—
127C22×D4—306no—
128C22×D4—301no—
129C23×C4—31no—
130AGL(1,ℤ/8)—1548no—
131AGL(1,ℤ/8)—1516no—
132C2×SD16—1512no—
133C2×SD16—1512no—
134C2×D8—1524no—
135C2×M16—1512no—
136C22×C8—152no—
137C2×C3×C5—46no—
138C2×C3×C5—41no—
139D15—88no—
140C23×C3—41no—
141C22×D3—2012no—
142C22×D3—408no—
143C2×C3×C4—46no—
144D12—2016no—
145SL(2,𝔽3)C23×D511yescharacteristic, complemented
146C22×C5—34no—
147C22×C5—612no—
148C22×C5#98614yescomplemented
149C22×C5C22×S413yes—
150C2×D5—68no—
151C2×D5—1232no—
152C2×D5—1224no—
153C4×C5—31no—
154C4×C5—33no—
155C4×C5C22×S414yes—
156C24—31no—
157C24—3012no—
158C24—302no—
159C24—608no—
160#41—312no—
161#41—64no—
162#41C22×D1514yescomplemented
163C2×Q8—33no—
164C2×Q8C22×D1513yes—
165C2×D4—36no—
166C2×D4—63no—
167C2×D4—1512no—
168C2×D4—1516no—
169C2×D4—306no—
170C2×D4—3024no—
171C2×D4—3012no—
172C22×C4—31no—
173C22×C4—36no—
174C22×C4—36no—
175C22×C4C5⋊S411yescharacteristic
176SD16—1524no—
177SD16—158no—
178D8—1532no—
179M16—1516no—
180C2×C8—1512no—
181C3×C5—41noHall
182C22×C3—44no—
183C22×C3—43no—
184C2×D3—208no—
185C2×D3—4024no—
186C3×C4—44no—
187C2×C5—64no—
188C2×C5C2×#98616yescomplemented
189C2×C5C23×S411yescharacteristic
190D5—128no—
191C23—36no—
192C23—64no—
193C23—3016no—
194C23—3012no—
195C23—6048no—
196C23—608no—
197C23C2×C5⋊S411yescharacteristic
198Q8—33no—
199Q8—61no—
200Q8C23×D1511yescharacteristic
201D4—34no—
202D4—66no—
203D4—158no—
204D4—3012no—
205D4—3016no—
206C2×C4—33no—
207C2×C4—33no—
208C2×C4—34no—
209C2×C4—312no—
210C2×C4C2×C5⋊S416yes—
211C8—158no—
212C2×C3—46no—
213C2×C3—41no—
214D3—408no—
215C5C22×#98611yescharacteristic, complemented, Sylow
216C22—34no—
217C22—612no—
218C22—308no—
219C22—6032no—
220C22—6024no—
221C22#9195614yesdirect product factor
222C22C22×C5⋊S413yes—
223C4—31no—
224C4—33no—
225C4C22×C5⋊S414yes—
226C3—41noSylow
227C2—64no—
228C2—608no—
229C2C2×#9195616yesdirect product factor
230C2C23×C5⋊S411yescharacteristic
subgroupG/H
centerC23C2×C5⋊S4
commutator, cosocle, hypocenterC5×SL(2,𝔽3)C24
FrattiniC2C23×C5⋊S4
FittingC22×C5×#41D3
socleC23×C5C2×S4
hypercenterC22×C4C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#41⋊C3C2semidirect
2. C2×#91956C2direct (N × H)
3. C22×C5⋊GL(2,𝔽3)C2semidirect
6. C2×C5×#41⋊C3C22semidirect
7. C22×C5×SL(2,𝔽3)C22semidirect
8. #91956C22direct (N × H)
9. C2×C5⋊GL(2,𝔽3)C22semidirect
11. C22×C5×#41D3semidirect
21. C5×#41⋊C3C23semidirect
22. C2×C5×SL(2,𝔽3)C23semidirect
23. C5⋊GL(2,𝔽3)C23semidirect
24. C22×#41⋊C3D5semidirect
29. C2×C5×#41C2×D3semidirect
50. C5×SL(2,𝔽3)C24semidirect
52. C2×#41⋊C3C2×D5semidirect
53. C22×SL(2,𝔽3)C2×D5semidirect
62. C5×#41C22×D3semidirect
81. C22×#41D15semidirect
96. #41⋊C3C22×D5semidirect
97. C2×SL(2,𝔽3)C22×D5semidirect
122. C2×#41C2×D15semidirect
145. SL(2,𝔽3)C23×D5semidirect
148. C22×C5#986semidirect
162. #41C22×D15semidirect
188. C2×C5C2×#986semidirect
215. C5C22×#986semidirect
221. C22#91956direct (N × H)
229. C2C2×#91956direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#41⋊C32
C2×#919562
C22×C5⋊GL(2,𝔽3)2
C22×#40953
C22×D604
C22×#9865