Finite Group Databasebeta

← C22×#4150⋊C3 #14514658

Subgroups — C22×#4150⋊C3 #14514658

Order 1920.

2574 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 2574 conjugacy classes of subgroups — too many to draw. Only its 271 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×#4150⋊C3C2112yesmaximal, direct product factor
3C22×D5×SL(2,𝔽3)C212yesmaximal, complemented
4C22×#4150C311yesmaximal, characteristic, complemented, Hall
5C22×C3×D20—41nomaximal
6C2×C5×#41⋊C3C2216yescomplemented
7C22×C5×SL(2,𝔽3)C2211yescharacteristic
8#4150⋊C3C22116yesdirect product factor
9C2×D5×SL(2,𝔽3)C22112yescomplemented
10C22×2−1+4⋊C3—51nomaximal, Hall
11C22×C5×#41C2×C311yescharacteristic, complemented
12C2×#4150—312no—
13C2×#4150C2×C3112yescomplemented
14C22×Q8×D5C2×C312yescomplemented
15C22×#711—32no—
16C22×#709—31no—
17C23×Dic10—31no—
18C23×C3×D5—42no—
19C22×C3×C4×C5—41no—
20C2×C3×D20—412no—
21C5×#41⋊C3C2314yescomplemented
22C2×C5×SL(2,𝔽3)C2313yes—
23D5×SL(2,𝔽3)C2318yescomplemented
24C2×2−1+4⋊C3—512no—
25C22×#41⋊C3D511yescharacteristic, complemented
26C23×SL(2,𝔽3)—52no—
27C2×C5×#41—36no—
28C2×C5×#41C22×C316yescomplemented
29C22×C5×Q8C22×C311yescharacteristic
30C22×C5×D4—31no—
31C23×C4×C5—31no—
32C22×C22⋊D5—32no—
33C23×Dic5—32no—
34#4150—332no—
35#4150—348no—
36#4150C22×C3116yescomplemented
37C2×Q8×D5—312no—
38C2×Q8×D5C22×C3112yescomplemented
39C2×#711—324no—
40C2×#711—324no—
41C2×#709—312no—
42C2×#709—312no—
43C22×D20A411yescharacteristic
44C22×C4×D5—32no—
45C22×Dic10—312no—
46C22×Dic10—31no—
47C22×Dic10—32no—
48C22×Dic10—312no—
49C22×2−1+4—51noSylow
50C23×C3×C5—41no—
51C22×C3×D5—412no—
52C22×C3×D5—88no—
53C2×C3×C4×C5—46no—
54C3×D20—416no—
55C5×SL(2,𝔽3)C2411yescharacteristic
56C22×C3×D4—201no—
572−1+4⋊C3—516no—
58C2×#41⋊C3C2×D516yescomplemented
59C22×SL(2,𝔽3)—512no—
60C22×SL(2,𝔽3)C2×D511yescharacteristic
61C24×C5—31no—
62C23×D5C2×A412yes—
63C5×#41—38no—
64C5×#41—312no—
65C5×#41C23×C314yescomplemented
66C2×C5×Q8—33no—
67C2×C5×Q8C23×C313yes—
68C2×C5×D4—36no—
69C2×C5×D4—36no—
70C22×C4×C5—31no—
71C22×C4×C5—36no—
72C22×C4×C5—36no—
73C22×C4×C5C2×A411yescharacteristic
74C2×C22⋊D5—324no—
75C22×Dic5—324no—
76C22×Dic5—32no—
77Q8×D5—316no—
78Q8×D5—324no—
79Q8×D5C23×C318yescomplemented
80#711—396no—
81#711—332no—
82#709—348no—
83#709—316no—
84C2×D20C2×A4112yes—
85C2×C4×D5—312no—
86C2×C4×D5—312no—
87C2×Dic10—312no—
88C2×Dic10—348no—
89C2×Dic10—312no—
90C2×Dic10—312no—
91C2×Dic10—316no—
92C2×2−1+4—512no—
93C2×2−1+4—1512no—
94C22×#41—151no—
95C22×#41—152no—
96C22×#41C3×D511yescharacteristic, complemented
97C23×Q8—52no—
98C23×Q8—151no—
99C22×C3×C5—44no—
100C22×C3×C5—43no—
101C2×C3×D5—48no—
102C2×C3×D5—824no—
103C3×C4×C5—44no—
104C24×C3—202no—
105C2×C3×D4—2012no—
106C22×C3×C4—41no—
107#41⋊C3C22×D514yescomplemented
108C2×SL(2,𝔽3)—58no—
109C2×SL(2,𝔽3)C22×D513yes—
110C23×C5—36no—
111C23×C5—64no—
112C23×C5C22×A411yescharacteristic
113C22×D5—28no—
114C22×D5C22×A4112yes—
115C5×Q8—33no—
116C5×Q8—32no—
117C5×Q8C24×C311yescharacteristic
118C5×D4—34no—
119C5×D4—312no—
120C2×C4×C5—33no—
121C2×C4×C5—33no—
122C2×C4×C5—312no—
123C2×C4×C5—34no—
124C2×C4×C5C22×A416yes—
125C22⋊D5—332no—
126C2×Dic5—332no—
127C2×Dic5—312no—
128D20C22×A4116yes—
129C4×D5—324no—
130C4×D5—38no—
131Dic10—324no—
132Dic10—316no—
133Dic10—38no—
1342−1+4—516no—
1352−1+4—1548no—
1362−1+4—1532no—
137C2×#41—36no—
138C2×#41—1512no—
139C2×#41—1512no—
140C2×#41—1524no—
141C2×#41—1524no—
142C2×#41C2×C3×D516yescomplemented
143C22×Q8—512no—
144C22×Q8—1512no—
145C22×Q8—1512no—
146C22×Q8—152no—
147C22×Q8—151no—
148C22×Q8—1512no—
149C22×Q8C2×C3×D511yescharacteristic
150C22×D4—31no—
151C22×D4—51no—
152C22×D4—152no—
153C23×C4—31no—
154C23×C4—152no—
155C23×C4—152no—
156C2×C3×C5—46no—
157C2×C3×C5—41no—
158C3×D5—88no—
159C23×C3—41no—
160C23×C3—2012no—
161C23×C3—408no—
162C3×D4—2016no—
163C2×C3×C4—46no—
164SL(2,𝔽3)C23×D511yescharacteristic
165C22×C5—34no—
166C22×C5—612no—
167C22×C52−1+4⋊C314yescomplemented
168C22×C5C23×A413yes—
169C2×D5—224no—
170C2×D5C23×A418yes—
171C4×C5—33no—
172C4×C5—31no—
173C4×C5C23×A414yes—
174Dic5—38no—
175C24—31no—
176C24—52no—
177#41—38no—
178#41—312no—
179#41—1516no—
180#41—1548no—
181#41—1596no—
182#41—1532no—
183#41C22×C3×D514yescomplemented
184C2×Q8—33no—
185C2×Q8—58no—
186C2×Q8—1516no—
187C2×Q8—1512no—
188C2×Q8—1548no—
189C2×Q8—1512no—
190C2×Q8—1516no—
191C2×Q8—1512no—
192C2×Q8—1524no—
193C2×Q8C22×C3×D513yes—
194C2×D4—36no—
195C2×D4—36no—
196C2×D4—512no—
197C2×D4—1524no—
198C22×C4—31no—
199C22×C4—36no—
200C22×C4—36no—
201C22×C4—1512no—
202C22×C4—1512no—
203C22×C4—1524no—
204C22×C4—152no—
205C22×C4D5×A411yescharacteristic
206C3×C5—41noHall
207C22×C3—44no—
208C22×C3—43no—
209C22×C3—208no—
210C22×C3—4024no—
211C3×C4—44no—
212C2×C5—64no—
213C2×C5C2×2−1+4⋊C316yescomplemented
214C2×C5C24×A411yescharacteristic
215D5—28no—
216C23—36no—
217C23—512no—
218C23—64no—
219C23—108no—
220C23C2×D5×A411yescharacteristic
221Q8—33no—
222Q8—32no—
223Q8—158no—
224Q8—1524no—
225Q8—1516no—
226Q8C23×C3×D511yescharacteristic
227D4—34no—
228D4—312no—
229D4—516no—
230D4—1532no—
231C2×C4—33no—
232C2×C4—33no—
233C2×C4—34no—
234C2×C4—312no—
235C2×C4—158no—
236C2×C4—1524no—
237C2×C4—1532no—
238C2×C4—1512no—
239C2×C4C2×D5×A416yes—
240C2×C3—41no—
241C2×C3—46no—
242C2×C3—408no—
243C5C22×2−1+4⋊C311yescharacteristic, complemented, Sylow
244C22—34no—
245C22—58no—
246C22—612no—
247C22—1024no—
248C22#4150⋊C314yesdirect product factor
249C22C22×D5×A413yes—
250C4—31no—
251C4—33no—
252C4—158no—
253C4C22×D5×A414yes—
254C3—41noSylow
255C2—64no—
256C2—108no—
257C2C2×#4150⋊C316yesdirect product factor
258C2C23×D5×A411yescharacteristic
subgroupG/H
centerC23C2×D5×A4
commutator, cosocle, hypocenterC5×Q8C24×C3
FrattiniC2C23×D5×A4
FittingC22×C5×#41C2×C3
socleC23×C5C22×A4
hypercenterC22×C4D5×A4
LCSG ▷ C5×Q8
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×#4150⋊C3C2direct (N × H)
3. C22×D5×SL(2,𝔽3)C2semidirect
4. C22×#4150C3semidirect
6. C2×C5×#41⋊C3C22semidirect
8. #4150⋊C3C22direct (N × H)
9. C2×D5×SL(2,𝔽3)C22semidirect
11. C22×C5×#41C2×C3semidirect
13. C2×#4150C2×C3semidirect
14. C22×Q8×D5C2×C3semidirect
21. C5×#41⋊C3C23semidirect
23. D5×SL(2,𝔽3)C23semidirect
25. C22×#41⋊C3D5semidirect
28. C2×C5×#41C22×C3semidirect
36. #4150C22×C3semidirect
38. C2×Q8×D5C22×C3semidirect
58. C2×#41⋊C3C2×D5semidirect
65. C5×#41C23×C3semidirect
79. Q8×D5C23×C3semidirect
96. C22×#41C3×D5semidirect
107. #41⋊C3C22×D5semidirect
142. C2×#41C2×C3×D5semidirect
167. C22×C52−1+4⋊C3semidirect
183. #41C22×C3×D5semidirect
213. C2×C5C2×2−1+4⋊C3semidirect
243. C5C22×2−1+4⋊C3semidirect
248. C22#4150⋊C3direct (N × H)
257. C2C2×#4150⋊C3direct (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×#4150⋊C32
C22×D5×SL(2,𝔽3)2
C22×#41503
C22×C3×D204
C22×2−1+4⋊C35