Finite Group Databasebeta

← C22×#91886 #14514374

Subgroups — C22×#91886 #14514374

Order 1920.

878 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 136 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×D5×SL(2,𝔽3)C211yesmaximal, characteristic
2C2×#91886C216yesmaximal, direct product factor
3C22×#4009—31nomaximal, Hall
4C23×ΓL(1,𝔽16)—41nomaximal
5C22×C5×SL(2,𝔽3)C411yescharacteristic, complemented
6C2×D5×SL(2,𝔽3)C413yescomplemented
7C2×D5×SL(2,𝔽3)C2213yes—
8#91886C2214yesdirect product factor
9C22×#859—51nomaximal, Hall
10C22×Q8×D5D311yescharacteristic
11C22×C4⋊AGL(1,𝔽5)—31no—
12C22×D5⋊C8—31no—
13C2×#4009—36no—
14C2×#4009—36no—
15C23×C3×D5—41no—
16C22×ΓL(1,𝔽16)—46no—
17C22×ΓL(1,𝔽16)—48no—
18C2×C5×SL(2,𝔽3)C2×C413yescomplemented
19D5×SL(2,𝔽3)C2×C413yescomplemented
20D5×SL(2,𝔽3)C2311yescharacteristic
21C23×SL(2,𝔽3)—51no—
22C2×#859—56no—
23C23×AGL(1,𝔽5)—61no—
24C22×C5×Q8Dic311yescharacteristic, complemented
25C2×Q8×D5—33no—
26C2×Q8×D5—33no—
27C2×Q8×D5Dic313yescomplemented
28C2×Q8×D5C2×D313yes—
29C22×C4×D5—31no—
30C22×Dic10—31no—
31C22×#170—61no—
32C2×C4⋊AGL(1,𝔽5)—36no—
33C2×C4⋊AGL(1,𝔽5)—63no—
34C2×D5⋊C8—36no—
35C2×D5⋊C8—63no—
36#4009—312no—
37#4009—34no—
38C22×#103—151noSylow
39C23×C3×C5—41no—
40C22×C3×D5—44no—
41C22×C3×D5—44no—
42C22×C3×D5—43no—
43C22×C3×D5—43no—
44C2×ΓL(1,𝔽16)—44no—
45C2×ΓL(1,𝔽16)—424no—
46C5×SL(2,𝔽3)C22×C411yescharacteristic, complemented
47C23×Dic3—201no—
48C22×SL(2,𝔽3)—53no—
49C22×SL(2,𝔽3)—53no—
50C22×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic, complemented
51#859—54no—
52C23×D5S411yescharacteristic
53C22×AGL(1,𝔽5)—66no—
54C22×AGL(1,𝔽5)—124no—
55C2×C5×Q8—33no—
56C2×C5×Q8C2×Dic313yescomplemented
57C22×C4×C5—31no—
58C22×Dic5—31no—
59Q8×D5—36no—
60Q8×D5—33no—
61Q8×D5—33no—
62Q8×D5—63no—
63Q8×D5—61no—
64Q8×D5C2×Dic313yescomplemented
65Q8×D5C22×D311yescharacteristic
66C2×C4×D5—33no—
67C2×C4×D5—33no—
68C2×C4×D5—33no—
69C2×C4×D5—33no—
70C2×Dic10—33no—
71C2×Dic10—33no—
72C2×Dic10—63no—
73C2×#170—66no—
74C4⋊AGL(1,𝔽5)—34no—
75C4⋊AGL(1,𝔽5)—66no—
76D5⋊C8—34no—
77D5⋊C8—66no—
78C23×Q8—51no—
79C23×C8—151no—
80C22×C4⋊C4—151no—
81C2×#103—156no—
82C2×#103—156no—
83C22×C3×C5—44no—
84C22×C3×C5—43no—
85C2×C3×D5—412no—
86C2×C3×D5—46no—
87C2×C3×D5—46no—
88C2×C3×D5—43no—
89C2×C3×D5—41no—
90ΓL(1,𝔽16)—48no—
91C24×C3—201no—
92C22×Dic3—206no—
93C22×Dic3—208no—
94C2×SL(2,𝔽3)—51no—
95C2×SL(2,𝔽3)—53no—
96C2×SL(2,𝔽3)C2×AGL(1,𝔽5)13yescomplemented
97C23×C5SL(2,ℤ/4)11yescharacteristic
98C22×D5#22614yes—
99C22×D5GL(2,𝔽3)14yes—
100C22×D5SL(2,ℤ/4)13yes—
101C22×D5C2×S413yes—
102C2×AGL(1,𝔽5)—64no—
103C2×AGL(1,𝔽5)—1212no—
104C5×Q8—33no—
105C5×Q8—61no—
106C5×Q8C22×Dic311yescharacteristic, complemented
107C2×C4×C5—33no—
108C2×C4×C5—33no—
109C2×Dic5—33no—
110C2×Dic5—33no—
111C4×D5—33no—
112C4×D5—33no—
113C4×D5—36no—
114C4×D5—31no—
115C4×D5—33no—
116Dic10—33no—
117Dic10—31no—
118Dic10—63no—
119Dic10—63no—
120#170—64no—
121C22×Q8—53no—
122C22×Q8—53no—
123C22×Q8—151no—
124C22×Q8—153no—
125C22×Q8—153no—
126C22×Q8ΓL(1,𝔽16)11yescharacteristic, complemented
127C23×C4—151no—
128C23×C4—301no—
129C22×C8—156no—
130C22×C8—303no—
131C22×C8—301no—
132C2×C4⋊C4—156no—
133C2×C4⋊C4—303no—
134#103—154no—
135#103—1512no—
136C2×C3×C5—41no—
137C2×C3×C5—46no—
138C3×D5—41no—
139C3×D5—41no—
140C3×D5—46no—
141C23×C3—41no—
142C23×C3—203no—
143C23×C3—203no—
144C23×C3—204no—
145C23×C3—204no—
146C2×Dic3—204no—
147C2×Dic3—2024no—
148SL(2,𝔽3)C22×AGL(1,𝔽5)11yescharacteristic, complemented
149C22×C5#85914yescomplemented
150C22×C5C2×SL(2,ℤ/4)13yes—
151C2×D5#859112yescomplemented
152C2×D5C2×#22616yes—
153C2×D5C2×GL(2,𝔽3)16yes—
154C2×D5C2×SL(2,ℤ/4)13yes—
155C2×D5C22×S411yescharacteristic
156AGL(1,𝔽5)—124no—
157C4×C5—31no—
158C4×C5—33no—
159Dic5—31no—
160Dic5—33no—
161C24—51no—
162C2×Q8—33no—
163C2×Q8—51no—
164C2×Q8—53no—
165C2×Q8—153no—
166C2×Q8—153no—
167C2×Q8—153no—
168C2×Q8—153no—
169C2×Q8—156no—
170C2×Q8—303no—
171C2×Q8—301no—
172C2×Q8—303no—
173C2×Q8C2×ΓL(1,𝔽16)13yescomplemented
174C22×C4—31no—
175C22×C4—153no—
176C22×C4—153no—
177C22×C4—153no—
178C22×C4—153no—
179C22×C4—151no—
180C22×C4—306no—
181C22×C4—604no—
182C2×C8—154no—
183C2×C8—306no—
184C2×C8—306no—
185C4⋊C4—154no—
186C4⋊C4—306no—
187C3×C5—41noHall
188C22×C3—43no—
189C22×C3—44no—
190C22×C3—206no—
191C22×C3—201no—
192C22×C3—2012no—
193C22×C3—206no—
194C22×C3—203no—
195Dic3—208no—
196C2×C5C2×#85916yescomplemented
197C2×C5C22×SL(2,ℤ/4)11yescharacteristic
198D5C2×#85916yescomplemented
199D5C22×#22611yescharacteristic
200D5C22×GL(2,𝔽3)11yescharacteristic
201C23—53no—
202C23—53no—
203C23—54no—
204C23—54no—
205C23A4⋊AGL(1,𝔽5)11yescharacteristic
206Q8—33no—
207Q8—61no—
208Q8—151no—
209Q8—153no—
210Q8—303no—
211Q8—303no—
212Q8C22×ΓL(1,𝔽16)11yescharacteristic, complemented
213C2×C4—33no—
214C2×C4—33no—
215C2×C4—151no—
216C2×C4—153no—
217C2×C4—153no—
218C2×C4—153no—
219C2×C4—156no—
220C2×C4—153no—
221C2×C4—153no—
222C2×C4—304no—
223C2×C4—6012no—
224C8—304no—
225C2×C3—41no—
226C2×C3—46no—
227C2×C3—201no—
228C2×C3—201no—
229C2×C3—206no—
230C5C22×#85911yescharacteristic, complemented, Sylow
231C22—51no—
232C22—53no—
233C22—56no—
234C22—512no—
235C22—56no—
236C22#9188614yesdirect product factor
237C22C2×A4⋊AGL(1,𝔽5)13yes—
238C4—31no—
239C4—33no—
240C4—151no—
241C4—153no—
242C4—604no—
243C3—41noSylow
244C2—51no—
245C2—51no—
246C2—56no—
247C2C2×#9188616yesdirect product factor
248C2C22×A4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC23A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FrattiniC2C22×A4⋊AGL(1,𝔽5)
FittingC22×C5×Q8Dic3
socleC23×C5SL(2,ℤ/4)
prime radicalC22×D5×SL(2,𝔽3)C2
cosocleD5×SL(2,𝔽3)C23
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#91886C2direct (N × H)
5. C22×C5×SL(2,𝔽3)C4semidirect
6. C2×D5×SL(2,𝔽3)C4semidirect
8. #91886C22direct (N × H)
18. C2×C5×SL(2,𝔽3)C2×C4semidirect
19. D5×SL(2,𝔽3)C2×C4semidirect
24. C22×C5×Q8Dic3semidirect
27. C2×Q8×D5Dic3semidirect
46. C5×SL(2,𝔽3)C22×C4semidirect
50. C22×SL(2,𝔽3)AGL(1,𝔽5)semidirect
56. C2×C5×Q8C2×Dic3semidirect
64. Q8×D5C2×Dic3semidirect
96. C2×SL(2,𝔽3)C2×AGL(1,𝔽5)semidirect
106. C5×Q8C22×Dic3semidirect
126. C22×Q8ΓL(1,𝔽16)semidirect
148. SL(2,𝔽3)C22×AGL(1,𝔽5)semidirect
149. C22×C5#859semidirect
151. C2×D5#859semidirect
173. C2×Q8C2×ΓL(1,𝔽16)semidirect
196. C2×C5C2×#859semidirect
198. D5C2×#859semidirect
212. Q8C22×ΓL(1,𝔽16)semidirect
230. C5C22×#859semidirect
236. C22#91886direct (N × H)
247. C2C2×#91886direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×SL(2,𝔽3)2
C2×#918862
C22×#40093
C23×ΓL(1,𝔽16)4
C22×#8595