Finite Group Databasebeta

← #14298638

Subgroups — #14298638

Order 1920.

592 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C3×#65855C211yesmaximal, characteristic
2C2×#91228C212yesmaximal
3#11746737C214yesmaximal, complemented
4#10604385—31nomaximal, Hall
5C22×C3×D20C2211yescharacteristic
6C2×#6763C2214yes—
7C3×C5×#117C411yescharacteristic, complemented
8C3×#4072C411yescharacteristic, complemented
9C3×#4039—22no—
10C3×D5×C22⋊C4C412yescomplemented
11C3×D5×C22⋊C4C2212yes—
12C3×C4×D20—22no—
13#91228—22no—
14#91228—22no—
15#71653—51nomaximal, Hall
16#65855D311yescharacteristic
17C2×#3999—32no—
18#64866—34no—
19C23×C3×D5C2×C411yescharacteristic
20C23×C3×D5C2311yescharacteristic
21C22×ΓL(1,𝔽16)—24no—
22C22×C3×C4×C5C2×C411yescharacteristic
23C2×C3×D20—24no—
24C2×C3×D20D412yes—
25C2×C3×D20D412yes—
26C2×C3×C4×D5—22no—
27C2×C3×C4×D5—22no—
28#6763—24no—
29#6763—24no—
30C3×C5×C4⋊C4—21no—
31C3×C5×C22⋊C4C2×C412yes—
32C3×C42×C5—21no—
33C3×C22⋊Dic5C2×C412yes—
34C3×#685—22no—
35C3×#685—22no—
36C3×C4⋊Dic5—21no—
37C3×C4×Dic5—21no—
38C3×#518—51no—
39C2×#834—52no—
40#4527—54no—
41C22×D20C2×D311yescharacteristic
42C2×C22⋊AGL(1,𝔽5)—34no—
43C5×#117Dic311yescharacteristic, complemented
44#4072Dic311yescharacteristic, complemented
45#4039—22no—
46D5×C22⋊C4Dic312yescomplemented
47D5×C22⋊C4C2×D312yes—
48C4×D20—22no—
49#3999—62no—
50#3999—62no—
51#1828—151noSylow
52C23×C3×C5C22×C411yescharacteristic
53C22×C3×D5—22no—
54C22×C3×D5—81no—
55C22×C3×D5—81no—
56C22×C3×D5C22⋊C412yes—
57C22×C3×D5C2×D412yes—
58C22×C3×D5#4114yes—
59C2×ΓL(1,𝔽16)—44no—
60C2×ΓL(1,𝔽16)—84no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5C22⋊C411yescharacteristic
64C2×C3×C4×C5C22⋊C411yescharacteristic
65C2×C3×Dic5—22no—
66C3×D20—24no—
67C3×D20—24no—
68C3×C4×D5—82no—
69C3×C4×D5—82no—
70C22×C3×D4—51no—
71C3×C4×D4—102no—
72C3×C4×D4—102no—
73C3×#117—51no—
74C3×#117AGL(1,𝔽5)11yescharacteristic, complemented
75C2×C3×C22⋊C4—52no—
76C2×C3×C22⋊C4—52no—
77C2×#217—54no—
78#834—102no—
79#834—102no—
80C23×D5C2×Dic311yescharacteristic
81C23×D5C22×D311yescharacteristic
82C22×AGL(1,𝔽5)—64no—
83C22×C4×C5C2×Dic311yescharacteristic
84C2×D20—24no—
85C2×D20#6712yes—
86C2×D20#6712yes—
87C2×C4×D5—22no—
88C2×C4×D5—22no—
89C22⋊AGL(1,𝔽5)—64no—
90C22⋊AGL(1,𝔽5)—64no—
91C5×C4⋊C4—21no—
92C5×C22⋊C4C2×Dic312yes—
93C42×C5—21no—
94C22⋊Dic5C2×Dic312yes—
95#685—22no—
96#685—22no—
97C4⋊Dic5—21no—
98C4×Dic5—21no—
99#518—51no—
100C2×#99—152no—
101#342—154no—
102C22×C3×C5—41no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C22×C3×C5#11712yes—
105C2×C3×D5—22no—
106C2×C3×D5—42no—
107C2×C3×D5—44no—
108C2×C3×D5—42no—
109C2×C3×D5—82no—
110C2×C3×D5#12314yes—
111ΓL(1,𝔽16)—84no—
112C3×C4×C5—21no—
113C3×C4×C5—21no—
114C3×C4×C5—42no—
115C3×Dic5—42no—
116C24×C3—51no—
117C24×C3—51no—
118C2×C3×D4—52no—
119C2×C3×D4—52no—
120C2×C3×D4—104no—
121C22×C3×C4—102no—
122C22×C3×C4—102no—
123C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
124C22×Dic3—104no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—101no—
127C3×C22⋊C4—52no—
128C3×C22⋊C4—102no—
129C3×C22⋊C4—102no—
130C3×C22⋊C4C2×AGL(1,𝔽5)12yes—
131C3×C42—21no—
132C3×C42—101no—
133#217—104no—
134#217—104no—
135C23×C5C22×Dic311yescharacteristic
136C22×D5—22no—
137C22×D5—81no—
138C22×D5—81no—
139C22×D5#21712yes—
140C22×D5#23514yes—
141C22×D5C2×#6712yes—
142C2×AGL(1,𝔽5)—124no—
143C2×AGL(1,𝔽5)—244no—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5#21711yescharacteristic
147C2×C4×C5#21711yescharacteristic
148C2×Dic5—22no—
149D20—24no—
150D20—24no—
151C4×D5—82no—
152C4×D5—82no—
153C22×D4—51no—
154C4×D4—102no—
155C4×D4—102no—
156#117—51no—
157#117ΓL(1,𝔽16)11yescharacteristic, complemented
158C2×C22⋊C4—52no—
159C2×C22⋊C4—52no—
160C2×C22⋊C4—154no—
161#99—302no—
162#99—302no—
163C2×C3×C5—21no—
164C2×C3×C5—22no—
165C2×C3×C5#38111yescharacteristic
166C3×D5—24no—
167C3×D5—42no—
168C23×C3—54no—
169C23×C3—52no—
170C23×C3—52no—
171C23×C3—102no—
172C23×C3—401no—
173C23×C3—401no—
174C23×C3C22×AGL(1,𝔽5)11yescharacteristic
175C3×D4—104no—
176C3×D4—104no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—102no—
180C2×C3×C4—402no—
181C2×C3×C4—402no—
182C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
183C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
184C2×Dic3—204no—
185C2×Dic3—404no—
186C22×C5—41no—
187C22×C5#92612yes—
188C22×C5C2×#21711yescharacteristic
189C2×D5—22no—
190C2×D5—42no—
191C2×D5—44no—
192C2×D5—42no—
193C2×D5—82no—
194C2×D5#92914yes—
195AGL(1,𝔽5)—244no—
196C4×C5—21no—
197C4×C5—21no—
198C4×C5—42no—
199Dic5—42no—
200C24—51no—
201C24—51no—
202C2×D4—52no—
203C2×D4—52no—
204C2×D4—104no—
205C22×C4—102no—
206C22×C4—102no—
207C22×C4—304no—
208C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—101no—
211C22⋊C4—52no—
212C22⋊C4—102no—
213C22⋊C4—102no—
214C22⋊C4—304no—
215C22⋊C4—304no—
216C22⋊C4C2×ΓL(1,𝔽16)12yes—
217C42—21no—
218C42—101no—
219C3×C5#182811yescharacteristic, complemented, Hall
220C22×C3—41no—
221C22×C3—54no—
222C22×C3—102no—
223C22×C3—204no—
224C22×C3—202no—
225C22×C3—202no—
226C22×C3—402no—
227C22×C3#413012yes—
228C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—42no—
232C3×C4—202no—
233Dic3—404no—
234C2×C5—21no—
235C2×C5—22no—
236C2×C5#521111yescharacteristic
237D5—24no—
238D5—42no—
239C23—54no—
240C23—52no—
241C23—52no—
242C23—102no—
243C23—401no—
244C23—401no—
245C23C22×ΓL(1,𝔽16)11yescharacteristic
246D4—104no—
247D4—104no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—102no—
251C2×C4—402no—
252C2×C4—402no—
253C2×C4—604no—
254C2×C4—1204no—
255C2×C4#676311yescharacteristic
256C2×C4#676311yescharacteristic
257C2×C3—21no—
258C2×C3—22no—
259C2×C3—104no—
260C2×C3—202no—
261C2×C3#6576411yescharacteristic
262C5#7165311yescharacteristic, complemented, Sylow
263C22—41no—
264C22—54no—
265C22—102no—
266C22—202no—
267C22—204no—
268C22—202no—
269C22—402no—
270C22#9198912yes—
271C22C2×#676311yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—202no—
276C4—1204no—
277C3#1060438511yescharacteristic, complemented, Sylow
278C2—21no—
279C2—22no—
280C2—104no—
281C2—202no—
282C2#1175242311yescharacteristic
subgroupG/H
centerC2#11752423
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#117C4
socleC2×C3×C5#381
prime radicalC22×C3×D20C22
cosocleC23×C3×D5C23
hypercenter#117ΓL(1,𝔽16)
hypocenterC3×C5#1828
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #11746737C2semidirect
7. C3×C5×#117C4semidirect
8. C3×#4072C4semidirect
10. C3×D5×C22⋊C4C4semidirect
43. C5×#117Dic3semidirect
44. #4072Dic3semidirect
46. D5×C22⋊C4Dic3semidirect
74. C3×#117AGL(1,𝔽5)semidirect
157. #117ΓL(1,𝔽16)semidirect
219. C3×C5#1828semidirect
262. C5#71653semidirect
277. C3#10604385semidirect

Maximal subgroups

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

subgroupindex
C3×#658552
C2×#912282
#117467372
#106043853
#716535