Finite Group Databasebeta

← #14301462

Subgroups — #14301462

Order 1920.

720 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 160 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
1#11756557C211yesmaximal, characteristic
2C2×C5×#936C211yesmaximal, characteristic
3C2×C3×#3965C211yesmaximal, characteristic
4#11748409C212yesmaximal, complemented
5#11745976C212yesmaximal, complemented
6#10602516—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C5×Dic6C2211yescharacteristic
9C2×#6719—22no—
10D4×Dic15—24no—
11#91815C2212yes—
12C2×C5×#217—22no—
13C5×#936—22no—
14C5×#936C414yescomplemented
15C2×C4×C5×Dic3C2211yescharacteristic
16C2×C3×#681C2212yes—
17C3×#3965—22no—
18#90973—24no—
19#70069—51nomaximal, Hall
20C2×C5×#124—31no—
21#66132—31no—
22#65514—32no—
23C2×#3965D311yescharacteristic
24#64743—32no—
25C24×C3×C5D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C412yes—
29C2×C3×C5×D4D412yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—24no—
32C22×C5×Dic3—21no—
33C22×C5×Dic3—21no—
34C2×C5×Dic6—22no—
35C2×C5×Dic6—22no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6C2×C412yescomplemented
38#6719—24no—
39#6719—22no—
40C4⋊Dic15D414yes—
41C4×Dic15—22no—
42C5×#217—28no—
43C4×C5×Dic3—21no—
44C4×C5×Dic3C2×C412yescomplemented
45C3×#681—22no—
46C3×#681—22no—
47C2×C3×#168—22no—
48#5798—51no—
49C2×#936D511yescharacteristic
50C2×C3×#100—51no—
51#5120—52no—
52#4555—52no—
53C22×C5×Q8—31no—
54C22×C5×D4C2×D311yescharacteristic
55C5×#124—34no—
56C5×#124—62no—
57C2×C5×C22⋊C4—62no—
58C2×C42×C5—31no—
59C2×C22⋊Dic5—62no—
60D4×Dic5—64no—
61#4072—32no—
62C2×#681C2×D312yes—
63#3967—64no—
64#3965—22no—
65#1885—151noSylow
66C23×C3×C5—22no—
67C23×C3×C5—22no—
68C23×C3×C5—44no—
69C23×C3×C5C22⋊C414yes—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×D4—24no—
72C3×C5×D4—24no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×Dic15—24no—
78C2×Dic15—84no—
79C2×C5×Dic3—22no—
80C2×C5×Dic3—22no—
81C2×C5×Dic3—42no—
82C2×C5×Dic3—41no—
83C2×C5×Dic3—41no—
84C5×Dic6—24no—
85C5×Dic6—42no—
86C3×#168—42no—
87C22×C3×D4C2×D511yescharacteristic
88C22×Dic6C2×D511yescharacteristic
89C2×C3×M16—52no—
90C2×#217—22no—
91C2×#217—102no—
92#936—22no—
93#936Dic514yescomplemented
94D4×Dic3—104no—
95#926—52no—
96C2×C4×Dic3C2×D511yescharacteristic
97C3×#100—102no—
98#816—104no—
99C24×C5D1212yes—
100C2×C5×Q8—32no—
101C2×C5×Q8—61no—
102C2×C5×Q8—62no—
103C2×C5×Q8—62no—
104C2×C5×D4—22no—
105C2×C5×D4—22no—
106C2×C5×D4C4×D312yes—
107C2×C5×D4#6712yes—
108C22×C4×C5—61no—
109C22×C4×C5—61no—
110C22×C4×C5C22×D311yescharacteristic
111C22×Dic5—64no—
112C5×C22⋊C4—68no—
113C42×C5—32no—
114C42×C5—61no—
115C22⋊Dic5—64no—
116C22⋊Dic5—62no—
117C4⋊Dic5—34no—
118C4×Dic5—62no—
119#681—22no—
120#681—22no—
121C2×#168—22no—
122C2×#124—31no—
123#518—151no—
124#419—152no—
125C2×#100—51no—
126#339—152no—
127C22×C3×C5—22no—
128C22×C3×C5—24no—
129C22×C3×C5—44no—
130C22×C3×C5—44no—
131C22×C3×C5—82no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12011yescharacteristic
134C22×C3×C5#12311yescharacteristic
135C3×C4×C5C4×D412yes—
136C3×C4×C5#12112yes—
137Dic15—44no—
138C5×Dic3—42no—
139C5×Dic3—42no—
140C24×C3C22⋊D512yes—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4C2×Dic512yes—
144C2×C3×D4C22⋊D512yes—
145C22×C3×C4C22×D511yescharacteristic
146C22×Dic3—21no—
147C22×Dic3—21no—
148C22×Dic3—104no—
149C2×Dic6—22no—
150C2×Dic6—22no—
151C2×Dic6—21no—
152C2×Dic6C2×Dic512yescomplemented
153C3×M16—102no—
154C3×M16—102no—
155C2×C3×C8—102no—
156#217—28no—
157#217—104no—
158#217—102no—
159C4⋊Dic3—54no—
160C4×Dic3—21no—
161C4×Dic3—102no—
162C4×Dic3C2×Dic512yescomplemented
163C23×C5—22no—
164C23×C5—22no—
165C23×C5—44no—
166C23×C5(C2×D3)⋊C414yes—
167C23×C5C2×D1211yescharacteristic
168C5×Q8—64no—
169C5×Q8—122no—
170C5×D4—24no—
171C5×D4—24no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5—122no—
175C2×C4×C5—121no—
176C2×C4×C5—121no—
177C2×C4×C5C2×C4×D311yescharacteristic
178C2×C4×C5D3×D412yes—
179C2×C4×C5#23712yes—
180C2×C4×C5C2×#6711yescharacteristic
181C2×Dic5—64no—
182C2×Dic5—244no—
183#168—42no—
184C22×Q8—31no—
185C22×D4D3×D511yescharacteristic
186C2×M16—52no—
187#124—34no—
188#124—62no—
189C4×D4—304no—
190#117—152no—
191C2×C22⋊C4—62no—
192C2×C22⋊C4—302no—
193C2×C42—31no—
194#103—304no—
195#100—102no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5—44no—
199C2×C3×C5#38611yescharacteristic
200C2×C3×C5#45512yes—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—44no—
204C23×C3C22⋊Dic514yes—
205C23×C3C2×C22⋊D511yescharacteristic
206C3×D4—24no—
207C3×D4—24no—
208C2×C3×C4D4×D512yes—
209C2×C3×C4#71112yes—
210C2×C3×C4C22×Dic511yescharacteristic
211C2×C3×C4C2×C22⋊D511yescharacteristic
212C2×Dic3—22no—
213C2×Dic3—22no—
214C2×Dic3—42no—
215C2×Dic3—41no—
216C2×Dic3—41no—
217C2×Dic3—104no—
218C2×Dic3—404no—
219Dic6—24no—
220Dic6—42no—
221C3×C8—202no—
222C22×C5—22no—
223C22×C5—24no—
224C22×C5—44no—
225C22×C5—44no—
226C22×C5—82no—
227C22×C5#88211yescharacteristic
228C22×C5#88611yescharacteristic
229C22×C5C2×(C2×D3)⋊C411yescharacteristic
230C4×C5—122no—
231C4×C5—122no—
232C4×C5#67⋊C412yes—
233C4×C5#93912yes—
234Dic5—124no—
235C24#120312yes—
236C2×Q8—32no—
237C2×Q8—61no—
238C2×Q8—62no—
239C2×Q8—62no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4D3×Dic512yes—
243C2×D4#120112yes—
244C22×C4—61no—
245C22×C4—61no—
246C22×C4—304no—
247C22×C4C2×D3×D511yescharacteristic
248M16—102no—
249M16—102no—
250C2×C8—102no—
251C4⋊C4—154no—
252C22⋊C4—68no—
253C22⋊C4—304no—
254C22⋊C4—302no—
255C42—32no—
256C42—61no—
257C42—302no—
258C3×C5#188511yescharacteristic, complemented, Hall
259C22×C3—22no—
260C22×C3—24no—
261C22×C3—44no—
262C22×C3—44no—
263C22×C3—82no—
264C22×C3#408111yescharacteristic
265C22×C3#408311yescharacteristic
266C22×C3C2×C22⋊Dic511yescharacteristic
267C3×C4D4×Dic512yes—
268C3×C4#408512yes—
269Dic3—42no—
270Dic3—42no—
271Dic3—204no—
272C2×C5—21no—
273C2×C5—21no—
274C2×C5—44no—
275C2×C5#474612yes—
276C2×C5#495811yescharacteristic
277C23—22no—
278C23—22no—
279C23—44no—
280C23(C2×D3)⋊Dic514yes—
281C23C2×#120311yescharacteristic
282Q8—64no—
283Q8—122no—
284D4—24no—
285D4—24no—
286C2×C4—62no—
287C2×C4—62no—
288C2×C4—122no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—304no—
292C2×C4—1204no—
293C2×C4#678012yes—
294C2×C4C2×D3×Dic511yescharacteristic
295C2×C4C2×#120111yescharacteristic
296C2×C4#679012yes—
297C8—202no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—44no—
301C2×C3#6535012yes—
302C2×C3#6550911yescharacteristic
303C5#7006911yescharacteristic, complemented, Sylow
304C22—22no—
305C22—24no—
306C22—44no—
307C22—44no—
308C22—82no—
309C22C2×(C2×D3)⋊Dic511yescharacteristic
310C22#9154311yescharacteristic
311C22#9157311yescharacteristic
312C4—122no—
313C4—122no—
314C4—604no—
315C4#67⋊Dic512yes—
316C4#9157112yes—
317C3#1060251611yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2—44no—
321C2#1174915012yes—
322C2#1174950111yescharacteristic
subgroupG/H
centerC22#91573
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1885
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748409C2semidirect
5. #11745976C2semidirect
14. C5×#936C4semidirect
37. C2×C5×Dic6C2×C4semidirect
44. C4×C5×Dic3C2×C4semidirect
93. #936Dic5semidirect
152. C2×Dic6C2×Dic5semidirect
162. C4×Dic3C2×Dic5semidirect
258. C3×C5#1885semidirect
303. C5#70069semidirect
317. C3#10602516semidirect

Maximal subgroups

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

subgroupindex
#117565572
C2×C5×#9362
C2×C3×#39652
#117484092
#117459762
#106025163
#700695