Finite Group Databasebeta

← #14301524

Subgroups — #14301524

Order 1920.

888 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C2×#91829C211yesmaximal, characteristic
2#11756557C211yesmaximal, characteristic, complemented
3C2×C3×C5×#100C211yesmaximal, characteristic, complemented
4#11751232C212yesmaximal, complemented
5#11746376C212yesmaximal, complemented
6#10600863—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×#1220—22no—
9C22×D60C2211yescharacteristic
10C2×C3×C5×M16C2212yes—
11C2×#6719—22no—
12#91829—22no—
13#91829C414yescomplemented
14D4×Dic15—24no—
15#91815C2212yes—
16C2×C4×Dic15C2211yescharacteristic
17C3×C5×#100—22no—
18#91105—24no—
19#70070—51nomaximal, Hall
20C2×#4086—31no—
21#66132—31no—
22C2×C5×#100D311yescharacteristic, complemented
23#65420—32no—
24#64775—32no—
25C24×C3×C5D412yes—
26C23×D15—21no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4C2×C412yes—
30C2×C3×C5×D4D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×#1220—28no—
33C2×#1220—48no—
34C22×Dic15—21no—
35C22×Dic15—24no—
36C2×D60—22no—
37C2×D60—22no—
38C2×D60—21no—
39C2×D60C2×C412yescomplemented
40C3×C5×M16—22no—
41C3×C5×M16—22no—
42C2×C3×C5×C8—22no—
43#6719—24no—
44#6719—22no—
45C4⋊Dic15D414yescomplemented
46C4×Dic15—21no—
47C4×Dic15—22no—
48C4×Dic15C2×C412yescomplemented
49C2×#940—51no—
50#5798—51no—
51C2×C3×#100D511yescharacteristic, complemented
52#5131—52no—
53#4555—52no—
54C22×C5×D4C2×D311yescharacteristic
55C22×C22⋊D5—62no—
56C22×D20—31no—
57C2×C5×M16C2×D312yes—
58C2×C22⋊Dic5—62no—
59#4086—34no—
60#4086—62no—
61D4×Dic5—64no—
62#4072—32no—
63C2×C4×Dic5—31no—
64C5×#100—22no—
65#3953—64no—
66#1887—151noSylow
67C23×C3×C5—22no—
68C23×C3×C5—22no—
69C23×C3×C5—44no—
70C23×C3×C5C22⋊C414yes—
71C23×C3×C5C2×D411yescharacteristic
72C22×D15—22no—
73C22×D15—44no—
74C22×D15—41no—
75C22×D15—41no—
76C3×C5×D4—24no—
77C3×C5×D4—24no—
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×C4×C5C2×D412yes—
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5#4112yes—
82#1220—416no—
83C2×Dic15—24no—
84C2×Dic15—22no—
85C2×Dic15—24no—
86C2×Dic15—84no—
87D60—24no—
88D60—42no—
89C3×C5×C8—42no—
90C22×C3×D4C2×D511yescharacteristic
91C22×#67—102no—
92C22×D12—51no—
93C2×C3×M16C2×D512yes—
94C2×#217—102no—
95#940—54no—
96#940—102no—
97D4×Dic3—104no—
98#926—52no—
99C2×C4×Dic3—51no—
100C3×#100—22no—
101#821—104no—
102C24×C5D1212yes—
103C23×D5—61no—
104C2×C5×D4—22no—
105C2×C5×D4—22no—
106C2×C5×D4C4×D312yes—
107C2×C5×D4#6712yes—
108C22×C4×C5C22×D311yescharacteristic
109C2×C22⋊D5—68no—
110C2×C22⋊D5—128no—
111C22×Dic5—61no—
112C22×Dic5—64no—
113C2×D20—32no—
114C2×D20—62no—
115C2×D20—62no—
116C2×D20—61no—
117C5×M16—22no—
118C5×M16—22no—
119C2×C5×C8—22no—
120C22⋊Dic5—64no—
121C22⋊Dic5—62no—
122C4⋊Dic5—34no—
123C4×Dic5—32no—
124C4×Dic5—62no—
125C4×Dic5—61no—
126C2×#127—151no—
127#518—151no—
128#418—152no—
129C2×#100D1511yescharacteristic, complemented
130#339—152no—
131C22×C3×C5—22no—
132C22×C3×C5—24no—
133C22×C3×C5—44no—
134C22×C3×C5—44no—
135C22×C3×C5—82no—
136C22×C3×C5C2×C22⋊C411yescharacteristic
137C22×C3×C5#12011yescharacteristic
138C22×C3×C5#12311yescharacteristic
139C2×D15—44no—
140C2×D15—42no—
141C2×D15—82no—
142C2×D15—82no—
143C3×C4×C5C4×D412yes—
144C3×C4×C5#12112yes—
145Dic15—24no—
146Dic15—44no—
147C24×C3D2012yes—
148C23×D3—101no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4C4×D512yes—
152C2×C3×D4C22⋊D512yes—
153C22×C3×C4C22×D511yescharacteristic
154C2×#67—108no—
155C2×#67—208no—
156C22×Dic3—101no—
157C22×Dic3—104no—
158C2×D12—52no—
159C2×D12—102no—
160C2×D12—102no—
161C2×D12—101no—
162C3×M16—22no—
163C3×M16—22no—
164C2×C3×C8—22no—
165#217—104no—
166#217—102no—
167C4⋊Dic3—54no—
168C4×Dic3—52no—
169C4×Dic3—102no—
170C4×Dic3—101no—
171C23×C5—22no—
172C23×C5—22no—
173C23×C5—44no—
174C23×C5(C2×D3)⋊C414yes—
175C23×C5C2×D1211yescharacteristic
176C22×D5—62no—
177C22×D5—124no—
178C22×D5—121no—
179C22×D5—121no—
180C5×D4—24no—
181C5×D4—24no—
182C2×C4×C5C2×C4×D311yescharacteristic
183C2×C4×C5D3×D412yes—
184C2×C4×C5#23712yes—
185C2×C4×C5C2×#6711yescharacteristic
186C22⋊D5—1216no—
187C2×Dic5—64no—
188C2×Dic5—62no—
189C2×Dic5—64no—
190C2×Dic5—244no—
191D20—64no—
192D20—122no—
193C5×C8—42no—
194C22×D4—151no—
195C22×D4—302no—
196C22×D4C2×D1511yescharacteristic
197C2×M16C2×D1512yes—
198#127—154no—
199#127—302no—
200C4×D4—304no—
201#117—152no—
202C2×C22⋊C4—302no—
203C2×C42—151no—
204#102—304no—
205#100—22no—
206C2×C3×C5—21no—
207C2×C3×C5—21no—
208C2×C3×C5—44no—
209C2×C3×C5#38611yescharacteristic
210C2×C3×C5#45312yes—
211D15—82no—
212C23×C3—22no—
213C23×C3—22no—
214C23×C3—44no—
215C23×C3#68514yes—
216C23×C3C2×D2011yescharacteristic
217C22×D3—102no—
218C22×D3—204no—
219C22×D3—201no—
220C22×D3—201no—
221C3×D4—24no—
222C3×D4—24no—
223C2×C3×C4C2×C4×D511yescharacteristic
224C2×C3×C4D4×D512yes—
225C2×C3×C4#71112yes—
226C2×C3×C4C2×C22⋊D511yescharacteristic
227#67—2016no—
228C2×Dic3—104no—
229C2×Dic3—102no—
230C2×Dic3—104no—
231C2×Dic3—404no—
232D12—104no—
233D12—202no—
234C3×C8—42no—
235C22×C5—22no—
236C22×C5—24no—
237C22×C5—44no—
238C22×C5—44no—
239C22×C5—82no—
240C22×C5#88211yescharacteristic
241C22×C5#88611yescharacteristic
242C22×C5C2×(C2×D3)⋊C411yescharacteristic
243C2×D5—124no—
244C2×D5—122no—
245C2×D5—242no—
246C2×D5—242no—
247C4×C5#67⋊C412yes—
248C4×C5#93912yes—
249Dic5—64no—
250Dic5—124no—
251C24—301no—
252C24D6012yes—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—152no—
256C2×D4—308no—
257C2×D4—302no—
258C2×D4—302no—
259C2×D4—301no—
260C2×D4—608no—
261C2×D4C4×D1512yes—
262C2×D4#122012yes—
263C22×C4—301no—
264C22×C4—304no—
265C22×C4C22×D1511yescharacteristic
266M16—22no—
267M16—22no—
268C2×C8—22no—
269C4⋊C4—154no—
270C22⋊C4—304no—
271C22⋊C4—302no—
272C42—152no—
273C42—302no—
274C42—301no—
275C3×C5#188711yescharacteristic, complemented, Hall
276C22×C3—22no—
277C22×C3—24no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3—82no—
281C22×C3#402811yescharacteristic
282C22×C3#403211yescharacteristic
283C22×C3C2×#68511yescharacteristic
284C2×D3—204no—
285C2×D3—202no—
286C2×D3—402no—
287C2×D3—402no—
288C3×C4#402712yes—
289C3×C4#408512yes—
290Dic3—104no—
291Dic3—204no—
292C2×C5—21no—
293C2×C5—21no—
294C2×C5—44no—
295C2×C5#474712yes—
296C2×C5#495811yescharacteristic
297D5—242no—
298C23—22no—
299C23—22no—
300C23—44no—
301C23—302no—
302C23—604no—
303C23—601no—
304C23—601no—
305C23#671414yes—
306C23C2×D6011yescharacteristic
307D4—24no—
308D4—24no—
309D4—304no—
310D4—6016no—
311D4—602no—
312C2×C4—304no—
313C2×C4—302no—
314C2×C4—304no—
315C2×C4—1204no—
316C2×C4C2×C4×D1511yescharacteristic
317C2×C4D4×D1512yes—
318C2×C4#681912yes—
319C2×C4C2×#122011yescharacteristic
320C8—42no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—44no—
324C2×C3#6503612yes—
325C2×C3#6524711yescharacteristic
326D3—402no—
327C5#7007011yescharacteristic, complemented, Sylow
328C22—22no—
329C22—24no—
330C22—44no—
331C22—44no—
332C22—82no—
333C22—604no—
334C22—602no—
335C22—1202no—
336C22—1202no—
337C22#9177111yescharacteristic
338C22#9177511yescharacteristic
339C22C2×#671411yescharacteristic
340C4—304no—
341C4—604no—
342C4#9177012yes—
343C4#9182812yes—
344C3#1060086311yescharacteristic, complemented, Sylow
345C2—21no—
346C2—21no—
347C2—44no—
348C2—1202no—
349C2#1175084812yes—
350C2#1175105911yescharacteristic
subgroupG/H
centerC22#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#100C2
socleC22×C3×C5#120
prime radicalC2×#91829C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#100D15
hypocenterC3×C5#1887
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #11756557C2semidirect
3. C2×C3×C5×#100C2semidirect
4. #11751232C2semidirect
5. #11746376C2semidirect
13. #91829C4semidirect
22. C2×C5×#100D3semidirect
39. C2×D60C2×C4semidirect
45. C4⋊Dic15D4semidirect
48. C4×Dic15C2×C4semidirect
51. C2×C3×#100D5semidirect
129. C2×#100D15semidirect
275. C3×C5#1887semidirect
327. C5#70070semidirect
344. C3#10600863semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
#117565572
C2×C3×C5×#1002
#117512322
#117463762
#106008633
#700705