Finite Group Databasebeta

← #14320030

Subgroups — #14320030

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×D15C211yesmaximal, characteristic
2C3×C5×#376C211yesmaximal, characteristic, complemented
3C4×#6714C212yesmaximal
4#11751033C211yesmaximal, characteristic, complemented
5C4×#6712C212yesmaximal, complemented
6#11750768C212yesmaximal
7#11750765C212yesmaximal
8#11750752C212yesmaximal, complemented
9#11750751C212yesmaximal, complemented
10#10605144—31nomaximal, Hall
11C22×C4×D15C2211yescharacteristic
12C22×C4×D15C2211yescharacteristic
13C22×C4×D15C2211yescharacteristic
14C2×C3×C42×C5C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×#6714C2214yes—
17C2×#6712C2214yes—
18C2×C4×Dic15C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C42×D15C418yescomplemented
23C3×C5×#95C2212yes—
24C3×C5×#95C2212yes—
25#91115C2214yes—
26#91115C2212yes—
27#91115C2214yes—
28#91115C2212yes—
29#73413—51nomaximal, Hall
30C2×C42×D5—31no—
31C5×#376D311yescharacteristic, complemented
32C4×#685—32no—
33#65221—31no—
34C4×#683—32no—
35#64956—32no—
36#64953—32no—
37#64940—32no—
38#64939—32no—
39C23×D15C2311yescharacteristic
40C22×C3×C4×C5C2314yes—
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15C2314yes—
45C22×Dic15C2311yescharacteristic
46C22×Dic15C2311yescharacteristic
47C22×Dic15C2311yescharacteristic
48C2×C4×D15—24no—
49C2×C4×D15—24no—
50C2×C4×D15—24no—
51C2×C4×D15C2×C414yes—
52C2×C4×D15C2×C414yes—
53C2×C4×D15C2×C414yes—
54C3×C42×C5—24no—
55C3×C42×C5C2×C414yes—
56#6714—28no—
57#6712—28no—
58C4×Dic15—24no—
59C4×Dic15C2×C414yes—
60C4×Dic15C2×C414yes—
61C4×Dic15C2×C414yes—
62C2×C42×D3—51no—
63C3×#376D511yescharacteristic, complemented
64C4×(C2×D3)⋊C4—52no—
65#4932—51no—
66C4×Dic3⋊C4—52no—
67#4667—52no—
68#4664—52no—
69#4651—52no—
70#4650—52no—
71C22×C4×D5—31no—
72C22×C4×D5—31no—
73C22×C4×D5—31no—
74C2×C42×C5C2×D312yes—
75C2×C42×C5C2×D311yescharacteristic
76C2×#685—34no—
77C2×#683—34no—
78C2×C4×Dic5—31no—
79C2×C4×Dic5—31no—
80C2×C4×Dic5—31no—
81C2×C4×Dic5—32no—
82C42×D5—38no—
83C5×#95C2×D312yes—
84C5×#95C2×D312yes—
85#3963—34no—
86#3963—32no—
87#3963—34no—
88#3963—32no—
89#2283—151noSylow
90C23×C3×C5C2411yescharacteristic
91C22×D15—22no—
92C22×D15—22no—
93C22×D15C22×C412yes—
94C22×D15#4114yes—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—24no—
98C2×C3×C4×C5—24no—
99C2×C3×C4×C5—24no—
100C2×C3×C4×C5C22×C412yes—
101C2×C3×C4×C5C22×C412yes—
102C2×C3×C4×C5C22×C412yes—
103C2×C3×C4×C5#4114yes—
104C2×Dic15—22no—
105C2×Dic15—22no—
106C2×Dic15—24no—
107C2×Dic15—24no—
108C2×Dic15—24no—
109C2×Dic15C22×C412yes—
110C2×Dic15C22×C412yes—
111C2×Dic15C22×C412yes—
112C2×Dic15#4114yes—
113C4×D15—28no—
114C4×D15—28no—
115C4×D15—28no—
116C22×C4×D3—51no—
117C22×C4×D3—51no—
118C22×C4×D3—51no—
119C2×C3×C42C2×D512yes—
120C2×C3×C42C2×D511yescharacteristic
121C2×(C2×D3)⋊C4—54no—
122C2×Dic3⋊C4—54no—
123C2×C4×Dic3—51no—
124C2×C4×Dic3—51no—
125C2×C4×Dic3—51no—
126C2×C4×Dic3—52no—
127C42×D3—58no—
128C3×#95C2×D512yes—
129C3×#95C2×D512yes—
130C3⋊#95—54no—
131C3⋊#95—52no—
132C3⋊#95—54no—
133C3⋊#95—52no—
134C23×D5—31no—
135C22×C4×C5C22×D314yes—
136C22×C4×C5C22×D311yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C22×C4×C5C22×D311yescharacteristic
139C22×Dic5—31no—
140C22×Dic5—31no—
141C22×Dic5—31no—
142C22×Dic5—34no—
143C2×C4×D5—34no—
144C2×C4×D5—34no—
145C2×C4×D5—34no—
146C2×C4×D5—64no—
147C2×C4×D5—64no—
148C2×C4×D5—64no—
149C42×C5—24no—
150C42×C5C4×D314yes—
151#685—68no—
152#683—68no—
153C4×Dic5—34no—
154C4×Dic5—34no—
155C4×Dic5—34no—
156C4×Dic5—64no—
157C22×C42—151no—
158#383—152no—
159#382—152no—
160#381—152no—
161#380—152no—
162C4×C4⋊C4—152no—
163C4×C22⋊C4—152no—
164#376—151no—
165#376D1511yescharacteristic, complemented
166C22×C3×C5C23×C411yescharacteristic
167C22×C3×C5C2×#4112yes—
168C22×C3×C5C2×#4112yes—
169C22×C3×C5C2×#4112yes—
170C2×D15—22no—
171C2×D15—22no—
172C2×D15—28no—
173C2×D15#11714yes—
174C3×C4×C5—22no—
175C3×C4×C5—22no—
176C3×C4×C5—44no—
177C3×C4×C5#11714yes—
178Dic15—22no—
179Dic15—22no—
180Dic15—44no—
181Dic15#11714yes—
182C23×D3—51no—
183C22×C3×C4C22×D514yes—
184C22×C3×C4C22×D511yescharacteristic
185C22×C3×C4C22×D511yescharacteristic
186C22×C3×C4C22×D511yescharacteristic
187C22×Dic3—51no—
188C22×Dic3—51no—
189C22×Dic3—51no—
190C22×Dic3—54no—
191C2×C4×D3—54no—
192C2×C4×D3—54no—
193C2×C4×D3—54no—
194C2×C4×D3—104no—
195C2×C4×D3—104no—
196C2×C4×D3—104no—
197C3×C42—24no—
198C3×C42C4×D514yes—
199(C2×D3)⋊C4—108no—
200Dic3⋊C4—108no—
201C4×Dic3—54no—
202C4×Dic3—54no—
203C4×Dic3—54no—
204C4×Dic3—104no—
205C23×C5C23×D311yescharacteristic
206C22×D5—32no—
207C22×D5—34no—
208C22×D5—62no—
209C22×D5—62no—
210C2×C4×C5—22no—
211C2×C4×C5—22no—
212C2×C4×C5—24no—
213C2×C4×C5—24no—
214C2×C4×C5—24no—
215C2×C4×C5C2×C4×D312yes—
216C2×C4×C5C2×C4×D312yes—
217C2×C4×C5C2×C4×D312yes—
218C2×C4×C5#23514yes—
219C2×Dic5—32no—
220C2×Dic5—34no—
221C2×Dic5—32no—
222C2×Dic5—32no—
223C2×Dic5—62no—
224C2×Dic5—62no—
225C2×Dic5—64no—
226C2×Dic5—64no—
227C2×Dic5—64no—
228C4×D5—68no—
229C4×D5—68no—
230C4×D5—68no—
231C23×C4—151no—
232C23×C4—151no—
233C23×C4—151no—
234C2×C4⋊C4—154no—
235C2×C22⋊C4—154no—
236C2×C42—151no—
237C2×C42—151no—
238C2×C42—151no—
239C2×C42—158no—
240C2×C42—152no—
241C2×C42C2×D1512yes—
242C2×C42C2×D1511yescharacteristic
243#95—152no—
244#95—152no—
245#95—154no—
246#95—154no—
247#95C2×D1512yes—
248#95C2×D1512yes—
249C2×C3×C5C2×#11711yescharacteristic
250C2×C3×C5C2×#11711yescharacteristic
251C2×C3×C5C2×#11711yescharacteristic
252C2×C3×C5#52914yes—
253D15—24no—
254C23×C3C23×D511yescharacteristic
255C22×D3—52no—
256C22×D3—54no—
257C22×D3—102no—
258C22×D3—102no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4C2×C4×D512yes—
265C2×C3×C4C2×C4×D512yes—
266C2×C3×C4C2×C4×D512yes—
267C2×C3×C4#70914yes—
268C2×Dic3—52no—
269C2×Dic3—54no—
270C2×Dic3—52no—
271C2×Dic3—52no—
272C2×Dic3—102no—
273C2×Dic3—102no—
274C2×Dic3—104no—
275C2×Dic3—104no—
276C2×Dic3—104no—
277C4×D3—108no—
278C4×D3—108no—
279C4×D3—108no—
280C22×C5C22×C4×D311yescharacteristic
281C22×C5C2×#23512yes—
282C22×C5D3×#4112yes—
283C22×C5D3×#4112yes—
284C2×D5—34no—
285C2×D5—62no—
286C2×D5—62no—
287C2×D5—68no—
288C4×C5—22no—
289C4×C5—22no—
290C4×C5—44no—
291C4×C5#87214yes—
292Dic5—34no—
293Dic5—62no—
294Dic5—62no—
295Dic5—124no—
296C24—151no—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4—151no—
300C22×C4—154no—
301C22×C4—154no—
302C22×C4—154no—
303C22×C4—154no—
304C22×C4—304no—
305C22×C4—304no—
306C22×C4—304no—
307C22×C4C22×D1514yes—
308C22×C4C22×D1511yescharacteristic
309C22×C4C22×D1511yescharacteristic
310C22×C4C22×D1511yescharacteristic
311C4⋊C4—308no—
312C22⋊C4—308no—
313C42—24no—
314C42—154no—
315C42—154no—
316C42—154no—
317C42—304no—
318C42C4×D1514yes—
319C3×C5#228311yescharacteristic, complemented, Hall
320C22×C3C22×C4×D511yescharacteristic
321C22×C3C2×#70912yes—
322C22×C3D5×#4112yes—
323C22×C3D5×#4112yes—
324C2×D3—54no—
325C2×D3—102no—
326C2×D3—102no—
327C2×D3—108no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—44no—
331C3×C4#401814yes—
332Dic3—54no—
333Dic3—102no—
334Dic3—102no—
335Dic3—204no—
336C2×C5C2×#87211yescharacteristic
337C2×C5D3×#11711yescharacteristic
338C2×C5D3×#11711yescharacteristic
339C2×C5#552814yes—
340D5—64no—
341C23—152no—
342C23—154no—
343C23—302no—
344C23—302no—
345C23C23×D1511yescharacteristic
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—152no—
352C2×C4—154no—
353C2×C4—152no—
354C2×C4—152no—
355C2×C4—308no—
356C2×C4—308no—
357C2×C4—302no—
358C2×C4—302no—
359C2×C4—308no—
360C2×C4—304no—
361C2×C4—304no—
362C2×C4—304no—
363C2×C4C2×C4×D1512yes—
364C2×C4C2×C4×D1512yes—
365C2×C4C2×C4×D1512yes—
366C2×C4#681714yes—
367C2×C3C2×#401811yescharacteristic
368C2×C3D5×#11711yescharacteristic
369C2×C3D5×#11711yescharacteristic
370C2×C3#6586214yes—
371D3—104no—
372C5#7341311yescharacteristic, complemented, Sylow
373C22—154no—
374C22—302no—
375C22—302no—
376C22—308no—
377C22C22×C4×D1511yescharacteristic
378C22C2×#681712yes—
379C22#41×D1512yes—
380C22#41×D1512yes—
381C4—22no—
382C4—22no—
383C4—44no—
384C4—154no—
385C4—302no—
386C4—302no—
387C4—604no—
388C4#9176114yes—
389C3#1060514411yescharacteristic, complemented, Sylow
390C2—304no—
391C2C2×#9176111yescharacteristic
392C2D15×#11711yescharacteristic
393C2D15×#11711yescharacteristic
394C2#1175628714yes—
subgroupG/H
centerC22×C4C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC3×C5×#376C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#376D15
hypocenterC3×C5#2283
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C3×C5×#376C2semidirect
4. #11751033C2semidirect
5. C4×#6712C2semidirect
8. #11750752C2semidirect
9. #11750751C2semidirect
22. C42×D15C4semidirect
31. C5×#376D3semidirect
63. C3×#376D5semidirect
165. #376D15semidirect
319. C3×C5#2283semidirect
372. C5#73413semidirect
389. C3#10605144semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D152
C3×C5×#3762
C4×#67142
#117510332
C4×#67122
#117507682
#117507652
#117507522
#117507512
#106051443
#734135