Finite Group Databasebeta

← #14326445

Subgroups — #14326445

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#872C211yesmaximal, characteristic
2#11751037C211yesmaximal, characteristic, complemented
3C3×#65221C211yesmaximal, characteristic, complemented
4#11748903C212yesmaximal
5D3×#3963C211yesmaximal, characteristic
6Dic5×(C2×D3)⋊C4C212yesmaximal
7#11748777C211yesmaximal, characteristic
8#11748684C212yesmaximal, complemented
9#11748667C211yesmaximal, characteristic, complemented
10#11748618C211yesmaximal, characteristic, complemented
11#11748573C212yesmaximal, complemented
12#10613968—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×C4⋊Dic15C2212yes—
17C2×C5×(C2×D3)⋊C4C2211yescharacteristic
18C2×C5×(C2×D3)⋊C4C2211yescharacteristic
19C2×C5×Dic3⋊C4C2211yescharacteristic
20C2×C5×Dic3⋊C4C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C5×#872C418yescomplemented
23C2×C3×C4×Dic5C2212yes—
24C2×Dic3⋊Dic5C2212yes—
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×Dic3×Dic5C2212yes—
27#91115C2212yes—
28#91115C2211yescharacteristic
29#91115C2211yescharacteristic
30C3×#3963C2211yescharacteristic
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73416—51nomaximal, Hall
38C2×C5×#117—31no—
39#65500—31no—
40C2×#3963—31no—
41#65270—32no—
42#65270—32no—
43#65239—32no—
44C22⋊C4×Dic5—32no—
45#65226—31no—
46#65225—31no—
47C4×C4⋊Dic5—31no—
48#65221D311yescharacteristic, complemented
49C23×C5×D3C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2312yes—
55C22×C5×Dic3C2311yescharacteristic
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2311yescharacteristic
58C2×C4×C5×D3—24no—
59C2×C4×C5×D3C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2312yes—
62C2×D3×Dic5—24no—
63C2×D3×Dic5—24no—
64C2×D3×Dic5—42no—
65C3×C42×C5C2×C414yescomplemented
66C4⋊Dic15—42no—
67C5×(C2×D3)⋊C4C2×C414yes—
68C5×(C2×D3)⋊C4C2×C414yes—
69C5×Dic3⋊C4C2×C414yescomplemented
70C5×Dic3⋊C4C2×C414yescomplemented
71C4×C5×Dic3C2×C414yescomplemented
72C3×C4×Dic5—24no—
73Dic3⋊Dic5—24no—
74(C2×D3)⋊Dic5—24no—
75Dic3×Dic5—42no—
76C2×#872D511yescharacteristic
77C3×#376—51no—
78C4×(C2×D3)⋊C4—52no—
79#4936—51no—
80#4933—52no—
81#4668—52no—
82#4664—51no—
83D3×#95—51no—
84#4655—52no—
85#4651—51no—
86#4649—51no—
87C23×C4×C5—31no—
88C23×Dic5—32no—
89C5×#117—38no—
90C2×C5×C4⋊C4—31no—
91C2×C5×C4⋊C4—31no—
92C2×C5×C22⋊C4—31no—
93C2×C5×C22⋊C4—31no—
94C2×C42×C5—31no—
95C2×C42×C5C2×D311yescharacteristic
96C2×C22⋊Dic5—32no—
97C2×C4⋊Dic5—32no—
98C2×C4⋊Dic5—32no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5C2×D312yes—
101#3963—31no—
102#3963—31no—
103#3963—32no—
104#3963—32no—
105#3963—32no—
106#3963—32no—
107#3963—32no—
108#3963C2×D311yescharacteristic
109#3963C2×D311yescharacteristic
110#3963C2×D312yes—
111#2343—151noSylow
112C23×C3×C5C2411yescharacteristic
113C22×C5×D3—22no—
114C22×C5×D3—21no—
115C22×C5×D3—21no—
116C22×C5×D3C22×C412yes—
117C22×C5×D3#4114yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5C22×C412yes—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C22×C412yes—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—21no—
134C2×C5×Dic3—21no—
135C2×C5×Dic3C22×C412yes—
136C2×C5×Dic3C22×C412yes—
137C2×C5×Dic3C22×C412yes—
138C4×C5×D3—28no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5#4114yes—
145D3×Dic5—48no—
146C22×C4×D3—52no—
147C22×C4×D3C2×D511yescharacteristic
148C2×C3×C42—52no—
149C2×C3×C42C2×D511yescharacteristic
150C2×(C2×D3)⋊C4—52no—
151C2×(C2×D3)⋊C4C2×D511yescharacteristic
152C2×(C2×D3)⋊C4C2×D511yescharacteristic
153C2×C4⋊Dic3—52no—
154C2×Dic3⋊C4—52no—
155C2×Dic3⋊C4C2×D511yescharacteristic
156C2×Dic3⋊C4C2×D511yescharacteristic
157C2×C4×Dic3—52no—
158C2×C4×Dic3C2×D511yescharacteristic
159#872Dic518yescomplemented
160C3×#95—51no—
161C3×#95—51no—
162C3×#95—52no—
163C3⋊#95—51no—
164C3⋊#95—51no—
165C3⋊#95—52no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C24×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—34no—
175C22×C4×C5—64no—
176C22×C4×C5C22×D311yescharacteristic
177C22×C4×C5C22×D311yescharacteristic
178C22×C4×C5C22×D311yescharacteristic
179C22×Dic5—32no—
180C22×Dic5—32no—
181C22×Dic5—64no—
182C22×Dic5—64no—
183C22×Dic5—122no—
184C22×Dic5C22×D312yes—
185C22×Dic5C22×D312yes—
186C5×C4⋊C4—34no—
187C5×C4⋊C4—34no—
188C5×C22⋊C4—34no—
189C5×C22⋊C4—34no—
190C42×C5—34no—
191C42×C5C4×D314yescomplemented
192C22⋊Dic5—64no—
193C4⋊Dic5—64no—
194C4⋊Dic5—122no—
195C4×Dic5—24no—
196C4×Dic5—122no—
197C2×#117—31no—
198#387—152no—
199#387—152no—
200#385—152no—
201#383—151no—
202#382—151no—
203#381—151no—
204C4×C4⋊C4—151no—
205C4×C22⋊C4—152no—
206#376—51no—
207C2×#95—151no—
208C22×C3×C5C23×C411yescharacteristic
209C22×C3×C5C2×#4112yes—
210C22×C3×C5C2×#4112yes—
211C22×C3×C5H(5,𝔽2)11yescharacteristic
212C22×C3×C52−1+411yescharacteristic
213C2×C5×D3—22no—
214C2×C5×D3—22no—
215C2×C5×D3—24no—
216C2×C5×D3—24no—
217C2×C5×D3#11714yes—
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221Dic15—42no—
222Dic15—42no—
223C3×Dic5—24no—
224C3×Dic5—42no—
225C5×Dic3—22no—
226C5×Dic3—22no—
227C5×Dic3—22no—
228C23×D3C22×D511yescharacteristic
229C22×C3×C4—52no—
230C22×C3×C4—52no—
231C22×C3×C4C22×D511yescharacteristic
232C22×C3×C4C22×D511yescharacteristic
233C22×C3×C4C22×D511yescharacteristic
234C22×Dic3—52no—
235C22×Dic3—52no—
236C22×Dic3C22×D511yescharacteristic
237C22×Dic3C22×D511yescharacteristic
238C22×Dic3C22×D511yescharacteristic
239C2×C4×D3—24no—
240C2×C4×D3—104no—
241C2×C4×D3—104no—
242C2×C4×D3—202no—
243C2×C4×D3C2×Dic514yes—
244C3×C42—104no—
245C3×C42C2×Dic514yescomplemented
246(C2×D3)⋊C4—104no—
247(C2×D3)⋊C4C2×Dic514yes—
248(C2×D3)⋊C4C2×Dic514yes—
249C4⋊Dic3—202no—
250Dic3⋊C4—104no—
251Dic3⋊C4C2×Dic514yescomplemented
252Dic3⋊C4C2×Dic514yescomplemented
253C4×Dic3—202no—
254C4×Dic3C2×Dic514yescomplemented
255C23×C5—32no—
256C23×C5—34no—
257C23×C5—62no—
258C23×C5—61no—
259C23×C5—61no—
260C23×C5C23×D311yescharacteristic
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—32no—
266C2×C4×C5—32no—
267C2×C4×C5—32no—
268C2×C4×C5—68no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5C2×C4×D312yes—
274C2×C4×C5C2×C4×D312yes—
275C2×C4×C5C2×C4×D312yes—
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—128no—
288C2×Dic5#23514yes—
289C23×C4—31no—
290C23×C4—152no—
291#117—38no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—152no—
295C2×C4⋊C4—152no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—152no—
299C2×C42—31no—
300C2×C42—52no—
301C2×C42—152no—
302C2×C42D3×D511yescharacteristic
303#95—51no—
304#95—51no—
305#95—52no—
306#95—152no—
307#95—152no—
308#95—152no—
309#95—152no—
310#95—151no—
311#95—152no—
312#95—151no—
313C2×C3×C5C2×#11711yescharacteristic
314C2×C3×C5C4×#4111yescharacteristic
315C2×C3×C5#52011yescharacteristic
316C2×C3×C5#55112yes—
317C2×C3×C5#55212yes—
318C5×D3—24no—
319C23×C3C23×D511yescharacteristic
320C22×D3—22no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3#70914yes—
324C22×D3C22×Dic512yes—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—54no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—102no—
335C2×C3×C4C22×Dic512yes—
336C2×C3×C4C22×Dic512yes—
337C2×C3×C4C22×Dic512yes—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—102no—
343C2×Dic3—102no—
344C2×Dic3—102no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3C22×Dic512yes—
349C2×Dic3C22×Dic512yes—
350C2×Dic3C22×Dic512yes—
351C4×D3—28no—
352C4×D3—208no—
353C22×C5—34no—
354C22×C5—62no—
355C22×C5—62no—
356C22×C5—64no—
357C22×C5—64no—
358C22×C5C22×C4×D311yescharacteristic
359C22×C5C2×#23512yes—
360C22×C5D3×#4112yes—
361C22×C5#100911yescharacteristic
362C22×C5#101011yescharacteristic
363C4×C5—22no—
364C4×C5—22no—
365C4×C5—22no—
366C4×C5—62no—
367C4×C5—62no—
368C4×C5—62no—
369Dic5—24no—
370Dic5—42no—
371Dic5—122no—
372Dic5—122no—
373C24—31no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—34no—
378C22×C4—52no—
379C22×C4—52no—
380C22×C4—64no—
381C22×C4—152no—
382C22×C4—152no—
383C22×C4—304no—
384C22×C4—304no—
385C22×C4—602no—
386C22×C4C2×D3×D511yescharacteristic
387C22×C4C2×D3×D511yescharacteristic
388C22×C4C2×D3×D511yescharacteristic
389C4⋊C4—34no—
390C4⋊C4—34no—
391C4⋊C4—304no—
392C4⋊C4—602no—
393C22⋊C4—34no—
394C22⋊C4—34no—
395C22⋊C4—304no—
396C42—34no—
397C42—104no—
398C42—602no—
399C42D3×Dic514yescomplemented
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3C2×#70912yes—
402C22×C3D5×#4112yes—
403C22×C3#414911yescharacteristic
404C22×C3#415011yescharacteristic
405C22×C3C23×Dic511yescharacteristic
406C2×D3—24no—
407C2×D3—24no—
408C2×D3—22no—
409C2×D3—22no—
410C2×D3#407214yes—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—104no—
415C3×C4—202no—
416Dic3—22no—
417Dic3—22no—
418Dic3—22no—
419Dic3—202no—
420Dic3—202no—
421C2×C5—64no—
422C2×C5C4×#23511yescharacteristic
423C2×C5D3×#11711yescharacteristic
424C2×C5#552311yescharacteristic
425C2×C5#552712yes—
426C2×C5#552912yes—
427C23—34no—
428C23—32no—
429C23—61no—
430C23—62no—
431C23—61no—
432C23C22×D3×D511yescharacteristic
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—32no—
438C2×C4—32no—
439C2×C4—32no—
440C2×C4—54no—
441C2×C4—68no—
442C2×C4—61no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—61no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4—302no—
457C2×C4—608no—
458C2×C4C2×D3×Dic512yes—
459C2×C4C2×D3×Dic512yes—
460C2×C4C2×D3×Dic512yes—
461C2×C3#6586112yes—
462C2×C3#6586512yes—
463C2×C3C2×#407211yescharacteristic
464C2×C3#41×Dic511yescharacteristic
465C2×C3#6616111yescharacteristic
466D3—24no—
467C5#7341611yescharacteristic, complemented, Sylow
468C22—34no—
469C22—62no—
470C22—64no—
471C22—62no—
472C22—64no—
473C22#9200111yescharacteristic
474C22D5×#23512yes—
475C22D3×#70912yes—
476C22#9201911yescharacteristic
477C22C22×D3×Dic511yescharacteristic
478C4—22no—
479C4—22no—
480C4—22no—
481C4—62no—
482C4—62no—
483C4—62no—
484C4—104no—
485C4—202no—
486C4—602no—
487C4—602no—
488C3#1061396811yescharacteristic, complemented, Sylow
489C2—64no—
490C2#1175268612yes—
491C2#1175275712yes—
492C2Dic5×#23511yescharacteristic
493C2D3×#407211yescharacteristic
494C2#1175451311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751037C2semidirect
3. C3×#65221C2semidirect
8. #11748684C2semidirect
9. #11748667C2semidirect
10. #11748618C2semidirect
11. #11748573C2semidirect
22. C5×#872C4semidirect
48. #65221D3semidirect
65. C3×C42×C5C2×C4semidirect
69. C5×Dic3⋊C4C2×C4semidirect
70. C5×Dic3⋊C4C2×C4semidirect
71. C4×C5×Dic3C2×C4semidirect
159. #872Dic5semidirect
191. C42×C5C4×D3semidirect
245. C3×C42C2×Dic5semidirect
251. Dic3⋊C4C2×Dic5semidirect
252. Dic3⋊C4C2×Dic5semidirect
254. C4×Dic3C2×Dic5semidirect
399. C42D3×Dic5semidirect
400. C3×C5#2343semidirect
467. C5#73416semidirect
488. C3#10613968semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
#117510372
C3×#652212
#117489032
D3×#39632
Dic5×(C2×D3)⋊C42
#117487772
#117486842
#117486672
#117486182
#117485732
#106139683
#734165