Finite Group Databasebeta

← #14326470

Subgroups — #14326470

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×#91386C211yesmaximal, characteristic
2#11750765C211yesmaximal, characteristic
3C5×#4651C211yesmaximal, characteristic, complemented
4C3×#64937C211yesmaximal, characteristic, complemented
5#11748895C212yesmaximal
6#11748888C211yesmaximal, characteristic
7#11748875C212yesmaximal
8#11748815C212yesmaximal, complemented
9#11748667C211yesmaximal, characteristic, complemented
10#11748649C212yesmaximal, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10606027—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×#1200C2212yes—
15C2×#6714C2212yes—
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×C4×Dic5C2212yes—
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×Dic3⋊Dic5C2212yes—
20C2×#6669C2211yescharacteristic
21C2×#6669C2211yescharacteristic
22C2×#6668C2212yes—
23C2×#6667C2211yescharacteristic
24C2×#6667C2211yescharacteristic
25C2×Dic3×Dic5C2212yes—
26#91386C418yescomplemented
27C3×C5×#95C2211yescharacteristic
28#91115C2212yes—
29#91115C2211yescharacteristic
30C5×C3⋊#95C2212yes—
31C5×C3⋊#95C2211yescharacteristic
32C5×C3⋊#95C2212yes—
33C3×#3963C2211yescharacteristic
34C3×#3963C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73416—51nomaximal, Hall
38C2×#4018—31no—
39C5×#383—31no—
40C4×C4⋊Dic5—31no—
41#64957—32no—
42#64955—32no—
43#64953—31no—
44D5×#95—31no—
45#64944—32no—
46#64941—32no—
47#64939—31no—
48#64937D311yescharacteristic, complemented
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C2×C4×D15—24no—
55C2×C4×D15C2×C414yes—
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2312yes—
62C2×#1200—24no—
63C2×#1200—24no—
64C2×#1200—42no—
65#6714—24no—
66C4×C5×Dic3C2×C414yescomplemented
67C3×C4×Dic5—24no—
68C3×C4×Dic5C2×C414yescomplemented
69Dic3⋊Dic5—24no—
70#6669C2×C414yescomplemented
71#6669C2×C414yescomplemented
72#6668—42no—
73#6667C2×C414yes—
74#6667C2×C414yes—
75Dic3×Dic5—42no—
76C2×#872—51no—
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#4651D511yescharacteristic, complemented
86#4649—51no—
87C22×C4×D5—31no—
88C22×C4×D5—32no—
89C2×C42×C5—31no—
90C2×#685—31no—
91C2×#685—31no—
92C2×#685—32no—
93C2×C4⋊Dic5—32no—
94C2×#683—31no—
95C2×#683—31no—
96C2×#683—32no—
97C2×C4×Dic5—32no—
98C2×C4×Dic5C2×D312yes—
99C2×C4×Dic5C2×D311yescharacteristic
100#4018—38no—
101C5×#95—31no—
102C5×#95—32no—
103C5×#95—32no—
104C5×#95C2×D311yescharacteristic
105#3963—31no—
106#3963—32no—
107#3963—32no—
108#3963—32no—
109#3963C2×D312yes—
110#3963C2×D311yescharacteristic
111#2343—151noSylow
112C23×C3×C5C2411yescharacteristic
113C22×D15—22no—
114C22×D15—21no—
115C22×D15—21no—
116C22×D15C22×C412yes—
117C22×D15#4114yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5C22×C412yes—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15C22×C412yes—
128C4×D15—28no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3—21no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3C22×C412yes—
136C2×C5×Dic3C22×C412yes—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5C22×C412yes—
143C2×C3×Dic5C22×C412yes—
144C2×C3×Dic5#4114yes—
145#1200—48no—
146C22×C4×D3—51no—
147C22×C4×D3—52no—
148C2×C3×C42—51no—
149C2×C3×C42—52no—
150C2×(C2×D3)⋊C4—51no—
151C2×(C2×D3)⋊C4—51no—
152C2×(C2×D3)⋊C4—52no—
153C2×C4⋊Dic3—52no—
154C2×Dic3⋊C4—51no—
155C2×Dic3⋊C4—51no—
156C2×Dic3⋊C4—52no—
157C2×C4×Dic3—52no—
158C2×C4×Dic3C2×D511yescharacteristic
159#872—58no—
160C3×#95—51no—
161C3×#95—52no—
162C3×#95C2×D511yescharacteristic
163C3⋊#95—51no—
164C3⋊#95—52no—
165C3⋊#95—52no—
166C3⋊#95—52no—
167C3⋊#95C2×D512yes—
168C3⋊#95C2×D511yescharacteristic
169C3⋊#95C2×D512yes—
170C23×D5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—32no—
174C22×C4×C5C22×D312yes—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—31no—
177C22×Dic5—32no—
178C22×Dic5C22×D311yescharacteristic
179C22×Dic5C22×D311yescharacteristic
180C22×Dic5C22×D312yes—
181C2×C4×D5—34no—
182C2×C4×D5—64no—
183C2×C4×D5—64no—
184C2×C4×D5—64no—
185C2×C4×D5—122no—
186C42×C5—34no—
187#685—34no—
188#685—34no—
189#685—64no—
190C4⋊Dic5—64no—
191#683—34no—
192#683—34no—
193#683—122no—
194C4×Dic5—24no—
195C4×Dic5—122no—
196C4×Dic5C4×D314yescomplemented
197C2×#117—151no—
198#387—152no—
199#387—152no—
200#385—152no—
201#383—31no—
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×D15—22no—
214C2×D15—22no—
215C2×D15—24no—
216C2×D15—24no—
217C2×D15#11714yes—
218C3×C4×C5—22no—
219C3×C4×C5—42no—
220Dic15—22no—
221Dic15—42no—
222C3×Dic5—22no—
223C3×Dic5—22no—
224C3×Dic5—24no—
225C5×Dic3—22no—
226C5×Dic3—22no—
227C5×Dic3—42no—
228C23×D3—51no—
229C22×C3×C4—51no—
230C22×C3×C4—52no—
231C22×C3×C4—51no—
232C22×C3×C4C22×D512yes—
233C22×C3×C4C22×D511yescharacteristic
234C22×Dic3—51no—
235C22×Dic3—52no—
236C22×Dic3C22×D512yes—
237C22×Dic3C22×D511yescharacteristic
238C22×Dic3C22×D511yescharacteristic
239C2×C4×D3—54no—
240C2×C4×D3—104no—
241C2×C4×D3—104no—
242C2×C4×D3—104no—
243C2×C4×D3—202no—
244C3×C42—54no—
245C3×C42—104no—
246(C2×D3)⋊C4—54no—
247(C2×D3)⋊C4—54no—
248(C2×D3)⋊C4—104no—
249C4⋊Dic3—202no—
250Dic3⋊C4—54no—
251Dic3⋊C4—54no—
252Dic3⋊C4—104no—
253C4×Dic3—202no—
254C4×Dic3C4×D514yescomplemented
255C23×C5C23×D311yescharacteristic
256C22×D5—32no—
257C22×D5—34no—
258C22×D5—62no—
259C22×D5—61no—
260C22×D5—61no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—32no—
266C2×C4×C5—32no—
267C2×C4×C5—62no—
268C2×C4×C5—61no—
269C2×C4×C5—61no—
270C2×C4×C5—62no—
271C2×C4×C5—62no—
272C2×C4×C5—62no—
273C2×C4×C5C2×C4×D312yes—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—32no—
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5C2×C4×D312yes—
285C2×Dic5C2×C4×D312yes—
286C2×Dic5#23514yes—
287C4×D5—68no—
288C4×D5—128no—
289C23×C4—152no—
290C23×C4—151no—
291#117—158no—
292C2×C4⋊C4—151no—
293C2×C4⋊C4—151no—
294C2×C4⋊C4—152no—
295C2×C4⋊C4—152no—
296C2×C22⋊C4—151no—
297C2×C22⋊C4—151no—
298C2×C22⋊C4—152no—
299C2×C42—31no—
300C2×C42—51no—
301C2×C42—52no—
302C2×C42—152no—
303#95—31no—
304#95—32no—
305#95—32no—
306#95—51no—
307#95—52no—
308#95—152no—
309#95—152no—
310#95—151no—
311#95—152no—
312#95D3×D511yescharacteristic
313C2×C3×C5C2×#11711yescharacteristic
314C2×C3×C5C4×#4111yescharacteristic
315C2×C3×C5#52011yescharacteristic
316C2×C3×C5#55112yes—
317C2×C3×C5#55212yes—
318D15—24no—
319C23×C3C23×D511yescharacteristic
320C22×D3—52no—
321C22×D3—54no—
322C22×D3—102no—
323C22×D3—101no—
324C22×D3—101no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—52no—
330C2×C3×C4—52no—
331C2×C3×C4—54no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—102no—
335C2×C3×C4—101no—
336C2×C3×C4—101no—
337C2×C3×C4C2×C4×D512yes—
338C2×Dic3—22no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—52no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3C2×C4×D512yes—
350C2×Dic3C2×C4×D512yes—
351C4×D3—108no—
352C4×D3—208no—
353C22×C5C22×C4×D311yescharacteristic
354C22×C5C2×#23512yes—
355C22×C5D3×#4112yes—
356C22×C5#100911yescharacteristic
357C22×C5#101011yescharacteristic
358C2×D5—34no—
359C2×D5—62no—
360C2×D5—62no—
361C2×D5—64no—
362C2×D5—64no—
363C4×C5—22no—
364C4×C5—42no—
365C4×C5—62no—
366C4×C5—62no—
367C4×C5—122no—
368Dic5—22no—
369Dic5—22no—
370Dic5—24no—
371Dic5—62no—
372Dic5—122no—
373C24—151no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—32no—
377C22×C4—52no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—151no—
381C22×C4—154no—
382C22×C4—152no—
383C22×C4—304no—
384C22×C4—304no—
385C22×C4—304no—
386C22×C4—602no—
387C22×C4C2×D3×D512yes—
388C22×C4C2×D3×D511yescharacteristic
389C4⋊C4—154no—
390C4⋊C4—154no—
391C4⋊C4—304no—
392C4⋊C4—602no—
393C22⋊C4—154no—
394C22⋊C4—154no—
395C22⋊C4—304no—
396C42—34no—
397C42—54no—
398C42—104no—
399C42—602no—
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3C22×C4×D511yescharacteristic
402C22×C3D5×#4112yes—
403C22×C3D5×#4112yes—
404C22×C3#414911yescharacteristic
405C22×C3#415011yescharacteristic
406C2×D3—54no—
407C2×D3—102no—
408C2×D3—102no—
409C2×D3—104no—
410C2×D3—104no—
411C3×C4—22no—
412C3×C4—42no—
413C3×C4—102no—
414C3×C4—102no—
415C3×C4—104no—
416Dic3—22no—
417Dic3—22no—
418Dic3—42no—
419Dic3—102no—
420Dic3—202no—
421C2×C5C4×#23511yescharacteristic
422C2×C5D3×#11711yescharacteristic
423C2×C5#552311yescharacteristic
424C2×C5#552712yes—
425C2×C5#552912yes—
426D5—64no—
427C23—152no—
428C23—154no—
429C23—302no—
430C23—301no—
431C23—301no—
432C23C22×D3×D511yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—32no—
438C2×C4—32no—
439C2×C4—52no—
440C2×C4—52no—
441C2×C4—54no—
442C2×C4—62no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—102no—
449C2×C4—101no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—101no—
453C2×C4—152no—
454C2×C4—308no—
455C2×C4—302no—
456C2×C4—302no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4—608no—
460C2×C4C4×D3×D512yes—
461C2×C3D5×#11711yescharacteristic
462C2×C3#6585611yescharacteristic
463C2×C3#6585711yescharacteristic
464C2×C3#6603912yes—
465C2×C3#6604212yes—
466D3—104no—
467C5#7341611yescharacteristic, complemented, Sylow
468C22—154no—
469C22—304no—
470C22—302no—
471C22—304no—
472C22—302no—
473C22C2×C4×D3×D511yescharacteristic
474C22D5×#23512yes—
475C22#9202011yescharacteristic
476C22#9202412yes—
477C22#9203511yescharacteristic
478C4—22no—
479C4—42no—
480C4—62no—
481C4—62no—
482C4—104no—
483C4—102no—
484C4—102no—
485C4—122no—
486C4—302no—
487C4—602no—
488C3#1060602711yescharacteristic, complemented, Sylow
489C2—304no—
490C2#1175266511yescharacteristic
491C2#1175282511yescharacteristic
492C2#1175290912yes—
493C2#1175367011yescharacteristic
494C2#1175389912yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#95D3×D5
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C5×#4651C2semidirect
4. C3×#64937C2semidirect
8. #11748815C2semidirect
9. #11748667C2semidirect
10. #11748649C2semidirect
11. #11748580C2semidirect
26. #91386C4semidirect
48. #64937D3semidirect
66. C4×C5×Dic3C2×C4semidirect
68. C3×C4×Dic5C2×C4semidirect
70. #6669C2×C4semidirect
71. #6669C2×C4semidirect
85. #4651D5semidirect
196. C4×Dic5C4×D3semidirect
254. C4×Dic3C4×D5semidirect
400. C3×C5#2343semidirect
467. C5#73416semidirect
488. C3#10606027semidirect

Maximal subgroups

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

subgroupindex
C2×#913862
#117507652
C5×#46512
C3×#649372
#117488952
#117488882
#117488752
#117488152
#117486672
#117486492
#117485802
#106060273
#734165