Finite Group Databasebeta

← #14330911

Subgroups — #14330911

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2#11751312C211yesmaximal, characteristic, complemented
3C5×#5212C211yesmaximal, characteristic, complemented
4#11749518C212yesmaximal, complemented
5#11749489C212yesmaximal, complemented
6#11748899C212yesmaximal, complemented
7#11748896C212yesmaximal, complemented
8#11748771C212yesmaximal, complemented
9#11748697C212yesmaximal, complemented
10#10605745—31nomaximal, Hall
11C23×C3×C4×C5C2211yescharacteristic
12C22×C3×C22⋊D5C2212yes—
13C22×C3×D20C2211yescharacteristic
14C22×D5×Dic3C2212yes—
15C2×#6719C2212yes—
16C2×C5×#217C2211yescharacteristic
17C2×C5×#217C2211yescharacteristic
18C2×C5×C4⋊Dic3C2212yes—
19C3×#4076C418yescomplemented
20C2×C3×#685C2212yes—
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×#6668C2212yes—
23C2×#6665C2212yes—
24C2×#6665C2212yes—
25C2×#6665C2212yes—
26C2×Dic3×Dic5C2212yes—
27#91115C2212yes—
28#91115C2211yescharacteristic
29#91115C2211yescharacteristic
30C5×C3⋊#95C2212yes—
31#90994C2212yes—
32#90994C2212yes—
33#82639—51nomaximal, Hall
34C2×#4076D311yescharacteristic
35C5×#380—31no—
36#65500—31no—
37#65279—32no—
38#65278—32no—
39#65246—32no—
40#65245—32no—
41#64954—32no—
42#64942—32no—
43C24×C3×C5C2311yescharacteristic
44C23×C3×D5C2312yes—
45C22×C3×C4×C5—42no—
46C22×C3×C4×C5C2×C414yescomplemented
47C22×C3×C4×C5C2311yescharacteristic
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15C2312yes—
50C22×Dic15C2312yes—
51C22×C5×Dic3C2312yes—
52C22×C5×Dic3C2312yes—
53C2×C3×C22⋊D5—42no—
54C2×C3×C22⋊D5—42no—
55C2×C3×C22⋊D5C2×C418yescomplemented
56C22×C3×Dic5C2312yes—
57C2×C3×D20—42no—
58C2×C3×D20C2×C414yes—
59C2×D5×Dic3—42no—
60C2×D5×Dic3—42no—
61C2×D5×Dic3—42no—
62#6719—42no—
63C5×#217—41no—
64C5×#217—41no—
65C5×C4⋊Dic3—42no—
66C3×#685C2×C418yescomplemented
67C3×C4⋊Dic5C2×C414yescomplemented
68#6668—42no—
69#6665—42no—
70#6665—42no—
71#6665—42no—
72Dic3×Dic5—42no—
73C2×C3×#121—51no—
74#5221—52no—
75#5220—52no—
76#5220—52no—
77#5212D511yescharacteristic, complemented
78#5211—51no—
79#4980—52no—
80#4951—52no—
81#4950—52no—
82C23×C4×C5C2×D311yescharacteristic
83C22×C22⋊D5C2×D312yes—
84C22×D20C2×D311yescharacteristic
85C22×C4×D5—32no—
86C2×C5×C4⋊C4—32no—
87C2×C5×C22⋊C4—31no—
88C2×C5×C22⋊C4—31no—
89C2×C22⋊Dic5—32no—
90#4076Dic318yescomplemented
91C2×#685—32no—
92C2×#685—32no—
93C2×#685—32no—
94C2×#685C2×D312yes—
95C2×C4⋊Dic5C2×D311yescharacteristic
96C2×#683—32no—
97C2×C4×Dic5—32no—
98C5×#95—32no—
99#3963—32no—
100#3963—31no—
101#3963—31no—
102#3963—32no—
103#3963—32no—
104#2377—151noSylow
105C23×C3×C5—21no—
106C23×C3×C5—22no—
107C23×C3×C5—22no—
108C23×C3×C5—21no—
109C23×C3×C5C22×C412yes—
110C23×C3×C5C2411yescharacteristic
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—22no—
116C22×C3×D5—22no—
117C22×C3×D5C22×C414yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—44no—
121C2×C3×C4×C5C22×C412yes—
122C2×C3×C4×C5C22×C412yes—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C3×C22⋊D5—48no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C22×C414yes—
139C3×D20—44no—
140D5×Dic3—48no—
141C22×C3×D4—52no—
142C22×C3×D4—51no—
143C23×C3×C4C2×D511yescharacteristic
144C23×Dic3—52no—
145C3×#121—58no—
146C2×C3×C4⋊C4—51no—
147C2×C3×C22⋊C4—52no—
148C2×#217—52no—
149C2×#217—52no—
150C2×#217—52no—
151C2×#217—52no—
152C2×#217C2×D511yescharacteristic
153C2×#217C2×D511yescharacteristic
154C2×C4⋊Dic3—52no—
155C2×C4⋊Dic3C2×D512yes—
156C2×C4×Dic3—52no—
157C3⋊#95—51no—
158C3⋊#95—51no—
159C3⋊#95—52no—
160C3⋊#95—52no—
161C3⋊#95—52no—
162C3⋊#95C2×D512yes—
163C24×C5C22×D311yescharacteristic
164C23×D5C22×D312yes—
165C22×C4×C5—32no—
166C22×C4×C5—32no—
167C22×C4×C5—42no—
168C22×C4×C5C2×Dic314yescomplemented
169C22×C4×C5C22×D311yescharacteristic
170C22×C4×C5C22×D311yescharacteristic
171C2×C22⋊D5—42no—
172C2×C22⋊D5—42no—
173C2×C22⋊D5C2×Dic318yescomplemented
174C22×Dic5—32no—
175C22×Dic5—32no—
176C22×Dic5C22×D312yes—
177C2×D20—42no—
178C2×D20C2×Dic314yes—
179C2×C4×D5—122no—
180C2×C4×D5—122no—
181C2×C4×D5—122no—
182C5×C4⋊C4—122no—
183C5×C22⋊C4—121no—
184C5×C22⋊C4—121no—
185C22⋊Dic5—122no—
186#685—122no—
187#685—122no—
188#685—122no—
189#685C2×Dic318yescomplemented
190C4⋊Dic5C2×Dic314yescomplemented
191#683—122no—
192C4×Dic5—122no—
193C2×#121—51no—
194#390—152no—
195#388—152no—
196#387—152no—
197#386—152no—
198#386—152no—
199#385—152no—
200#381—151no—
201#380—31no—
202C22×C3×C5—22no—
203C22×C3×C5—22no—
204C22×C3×C5—22no—
205C22×C3×C5—42no—
206C22×C3×C5—42no—
207C22×C3×C5C23×C411yescharacteristic
208C22×C3×C5H(5,𝔽2)12yes—
209C22×C3×C5H(5,𝔽2)11yescharacteristic
210C22×C3×C5H(5,𝔽2)12yes—
211C22×C3×C52−1+411yescharacteristic
212C2×C3×D5—24no—
213C2×C3×D5—24no—
214C2×C3×D5—24no—
215C2×C3×D5—42no—
216C2×C3×D5—42no—
217C2×C3×D5—42no—
218C2×C3×D5—42no—
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221Dic15—42no—
222Dic15—42no—
223C3×Dic5—24no—
224C5×Dic3—42no—
225C5×Dic3—42no—
226C24×C3—52no—
227C24×C3C22×D511yescharacteristic
228C2×C3×D4—58no—
229C2×C3×D4—54no—
230C2×C3×D4—202no—
231C2×C3×D4—202no—
232C2×C3×D4—202no—
233C22×C3×C4—42no—
234C22×C3×C4—52no—
235C22×C3×C4C4×D514yescomplemented
236C22×C3×C4C22×D511yescharacteristic
237C22×C3×C4C22×D511yescharacteristic
238C22×Dic3—52no—
239C22×Dic3—52no—
240C22×Dic3—202no—
241C22×Dic3—202no—
242C22×Dic3—202no—
243C22×Dic3C22×D512yes—
244C22×Dic3C22×D512yes—
245C3×C4⋊C4—54no—
246C3×C22⋊C4—58no—
247#217—41no—
248#217—41no—
249#217—202no—
250#217—202no—
251#217—202no—
252#217—202no—
253C4⋊Dic3—42no—
254C4⋊Dic3—202no—
255C4×Dic3—202no—
256C23×C5—22no—
257C23×C5—22no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5C22×Dic312yes—
261C23×C5C23×D311yescharacteristic
262C22×D5—22no—
263C22×D5—22no—
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—22no—
267C22×D5—22no—
268C22×D5C22×Dic314yes—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—44no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5C22×Dic312yes—
279C2×C4×C5C22×Dic312yes—
280C22⋊D5—48no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5—62no—
289C2×Dic5C22×Dic314yes—
290D20—44no—
291C4×D5—128no—
292C22×D4—52no—
293C22×D4—51no—
294C23×C4—152no—
295C23×C4D3×D511yescharacteristic
296#121—58no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—51no—
299C2×C4⋊C4—152no—
300C2×C22⋊C4—31no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—52no—
303C2×C22⋊C4—152no—
304C2×C22⋊C4—152no—
305C2×C22⋊C4—152no—
306C2×C22⋊C4—152no—
307C2×C42—152no—
308#95—32no—
309#95—152no—
310#95—152no—
311#95—151no—
312#95—152no—
313#95—151no—
314C2×C3×C5—42no—
315C2×C3×C5#51811yescharacteristic
316C2×C3×C5#51811yescharacteristic
317C2×C3×C5#52011yescharacteristic
318C2×C3×C5#56012yes—
319C2×C3×C5#56212yes—
320C3×D5—44no—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—21no—
324C23×C3—22no—
325C23×C3—54no—
326C23×C3—102no—
327C23×C3—102no—
328C23×C3—102no—
329C23×C3—102no—
330C23×C3—102no—
331C23×C3—102no—
332C23×C3C2×C4×D512yes—
333C23×C3C23×D511yescharacteristic
334C3×D4—204no—
335C3×D4—208no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—44no—
339C2×C3×C4—54no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4C2×C4×D512yes—
343C2×C3×C4C2×C4×D512yes—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352C2×Dic3—102no—
353C2×Dic3—102no—
354C2×Dic3—102no—
355C2×Dic3—102no—
356C2×Dic3—208no—
357C22×C5—22no—
358C22×C5—22no—
359C22×C5—22no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5#100412yes—
363C22×C5#100412yes—
364C22×C5#100911yescharacteristic
365C22×C5#101011yescharacteristic
366C22×C5C23×Dic311yescharacteristic
367C2×D5—24no—
368C2×D5—24no—
369C2×D5—24no—
370C2×D5—42no—
371C2×D5—42no—
372C2×D5—42no—
373C2×D5—42no—
374C4×C5—22no—
375C4×C5—22no—
376C4×C5—122no—
377C4×C5—122no—
378Dic5—24no—
379Dic5—122no—
380Dic5—122no—
381C24—52no—
382C24C2×D3×D511yescharacteristic
383C2×D4—58no—
384C2×D4—54no—
385C2×D4—202no—
386C2×D4—202no—
387C2×D4—202no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—42no—
391C22×C4—52no—
392C22×C4—152no—
393C22×C4—152no—
394C22×C4—602no—
395C22×C4—602no—
396C22×C4—602no—
397C22×C4D5×Dic314yescomplemented
398C22×C4C2×D3×D511yescharacteristic
399C22×C4C2×D3×D511yescharacteristic
400C4⋊C4—54no—
401C4⋊C4—122no—
402C4⋊C4—602no—
403C22⋊C4—58no—
404C22⋊C4—121no—
405C22⋊C4—121no—
406C22⋊C4—602no—
407C22⋊C4—602no—
408C22⋊C4—602no—
409C22⋊C4—602no—
410C42—602no—
411C3×C5#237711yescharacteristic, complemented, Hall
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—104no—
418C22×C3—104no—
419C22×C3—104no—
420C22×C3—202no—
421C22×C3—202no—
422C22×C3—202no—
423C22×C3—202no—
424C22×C3C22×C4×D511yescharacteristic
425C22×C3#414411yescharacteristic
426C22×C3#414412yes—
427C22×C3#414711yescharacteristic
428C22×C3#414912yes—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—104no—
432Dic3—42no—
433Dic3—42no—
434Dic3—202no—
435Dic3—202no—
436C2×C5—42no—
437C2×C5#562012yes—
438C2×C5#562112yes—
439C2×C5#579811yescharacteristic
440C2×C5#579811yescharacteristic
441C2×C5#582711yescharacteristic
442D5—44no—
443C23—21no—
444C23—22no—
445C23—21no—
446C23—22no—
447C23—54no—
448C23—102no—
449C23—102no—
450C23—102no—
451C23—102no—
452C23—102no—
453C23—102no—
454C23C2×D5×Dic312yes—
455C23C22×D3×D511yescharacteristic
456D4—204no—
457D4—208no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—44no—
461C2×C4—54no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—102no—
469C2×C4—102no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—302no—
476C2×C4—608no—
477C2×C4C2×D5×Dic312yes—
478C2×C4C2×D5×Dic312yes—
479C2×C3—42no—
480C2×C3—204no—
481C2×C3#6582011yescharacteristic
482C2×C3#6583811yescharacteristic
483C2×C3#6585511yescharacteristic
484C2×C3#6595412yes—
485C2×C3#6598112yes—
486C5#8263911yescharacteristic, complemented, Sylow
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—104no—
493C22—104no—
494C22—104no—
495C22—202no—
496C22—202no—
497C22—202no—
498C22—202no—
499C22#9200011yescharacteristic
500C22#9201712yes—
501C22#9201811yescharacteristic
502C22C22×D5×Dic311yescharacteristic
503C22#9204912yes—
504C4—22no—
505C4—22no—
506C4—104no—
507C4—122no—
508C4—122no—
509C4—602no—
510C4—602no—
511C3#1060574511yescharacteristic, complemented, Sylow
512C2—42no—
513C2—204no—
514C2#1175447312yes—
515C2#1175448811yescharacteristic
516C2#1175449911yescharacteristic
517C2#1175468612yes—
518C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4076C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2377
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751312C2semidirect
3. C5×#5212C2semidirect
4. #11749518C2semidirect
5. #11749489C2semidirect
6. #11748899C2semidirect
7. #11748896C2semidirect
8. #11748771C2semidirect
9. #11748697C2semidirect
19. C3×#4076C4semidirect
46. C22×C3×C4×C5C2×C4semidirect
55. C2×C3×C22⋊D5C2×C4semidirect
66. C3×#685C2×C4semidirect
67. C3×C4⋊Dic5C2×C4semidirect
77. #5212D5semidirect
90. #4076Dic3semidirect
168. C22×C4×C5C2×Dic3semidirect
173. C2×C22⋊D5C2×Dic3semidirect
189. #685C2×Dic3semidirect
190. C4⋊Dic5C2×Dic3semidirect
235. C22×C3×C4C4×D5semidirect
397. C22×C4D5×Dic3semidirect
411. C3×C5#2377semidirect
486. C5#82639semidirect
511. C3#10605745semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40762
#117513122
C5×#52122
#117495182
#117494892
#117488992
#117488962
#117487712
#117486972
#106057453
#826395