Finite Group Databasebeta

← #14330842

Subgroups — #14330842

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×#91819C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic, complemented
3#11751312C211yesmaximal, characteristic, complemented
4#11751091C212yesmaximal, complemented
5#11751090C212yesmaximal, complemented
6#11751058C212yesmaximal, complemented
7#11751057C212yesmaximal, complemented
8#11750766C212yesmaximal, complemented
9#11750754C212yesmaximal, complemented
10#10605745—31nomaximal, Hall
11C23×C3×C4×C5C2211yescharacteristic
12C22×#1220C2212yes—
13C22×D60C2211yescharacteristic
14C22×C4×D15C2212yes—
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C5×C22⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×#6719C2212yes—
19#91819C418yescomplemented
20C2×#6714C2212yes—
21C2×#6714C2212yes—
22C2×#6714C2212yes—
23C2×#6714C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25C2×#6712C2212yes—
26C2×C4×Dic15C2212yes—
27C3×C5×#95C2212yes—
28#91115C2212yes—
29#91115C2212yes—
30#91115C2212yes—
31#91115C2211yescharacteristic
32#91115C2211yescharacteristic
33#74014—51nomaximal, Hall
34C2×#4076—31no—
35C5×#380D311yescharacteristic, complemented
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×D15C2312yes—
45C22×C3×C4×C5—42no—
46C22×C3×C4×C5C2×C414yescomplemented
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—42no—
52C2×#1220—42no—
53C2×#1220C2×C418yescomplemented
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C2×D60—42no—
58C2×D60C2×C414yes—
59C2×C4×D15—42no—
60C2×C4×D15—42no—
61C2×C4×D15—42no—
62C3×C5×C4⋊C4—42no—
63C3×C5×C22⋊C4—41no—
64C3×C5×C22⋊C4—41no—
65#6719—42no—
66#6714—42no—
67#6714—42no—
68#6714—42no—
69#6714C2×C418yescomplemented
70C4⋊Dic15C2×C414yescomplemented
71#6712—42no—
72C4×Dic15—42no—
73C2×#930—51no—
74C3×#380D511yescharacteristic, complemented
75#5211—51no—
76#4990—52no—
77#4989—52no—
78#4957—52no—
79#4956—52no—
80#4665—52no—
81#4653—52no—
82C23×C4×C5C2×D311yescharacteristic
83C22×C22⋊D5—32no—
84C22×D20—31no—
85C22×C4×D5—32no—
86C2×C5×C4⋊C4C2×D312yes—
87C2×C5×C22⋊C4C2×D311yescharacteristic
88C2×C5×C22⋊C4C2×D311yescharacteristic
89C2×C22⋊Dic5—32no—
90#4076—38no—
91C2×#685—32no—
92C2×#685—32no—
93C2×#685—32no—
94C2×#685—32no—
95C2×C4⋊Dic5—31no—
96C2×#683—32no—
97C2×C4×Dic5—32no—
98C5×#95C2×D312yes—
99#3963—32no—
100#3963—32no—
101#3963—32no—
102#3963—31no—
103#3963—31no—
104#2377—151noSylow
105C23×C3×C5—22no—
106C23×C3×C5—21no—
107C23×C3×C5—22no—
108C23×C3×C5—21no—
109C23×C3×C5C22×C412yes—
110C23×C3×C5C2411yescharacteristic
111C22×D15—22no—
112C22×D15—22no—
113C22×D15—22no—
114C22×D15—22no—
115C22×D15—22no—
116C22×D15—22no—
117C22×D15C22×C414yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—44no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C412yes—
129#1220—48no—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15C22×C414yes—
139D60—44no—
140C4×D15—48no—
141C23×C3×C4C2×D511yescharacteristic
142C22×#67—52no—
143C22×D12—51no—
144C22×C4×D3—52no—
145C2×C3×C4⋊C4C2×D512yes—
146C2×C3×C22⋊C4C2×D511yescharacteristic
147C2×C3×C22⋊C4C2×D511yescharacteristic
148C2×#217—52no—
149#930—58no—
150C2×(C2×D3)⋊C4—52no—
151C2×(C2×D3)⋊C4—52no—
152C2×(C2×D3)⋊C4—52no—
153C2×(C2×D3)⋊C4—52no—
154C2×C4⋊Dic3—51no—
155C2×Dic3⋊C4—52no—
156C2×C4×Dic3—52no—
157C3×#95C2×D512yes—
158C3⋊#95—52no—
159C3⋊#95—52no—
160C3⋊#95—52no—
161C3⋊#95—51no—
162C3⋊#95—51no—
163C24×C5C22×D311yescharacteristic
164C23×D5—32no—
165C22×C4×C5—42no—
166C22×C4×C5C4×D314yescomplemented
167C22×C4×C5C22×D312yes—
168C22×C4×C5C22×D312yes—
169C22×C4×C5C22×D311yescharacteristic
170C22×C4×C5C22×D311yescharacteristic
171C2×C22⋊D5—38no—
172C2×C22⋊D5—122no—
173C2×C22⋊D5—122no—
174C22×Dic5—32no—
175C22×Dic5—32no—
176C22×Dic5—32no—
177C2×D20—34no—
178C2×D20—122no—
179C2×C4×D5—122no—
180C2×C4×D5—122no—
181C2×C4×D5—122no—
182C5×C4⋊C4—42no—
183C5×C22⋊C4—41no—
184C5×C22⋊C4—41no—
185C22⋊Dic5—122no—
186#685—38no—
187#685—122no—
188#685—122no—
189#685—122no—
190C4⋊Dic5—34no—
191#683—122no—
192C4×Dic5—122no—
193C2×#121—151no—
194#390—152no—
195#388—152no—
196#387—152no—
197#386—152no—
198#386—152no—
199#385—152no—
200#381—151no—
201#380D1511yescharacteristic, complemented
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×D15—24no—
213C2×D15—24no—
214C2×D15—24no—
215C2×D15—42no—
216C2×D15—42no—
217C2×D15—42no—
218C2×D15—42no—
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221C3×C4×C5—42no—
222C3×C4×C5—42no—
223Dic15—24no—
224Dic15—42no—
225Dic15—42no—
226C24×C3C22×D511yescharacteristic
227C23×D3—52no—
228C22×C3×C4—42no—
229C22×C3×C4C4×D514yescomplemented
230C22×C3×C4C22×D512yes—
231C22×C3×C4C22×D512yes—
232C22×C3×C4C22×D511yescharacteristic
233C22×C3×C4C22×D511yescharacteristic
234C2×#67—58no—
235C2×#67—202no—
236C2×#67—202no—
237C22×Dic3—52no—
238C22×Dic3—52no—
239C22×Dic3—52no—
240C2×D12—54no—
241C2×D12—202no—
242C2×C4×D3—202no—
243C2×C4×D3—202no—
244C2×C4×D3—202no—
245C3×C4⋊C4—42no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—41no—
248#217—202no—
249(C2×D3)⋊C4—58no—
250(C2×D3)⋊C4—202no—
251(C2×D3)⋊C4—202no—
252(C2×D3)⋊C4—202no—
253C4⋊Dic3—54no—
254Dic3⋊C4—202no—
255C4×Dic3—202no—
256C23×C5—22no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—22no—
260C23×C5C2×C4×D312yes—
261C23×C5C23×D311yescharacteristic
262C22×D5—34no—
263C22×D5—62no—
264C22×D5—62no—
265C22×D5—62no—
266C22×D5—62no—
267C22×D5—62no—
268C22×D5—62no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—44no—
278C2×C4×C5C2×C4×D312yes—
279C2×C4×C5C2×C4×D312yes—
280C22⋊D5—128no—
281C2×Dic5—34no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5—62no—
289C2×Dic5—62no—
290D20—124no—
291C4×D5—128no—
292C22×D4—152no—
293C22×D4—151no—
294C23×C4—152no—
295C23×C4C2×D1511yescharacteristic
296#121—158no—
297C2×C4⋊C4—151no—
298C2×C4⋊C4—152no—
299C2×C4⋊C4C2×D1512yes—
300C2×C22⋊C4—152no—
301C2×C22⋊C4—152no—
302C2×C22⋊C4—152no—
303C2×C22⋊C4—152no—
304C2×C22⋊C4—152no—
305C2×C22⋊C4C2×D1511yescharacteristic
306C2×C22⋊C4C2×D1511yescharacteristic
307C2×C42—152no—
308#95—151no—
309#95—152no—
310#95—151no—
311#95—152no—
312#95—152no—
313#95C2×D1512yes—
314C2×C3×C5—42no—
315C2×C3×C5#51811yescharacteristic
316C2×C3×C5#51811yescharacteristic
317C2×C3×C5#52011yescharacteristic
318C2×C3×C5#56012yes—
319C2×C3×C5#56212yes—
320D15—44no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—22no—
325C23×C3C2×C4×D512yes—
326C23×C3C23×D511yescharacteristic
327C22×D3—54no—
328C22×D3—102no—
329C22×D3—102no—
330C22×D3—102no—
331C22×D3—102no—
332C22×D3—102no—
333C22×D3—102no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—44no—
343C2×C3×C4C2×C4×D512yes—
344C2×C3×C4C2×C4×D512yes—
345#67—208no—
346C2×Dic3—54no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3—102no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352C2×Dic3—102no—
353C2×Dic3—102no—
354C2×Dic3—102no—
355D12—204no—
356C4×D3—208no—
357C22×C5—22no—
358C22×C5—22no—
359C22×C5—22no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5C22×C4×D311yescharacteristic
363C22×C5#100412yes—
364C22×C5#100411yescharacteristic
365C22×C5#100711yescharacteristic
366C22×C5#100912yes—
367C2×D5—64no—
368C2×D5—64no—
369C2×D5—64no—
370C2×D5—122no—
371C2×D5—122no—
372C2×D5—122no—
373C2×D5—122no—
374C4×C5—22no—
375C4×C5—22no—
376C4×C5—42no—
377C4×C5—42no—
378Dic5—64no—
379Dic5—122no—
380Dic5—122no—
381C24—152no—
382C24C22×D1511yescharacteristic
383C2×D4—158no—
384C2×D4—154no—
385C2×D4—602no—
386C2×D4—602no—
387C2×D4—602no—
388C22×C4—42no—
389C22×C4—152no—
390C22×C4—152no—
391C22×C4—152no—
392C22×C4—602no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C4×D1514yescomplemented
396C22×C4C22×D1512yes—
397C22×C4C22×D1512yes—
398C22×C4C22×D1511yescharacteristic
399C22×C4C22×D1511yescharacteristic
400C4⋊C4—42no—
401C4⋊C4—154no—
402C4⋊C4—602no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—158no—
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×C3C22×C4×D511yescharacteristic
418C22×C3#414412yes—
419C22×C3#414411yescharacteristic
420C22×C3#414711yescharacteristic
421C22×C3#414912yes—
422C2×D3—104no—
423C2×D3—104no—
424C2×D3—104no—
425C2×D3—202no—
426C2×D3—202no—
427C2×D3—202no—
428C2×D3—202no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—42no—
432C3×C4—42no—
433Dic3—104no—
434Dic3—202no—
435Dic3—202no—
436C2×C5—42no—
437C2×C5#548611yescharacteristic
438C2×C5#550411yescharacteristic
439C2×C5#552111yescharacteristic
440C2×C5#562012yes—
441C2×C5#564712yes—
442D5—124no—
443C23—21no—
444C23—22no—
445C23—21no—
446C23—22no—
447C23—154no—
448C23—302no—
449C23—302no—
450C23—302no—
451C23—302no—
452C23—302no—
453C23—302no—
454C23C2×C4×D1512yes—
455C23C23×D1511yescharacteristic
456D4—604no—
457D4—608no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—44no—
467C2×C4—154no—
468C2×C4—302no—
469C2×C4—302no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—302no—
476C2×C4—608no—
477C2×C4C2×C4×D1512yes—
478C2×C4C2×C4×D1512yes—
479C2×C3—42no—
480C2×C3#6582011yescharacteristic
481C2×C3#6583811yescharacteristic
482C2×C3#6585511yescharacteristic
483C2×C3#6595412yes—
484C2×C3#6598112yes—
485D3—204no—
486C5#7401411yescharacteristic, complemented, Sylow
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—304no—
493C22—304no—
494C22—304no—
495C22—602no—
496C22—602no—
497C22—602no—
498C22—602no—
499C22C22×C4×D1511yescharacteristic
500C22#9209511yescharacteristic
501C22#9209512yes—
502C22#9209811yescharacteristic
503C22#9210012yes—
504C4—22no—
505C4—22no—
506C4—42no—
507C4—42no—
508C4—304no—
509C4—602no—
510C4—602no—
511C3#1060574511yescharacteristic, complemented, Sylow
512C2—42no—
513C2—604no—
514C2#1175624511yescharacteristic
515C2#1175626311yescharacteristic
516C2#1175628011yescharacteristic
517C2#1175637912yes—
518C2#1175640612yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#380C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91819C2
hypercenter#380D15
hypocenterC3×C5#2377
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C3×C5×#380C2semidirect
3. #11751312C2semidirect
4. #11751091C2semidirect
5. #11751090C2semidirect
6. #11751058C2semidirect
7. #11751057C2semidirect
8. #11750766C2semidirect
9. #11750754C2semidirect
19. #91819C4semidirect
35. C5×#380D3semidirect
46. C22×C3×C4×C5C2×C4semidirect
53. C2×#1220C2×C4semidirect
69. #6714C2×C4semidirect
70. C4⋊Dic15C2×C4semidirect
74. C3×#380D5semidirect
166. C22×C4×C5C4×D3semidirect
201. #380D15semidirect
229. C22×C3×C4C4×D5semidirect
395. C22×C4C4×D15semidirect
411. C3×C5#2377semidirect
486. C5#74014semidirect
511. C3#10605745semidirect

Maximal subgroups

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

subgroupindex
C2×#918192
C3×C5×#3802
#117513122
#117510912
#117510902
#117510582
#117510572
#117507662
#117507542
#106057453
#740145