Finite Group Databasebeta

← #14320617

Subgroups — #14320617

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
3C2×#91386C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic, complemented
5#11749508C212yesmaximal, complemented
6#11749494C212yesmaximal
7#11748829C212yesmaximal, complemented
8#11748824C212yesmaximal, complemented
9C4×#6669C211yesmaximal, characteristic, complemented
10C4×#6667C211yesmaximal, characteristic, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10605169—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C2×#6719C2211yescharacteristic
18C4×#1220C418yescomplemented
19C2×#6714C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×#217C2212yes—
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×C4×Dic5—24no—
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×#6669C2212yes—
30C2×#6669C2212yes—
31C2×#6667C2212yes—
32C2×#6667C2212yes—
33#91386—24no—
34C5×C3⋊#95C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82065—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C22×C4×Dic5D311yescharacteristic, complemented
42C2×#4018—31no—
43C4×C5×C22⋊C4—31no—
44#65247—32no—
45#65235—32no—
46C4×#685—31no—
47#65221—31no—
48C4×#683—31no—
49#64958—32no—
50#64941—32no—
51C24×C3×C5C2311yescharacteristic
52C23×D15C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—24no—
59C2×#1220C2×C414yes—
60C22×Dic15C2311yescharacteristic
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C2×C4×D15—22no—
64C2×C4×D15—22no—
65C2×C4×D15C2×C414yescomplemented
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2312yes—
68C22×C3×Dic5—24no—
69C22×C3×Dic5—24no—
70C22×C3×Dic5—24no—
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2312yes—
73#6719C2×C414yes—
74#6714C2×C414yescomplemented
75#6712C2×C414yescomplemented
76C4×Dic15C2×C414yescomplemented
77C5×#217—24no—
78C4×C5×Dic3—22no—
79C4×C5×Dic3—22no—
80C3×C4×Dic5—22no—
81C3×C4×Dic5—24no—
82C3×C4×Dic5D414yescomplemented
83#6669—24no—
84#6669—24no—
85#6667—24no—
86#6667—24no—
87C22×C3×C42—51no—
88C2×C4×#67—51no—
89C2×#872—51no—
90#5213—52no—
91#5210—52no—
92C4×#217D511yescharacteristic, complemented
93#4940—52no—
94C4×(C2×D3)⋊C4—51no—
95#4933—52no—
96#4932—51no—
97C4×Dic3⋊C4—51no—
98C23×C4×C5C2×D311yescharacteristic
99C22×C22⋊D5—31no—
100C23×Dic5C2×D312yes—
101C22×C4×D5—31no—
102C2×C5×C22⋊C4—32no—
103C2×C42×C5—31no—
104C2×C42×C5—31no—
105C2×C22⋊Dic5—31no—
106C4×C22⋊D5—38no—
107C2×#685—31no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#683—31no—
111C2×#683—32no—
112C2×#683—32no—
113C2×C4×Dic5—24no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5C2×D312yes—
116C2×C4×Dic5C2×D311yescharacteristic
117C2×C4×Dic5C2×D311yescharacteristic
118#4018—64no—
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2290—151noSylow
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5C22×C412yes—
129C23×C3×C5#4114yes—
130C23×C3×C5C2411yescharacteristic
131C22×D15—21no—
132C22×D15—22no—
133C22×D15—21no—
134C22×D15—22no—
135C22×D15C22×C412yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—28no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5#4112yes—
143#1220—28no—
144C2×Dic15—21no—
145C2×Dic15—22no—
146C2×Dic15—21no—
147C2×Dic15—22no—
148C2×Dic15C22×C412yes—
149C2×Dic15C22×C412yes—
150C2×Dic15C22×C412yes—
151C4×D15—28no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C3×Dic5—216no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5C2×D414yes—
164C2×C3×Dic5#4114yes—
165C23×C3×C4—52no—
166C23×C3×C4C2×D511yescharacteristic
167C22×#67—51no—
168C22×C4×D3—51no—
169C2×C3×C42—51no—
170C2×C3×C42—51no—
171C2×C3×C42—52no—
172C2×C3×C42—104no—
173C2×#217—51no—
174C2×#217C2×D512yes—
175C4×#67—58no—
176C2×(C2×D3)⋊C4—51no—
177C2×(C2×D3)⋊C4—52no—
178C2×(C2×D3)⋊C4—52no—
179C2×Dic3⋊C4—51no—
180C2×Dic3⋊C4—52no—
181C2×Dic3⋊C4—52no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3C2×D511yescharacteristic
184C2×C4×Dic3C2×D511yescharacteristic
185#872—104no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95C2×D512yes—
191C24×C5C22×D311yescharacteristic
192C23×D5—31no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—32no—
196C22×C4×C5—32no—
197C22×C4×C5C4×D314yes—
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—34no—
201C2×C22⋊D5—64no—
202C22×Dic5—24no—
203C22×Dic5—24no—
204C22×Dic5—24no—
205C22×Dic5—31no—
206C22×Dic5—31no—
207C22×Dic5—31no—
208C22×Dic5C22×D312yes—
209C22×Dic5C22×D312yes—
210C2×C4×D5—34no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C5×C22⋊C4—64no—
214C42×C5—62no—
215C42×C5—62no—
216C22⋊Dic5—34no—
217#685—34no—
218#685—64no—
219#685—64no—
220#683—34no—
221#683—64no—
222#683—64no—
223C4×Dic5—22no—
224C4×Dic5—24no—
225C4×Dic5—34no—
226C4×Dic5#6714yescomplemented
227C2×C4×D4—151no—
228C2×#117—151no—
229C22×C42—51no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5—24no—
242C22×C3×C5#11714yescomplemented
243C22×C3×C5C23×C411yescharacteristic
244C22×C3×C5C22×D411yescharacteristic
245C22×C3×C5C2×#4112yes—
246C22×C3×C5C2×#4111yescharacteristic
247C22×C3×C5C2×#4112yes—
248C2×D15—22no—
249C2×D15—22no—
250C2×D15—22no—
251C2×D15—42no—
252C2×D15—42no—
253C3×C4×C5—22no—
254C3×C4×C5C4×D414yes—
255Dic15—22no—
256Dic15—22no—
257Dic15—22no—
258C3×Dic5—24no—
259C3×Dic5—24no—
260C5×Dic3—42no—
261C5×Dic3—42no—
262C24×C3C22×D511yescharacteristic
263C23×D3—51no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—52no—
267C22×C3×C4—52no—
268C22×C3×C4—104no—
269C22×C3×C4—104no—
270C22×C3×C4—104no—
271C22×C3×C4C4×D514yes—
272C22×C3×C4C22×D511yescharacteristic
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—54no—
275C2×#67—104no—
276C22×Dic3—51no—
277C22×Dic3—51no—
278C22×Dic3—51no—
279C22×Dic3C22×D512yes—
280C22×Dic3C22×D512yes—
281C2×C4×D3—54no—
282C2×C4×D3—102no—
283C2×C4×D3—102no—
284C3×C42—54no—
285C3×C42—104no—
286C3×C42—102no—
287#217—24no—
288#217—54no—
289(C2×D3)⋊C4—54no—
290(C2×D3)⋊C4—104no—
291(C2×D3)⋊C4—104no—
292Dic3⋊C4—54no—
293Dic3⋊C4—104no—
294Dic3⋊C4—104no—
295C4×Dic3—22no—
296C4×Dic3—22no—
297C4×Dic3—54no—
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5C2×C4×D312yes—
302C23×C5#23514yes—
303C23×C5C23×D311yescharacteristic
304C22×D5—32no—
305C22×D5—62no—
306C22×D5—61no—
307C22×D5—62no—
308C22×D5—61no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—28no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5#23512yes—
321C2×C4×C5C2×#6712yes—
322C22⋊D5—68no—
323C2×Dic5—216no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—32no—
329C2×Dic5—32no—
330C2×Dic5—32no—
331C2×Dic5—62no—
332C2×Dic5—61no—
333C2×Dic5—62no—
334C2×Dic5—61no—
335C2×Dic5#23514yes—
336C2×Dic5C2×#6714yes—
337C4×D5—68no—
338C22×D4—151no—
339C23×C4—52no—
340C23×C4—151no—
341C23×C4D3×D511yescharacteristic
342C4×D4—158no—
343#117—304no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—32no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—31no—
354C2×C42—51no—
355C2×C42—52no—
356C2×C42—51no—
357C2×C42—104no—
358C2×C42—151no—
359#95—32no—
360#95—152no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5—24no—
365C2×C3×C5C2×#11711yescharacteristic
366C2×C3×C5C2×C4×D411yescharacteristic
367C2×C3×C5C4×#4111yescharacteristic
368C2×C3×C5#52512yes—
369C2×C3×C5#52912yes—
370D15—42no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3C2×C4×D512yes—
375C23×C3#70914yes—
376C23×C3C23×D511yescharacteristic
377C22×D3—52no—
378C22×D3—102no—
379C22×D3—101no—
380C22×D3—101no—
381C22×D3—102no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—28no—
385C2×C3×C4—54no—
386C2×C3×C4—54no—
387C2×C3×C4—1016no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4C2×C4×D512yes—
394C2×C3×C4D4×D512yes—
395C2×C3×C4#71112yes—
396#67—108no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—52no—
404C2×Dic3—52no—
405C2×Dic3—52no—
406C2×Dic3—102no—
407C2×Dic3—101no—
408C2×Dic3—101no—
409C2×Dic3—102no—
410C4×D3—108no—
411C22×C5—22no—
412C22×C5—24no—
413C22×C5—22no—
414C22×C5—24no—
415C22×C5#87214yescomplemented
416C22×C5C22×C4×D311yescharacteristic
417C22×C5C2×#23512yes—
418C22×C5C2×#23512yes—
419C22×C5C2×#23511yescharacteristic
420C22×C5C22×#6711yescharacteristic
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—62no—
424C2×D5—122no—
425C2×D5—122no—
426C4×C5—22no—
427C4×C5—122no—
428C4×C5—122no—
429C4×C5C4×#6714yes—
430Dic5—24no—
431Dic5—24no—
432Dic5—62no—
433Dic5—62no—
434Dic5—62no—
435C24—151no—
436C24C2×D3×D511yescharacteristic
437C2×D4—154no—
438C2×D4—304no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—52no—
444C22×C4—52no—
445C22×C4—104no—
446C22×C4—104no—
447C22×C4—104no—
448C22×C4—151no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—154no—
452C22×C4—302no—
453C22×C4—302no—
454C22×C4#120014yes—
455C22×C4C2×D3×D511yescharacteristic
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—154no—
458C4⋊C4—304no—
459C4⋊C4—304no—
460C22⋊C4—64no—
461C22⋊C4—154no—
462C22⋊C4—154no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—54no—
466C42—62no—
467C42—62no—
468C42—104no—
469C42—102no—
470C42—154no—
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3#401814yescomplemented
477C22×C3C22×C4×D511yescharacteristic
478C22×C3C2×#70912yes—
479C22×C3C2×D4×D511yescharacteristic
480C22×C3C2×#71111yescharacteristic
481C22×C3D5×#4112yes—
482C2×D3—102no—
483C2×D3—102no—
484C2×D3—102no—
485C2×D3—202no—
486C2×D3—202no—
487C3×C4—22no—
488C3×C4—104no—
489C3×C4—104no—
490C3×C4#402714yes—
491Dic3—42no—
492Dic3—42no—
493Dic3—102no—
494Dic3—102no—
495Dic3—102no—
496C2×C5—24no—
497C2×C5C2×#87211yescharacteristic
498C2×C5C4×#23511yescharacteristic
499C2×C5#547912yes—
500C2×C5C2×C4×#6711yescharacteristic
501C2×C5#579112yes—
502D5—122no—
503C23—22no—
504C23—21no—
505C23—21no—
506C23—152no—
507C23—302no—
508C23—302no—
509C23—301no—
510C23—301no—
511C23#677114yes—
512C23C2×#120012yes—
513C23C22×D3×D511yescharacteristic
514D4—308no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—28no—
518C2×C4—54no—
519C2×C4—54no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—1016no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—152no—
532C2×C4—152no—
533C2×C4—152no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—308no—
539C2×C4#678212yes—
540C2×C4C2×#120012yes—
541C2×C4C2×#120012yes—
542C2×C4D5×#6712yes—
543C2×C3—24no—
544C2×C3C2×#401811yescharacteristic
545C2×C3C2×#402711yescharacteristic
546C2×C3#6585611yescharacteristic
547C2×C3#6587212yes—
548C2×C3#6588112yes—
549D3—202no—
550C5#8206511yescharacteristic, complemented, Sylow
551C22—24no—
552C22—22no—
553C22—22no—
554C22—24no—
555C22—302no—
556C22—302no—
557C22—302no—
558C22—602no—
559C22—602no—
560C22#9138614yescomplemented
561C22C2×#677112yes—
562C22D5×#23512yes—
563C22C2×#678211yescharacteristic
564C22C22×#120011yescharacteristic
565C22C2×D5×#6711yescharacteristic
566C4—22no—
567C4—104no—
568C4—104no—
569C4—122no—
570C4—122no—
571C4—302no—
572C4—302no—
573C4—302no—
574C4#9155214yes—
575C3#1060516911yescharacteristic, complemented, Sylow
576C2—24no—
577C2—602no—
578C2#1175422912yes—
579C2C2×#9138611yescharacteristic
580C2#1175441411yescharacteristic
581C2#1175452512yes—
582C2C2×#9155211yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×Dic5C2semidirect
3. C2×#91386C2semidirect
4. C4×C5×#217C2semidirect
5. #11749508C2semidirect
7. #11748829C2semidirect
8. #11748824C2semidirect
9. C4×#6669C2semidirect
10. C4×#6667C2semidirect
11. #11748611C2semidirect
18. C4×#1220C4semidirect
41. C22×C4×Dic5D3semidirect
65. C2×C4×D15C2×C4semidirect
74. #6714C2×C4semidirect
75. #6712C2×C4semidirect
76. C4×Dic15C2×C4semidirect
82. C3×C4×Dic5D4semidirect
92. C4×#217D5semidirect
226. C4×Dic5#67semidirect
242. C22×C3×C5#117semidirect
415. C22×C5#872semidirect
471. C3×C5#2290semidirect
476. C22×C3#4018semidirect
550. C5#82065semidirect
560. C22#91386semidirect
575. C3#10605169semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C22×C3×C4×Dic52
C2×#913862
C4×C5×#2172
#117495082
#117494942
#117488292
#117488242
C4×#66692
C4×#66672
#117486112
#106051693
#820655