Finite Group Databasebeta

← #14320616

Subgroups — #14320616

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×#91761C211yesmaximal, characteristic, complemented
2C2×C3×C42×D5C211yesmaximal, characteristic, complemented
3C2×C4×#1202C211yesmaximal, characteristic
4C5×#4932C211yesmaximal, characteristic, complemented
5#11748907C212yesmaximal
6C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
7#11748814C212yesmaximal, complemented
8#11748726C212yesmaximal, complemented
9C4×#6667C211yesmaximal, characteristic, complemented
10#11748704C212yesmaximal, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12#10605145—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1202C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6714C2212yes—
19C2×#6712C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21#91761—24no—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2212yes—
26C3×C42×D5—24no—
27C2×Dic3⋊Dic5C2212yes—
28C2×Dic3⋊Dic5C2211yescharacteristic
29C2×#6667C2212yes—
30C2×#6667C2211yescharacteristic
31C2×#6665C2212yes—
32C2×#6665C2211yescharacteristic
33C4×#1202C418yescomplemented
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82065—51nomaximal, Hall
40C2×C4×D20—31no—
41C2×#4018—31no—
42C2×C42×D5D311yescharacteristic, complemented
43C5×#376—31no—
44C4×#685—31no—
45C4×#685—31no—
46C4×C4⋊Dic5—31no—
47#64959—32no—
48#64957—32no—
49#64954—32no—
50#64942—32no—
51C23×D15C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15C2×C414yescomplemented
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—24no—
70C2×C3×C4×D5C2×C414yes—
71C2×#1202—24no—
72C2×#1202C2×C414yes—
73C3×C42×C5D414yescomplemented
74#6714—24no—
75#6712—24no—
76C4×Dic15—22no—
77C4×C5×Dic3—22no—
78C4×C5×Dic3C2×C414yescomplemented
79C3×C4×Dic5—24no—
80C3×C4×Dic5—22no—
81Dic3⋊Dic5—24no—
82Dic3⋊Dic5C2×C414yescomplemented
83#6667—24no—
84#6667C2×C414yescomplemented
85#6665—24no—
86#6665C2×C414yes—
87C22×C3×C42—51no—
88C2×C4×#67—51no—
89C2×#872—51no—
90#5213—52no—
91#5210—52no—
92C4×#217—51no—
93#4940—52no—
94C4×(C2×D3)⋊C4—51no—
95#4933—52no—
96#4932D511yescharacteristic, complemented
97C4×Dic3⋊C4—51no—
98C22×D20—31no—
99C22×C4×D5—31no—
100C22×C4×D5C2×D312yes—
101C22×C4×D5C2×D311yescharacteristic
102C2×C42×C5—31no—
103C2×C42×C5—31no—
104C2×C42×C5C2×D311yescharacteristic
105C2×#685—31no—
106C2×#685—31no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685—32no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—32no—
112C2×#683—32no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5C2×D312yes—
115C2×C4×Dic5C2×D311yescharacteristic
116C4×D20—38no—
117#4018—64no—
118C42×D5—24no—
119C5×#95—32no—
120C5×#95—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2290—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×D15—21no—
127C22×D15—22no—
128C22×D15—22no—
129C22×D15—21no—
130C22×D15C22×C412yes—
131C22×C3×D5—21no—
132C22×C3×D5—21no—
133C22×C3×D5—22no—
134C22×C3×D5C22×C412yes—
135C22×C3×D5#4114yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C2×D414yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C412yes—
148C4×D15—28no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3C22×C412yes—
155C2×C5×Dic3C22×C412yes—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5#4114yes—
162C3×C4×D5—216no—
163C3×C4×D5—28no—
164#1202—28no—
165C23×C3×C4—51no—
166C23×C3×C4—52no—
167C22×#67—51no—
168C22×C4×D3—51no—
169C2×C3×C42—51no—
170C2×C3×C42—52no—
171C2×C3×C42—104no—
172C2×C3×C42C2×D511yescharacteristic
173C2×#217—51no—
174C2×#217—52no—
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⋊#95C2×D512yes—
190C3⋊#95C2×D512yes—
191C23×D5—31no—
192C23×D5C22×D311yescharacteristic
193C22×C4×C5—31no—
194C22×C4×C5—31no—
195C22×C4×C5—32no—
196C22×C4×C5C22×D312yes—
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—31no—
199C22×Dic5—32no—
200C22×Dic5C22×D311yescharacteristic
201C22×Dic5C22×D312yes—
202C2×D20—34no—
203C2×D20—64no—
204C2×C4×D5—24no—
205C2×C4×D5—22no—
206C2×C4×D5—24no—
207C2×C4×D5—22no—
208C2×C4×D5—24no—
209C2×C4×D5—34no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×C4×D5C4×D314yes—
213C42×C5—34no—
214C42×C5—62no—
215C42×C5#6714yescomplemented
216#685—34no—
217#685—34no—
218#685—64no—
219#685—64no—
220#685—64no—
221C4⋊Dic5—34no—
222C4⋊Dic5—64no—
223#683—64no—
224C4×Dic5—24no—
225C4×Dic5—22no—
226C4×Dic5—62no—
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—151no—
236C4×C22⋊C4—151no—
237#376—31no—
238C22×C3×C5C23×C411yescharacteristic
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4112yes—
242C22×C3×C5C2×#4112yes—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—42no—
247C2×D15—42no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—24no—
251C2×C3×D5—24no—
252C2×C3×D5#11714yescomplemented
253C3×C4×C5—24no—
254C3×C4×C5C4×D414yes—
255Dic15—22no—
256Dic15—42no—
257C3×Dic5—22no—
258C3×Dic5—24no—
259C5×Dic3—22no—
260C5×Dic3—22no—
261C5×Dic3—42no—
262C24×C3—51no—
263C23×D3—51no—
264C22×C3×C4—51no—
265C22×C3×C4—52no—
266C22×C3×C4—54no—
267C22×C3×C4—104no—
268C22×C3×C4—104no—
269C22×C3×C4—104no—
270C22×C3×C4—102no—
271C22×C3×C4—102no—
272C22×C3×C4C22×D512yes—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—54no—
275C2×#67—104no—
276C22×Dic3—51no—
277C22×Dic3—52no—
278C22×Dic3C22×D512yes—
279C22×Dic3C22×D511yescharacteristic
280C22×Dic3C22×D511yescharacteristic
281C2×C4×D3—54no—
282C2×C4×D3—102no—
283C2×C4×D3—102no—
284C3×C42—104no—
285C3×C42—102no—
286C3×C42D2014yescomplemented
287#217—54no—
288#217—104no—
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—102no—
297C4×Dic3C4×D514yescomplemented
298C23×C5C23×D311yescharacteristic
299C22×D5—21no—
300C22×D5—22no—
301C22×D5—21no—
302C22×D5—32no—
303C22×D5—62no—
304C22×D5—61no—
305C22×D5—62no—
306C22×D5—61no—
307C22×D5C2×C4×D312yes—
308C22×D5#23514yes—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—32no—
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×C5#23512yes—
320C2×C4×C5C2×#6714yes—
321C2×C4×C5C2×#6712yes—
322C2×Dic5—21no—
323C2×Dic5—22no—
324C2×Dic5—21no—
325C2×Dic5—22no—
326C2×Dic5—32no—
327C2×Dic5—61no—
328C2×Dic5—61no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5C2×C4×D312yes—
333C2×Dic5#23514yes—
334D20—68no—
335C4×D5—216no—
336C4×D5—28no—
337C4×D5—68no—
338C22×D4—151no—
339C23×C4—51no—
340C23×C4—52no—
341C23×C4—151no—
342C4×D4—158no—
343#117—304no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—151no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—31no—
354C2×C42—52no—
355C2×C42—51no—
356C2×C42—104no—
357C2×C42—151no—
358C2×C42D3×D511yescharacteristic
359#95—32no—
360#95—32no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5C2×C4×D411yescharacteristic
366C2×C3×C5C4×#4111yescharacteristic
367C2×C3×C5#52512yes—
368C2×C3×C5#52912yes—
369D15—42no—
370C3×D5—24no—
371C23×C3—52no—
372C23×C3—54no—
373C23×C3—101no—
374C23×C3—101no—
375C23×C3—102no—
376C23×C3C23×D511yescharacteristic
377C22×D3—52no—
378C22×D3—101no—
379C22×D3—101no—
380C22×D3—102no—
381C22×D3—102no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—52no—
385C2×C3×C4—54no—
386C2×C3×C4—1016no—
387C2×C3×C4—101no—
388C2×C3×C4—102no—
389C2×C3×C4—101no—
390C2×C3×C4—102no—
391C2×C3×C4—108no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4C2×D2014yes—
394C2×C3×C4C2×D2012yes—
395C2×C3×C4#70912yes—
396#67—108no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—52no—
403C2×Dic3—101no—
404C2×Dic3—101no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3C2×C4×D512yes—
409C2×Dic3C2×C4×D512yes—
410C4×D3—108no—
411C22×C5C22×C4×D311yescharacteristic
412C22×C5C2×#23511yescharacteristic
413C22×C5C2×#23512yes—
414C22×C5C2×#23512yes—
415C22×C5C22×#6711yescharacteristic
416C2×D5—22no—
417C2×D5—24no—
418C2×D5—22no—
419C2×D5—24no—
420C2×D5—62no—
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—122no—
424C2×D5—122no—
425C2×D5#87214yescomplemented
426C4×C5—24no—
427C4×C5—62no—
428C4×C5—62no—
429C4×C5—122no—
430C4×C5C4×#6714yes—
431Dic5—22no—
432Dic5—24no—
433Dic5—62no—
434Dic5—122no—
435C24—51no—
436C24—151no—
437C2×D4—154no—
438C2×D4—304no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—51no—
443C22×C4—52no—
444C22×C4—54no—
445C22×C4—104no—
446C22×C4—104no—
447C22×C4—102no—
448C22×C4—104no—
449C22×C4—102no—
450C22×C4—151no—
451C22×C4—154no—
452C22×C4—152no—
453C22×C4—302no—
454C22×C4—302no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—154no—
458C4⋊C4—304no—
459C4⋊C4—304no—
460C22⋊C4—154no—
461C22⋊C4—154no—
462C22⋊C4—304no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—34no—
466C42—62no—
467C42—104no—
468C42—102no—
469C42—302no—
470C42#120214yescomplemented
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—54no—
473C22×C3—102no—
474C22×C3—102no—
475C22×C3—104no—
476C22×C3—104no—
477C22×C3C22×C4×D511yescharacteristic
478C22×C3C22×D2011yescharacteristic
479C22×C3C2×#70911yescharacteristic
480C22×C3D5×#4112yes—
481C22×C3D5×#4112yes—
482C2×D3—102no—
483C2×D3—102no—
484C2×D3—102no—
485C2×D3—202no—
486C2×D3—202no—
487C3×C4—24no—
488C3×C4—102no—
489C3×C4—104no—
490C3×C4C4×D2014yes—
491Dic3—22no—
492Dic3—22no—
493Dic3—42no—
494Dic3—102no—
495Dic3—202no—
496C2×C5C2×#87211yescharacteristic
497C2×C5C4×#23511yescharacteristic
498C2×C5#547912yes—
499C2×C5C2×C4×#6711yescharacteristic
500C2×C5#579112yes—
501D5—24no—
502D5—122no—
503C23—52no—
504C23—54no—
505C23—101no—
506C23—102no—
507C23—101no—
508C23—152no—
509C23—301no—
510C23—302no—
511C23—302no—
512C23—301no—
513C23C22×D3×D511yescharacteristic
514D4—308no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—52no—
520C2×C4—54no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—1016no—
527C2×C4—101no—
528C2×C4—102no—
529C2×C4—101no—
530C2×C4—102no—
531C2×C4—108no—
532C2×C4—152no—
533C2×C4—301no—
534C2×C4—301no—
535C2×C4—308no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4#677112yes—
540C2×C4C4×D3×D512yes—
541C2×C4C2×#120214yes—
542C2×C4C2×#120212yes—
543C2×C3—104no—
544C2×C3C2×C4×D2011yescharacteristic
545C2×C3D5×#11711yescharacteristic
546C2×C3#6585611yescharacteristic
547C2×C3#6585812yes—
548C2×C3#6586212yes—
549D3—202no—
550C5#8206511yescharacteristic, complemented, Sylow
551C22—54no—
552C22—102no—
553C22—104no—
554C22—102no—
555C22—104no—
556C22—302no—
557C22—302no—
558C22—302no—
559C22—602no—
560C22—602no—
561C22C2×#677111yescharacteristic
562C22C2×C4×D3×D511yescharacteristic
563C22D5×#23512yes—
564C22D5×#23512yes—
565C22C22×#120211yescharacteristic
566C4—24no—
567C4—62no—
568C4—62no—
569C4—102no—
570C4—104no—
571C4—122no—
572C4—302no—
573C4—602no—
574C4C4×#120214yes—
575C3#1060514511yescharacteristic, complemented, Sylow
576C2—104no—
577C2—602no—
578C2#1175266511yescharacteristic
579C2#1175268112yes—
580C2D5×#87211yescharacteristic
581C2C2×C4×#120211yescharacteristic
582C2#1175456412yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91761C2semidirect
2. C2×C3×C42×D5C2semidirect
4. C5×#4932C2semidirect
6. C4×Dic3⋊Dic5C2semidirect
7. #11748814C2semidirect
8. #11748726C2semidirect
9. C4×#6667C2semidirect
10. #11748704C2semidirect
11. C4×#6665C2semidirect
33. C4×#1202C4semidirect
42. C2×C42×D5D3semidirect
59. C2×C4×D15C2×C4semidirect
73. C3×C42×C5D4semidirect
78. C4×C5×Dic3C2×C4semidirect
82. Dic3⋊Dic5C2×C4semidirect
84. #6667C2×C4semidirect
96. #4932D5semidirect
215. C42×C5#67semidirect
252. C2×C3×D5#117semidirect
286. C3×C42D20semidirect
297. C4×Dic3C4×D5semidirect
425. C2×D5#872semidirect
470. C42#1202semidirect
471. C3×C5#2290semidirect
550. C5#82065semidirect
575. C3#10605145semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
C2×C3×C42×D52
C2×C4×#12022
C5×#49322
#117489072
C4×Dic3⋊Dic52
#117488142
#117487262
C4×#66672
#117487042
C4×#66652
#106051453
#820655