Finite Group Databasebeta

← #14331222

Subgroups — #14331222

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#940C211yesmaximal, characteristic
2#11751321C211yesmaximal, characteristic, complemented
3C3×#65509C211yesmaximal, characteristic, complemented
4#11749519C212yesmaximal, complemented
5#11749519C212yesmaximal, complemented
6#11749501C212yesmaximal, complemented
7#11749492C212yesmaximal, complemented
8#11748901C212yesmaximal, complemented
9#11748618C212yesmaximal, complemented
10#10614905—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C22×C5×#67C2212yes—
14C22×C5×#67C2212yes—
15C22×C5×D12C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×D3×Dic5C2212yes—
18C2×#6719C2212yes—
19C2×#6719C2211yescharacteristic
20C5×#940C418yescomplemented
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×(C2×D3)⋊Dic5C2212yes—
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×(C2×D3)⋊Dic5C2212yes—
27#91115C2212yes—
28C3×#3963C2212yes—
29#90994C2212yes—
30#90994C2212yes—
31#90994C2212yes—
32#90994C2212yes—
33#74685—51nomaximal, Hall
34C2×C5×#127—31no—
35#65509—32no—
36#65509—31no—
37#65509—32no—
38#65509—32no—
39#65509—32no—
40#65509—32no—
41#65509D311yescharacteristic, complemented
42#65226—32no—
43C24×C3×C5C2311yescharacteristic
44C24×C3×C5C2311yescharacteristic
45C23×C5×D3C2312yes—
46C2×C3×C5×D4—41no—
47C2×C3×C5×D4—41no—
48C2×C3×C5×D4C2×C414yescomplemented
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—41no—
51C22×Dic15—42no—
52C22×Dic15C2312yes—
53C22×Dic15C2312yes—
54C2×C5×#67—42no—
55C2×C5×#67—42no—
56C2×C5×#67—42no—
57C2×C5×#67—42no—
58C2×C5×#67C2×C418yescomplemented
59C2×C5×#67C2×C418yescomplemented
60C22×C5×Dic3C2312yes—
61C2×C5×D12—41no—
62C2×C5×D12—41no—
63C2×C5×D12C2×C414yescomplemented
64C22×C3×Dic5—41no—
65C22×C3×Dic5—42no—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×D3×Dic5—42no—
69C2×D3×Dic5—42no—
70C2×D3×Dic5—42no—
71#6719—41no—
72#6719—42no—
73C4×C5×Dic3C2×C414yescomplemented
74C3×C22⋊Dic5—41no—
75C3×C22⋊Dic5—42no—
76(C2×D3)⋊Dic5—42no—
77(C2×D3)⋊Dic5—42no—
78(C2×D3)⋊Dic5—42no—
79C2×#940D511yescharacteristic
80C3×#386—51no—
81#5220—51no—
82#5213—52no—
83#4958—52no—
84#4956—52no—
85#4956—52no—
86#4665—52no—
87#4651—52no—
88C22×C5×D4—32no—
89C22×C5×D4—32no—
90C22×C5×D4—31no—
91C22×C5×D4C2×D311yescharacteristic
92C23×Dic5—31no—
93C23×Dic5—32no—
94C23×Dic5C2×D311yescharacteristic
95C5×#127—38no—
96C2×C42×C5—31no—
97C2×C22⋊Dic5—32no—
98C2×C22⋊Dic5—31no—
99C2×C22⋊Dic5—32no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5—32no—
102C2×C22⋊Dic5C2×D312yes—
103C2×C22⋊Dic5C2×D311yescharacteristic
104#3963—32no—
105#3963—32no—
106#3963—32no—
107#3963—32no—
108#3963—32no—
109#3963C2×D312yes—
110#2380—151noSylow
111C23×C3×C5—22no—
112C23×C3×C5—21no—
113C23×C3×C5—22no—
114C23×C3×C5—21no—
115C23×C3×C5—22no—
116C23×C3×C5—21no—
117C23×C3×C5—22no—
118C23×C3×C5—21no—
119C23×C3×C5C22×C412yes—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C5×D3—22no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—22no—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3C22×C414yes—
129C3×C5×D4—44no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5C22×C412yes—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—44no—
140C5×#67—48no—
141C5×#67—48no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3C22×C414yes—
145C5×D12—44no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—44no—
153D3×Dic5—48no—
154C22×C3×D4C2×D511yescharacteristic
155C23×C3×C4—51no—
156C22×#67C2×D512yes—
157C22×#67C2×D512yes—
158C23×Dic3—51no—
159C22×D12C2×D511yescharacteristic
160C22×C4×D3—52no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C22⋊C4—52no—
163C2×#217—51no—
164C2×#217—52no—
165#940Dic518yescomplemented
166C2×(C2×D3)⋊C4—52no—
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×C4×Dic3C2×D511yescharacteristic
170C3×#95—52no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C24×C5—32no—
177C24×C5C22×D311yescharacteristic
178C24×C5C22×D311yescharacteristic
179C2×C5×D4—38no—
180C2×C5×D4—38no—
181C2×C5×D4—34no—
182C2×C5×D4—41no—
183C2×C5×D4—41no—
184C2×C5×D4—121no—
185C2×C5×D4—121no—
186C2×C5×D4—122no—
187C2×C5×D4—122no—
188C2×C5×D4—122no—
189C2×C5×D4—122no—
190C2×C5×D4C4×D314yescomplemented
191C22×C4×C5—32no—
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—32no—
194C22×Dic5—32no—
195C22×Dic5—42no—
196C22×Dic5—41no—
197C22×Dic5—122no—
198C22×Dic5—122no—
199C22×Dic5—122no—
200C22×Dic5—121no—
201C22×Dic5—122no—
202C22×Dic5C22×D312yes—
203C22×Dic5C22×D312yes—
204C42×C5—34no—
205C22⋊Dic5—42no—
206C22⋊Dic5—41no—
207C22⋊Dic5—122no—
208C22⋊Dic5—122no—
209C22⋊Dic5—122no—
210C22⋊Dic5—121no—
211C22⋊Dic5—122no—
212C2×#127—31no—
213#386—51no—
214#386—152no—
215#386—152no—
216#386—152no—
217#386—152no—
218#386—152no—
219#386—151no—
220#383—152no—
221C22×C3×C5—24no—
222C22×C3×C5—24no—
223C22×C3×C5—22no—
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5—42no—
230C22×C3×C5—42no—
231C22×C3×C5C23×C411yescharacteristic
232C22×C3×C5H(5,𝔽2)12yes—
233C22×C3×C5H(5,𝔽2)11yescharacteristic
234C22×C3×C5H(5,𝔽2)11yescharacteristic
235C22×C3×C5H(5,𝔽2)12yes—
236C2×C5×D3—24no—
237C2×C5×D3—24no—
238C2×C5×D3—24no—
239C2×C5×D3—42no—
240C2×C5×D3—42no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C3×C4×C5—22no—
244Dic15—42no—
245Dic15—42no—
246C3×Dic5—42no—
247C3×Dic5—42no—
248C5×Dic3—24no—
249C24×C3C22×D511yescharacteristic
250C24×C3C22×D511yescharacteristic
251C23×D3C22×D512yes—
252C2×C3×D4—41no—
253C2×C3×D4—41no—
254C2×C3×D4C2×Dic514yescomplemented
255C22×C3×C4—52no—
256C22×C3×C4—52no—
257C22×C3×C4—201no—
258C22×C3×C4—202no—
259C22×C3×C4C22×D511yescharacteristic
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67C2×Dic518yescomplemented
265C2×#67C2×Dic518yescomplemented
266C22×Dic3—52no—
267C22×Dic3—52no—
268C22×Dic3—201no—
269C22×Dic3—202no—
270C22×Dic3C22×D512yes—
271C2×D12—41no—
272C2×D12—41no—
273C2×D12C2×Dic514yescomplemented
274C2×C4×D3—202no—
275C2×C4×D3—202no—
276C2×C4×D3—202no—
277C3×C22⋊C4—201no—
278C3×C22⋊C4—202no—
279#217—201no—
280#217—202no—
281(C2×D3)⋊C4—202no—
282(C2×D3)⋊C4—202no—
283(C2×D3)⋊C4—202no—
284C4×Dic3C2×Dic514yescomplemented
285C23×C5—21no—
286C23×C5—22no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—22no—
290C23×C5—21no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—34no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5—62no—
299C23×C5—62no—
300C23×C5C2×C4×D312yes—
301C23×C5C2×C4×D312yes—
302C23×C5C23×D311yescharacteristic
303C5×D4—44no—
304C5×D4—124no—
305C5×D4—128no—
306C5×D4—128no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—34no—
310C2×C4×C5—62no—
311C2×C4×C5—62no—
312C2×C4×C5C2×C4×D312yes—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—44no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—128no—
327C2×Dic5—124no—
328C22×D4—32no—
329C22×D4—32no—
330C22×D4—31no—
331C22×D4D3×D511yescharacteristic
332C23×C4—51no—
333C23×C4—152no—
334C23×C4—151no—
335#127—38no—
336C2×C22⋊C4—51no—
337C2×C22⋊C4—52no—
338C2×C22⋊C4—152no—
339C2×C22⋊C4—152no—
340C2×C22⋊C4—152no—
341C2×C22⋊C4—151no—
342C2×C22⋊C4—152no—
343C2×C42—31no—
344#95—52no—
345#95—152no—
346#95—152no—
347#95—152no—
348#95—152no—
349#95—152no—
350C2×C3×C5—42no—
351C2×C3×C5—42no—
352C2×C3×C5#51811yescharacteristic
353C2×C3×C5#51812yes—
354C2×C3×C5#56011yescharacteristic
355C2×C3×C5#56011yescharacteristic
356C2×C3×C5#56012yes—
357C5×D3—44no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—22no—
361C23×C3—21no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—22no—
365C23×C3—21no—
366C23×C3C22×Dic512yes—
367C23×C3C22×Dic512yes—
368C23×C3C23×D511yescharacteristic
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3C22×Dic514yes—
376C3×D4—44no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—102no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4—204no—
386C2×C3×C4C22×Dic512yes—
387#67—48no—
388#67—48no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—102no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—204no—
398C2×Dic3C22×Dic514yes—
399D12—44no—
400C4×D3—208no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—42no—
410C22×C5—42no—
411C22×C5—64no—
412C22×C5—64no—
413C22×C5—64no—
414C22×C5—122no—
415C22×C5—122no—
416C22×C5—122no—
417C22×C5—122no—
418C22×C5C22×C4×D311yescharacteristic
419C22×C5#100412yes—
420C22×C5#100411yescharacteristic
421C22×C5#100411yescharacteristic
422C22×C5#100912yes—
423C4×C5—22no—
424C4×C5—64no—
425Dic5—42no—
426Dic5—42no—
427Dic5—122no—
428Dic5—122no—
429C24—32no—
430C24C2×D3×D511yescharacteristic
431C24C2×D3×D511yescharacteristic
432C2×D4—38no—
433C2×D4—38no—
434C2×D4—34no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—121no—
438C2×D4—121no—
439C2×D4—122no—
440C2×D4—122no—
441C2×D4—122no—
442C2×D4—122no—
443C2×D4D3×Dic514yescomplemented
444C22×C4—32no—
445C22×C4—52no—
446C22×C4—52no—
447C22×C4—152no—
448C22×C4—152no—
449C22×C4—202no—
450C22×C4—201no—
451C22×C4—602no—
452C22×C4—602no—
453C22×C4—602no—
454C22×C4—602no—
455C22×C4—601no—
456C22×C4C2×D3×D511yescharacteristic
457C22⋊C4—202no—
458C22⋊C4—201no—
459C22⋊C4—602no—
460C22⋊C4—602no—
461C22⋊C4—602no—
462C22⋊C4—602no—
463C22⋊C4—601no—
464C42—34no—
465C3×C5#238011yescharacteristic, complemented, Hall
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3#414412yes—
477C22×C3#414412yes—
478C22×C3#414411yescharacteristic
479C22×C3#414411yescharacteristic
480C22×C3C23×Dic511yescharacteristic
481C2×D3—24no—
482C2×D3—24no—
483C2×D3—24no—
484C2×D3—42no—
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—42no—
488C3×C4—22no—
489C3×C4—202no—
490C3×C4—202no—
491Dic3—24no—
492Dic3—202no—
493Dic3—202no—
494C2×C5—42no—
495C2×C5—42no—
496C2×C5—124no—
497C2×C5#548611yescharacteristic
498C2×C5#554512yes—
499C2×C5#559511yescharacteristic
500C2×C5#562012yes—
501C2×C5#566611yescharacteristic
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—34no—
511C23—62no—
512C23—62no—
513C23—62no—
514C23—62no—
515C23—62no—
516C23—62no—
517C23C2×D3×Dic512yes—
518C23C2×D3×Dic512yes—
519C23C22×D3×D511yescharacteristic
520D4—44no—
521D4—124no—
522D4—128no—
523D4—128no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—34no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—102no—
535C2×C4—204no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—302no—
542C2×C4—608no—
543C2×C4—604no—
544C2×C4C2×D3×Dic512yes—
545C2×C3—42no—
546C2×C3—42no—
547C2×C3#6605412yes—
548C2×C3#6605411yescharacteristic
549C2×C3#6605411yescharacteristic
550C2×C3#6613211yescharacteristic
551C2×C3#6613212yes—
552D3—44no—
553C5#7468511yescharacteristic, complemented, Sylow
554C22—22no—
555C22—22no—
556C22—24no—
557C22—24no—
558C22—42no—
559C22—42no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—64no—
565C22—64no—
566C22—64no—
567C22—122no—
568C22—122no—
569C22—122no—
570C22—122no—
571C22#9202512yes—
572C22#9202712yes—
573C22C22×D3×Dic511yescharacteristic
574C22#9204911yescharacteristic
575C22#9204911yescharacteristic
576C4—22no—
577C4—64no—
578C4—202no—
579C4—202no—
580C4—602no—
581C4—602no—
582C3#1061490511yescharacteristic, complemented, Sylow
583C2—42no—
584C2—42no—
585C2—124no—
586C2#1175491412yes—
587C2#1175498611yescharacteristic
588C2#1175500211yescharacteristic
589C2#1175507912yes—
590C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#940C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2380
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11751321C2semidirect
3. C3×#65509C2semidirect
4. #11749519C2semidirect
5. #11749519C2semidirect
6. #11749501C2semidirect
7. #11749492C2semidirect
8. #11748901C2semidirect
9. #11748618C2semidirect
20. C5×#940C4semidirect
41. #65509D3semidirect
48. C2×C3×C5×D4C2×C4semidirect
58. C2×C5×#67C2×C4semidirect
59. C2×C5×#67C2×C4semidirect
63. C2×C5×D12C2×C4semidirect
73. C4×C5×Dic3C2×C4semidirect
165. #940Dic5semidirect
190. C2×C5×D4C4×D3semidirect
254. C2×C3×D4C2×Dic5semidirect
264. C2×#67C2×Dic5semidirect
265. C2×#67C2×Dic5semidirect
273. C2×D12C2×Dic5semidirect
284. C4×Dic3C2×Dic5semidirect
443. C2×D4D3×Dic5semidirect
465. C3×C5#2380semidirect
553. C5#74685semidirect
582. C3#10614905semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9402
#117513212
C3×#655092
#117495192
#117495012
#117494922
#117489012
#117486182
#106149053
#746855