Finite Group Databasebeta

← #14298559

Subgroups — #14298559

Order 1920.

612 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#117C211yesmaximal, characteristic
2C4×#6665C211yesmaximal, characteristic
3#11748341C211yesmaximal, characteristic
4#11746353C211yesmaximal, characteristic, complemented
5C5×#4532C211yesmaximal, characteristic, complemented
6#11745974C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10599547—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C3×#4038C411yescharacteristic, complemented
17C3×#4038C411yescharacteristic, complemented
18C3×D5×C4⋊C4C411yescharacteristic, complemented
19C3×D5×C4⋊C4C411yescharacteristic, complemented
20C3×D5×C22⋊C4—21no—
21C3×#4023—21no—
22C3×#4018—21no—
23C3×C42×D5—21no—
24C2×#6665—21no—
25#90994—21no—
26#90955—21no—
27#90955—21no—
28#71590—51nomaximal, Hall
29D5×#117D311yescharacteristic
30#65415—31no—
31C4×#685—31no—
32C5×#339—31no—
33#64775—31no—
34#64752—31no—
35#64743—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C22×C3×Dic5D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C3×C5×C4⋊C4C2×C411yescharacteristic
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C42×C5—21no—
55C4×Dic15—21no—
56C4×Dic15—21no—
57#6710—21no—
58#6710—21no—
59C2×C3⋊#168—21no—
60C4×C5×Dic3—21no—
61C4×C5×Dic3—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×C22⋊Dic5—21no—
66C3×#685—21no—
67C3×#685—21no—
68C3×C4⋊Dic5C2×C411yescharacteristic
69C3×C4⋊Dic5C2×C411yescharacteristic
70C3×#683—21no—
71C3×#683—21no—
72C3×C4×Dic5—21no—
73C3×C4×Dic5—21no—
74C3×C4×Dic5—21no—
75#6665—24no—
76C2×C3×#117—51no—
77C4×#217—51no—
78#5207—51no—
79#4532—51no—
80#4532—51no—
81#4532—51no—
82#4532D511yescharacteristic, complemented
83C22×C4×D5C2×D311yescharacteristic
84C2×C5×M16—31no—
85C5×#117C2×D311yescharacteristic
86C2×C42×C5—31no—
87C2×#685—61no—
88#4072C2×D311yescharacteristic
89C2×C4×Dic5—31no—
90C2×#681—31no—
91#4038Dic311yescharacteristic, complemented
92#4038Dic311yescharacteristic, complemented
93D5×C4⋊C4Dic311yescharacteristic, complemented
94D5×C4⋊C4Dic311yescharacteristic, complemented
95D5×C22⋊C4—21no—
96#4023—21no—
97#4018—21no—
98C42×D5—21no—
99#3963—61no—
100#3952—61no—
101#3952—61no—
102#1826—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—21no—
105C22×C3×D5—21no—
106C22×C3×D5—22no—
107C22×C3×D5—41no—
108C22×C3×D5C22⋊C411yescharacteristic
109C22×C3×D5C22⋊C411yescharacteristic
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×Dic15—22no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×C5×Dic3—22no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5C22⋊C411yescharacteristic
129C2×C3×Dic5C22⋊C411yescharacteristic
130C3×C4×D5—21no—
131C3×C4×D5—21no—
132C3×C4×D5—21no—
133C3×C4×D5—21no—
134C3×C4×D5—21no—
135C3×C4×D5—21no—
136C3×C4×D5—21no—
137C3×C4×D5—21no—
138C3×C4×D5—42no—
139C3×C4×D5—42no—
140C3⋊#168—41no—
141C5×C3⋊C8—41no—
142C23×C3×C4—51no—
143C3×#117—51no—
144C3×#117—51no—
145C3×#117—51no—
146C3×#117—101no—
147C3×#117—101no—
148C3×#117C2×D511yescharacteristic
149C2×C3×C4⋊C4—51no—
150C2×C3×C4⋊C4—51no—
151C2×C3×C22⋊C4—101no—
152C2×C3×C42—101no—
153C2×#217—101no—
154C2×C4×Dic3—51no—
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208—51no—
157C2×#208C2×D511yescharacteristic
158C3⋊#95—101no—
159#830—101no—
160#830—101no—
161C23×D5#6711yescharacteristic
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C22×Dic5—61no—
165C22×Dic5#6711yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5C2×Dic311yescharacteristic
173C2×C4×D5C2×Dic311yescharacteristic
174C2×C4×D5#6711yescharacteristic
175C2×C4×D5#6711yescharacteristic
176C5×M16—61no—
177C5×M16—61no—
178C2×C5×C8—61no—
179C5×C4⋊C4C2×Dic311yescharacteristic
180C5×C4⋊C4C2×Dic311yescharacteristic
181C5×C22⋊C4—21no—
182C42×C5—21no—
183C42×C5—61no—
184C42×C5—61no—
185C22⋊Dic5—21no—
186#685—21no—
187#685—21no—
188#685—64no—
189C4⋊Dic5C2×Dic311yescharacteristic
190C4⋊Dic5C2×Dic311yescharacteristic
191#683—21no—
192#683—21no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5—61no—
197C4×Dic5—61no—
198#681—61no—
199#681—61no—
200C2×#168—61no—
201C2×#117—51no—
202#407—151no—
203C4×C22⋊C4—151no—
204#339—31no—
205#339—151no—
206#339—151no—
207#339—151no—
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5C2×C22⋊C411yescharacteristic
211C22×C3×C5#12311yescharacteristic
212C22×C3×C5#12311yescharacteristic
213C2×C3×D5—21no—
214C2×C3×D5—21no—
215C2×C3×D5—21no—
216C2×C3×D5—21no—
217C2×C3×D5—21no—
218C2×C3×D5—42no—
219C2×C3×D5—42no—
220C2×C3×D5#10412yes—
221C3×C4×C5—41no—
222C3×C4×C5—41no—
223C3×C4×C5#11711yescharacteristic
224C3×C4×C5#11711yescharacteristic
225C3×C4×C5#12311yescharacteristic
226C3×C4×C5#12311yescharacteristic
227Dic15—42no—
228C3×Dic5—21no—
229C3×Dic5—21no—
230C3×Dic5—41no—
231C3×Dic5—41no—
232C5×Dic3—42no—
233C24×C3—51no—
234C22×C3×C4—51no—
235C22×C3×C4—51no—
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C22×C3×C4—51no—
239C22×C3×C4—101no—
240C22×C3×C4—101no—
241C22×C3×C4—101no—
242C22×C3×C4—101no—
243C22×C3×C4—101no—
244C22×C3×C4—101no—
245C22×C3×C4C22×D511yescharacteristic
246C22×Dic3—21no—
247C22×Dic3—101no—
248C3×C4⋊C4—51no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—101no—
251C3×C4⋊C4—101no—
252C3×C4⋊C4C4×D511yescharacteristic
253C3×C4⋊C4C4×D511yescharacteristic
254C3×C22⋊C4—21no—
255C3×C22⋊C4—101no—
256C3×C22⋊C4—101no—
257C3×C22⋊C4—101no—
258C3×C42—21no—
259C3×C42—101no—
260C3×C42—101no—
261C3×C42—101no—
262#217—104no—
263C4×Dic3—21no—
264C4×Dic3—21no—
265C4×Dic3—101no—
266C4×Dic3—101no—
267#208—21no—
268#208—21no—
269#208—101no—
270#208—101no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—101no—
273C23×C5C2×#6711yescharacteristic
274C22×D5—21no—
275C22×D5—21no—
276C22×D5—22no—
277C22×D5—41no—
278C22×D5#21711yescharacteristic
279C22×D5#21711yescharacteristic
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—62no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5#23511yescharacteristic
286C2×C4×C5#23511yescharacteristic
287C2×C4×C5#23511yescharacteristic
288C2×C4×C5#23511yescharacteristic
289C2×C4×C5C22×Dic311yescharacteristic
290C2×C4×C5C2×#6711yescharacteristic
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—62no—
296C2×Dic5—121no—
297C2×Dic5—121no—
298C2×Dic5#21711yescharacteristic
299C2×Dic5#21711yescharacteristic
300C4×D5—21no—
301C4×D5—21no—
302C4×D5—21no—
303C4×D5—21no—
304C4×D5—21no—
305C4×D5—21no—
306C4×D5—21no—
307C4×D5—21no—
308C4×D5—42no—
309C4×D5—42no—
310C5×C8—121no—
311#168—121no—
312C23×C4—51no—
313C2×M16—31no—
314C2×M16—151no—
315#117—51no—
316#117—51no—
317#117—51no—
318#117—101no—
319#117—101no—
320#117D3×D511yescharacteristic
321C2×C4⋊C4—51no—
322C2×C4⋊C4—51no—
323C2×C22⋊C4—101no—
324C2×C22⋊C4—301no—
325C2×C42—31no—
326C2×C42—101no—
327C2×C42—151no—
328C22⋊C8—301no—
329C22⋊C8—301no—
330#95—301no—
331C2×C3×C5—21no—
332C2×C3×C5—21no—
333C2×C3×C5#38111yescharacteristic
334C2×C3×C5C2×#10411yescharacteristic
335C2×C3×C5#42111yescharacteristic
336C3×D5—22no—
337C3×D5—41no—
338C23×C3—51no—
339C23×C3—51no—
340C23×C3—102no—
341C23×C3—101no—
342C23×C3—101no—
343C23×C3—201no—
344C23×C3D4×D511yescharacteristic
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—51no—
348C2×C3×C4—51no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4—101no—
357C2×C3×C4—101no—
358C2×C3×C4—101no—
359C2×C3×C4—101no—
360C2×C3×C4—101no—
361C2×C3×C4—202no—
362C2×C3×C4—202no—
363C2×C3×C4C2×C4×D511yescharacteristic
364C2×C3×C4#70911yescharacteristic
365C2×C3×C4#70911yescharacteristic
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4#71111yescharacteristic
368C2×C3×C4#71311yescharacteristic
369C2×Dic3—22no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—102no—
373C2×Dic3—201no—
374C2×Dic3—201no—
375C3⋊C8—41no—
376C3⋊C8—201no—
377C22×C5—21no—
378C22×C5—21no—
379C22×C5#92911yescharacteristic
380C22×C5#92911yescharacteristic
381C22×C5C2×#21711yescharacteristic
382C2×D5—21no—
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—21no—
386C2×D5—21no—
387C2×D5—42no—
388C2×D5—42no—
389C2×D5#83712yes—
390C4×C5—41no—
391C4×C5—41no—
392C4×C5—122no—
393C4×C5#92611yescharacteristic
394C4×C5#92611yescharacteristic
395C4×C5#92911yescharacteristic
396C4×C5#92911yescharacteristic
397Dic5—21no—
398Dic5—21no—
399Dic5—41no—
400Dic5—41no—
401Dic5—122no—
402C24—51no—
403C22×C4—51no—
404C22×C4—51no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—51no—
408C22×C4—61no—
409C22×C4—101no—
410C22×C4—101no—
411C22×C4—101no—
412C22×C4—101no—
413C22×C4—101no—
414C22×C4—101no—
415C22×C4—301no—
416C22×C4C2×D3×D511yescharacteristic
417M16—61no—
418M16—61no—
419M16—301no—
420M16—301no—
421C2×C8—61no—
422C2×C8—301no—
423C4⋊C4—51no—
424C4⋊C4—51no—
425C4⋊C4—101no—
426C4⋊C4—101no—
427C4⋊C4D5×Dic311yescharacteristic
428C4⋊C4D5×Dic311yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—101no—
431C22⋊C4—101no—
432C22⋊C4—101no—
433C22⋊C4—304no—
434C42—21no—
435C42—61no—
436C42—61no—
437C42—101no—
438C42—101no—
439C42—101no—
440C42—301no—
441C42—301no—
442C3×C5#182611yescharacteristic, complemented, Hall
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—52no—
446C22×C3—101no—
447C22×C3—101no—
448C22×C3—101no—
449C22×C3—101no—
450C22×C3—101no—
451C22×C3—202no—
452C22×C3—202no—
453C22×C3D5×C22⋊C411yescharacteristic
454C22×C3#402911yescharacteristic
455C22×C3#404011yescharacteristic
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—101no—
459C3×C4—101no—
460C3×C4—201no—
461C3×C4—201no—
462C3×C4#401811yescharacteristic
463C3×C4#402911yescharacteristic
464C3×C4#403811yescharacteristic
465C3×C4#404011yescharacteristic
466Dic3—42no—
467Dic3—202no—
468C2×C5—21no—
469C2×C5—21no—
470C2×C5#521111yescharacteristic
471C2×C5C2×#83711yescharacteristic
472C2×C5#523611yescharacteristic
473D5—22no—
474D5—41no—
475C23—51no—
476C23—51no—
477C23—102no—
478C23—101no—
479C23—101no—
480C23—201no—
481C23D5×#6711yescharacteristic
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—62no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—101no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—101no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—101no—
496C2×C4—101no—
497C2×C4—101no—
498C2×C4—101no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—202no—
502C2×C4—202no—
503C2×C4—302no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4#677111yescharacteristic
507C2×C4#677111yescharacteristic
508C2×C4#677211yescharacteristic
509C2×C4#677311yescharacteristic
510C2×C4C2×D5×Dic311yescharacteristic
511C2×C4D5×#6711yescharacteristic
512C8—121no—
513C8—601no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—102no—
517C2×C3—201no—
518C2×C3#6495311yescharacteristic
519C2×C3D5×#10411yescharacteristic
520C2×C3#6511011yescharacteristic
521C5#7159011yescharacteristic, complemented, Sylow
522C22—21no—
523C22—21no—
524C22—52no—
525C22—101no—
526C22—101no—
527C22—101no—
528C22—101no—
529C22—101no—
530C22—202no—
531C22—202no—
532C22#9134811yescharacteristic
533C22#9144711yescharacteristic
534C22D5×#21711yescharacteristic
535C4—41no—
536C4—41no—
537C4—101no—
538C4—101no—
539C4—122no—
540C4—201no—
541C4—201no—
542C4—602no—
543C4#9134811yescharacteristic
544C4#9135711yescharacteristic
545C4#9135811yescharacteristic
546C4#9144711yescharacteristic
547C3#1059954711yescharacteristic, complemented, Sylow
548C2—21no—
549C2—21no—
550C2—102no—
551C2—201no—
552C2#1174873711yescharacteristic
553C2D5×#83711yescharacteristic
554C2#1174942711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1826
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11746353C2semidirect
5. C5×#4532C2semidirect
6. #11745974C2semidirect
7. #11745973C2semidirect
16. C3×#4038C4semidirect
17. C3×#4038C4semidirect
18. C3×D5×C4⋊C4C4semidirect
19. C3×D5×C4⋊C4C4semidirect
82. #4532D5semidirect
91. #4038Dic3semidirect
92. #4038Dic3semidirect
93. D5×C4⋊C4Dic3semidirect
94. D5×C4⋊C4Dic3semidirect
442. C3×C5#1826semidirect
521. C5#71590semidirect
547. C3#10599547semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1172
C4×#66652
#117483412
#117463532
C5×#45322
#117459742
#117459732
#105995473
#715905