Finite Group Databasebeta

← #14298561

Subgroups — #14298561

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
1C5×D3×#117C211yesmaximal, characteristic
2C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic
3#11748346C211yesmaximal, characteristic
4#11746353C211yesmaximal, characteristic, complemented
5C3×#64752C211yesmaximal, characteristic, complemented
6#11745977C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10602383—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C5×#892C411yescharacteristic, complemented
15C5×#892C411yescharacteristic, complemented
16C5×D3×C4⋊C4C411yescharacteristic, complemented
17C5×D3×C4⋊C4C411yescharacteristic, complemented
18C5×D3×C22⋊C4—21no—
19C5×#877—21no—
20C5×#872—21no—
21C42×C5×D3—21no—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24C2×(C2×D3)⋊Dic5—21no—
25#90994—21no—
26(C2×D3)⋊#168—21no—
27(C2×D3)⋊#168—21no—
28#68754—51nomaximal, Hall
29C2×C5×#117—31no—
30C4×C22⋊Dic5—31no—
31#65496—31no—
32#64752—31no—
33#64752—31no—
34#64752—31no—
35#64752D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3D411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C4×C5×D3—21no—
42C2×C4×C5×D3—21no—
43C2×C4×C5×D3—21no—
44C2×C4×C5×D3—21no—
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3C2×C411yescharacteristic
47C2×C4×C5×D3C2×C411yescharacteristic
48C2×C4×C5×D3D411yescharacteristic
49C2×C4×C5×D3D411yescharacteristic
50C22×C3×Dic5—21no—
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—
60C5×#217—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×C4⋊Dic3C2×C411yescharacteristic
64C5×C4⋊Dic3C2×C411yescharacteristic
65C5×Dic3⋊C4—21no—
66C5×Dic3⋊C4—21no—
67C4×C5×Dic3—21no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3—21no—
70C3×C4×Dic5—21no—
71C3×C4×Dic5—21no—
72C3×#681—21no—
73C3×#681—21no—
74C2×C3×#168—21no—
75(C2×D3)⋊Dic5—24no—
76D3×#117D511yescharacteristic
77#5126—51no—
78C4×(C2×D3)⋊C4—51no—
79C3×#339—51no—
80#4555—51no—
81#4532—51no—
82#4523—51no—
83C23×C4×C5—31no—
84C5×#117—31no—
85C5×#117—31no—
86C5×#117—31no—
87C5×#117—61no—
88C5×#117—61no—
89C5×#117C2×D311yescharacteristic
90C2×C5×C4⋊C4—31no—
91C2×C5×C4⋊C4—31no—
92C2×C5×C22⋊C4—61no—
93C2×C42×C5—61no—
94C2×C22⋊Dic5—61no—
95C2×C4×Dic5—31no—
96C2×C4×Dic5C2×D311yescharacteristic
97C2×#681—31no—
98C2×#681C2×D311yescharacteristic
99#3963—61no—
100C22⋊#168—61no—
101C22⋊#168—61no—
102#1826—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3—21no—
105C22×C5×D3—21no—
106C22×C5×D3—22no—
107C22×C5×D3—41no—
108C22×C5×D3C22⋊C411yescharacteristic
109C22×C5×D3C22⋊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—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3C22⋊C411yescharacteristic
126C2×C5×Dic3C22⋊C411yescharacteristic
127C4×C5×D3—21no—
128C4×C5×D3—21no—
129C4×C5×D3—21no—
130C4×C5×D3—21no—
131C4×C5×D3—21no—
132C4×C5×D3—21no—
133C4×C5×D3—21no—
134C4×C5×D3—21no—
135C4×C5×D3—42no—
136C4×C5×D3—42no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—41no—
139C2×C3×Dic5—41no—
140C3⋊#168—41no—
141C3×#168—41no—
142C22×C4×D3C2×D511yescharacteristic
143C2×C3×M16—51no—
144C3×#117C2×D511yescharacteristic
145C2×C3×C42—51no—
146C2×(C2×D3)⋊C4—101no—
147#926C2×D511yescharacteristic
148C2×C4×Dic3—51no—
149C2×#208—51no—
150#892Dic511yescharacteristic, complemented
151#892Dic511yescharacteristic, complemented
152D3×C4⋊C4Dic511yescharacteristic, complemented
153D3×C4⋊C4Dic511yescharacteristic, complemented
154D3×C22⋊C4—21no—
155#877—21no—
156#872—21no—
157C42×D3—21no—
158C3⋊#95—101no—
159(C2×D3)⋊C8—101no—
160(C2×D3)⋊C8—101no—
161C24×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—31no—
166C22×C4×C5—31no—
167C22×C4×C5—61no—
168C22×C4×C5—61no—
169C22×C4×C5—61no—
170C22×C4×C5—61no—
171C22×C4×C5—61no—
172C22×C4×C5—61no—
173C22×C4×C5C22×D311yescharacteristic
174C22×Dic5—21no—
175C22×Dic5—61no—
176C5×C4⋊C4—31no—
177C5×C4⋊C4—31no—
178C5×C4⋊C4—61no—
179C5×C4⋊C4—61no—
180C5×C4⋊C4C4×D311yescharacteristic
181C5×C4⋊C4C4×D311yescharacteristic
182C5×C22⋊C4—21no—
183C5×C22⋊C4—61no—
184C5×C22⋊C4—61no—
185C5×C22⋊C4—61no—
186C42×C5—21no—
187C42×C5—61no—
188C42×C5—61no—
189C42×C5—61no—
190C22⋊Dic5—64no—
191C4×Dic5—21no—
192C4×Dic5—21no—
193C4×Dic5—61no—
194C4×Dic5—61no—
195#681—21no—
196#681—21no—
197#681—61no—
198#681—61no—
199C2×#168—21no—
200C2×#168—61no—
201C2×#117—31no—
202#407—151no—
203C4×C22⋊C4—151no—
204#339—51no—
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×C5×D3—21no—
214C2×C5×D3—21no—
215C2×C5×D3—21no—
216C2×C5×D3—21no—
217C2×C5×D3—21no—
218C2×C5×D3—42no—
219C2×C5×D3—42no—
220C2×C5×D3#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—42no—
229C5×Dic3—21no—
230C5×Dic3—21no—
231C5×Dic3—41no—
232C5×Dic3—41no—
233C23×D3C22⋊D511yescharacteristic
234C22×C3×C4—101no—
235C22×C3×C4C22×D511yescharacteristic
236C22×Dic3—101no—
237C22×Dic3C22⋊D511yescharacteristic
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3C2×Dic511yescharacteristic
245C2×C4×D3C2×Dic511yescharacteristic
246C2×C4×D3C22⋊D511yescharacteristic
247C2×C4×D3C22⋊D511yescharacteristic
248C3×M16—101no—
249C3×M16—101no—
250C2×C3×C8—101no—
251C3×C4⋊C4C2×Dic511yescharacteristic
252C3×C4⋊C4C2×Dic511yescharacteristic
253C3×C22⋊C4—21no—
254C3×C42—21no—
255C3×C42—101no—
256C3×C42—101no—
257#217—21no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—104no—
261C4⋊Dic3C2×Dic511yescharacteristic
262C4⋊Dic3C2×Dic511yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—21no—
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3—21no—
268C4×Dic3—101no—
269C4×Dic3—101no—
270#208—101no—
271#208—101no—
272C2×C3⋊C8—101no—
273C23×C5—31no—
274C23×C5—31no—
275C23×C5—62no—
276C23×C5—61no—
277C23×C5—61no—
278C23×C5—121no—
279C23×C5D3×D411yescharacteristic
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—31no—
283C2×C4×C5—31no—
284C2×C4×C5—61no—
285C2×C4×C5—61no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—61no—
294C2×C4×C5—61no—
295C2×C4×C5—61no—
296C2×C4×C5—122no—
297C2×C4×C5—122no—
298C2×C4×C5C2×C4×D311yescharacteristic
299C2×C4×C5#23511yescharacteristic
300C2×C4×C5#23511yescharacteristic
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5#23711yescharacteristic
303C2×C4×C5#23911yescharacteristic
304C2×Dic5—22no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—62no—
308C2×Dic5—121no—
309C2×Dic5—121no—
310#168—41no—
311#168—121no—
312C23×C4—31no—
313C2×M16—51no—
314C2×M16—151no—
315#117—31no—
316#117—31no—
317#117—31no—
318#117—61no—
319#117—61no—
320#117D3×D511yescharacteristic
321C2×C4⋊C4—31no—
322C2×C4⋊C4—31no—
323C2×C22⋊C4—61no—
324C2×C22⋊C4—301no—
325C2×C42—51no—
326C2×C42—61no—
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
336C5×D3—22no—
337C5×D3—41no—
338C23×C3C2×C22⋊D511yescharacteristic
339C22×D3—21no—
340C22×D3—21no—
341C22×D3—22no—
342C22×D3—41no—
343C22×D3C22⋊Dic511yescharacteristic
344C22×D3C22⋊Dic511yescharacteristic
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—102no—
348C2×C3×C4—201no—
349C2×C3×C4—201no—
350C2×C3×C4#70911yescharacteristic
351C2×C3×C4#70911yescharacteristic
352C2×C3×C4#70911yescharacteristic
353C2×C3×C4#70911yescharacteristic
354C2×C3×C4C22×Dic511yescharacteristic
355C2×C3×C4C2×C22⋊D511yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—102no—
361C2×Dic3—201no—
362C2×Dic3—201no—
363C2×Dic3C22⋊Dic511yescharacteristic
364C2×Dic3C22⋊Dic511yescharacteristic
365C4×D3—21no—
366C4×D3—21no—
367C4×D3—21no—
368C4×D3—21no—
369C4×D3—21no—
370C4×D3—21no—
371C4×D3—21no—
372C4×D3—21no—
373C4×D3—42no—
374C4×D3—42no—
375C3×C8—201no—
376C3⋊C8—201no—
377C22×C5—21no—
378C22×C5—21no—
379C22×C5—32no—
380C22×C5—61no—
381C22×C5—61no—
382C22×C5—61no—
383C22×C5—61no—
384C22×C5—61no—
385C22×C5—122no—
386C22×C5—122no—
387C22×C5D3×C22⋊C411yescharacteristic
388C22×C5#88311yescharacteristic
389C22×C5#89411yescharacteristic
390C4×C5—41no—
391C4×C5—41no—
392C4×C5—61no—
393C4×C5—61no—
394C4×C5—121no—
395C4×C5—121no—
396C4×C5#87211yescharacteristic
397C4×C5#88311yescharacteristic
398C4×C5#89211yescharacteristic
399C4×C5#89411yescharacteristic
400Dic5—42no—
401Dic5—122no—
402C24—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—101no—
415C22×C4—301no—
416C22×C4C2×D3×D511yescharacteristic
417M16—101no—
418M16—101no—
419M16—301no—
420M16—301no—
421C2×C8—101no—
422C2×C8—301no—
423C4⋊C4—31no—
424C4⋊C4—31no—
425C4⋊C4—61no—
426C4⋊C4—61no—
427C4⋊C4D3×Dic511yescharacteristic
428C4⋊C4D3×Dic511yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—61no—
431C22⋊C4—61no—
432C22⋊C4—61no—
433C22⋊C4—304no—
434C42—21no—
435C42—61no—
436C42—61no—
437C42—61no—
438C42—101no—
439C42—101no—
440C42—301no—
441C42—301no—
442C3×C5#182611yescharacteristic, complemented, Hall
443C22×C3—21no—
444C22×C3—21no—
445C22×C3#407511yescharacteristic
446C22×C3#407511yescharacteristic
447C22×C3C2×C22⋊Dic511yescharacteristic
448C2×D3—21no—
449C2×D3—21no—
450C2×D3—21no—
451C2×D3—21no—
452C2×D3—21no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3#396912yes—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—202no—
459C3×C4#407211yescharacteristic
460C3×C4#407211yescharacteristic
461C3×C4#407511yescharacteristic
462C3×C4#407511yescharacteristic
463Dic3—21no—
464Dic3—21no—
465Dic3—41no—
466Dic3—41no—
467Dic3—202no—
468C2×C5—21no—
469C2×C5—21no—
470C2×C5—62no—
471C2×C5—121no—
472C2×C5#466411yescharacteristic
473C2×C5D3×#10411yescharacteristic
474C2×C5#482111yescharacteristic
475C23—31no—
476C23—31no—
477C23—62no—
478C23—61no—
479C23—61no—
480C23—121no—
481C23D3×C22⋊D511yescharacteristic
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—31no—
485C2×C4—31no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—102no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—201no—
502C2×C4—201no—
503C2×C4—302no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4#676511yescharacteristic
507C2×C4#676911yescharacteristic
508C2×C4#677111yescharacteristic
509C2×C4#677111yescharacteristic
510C2×C4C2×D3×Dic511yescharacteristic
511C2×C4D3×C22⋊D511yescharacteristic
512C8—201no—
513C8—601no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3#6550011yescharacteristic
517C2×C3C2×#396911yescharacteristic
518C2×C3#6552511yescharacteristic
519D3—22no—
520D3—41no—
521C5#6875411yescharacteristic, complemented, Sylow
522C22—21no—
523C22—21no—
524C22—32no—
525C22—61no—
526C22—61no—
527C22—61no—
528C22—61no—
529C22—61no—
530C22—122no—
531C22—122no—
532C22#9135111yescharacteristic
533C22#9145211yescharacteristic
534C22D3×C22⋊Dic511yescharacteristic
535C4—41no—
536C4—41no—
537C4—61no—
538C4—61no—
539C4—121no—
540C4—121no—
541C4—202no—
542C4—602no—
543C4#9133811yescharacteristic
544C4#9135111yescharacteristic
545C4#9137111yescharacteristic
546C4#9145211yescharacteristic
547C3#1060238311yescharacteristic, complemented, Sylow
548C2—21no—
549C2—21no—
550C2—62no—
551C2—121no—
552C2#1174877711yescharacteristic
553C2D3×#396911yescharacteristic
554C2#1174942911yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3D4
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. C3×#64752C2semidirect
6. #11745977C2semidirect
7. #11745975C2semidirect
14. C5×#892C4semidirect
15. C5×#892C4semidirect
16. C5×D3×C4⋊C4C4semidirect
17. C5×D3×C4⋊C4C4semidirect
35. #64752D3semidirect
150. #892Dic5semidirect
151. #892Dic5semidirect
152. D3×C4⋊C4Dic5semidirect
153. D3×C4⋊C4Dic5semidirect
442. C3×C5#1826semidirect
521. C5#68754semidirect
547. C3#10602383semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1172
C4×(C2×D3)⋊Dic52
#117483462
#117463532
C3×#647522
#117459772
#117459752
#106023833
#687545