Finite Group Databasebeta

← #14298551

Subgroups — #14298551

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
1D5×#926C211yesmaximal, characteristic
2C3×#65415C211yesmaximal, characteristic
3C4×#6665C211yesmaximal, characteristic
4#11746376C211yesmaximal, characteristic, complemented
5C5×#4555C211yesmaximal, characteristic, complemented
6#11745976C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10599547—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16D5×#217—21no—
17C2×#6665—21no—
18#91528—21no—
19D5×C4⋊Dic3C411yescharacteristic, complemented
20D5×C4⋊Dic3C411yescharacteristic, complemented
21C4×D5×Dic3—21no—
22#91358C411yescharacteristic, complemented
23#91358C411yescharacteristic, complemented
24#91357—21no—
25C3×#3952—21no—
26C3×#3952—21no—
27#90994—21no—
28#69975—51nomaximal, Hall
29D5×#117—31no—
30#65415D311yescharacteristic
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×D5C2×C411yescharacteristic
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×D5×Dic3—21no—
50C2×D5×Dic3—21no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8—21no—
54#6719—21no—
55C4⋊Dic15C2×C411yescharacteristic
56C4⋊Dic15C2×C411yescharacteristic
57C4×Dic15—21no—
58C4×Dic15—21no—
59C4×Dic15—21no—
60C5×#217—21no—
61C5×C4⋊Dic3C2×C411yescharacteristic
62C5×C4⋊Dic3C2×C411yescharacteristic
63C4×C5×Dic3—21no—
64C4×C5×Dic3—21no—
65C4×C5×Dic3—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168—21no—
69#6668—21no—
70#6668—21no—
71#6665—24no—
72#6665—21no—
73#6665—21no—
74Dic3×Dic5—21no—
75Dic3×Dic5—21no—
76C2×#926—51no—
77C3×#407—51no—
78C4×#217—51no—
79#4555—51no—
80#4555—51no—
81#4555—51no—
82#4555D511yescharacteristic, complemented
83C22×C4×D5C2×D311yescharacteristic
84C2×C5×M16C2×D311yescharacteristic
85C5×#117—31no—
86C2×C42×C5—31no—
87C2×#685—61no—
88#4072—31no—
89C2×C4×Dic5—31no—
90C2×#681C2×D311yescharacteristic
91#4038—31no—
92#4038—31no—
93D5×C4⋊C4—31no—
94D5×C4⋊C4—31no—
95D5×C22⋊C4—61no—
96#4023—61no—
97#4018—61no—
98C42×D5—61no—
99#3963—61no—
100#3952—21no—
101#3952—21no—
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×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×Dic15—22no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×C5×Dic3—22no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
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—
138D5×Dic3—42no—
139D5×Dic3—42no—
140C3×C5×C8—41no—
141C3×#168—41no—
142C23×C3×C4—51no—
143C2×C3×M16—51no—
144C2×C3×M16C2×D511yescharacteristic
145C2×#217—101no—
146C2×#217—101no—
147#926—51no—
148#926—51no—
149#926—51no—
150#926—101no—
151#926—101no—
152#926C2×D511yescharacteristic
153C2×C4⋊Dic3—51no—
154C2×C4⋊Dic3—51no—
155C2×C4×Dic3—51no—
156C2×C4×Dic3—101no—
157C2×C4×Dic3C2×D511yescharacteristic
158C3×C22⋊C8—101no—
159C3×C22⋊C8—101no—
160C3⋊#95—101no—
161C23×D5D1211yescharacteristic
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C22×Dic5—61no—
165C22×Dic5D1211yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—61no—
171C2×C4×D5—61no—
172C2×C4×D5C4×D311yescharacteristic
173C2×C4×D5C4×D311yescharacteristic
174C2×C4×D5#6711yescharacteristic
175C2×C4×D5#6711yescharacteristic
176C5×M16—21no—
177C5×M16—21no—
178C2×C5×C8—21no—
179C5×C4⋊C4—31no—
180C5×C4⋊C4—31no—
181C5×C22⋊C4—61no—
182C42×C5—61no—
183C42×C5—61no—
184C42×C5—61no—
185C22⋊Dic5—61no—
186#685—64no—
187#685—61no—
188#685—61no—
189C4⋊Dic5—31no—
190C4⋊Dic5—31no—
191#683—61no—
192#683—61no—
193C4×Dic5—61no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196C4×Dic5—61no—
197C4×Dic5—61no—
198#681—21no—
199#681—21no—
200C2×#168—21no—
201C2×#117—151no—
202#407—51no—
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#11711yescharacteristic
222C3×C4×C5#11711yescharacteristic
223C3×C4×C5#12311yescharacteristic
224C3×C4×C5#12311yescharacteristic
225Dic15—42no—
226Dic15—41no—
227Dic15—41no—
228C3×Dic5—21no—
229C3×Dic5—21no—
230C5×Dic3—42no—
231C5×Dic3—41no—
232C5×Dic3—41no—
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×C4C22×D511yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—101no—
246C22×Dic3—101no—
247C22×Dic3—101no—
248C3×M16—21no—
249C3×M16—21no—
250C3×M16—101no—
251C3×M16—101no—
252C2×C3×C8—21no—
253C2×C3×C8—101no—
254#217—21no—
255#217—101no—
256#217—101no—
257#217—104no—
258#217—101no—
259C4⋊Dic3—51no—
260C4⋊Dic3—51no—
261C4⋊Dic3—101no—
262C4⋊Dic3—101no—
263C4⋊Dic3C4×D511yescharacteristic
264C4⋊Dic3C4×D511yescharacteristic
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3—21no—
268C4×Dic3—101no—
269C4×Dic3—101no—
270C4×Dic3—101no—
271C4×Dic3—101no—
272C4×Dic3—101no—
273C23×C5C2×D1211yescharacteristic
274C22×D5—21no—
275C22×D5—21no—
276C22×D5—22no—
277C22×D5—41no—
278C22×D5(C2×D3)⋊C411yescharacteristic
279C22×D5(C2×D3)⋊C411yescharacteristic
280C2×C4×C5—62no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×C4×C5#23711yescharacteristic
287C2×C4×C5#23711yescharacteristic
288C2×C4×C5#23711yescharacteristic
289C2×C4×C5#23711yescharacteristic
290C2×C4×C5C2×#6711yescharacteristic
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—62no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—121no—
297C2×Dic5—121no—
298C2×Dic5(C2×D3)⋊C411yescharacteristic
299C2×Dic5(C2×D3)⋊C411yescharacteristic
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—122no—
309C4×D5—122no—
310C5×C8—41no—
311#168—41no—
312C23×C4—51no—
313C2×M16—51no—
314C2×M16D3×D511yescharacteristic
315#117—31no—
316#117—151no—
317#117—151no—
318#117—151no—
319#117—301no—
320#117—301no—
321C2×C4⋊C4—151no—
322C2×C4⋊C4—151no—
323C2×C22⋊C4—301no—
324C2×C22⋊C4—301no—
325C2×C42—31no—
326C2×C42—151no—
327C2×C42—301no—
328C22⋊C8—101no—
329C22⋊C8—101no—
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—51no—
346C2×C3×C4—51no—
347C2×C3×C4—101no—
348C2×C3×C4—101no—
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×C4C2×C4×D511yescharacteristic
358C2×C3×C4#70911yescharacteristic
359C2×C3×C4#70911yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4#71111yescharacteristic
362C2×C3×C4#71311yescharacteristic
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—102no—
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—202no—
372C2×Dic3—202no—
373C2×Dic3—201no—
374C2×Dic3—201no—
375C3×C8—41no—
376C3×C8—201no—
377C22×C5—21no—
378C22×C5—21no—
379C22×C5#88611yescharacteristic
380C22×C5#88611yescharacteristic
381C22×C5C2×(C2×D3)⋊C411yescharacteristic
382C2×D5—21no—
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—21no—
386C2×D5—21no—
387C2×D5—42no—
388C2×D5—42no—
389C2×D5#82512yes—
390C4×C5—122no—
391C4×C5—121no—
392C4×C5—121no—
393C4×C5#87711yescharacteristic
394C4×C5#87711yescharacteristic
395C4×C5#93511yescharacteristic
396C4×C5#93511yescharacteristic
397Dic5—21no—
398Dic5—21no—
399Dic5—122no—
400Dic5—121no—
401Dic5—121no—
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—301no—
414C22×C4—301no—
415C22×C4—301no—
416C22×C4C2×D3×D511yescharacteristic
417M16—21no—
418M16—21no—
419M16—101no—
420M16—101no—
421C2×C8—21no—
422C2×C8—101no—
423C4⋊C4—31no—
424C4⋊C4—31no—
425C4⋊C4—151no—
426C4⋊C4—151no—
427C4⋊C4—301no—
428C4⋊C4—301no—
429C22⋊C4—61no—
430C22⋊C4—301no—
431C22⋊C4—301no—
432C22⋊C4—304no—
433C22⋊C4—301no—
434C42—61no—
435C42—61no—
436C42—61no—
437C42—301no—
438C42—301no—
439C42—301no—
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—101no—
457C3×C4—101no—
458C3×C4#401811yescharacteristic
459C3×C4#402911yescharacteristic
460C3×C4#403811yescharacteristic
461C3×C4#404011yescharacteristic
462Dic3—42no—
463Dic3—41no—
464Dic3—41no—
465Dic3—202no—
466Dic3—201no—
467Dic3—201no—
468C2×C5—21no—
469C2×C5—21no—
470C2×C5#494311yescharacteristic
471C2×C5C2×#82511yescharacteristic
472C2×C5#513911yescharacteristic
473D5—22no—
474D5—41no—
475C23—51no—
476C23—51no—
477C23—102no—
478C23—101no—
479C23—101no—
480C23—201no—
481C23D5×D1211yescharacteristic
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—61no—
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—121no—
498C2×C4—121no—
499C2×C4—302no—
500C2×C4—301no—
501C2×C4—301no—
502C2×C4—602no—
503C2×C4—602no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4#676511yescharacteristic
507C2×C4#676611yescharacteristic
508C2×C4C4×D3×D511yescharacteristic
509C2×C4#677911yescharacteristic
510C2×C4#678011yescharacteristic
511C2×C4D5×#6711yescharacteristic
512C8—41no—
513C8—201no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—102no—
517C2×C3—201no—
518C2×C3#6495311yescharacteristic
519C2×C3D5×#10411yescharacteristic
520C2×C3#6511011yescharacteristic
521C5#6997511yescharacteristic, complemented, Sylow
522C22—21no—
523C22—21no—
524C22—52no—
525C22—101no—
526C22—101no—
527C22—101no—
528C22—101no—
529C22—101no—
530C22—202no—
531C22—202no—
532C22#9141311yescharacteristic
533C22#9141411yescharacteristic
534C22D5×(C2×D3)⋊C411yescharacteristic
535C4—101no—
536C4—101no—
537C4—122no—
538C4—121no—
539C4—121no—
540C4—602no—
541C4—601no—
542C4—601no—
543C4#9139311yescharacteristic
544C4#9139411yescharacteristic
545C4#9140711yescharacteristic
546C4#9154811yescharacteristic
547C3#1059954711yescharacteristic, complemented, Sylow
548C2—21no—
549C2—21no—
550C2—102no—
551C2—201no—
552C2D5×#82511yescharacteristic
553C2#1174822911yescharacteristic
554C2#1174887111yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1826
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11746376C2semidirect
5. C5×#4555C2semidirect
6. #11745976C2semidirect
7. #11745975C2semidirect
19. D5×C4⋊Dic3C4semidirect
20. D5×C4⋊Dic3C4semidirect
22. #91358C4semidirect
23. #91358C4semidirect
82. #4555D5semidirect
442. C3×C5#1826semidirect
521. C5#69975semidirect
547. C3#10599547semidirect

Maximal subgroups

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

subgroupindex
D5×#9262
C3×#654152
C4×#66652
#117463762
C5×#45552
#117459762
#117459752
#105995473
#699755