Finite Group Databasebeta

← #14300723

Subgroups — #14300723

Order 1920.

824 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×#91827C211yesmaximal, characteristic
2C2×#91781C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic, complemented
4C2×#91116C211yesmaximal, characteristic, complemented
5C2×#91104C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10600994—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—21no—
11C22×C4×D15C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×#6719—21no—
15#91827—22no—
16#91827C414yescomplemented
17C2×#6714—21no—
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4×Dic15—21no—
21C22×C3⋊#168C2211yescharacteristic
22#91781—22no—
23#91781—22no—
24C3×C5×#102—22no—
25#91116—22no—
26#91104—22no—
27#70201—51nomaximal, Hall
28C2×#4084—31no—
29C2×#4038—31no—
30C2×C5×#102D311yescharacteristic, complemented
31C2×#3964—31no—
32C2×#3952—31no—
33#64771—31no—
34#64749—31no—
35C24×C3×C5—21no—
36C23×D15D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C412yes—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×#1220—24no—
46C2×#1220—42no—
47C2×#1220—42no—
48C22×Dic15—21no—
49C22×Dic15—21no—
50C22×Dic15D411yescharacteristic
51C2×C4×D15—21no—
52C2×C4×D15—21no—
53C2×C4×D15—21no—
54C2×C4×D15—21no—
55C2×C4×D15C2×C412yes—
56C2×C4×D15D412yes—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4D412yescomplemented
62#6719—24no—
63#6714—24no—
64C4⋊Dic15—21no—
65C4⋊Dic15—21no—
66C4⋊Dic15C2×C412yes—
67C4⋊Dic15D412yescomplemented
68C4×Dic15—24no—
69C2×C3⋊#168—21no—
70C2×C3⋊#168—21no—
71C2×C3⋊#168—21no—
72C2×#938—51no—
73C2×#892—51no—
74C2×C3×#102D511yescharacteristic, complemented
75C2×#832—51no—
76C2×(C2×D3)⋊C8—51no—
77#4551—51no—
78#4529—51no—
79C22×C5×D4C2×D311yescharacteristic
80C22×C22⋊D5—61no—
81C22×C4×D5—31no—
82C22×C5×C8C2×D311yescharacteristic
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×C22⋊Dic5—61no—
85#4084—34no—
86#4084—62no—
87C2×#685—61no—
88C2×C4⋊Dic5—31no—
89C2×C4⋊Dic5—31no—
90C2×C4×Dic5—61no—
91C22×#168—31no—
92#4038—62no—
93#4038—62no—
94C5×#102—22no—
95#3964—62no—
96#3952—62no—
97#1875—151noSylow
98C23×C3×C5—22no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5C2×D411yescharacteristic
106C22×D15—21no—
107C22×D15—21no—
108C22×D15—21no—
109C22×D15—21no—
110C22×D15—21no—
111C22×D15—21no—
112C22×D15C22⋊C412yes—
113C3×C5×D4—22no—
114C3×C5×D4—22no—
115C3×C5×D4—41no—
116C3×C5×D4—41no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5C22×C411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5#4111yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126#1220—48no—
127C2×Dic15—21no—
128C2×Dic15—21no—
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×Dic15—41no—
132C2×Dic15—41no—
133C2×Dic15—41no—
134C2×Dic15—41no—
135C2×Dic15C22⋊C412yes—
136C4×D15—22no—
137C4×D15—22no—
138C4×D15—22no—
139C4×D15—22no—
140C3×C5×C8—41no—
141C3⋊#168—41no—
142C22×C3×D4C2×D511yescharacteristic
143C22×#67—101no—
144C22×C4×D3—51no—
145C22×C3×C8C2×D511yescharacteristic
146C2×C3×C4⋊C4C2×D511yescharacteristic
147C2×#217—101no—
148#938—54no—
149#938—102no—
150C2×(C2×D3)⋊C4—101no—
151C2×C4⋊Dic3—51no—
152C2×C4⋊Dic3—51no—
153C2×C4×Dic3—101no—
154C22×C3⋊C8—51no—
155#892—102no—
156#892—102no—
157C3×#102—22no—
158#832—102no—
159(C2×D3)⋊C8—102no—
160C24×C5—21no—
161C23×D5—31no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4C4×D312yes—
168C22×C4×C5—21no—
169C22×C4×C5C22×D311yescharacteristic
170C2×C22⋊D5—64no—
171C2×C22⋊D5—122no—
172C2×C22⋊D5—122no—
173C22×Dic5—31no—
174C22×Dic5—61no—
175C22×Dic5—61no—
176C2×C4×D5—32no—
177C2×C4×D5—32no—
178C2×C4×D5—61no—
179C2×C4×D5—61no—
180C2×C4×D5—61no—
181C2×C4×D5—61no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4#6712yescomplemented
187C22⋊Dic5—64no—
188#685—64no—
189C4⋊Dic5—32no—
190C4⋊Dic5—32no—
191C4⋊Dic5—61no—
192C4⋊Dic5—61no—
193C4×Dic5—64no—
194C2×#168—61no—
195C2×#168—61no—
196C2×#168—61no—
197C2×#121—151no—
198C2×#117—151no—
199C2×#102—151no—
200C2×#102D1511yescharacteristic, complemented
201C2×C22⋊C8—151no—
202#340—151no—
203#340—151no—
204C22×C3×C5—42no—
205C22×C3×C5—42no—
206C22×C3×C5—42no—
207C22×C3×C5—81no—
208C22×C3×C5—81no—
209C22×C3×C5—81no—
210C22×C3×C5—81no—
211C22×C3×C5C2×C22⋊C411yescharacteristic
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12311yescharacteristic
214C22×C3×C5#13511yescharacteristic
215C22×C3×C5#13511yescharacteristic
216C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
217C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
218C2×D15—22no—
219C2×D15—22no—
220C2×D15—22no—
221C2×D15—41no—
222C2×D15—41no—
223C2×D15—41no—
224C2×D15—41no—
225C3×C4×C5—42no—
226C3×C4×C5C4×D411yescharacteristic
227C3×C4×C5C4×D411yescharacteristic
228C3×C4×C5#12111yescharacteristic
229C3×C4×C5#12111yescharacteristic
230Dic15—22no—
231Dic15—42no—
232Dic15—42no—
233C24×C3—21no—
234C23×D3—51no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4C4×D512yes—
241C22×C3×C4—21no—
242C22×C3×C4C22×D511yescharacteristic
243C2×#67—104no—
244C2×#67—202no—
245C2×#67—202no—
246C22×Dic3—51no—
247C22×Dic3—101no—
248C22×Dic3—101no—
249C2×C4×D3—52no—
250C2×C4×D3—52no—
251C2×C4×D3—101no—
252C2×C4×D3—101no—
253C2×C4×D3—101no—
254C2×C4×D3—101no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4C22⋊D512yescomplemented
260#217—104no—
261(C2×D3)⋊C4—104no—
262C4⋊Dic3—52no—
263C4⋊Dic3—52no—
264C4⋊Dic3—101no—
265C4⋊Dic3—101no—
266C4×Dic3—104no—
267C2×C3⋊C8—101no—
268C2×C3⋊C8—101no—
269C2×C3⋊C8—101no—
270C23×C5—22no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5D3×D411yescharacteristic
278C22×D5—32no—
279C22×D5—61no—
280C22×D5—61no—
281C22×D5—61no—
282C22×D5—61no—
283C22×D5—61no—
284C22×D5—61no—
285C5×D4—22no—
286C5×D4—22no—
287C5×D4—41no—
288C5×D4—41no—
289C2×C4×C5—22no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5C2×C4×D311yescharacteristic
293C2×C4×C5#23511yescharacteristic
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5#23711yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C22⋊D5—128no—
299C2×Dic5—32no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—121no—
305C2×Dic5—121no—
306C2×Dic5—121no—
307C2×Dic5—121no—
308C4×D5—62no—
309C4×D5—62no—
310C4×D5—62no—
311C4×D5—62no—
312C5×C8—41no—
313#168—121no—
314C22×D4—301no—
315C22×D4C2×D1511yescharacteristic
316C23×C4—151no—
317C22×C8—151no—
318C22×C8C2×D1511yescharacteristic
319#121—154no—
320#121—302no—
321#117—302no—
322#117—302no—
323C2×C4⋊C4—151no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4C2×D1511yescharacteristic
326C2×C22⋊C4—301no—
327C2×C22⋊C4—301no—
328C2×C42—301no—
329#102—22no—
330#102—302no—
331C22⋊C8—302no—
332C2×C3×C5—82no—
333C2×C3×C5#38611yescharacteristic
334C2×C3×C5#41611yescharacteristic
335C2×C3×C5#41811yescharacteristic
336C2×C3×C5#44911yescharacteristic
337C2×C3×C5#44911yescharacteristic
338C2×C3×C5#48211yescharacteristic
339C2×C3×C5#48211yescharacteristic
340D15—42no—
341C23×C3—22no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3D4×D511yescharacteristic
349C22×D3—52no—
350C22×D3—101no—
351C22×D3—101no—
352C22×D3—101no—
353C22×D3—101no—
354C22×D3—101no—
355C22×D3—101no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—41no—
359C3×D4—41no—
360C2×C3×C4—22no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4C2×C4×D511yescharacteristic
364C2×C3×C4#70911yescharacteristic
365C2×C3×C4D4×D511yescharacteristic
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4#71111yescharacteristic
368C2×C3×C4C2×C22⋊D511yescharacteristic
369#67—208no—
370C2×Dic3—52no—
371C2×Dic3—101no—
372C2×Dic3—101no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—201no—
376C2×Dic3—201no—
377C2×Dic3—201no—
378C2×Dic3—201no—
379C4×D3—102no—
380C4×D3—102no—
381C4×D3—102no—
382C4×D3—102no—
383C3×C8—41no—
384C3⋊C8—201no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5—42no—
388C22×C5—81no—
389C22×C5—81no—
390C22×C5—81no—
391C22×C5—81no—
392C22×C5D3×C22⋊C411yescharacteristic
393C22×C5#88311yescharacteristic
394C22×C5#91111yescharacteristic
395C22×C5#91211yescharacteristic
396C22×C5#91411yescharacteristic
397C22×C5#91611yescharacteristic
398C22×C5#93711yescharacteristic
399C2×D5—62no—
400C2×D5—62no—
401C2×D5—62no—
402C2×D5—121no—
403C2×D5—121no—
404C2×D5—121no—
405C2×D5—121no—
406C4×C5—42no—
407C4×C5#67⋊C411yescharacteristic
408C4×C5#88411yescharacteristic
409C4×C5C4×#6711yescharacteristic
410C4×C5#93811yescharacteristic
411Dic5—62no—
412Dic5—122no—
413Dic5—122no—
414C24—21no—
415C24—151no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—304no—
422C2×D4—602no—
423C2×D4—602no—
424C2×D4C4×D1512yes—
425C22×C4—21no—
426C22×C4—151no—
427C22×C4—152no—
428C22×C4—152no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4—301no—
432C22×C4—301no—
433C22×C4—301no—
434C22×C4—301no—
435C22×C4C22×D1511yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—301no—
440C2×C8—301no—
441C2×C8—301no—
442C4⋊C4—21no—
443C4⋊C4—152no—
444C4⋊C4—152no—
445C4⋊C4—301no—
446C4⋊C4—301no—
447C4⋊C4#122012yescomplemented
448C22⋊C4—304no—
449C22⋊C4—304no—
450C42—304no—
451C3×C5#187511yescharacteristic, complemented, Hall
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3D5×C22⋊C411yescharacteristic
460C22×C3#402911yescharacteristic
461C22×C3#405711yescharacteristic
462C22×C3#405811yescharacteristic
463C22×C3#406011yescharacteristic
464C22×C3#406211yescharacteristic
465C22×C3#408311yescharacteristic
466C2×D3—102no—
467C2×D3—102no—
468C2×D3—102no—
469C2×D3—201no—
470C2×D3—201no—
471C2×D3—201no—
472C2×D3—201no—
473C3×C4—42no—
474C3×C4#402711yescharacteristic
475C3×C4#403011yescharacteristic
476C3×C4C4×C22⋊D511yescharacteristic
477C3×C4#408411yescharacteristic
478Dic3—102no—
479Dic3—202no—
480Dic3—202no—
481C2×C5—82no—
482C2×C5#477011yescharacteristic
483C2×C5#477211yescharacteristic
484C2×C5#477911yescharacteristic
485C2×C5#478411yescharacteristic
486C2×C5#495611yescharacteristic
487C2×C5#515811yescharacteristic
488C2×C5#517211yescharacteristic
489D5—122no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—152no—
498C23—301no—
499C23—301no—
500C23—301no—
501C23—301no—
502C23—301no—
503C23—301no—
504C23D4×D1511yescharacteristic
505D4—22no—
506D4—22no—
507D4—41no—
508D4—41no—
509D4—608no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—152no—
514C2×C4—301no—
515C2×C4—301no—
516C2×C4—302no—
517C2×C4—302no—
518C2×C4—302no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—601no—
523C2×C4—601no—
524C2×C4—601no—
525C2×C4—601no—
526C2×C4C2×C4×D1511yescharacteristic
527C2×C4#681711yescharacteristic
528C2×C4D4×D1511yescharacteristic
529C2×C4D4×D1511yescharacteristic
530C2×C4#681911yescharacteristic
531C2×C4C2×#122011yescharacteristic
532C8—41no—
533C8—601no—
534C2×C3—82no—
535C2×C3#6505911yescharacteristic
536C2×C3#6506111yescharacteristic
537C2×C3#6506811yescharacteristic
538C2×C3#6507311yescharacteristic
539C2×C3#6524511yescharacteristic
540C2×C3#6544711yescharacteristic
541C2×C3#6546111yescharacteristic
542D3—202no—
543C5#7020111yescharacteristic, complemented, Sylow
544C22—42no—
545C22—42no—
546C22—42no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—302no—
552C22—302no—
553C22—302no—
554C22—601no—
555C22—601no—
556C22—601no—
557C22—601no—
558C22C22⋊C4×D1511yescharacteristic
559C22#9177211yescharacteristic
560C22#9180011yescharacteristic
561C22#9180111yescharacteristic
562C22#9180311yescharacteristic
563C22#9180511yescharacteristic
564C22#9182611yescharacteristic
565C4—42no—
566C4—302no—
567C4—602no—
568C4—602no—
569C4#9177011yescharacteristic
570C4#9177311yescharacteristic
571C4C4×#122011yescharacteristic
572C4#9182711yescharacteristic
573C3#1060099411yescharacteristic, complemented, Sylow
574C2—82no—
575C2—602no—
576C2#1175087111yescharacteristic
577C2#1175087311yescharacteristic
578C2#1175088011yescharacteristic
579C2#1175088511yescharacteristic
580C2#1175105711yescharacteristic
581C2#1175125911yescharacteristic
582C2#1175127311yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×#91827C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#102D15
hypocenterC3×C5#1875
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#91781C2semidirect
3. C2×C3×C5×#102C2semidirect
4. C2×#91116C2semidirect
5. C2×#91104C2semidirect
6. #11746372C2semidirect
7. #11746350C2semidirect
16. #91827C4semidirect
30. C2×C5×#102D3semidirect
61. C3×C5×C4⋊C4D4semidirect
67. C4⋊Dic15D4semidirect
74. C2×C3×#102D5semidirect
186. C5×C4⋊C4#67semidirect
200. C2×#102D15semidirect
259. C3×C4⋊C4C22⋊D5semidirect
447. C4⋊C4#1220semidirect
451. C3×C5#1875semidirect
543. C5#70201semidirect
573. C3#10600994semidirect

Maximal subgroups

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

subgroupindex
C2×#918272
C2×#917812
C2×C3×C5×#1022
C2×#911162
C2×#911042
#117463722
#117463502
#106009943
#702015