Finite Group Databasebeta

← #14307476

Subgroups — #14307476

Order 1920.

648 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×#91767C211yesmaximal, characteristic
2#11751043C211yesmaximal, characteristic
3C22⋊C4×Dic15C211yesmaximal, characteristic
4C3×C5×#342C211yesmaximal, characteristic
5#11746348C211yesmaximal, characteristic
6#11746348C211yesmaximal, characteristic
7#11746347C211yesmaximal, characteristic
8#10599748—31nomaximal, Hall
9C23×Dic15C2211yescharacteristic
10C22×Dic30C411yescharacteristic, complemented
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×#6719C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C2×C4⋊Dic15C411yescharacteristic, complemented
18C2×#6712—21no—
19C2×#6712C411yescharacteristic, complemented
20C2×#6712C411yescharacteristic, complemented
21C2×C4×Dic15—21no—
22#91767—21no—
23#91767—21no—
24#91767—21no—
25#91767—21no—
26#91115—21no—
27#91115—21no—
28#68955—51nomaximal, Hall
29C2×#4024—31no—
30#65231—31no—
31C22⋊C4×Dic5—31no—
32C5×#342D311yescharacteristic
33#64747—31no—
34#64747—31no—
35#64746—31no—
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×Dic15—21no—
42C22×Dic15—21no—
43C22×Dic15—42no—
44C22×Dic15C2×C411yescharacteristic
45C22×Dic15C2×C411yescharacteristic
46C22×Dic15C2×C411yescharacteristic
47C22×Dic15C2×C411yescharacteristic
48C22×Dic15D411yescharacteristic
49C22×Dic15D411yescharacteristic
50C22×Dic15D411yescharacteristic
51C22×Dic15D411yescharacteristic
52C2×Dic30—21no—
53C2×Dic30—21no—
54C2×Dic30—42no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4Q812yescomplemented
61#6719—21no—
62#6719—21no—
63#6719—21no—
64#6719—21no—
65#6719—21no—
66#6719Q812yescomplemented
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69#6712—21no—
70#6712—21no—
71#6712—21no—
72#6712—21no—
73#6712—42no—
74C4×Dic15—42no—
75C2×#878—51no—
76#4942—51no—
77Dic3×C22⋊C4—51no—
78C3×#342D511yescharacteristic
79#4527—51no—
80#4527—51no—
81#4526—51no—
82C23×Dic5—31no—
83C22×Dic10—31no—
84C2×C5×C22⋊C4C2×D311yescharacteristic
85C2×C5×C22⋊C4C2×D311yescharacteristic
86C2×C5×C22⋊C4C2×D311yescharacteristic
87C2×C22⋊Dic5—31no—
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5—31no—
90C2×C4⋊Dic5—31no—
91C2×#683—31no—
92C2×#683—31no—
93C2×#683—61no—
94C2×C4×Dic5—61no—
95#4024—61no—
96#4024—61no—
97#4024—61no—
98#4024—61no—
99#3963—61no—
100#3963—61no—
101#1996—151noSylow
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×Q811yescharacteristic
108C23×C3×C5C2×Q811yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5—41no—
121C2×Dic15—22no—
122C2×Dic15—22no—
123C2×Dic15—22no—
124C2×Dic15—21no—
125C2×Dic15—21no—
126C2×Dic15—22no—
127C2×Dic15—41no—
128C2×Dic15—41no—
129C2×Dic15—41no—
130C2×Dic15—41no—
131C2×Dic15—41no—
132C2×Dic15—41no—
133C2×Dic15—41no—
134C2×Dic15—41no—
135C2×Dic15—41no—
136C2×Dic15—41no—
137C2×Dic15C22⋊C411yescharacteristic
138C2×Dic15C22⋊C411yescharacteristic
139C2×Dic15C22⋊C411yescharacteristic
140C2×Dic15C22⋊C411yescharacteristic
141Dic30—42no—
142Dic30—42no—
143C23×Dic3—51no—
144C22×Dic6—51no—
145C2×C3×C22⋊C4C2×D511yescharacteristic
146C2×C3×C22⋊C4C2×D511yescharacteristic
147C2×C3×C22⋊C4C2×D511yescharacteristic
148C2×#217—51no—
149C2×#217—51no—
150C2×#217—51no—
151C2×C4⋊Dic3—51no—
152C2×Dic3⋊C4—51no—
153C2×Dic3⋊C4—51no—
154C2×Dic3⋊C4—101no—
155C2×C4×Dic3—101no—
156#878—101no—
157#878—101no—
158#878—101no—
159#878—101no—
160C3⋊#95—101no—
161C3⋊#95—101no—
162C24×C5C22×D311yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5C4×D311yescharacteristic
166C22×C4×C5C4×D311yescharacteristic
167C22×Dic5—31no—
168C22×Dic5—31no—
169C22×Dic5—31no—
170C22×Dic5—31no—
171C22×Dic5—31no—
172C22×Dic5—31no—
173C22×Dic5—31no—
174C22×Dic5—31no—
175C22×Dic5—61no—
176C22×Dic5—61no—
177C22×Dic5—122no—
178C2×Dic10—61no—
179C2×Dic10—61no—
180C2×Dic10—122no—
181C5×C22⋊C4—21no—
182C5×C22⋊C4—21no—
183C5×C22⋊C4—21no—
184C5×C22⋊C4—21no—
185C5×C22⋊C4—21no—
186C5×C22⋊C4Dic612yescomplemented
187C22⋊Dic5—32no—
188C22⋊Dic5—61no—
189C22⋊Dic5—61no—
190C22⋊Dic5—61no—
191C22⋊Dic5—61no—
192C22⋊Dic5—61no—
193C4⋊Dic5—61no—
194C4⋊Dic5—61no—
195#683—61no—
196#683—61no—
197#683—61no—
198#683—61no—
199#683—122no—
200C4×Dic5—122no—
201C2×C22⋊Q8—151no—
202#380—151no—
203C4×C22⋊C4—151no—
204#342—151no—
205#342—151no—
206#342—151no—
207#342D1511yescharacteristic
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5—21no—
213C22×C3×C5—21no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×Q811yescharacteristic
220C22×C3×C5C4×Q811yescharacteristic
221C22×C3×C5C22⋊Q811yescharacteristic
222C22×C3×C5C22⋊Q811yescharacteristic
223C22×C3×C5#12411yescharacteristic
224C22×C3×C5C4⋊Q811yescharacteristic
225C3×C4×C5—42no—
226C3×C4×C5—41no—
227C3×C4×C5—41no—
228C3×C4×C5—81no—
229Dic15—21no—
230Dic15—21no—
231Dic15—21no—
232Dic15—42no—
233Dic15—41no—
234Dic15—41no—
235Dic15—81no—
236Dic15#9912yes—
237C24×C3C22×D511yescharacteristic
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C4×D511yescharacteristic
241C22×C3×C4C4×D511yescharacteristic
242C22×Dic3—51no—
243C22×Dic3—51no—
244C22×Dic3—51no—
245C22×Dic3—51no—
246C22×Dic3—51no—
247C22×Dic3—51no—
248C22×Dic3—51no—
249C22×Dic3—51no—
250C22×Dic3—101no—
251C22×Dic3—101no—
252C22×Dic3—202no—
253C2×Dic6—101no—
254C2×Dic6—101no—
255C2×Dic6—202no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—21no—
261C3×C22⋊C4Dic1012yescomplemented
262#217—52no—
263#217—101no—
264#217—101no—
265#217—101no—
266#217—101no—
267#217—101no—
268C4⋊Dic3—101no—
269C4⋊Dic3—101no—
270Dic3⋊C4—101no—
271Dic3⋊C4—101no—
272Dic3⋊C4—101no—
273Dic3⋊C4—101no—
274Dic3⋊C4—202no—
275C4×Dic3—202no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5C2×Dic611yescharacteristic
279C23×C5C2×C4×D311yescharacteristic
280C23×C5#23511yescharacteristic
281C23×C5D3×D411yescharacteristic
282C23×C5D3×D411yescharacteristic
283C23×C5#23711yescharacteristic
284C23×C5D3×Q811yescharacteristic
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×Dic5—31no—
296C2×Dic5—31no—
297C2×Dic5—31no—
298C2×Dic5—31no—
299C2×Dic5—62no—
300C2×Dic5—62no—
301C2×Dic5—62no—
302C2×Dic5—61no—
303C2×Dic5—61no—
304C2×Dic5—62no—
305C2×Dic5—121no—
306C2×Dic5—121no—
307C2×Dic5—121no—
308C2×Dic5—121no—
309C2×Dic5—121no—
310C2×Dic5—121no—
311C2×Dic5—121no—
312C2×Dic5—121no—
313C2×Dic5—121no—
314C2×Dic5—121no—
315Dic10—122no—
316Dic10—122no—
317C22×Q8—151no—
318C23×C4—151no—
319C22⋊Q8—301no—
320C22⋊Q8—301no—
321C22⋊Q8—301no—
322C22⋊Q8—301no—
323C2×C4⋊C4—151no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4—151no—
326C2×C4⋊C4—301no—
327C2×C22⋊C4—151no—
328C2×C22⋊C4—151no—
329C2×C22⋊C4—151no—
330C2×C22⋊C4C2×D1511yescharacteristic
331C2×C22⋊C4C2×D1511yescharacteristic
332C2×C22⋊C4C2×D1511yescharacteristic
333C2×C42—301no—
334#95—301no—
335#95—301no—
336C2×C3×C5—21no—
337C2×C3×C5—21no—
338C2×C3×C5—21no—
339C2×C3×C5—21no—
340C2×C3×C5—21no—
341C2×C3×C5—21no—
342C2×C3×C5#39111yescharacteristic
343C2×C3×C5C2×#9911yescharacteristic
344C2×C3×C5#41011yescharacteristic
345C23×C3—41no—
346C23×C3—41no—
347C23×C3C2×Dic1011yescharacteristic
348C23×C3C2×C4×D511yescharacteristic
349C23×C3#70911yescharacteristic
350C23×C3D4×D511yescharacteristic
351C23×C3D4×D511yescharacteristic
352C23×C3#71111yescharacteristic
353C23×C3Q8×D511yescharacteristic
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×Dic3—51no—
365C2×Dic3—51no—
366C2×Dic3—51no—
367C2×Dic3—51no—
368C2×Dic3—102no—
369C2×Dic3—102no—
370C2×Dic3—102no—
371C2×Dic3—101no—
372C2×Dic3—101no—
373C2×Dic3—102no—
374C2×Dic3—201no—
375C2×Dic3—201no—
376C2×Dic3—201no—
377C2×Dic3—201no—
378C2×Dic3—201no—
379C2×Dic3—201no—
380C2×Dic3—201no—
381C2×Dic3—201no—
382C2×Dic3—201no—
383C2×Dic3—201no—
384Dic6—202no—
385Dic6—202no—
386C22×C5—21no—
387C22×C5—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5C4×Dic611yescharacteristic
397C22×C5#87811yescharacteristic
398C22×C5D3×C22⋊C411yescharacteristic
399C22×C5#88511yescharacteristic
400C22×C5#88711yescharacteristic
401C22×C5#88811yescharacteristic
402C22×C5#89611yescharacteristic
403C4×C5—42no—
404C4×C5—41no—
405C4×C5—41no—
406C4×C5—81no—
407Dic5—32no—
408Dic5—61no—
409Dic5—61no—
410Dic5—61no—
411Dic5—122no—
412Dic5—121no—
413Dic5—121no—
414Dic5—241no—
415C24C22×D1511yescharacteristic
416C2×Q8—301no—
417C2×Q8—301no—
418C2×Q8—602no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—151no—
422C22×C4—151no—
423C22×C4—151no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—151no—
428C22×C4—151no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4—602no—
432C22×C4C4×D1511yescharacteristic
433C22×C4C4×D1511yescharacteristic
434C4⋊C4—301no—
435C4⋊C4—301no—
436C4⋊C4—301no—
437C4⋊C4—301no—
438C4⋊C4—301no—
439C4⋊C4—301no—
440C4⋊C4—602no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—152no—
447C22⋊C4—301no—
448C22⋊C4—301no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C22⋊C4—301no—
452C22⋊C4Dic3012yescomplemented
453C42—602no—
454C3×C5#199611yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3C4×Dic1011yescharacteristic
466C22×C3#402411yescharacteristic
467C22×C3D5×C22⋊C411yescharacteristic
468C22×C3#403111yescharacteristic
469C22×C3#403311yescharacteristic
470C22×C3#403411yescharacteristic
471C22×C3#404211yescharacteristic
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—81no—
476Dic3—52no—
477Dic3—101no—
478Dic3—101no—
479Dic3—101no—
480Dic3—202no—
481Dic3—201no—
482Dic3—201no—
483Dic3—401no—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—21no—
489C2×C5—21no—
490C2×C5#464611yescharacteristic
491C2×C5#474011yescharacteristic
492C2×C5D3×#9911yescharacteristic
493C23—41no—
494C23—41no—
495C23C2×Dic3011yescharacteristic
496C23C2×C4×D1511yescharacteristic
497C23#681711yescharacteristic
498C23D4×D1511yescharacteristic
499C23D4×D1511yescharacteristic
500C23#681911yescharacteristic
501C23Q8×D1511yescharacteristic
502Q8—602no—
503Q8—602no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—151no—
515C2×C4—151no—
516C2×C4—151no—
517C2×C4—151no—
518C2×C4—302no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—301no—
522C2×C4—301no—
523C2×C4—302no—
524C2×C4—601no—
525C2×C4—601no—
526C2×C4—601no—
527C2×C4—601no—
528C2×C4—601no—
529C2×C4—601no—
530C2×C4—601no—
531C2×C4—601no—
532C2×C4—601no—
533C2×C4—601no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3#6493511yescharacteristic
541C2×C3#6502911yescharacteristic
542C2×C3D5×#9911yescharacteristic
543C5#6895511yescharacteristic, complemented, Sylow
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22C4×Dic3011yescharacteristic
555C22#9176711yescharacteristic
556C22C22⋊C4×D1511yescharacteristic
557C22#9177411yescharacteristic
558C22#9177611yescharacteristic
559C22#9177711yescharacteristic
560C22#9178511yescharacteristic
561C4—42no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—152no—
566C4—301no—
567C4—301no—
568C4—301no—
569C4—602no—
570C4—601no—
571C4—601no—
572C4—1201no—
573C3#1059974811yescharacteristic, complemented, Sylow
574C2—21no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2#1175074711yescharacteristic
581C2#1175084111yescharacteristic
582C2D15×#9911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC22×C3×C5C2×C22⋊C4
prime radical, cosocleC24×C3×C5C23
hypercenter#342D15
hypocenterC3×C5#1996
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
10. C22×Dic30C4semidirect
17. C2×C4⋊Dic15C4semidirect
19. C2×#6712C4semidirect
20. C2×#6712C4semidirect
60. C3×C5×C22⋊C4Q8semidirect
66. #6719Q8semidirect
186. C5×C22⋊C4Dic6semidirect
261. C3×C22⋊C4Dic10semidirect
452. C22⋊C4Dic30semidirect
454. C3×C5#1996semidirect
543. C5#68955semidirect
573. C3#10599748semidirect

Maximal subgroups

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

subgroupindex
C2×#917672
#117510432
C22⋊C4×Dic152
C3×C5×#3422
#117463482
#117463472
#105997483
#689555