Finite Group Databasebeta

← #14435435

Subgroups — #14435435

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756450C211yesmaximal, characteristic
2C4×Q8×D15C211yesmaximal, characteristic, complemented
3C3×C5×#479C211yesmaximal, characteristic, complemented
4#11751164C211yesmaximal, characteristic, complemented
5#11751129C211yesmaximal, characteristic, complemented
6#11750990C211yesmaximal, characteristic, complemented
7#11750985C211yesmaximal, characteristic, complemented
8#11750964C211yesmaximal, characteristic
9#11750954C211yesmaximal, characteristic, complemented
10#11750946C211yesmaximal, characteristic, complemented
11#11750936C211yesmaximal, characteristic, complemented
12#11750918C211yesmaximal, characteristic, complemented
13#11750910C211yesmaximal, characteristic, complemented
14#11750907C211yesmaximal, characteristic
15#11750890C211yesmaximal, characteristic, complemented
16#10612938—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21C2×#6718C2211yescharacteristic
22C2×#6717C2211yescharacteristic
23C2×Dic60C2211yescharacteristic
24C2×#6706C2211yescharacteristic
25#91787—21no—
26#91786C2211yescharacteristic
27#91784C2211yescharacteristic
28#91783—21no—
29#91782—21no—
30#91782C2211yescharacteristic
31#91781—21no—
32C4⋊C4×D15—21no—
33C4⋊C4×D15C2211yescharacteristic
34#91776—21no—
35#91776C2211yescharacteristic
36#91776C2211yescharacteristic
37#91764C2211yescharacteristic
38C42×D15—21no—
39C42×D15C2211yescharacteristic
40C4×Dic30—21no—
41C4×Dic30C2211yescharacteristic
42C3×C5×#107C2211yescharacteristic
43C3×C5×#106C2211yescharacteristic
44C3×C5×C4⋊C8C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47#91105C2211yescharacteristic
48#91104C2211yescharacteristic
49#91104C2211yescharacteristic
50#91100C2211yescharacteristic
51#91099C2211yescharacteristic
52#91099C2211yescharacteristic
53#91094C2211yescharacteristic
54#91094C2211yescharacteristic
55#91094C2211yescharacteristic
56#91093C2211yescharacteristic
57#91092C2211yescharacteristic
58#91091C2211yescharacteristic
59C4⋊(C3⋊#168)C2211yescharacteristic
60#81207—51nomaximal, Hall
61#66025—31no—
62C4×Q8×D5—31no—
63C5×#479D311yescharacteristic, complemented
64#65352—31no—
65#65317—31no—
66#65178—31no—
67#65173—31no—
68#65152—31no—
69#65142—31no—
70#65134—31no—
71#65124—31no—
72#65106—31no—
73#65097—31no—
74#65095—31no—
75#65078—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77Q8×D15—22no—
78Q8×D15—22no—
79C2×D60—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C4×D15—21no—
83C2×C4×D15—21no—
84C2×C4×D15D411yescharacteristic
85C2×C4×D15D411yescharacteristic
86C2×C4×D15C2311yescharacteristic
87C2×Dic30—21no—
88C2×Dic30C2311yescharacteristic
89C2×Dic30C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C42×C5—21no—
99C3×C42×C5C2311yescharacteristic
100#6718—22no—
101#6717—22no—
102#6714—21no—
103#6714—21no—
104#6714—21no—
105#6714—21no—
106#6714—21no—
107C4⋊Dic15—21no—
108C4⋊Dic15—21no—
109C4⋊Dic15C2311yescharacteristic
110#6712—21no—
111#6712—21no—
112#6712—21no—
113#6712—21no—
114C4×Dic15—21no—
115C4×Dic15—21no—
116C4×Dic15—21no—
117C4×Dic15—21no—
118C4×Dic15D411yescharacteristic
119C4×Dic15D411yescharacteristic
120C4×Dic15C2311yescharacteristic
121C2×C3⋊#168C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123Dic60—22no—
124#6706—22no—
125#5691—51no—
126C4×D3×Q8—51no—
127C3×#479D511yescharacteristic, complemented
128#5063—51no—
129#5028—51no—
130#4889—51no—
131#4884—51no—
132#4863—51no—
133#4853—51no—
134#4845—51no—
135#4835—51no—
136#4817—51no—
137#4809—51no—
138#4806—51no—
139#4789—51no—
140C2×Q8×D5—31no—
141C5×#125C2×D311yescharacteristic
142C4×C5×Q8C2×D311yescharacteristic
143Q8×Dic5—31no—
144C2×#689—31no—
145C2×#688—31no—
146C2×Dic20—31no—
147C2×#677—31no—
148#4044—61no—
149#4043—31no—
150#4041—31no—
151#4040—61no—
152#4039—31no—
153#4039—61no—
154#4038—61no—
155D5×C4⋊C4—31no—
156D5×C4⋊C4—61no—
157#4033—31no—
158#4033—31no—
159#4033—61no—
160#4021—31no—
161C42×D5—31no—
162C42×D5—61no—
163C4×Dic10—31no—
164C4×Dic10—61no—
165C5×#107C2×D311yescharacteristic
166C5×#106C2×D311yescharacteristic
167C5×C4⋊C8C2×D311yescharacteristic
168C5×#103C2×D311yescharacteristic
169C5×#103C2×D311yescharacteristic
170#3953—31no—
171#3952—31no—
172#3952—31no—
173#3948—31no—
174#3947—31no—
175#3947—31no—
176#3942—31no—
177#3942—31no—
178#3942—31no—
179#3941—31no—
180#3940—31no—
181#3939—31no—
182C4⋊#168—31no—
183#3117—151noSylow
184C22×D15—21no—
185C22×D15C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15C2×D411yescharacteristic
199C2×Dic15C2×D411yescharacteristic
200C2×Dic15C2×D411yescharacteristic
201D60—21no—
202D60—21no—
203D60—42no—
204C4×D15—24no—
205C4×D15—22no—
206C4×D15—21no—
207C4×D15—21no—
208C4×D15—41no—
209C4×D15—42no—
210C4×D15—42no—
211Dic30—24no—
212Dic30—21no—
213Dic30—21no—
214Dic30—21no—
215Dic30#4112yes—
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C3⋊#168—21no—
219C3⋊#168—21no—
220C2×D3×Q8—51no—
221C3×#125C2×D511yescharacteristic
222C3×C4×Q8C2×D511yescharacteristic
223Q8×Dic3—51no—
224C2×#216—51no—
225C2×#215—51no—
226C2×Dic12—51no—
227C2×#204—51no—
228#898—101no—
229#897—51no—
230#895—51no—
231#894—101no—
232#893—51no—
233#893—101no—
234#892—101no—
235D3×C4⋊C4—51no—
236D3×C4⋊C4—101no—
237#887—51no—
238#887—51no—
239#887—101no—
240#875—51no—
241C42×D3—51no—
242C42×D3—101no—
243C4×Dic6—51no—
244C4×Dic6—101no—
245C3×#107C2×D511yescharacteristic
246C3×#106C2×D511yescharacteristic
247C3×C4⋊C8C2×D511yescharacteristic
248C3×#103C2×D511yescharacteristic
249C3×#103C2×D511yescharacteristic
250#821—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
253#816—51no—
254#815—51no—
255#815—51no—
256#810—51no—
257#810—51no—
258#810—51no—
259#809—51no—
260#808—51no—
261#807—51no—
262C4⋊(C3⋊C8)—51no—
263C2×C5×Q8C22×D311yescharacteristic
264Q8×D5—62no—
265Q8×D5—62no—
266C2×D20—31no—
267C2×D20—61no—
268C2×C4×D5—31no—
269C2×C4×D5—31no—
270C2×C4×D5—31no—
271C2×C4×D5—61no—
272C2×C4×D5—61no—
273C2×C4×D5—61no—
274C2×Dic10—31no—
275C2×Dic10—31no—
276C2×Dic10—61no—
277C2×C5×C8C22×D311yescharacteristic
278C2×C5×C8C22×D311yescharacteristic
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4C22×D311yescharacteristic
283C5×C4⋊C4C22×D311yescharacteristic
284C5×C4⋊C4C22×D311yescharacteristic
285C42×C5—21no—
286C42×C5C22×D311yescharacteristic
287#689—62no—
288#688—62no—
289#685—61no—
290#685—61no—
291#685—61no—
292#685—61no—
293#685—61no—
294C4⋊Dic5—31no—
295C4⋊Dic5—61no—
296C4⋊Dic5—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301C4×Dic5—31no—
302C4×Dic5—31no—
303C4×Dic5—31no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C4×Dic5—61no—
307C4×Dic5—61no—
308C2×#168—31no—
309C2×#168—31no—
310Dic20—62no—
311#677—62no—
312#529—151no—
313C2×C4×Q8—151no—
314#484—151no—
315#481—151no—
316#479—151no—
317#479D1511yescharacteristic, complemented
318#464—151no—
319#464—151no—
320#451—151no—
321#448—151no—
322#441—151no—
323#441—151no—
324#440—151no—
325#440—151no—
326#432—151no—
327C22×C3×C5C22×D411yescharacteristic
328C2×D15—21no—
329C2×D15—21no—
330C2×D15—41no—
331C2×D15—41no—
332C2×D15—41no—
333C2×D15#13712yes—
334C3×C4×C5—22no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5—41no—
340C3×C4×C5C2×#4111yescharacteristic
341C3×C4×C5C2×#4111yescharacteristic
342Dic15—21no—
343Dic15—22no—
344Dic15—21no—
345Dic15—21no—
346Dic15—41no—
347Dic15—41no—
348C2×C3×Q8C22×D511yescharacteristic
349D3×Q8—102no—
350D3×Q8—102no—
351C2×D12—51no—
352C2×D12—101no—
353C2×C4×D3—51no—
354C2×C4×D3—51no—
355C2×C4×D3—51no—
356C2×C4×D3—101no—
357C2×C4×D3—101no—
358C2×C4×D3—101no—
359C2×Dic6—51no—
360C2×Dic6—51no—
361C2×Dic6—101no—
362C2×C3×C8C22×D511yescharacteristic
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C4⋊C4C22×D511yescharacteristic
369C3×C4⋊C4C22×D511yescharacteristic
370C3×C42—21no—
371C3×C42C22×D511yescharacteristic
372#216—102no—
373#215—102no—
374(C2×D3)⋊C4—101no—
375(C2×D3)⋊C4—101no—
376(C2×D3)⋊C4—101no—
377(C2×D3)⋊C4—101no—
378(C2×D3)⋊C4—101no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386C4×Dic3—51no—
387C4×Dic3—51no—
388C4×Dic3—51no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C4×Dic3—101no—
392C4×Dic3—101no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395Dic12—102no—
396#204—102no—
397C22×D5—31no—
398C22×D5—61no—
399C5×Q8—21no—
400C5×Q8#23912yes—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5D3×D411yescharacteristic
406C2×C4×C5D3×D411yescharacteristic
407C2×C4×C5C23×D311yescharacteristic
408C2×Dic5—31no—
409C2×Dic5—31no—
410C2×Dic5—31no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414D20—61no—
415D20—61no—
416D20—122no—
417C4×D5—62no—
418C4×D5—64no—
419C4×D5—61no—
420C4×D5—61no—
421C4×D5—121no—
422C4×D5—122no—
423C4×D5—122no—
424Dic10—32no—
425Dic10—64no—
426Dic10—61no—
427Dic10—61no—
428Dic10—61no—
429C5×C8—21no—
430C5×C8—21no—
431#168—61no—
432#168—61no—
433C22×Q8—151no—
434C2×Q16—151no—
435C2×Q16—151no—
436C2×SD16—151no—
437C2×SD16—151no—
438#126—301no—
439#125C2×D1511yescharacteristic
440#124—151no—
441#123—301no—
442C22⋊Q8—151no—
443#121—151no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×Q8—151no—
447C4×Q8—151no—
448C4×Q8—301no—
449C4×Q8—301no—
450C4×Q8C2×D1511yescharacteristic
451C4×D4—151no—
452C4×D4—301no—
453#117—301no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—301no—
456C2×C42—151no—
457C2×C42—301no—
458#107—151no—
459#107C2×D1511yescharacteristic
460#106—151no—
461#106C2×D1511yescharacteristic
462C4⋊C8—151no—
463C4⋊C8C2×D1511yescharacteristic
464#103—151no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103C2×D1511yescharacteristic
469#103C2×D1511yescharacteristic
470#102—151no—
471#102—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474#97—151no—
475#97—151no—
476C2×C3×C5#52511yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5#57511yescharacteristic
479D15—22no—
480D15—81no—
481C22×D3—51no—
482C22×D3—101no—
483C3×Q8—21no—
484C3×Q8#71312yes—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4D4×D511yescharacteristic
490C2×C3×C4D4×D511yescharacteristic
491C2×C3×C4C23×D511yescharacteristic
492C2×Dic3—51no—
493C2×Dic3—51no—
494C2×Dic3—51no—
495C2×Dic3—101no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498D12—101no—
499D12—101no—
500D12—202no—
501C4×D3—102no—
502C4×D3—104no—
503C4×D3—101no—
504C4×D3—101no—
505C4×D3—201no—
506C4×D3—202no—
507C4×D3—202no—
508Dic6—52no—
509Dic6—104no—
510Dic6—101no—
511Dic6—101no—
512Dic6—101no—
513C3×C8—21no—
514C3×C8—21no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5C2×D3×D411yescharacteristic
518C2×D5—32no—
519C2×D5—61no—
520C2×D5—61no—
521C2×D5—121no—
522C2×D5—121no—
523C2×D5—121no—
524C4×C5—21no—
525C4×C5—21no—
526C4×C5—22no—
527C4×C5—41no—
528C4×C5—41no—
529C4×C5—41no—
530C4×C5C2×#23911yescharacteristic
531C4×C5D3×#4111yescharacteristic
532Dic5—61no—
533Dic5—61no—
534Dic5—62no—
535Dic5—61no—
536Dic5—121no—
537Dic5—121no—
538C2×Q8—151no—
539C2×Q8—151no—
540C2×Q8—301no—
541C2×Q8—302no—
542C2×Q8—302no—
543C2×Q8C22×D1511yescharacteristic
544C2×D4—151no—
545C2×D4—301no—
546C22×C4—151no—
547C22×C4—151no—
548C22×C4—151no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4—301no—
552Q16—302no—
553Q16—302no—
554SD16—302no—
555SD16—302no—
556C2×C8—151no—
557C2×C8—151no—
558C2×C8C22×D1511yescharacteristic
559C2×C8C22×D1511yescharacteristic
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4C22×D1511yescharacteristic
571C4⋊C4C22×D1511yescharacteristic
572C4⋊C4C22×D1511yescharacteristic
573C22⋊C4—301no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C22⋊C4—301no—
577C22⋊C4—301no—
578C42—21no—
579C42—151no—
580C42—151no—
581C42—151no—
582C42—301no—
583C42—301no—
584C42—301no—
585C42—301no—
586C42C22×D1511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3C2×D4×D511yescharacteristic
589C2×D3—52no—
590C2×D3—101no—
591C2×D3—101no—
592C2×D3—201no—
593C2×D3—201no—
594C2×D3—201no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—22no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4C2×#71311yescharacteristic
602C3×C4D5×#4111yescharacteristic
603Dic3—101no—
604Dic3—101no—
605Dic3—102no—
606Dic3—101no—
607Dic3—201no—
608Dic3—201no—
609C2×C5#562711yescharacteristic
610C2×C5#576811yescharacteristic
611C2×C5D3×#13711yescharacteristic
612D5—62no—
613D5—241no—
614C23—151no—
615C23—301no—
616Q8—21no—
617Q8—152no—
618Q8—304no—
619Q8—301no—
620Q8—301no—
621Q8—301no—
622Q8#682112yes—
623D4—301no—
624D4—301no—
625D4—602no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—151no—
631C2×C4—151no—
632C2×C4—151no—
633C2×C4—302no—
634C2×C4—304no—
635C2×C4—301no—
636C2×C4—301no—
637C2×C4—301no—
638C2×C4—301no—
639C2×C4—301no—
640C2×C4—601no—
641C2×C4—602no—
642C2×C4—602no—
643C2×C4D4×D1511yescharacteristic
644C2×C4D4×D1511yescharacteristic
645C2×C4C23×D1511yescharacteristic
646C8—21no—
647C8—21no—
648C8—301no—
649C8—301no—
650C2×C3#6596111yescharacteristic
651C2×C3#6610211yescharacteristic
652C2×C3D5×#13711yescharacteristic
653D3—102no—
654D3—401no—
655C5#8120711yescharacteristic, complemented, Sylow
656C22—152no—
657C22—301no—
658C22—301no—
659C22—601no—
660C22—601no—
661C22—601no—
662C22C2×D4×D1511yescharacteristic
663C4—22no—
664C4—21no—
665C4—21no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—301no—
670C4—302no—
671C4—301no—
672C4—301no—
673C4—601no—
674C4—601no—
675C4C2×#682111yescharacteristic
676C4#41×D1511yescharacteristic
677C3#1061293811yescharacteristic, complemented, Sylow
678C2—302no—
679C2—1201no—
680C2#1175638611yescharacteristic
681C2#1175652711yescharacteristic
682C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#479C2
socleC22×C3×C5C22×D4
prime radical#91784C22
hypercenter#479D15
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D15C2semidirect
3. C3×C5×#479C2semidirect
4. #11751164C2semidirect
5. #11751129C2semidirect
6. #11750990C2semidirect
7. #11750985C2semidirect
9. #11750954C2semidirect
10. #11750946C2semidirect
11. #11750936C2semidirect
12. #11750918C2semidirect
13. #11750910C2semidirect
15. #11750890C2semidirect
63. C5×#479D3semidirect
127. C3×#479D5semidirect
317. #479D15semidirect
587. C3×C5#3117semidirect
655. C5#81207semidirect
677. C3#10612938semidirect

Maximal subgroups

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

subgroupindex
#117564502
C4×Q8×D152
C3×C5×#4792
#117511642
#117511292
#117509902
#117509852
#117509642
#117509542
#117509462
#117509362
#117509182
#117509102
#117509072
#117508902
#106129383
#812075