Finite Group Databasebeta

← #14472093

Subgroups — #14472093

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5671C211yesmaximal, characteristic
2#11752465C211yesmaximal, characteristic, complemented
3#11751157C211yesmaximal, characteristic
4C3×#65343C211yesmaximal, characteristic
5#11749333C211yesmaximal, characteristic, complemented
6Dic3×#689C211yesmaximal, characteristic, complemented
7#11749251C211yesmaximal, characteristic, complemented
8#11749187C211yesmaximal, characteristic, complemented
9#11749112C211yesmaximal, characteristic
10Dic3×#687C211yesmaximal, characteristic
11#11749006C211yesmaximal, characteristic
12#11748942C211yesmaximal, characteristic
13C4×#6661C211yesmaximal, characteristic, complemented
14#11746965C211yesmaximal, characteristic, complemented
15#11746857C211yesmaximal, characteristic, complemented
16#10615407—31nomaximal, Hall
17C3×C5×#124C2211yescharacteristic
18#91759C2211yescharacteristic
19C5×Q8×Dic3C2211yescharacteristic
20C5×#944C2211yescharacteristic
21C5×#936C2211yescharacteristic
22C5×D4×Dic3C2211yescharacteristic
23C5×#879—21no—
24C5×#879—21no—
25C5×#878—21no—
26C5×#877—21no—
27C4×C5×Dic6C2211yescharacteristic
28C4×C5×Dic6C2211yescharacteristic
29C2×C3×#689C2211yescharacteristic
30C2×C3×#687C2211yescharacteristic
31C3×C4×Dic10C2211yescharacteristic
32#91469C2211yescharacteristic
33#91381C2211yescharacteristic
34#91378—21no—
35#91335—21no—
36Dic3×Dic10C2211yescharacteristic
37Dic3×Dic10C2211yescharacteristic
38#91329—21no—
39#91323—21no—
40C2×#6661C2211yescharacteristic
41#91119C2211yescharacteristic
42#91119C2211yescharacteristic
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic
45C4×C3⋊#168C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×C4⋊#168C2211yescharacteristic
49#90989C2211yescharacteristic
50#90988C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90973C2211yescharacteristic
55#90973C2211yescharacteristic
56#90972C2211yescharacteristic
57#90970C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80580—51nomaximal, Hall
61C5×#556—31no—
62#65901—31no—
63#65379—31no—
64#65370—31no—
65#65345—31no—
66#65345—31no—
67#65343—31no—
68#65343D311yescharacteristic
69C4×#689—31no—
70C4×#689—31no—
71Q8×#168—31no—
72#65311—31no—
73#65311—31no—
74C4×#687—31no—
75#65296—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C22×C5×Dic3—21no—
79C2×C5×Dic6D411yescharacteristic
80C2×C5×Dic6C2311yescharacteristic
81C2×C3×Dic10C2311yescharacteristic
82C2×#1204—21no—
83C3×C5×C22⋊C4—21no—
84C3×C5×C22⋊C4—21no—
85C3×C42×C5C2311yescharacteristic
86C4⋊Dic15C2311yescharacteristic
87C4⋊Dic15C2311yescharacteristic
88#6712—21no—
89#6712—21no—
90C2×C3⋊#168C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C5×#217—21no—
93C5×#217—21no—
94C5×#217—21no—
95C5×C4⋊Dic3—21no—
96C5×C4⋊Dic3D411yescharacteristic
97C5×C4⋊Dic3C2311yescharacteristic
98C5×Dic3⋊C4—21no—
99C5×Dic3⋊C4—21no—
100C5×Dic3⋊C4—21no—
101C5×Dic3⋊C4D411yescharacteristic
102C5×Dic3⋊C4D411yescharacteristic
103C4×C5×Dic3—21no—
104C4×C5×Dic3—21no—
105C4×C5×Dic3C2311yescharacteristic
106C4×C5×Dic3C2311yescharacteristic
107C3×#689—22no—
108C3×#687—22no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×C4×Dic5—21no—
112C2×C3×#168C2311yescharacteristic
113C2×C3×#168C2311yescharacteristic
114Dic3⋊Dic5—21no—
115#6669—21no—
116#6668—21no—
117#6668—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6661—22no—
122#5671D511yescharacteristic
123#5569—51no—
124C3×#464—51no—
125#5182—51no—
126Dic3×Q16—51no—
127#5166—51no—
128Dic3×SD16—51no—
129#5056—51no—
130C4×#216—51no—
131#4830—51no—
132#4829—51no—
133#4799—51no—
134#4792—51no—
135#4768—51no—
136#4759—51no—
137C5×C4⋊Q8—31no—
138C5×#126—61no—
139C5×#126—61no—
140C5×#124—31no—
141C5×#124C2×D311yescharacteristic
142C5×C22⋊Q8—61no—
143C4×C5×Q8—31no—
144C4×C5×Q8—31no—
145C4×C5×Q8—31no—
146C4×C5×D4—31no—
147C5×#117—61no—
148#4090—61no—
149C2×#689—31no—
150C2×#689C2×D311yescharacteristic
151C2×#687C2×D311yescharacteristic
152#4035—61no—
153#4035—61no—
154#4033—61no—
155#4016—31no—
156#4016—31no—
157#4015—31no—
158C4×Dic10—31no—
159C4×Dic10—31no—
160C4×Dic10C2×D311yescharacteristic
161#3967—31no—
162#3967—31no—
163#3967—31no—
164#3967—31no—
165#3967—31no—
166#3967C2×D311yescharacteristic
167#3964—31no—
168#3964—31no—
169#3964C2×D311yescharacteristic
170#3942—31no—
171#3940—31no—
172#3939—31no—
173#3939—31no—
174C4⋊#168—31no—
175C4⋊#168—31no—
176C4⋊#168C2×D311yescharacteristic
177C4×#168—31no—
178C4×#168—31no—
179C4×#168—31no—
180#3364—151noSylow
181C23×C3×C5—21no—
182C3×C5×Q8—21no—
183C3×C5×Q8—21no—
184C3×C5×D4—21no—
185C3×C5×D4—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—42no—
195C2×C5×Dic3C2×D411yescharacteristic
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C2×C5×Dic3C2×D411yescharacteristic
199C5×Dic6—22no—
200C5×Dic6—21no—
201C5×Dic6—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C3×Dic10—21no—
205C3×Dic10#4112yes—
206#1204—42no—
207C3⋊#168—21no—
208C3⋊#168—21no—
209C3×#168—21no—
210C3×#168—21no—
211C2×C3×Q16—51no—
212C2×C3×SD16—51no—
213C3×#124C2×D511yescharacteristic
214C3×C4×Q8—51no—
215Q8×Dic3—51no—
216Q8×Dic3—51no—
217Q8×Dic3C2×D511yescharacteristic
218#944C2×D511yescharacteristic
219C2×#216—51no—
220#936C2×D511yescharacteristic
221D4×Dic3C2×D511yescharacteristic
222#890—51no—
223#890—101no—
224#888—51no—
225#888—101no—
226#879—21no—
227#879—21no—
228#878—21no—
229#877—21no—
230#870—51no—
231#870—101no—
232C4×Dic6—101no—
233C4×Dic6C2×D511yescharacteristic
234C4×Dic6C2×D511yescharacteristic
235C3×C4⋊C8—51no—
236C3×#103—51no—
237C3×#102—51no—
238#835—51no—
239#835—51no—
240#835—51no—
241#832—51no—
242#832—51no—
243#818—51no—
244#817—51no—
245#816—51no—
246#816—51no—
247Dic3⋊C8—51no—
248Dic3⋊C8—51no—
249C8×Dic3—51no—
250C8×Dic3—51no—
251#810—51no—
252#807—51no—
253C4×C3⋊C8—51no—
254C2×C5×Q8—31no—
255C2×C5×Q8—31no—
256C2×C5×Q8C22×D311yescharacteristic
257C2×C5×D4C22×D311yescharacteristic
258C22×C4×C5—61no—
259C2×Dic10—61no—
260C2×Dic10C22×D311yescharacteristic
261C5×C4⋊C4—31no—
262C5×C4⋊C4—31no—
263C5×C4⋊C4—31no—
264C5×C4⋊C4—31no—
265C5×C4⋊C4—61no—
266C5×C4⋊C4—61no—
267C5×C4⋊C4—61no—
268C5×C4⋊C4—61no—
269C5×C22⋊C4—21no—
270C5×C22⋊C4—21no—
271C5×C22⋊C4—61no—
272C5×C22⋊C4—61no—
273C5×C22⋊C4—61no—
274C42×C5—31no—
275C42×C5—31no—
276C42×C5—61no—
277C42×C5—61no—
278C42×C5C22×D311yescharacteristic
279#689—22no—
280#689—62no—
281#687—22no—
282C4⋊Dic5—31no—
283C4⋊Dic5—31no—
284C4⋊Dic5—61no—
285C4⋊Dic5C22×D311yescharacteristic
286#683—21no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293C4×Dic5—21no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C2×#168—31no—
297C2×#168—31no—
298C2×#168C22×D311yescharacteristic
299C2×#168C22×D311yescharacteristic
300#557—151no—
301#556—31no—
302#488—151no—
303#488—151no—
304#487—151no—
305#479—151no—
306#479—151no—
307#474—151no—
308#464—51no—
309#464—151no—
310#462—151no—
311C8×Q8—151no—
312C4×Q16—151no—
313C4×Q16—151no—
314C4×SD16—151no—
315C22×C3×C5—41no—
316C22×C3×C5—41no—
317C22×C3×C5—41no—
318C22×C3×C5C22×D411yescharacteristic
319C3×C4×C5—21no—
320C3×C4×C5—21no—
321C3×C4×C5—41no—
322C3×C4×C5C2×#4111yescharacteristic
323C3×C4×C52−1+411yescharacteristic
324Dic15—41no—
325Dic15—41no—
326C3×Dic5—22no—
327C3×Dic5—41no—
328C5×Dic3—21no—
329C5×Dic3—21no—
330C5×Dic3—21no—
331C5×Dic3—41no—
332C5×Dic3—41no—
333C5×Dic3#13512yes—
334C2×C3×Q8—51no—
335C2×C3×Q8C22×D511yescharacteristic
336C2×C3×D4C22×D511yescharacteristic
337C22×Dic3—21no—
338C2×Dic6—101no—
339C2×Dic6C22⋊D511yescharacteristic
340C2×Dic6C22×D511yescharacteristic
341C3×Q16—102no—
342C3×SD16—102no—
343C2×C3×C8—51no—
344C2×C3×C8—51no—
345C3×C4⋊C4—51no—
346C3×C4⋊C4—101no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C42—101no—
350C3×C42C22×D511yescharacteristic
351#217—21no—
352#217—21no—
353#217—21no—
354#216—102no—
355C4⋊Dic3—21no—
356C4⋊Dic3—51no—
357C4⋊Dic3—51no—
358C4⋊Dic3—101no—
359C4⋊Dic3—101no—
360C4⋊Dic3—101no—
361C4⋊Dic3C22⋊D511yescharacteristic
362C4⋊Dic3C22×D511yescharacteristic
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4C22⋊D511yescharacteristic
371Dic3⋊C4C22⋊D511yescharacteristic
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C4×Dic3C22×D511yescharacteristic
377C4×Dic3C22×D511yescharacteristic
378C2×C3⋊C8—51no—
379C2×C3⋊C8—51no—
380C23×C5—21no—
381C5×Q8—21no—
382C5×Q8—21no—
383C5×Q8—62no—
384C5×Q8—61no—
385C5×Q8—61no—
386C5×D4—21no—
387C5×D4—21no—
388C2×C4×C5—21no—
389C2×C4×C5—31no—
390C2×C4×C5—31no—
391C2×C4×C5—31no—
392C2×C4×C5—31no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—122no—
396C2×C4×C5D3×D411yescharacteristic
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—61no—
402C2×Dic5—61no—
403Dic10—21no—
404Dic10—122no—
405Dic10#23712yes—
406#168—21no—
407#168—21no—
408#168—61no—
409#168—61no—
410C2×Q16—51no—
411C2×Q16—151no—
412C2×SD16—51no—
413C4⋊Q8—31no—
414C4⋊Q8—151no—
415C4⋊Q8—301no—
416#126—61no—
417#126—61no—
418#125—151no—
419#125—151no—
420#125—301no—
421#125—301no—
422#124—31no—
423#124D3×D511yescharacteristic
424C22⋊Q8—61no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—51no—
429C4×Q8—151no—
430C4×Q8—151no—
431C4×Q8—301no—
432C4×D4—31no—
433#117—61no—
434#107—151no—
435#107—151no—
436#106—151no—
437C4⋊C8—51no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440#103—51no—
441#103—151no—
442#103—151no—
443#103—151no—
444#103—151no—
445#103—151no—
446#103—151no—
447#102—51no—
448#102—151no—
449#102—151no—
450C4×C8—151no—
451C4×C8—151no—
452C4×C8—151no—
453C2×C3×C5—81no—
454C2×C3×C5#54811yescharacteristic
455C2×C3×C5C2×#13511yescharacteristic
456C2×C3×C5#57811yescharacteristic
457C23×C3—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—52no—
461C3×Q8—101no—
462C3×D4—21no—
463C3×D4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—101no—
466C2×C3×C4—101no—
467C2×C3×C4C2×C22⋊D511yescharacteristic
468C2×C3×C4C2×C22⋊D511yescharacteristic
469C2×C3×C4C23×D511yescharacteristic
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—42no—
473C2×Dic3—101no—
474C2×Dic3—101no—
475C2×Dic3C2×C22⋊D511yescharacteristic
476C2×Dic3C2×C22⋊D511yescharacteristic
477C2×Dic3C2×C22⋊D511yescharacteristic
478C2×Dic3C2×C22⋊D511yescharacteristic
479Dic6—22no—
480Dic6—21no—
481Dic6—21no—
482Dic6—202no—
483C3×C8—101no—
484C3×C8—101no—
485C3⋊C8—101no—
486C3⋊C8—101no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5C2×D3×D411yescharacteristic
491C4×C5—21no—
492C4×C5—21no—
493C4×C5—32no—
494C4×C5—41no—
495C4×C5—61no—
496C4×C5—61no—
497C4×C5—61no—
498C4×C5—121no—
499C4×C5—121no—
500C4×C5C2×#23711yescharacteristic
501C4×C5#101011yescharacteristic
502Dic5—22no—
503Dic5—41no—
504Dic5—121no—
505Dic5—121no—
506C2×Q8—31no—
507C2×Q8—31no—
508C2×Q8—51no—
509C2×Q8—301no—
510C2×Q8C2×D3×D511yescharacteristic
511C2×D4C2×D3×D511yescharacteristic
512C22×C4—61no—
513Q16—102no—
514Q16—302no—
515SD16—102no—
516C2×C8—51no—
517C2×C8—51no—
518C2×C8—151no—
519C2×C8—151no—
520C4⋊C4—31no—
521C4⋊C4—31no—
522C4⋊C4—31no—
523C4⋊C4—31no—
524C4⋊C4—51no—
525C4⋊C4—61no—
526C4⋊C4—61no—
527C4⋊C4—61no—
528C4⋊C4—61no—
529C4⋊C4—101no—
530C4⋊C4—151no—
531C4⋊C4—151no—
532C4⋊C4—301no—
533C4⋊C4—301no—
534C4⋊C4—301no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4—301no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—61no—
542C22⋊C4—61no—
543C22⋊C4—61no—
544C42—31no—
545C42—31no—
546C42—61no—
547C42—61no—
548C42—101no—
549C42—301no—
550C42—301no—
551C42C2×D3×D511yescharacteristic
552C3×C5#336411yescharacteristic, complemented, Hall
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3C22×C22⋊D511yescharacteristic
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—41no—
560C3×C4—102no—
561C3×C4—201no—
562C3×C4D5×#4111yescharacteristic
563C3×C4#415011yescharacteristic
564Dic3—21no—
565Dic3—21no—
566Dic3—21no—
567Dic3—41no—
568Dic3—41no—
569Dic3—201no—
570Dic3—201no—
571Dic3#409612yes—
572C2×C5—81no—
573C2×C5#559811yescharacteristic
574C2×C5D3×#13511yescharacteristic
575C2×C5#577911yescharacteristic
576C23—21no—
577Q8—21no—
578Q8—21no—
579Q8—52no—
580Q8—62no—
581Q8—61no—
582Q8—61no—
583Q8—101no—
584Q8—602no—
585D4—21no—
586D4—21no—
587C2×C4—21no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—101no—
595C2×C4—101no—
596C2×C4—122no—
597C2×C4—301no—
598C2×C4—301no—
599C2×C4D3×C22⋊D511yescharacteristic
600C2×C4D3×C22⋊D511yescharacteristic
601C2×C4C22×D3×D511yescharacteristic
602C8—101no—
603C8—101no—
604C8—301no—
605C8—301no—
606C2×C3—81no—
607C2×C3C2×#409611yescharacteristic
608C2×C3#6616511yescharacteristic
609C2×C3#6617211yescharacteristic
610C5#8058011yescharacteristic, complemented, Sylow
611C22—41no—
612C22—41no—
613C22—41no—
614C22C2×D3×C22⋊D511yescharacteristic
615C4—21no—
616C4—21no—
617C4—32no—
618C4—41no—
619C4—61no—
620C4—61no—
621C4—61no—
622C4—102no—
623C4—121no—
624C4—121no—
625C4—201no—
626C4—601no—
627C4—601no—
628C4#9202011yescharacteristic
629C4D5×#23711yescharacteristic
630C3#1061540711yescharacteristic, complemented, Sylow
631C2—81no—
632C2#1175480211yescharacteristic
633C2D3×#409611yescharacteristic
634C2#1175534111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenter#124D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752465C2semidirect
5. #11749333C2semidirect
6. Dic3×#689C2semidirect
7. #11749251C2semidirect
8. #11749187C2semidirect
13. C4×#6661C2semidirect
14. #11746965C2semidirect
15. #11746857C2semidirect
552. C3×C5#3364semidirect
610. C5#80580semidirect
630. C3#10615407semidirect

Maximal subgroups

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

subgroupindex
C5×#56712
#117524652
#117511572
C3×#653432
#117493332
Dic3×#6892
#117492512
#117491872
#117491122
Dic3×#6872
#117490062
#117489422
C4×#66612
#117469652
#117468572
#106154073
#805805