Finite Group Databasebeta

← #14430968

Subgroups — #14430968

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66023C211yesmaximal, characteristic
2#11752516C211yesmaximal, characteristic
3#11751164C211yesmaximal, characteristic, complemented
4C5×#5063C211yesmaximal, characteristic, complemented
5#11747487C211yesmaximal, characteristic
6D5×#810C211yesmaximal, characteristic
7#11747452C211yesmaximal, characteristic
8#11747433C211yesmaximal, characteristic
9#11747289C211yesmaximal, characteristic, complemented
10#11747286C211yesmaximal, characteristic, complemented
11#11747285C211yesmaximal, characteristic, complemented
12#11747282C211yesmaximal, characteristic, complemented
13#11746985C211yesmaximal, characteristic
14#11746959C211yesmaximal, characteristic, complemented
15#11746949C211yesmaximal, characteristic, complemented
16#10612964—31nomaximal, Hall
17C2×D5×Dic6C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C4×C5×Dic6C2211yescharacteristic
21C3×#4043—21no—
22C3×#4042—21no—
23C3×#4038C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25C3×#4036C2211yescharacteristic
26C3×#4035—21no—
27C3×#4034—21no—
28C3×#4034C2211yescharacteristic
29C3×#4018C2211yescharacteristic
30C3×#4015C2211yescharacteristic
31#91394—21no—
32#91393—21no—
33#91358C2211yescharacteristic
34#91333C2211yescharacteristic
35Dic5×Dic6C2211yescharacteristic
36#91325—21no—
37#91324—21no—
38C2×#6649C2211yescharacteristic
39C2×D5×C3⋊C8C2211yescharacteristic
40#91094C2211yescharacteristic
41#91094C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#810C2211yescharacteristic
46C5×#810C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90989C2211yescharacteristic
51#90989C2211yescharacteristic
52#90987C2211yescharacteristic
53#90987C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90974C2211yescharacteristic
57#90974C2211yescharacteristic
58#90972C2211yescharacteristic
59#90972C2211yescharacteristic
60#83480—51nomaximal, Hall
61#66023D311yescharacteristic
62#65906—31no—
63C5×#479—31no—
64#65352—31no—
65#65310—31no—
66#65170—31no—
67#65164—31no—
68#65149—31no—
69#65146—31no—
70#65140—31no—
71#65128—31no—
72#65091—31no—
73D5×#103—31no—
74#65088—31no—
75#65080—31no—
76C2×Dic30C2311yescharacteristic
77C2×C5×Dic6C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×C4×D5C2311yescharacteristic
80C2×C3×Dic10—21no—
81C2×C3×Dic10—21no—
82C2×#1204—21no—
83C2×D5×Dic3—21no—
84D5×Dic6—22no—
85D5×Dic6Q814yescomplemented
86C3×C5×C4⋊C4—21no—
87C3×C5×C4⋊C4—21no—
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C42×C5C2311yescharacteristic
91C4⋊Dic15C2311yescharacteristic
92#6712—21no—
93C4×Dic15—21no—
94C2×C3⋊#168C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C5×C4⋊Dic3C2311yescharacteristic
97C5×Dic3⋊C4—21no—
98C4×C5×Dic3—21no—
99C2×C5×C3⋊C8C2311yescharacteristic
100C2×C5×C3⋊C8C2311yescharacteristic
101C3×#685—21no—
102C3×#685D411yescharacteristic
103C3×#685D411yescharacteristic
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5—21no—
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683D411yescharacteristic
112C3×#683D411yescharacteristic
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6665—21no—
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6649—22no—
122D5×C3⋊C8—22no—
123C3×#544—51no—
124#5516—51no—
125#5094—51no—
126#5094—51no—
127#5091—51no—
128#5091—51no—
129#5063—51no—
130#5063—51no—
131#5063—51no—
132#5063D511yescharacteristic, complemented
133#5004—51no—
134#4999—51no—
135#4998—51no—
136C2×#810—51no—
137#4964—51no—
138C2×Q8×D5—31no—
139C5×#125C2×D311yescharacteristic
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142C2×#676—31no—
143C2×C8×D5—31no—
144#4043—21no—
145#4042—21no—
146#4038—31no—
147#4038—61no—
148#4038C2×D311yescharacteristic
149D5×C4⋊C4C2×D311yescharacteristic
150#4036C2×D311yescharacteristic
151#4035—21no—
152#4034—21no—
153#4034C2×D311yescharacteristic
154#4033—31no—
155#4033—61no—
156#4018—61no—
157#4018C2×D311yescharacteristic
158#4015C2×D311yescharacteristic
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3949—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3082—151noSylow
182C22×C3×D5C2×D411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190Dic30—21no—
191Dic30C2×Q812yes—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C5×Dic6—21no—
195C5×Dic6C2×Q812yes—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5C2×D411yescharacteristic
199C2×C3×Dic5C2×D411yescharacteristic
200C2×C3×Dic5C2×D411yescharacteristic
201C3×C4×D5—81no—
202C3×C4×D5C2×Q812yes—
203C3×C4×D5#4112yes—
204C3×Dic10—81no—
205C3×Dic10—81no—
206#1204—24no—
207D5×Dic3—24no—
208C3⋊#168—21no—
209C3⋊#168—21no—
210C5×C3⋊C8—21no—
211C5×C3⋊C8—21no—
212C22×Dic6—51no—
213C3×C4⋊Q8—51no—
214C3×C4⋊Q8—51no—
215C3×C4⋊Q8—101no—
216C3×#125—51no—
217C3×#125—101no—
218C3×#125C2×D511yescharacteristic
219C3×C22⋊Q8—101no—
220C3×C22⋊Q8—101no—
221C3×#117—51no—
222C3×#117—51no—
223C2×C3×C4⋊C4—51no—
224#926—51no—
225C2×#208—51no—
226C22×C3⋊C8—51no—
227#887—101no—
228#887—101no—
229#877—101no—
230#877—101no—
231C4×Dic6—51no—
232C4×Dic6—51no—
233C4×Dic6—51no—
234C4×Dic6C2×D511yescharacteristic
235#810—51no—
236#810—51no—
237#810—51no—
238#810—51no—
239#810—51no—
240#810—51no—
241#810C2×D511yescharacteristic
242#810C2×D511yescharacteristic
243#808—51no—
244#808—51no—
245#808—51no—
246#808C2×D511yescharacteristic
247#807—51no—
248#807—51no—
249#807—51no—
250#807C2×D511yescharacteristic
251C4⋊(C3⋊C8)—51no—
252C4⋊(C3⋊C8)—51no—
253C4⋊(C3⋊C8)—51no—
254C4⋊(C3⋊C8)C2×D511yescharacteristic
255C2×C5×Q8—31no—
256Q8×D5—34no—
257Q8×D5—62no—
258C2×C4×D5—21no—
259C2×C4×D5—61no—
260C2×C4×D5C22×D311yescharacteristic
261C2×Dic10—21no—
262C2×Dic10—21no—
263C2×Dic10—31no—
264C2×Dic10—61no—
265C2×C5×C8—31no—
266C2×C5×C8—31no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—61no—
271C5×C4⋊C4C22×D311yescharacteristic
272C5×C4⋊C4C22×D311yescharacteristic
273C42×C5—61no—
274C42×C5C22×D311yescharacteristic
275#685—21no—
276#685—61no—
277#685#6711yescharacteristic
278#685#6711yescharacteristic
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—31no—
282C4⋊Dic5—61no—
283C4⋊Dic5C22×D311yescharacteristic
284C4⋊Dic5C22×D311yescharacteristic
285#683—21no—
286#683—21no—
287#683—21no—
288#683—61no—
289#683—61no—
290#683#6711yescharacteristic
291#683#6711yescharacteristic
292C4×Dic5—21no—
293C4×Dic5—61no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5C22×D311yescharacteristic
298C2×#168—31no—
299C2×#168—31no—
300#676—62no—
301C8×D5—62no—
302#544—51no—
303#519—151no—
304#479—31no—
305#479—151no—
306#479—151no—
307#479—151no—
308#477—151no—
309#477—151no—
310#475—151no—
311#475—151no—
312#428—151no—
313#427—151no—
314#424—151no—
315#419—151no—
316C2×#103—151no—
317C22×C3×C5C22×D411yescharacteristic
318C2×C3×D5—21no—
319C2×C3×D5—21no—
320C2×C3×D5C22⋊Q812yes—
321C3×C4×C5—21no—
322C3×C4×C5—21no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5C22×Q811yescharacteristic
326C3×C4×C5C2×#4111yescharacteristic
327Dic15—22no—
328Dic15—41no—
329C3×Dic5—21no—
330C3×Dic5—21no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C3×Dic5C22⋊Q812yes—
334C5×Dic3—22no—
335C5×Dic3—41no—
336C2×C3×Q8—101no—
337C2×C3×Q8—101no—
338C22×C3×C4—51no—
339C22×C3×C4—101no—
340C22×Dic3—101no—
341C2×Dic6—51no—
342C2×Dic6—54no—
343C2×Dic6—102no—
344C2×Dic6—101no—
345C2×Dic6C22×D511yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—51no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4—51no—
351C3×C4⋊C4—51no—
352C3×C4⋊C4—101no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C4⋊C4C22×D511yescharacteristic
359C3×C22⋊C4—51no—
360C3×C22⋊C4—51no—
361C3×C22⋊C4—101no—
362C3×C42—51no—
363C3×C42—101no—
364C3×C42C22×D511yescharacteristic
365#217—101no—
366C4⋊Dic3—51no—
367C4⋊Dic3C22×D511yescharacteristic
368Dic3⋊C4—21no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372C4×Dic3—21no—
373C4×Dic3—101no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377#208—102no—
378C2×C3⋊C8—51no—
379C2×C3⋊C8—51no—
380C2×C3⋊C8—102no—
381C2×C3⋊C8C22×D511yescharacteristic
382C2×C3⋊C8C22×D511yescharacteristic
383C22×D5C2×#6711yescharacteristic
384C5×Q8—32no—
385C5×Q8—61no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—61no—
389C2×C4×C5—61no—
390C2×C4×C5C2×#6711yescharacteristic
391C2×C4×C5C2×#6711yescharacteristic
392C2×C4×C5C23×D311yescharacteristic
393C2×Dic5—21no—
394C2×Dic5—21no—
395C2×Dic5—61no—
396C2×Dic5—61no—
397C2×Dic5C2×#6711yescharacteristic
398C2×Dic5C2×#6711yescharacteristic
399C2×Dic5C2×#6711yescharacteristic
400C4×D5—64no—
401C4×D5—81no—
402C4×D5D3×Q812yes—
403C4×D5#23912yes—
404Dic10—32no—
405Dic10—61no—
406Dic10—64no—
407Dic10—81no—
408Dic10—81no—
409C5×C8—61no—
410C5×C8—61no—
411#168—61no—
412#168—61no—
413C22×Q8—151no—
414C2×M16—151no—
415C22×C8—151no—
416C4⋊Q8—51no—
417C4⋊Q8—51no—
418C4⋊Q8—101no—
419#125—51no—
420#125—101no—
421#125D3×D511yescharacteristic
422C22⋊Q8—101no—
423C22⋊Q8—101no—
424C4×Q8—31no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—301no—
429C4×Q8—301no—
430#117—51no—
431#117—51no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—51no—
436#107—31no—
437#107—151no—
438#107—151no—
439#107—151no—
440#106—31no—
441#106—151no—
442#106—151no—
443#106—151no—
444C4⋊C8—31no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—31no—
449#103—31no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#103—151no—
455#103—151no—
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459C3×D5—22no—
460C23×C3—51no—
461C3×Q8—401no—
462C3×Q8—401no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—51no—
466C2×C3×C4—52no—
467C2×C3×C4—52no—
468C2×C3×C4—51no—
469C2×C3×C4—51no—
470C2×C3×C4—101no—
471C2×C3×C4—101no—
472C2×C3×C4—401no—
473C2×C3×C4D4×D511yescharacteristic
474C2×C3×C4D4×D511yescharacteristic
475C2×C3×C4C23×D511yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—104no—
479C2×Dic3—101no—
480C2×Dic3—101no—
481Dic6—21no—
482Dic6—52no—
483Dic6—104no—
484Dic6—101no—
485Dic6Q8×D512yes—
486C3⋊C8—21no—
487C3⋊C8—21no—
488C3⋊C8—101no—
489C3⋊C8—101no—
490C22×C5C22×#6711yescharacteristic
491C2×D5—21no—
492C2×D5—21no—
493C2×D5#94612yes—
494C4×C5—21no—
495C4×C5—21no—
496C4×C5—41no—
497C4×C5—41no—
498C4×C5—62no—
499C4×C5—121no—
500C4×C5C2×D3×Q811yescharacteristic
501C4×C5C2×#23911yescharacteristic
502Dic5—21no—
503Dic5—21no—
504Dic5—41no—
505Dic5—41no—
506Dic5—62no—
507Dic5—121no—
508Dic5#94612yes—
509C2×Q8—31no—
510C2×Q8—101no—
511C2×Q8—101no—
512C2×Q8—154no—
513C2×Q8—151no—
514C2×Q8—301no—
515C2×Q8—302no—
516C22×C4—51no—
517C22×C4—101no—
518C22×C4—301no—
519M16—302no—
520C2×C8—31no—
521C2×C8—31no—
522C2×C8—151no—
523C2×C8—151no—
524C2×C8—302no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—31no—
528C4⋊C4—51no—
529C4⋊C4—51no—
530C4⋊C4—51no—
531C4⋊C4—51no—
532C4⋊C4—61no—
533C4⋊C4—101no—
534C4⋊C4—101no—
535C4⋊C4—101no—
536C4⋊C4—101no—
537C4⋊C4—101no—
538C4⋊C4—151no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4—301no—
542C4⋊C4C2×D3×D511yescharacteristic
543C4⋊C4C2×D3×D511yescharacteristic
544C22⋊C4—51no—
545C22⋊C4—51no—
546C22⋊C4—101no—
547C22⋊C4—301no—
548C42—51no—
549C42—61no—
550C42—101no—
551C42—301no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42C2×D3×D511yescharacteristic
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3—52no—
558C22×C3—101no—
559C22×C3—101no—
560C22×C3C2×D4×D511yescharacteristic
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—41no—
564C3×C4—41no—
565C3×C4—52no—
566C3×C4—101no—
567C3×C4—101no—
568C3×C4—201no—
569C3×C4—201no—
570C3×C4C2×Q8×D511yescharacteristic
571C3×C4D5×#4111yescharacteristic
572Dic3—22no—
573Dic3—41no—
574Dic3—102no—
575Dic3—201no—
576C2×C5C2×#94611yescharacteristic
577C2×C5#583611yescharacteristic
578C2×C5#583811yescharacteristic
579D5—22no—
580C23—51no—
581Q8—32no—
582Q8—61no—
583Q8—152no—
584Q8—304no—
585Q8—301no—
586Q8—401no—
587Q8—401no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—51no—
591C2×C4—52no—
592C2×C4—52no—
593C2×C4—51no—
594C2×C4—51no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—101no—
598C2×C4—101no—
599C2×C4—304no—
600C2×C4—301no—
601C2×C4—301no—
602C2×C4—401no—
603C2×C4D5×#6711yescharacteristic
604C2×C4D5×#6711yescharacteristic
605C2×C4C22×D3×D511yescharacteristic
606C8—61no—
607C8—61no—
608C8—301no—
609C8—301no—
610C2×C3—102no—
611C2×C3D5×C22⋊Q811yescharacteristic
612C2×C3#6610411yescharacteristic
613C2×C3#6611311yescharacteristic
614C5#8348011yescharacteristic, complemented, Sylow
615C22—52no—
616C22—101no—
617C22—101no—
618C22C2×D5×#6711yescharacteristic
619C4—21no—
620C4—21no—
621C4—41no—
622C4—41no—
623C4—52no—
624C4—62no—
625C4—101no—
626C4—101no—
627C4—121no—
628C4—201no—
629C4—201no—
630C4—302no—
631C4—601no—
632C4D3×Q8×D511yescharacteristic
633C4D5×#23911yescharacteristic
634C3#1061296411yescharacteristic, complemented, Sylow
635C2—102no—
636C2D5×#94611yescharacteristic
637C2#1175533611yescharacteristic
638C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenter#125D3×D5
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11751164C2semidirect
4. C5×#5063C2semidirect
9. #11747289C2semidirect
10. #11747286C2semidirect
11. #11747285C2semidirect
12. #11747282C2semidirect
14. #11746959C2semidirect
15. #11746949C2semidirect
85. D5×Dic6Q8semidirect
132. #5063D5semidirect
556. C3×C5#3082semidirect
614. C5#83480semidirect
634. C3#10612964semidirect

Maximal subgroups

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

subgroupindex
C3×#660232
#117525162
#117511642
C5×#50632
#117474872
D5×#8102
#117474522
#117474332
#117472892
#117472862
#117472852
#117472822
#117469852
#117469592
#117469492
#106129643
#834805