Finite Group Databasebeta

← #14417551

Subgroups — #14417551

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755140C211yesmaximal, characteristic
2C2×D5×#216C211yesmaximal, characteristic
3#11753397C211yesmaximal, characteristic
4#11750890C211yesmaximal, characteristic, complemented
5C5×#4790C211yesmaximal, characteristic, complemented
6C3×#65091C211yesmaximal, characteristic
7#11749265C211yesmaximal, characteristic, complemented
8#11749260C211yesmaximal, characteristic, complemented
9#11748122C211yesmaximal, characteristic
10#11748050C211yesmaximal, characteristic
11#11747831C211yesmaximal, characteristic, complemented
12#11747829C211yesmaximal, characteristic, complemented
13#11747432C211yesmaximal, characteristic
14#11747271C211yesmaximal, characteristic, complemented
15#11747267C211yesmaximal, characteristic, complemented
16#10611451—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×D5×Dic6C2211yescharacteristic
19Q8×Dic15C2211yescharacteristic
20C2×#6718C2211yescharacteristic
21#91776C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C2×C5×#216C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C2×C3×#676C2211yescharacteristic
26C3×#4038C2211yescharacteristic
27D5×#216C418yescomplemented
28C4×#1204—21no—
29#91394—21no—
30#91393—21no—
31#91358—21no—
32#91358C2211yescharacteristic
33#91357—21no—
34#91357C2211yescharacteristic
35#91344C2211yescharacteristic
36#91340C2211yescharacteristic
37#91331—21no—
38#91331C2211yescharacteristic
39Dic3×Dic10—21no—
40Dic3×Dic10C2211yescharacteristic
41#91323—21no—
42C2×#6662C2211yescharacteristic
43C2×#6661C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46#91100C2211yescharacteristic
47#91099C2211yescharacteristic
48#91092C2211yescharacteristic
49C5×#816C2211yescharacteristic
50C5×C8×Dic3C2211yescharacteristic
51C5×#807C2211yescharacteristic
52C3×#3967C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3942C2211yescharacteristic
55#90990C2211yescharacteristic
56#90986C2211yescharacteristic
57#90975C2211yescharacteristic
58#90973C2211yescharacteristic
59#90953C2211yescharacteristic
60#90951C2211yescharacteristic
61#78948—51nomaximal, Hall
62C2×D5×Q16—31no—
63#65906—31no—
64#65906—31no—
65C4×C5×Q16—31no—
66Q16×Dic5—31no—
67#65319—31no—
68#65319—31no—
69#65169—31no—
70#65162—31no—
71#65091—31no—
72#65091D311yescharacteristic
73#65078—31no—
74#65078—31no—
75C4×Dic20—31no—
76#64978—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×Dic6C2311yescharacteristic
80C3×Q8×D5—22no—
81C3×Q8×D5C2×C414yes—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5C2311yescharacteristic
84C2×C3×Dic10—21no—
85C2×C3×Dic10C2311yescharacteristic
86C2×#1204—21no—
87C2×D5×Dic3—21no—
88D5×Dic6—22no—
89D5×Dic6C2×C414yes—
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92#6718C2×C414yes—
93C4⋊Dic15—21no—
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15—21no—
97C4×Dic15—21no—
98C4×Dic15C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C5×#216C2×C414yes—
101C5×C4⋊Dic3—21no—
102C5×C4⋊Dic3C2311yescharacteristic
103C5×Dic3⋊C4—21no—
104C4×C5×Dic3—21no—
105C4×C5×Dic3—21no—
106C4×C5×Dic3C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C3×#685—21no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×C4×Dic5—21no—
111C2×C3×#168C2311yescharacteristic
112C3×#676—22no—
113Dic3⋊Dic5—21no—
114#6669—21no—
115#6668—21no—
116#6668—21no—
117#6668D411yescharacteristic
118#6668D411yescharacteristic
119#6665—21no—
120#6665D411yescharacteristic
121#6665D411yescharacteristic
122Dic3×Dic5—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6662C2×C414yes—
128#6661C2×C414yes—
129D5×C3⋊C8C2×C414yes—
130#5812—51no—
131C22×#216—51no—
132#5516—51no—
133C3×#419—51no—
134#5122—51no—
135#5120—51no—
136#4998—51no—
137#4790—51no—
138#4790—51no—
139#4790—51no—
140#4790D511yescharacteristic, complemented
141#4789—51no—
142#4789—51no—
143#4789—51no—
144#4789—51no—
145C2×Q8×D5—31no—
146C2×Q8×D5C2×D311yescharacteristic
147C2×C5×Q16—31no—
148C4×C5×Q8—31no—
149C4×C5×Q8—31no—
150Q8×Dic5—31no—
151Q8×Dic5—31no—
152C2×#689—31no—
153C2×#689—31no—
154D5×Q16—38no—
155C2×Dic20—31no—
156C2×#676C2×D311yescharacteristic
157C2×C8×D5—31no—
158#4038—31no—
159#4038—61no—
160#4038—61no—
161#4038C2×D311yescharacteristic
162#4033—31no—
163#4033—31no—
164#4033—61no—
165#4033—61no—
166#4018—31no—
167#4018—61no—
168#4018—61no—
169C4×Dic10—31no—
170C4×Dic10—31no—
171C4×Dic10—61no—
172C4×Dic10—61no—
173C5×#107—31no—
174C5×#103—31no—
175C5×#103C2×D311yescharacteristic
176C4×C5×C8—31no—
177#3967—31no—
178#3967C2×D311yescharacteristic
179#3950—31no—
180#3948—31no—
181#3948C2×D311yescharacteristic
182#3947—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3942C2×D311yescharacteristic
186#3940—31no—
187#3940—31no—
188#3935—31no—
189#2950—151noSylow
190C22×C3×D5C2×D411yescharacteristic
191C3×C5×Q8—21no—
192C3×C5×Q8C22×C412yes—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5C2411yescharacteristic
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15C2×D411yescharacteristic
199C2×Dic15C2×D411yescharacteristic
200Dic30—21no—
201Dic30C22×C412yes—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3C2×D411yescharacteristic
205C2×C5×Dic3C2×D411yescharacteristic
206C5×Dic6—21no—
207C5×Dic6C22×C412yes—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5C2×D411yescharacteristic
211C3×C4×D5—24no—
212C3×C4×D5C22×C412yes—
213C3×C4×D5#4112yes—
214C3×Dic10—21no—
215C3×Dic10—24no—
216C3×Dic10C22×C412yes—
217#1204—24no—
218D5×Dic3—24no—
219C3×C5×C8—21no—
220C3⋊#168C22×C412yes—
221C3×#168—21no—
222C5×C3⋊C8C22×C412yes—
223C22×C3×Q8—51no—
224C22×Dic6—51no—
225C2×C3×M16—51no—
226C3×#117—51no—
227Q8×Dic3—51no—
228Q8×Dic3—51no—
229Q8×Dic3—51no—
230Q8×Dic3—101no—
231Q8×Dic3—101no—
232Q8×Dic3C2×D511yescharacteristic
233C2×#216—51no—
234C2×#216—51no—
235C2×#216—58no—
236C2×#216—51no—
237C2×#216C2×D511yescharacteristic
238#926—51no—
239#926—51no—
240#926—101no—
241#926—101no—
242C22×C3⋊C8—51no—
243#887—51no—
244#887—51no—
245#887—51no—
246#887C2×D511yescharacteristic
247#877—101no—
248#877—101no—
249C4×Dic6—101no—
250C4×Dic6—101no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103—51no—
254C3×#103C2×D511yescharacteristic
255#816—51no—
256#816—51no—
257#816—51no—
258#816C2×D511yescharacteristic
259#815—51no—
260#815—51no—
261C8×Dic3—51no—
262C8×Dic3C2×D511yescharacteristic
263#808—51no—
264#808—51no—
265#807—51no—
266#807C2×D511yescharacteristic
267C2×C5×Q8—31no—
268C2×C5×Q8C22×D311yescharacteristic
269Q8×D5—22no—
270Q8×D5—34no—
271Q8×D5—62no—
272Q8×D5C4×D314yes—
273C2×C4×D5—21no—
274C2×C4×D5—61no—
275C2×C4×D5C22×D311yescharacteristic
276C2×Dic10—21no—
277C2×Dic10—31no—
278C2×Dic10—61no—
279C2×Dic10C22×D311yescharacteristic
280C5×Q16—34no—
281C2×C5×C8—31no—
282C2×C5×C8C22×D311yescharacteristic
283C5×C4⋊C4—31no—
284C5×C4⋊C4—61no—
285C5×C4⋊C4—61no—
286C5×C4⋊C4C22×D311yescharacteristic
287C42×C5—31no—
288C42×C5—61no—
289C42×C5—61no—
290#689—34no—
291#689—34no—
292#685—21no—
293#685—31no—
294#685—31no—
295#685—61no—
296C4⋊Dic5—31no—
297C4⋊Dic5—61no—
298C4⋊Dic5—61no—
299C4⋊Dic5C22×D311yescharacteristic
300#683—31no—
301#683—31no—
302#683—61no—
303#683—61no—
304#683—61no—
305#683—61no—
306C4×Dic5—21no—
307C4×Dic5—31no—
308C4×Dic5—61no—
309C4×Dic5—61no—
310C4×Dic5—61no—
311C4×Dic5—61no—
312C4×Dic5—61no—
313C4×Dic5—61no—
314C4×Dic5—61no—
315C2×#168—31no—
316C2×#168C22×D311yescharacteristic
317Dic20—34no—
318#676—22no—
319C8×D5—34no—
320C22×Q16—151no—
321#519—151no—
322#519—151no—
323#441—151no—
324#441—151no—
325#441—151no—
326#441—151no—
327C4×Q16—31no—
328C4×Q16—151no—
329C4×Q16—151no—
330C4×Q16—151no—
331#427—151no—
332#419—51no—
333#419—151no—
334#405—151no—
335C22×C3×C5C22×D411yescharacteristic
336C2×C3×D5—21no—
337C2×C3×D5—21no—
338C2×C3×D5C4×D412yes—
339C3×C4×C5—22no—
340C3×C4×C5—41no—
341C3×C4×C5C23×C411yescharacteristic
342C3×C4×C5C2×#4111yescharacteristic
343Dic15—22no—
344Dic15—21no—
345Dic15—21no—
346Dic15—41no—
347C3×Dic5—22no—
348C3×Dic5—41no—
349C3×Dic5C4×D412yes—
350C5×Dic3—22no—
351C5×Dic3—21no—
352C5×Dic3—21no—
353C5×Dic3—41no—
354C2×C3×Q8—54no—
355C2×C3×Q8—51no—
356C2×C3×Q8—101no—
357C2×C3×Q8—102no—
358C2×C3×Q8C22×D511yescharacteristic
359C22×C3×C4—51no—
360C22×C3×C4—101no—
361C22×Dic3—101no—
362C2×Dic6—51no—
363C2×Dic6—54no—
364C2×Dic6—102no—
365C2×Dic6—101no—
366C2×Dic6C22×D511yescharacteristic
367C3×M16—102no—
368C2×C3×C8—51no—
369C2×C3×C8C22×D511yescharacteristic
370C3×C4⋊C4—51no—
371C3×C4⋊C4C22×D511yescharacteristic
372C3×C22⋊C4—101no—
373C3×C42—101no—
374#217—51no—
375#217—51no—
376#217—101no—
377#216—54no—
378#216—54no—
379#216—54no—
380#216C4×D514yes—
381C4⋊Dic3—21no—
382C4⋊Dic3—51no—
383C4⋊Dic3—51no—
384C4⋊Dic3—51no—
385C4⋊Dic3—101no—
386C4⋊Dic3—101no—
387C4⋊Dic3—101no—
388C4⋊Dic3C22×D511yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—101no—
391Dic3⋊C4—101no—
392Dic3⋊C4—101no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—51no—
396C4×Dic3—101no—
397C4×Dic3—101no—
398C4×Dic3—101no—
399C4×Dic3—101no—
400C4×Dic3—101no—
401C4×Dic3—101no—
402C4×Dic3—101no—
403C4×Dic3C22×D511yescharacteristic
404C2×C3⋊C8—51no—
405C2×C3⋊C8—54no—
406C2×C3⋊C8C22×D511yescharacteristic
407C22×D5D3×D411yescharacteristic
408C5×Q8—21no—
409C5×Q8—32no—
410C5×Q8—61no—
411C5×Q8C2×C4×D312yes—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—31no—
415C2×C4×C5—31no—
416C2×C4×C5—61no—
417C2×C4×C5—61no—
418C2×C4×C5C23×D311yescharacteristic
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—61no—
424C2×Dic5—61no—
425C2×Dic5D3×D411yescharacteristic
426C4×D5—24no—
427C4×D5—64no—
428C4×D5C2×C4×D312yes—
429C4×D5#23712yes—
430Dic10—21no—
431Dic10—24no—
432Dic10—32no—
433Dic10—61no—
434Dic10—64no—
435Dic10C2×C4×D312yes—
436C5×C8—21no—
437C5×C8—32no—
438#168—21no—
439#168—32no—
440C22×Q8—51no—
441C22×Q8—151no—
442C2×Q16—31no—
443C2×Q16—151no—
444C2×Q16—158no—
445C2×Q16—151no—
446C2×Q16—151no—
447C2×M16—51no—
448C22×C8—151no—
449C4×Q8—31no—
450C4×Q8—31no—
451C4×Q8—151no—
452C4×Q8—151no—
453C4×Q8—151no—
454C4×Q8—151no—
455C4×Q8—151no—
456C4×Q8—151no—
457C4×Q8—301no—
458C4×Q8—301no—
459C4×Q8—301no—
460C4×Q8—301no—
461#117—51no—
462#117—151no—
463#117—151no—
464#117—301no—
465#117—301no—
466#117—301no—
467#117—301no—
468#107—31no—
469#107—151no—
470#106—151no—
471#106—151no—
472#103—31no—
473#103—51no—
474#103—51no—
475#103—51no—
476#103—151no—
477#103—151no—
478#103—151no—
479#103D3×D511yescharacteristic
480#97—151no—
481#97—151no—
482C4×C8—31no—
483C4×C8—151no—
484C2×C3×C5C2×C4×D411yescharacteristic
485C2×C3×C5#57811yescharacteristic
486C2×C3×C5#57811yescharacteristic
487C3×D5—22no—
488C23×C3—51no—
489C3×Q8—21no—
490C3×Q8—52no—
491C3×Q8—104no—
492C3×Q8—101no—
493C3×Q8C2×C4×D512yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—51no—
497C2×C3×C4—52no—
498C2×C3×C4—52no—
499C2×C3×C4—104no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4C23×D511yescharacteristic
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—51no—
506C2×Dic3—51no—
507C2×Dic3—104no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3D4×D511yescharacteristic
511C2×Dic3D4×D511yescharacteristic
512Dic6—21no—
513Dic6—52no—
514Dic6—104no—
515Dic6—101no—
516Dic6C2×C4×D512yes—
517C3×C8—21no—
518C3×C8—101no—
519C3⋊C8—52no—
520C3⋊C8C2×C4×D512yes—
521C22×C5C2×D3×D411yescharacteristic
522C2×D5—21no—
523C2×D5—21no—
524C2×D5#67⋊C412yes—
525C4×C5—22no—
526C4×C5—41no—
527C4×C5—62no—
528C4×C5—61no—
529C4×C5—61no—
530C4×C5—121no—
531C4×C5C22×C4×D311yescharacteristic
532C4×C5C2×#23711yescharacteristic
533Dic5—22no—
534Dic5—41no—
535Dic5—62no—
536Dic5—61no—
537Dic5—61no—
538Dic5—121no—
539Dic5#67⋊C412yes—
540C2×Q8—31no—
541C2×Q8—54no—
542C2×Q8—51no—
543C2×Q8—101no—
544C2×Q8—102no—
545C2×Q8—154no—
546C2×Q8—151no—
547C2×Q8—301no—
548C2×Q8—302no—
549C2×Q8C2×D3×D511yescharacteristic
550C22×C4—51no—
551C22×C4—101no—
552C22×C4—301no—
553Q16—34no—
554Q16—154no—
555Q16—154no—
556Q16—154no—
557M16—102no—
558C2×C8—31no—
559C2×C8—51no—
560C2×C8—154no—
561C2×C8—151no—
562C2×C8C2×D3×D511yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—51no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—151no—
568C4⋊C4—151no—
569C4⋊C4—151no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C4⋊C4—301no—
574C4⋊C4—301no—
575C4⋊C4—301no—
576C4⋊C4C2×D3×D511yescharacteristic
577C22⋊C4—101no—
578C22⋊C4—151no—
579C22⋊C4—151no—
580C22⋊C4—301no—
581C42—31no—
582C42—61no—
583C42—61no—
584C42—101no—
585C42—151no—
586C42—301no—
587C42—301no—
588C42—301no—
589C42—301no—
590C42—301no—
591C42—301no—
592C42—301no—
593C3×C5#295011yescharacteristic, complemented, Hall
594C22×C3—52no—
595C22×C3—101no—
596C22×C3—101no—
597C22×C3C2×D4×D511yescharacteristic
598C3×C4—22no—
599C3×C4—41no—
600C3×C4—52no—
601C3×C4—102no—
602C3×C4—201no—
603C3×C4C22×C4×D511yescharacteristic
604C3×C4D5×#4111yescharacteristic
605Dic3—21no—
606Dic3—21no—
607Dic3—22no—
608Dic3—41no—
609Dic3—101no—
610Dic3—101no—
611Dic3—102no—
612Dic3—201no—
613C2×C5C2×#67⋊C411yescharacteristic
614C2×C5#577911yescharacteristic
615C2×C5#577911yescharacteristic
616D5—22no—
617C23—51no—
618Q8—21no—
619Q8—32no—
620Q8—52no—
621Q8—61no—
622Q8—104no—
623Q8—101no—
624Q8—152no—
625Q8—304no—
626Q8—301no—
627Q8C4×D3×D512yes—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—51no—
633C2×C4—52no—
634C2×C4—52no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—104no—
638C2×C4—101no—
639C2×C4—101no—
640C2×C4—151no—
641C2×C4—151no—
642C2×C4—304no—
643C2×C4—301no—
644C2×C4—301no—
645C2×C4C22×D3×D511yescharacteristic
646C8—21no—
647C8—32no—
648C8—101no—
649C8—152no—
650C2×C3—102no—
651C2×C3C4×D4×D511yescharacteristic
652C2×C3#6610011yescharacteristic
653C2×C3#6610511yescharacteristic
654C5#7894811yescharacteristic, complemented, Sylow
655C22—52no—
656C22—101no—
657C22—101no—
658C22D3×D4×D511yescharacteristic
659C4—22no—
660C4—41no—
661C4—52no—
662C4—61no—
663C4—61no—
664C4—62no—
665C4—102no—
666C4—121no—
667C4—201no—
668C4—301no—
669C4—301no—
670C4—302no—
671C4—601no—
672C4C2×C4×D3×D511yescharacteristic
673C4D5×#23711yescharacteristic
674C3#1061145111yescharacteristic, complemented, Sylow
675C2—102no—
676C2D5×#67⋊C411yescharacteristic
677C2#1175409111yescharacteristic
678C2#1175410811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. #11750890C2semidirect
5. C5×#4790C2semidirect
7. #11749265C2semidirect
8. #11749260C2semidirect
11. #11747831C2semidirect
12. #11747829C2semidirect
14. #11747271C2semidirect
15. #11747267C2semidirect
27. D5×#216C4semidirect
140. #4790D5semidirect
593. C3×C5#2950semidirect
654. C5#78948semidirect
674. C3#10611451semidirect

Maximal subgroups

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

subgroupindex
#117551402
C2×D5×#2162
#117533972
#117508902
C5×#47902
C3×#650912
#117492652
#117492602
#117481222
#117480502
#117478312
#117478292
#117474322
#117472712
#117472672
#106114513
#789485