Finite Group Databasebeta

← #14458289

Subgroups — #14458289

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756368C211yesmaximal, characteristic, complemented
2#11756266C211yesmaximal, characteristic, complemented
3C3×C5×#480C211yesmaximal, characteristic, complemented
4#11751139C211yesmaximal, characteristic, complemented
5C2×#91093C211yesmaximal, characteristic, complemented
6#11750991C211yesmaximal, characteristic, complemented
7#11750984C211yesmaximal, characteristic, complemented
8#11750983C211yesmaximal, characteristic, complemented
9#11750973C211yesmaximal, characteristic, complemented
10#11750887C211yesmaximal, characteristic, complemented
11#11750874C211yesmaximal, characteristic, complemented
12D15×#102C211yesmaximal, characteristic, complemented
13#11750861C211yesmaximal, characteristic, complemented
14#11750833C211yesmaximal, characteristic, complemented
15#11750826C211yesmaximal, characteristic, complemented
16#10613033—31nomaximal, Hall
17C2×D4×D15—21no—
18C2×D4×D15C2211yescharacteristic
19C2×#6817—21no—
20C22×D60C2211yescharacteristic
21C3×C5×#121C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23#91829C2211yescharacteristic
24#91826—21no—
25C2×#6715C2211yescharacteristic, complemented
26#91819C2211yescharacteristic, complemented
27#91818—21no—
28C4×#1220C2211yescharacteristic
29C22×C3⋊#168C2211yescharacteristic, complemented
30C2×D120C2211yescharacteristic
31C2×D120C2211yescharacteristic, complemented
32C2×C8×D15C2211yescharacteristic, complemented
33#91785—21no—
34#91784C2211yescharacteristic
35#91784C2211yescharacteristic, complemented
36#91783—21no—
37#91782C2211yescharacteristic
38#91782C2211yescharacteristic, complemented
39C4⋊C4×D15C2211yescharacteristic, complemented
40#91777C2211yescharacteristic, complemented
41#91773—21no—
42#91771—21no—
43C3×C5×#107C2211yescharacteristic, complemented
44C3×C5×#107C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic, complemented
46C3×C5×#102C2211yescharacteristic, complemented
47C3×C5×C22⋊C8C2211yescharacteristic, complemented
48#91116C2211yescharacteristic, complemented
49#91105C2211yescharacteristic
50#91105C2211yescharacteristic, complemented
51#91104C2211yescharacteristic, complemented
52#91098C2211yescharacteristic, complemented
53C8×Dic15C2211yescharacteristic, complemented
54#91093C2211yescharacteristic
55#91093C2211yescharacteristic
56#91093C2211yescharacteristic, complemented
57#91093C2211yescharacteristic, complemented
58#91093C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60#81302—51nomaximal, Hall
61#65943—31no—
62#65841—31no—
63C5×#480D311yescharacteristic, complemented
64#65327—31no—
65C2×#3941—31no—
66#65179—31no—
67#65172—31no—
68#65171—31no—
69#65161—31no—
70#65075—31no—
71#65062—31no—
72D5×#102—31no—
73#65049—31no—
74#65021—31no—
75#65014—31no—
76C23×D15—21no—
77C23×D15—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84C2×#1220—21no—
85C2×#1220—21no—
86C2×#1220D411yescharacteristic
87D4×D15—22no—
88D4×D15—41no—
89D4×D15—44no—
90#6817—44no—
91C2×D60—22no—
92C2×D60—21no—
93C2×D60—21no—
94C2×D60—21no—
95C2×D60—41no—
96C2×D60C2311yescharacteristic
97C2×D60C2311yescharacteristic
98C2×D60C2311yescharacteristic
99C2×C4×D15—21no—
100C2×C4×D15—21no—
101C2×C4×D15—21no—
102C2×C4×D15C2311yescharacteristic
103C2×Dic30—21no—
104C2×C3×C5×C8C2311yescharacteristic
105C2×C3×C5×C8C2311yescharacteristic
106C3×C5×C4⋊C4—21no—
107C3×C5×C4⋊C4C2311yescharacteristic
108C3×C5×C4⋊C4C2311yescharacteristic
109C3×C5×C4⋊C4C2311yescharacteristic
110C3×C5×C22⋊C4—21no—
111#6719D411yescharacteristic
112#6715—41no—
113#6714—21no—
114#6714—21no—
115#6714—21no—
116#6714—21no—
117#6714—21no—
118#6714D411yescharacteristic
119C4⋊Dic15C2311yescharacteristic
120#6712—21no—
121#6712—21no—
122#6712D411yescharacteristic
123C4×Dic15C2311yescharacteristic
124C2×C3⋊#168—41no—
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127D120—22no—
128D120—41no—
129C8×D15—41no—
130#5609—51no—
131#5507—51no—
132C3×#480D511yescharacteristic, complemented
133#5038—51no—
134C2×#809—51no—
135#4890—51no—
136#4883—51no—
137#4882—51no—
138#4872—51no—
139#4786—51no—
140#4773—51no—
141D3×#102—51no—
142#4760—51no—
143#4732—51no—
144#67⋊C8—51no—
145C2×D4×D5—31no—
146C2×D4×D5—61no—
147C2×#709—61no—
148C22×D20—31no—
149C5×#121C2×D311yescharacteristic
150C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
151#4086—31no—
152#4083—61no—
153C2×#686—31no—
154#4076—31no—
155#4075—61no—
156C4×C22⋊D5—31no—
157C22×#168—31no—
158C2×D40—31no—
159C2×D40—31no—
160C2×C8×D5—31no—
161#4042—61no—
162#4041—31no—
163#4041—31no—
164#4040—61no—
165#4039—31no—
166#4039—31no—
167D5×C4⋊C4—31no—
168#4034—31no—
169#4030—61no—
170#4028—61no—
171C5×#107C2×D311yescharacteristic, complemented
172C5×#107C2×D311yescharacteristic, complemented
173C5×#102C2×D311yescharacteristic, complemented
174C5×#102C2×D311yescharacteristic, complemented
175C5×C22⋊C8C2×D311yescharacteristic, complemented
176#3964—31no—
177#3953—31no—
178#3953—31no—
179#3952—31no—
180#3946—31no—
181C8×Dic5—31no—
182#3941—31no—
183#3941—31no—
184#3941—31no—
185#3941—31no—
186#3941—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5C2×D411yescharacteristic
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—42no—
195C22×D15—42no—
196C22×D15—42no—
197C22×D15—42no—
198C22×D15—81no—
199C22×D15—81no—
200C22×D15C2×D411yescharacteristic
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—42no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—42no—
210C2×C3×C4×C5C2×D411yescharacteristic
211C2×C3×C4×C5C2411yescharacteristic
212#1220—42no—
213#1220—42no—
214#1220—42no—
215#1220—81no—
216#1220D814yescomplemented
217C2×Dic15—21no—
218C2×Dic15C2×D411yescharacteristic
219C2×Dic15C2×D411yescharacteristic
220C2×Dic15C2×D411yescharacteristic
221D60—21no—
222D60—21no—
223D60—21no—
224D60—21no—
225D60—21no—
226D60—42no—
227D60—42no—
228D60—42no—
229D60#4112yescomplemented
230C4×D15—21no—
231C4×D15—21no—
232C4×D15—42no—
233C4×D15—42no—
234C4×D15—42no—
235Dic30—42no—
236C3×C5×C8—21no—
237C3×C5×C8—21no—
238C3⋊#168—21no—
239C3⋊#168—21no—
240C2×D3×D4—51no—
241C2×D3×D4—101no—
242C2×#235—101no—
243C22×D12—51no—
244C3×#121C2×D511yescharacteristic
245C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
246#940—51no—
247#937—101no—
248C2×#213—51no—
249#930—51no—
250#929—101no—
251C4×#67—51no—
252C22×C3⋊C8—51no—
253C2×D24—51no—
254C2×D24—51no—
255C2×D3×C8—51no—
256#896—101no—
257#895—51no—
258#895—51no—
259#894—101no—
260#893—51no—
261#893—51no—
262D3×C4⋊C4—51no—
263#888—51no—
264#884—101no—
265#882—101no—
266C3×#107C2×D511yescharacteristic, complemented
267C3×#107C2×D511yescharacteristic, complemented
268C3×#102C2×D511yescharacteristic, complemented
269C3×#102C2×D511yescharacteristic, complemented
270C3×C22⋊C8C2×D511yescharacteristic, complemented
271#832—51no—
272#821—51no—
273#821—51no—
274(C2×D3)⋊C8—51no—
275Dic3⋊C8—51no—
276C8×Dic3—51no—
277#809—51no—
278#809—51no—
279#809—51no—
280#809—51no—
281#809—51no—
282#807—51no—
283C23×D5—61no—
284C23×D5—61no—
285C2×C5×D4—21no—
286C2×C5×D4C22×D311yescharacteristic
287C22×C4×C5—21no—
288C22×C4×C5C22×D311yescharacteristic
289C2×C22⋊D5—31no—
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C2×C22⋊D5—61no—
293C2×C22⋊D5—61no—
294D4×D5—62no—
295D4×D5—121no—
296D4×D5—124no—
297#709—124no—
298C2×D20—31no—
299C2×D20—31no—
300C2×D20—31no—
301C2×D20—62no—
302C2×D20—61no—
303C2×D20—61no—
304C2×D20—61no—
305C2×D20—121no—
306C2×C4×D5—31no—
307C2×C4×D5—61no—
308C2×C4×D5—61no—
309C2×C4×D5—61no—
310C2×Dic10—61no—
311C2×C5×C8C22×D311yescharacteristic
312C2×C5×C8C22×D311yescharacteristic
313C5×C4⋊C4—21no—
314C5×C4⋊C4C22×D311yescharacteristic
315C5×C4⋊C4C22×D311yescharacteristic
316C5×C4⋊C4C22×D311yescharacteristic
317C5×C22⋊C4—21no—
318C22⋊Dic5—31no—
319#686—121no—
320#685—31no—
321#685—61no—
322#685—61no—
323#685—61no—
324#685—61no—
325#685—61no—
326C4⋊Dic5—31no—
327#683—31no—
328#683—61no—
329#683—61no—
330C4×Dic5—31no—
331C2×#168—31no—
332C2×#168—31no—
333C2×#168—121no—
334D40—62no—
335D40—121no—
336C8×D5—121no—
337#547—151no—
338D42—151no—
339#486—151no—
340#480—151no—
341#480D1511yescharacteristic, complemented
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—151no—
347#447—151no—
348C4×D8—151no—
349C8×D4—151no—
350C2×#102—151no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—41no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5C2×D812yes—
358C22×C3×C5C22×D411yescharacteristic
359C2×D15—21no—
360C2×D15—21no—
361C2×D15—22no—
362C2×D15—41no—
363C2×D15—41no—
364C2×D15—41no—
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C2×D15—41no—
369C2×D15—41no—
370C2×D15—84no—
371C2×D15—84no—
372C2×D15C2×D812yes—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5—41no—
376C3×C4×C5—41no—
377C3×C4×C5C2×#4111yescharacteristic
378C3×C4×C5H(5,𝔽2)11yescharacteristic
379Dic15—21no—
380Dic15—21no—
381Dic15—41no—
382Dic15C2×D812yes—
383C23×D3—101no—
384C23×D3—101no—
385C2×C3×D4—21no—
386C2×C3×D4C22×D511yescharacteristic
387C22×C3×C4—21no—
388C22×C3×C4C22×D511yescharacteristic
389C2×#67—51no—
390C2×#67—101no—
391C2×#67—101no—
392C2×#67—101no—
393C2×#67—101no—
394D3×D4—102no—
395D3×D4—201no—
396D3×D4—204no—
397#235—204no—
398C2×D12—51no—
399C2×D12—51no—
400C2×D12—51no—
401C2×D12—102no—
402C2×D12—101no—
403C2×D12—101no—
404C2×D12—101no—
405C2×D12—201no—
406C2×C4×D3—51no—
407C2×C4×D3—101no—
408C2×C4×D3—101no—
409C2×C4×D3—101no—
410C2×Dic6—101no—
411C2×C3×C8C22×D511yescharacteristic
412C2×C3×C8C22×D511yescharacteristic
413C3×C4⋊C4—21no—
414C3×C4⋊C4C22×D511yescharacteristic
415C3×C4⋊C4C22×D511yescharacteristic
416C3×C4⋊C4C22×D511yescharacteristic
417C3×C22⋊C4—21no—
418#217—51no—
419#213—201no—
420(C2×D3)⋊C4—51no—
421(C2×D3)⋊C4—101no—
422(C2×D3)⋊C4—101no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425(C2×D3)⋊C4—101no—
426C4⋊Dic3—51no—
427Dic3⋊C4—51no—
428Dic3⋊C4—101no—
429Dic3⋊C4—101no—
430C4×Dic3—51no—
431C2×C3⋊C8—51no—
432C2×C3⋊C8—51no—
433C2×C3⋊C8—201no—
434D24—102no—
435D24—201no—
436D3×C8—201no—
437C23×C5—21no—
438C23×C5D3×D411yescharacteristic
439C22×D5—31no—
440C22×D5—61no—
441C22×D5—61no—
442C22×D5—61no—
443C22×D5—122no—
444C22×D5—122no—
445C22×D5—122no—
446C22×D5—122no—
447C22×D5—241no—
448C22×D5—241no—
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—42no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—42no—
458C2×C4×C5D3×D411yescharacteristic
459C2×C4×C5C23×D311yescharacteristic
460C22⋊D5—34no—
461C22⋊D5—122no—
462C22⋊D5—122no—
463C22⋊D5—122no—
464C22⋊D5—241no—
465C2×Dic5—31no—
466C2×Dic5—31no—
467C2×Dic5—31no—
468C2×Dic5—61no—
469D20—32no—
470D20—61no—
471D20—61no—
472D20—61no—
473D20—61no—
474D20—61no—
475D20—122no—
476D20—122no—
477D20—122no—
478C4×D5—61no—
479C4×D5—61no—
480C4×D5—122no—
481C4×D5—122no—
482C4×D5—122no—
483Dic10—122no—
484C5×C8—21no—
485C5×C8—21no—
486#168—61no—
487#168—61no—
488C2×#41—301no—
489C22×D4—151no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—151no—
493C2×D8—151no—
494C2×D8—151no—
495C22×C8—151no—
496C22×C8—151no—
497C4⋊Q8—151no—
498#127—151no—
499#123—301no—
500#123—301no—
501C22⋊Q8—301no—
502#121—151no—
503#121—151no—
504#121—151no—
505#121—301no—
506#121C2×D1511yescharacteristic
507#120—301no—
508#120—301no—
509C4×D4—151no—
510C4×D4—151no—
511C4×D4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4C2×D1511yescharacteristic, complemented
514#107—151no—
515#107C2×D1511yescharacteristic, complemented
516#107C2×D1511yescharacteristic, complemented
517C4⋊C8—151no—
518#102—151no—
519#102—151no—
520#102—151no—
521#102—151no—
522#102—151no—
523#102—151no—
524#102—151no—
525#102—151no—
526#102C2×D1511yescharacteristic, complemented
527#102C2×D1511yescharacteristic, complemented
528C22⋊C8—151no—
529C22⋊C8C2×D1511yescharacteristic, complemented
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5—81no—
533C2×C3×C5#54611yescharacteristic
534C2×C3×C5C22×D811yescharacteristic
535C2×C3×C5#57711yescharacteristic
536D15—22no—
537D15—42no—
538D15—81no—
539D15—81no—
540C23×C3—21no—
541C23×C3D4×D511yescharacteristic
542C22×D3—51no—
543C22×D3—101no—
544C22×D3—101no—
545C22×D3—101no—
546C22×D3—202no—
547C22×D3—202no—
548C22×D3—202no—
549C22×D3—202no—
550C22×D3—401no—
551C22×D3—401no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—42no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—42no—
561C2×C3×C4D4×D511yescharacteristic
562C2×C3×C4C23×D511yescharacteristic
563#67—54no—
564#67—202no—
565#67—202no—
566#67—202no—
567#67—401no—
568C2×Dic3—51no—
569C2×Dic3—51no—
570C2×Dic3—51no—
571C2×Dic3—101no—
572D12—52no—
573D12—101no—
574D12—101no—
575D12—101no—
576D12—101no—
577D12—101no—
578D12—202no—
579D12—202no—
580D12—202no—
581C4×D3—101no—
582C4×D3—101no—
583C4×D3—202no—
584C4×D3—202no—
585C4×D3—202no—
586Dic6—202no—
587C3×C8—21no—
588C3×C8—21no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—41no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5D3×D812yes—
597C22×C5C2×D3×D411yescharacteristic
598C2×D5—32no—
599C2×D5—61no—
600C2×D5—61no—
601C2×D5—62no—
602C2×D5—121no—
603C2×D5—121no—
604C2×D5—121no—
605C2×D5—121no—
606C2×D5—121no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—244no—
611C2×D5—244no—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5—41no—
615C4×C5—41no—
616C4×C5D3×#4111yescharacteristic
617C4×C5#100911yescharacteristic
618Dic5—32no—
619Dic5—61no—
620Dic5—61no—
621Dic5—121no—
622C24—301no—
623C24—301no—
624#41—604no—
625C2×Q8—301no—
626C2×D4—21no—
627C2×D4—151no—
628C2×D4—151no—
629C2×D4—151no—
630C2×D4—151no—
631C2×D4—302no—
632C2×D4—301no—
633C2×D4—301no—
634C2×D4—301no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—302no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4—601no—
641C2×D4—601no—
642C2×D4—604no—
643C2×D4C22×D1511yescharacteristic
644C22×C4—21no—
645C22×C4—151no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4C22×D1511yescharacteristic
650D8—302no—
651D8—601no—
652D8—601no—
653C2×C8—151no—
654C2×C8—151no—
655C2×C8—601no—
656C2×C8—601no—
657C2×C8C22×D1511yescharacteristic
658C2×C8C22×D1511yescharacteristic
659C4⋊C4—21no—
660C4⋊C4—151no—
661C4⋊C4—151no—
662C4⋊C4—301no—
663C4⋊C4—301no—
664C4⋊C4C22×D1511yescharacteristic
665C4⋊C4C22×D1511yescharacteristic
666C4⋊C4C22×D1511yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—151no—
669C22⋊C4—151no—
670C22⋊C4—301no—
671C22⋊C4—301no—
672C22⋊C4—301no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—151no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3D5×D812yes—
683C22×C3C2×D4×D511yescharacteristic
684C2×D3—52no—
685C2×D3—101no—
686C2×D3—101no—
687C2×D3—102no—
688C2×D3—201no—
689C2×D3—201no—
690C2×D3—201no—
691C2×D3—201no—
692C2×D3—201no—
693C2×D3—201no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—404no—
697C2×D3—404no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4D5×#4111yescharacteristic
703C3×C4#414911yescharacteristic
704Dic3—52no—
705Dic3—101no—
706Dic3—101no—
707Dic3—201no—
708C2×C5—22no—
709C2×C5—81no—
710C2×C5#565411yescharacteristic
711C2×C5C2×D3×D811yescharacteristic
712C2×C5#577811yescharacteristic
713D5—62no—
714D5—122no—
715D5—241no—
716D5—241no—
717C23—21no—
718C23—151no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—602no—
723C23—602no—
724C23—602no—
725C23—602no—
726C23—1201no—
727C23—1201no—
728C23D4×D1511yescharacteristic
729Q8—602no—
730D4—21no—
731D4—21no—
732D4—42no—
733D4—154no—
734D4—152no—
735D4—301no—
736D4—301no—
737D4—301no—
738D4—301no—
739D4—301no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—602no—
746D4—1201no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—42no—
753C2×C4—151no—
754C2×C4—151no—
755C2×C4—151no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—602no—
760C2×C4—602no—
761C2×C4—602no—
762C2×C4D4×D1511yescharacteristic
763C2×C4C23×D1511yescharacteristic
764C8—21no—
765C8—21no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—81no—
770C2×C3#6598811yescharacteristic
771C2×C3C2×D5×D811yescharacteristic
772C2×C3#6611211yescharacteristic
773D3—102no—
774D3—202no—
775D3—401no—
776D3—401no—
777C5#8130211yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—152no—
784C22—301no—
785C22—301no—
786C22—302no—
787C22—601no—
788C22—601no—
789C22—601no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—1204no—
796C22—1204no—
797C22D8×D1512yes—
798C22C2×D4×D1511yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—152no—
804C4—301no—
805C4—301no—
806C4—601no—
807C4#41×D1511yescharacteristic
808C4#9210011yescharacteristic
809C3#1061303311yescharacteristic, complemented, Sylow
810C2—22no—
811C2—81no—
812C2—302no—
813C2—602no—
814C2—1201no—
815C2—1201no—
816C2#1175641311yescharacteristic
817C2C2×D8×D1511yescharacteristic
818C2#1175653711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#480C2
socleC22×C3×C5C22×D4
hypercenter#480D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #11756368C2semidirect
2. #11756266C2semidirect
3. C3×C5×#480C2semidirect
4. #11751139C2semidirect
5. C2×#91093C2semidirect
6. #11750991C2semidirect
7. #11750984C2semidirect
8. #11750983C2semidirect
9. #11750973C2semidirect
10. #11750887C2semidirect
11. #11750874C2semidirect
12. D15×#102C2semidirect
13. #11750861C2semidirect
14. #11750833C2semidirect
15. #11750826C2semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
25. C2×#6715C22semidirect
26. #91819C22semidirect
29. C22×C3⋊#168C22semidirect
31. C2×D120C22semidirect
32. C2×C8×D15C22semidirect
35. #91784C22semidirect
38. #91782C22semidirect
39. C4⋊C4×D15C22semidirect
40. #91777C22semidirect
43. C3×C5×#107C22semidirect
44. C3×C5×#107C22semidirect
45. C3×C5×#102C22semidirect
46. C3×C5×#102C22semidirect
47. C3×C5×C22⋊C8C22semidirect
48. #91116C22semidirect
50. #91105C22semidirect
51. #91104C22semidirect
52. #91098C22semidirect
53. C8×Dic15C22semidirect
56. #91093C22semidirect
57. #91093C22semidirect
58. #91093C22semidirect
59. #91091C22semidirect
63. C5×#480D3semidirect
132. C3×#480D5semidirect
150. C2×C5×C4⋊C4C2×D3semidirect
171. C5×#107C2×D3semidirect
172. C5×#107C2×D3semidirect
173. C5×#102C2×D3semidirect
174. C5×#102C2×D3semidirect
175. C5×C22⋊C8C2×D3semidirect
216. #1220D8semidirect
229. D60#41semidirect
245. C2×C3×C4⋊C4C2×D5semidirect
266. C3×#107C2×D5semidirect
267. C3×#107C2×D5semidirect
268. C3×#102C2×D5semidirect
269. C3×#102C2×D5semidirect
270. C3×C22⋊C8C2×D5semidirect
341. #480D15semidirect
513. C2×C4⋊C4C2×D15semidirect
515. #107C2×D15semidirect
516. #107C2×D15semidirect
526. #102C2×D15semidirect
527. #102C2×D15semidirect
529. C22⋊C8C2×D15semidirect
676. C3×C5#3294semidirect
777. C5#81302semidirect
809. C3#10613033semidirect

Maximal subgroups

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

subgroupindex
#117563682
#117562662
C3×C5×#4802
#117511392
C2×#910932
#117509912
#117509842
#117509832
#117509732
#117508872
#117508742
D15×#1022
#117508612
#117508332
#117508262
#106130333
#813025