Finite Group Databasebeta

← #14458478

Subgroups — #14458478

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5511C211yesmaximal, characteristic, complemented
2#67×D20C211yesmaximal, characteristic
3#11751069C211yesmaximal, characteristic, complemented
4C2×C3×#3941C211yesmaximal, characteristic, complemented
5#11748535C211yesmaximal, characteristic, complemented
6#11748527C211yesmaximal, characteristic, complemented
7#67×#168C211yesmaximal, characteristic, complemented
8#11747483C211yesmaximal, characteristic, complemented
9D3×#3941C211yesmaximal, characteristic, complemented
10#11747404C211yesmaximal, characteristic, complemented
11#11747403C211yesmaximal, characteristic, complemented
12#11747321C211yesmaximal, characteristic, complemented
13#11747320C211yesmaximal, characteristic, complemented
14#11747247C211yesmaximal, characteristic, complemented
15#11747221C211yesmaximal, characteristic, complemented
16#10615365—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C2×D5×#67—21no—
19C2×D3×D20C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
21#91819C2211yescharacteristic
22C4×C5×#67—21no—
23C4×C5×#67C2211yescharacteristic
24C5×#924—21no—
25C5×#924C2211yescharacteristic, complemented
26C5×#897C2211yescharacteristic, complemented
27C5×#896—21no—
28C5×D3×C4⋊C4C2211yescharacteristic, complemented
29C5×#889—21no—
30C5×#888C2211yescharacteristic, complemented
31C5×#887C2211yescharacteristic, complemented
32C22×C3×#168C2211yescharacteristic, complemented
33#91564—21no—
34#91474—21no—
35#91458C2211yescharacteristic
36#91456C2211yescharacteristic
37Dic3×D20C2211yescharacteristic
38#91409—21no—
39C2×#6660C2211yescharacteristic, complemented
40C2×#6655C2211yescharacteristic
41C2×#6655C2211yescharacteristic, complemented
42C2×D3×#168C2211yescharacteristic, complemented
43#91114C2211yescharacteristic, complemented
44#91093C2211yescharacteristic, complemented
45#91093C2211yescharacteristic, complemented
46#91092C2211yescharacteristic, complemented
47#91092C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50C3×#3941C2211yescharacteristic, complemented
51C3×#3941C2211yescharacteristic, complemented
52#90985C2211yescharacteristic, complemented
53Dic3⋊#168C2211yescharacteristic, complemented
54#90973C2211yescharacteristic, complemented
55#90969C2211yescharacteristic, complemented
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#78758—51nomaximal, Hall
61C5×#554—31no—
62D4×D20—31no—
63#65377—31no—
64#65373—31no—
65#65337—31no—
66#65337—31no—
67#65335—31no—
68#65335—31no—
69#65316—31no—
70C4×#688—31no—
71D4×#168—31no—
72#65257—31no—
73#65257—31no—
74C2×#3941—31no—
75C2×#3941D311yescharacteristic, complemented
76C23×C3×D5—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×D60C2311yescharacteristic
82C2×C5×#67D411yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3C2311yescharacteristic
85C2×C5×Dic6—21no—
86C2×C5×Dic6C2311yescharacteristic
87C2×C3×D20—22no—
88C2×C3×D20—21no—
89C2×C3×D20—41no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×D20C2311yescharacteristic
92D5×#67—44no—
93C2×#1202—21no—
94C2×#1202—21no—
95C2×#1202—21no—
96C2×#1201—21no—
97C2×D5×Dic3—21no—
98D3×D20—22no—
99D3×D20—41no—
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103#6714—21no—
104C4⋊Dic15C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#217—21no—
108C5×#217D411yescharacteristic
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4—21no—
115C5×Dic3⋊C4—21no—
116C5×Dic3⋊C4—21no—
117C5×Dic3⋊C4D411yescharacteristic
118C4×C5×Dic3—21no—
119C4×C5×Dic3C2311yescharacteristic
120C2×C3×#168—41no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123#6665—21no—
124#6665—21no—
125#6660—41no—
126#6655—22no—
127#6655—41no—
128D3×#168—41no—
129D4×#67—51no—
130#5511D511yescharacteristic, complemented
131C2×C3×#102—51no—
132#5218—51no—
133#5114—51no—
134C8×#67—51no—
135#4968—51no—
136#4778—51no—
137#4777—51no—
138#4776—51no—
139D3×#102—51no—
140#4762—51no—
141#4761—51no—
142#4760—51no—
143#4758—51no—
144C2×D4×D5—61no—
145C22×D20—31no—
146C22×D20C2×D311yescharacteristic
147C5×C4⋊Q8—31no—
148C5×#125—61no—
149C5×C22⋊Q8—31no—
150C5×C22⋊Q8—31no—
151C5×C22⋊Q8—61no—
152C5×C22⋊Q8—61no—
153C4×C5×Q8—31no—
154C4×C5×D4—31no—
155C4×C5×D4—61no—
156C2×C5×C4⋊C4—31no—
157C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
158C2×#688—31no—
159C2×#688—31no—
160C2×#688—31no—
161#4076—31no—
162#4076—31no—
163C22×#168—31no—
164C22×#168C2×D311yescharacteristic, complemented
165#4041—61no—
166#4028—61no—
167#4028—61no—
168#4020—31no—
169C4×D20—31no—
170#3967—31no—
171C22⋊#168—31no—
172C22⋊#168—31no—
173#3941—31no—
174#3941—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941C2×D311yescharacteristic
179#3941C2×D311yescharacteristic
180#3941C2×D311yescharacteristic, complemented
181#3941C2×D311yescharacteristic, complemented
182#3940—31no—
183#3940—31no—
184#3940—31no—
185C4⋊#168—31no—
186C4×#168—31no—
187#3295—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C5×D3C2×D411yescharacteristic
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—42no—
194C22×C3×D5—42no—
195C22×C3×D5—81no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C2×D3×D5—81no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2411yescharacteristic
206#1220—42no—
207C2×Dic15—21no—
208D60—21no—
209D60—21no—
210C5×#67SD1614yescomplemented
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C2×C5×Dic3C2×D411yescharacteristic
216C4×C5×D3—21no—
217C4×C5×D3—21no—
218C4×C5×D3—81no—
219C5×Dic6—21no—
220C5×Dic6—21no—
221C5×Dic6—81no—
222C3×D20—21no—
223C3×D20—21no—
224C3×D20—21no—
225C3×D20—42no—
226C3×D20#4112yes—
227#1202—42no—
228#1202—42no—
229#1202—81no—
230#1201—42no—
231D5×Dic3—42no—
232C3⋊#168—21no—
233C3⋊#168—21no—
234C3×#168—21no—
235C3×#168—21no—
236C22×C3×D4—51no—
237C22×#67—101no—
238C2×D3×D4—51no—
239C22×C3×C8—51no—
240C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
241#953—101no—
242#940—51no—
243#939—101no—
244#938—51no—
245#937—101no—
246D4×Dic3—51no—
247C2×#214—51no—
248C2×#214—51no—
249#930—51no—
250C4×#67—21no—
251C4×#67C2×D511yescharacteristic
252#924—21no—
253#924C2×D511yescharacteristic, complemented
254C2×#204—51no—
255C2×D3×C8—51no—
256#897C2×D511yescharacteristic, complemented
257#896—21no—
258D3×C4⋊C4C2×D511yescharacteristic, complemented
259#889—21no—
260#888C2×D511yescharacteristic, complemented
261#887C2×D511yescharacteristic, complemented
262C3×#102—51no—
263C3×#102—51no—
264C3×#102—51no—
265C3×#102—51no—
266#832—51no—
267#832—51no—
268#830—51no—
269#821—51no—
270(C2×D3)⋊C8—51no—
271#817—51no—
272#816—51no—
273Dic3⋊C8—51no—
274C8×Dic3—51no—
275#809—51no—
276#809—51no—
277#808—51no—
278#808—51no—
279C23×D5—21no—
280C23×D5—61no—
281C2×C5×Q8—31no—
282C2×C5×Q8—61no—
283C2×C5×D4—31no—
284C22×C4×C5—21no—
285C22×C4×C5—31no—
286C22×C4×C5—61no—
287C22×C4×C5C22×D311yescharacteristic
288C2×C22⋊D5—61no—
289C2×C22⋊D5—61no—
290D4×D5—124no—
291C2×D20—22no—
292C2×D20—21no—
293C2×D20—31no—
294C2×D20—41no—
295C2×D20—62no—
296C2×D20—61no—
297C2×D20—61no—
298C2×D20—61no—
299C2×D20—121no—
300C2×D20C22×D311yescharacteristic
301C2×D20C22×D311yescharacteristic
302C2×C4×D5—61no—
303C5×C4⋊C4—21no—
304C5×C4⋊C4—31no—
305C5×C4⋊C4—31no—
306C5×C4⋊C4—61no—
307C5×C4⋊C4—61no—
308C5×C4⋊C4—61no—
309C5×C4⋊C4—61no—
310C5×C4⋊C4—61no—
311C5×C4⋊C4C22×D311yescharacteristic
312C5×C4⋊C4C22×D311yescharacteristic
313C5×C22⋊C4—31no—
314C5×C22⋊C4—31no—
315C5×C22⋊C4—61no—
316C5×C22⋊C4—61no—
317C42×C5—31no—
318C42×C5—61no—
319#688—62no—
320#688—121no—
321#688—121no—
322#685—61no—
323#685—61no—
324#685—61no—
325C4⋊Dic5—31no—
326C2×#168—31no—
327C2×#168—31no—
328C2×#168—41no—
329C2×#168—121no—
330C2×#168C22×D311yescharacteristic
331C2×#168C22×D311yescharacteristic
332#554—31no—
333D42—151no—
334#486—151no—
335#481—151no—
336#481—151no—
337#476—151no—
338#465—151no—
339#465—151no—
340#460—151no—
341#450—151no—
342#450—151no—
343C4×SD16—151no—
344C8×D4—151no—
345C2×#102—51no—
346C2×#102—151no—
347C22×C3×C5—21no—
348C22×C3×C5—21no—
349C22×C3×C5C2×SD1612yes—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×C5×D3—21no—
355C2×C5×D3—21no—
356C2×C5×D3C2×SD1612yes—
357C2×C3×D5—22no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—41no—
363C2×C3×D5—84no—
364D3×D5—84no—
365C3×C4×C5—21no—
366C3×C4×C5—41no—
367C3×C4×C5—41no—
368C3×C4×C5C2×#4111yescharacteristic
369C3×C4×C5H(5,𝔽2)11yescharacteristic
370Dic15—41no—
371C5×Dic3—21no—
372C5×Dic3—21no—
373C5×Dic3—41no—
374C5×Dic3—41no—
375C5×Dic3C2×SD1612yes—
376C24×C3—101no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C2×C3×D4—51no—
380C2×C3×D4—102no—
381C2×C3×D4—101no—
382C2×C3×D4—201no—
383C22×C3×C4—21no—
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—101no—
386C2×#67—101no—
387C2×#67—101no—
388C2×#67—101no—
389C2×#67—101no—
390C2×#67—204no—
391C2×#67C22⋊D511yescharacteristic
392C22×Dic3—101no—
393D3×D4—102no—
394D3×D4—201no—
395C2×D12—51no—
396C2×C4×D3—21no—
397C2×C4×D3C22×D511yescharacteristic
398C2×Dic6—21no—
399C2×Dic6C22×D511yescharacteristic
400C2×C3×C8—51no—
401C2×C3×C8—51no—
402C2×C3×C8—201no—
403C3×C4⋊C4—21no—
404C3×C4⋊C4C22×D511yescharacteristic
405C3×C4⋊C4C22×D511yescharacteristic
406#217—21no—
407#217—101no—
408#217—101no—
409#217C22⋊D511yescharacteristic
410#214—102no—
411#214—201no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4C22⋊D511yescharacteristic
415C4⋊Dic3—21no—
416C4⋊Dic3—51no—
417C4⋊Dic3C22×D511yescharacteristic
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4C22⋊D511yescharacteristic
423C4×Dic3—21no—
424C4×Dic3C22×D511yescharacteristic
425C2×C3⋊C8—51no—
426C2×C3⋊C8—51no—
427#204—201no—
428D3×C8—201no—
429C23×C5—31no—
430C23×C5D3×D411yescharacteristic
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—42no—
434C22×D5—42no—
435C22×D5—61no—
436C22×D5—81no—
437C22×D5—122no—
438C22×D5—122no—
439C22×D5—241no—
440C5×Q8—61no—
441C5×Q8—61no—
442C5×Q8—241no—
443C5×D4—34no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—31no—
449C2×C4×C5—31no—
450C2×C4×C5—31no—
451C2×C4×C5—61no—
452C2×C4×C5—61no—
453C2×C4×C5—61no—
454C2×C4×C5—61no—
455C2×C4×C5—81no—
456C2×C4×C5—241no—
457C2×C4×C5D3×D411yescharacteristic
458C2×C4×C5C23×D311yescharacteristic
459C22⋊D5—122no—
460C22⋊D5—122no—
461C2×Dic5—61no—
462D20—21no—
463D20—21no—
464D20—21no—
465D20—42no—
466D20—61no—
467D20—61no—
468D20—122no—
469D20—122no—
470D20—241no—
471D20#23512yes—
472C4×D5—122no—
473#168—21no—
474#168—21no—
475#168—61no—
476#168—61no—
477C22×D4—51no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—151no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—51no—
484C22×C8—151no—
485C4⋊Q8—31no—
486#127—151no—
487#125—61no—
488C22⋊Q8—31no—
489C22⋊Q8—31no—
490C22⋊Q8—61no—
491C22⋊Q8—61no—
492#121—151no—
493#121—151no—
494#121—301no—
495#120—301no—
496#120—301no—
497C4×Q8—31no—
498C4×D4—31no—
499C4×D4—61no—
500C4×D4—151no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4D3×D511yescharacteristic, complemented
503#106—151no—
504#106—151no—
505#106—151no—
506C4⋊C8—151no—
507#103—151no—
508#102—51no—
509#102—51no—
510#102—51no—
511#102—51no—
512#102—151no—
513#102—151no—
514#102—151no—
515#102—151no—
516#102—151no—
517C22⋊C8—151no—
518C22⋊C8—151no—
519C4×C8—151no—
520C2×C3×C5—22no—
521C2×C3×C5#54611yescharacteristic
522C2×C3×C5C22×SD1611yescharacteristic
523C2×C3×C5#57611yescharacteristic
524D15—81no—
525C3×D5—42no—
526C3×D5—81no—
527C5×D3—22no—
528C23×C3—101no—
529C23×C3—101no—
530C23×C3—202no—
531C23×C3—202no—
532C23×C3—401no—
533C23×C3C2×C22⋊D511yescharacteristic
534C22×D3—101no—
535C22×D3—202no—
536C22×D3—202no—
537C22×D3—401no—
538C22×D3C2×C22⋊D511yescharacteristic
539C3×D4—52no—
540C3×D4—101no—
541C3×D4—101no—
542C3×D4—101no—
543C3×D4—202no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—81no—
549C2×C3×C4C2×C22⋊D511yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551#67—202no—
552#67—202no—
553#67—202no—
554#67—202no—
555#67—401no—
556#67#68814yescomplemented
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—101no—
560C2×Dic3—202no—
561C2×Dic3C2×C22⋊D511yescharacteristic
562C2×Dic3C2×C22⋊D511yescharacteristic
563C2×Dic3C2×C22⋊D511yescharacteristic
564D12—101no—
565D12—101no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—81no—
569Dic6—21no—
570Dic6—21no—
571Dic6—81no—
572C3×C8—101no—
573C3×C8—101no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—32no—
579C22×C5—61no—
580C22×C5—61no—
581C22×C5D3×SD1612yes—
582C22×C5C2×D3×D411yescharacteristic
583C2×D5—22no—
584C2×D5—41no—
585C2×D5—41no—
586C2×D5—41no—
587C2×D5—41no—
588C2×D5—41no—
589C2×D5—84no—
590C2×D5—121no—
591C2×D5—121no—
592C2×D5—121no—
593C2×D5—244no—
594C4×C5—21no—
595C4×C5—32no—
596C4×C5—41no—
597C4×C5—41no—
598C4×C5—61no—
599C4×C5—61no—
600C4×C5—121no—
601C4×C5—121no—
602C4×C5C2×#23511yescharacteristic
603C4×C5#100411yescharacteristic
604Dic5—121no—
605C24—101no—
606C24—301no—
607C2×Q8—31no—
608C2×Q8—61no—
609C2×D4—31no—
610C2×D4—51no—
611C2×D4—51no—
612C2×D4—102no—
613C2×D4—101no—
614C2×D4—151no—
615C2×D4—201no—
616C2×D4—301no—
617C2×D4—301no—
618C2×D4—301no—
619C2×D4—302no—
620C2×D4—301no—
621C2×D4—301no—
622C2×D4—601no—
623C2×D4—604no—
624C22×C4—21no—
625C22×C4—31no—
626C22×C4—61no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—302no—
630SD16—601no—
631SD16—601no—
632C2×C8—51no—
633C2×C8—51no—
634C2×C8—151no—
635C2×C8—151no—
636C2×C8—201no—
637C2×C8—601no—
638C4⋊C4—21no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—151no—
647C4⋊C4C2×D3×D511yescharacteristic
648C4⋊C4C2×D3×D511yescharacteristic
649C22⋊C4—31no—
650C22⋊C4—31no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—31no—
657C42—61no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—102no—
662C22×C3—201no—
663C22×C3—201no—
664C22×C3—201no—
665C22×C3—201no—
666C22×C3—201no—
667C22×C3—404no—
668C22×C3C2×#68812yes—
669C22×C3C22×C22⋊D511yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—201no—
673C2×D3—201no—
674C2×D3—201no—
675C2×D3—404no—
676C2×D3C2×#68812yes—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4D5×#4111yescharacteristic
681C3×C4#414911yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—201no—
687Dic3C2×#68812yes—
688C2×C5—22no—
689C2×C5—62no—
690C2×C5#549011yescharacteristic
691C2×C5#575711yescharacteristic
692C2×C5C2×D3×SD1611yescharacteristic
693D5—42no—
694D5—81no—
695D5—241no—
696C23—31no—
697C23—101no—
698C23—101no—
699C23—202no—
700C23—202no—
701C23—301no—
702C23—401no—
703C23—602no—
704C23—602no—
705C23—1201no—
706C23D3×C22⋊D511yescharacteristic
707Q8—61no—
708Q8—61no—
709Q8—241no—
710D4—34no—
711D4—52no—
712D4—101no—
713D4—101no—
714D4—101no—
715D4—202no—
716D4—301no—
717D4—301no—
718D4—602no—
719D4—602no—
720D4—602no—
721D4—602no—
722D4—1201no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—81no—
735C2×C4—241no—
736C2×C4—301no—
737C2×C4—602no—
738C2×C4D3×C22⋊D511yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—101no—
741C8—101no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—202no—
746C2×C3—401no—
747C2×C3C22×#68811yescharacteristic
748C2×C3#6616311yescharacteristic
749C2×C3#6616911yescharacteristic
750D3—22no—
751D3—401no—
752C5#7875811yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—102no—
759C22—201no—
760C22—201no—
761C22—201no—
762C22—201no—
763C22—201no—
764C22—404no—
765C22—601no—
766C22—601no—
767C22—601no—
768C22—1204no—
769C22D3×#68812yes—
770C22C2×D3×C22⋊D511yescharacteristic
771C4—21no—
772C4—32no—
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—601no—
780C4D5×#23511yescharacteristic
781C4#9201711yescharacteristic
782C3#1061536511yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—202no—
786C2—401no—
787C2—1201no—
788C2#1175465011yescharacteristic
789C2#1175469711yescharacteristic
790C2C2×D3×#68811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#67×D20C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5511C2semidirect
3. #11751069C2semidirect
4. C2×C3×#3941C2semidirect
5. #11748535C2semidirect
6. #11748527C2semidirect
7. #67×#168C2semidirect
8. #11747483C2semidirect
9. D3×#3941C2semidirect
10. #11747404C2semidirect
11. #11747403C2semidirect
12. #11747321C2semidirect
13. #11747320C2semidirect
14. #11747247C2semidirect
15. #11747221C2semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
25. C5×#924C22semidirect
26. C5×#897C22semidirect
28. C5×D3×C4⋊C4C22semidirect
30. C5×#888C22semidirect
31. C5×#887C22semidirect
32. C22×C3×#168C22semidirect
39. C2×#6660C22semidirect
41. C2×#6655C22semidirect
42. C2×D3×#168C22semidirect
43. #91114C22semidirect
44. #91093C22semidirect
45. #91093C22semidirect
46. #91092C22semidirect
47. #91092C22semidirect
50. C3×#3941C22semidirect
51. C3×#3941C22semidirect
52. #90985C22semidirect
53. Dic3⋊#168C22semidirect
54. #90973C22semidirect
55. #90969C22semidirect
57. #90964C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
75. C2×#3941D3semidirect
130. #5511D5semidirect
157. C2×C5×C4⋊C4C2×D3semidirect
164. C22×#168C2×D3semidirect
180. #3941C2×D3semidirect
181. #3941C2×D3semidirect
210. C5×#67SD16semidirect
240. C2×C3×C4⋊C4C2×D5semidirect
253. #924C2×D5semidirect
256. #897C2×D5semidirect
258. D3×C4⋊C4C2×D5semidirect
260. #888C2×D5semidirect
261. #887C2×D5semidirect
502. C2×C4⋊C4D3×D5semidirect
556. #67#688semidirect
658. C3×C5#3295semidirect
752. C5#78758semidirect
782. C3#10615365semidirect

Maximal subgroups

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

subgroupindex
C5×#55112
#67×D202
#117510692
C2×C3×#39412
#117485352
#117485272
#67×#1682
#117474832
D3×#39412
#117474042
#117474032
#117473212
#117473202
#117472472
#117472212
#106153653
#787585