Finite Group Databasebeta

← #14458483

Subgroups — #14458483

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
1#11754657C211yesmaximal, characteristic
2#11754508C211yesmaximal, characteristic, complemented
3C8×#1220C211yesmaximal, characteristic, complemented
4C2×C5×#821C211yesmaximal, characteristic, complemented
5C3×#65403C211yesmaximal, characteristic, complemented
6#11748537C211yesmaximal, characteristic, complemented
7#11748372C211yesmaximal, characteristic, complemented
8#11748111C211yesmaximal, characteristic, complemented
9#11748108C211yesmaximal, characteristic, complemented
10#11748011C211yesmaximal, characteristic, complemented
11#11747993C211yesmaximal, characteristic, complemented
12#11747928C211yesmaximal, characteristic, complemented
13#11747808C211yesmaximal, characteristic, complemented
14#11747737C211yesmaximal, characteristic, complemented
15#11747635C211yesmaximal, characteristic, complemented
16#10610489—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×D3×C22⋊D5—21no—
19C2×#6777C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C4×#1220C2211yescharacteristic
22C2×C8×D15C2211yescharacteristic, complemented
23C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
24C3×#4076C2211yescharacteristic
25C3×#4070C2211yescharacteristic, complemented
26C2×C3×#677C2211yescharacteristic, complemented
27#91575—21no—
28#91568—21no—
29#91556—21no—
30#91475—21no—
31#91470C2211yescharacteristic, complemented
32#91466C2211yescharacteristic
33#91463C2211yescharacteristic
34#91453—21no—
35#91437C2211yescharacteristic, complemented
36#91435C2211yescharacteristic
37#91419—21no—
38#91390C2211yescharacteristic, complemented
39#91336—21no—
40#91331C2211yescharacteristic, complemented
41C2×#6656C2211yescharacteristic
42C2×#6656C2211yescharacteristic, complemented
43#91114C2211yescharacteristic, complemented
44#91104C2211yescharacteristic, complemented
45#91098C2211yescharacteristic, complemented
46C8×Dic15C2211yescharacteristic, complemented
47C5×#821C2211yescharacteristic
48C5×#821C2211yescharacteristic
49C5×#821C2211yescharacteristic, complemented
50C5×#821C2211yescharacteristic, complemented
51C3×#3953C2211yescharacteristic, complemented
52C3×#3949C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90986C2211yescharacteristic, complemented
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60#80680—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65845—31no—
63C2×C5×#102—31no—
64#65507—31no—
65#65403D311yescharacteristic, complemented
66C8×C22⋊D5—31no—
67#65257—31no—
68#65067—31no—
69#65066—31no—
70#65065—31no—
71D5×#102—31no—
72#65051—31no—
73#65050—31no—
74#65049—31no—
75#65047—31no—
76C23×C5×D3—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220D411yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C22×C5×Dic3—21no—
82C2×C5×D12—22no—
83C2×C5×D12—21no—
84C2×C5×D12—41no—
85C2×C5×D12C2311yescharacteristic
86C2×C5×D12C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×Dic10C2311yescharacteristic
90D3×C22⋊D5—44no—
91C2×#1204—21no—
92C2×#1203—21no—
93C2×#1201—21no—
94C2×#1201—21no—
95C2×#1201—21no—
96C2×#1200—21no—
97C2×D3×Dic5—21no—
98#6777—22no—
99#6777—41no—
100C2×C3×C5×C8—41no—
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103#6719D411yescharacteristic
104#6714D411yescharacteristic
105#6712D411yescharacteristic
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109C8×D15—41no—
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C3×C22⋊Dic5—21no—
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#677—41no—
119Dic3⋊Dic5—21no—
120#6669—21no—
121#6669—21no—
122#6668—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125(C2×D3)⋊Dic5—21no—
126Dic3×Dic5—21no—
127#6656—22no—
128#6656—41no—
129#5635—51no—
130#5609—51no—
131C3×#465—51no—
132#5169—51no—
133#5163—51no—
134C2×#821D511yescharacteristic, complemented
135C8×#67—51no—
136#5046—51no—
137#5034—51no—
138#4870—51no—
139#4863—51no—
140#4807—51no—
141#4788—51no—
142D3×#102—51no—
143#4760—51no—
144C22×C5×D4—31no—
145C22×C22⋊D5—61no—
146C2×D4×D5—31no—
147C22×C5×C8C2×D311yescharacteristic, complemented
148C2×C5×C4⋊C4—31no—
149#4099—61no—
150#4086—31no—
151#4085—61no—
152#4084—31no—
153#4083—61no—
154D4×Dic5—31no—
155C2×#687—31no—
156C2×#687—31no—
157#4076C2×D311yescharacteristic
158C4×C22⋊D5—31no—
159C4×C22⋊D5—61no—
160#4070—61no—
161#4070C2×D311yescharacteristic, complemented
162C2×#677C2×D311yescharacteristic, complemented
163C2×C8×D5—31no—
164#4043—31no—
165#4042—61no—
166D5×C4⋊C4—31no—
167#4035—61no—
168#4034—31no—
169#4033—31no—
170C5×#102—31no—
171C5×#102—31no—
172C5×#102—31no—
173C5×#102—31no—
174#3964—31no—
175#3964—31no—
176C22⋊#168—31no—
177#3953C2×D311yescharacteristic, complemented
178#3952—31no—
179#3949C2×D311yescharacteristic, complemented
180#3948C2×D311yescharacteristic, complemented
181#3946—31no—
182C8×Dic5—31no—
183#3941—31no—
184#3941—31no—
185#3940—31no—
186#3940—31no—
187#3295—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×D15C2×D411yescharacteristic
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—42no—
193C22×C5×D3—42no—
194C22×C5×D3—81no—
195C22×C3×D5—21no—
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×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203#1220SD1614yescomplemented
204C2×Dic15C2×D411yescharacteristic
205C2×Dic15C2×D411yescharacteristic
206C2×Dic15C2×D411yescharacteristic
207C4×D15—21no—
208C4×D15—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—81no—
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—21no—
215C5×D12—42no—
216C5×D12#4112yes—
217C3×C22⋊D5—42no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C3×D20—21no—
222C3×D20—21no—
223C3×Dic10—21no—
224C3×Dic10—21no—
225#1204—81no—
226#1203—42no—
227#1201—42no—
228#1201—42no—
229#1201—81no—
230#1200—81no—
231D3×Dic5—42no—
232C3×C5×C8—21no—
233C3×C5×C8—21no—
234C3⋊#168—21no—
235C3⋊#168—21no—
236C2×D3×D4—51no—
237C2×D3×D4—101no—
238C22×D12C2×D511yescharacteristic
239C2×C3×SD16—51no—
240C22×C3×C8C2×D511yescharacteristic, complemented
241C3×C22⋊Q8—51no—
242C3×#121—51no—
243#946—51no—
244Q8×Dic3—51no—
245C2×#215—51no—
246C2×#215—51no—
247#940—51no—
248#937—101no—
249C4×#67—51no—
250C2×C4⋊Dic3C2×D511yescharacteristic, complemented
251C2×D3×C8—51no—
252#897—101no—
253#895—51no—
254#893—51no—
255D3×C4⋊C4—51no—
256#889—101no—
257#888—51no—
258#884—101no—
259#882—101no—
260#67⋊C4—101no—
261#878—101no—
262C3×#106—51no—
263C3×#103—51no—
264C3×#102—51no—
265#832—51no—
266#832—51no—
267#830—51no—
268#821C2×D511yescharacteristic
269#821C2×D511yescharacteristic
270#821C2×D511yescharacteristic, complemented
271#821C2×D511yescharacteristic, complemented
272(C2×D3)⋊C8—51no—
273Dic3⋊C8—51no—
274C8×Dic3—51no—
275#809—51no—
276#809—51no—
277#808—51no—
278#808—51no—
279C24×C5—61no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C2×C5×D4—31no—
283C2×C5×D4—62no—
284C2×C5×D4—61no—
285C2×C5×D4—121no—
286C22×C4×C5—61no—
287C22×C4×C5C22×D311yescharacteristic
288C2×C22⋊D5—21no—
289C2×C22⋊D5—31no—
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C2×C22⋊D5—61no—
293C2×C22⋊D5—61no—
294C2×C22⋊D5—124no—
295C22×Dic5—61no—
296D4×D5—62no—
297D4×D5—121no—
298C2×D20C22×D311yescharacteristic
299C2×C4×D5—31no—
300C2×C4×D5—61no—
301C2×Dic10—61no—
302C2×Dic10C22×D311yescharacteristic
303C2×C5×C8—41no—
304C2×C5×C8C22×D311yescharacteristic
305C2×C5×C8C22×D311yescharacteristic
306C5×C4⋊C4—31no—
307C5×C4⋊C4—31no—
308C5×C4⋊C4—61no—
309C22⋊Dic5—21no—
310C22⋊Dic5—31no—
311C22⋊Dic5—61no—
312C22⋊Dic5—61no—
313#687—62no—
314#687—121no—
315#685—21no—
316#685—31no—
317#685—61no—
318C4⋊Dic5—61no—
319C4⋊Dic5C22×D311yescharacteristic
320C4⋊Dic5C22×D311yescharacteristic
321#683—21no—
322#683—31no—
323#683—61no—
324#683—61no—
325#683—61no—
326C4×Dic5—31no—
327C4×Dic5—61no—
328C2×#168—31no—
329C2×#168—31no—
330#677—41no—
331C8×D5—121no—
332#554—151no—
333D42—151no—
334#486—151no—
335#481—151no—
336#481—151no—
337#476—151no—
338#465—51no—
339#465—151no—
340#460—151no—
341#450—151no—
342#450—151no—
343C4×SD16—151no—
344C8×D4—151no—
345C2×#102—31no—
346C2×#102—151no—
347C22×C3×C5—21no—
348C22×C3×C5—21no—
349C22×C3×C5C2×SD1612yes—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—21no—
352C2×D15—21no—
353C2×D15C2×SD1612yes—
354C2×C5×D3—22no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C5×D3—41no—
359C2×C5×D3—41no—
360C2×C5×D3—84no—
361C2×C3×D5—41no—
362C2×C3×D5—41no—
363C2×C3×D5—41no—
364D3×D5—84no—
365C3×C4×C5—21no—
366C3×C4×C5C2×#4111yescharacteristic
367C3×C4×C5H(5,𝔽2)11yescharacteristic
368Dic15—21no—
369Dic15—21no—
370Dic15C2×SD1612yes—
371C3×Dic5—41no—
372C3×Dic5—41no—
373C3×Dic5—41no—
374C5×Dic3—41no—
375C5×Dic3—41no—
376C23×D3—21no—
377C23×D3—101no—
378C2×C3×Q8—51no—
379C2×C3×D4—51no—
380C2×C3×D4—101no—
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—51no—
383C2×#67—101no—
384C2×#67—101no—
385C2×#67—101no—
386C22×Dic3—21no—
387D3×D4—102no—
388D3×D4—201no—
389D3×D4—204no—
390C2×D12—22no—
391C2×D12—21no—
392C2×D12—41no—
393C2×D12—101no—
394C2×D12C22×D511yescharacteristic
395C2×D12C22×D511yescharacteristic
396C2×C4×D3—51no—
397C2×C4×D3—101no—
398C2×C4×D3—101no—
399C2×Dic6—101no—
400C3×SD16—201no—
401C2×C3×C8—41no—
402C2×C3×C8C22×D511yescharacteristic
403C2×C3×C8C22×D511yescharacteristic
404C3×C4⋊C4—51no—
405C3×C4⋊C4—51no—
406C3×C4⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409#217—51no—
410#215—102no—
411#215—201no—
412(C2×D3)⋊C4—51no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415(C2×D3)⋊C4—101no—
416C4⋊Dic3—21no—
417C4⋊Dic3—101no—
418C4⋊Dic3C22×D511yescharacteristic
419C4⋊Dic3C22×D511yescharacteristic
420Dic3⋊C4—51no—
421Dic3⋊C4—101no—
422Dic3⋊C4—101no—
423Dic3⋊C4—101no—
424C4×Dic3—51no—
425C4×Dic3—101no—
426C2×C3⋊C8—51no—
427C2×C3⋊C8—51no—
428D3×C8—201no—
429C23×C5—61no—
430C23×C5—61no—
431C23×C5—122no—
432C23×C5—122no—
433C23×C5—241no—
434C23×C5D3×D411yescharacteristic
435C22×D5—21no—
436C22×D5—31no—
437C22×D5—122no—
438C22×D5—122no—
439C22×D5—241no—
440C5×D4—32no—
441C5×D4—61no—
442C5×D4—61no—
443C5×D4—61no—
444C5×D4—122no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—241no—
450C2×C4×C5D3×D411yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—34no—
453C22⋊D5—42no—
454C22⋊D5—122no—
455C22⋊D5—122no—
456C22⋊D5—122no—
457C22⋊D5—241no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—31no—
462C2×Dic5—31no—
463C2×Dic5—31no—
464C2×Dic5—122no—
465D20—21no—
466D20—21no—
467C4×D5—61no—
468C4×D5—61no—
469C4×D5—241no—
470Dic10—21no—
471Dic10—21no—
472Dic10—241no—
473C5×C8—21no—
474C5×C8—21no—
475#168—61no—
476#168—61no—
477C22×D4—31no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—51no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—151no—
484C22×C8D3×D511yescharacteristic, complemented
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—51no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—51no—
493#121—151no—
494#121—301no—
495#120—301no—
496#120—301no—
497C4×Q8—151no—
498C4×D4—151no—
499C4×D4—151no—
500C4×D4—301no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—151no—
503#106—51no—
504#106—151no—
505#106—151no—
506C4⋊C8—151no—
507#103—51no—
508#102—31no—
509#102—31no—
510#102—31no—
511#102—31no—
512#102—51no—
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—22no—
525C3×D5—81no—
526C5×D3—42no—
527C5×D3—81no—
528C23×C3—101no—
529C23×C3D4×D511yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—51no—
535C22×D3—81no—
536C22×D3—202no—
537C22×D3—202no—
538C22×D3—401no—
539C3×Q8—101no—
540C3×Q8—101no—
541C3×D4—101no—
542C3×D4—101no—
543C3×D4—202no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4D4×D511yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551#67—54no—
552#67—202no—
553#67—202no—
554#67—401no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—51no—
558C2×Dic3—51no—
559C2×Dic3—51no—
560C2×Dic3—81no—
561D12—21no—
562D12—21no—
563D12—21no—
564D12—42no—
565D12—202no—
566D12#70912yes—
567C4×D3—101no—
568C4×D3—101no—
569C4×D3—202no—
570C4×D3—401no—
571Dic6—401no—
572C3×C8—21no—
573C3×C8—21no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—62no—
579C22×C5—121no—
580C22×C5—121no—
581C22×C5—121no—
582C22×C5—121no—
583C22×C5—121no—
584C22×C5—244no—
585C22×C5D3×SD1612yes—
586C22×C5C2×D3×D411yescharacteristic
587C2×D5—32no—
588C2×D5—41no—
589C2×D5—41no—
590C2×D5—41no—
591C2×D5—61no—
592C2×D5—61no—
593C2×D5—244no—
594C4×C5—21no—
595C4×C5—121no—
596C4×C5—121no—
597C4×C5#100411yescharacteristic
598C4×C5D3×#4111yescharacteristic
599Dic5—32no—
600Dic5—41no—
601Dic5—41no—
602Dic5—41no—
603Dic5—61no—
604Dic5—61no—
605C24—61no—
606C24—301no—
607C2×Q8—51no—
608C2×Q8—301no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—51no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—101no—
615C2×D4—121no—
616C2×D4—151no—
617C2×D4—301no—
618C2×D4—301no—
619C2×D4—301no—
620C2×D4—301no—
621C2×D4—302no—
622C2×D4—601no—
623C2×D4—604no—
624C22×C4—61no—
625C22×C4—151no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—201no—
630SD16—302no—
631SD16—601no—
632C2×C8—41no—
633C2×C8—151no—
634C2×C8—151no—
635C2×C8—601no—
636C2×C8C2×D3×D511yescharacteristic
637C2×C8C2×D3×D511yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—51no—
641C4⋊C4—51no—
642C4⋊C4—61no—
643C4⋊C4—101no—
644C4⋊C4—151no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C22⋊C4—101no—
650C22⋊C4—101no—
651C22⋊C4—151no—
652C22⋊C4—151no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—151no—
657C42—301no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—201no—
662C22×C3—201no—
663C22×C3—201no—
664C22×C3D5×SD1612yes—
665C22×C3C2×D4×D511yescharacteristic
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—52no—
673C2×D3—84no—
674C2×D3—101no—
675C2×D3—101no—
676C2×D3—404no—
677C3×C4—21no—
678C3×C4—201no—
679C3×C4—201no—
680C3×C4—201no—
681C3×C4C2×#70911yescharacteristic
682C3×C4#414411yescharacteristic
683Dic3—41no—
684Dic3—41no—
685Dic3—52no—
686Dic3—101no—
687Dic3—101no—
688C2×C5—22no—
689C2×C5—122no—
690C2×C5—241no—
691C2×C5#561011yescharacteristic
692C2×C5C2×D3×SD1611yescharacteristic
693C2×C5#576911yescharacteristic
694D5—62no—
695D5—81no—
696C23—61no—
697C23—61no—
698C23—101no—
699C23—122no—
700C23—122no—
701C23—151no—
702C23—241no—
703C23—602no—
704C23—602no—
705C23—1201no—
706C23#677711yescharacteristic
707Q8—101no—
708Q8—101no—
709Q8—1201no—
710D4—32no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—101no—
715D4—101no—
716D4—122no—
717D4—154no—
718D4—202no—
719D4—602no—
720D4—602no—
721D4—602no—
722D4—1201no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—151no—
731C2×C4—151no—
732C2×C4—151no—
733C2×C4—241no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—602no—
737C2×C4—1201no—
738C2×C4#677711yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—21no—
741C8—21no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—401no—
746C2×C3#6582411yescharacteristic
747C2×C3#6609111yescharacteristic
748C2×C3C2×D5×SD1611yescharacteristic
749D3—42no—
750D3—81no—
751D3—102no—
752C5#8068011yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—62no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—152no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22—244no—
766C22—301no—
767C22—301no—
768C22—1204no—
769C22#9125512yes—
770C22C2×#677711yescharacteristic
771C4—21no—
772C4—121no—
773C4—121no—
774C4—152no—
775C4—201no—
776C4—201no—
777C4—201no—
778C4—301no—
779C4—301no—
780C4D3×#70911yescharacteristic
781C4#9204911yescharacteristic
782C3#1061048911yescharacteristic, complemented, Sylow
783C2—22no—
784C2—122no—
785C2—241no—
786C2—302no—
787C2—401no—
788C2C2×#9125511yescharacteristic
789C2#1175398311yescharacteristic
790C2#1175467311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11754657C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754508C2semidirect
3. C8×#1220C2semidirect
4. C2×C5×#821C2semidirect
5. C3×#65403C2semidirect
6. #11748537C2semidirect
7. #11748372C2semidirect
8. #11748111C2semidirect
9. #11748108C2semidirect
10. #11748011C2semidirect
11. #11747993C2semidirect
12. #11747928C2semidirect
13. #11747808C2semidirect
14. #11747737C2semidirect
15. #11747635C2semidirect
20. C22×C3×C5×C8C22semidirect
22. C2×C8×D15C22semidirect
23. C2×C5×C4⋊Dic3C22semidirect
25. C3×#4070C22semidirect
26. C2×C3×#677C22semidirect
31. #91470C22semidirect
35. #91437C22semidirect
38. #91390C22semidirect
40. #91331C22semidirect
42. C2×#6656C22semidirect
43. #91114C22semidirect
44. #91104C22semidirect
45. #91098C22semidirect
46. C8×Dic15C22semidirect
49. C5×#821C22semidirect
50. C5×#821C22semidirect
51. C3×#3953C22semidirect
52. C3×#3949C22semidirect
53. C3×#3948C22semidirect
54. #90986C22semidirect
55. #90986C22semidirect
57. #90966C22semidirect
58. #90964C22semidirect
59. #90964C22semidirect
65. #65403D3semidirect
134. C2×#821D5semidirect
147. C22×C5×C8C2×D3semidirect
161. #4070C2×D3semidirect
162. C2×#677C2×D3semidirect
177. #3953C2×D3semidirect
179. #3949C2×D3semidirect
180. #3948C2×D3semidirect
203. #1220SD16semidirect
240. C22×C3×C8C2×D5semidirect
250. C2×C4⋊Dic3C2×D5semidirect
270. #821C2×D5semidirect
271. #821C2×D5semidirect
484. C22×C8D3×D5semidirect
658. C3×C5#3295semidirect
752. C5#80680semidirect
782. C3#10610489semidirect

Maximal subgroups

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

subgroupindex
#117546572
#117545082
C8×#12202
C2×C5×#8212
C3×#654032
#117485372
#117483722
#117481112
#117481082
#117480112
#117479932
#117479282
#117478082
#117477372
#117476352
#106104893
#806805