Finite Group Databasebeta

← #14458518

Subgroups — #14458518

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
1C3×#65943C211yesmaximal, characteristic
2#11754500C211yesmaximal, characteristic, complemented
3#11751142C211yesmaximal, characteristic, complemented
4C5×#5034C211yesmaximal, characteristic, complemented
5#11749102C211yesmaximal, characteristic, complemented
6#11749045C211yesmaximal, characteristic, complemented
7#11749000C211yesmaximal, characteristic, complemented
8D5×#832C211yesmaximal, characteristic, complemented
9#11748530C211yesmaximal, characteristic, complemented
10#11748493C211yesmaximal, characteristic, complemented
11C2×#90964C211yesmaximal, characteristic, complemented
12#11747444C211yesmaximal, characteristic, complemented
13#11747415C211yesmaximal, characteristic, complemented
14#11747268C211yesmaximal, characteristic, complemented
15#11747195C211yesmaximal, characteristic, complemented
16#10613073—31nomaximal, Hall
17C2×C3×D4×D5—21no—
18C2×C3×D4×D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×#6716C2211yescharacteristic, complemented
22#91813C2211yescharacteristic, complemented
23C22×C3⋊#168C2211yescharacteristic, complemented
24C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
25C3×#4086C2211yescharacteristic
26C3×#4083—21no—
27C3×C4×C22⋊D5C2211yescharacteristic
28C3×#4041C2211yescharacteristic
29C3×#4039C2211yescharacteristic
30C3×#4030—21no—
31C3×#4028—21no—
32#91575—21no—
33Dic3×C22⋊D5—21no—
34#91468C2211yescharacteristic, complemented
35#91430—21no—
36D5×C4⋊Dic3C2211yescharacteristic, complemented
37#91360C2211yescharacteristic, complemented
38#91335—21no—
39#91333C2211yescharacteristic, complemented
40C2×#6657C2211yescharacteristic
41C2×#6657C2211yescharacteristic, complemented
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91116C2211yescharacteristic, complemented
44#91094C2211yescharacteristic, complemented
45#91092C2211yescharacteristic, complemented
46C5×#832C2211yescharacteristic, complemented
47C5×#832C2211yescharacteristic, complemented
48C5×#830C2211yescharacteristic, complemented
49C5×#808C2211yescharacteristic, complemented
50C5×#808C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90965C2211yescharacteristic
53#90965C2211yescharacteristic, complemented
54#90964C2211yescharacteristic
55#90964C2211yescharacteristic
56#90964C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83483—51nomaximal, Hall
61#65943D311yescharacteristic
62#65845—31no—
63C5×#481—31no—
64#65330—31no—
65C2×#3941—31no—
66#65159—31no—
67#65153—31no—
68#65152—31no—
69#65141—31no—
70#65065—31no—
71D5×#102—31no—
72#65051—31no—
73#65049—31no—
74#65020—31no—
75#65014—31no—
76C23×C3×D5—21no—
77C23×C3×D5—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C22×C5×Dic3—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5D411yescharacteristic
87C3×D4×D5—22no—
88C3×D4×D5—41no—
89C3×D4×D5—44no—
90C2×C3×D20—22no—
91C2×C3×D20—21no—
92C2×C3×D20—21no—
93C2×C3×D20—41no—
94C2×C3×D20C2311yescharacteristic
95C2×C3×D20C2311yescharacteristic
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5C2311yescharacteristic
98C2×#1204—21no—
99C2×D5×Dic3—21no—
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C22⋊C4—21no—
102#6719—21no—
103#6716—41no—
104C4⋊Dic15C2311yescharacteristic
105#6712—21no—
106C2×C3⋊#168—41no—
107C2×C3⋊#168C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109C5×C4⋊Dic3—21no—
110C5×C4⋊Dic3C2311yescharacteristic
111C5×C4⋊Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×C22⋊Dic5D411yescharacteristic
115C3×#685—21no—
116C3×#685—21no—
117C3×#685D411yescharacteristic
118C3×#683D411yescharacteristic
119C3×C4×Dic5C2311yescharacteristic
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123#6668—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6657—22no—
127#6657—41no—
128D5×C3⋊C8—41no—
129C3×D42—51no—
130#5543—51no—
131#5218—51no—
132#5218—51no—
133C2×#832—51no—
134C2×#832—51no—
135#5075—51no—
136#5070—51no—
137#5041—51no—
138#5041—51no—
139#5034—51no—
140#5034D511yescharacteristic, complemented
141C4×#214—51no—
142D4×C3⋊C8—51no—
143#5008—51no—
144C2×D4×D5—21no—
145C2×D4×D5C2×D311yescharacteristic
146C22×D20C2×D311yescharacteristic
147C5×#121C2×D311yescharacteristic
148C2×C5×C4⋊C4—31no—
149#4086C2×D311yescharacteristic
150#4083—21no—
151C2×#687—31no—
152C4×C22⋊D5—61no—
153C4×C22⋊D5C2×D311yescharacteristic
154#4070—31no—
155#4070—61no—
156C22×#168—31no—
157C2×#677—31no—
158C2×#677—31no—
159C2×C8×D5—31no—
160#4043—31no—
161#4042—61no—
162#4041C2×D311yescharacteristic
163#4039C2×D311yescharacteristic
164D5×C4⋊C4—31no—
165#4035—61no—
166#4034—31no—
167#4033—31no—
168#4030—21no—
169#4028—21no—
170C5×#106—31no—
171C5×#106—31no—
172C5×#102—31no—
173C5×#102—31no—
174C5×C22⋊C8—31no—
175#3964—31no—
176#3953—31no—
177#3953—31no—
178#3952—31no—
179#3946—31no—
180C8×Dic5—31no—
181#3942—31no—
182#3941—31no—
183#3941—31no—
184#3941—31no—
185#3941—31no—
186#3940—31no—
187#3295—151noSylow
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—42no—
193C22×C3×D5—42no—
194C22×C3×D5—42no—
195C22×C3×D5—42no—
196C22×C3×D5—81no—
197C22×C3×D5—81no—
198C22×C3×D5C2×D411yescharacteristic
199C3×C5×D4—21no—
200C3×C5×D4—21no—
201C3×C5×D4—42no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2411yescharacteristic
207C2×Dic15—21no—
208C2×Dic15—21no—
209Dic30—21no—
210Dic30—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—81no—
214C3×C22⋊D5—42no—
215C3×C22⋊D5—42no—
216C3×C22⋊D5—81no—
217C3×C22⋊D5SD1614yescomplemented
218C2×C3×Dic5C2×D411yescharacteristic
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20—21no—
223C3×D20—21no—
224C3×D20—42no—
225C3×D20—42no—
226C3×D20#4112yes—
227C3×C4×D5—21no—
228C3×C4×D5—21no—
229C3×C4×D5—42no—
230#1204—81no—
231D5×Dic3—81no—
232C3⋊#168—21no—
233C3⋊#168—21no—
234C5×C3⋊C8—21no—
235C5×C3⋊C8—21no—
236C22×C3×D4—51no—
237C22×C3×D4—51no—
238C22×C3×D4—101no—
239C3×#127—51no—
240C3×#121—51no—
241C3×#121—101no—
242C3×#121C2×D511yescharacteristic
243C3×#120—101no—
244C3×#120—101no—
245C3×C4×D4—51no—
246C3×C4×D4—51no—
247D4×Dic3—101no—
248C2×#214—51no—
249C2×#214—51no—
250C2×#214—51no—
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3C2×D511yescharacteristic, complemented
253#924—51no—
254#924—51no—
255C22×C3⋊C8—51no—
256C22×C3⋊C8—51no—
257#890—101no—
258#878—101no—
259#878—101no—
260#869—51no—
261C4×Dic6—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#832—51no—
266#832—51no—
267#832—51no—
268#832—51no—
269#832C2×D511yescharacteristic, complemented
270#832C2×D511yescharacteristic, complemented
271#830—51no—
272#830C2×D511yescharacteristic, complemented
273#810—51no—
274#808—51no—
275#808C2×D511yescharacteristic, complemented
276#808C2×D511yescharacteristic, complemented
277C4⋊(C3⋊C8)—51no—
278C4×C3⋊C8—51no—
279C23×D5—21no—
280C23×D5—21no—
281C2×C5×D4—21no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—61no—
284C22×C4×C5C22×D311yescharacteristic
285C2×C22⋊D5—21no—
286C2×C22⋊D5—21no—
287C2×C22⋊D5—21no—
288C2×C22⋊D5#6711yescharacteristic
289D4×D5—22no—
290D4×D5—41no—
291D4×D5—44no—
292C2×D20—22no—
293C2×D20—21no—
294C2×D20—21no—
295C2×D20—41no—
296C2×D20C22×D311yescharacteristic
297C2×D20C22×D311yescharacteristic
298C2×C4×D5—21no—
299C2×C4×D5—61no—
300C2×C4×D5C22×D311yescharacteristic
301C2×Dic10—31no—
302C2×Dic10—61no—
303C2×C5×C8—31no—
304C2×C5×C8—31no—
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4—61no—
308C5×C4⋊C4C22×D311yescharacteristic
309C5×C22⋊C4—21no—
310C22⋊Dic5—61no—
311C22⋊Dic5#6711yescharacteristic
312#687—121no—
313#685—21no—
314#685—21no—
315#685—61no—
316#685#6711yescharacteristic
317C4⋊Dic5—31no—
318C4⋊Dic5—61no—
319#683—61no—
320#683—61no—
321#683—61no—
322#683—61no—
323#683#6711yescharacteristic
324C4×Dic5—61no—
325C4×Dic5C22×D311yescharacteristic
326C2×#168—31no—
327C2×#168—31no—
328C2×#168—121no—
329#677—62no—
330#677—121no—
331C8×D5—121no—
332#554—151no—
333D42—51no—
334#486—151no—
335#481—31no—
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—151no—
346C2×#102—151no—
347C22×C3×C5—21no—
348C22×C3×C5—21no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5C2×SD1612yes—
353C22×C3×C5C22×D411yescharacteristic
354C2×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5—22no—
357C2×C3×D5—41no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—84no—
363C2×C3×D5—84no—
364C2×C3×D5C2×SD1612yes—
365C3×C4×C5—21no—
366C3×C4×C5—41no—
367C3×C4×C5C2×#4111yescharacteristic
368C3×C4×C5H(5,𝔽2)11yescharacteristic
369Dic15—41no—
370Dic15—41no—
371C3×Dic5—21no—
372C3×Dic5—21no—
373C3×Dic5C2×SD1612yes—
374C5×Dic3—41no—
375C5×Dic3—41no—
376C24×C3—101no—
377C24×C3—101no—
378C2×C3×D4—21no—
379C2×C3×D4—51no—
380C2×C3×D4—51no—
381C2×C3×D4—51no—
382C2×C3×D4—102no—
383C2×C3×D4—101no—
384C2×C3×D4—101no—
385C2×C3×D4—101no—
386C2×C3×D4—101no—
387C2×C3×D4—102no—
388C2×C3×D4—101no—
389C2×C3×D4—201no—
390C2×C3×D4—201no—
391C2×C3×D4—204no—
392C2×C3×D4C22×D511yescharacteristic
393C22×C3×C4—51no—
394C22×C3×C4—101no—
395C22×C3×C4C22×D511yescharacteristic
396C22×Dic3—21no—
397C22×Dic3—101no—
398C2×Dic6—51no—
399C2×Dic6—101no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—51no—
404C3×C22⋊C4—51no—
405C3×C22⋊C4—101no—
406C3×C22⋊C4—101no—
407C3×C42—51no—
408#217—101no—
409#217—101no—
410#214—102no—
411#214—201no—
412#214—201no—
413C4⋊Dic3—21no—
414C4⋊Dic3—51no—
415C4⋊Dic3—101no—
416C4⋊Dic3—101no—
417C4⋊Dic3C22×D511yescharacteristic
418C4⋊Dic3C22×D511yescharacteristic
419Dic3⋊C4—101no—
420Dic3⋊C4—101no—
421Dic3⋊C4—101no—
422C4×Dic3—101no—
423C2×C3⋊C8—51no—
424C2×C3⋊C8—51no—
425C2×C3⋊C8—201no—
426C2×C3⋊C8—201no—
427C2×C3⋊C8C22×D511yescharacteristic
428C2×C3⋊C8C22×D511yescharacteristic
429C23×C5—21no—
430C23×C5C2×#6711yescharacteristic
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—42no—
434C22×D5—42no—
435C22×D5—42no—
436C22×D5—42no—
437C22×D5—81no—
438C22×D5—81no—
439C22×D5C2×#6711yescharacteristic
440C5×D4—21no—
441C5×D4—21no—
442C5×D4—42no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—241no—
449C2×C4×C5C2×#6711yescharacteristic
450C2×C4×C5C23×D311yescharacteristic
451C22⋊D5—42no—
452C22⋊D5—42no—
453C22⋊D5—81no—
454C22⋊D5#21414yescomplemented
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5C2×#6711yescharacteristic
458C2×Dic5C2×#6711yescharacteristic
459C2×Dic5C2×#6711yescharacteristic
460D20—21no—
461D20—21no—
462D20—21no—
463D20—42no—
464D20—42no—
465D20#23712yes—
466C4×D5—21no—
467C4×D5—21no—
468C4×D5—42no—
469C4×D5—241no—
470Dic10—61no—
471Dic10—61no—
472Dic10—241no—
473C5×C8—61no—
474C5×C8—61no—
475#168—61no—
476#168—61no—
477C22×D4—51no—
478C22×D4—51no—
479C22×D4—101no—
480C2×SD16—151no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—151no—
484C22×C8—151no—
485C4⋊Q8—151no—
486#127—51no—
487#125—301no—
488C22⋊Q8—151no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—51no—
493#121—101no—
494#121D3×D511yescharacteristic
495#120—101no—
496#120—101no—
497C4×Q8—151no—
498C4×D4—51no—
499C4×D4—51no—
500C4×D4—301no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—151no—
503#106—31no—
504#106—31no—
505#106—151no—
506C4⋊C8—151no—
507#103—151no—
508#102—31no—
509#102—31no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#102—151no—
515#102—151no—
516#102—151no—
517C22⋊C8—31no—
518C22⋊C8—151no—
519C4×C8—151no—
520C2×C3×C5—22no—
521C2×C3×C5—81no—
522C2×C3×C5#54611yescharacteristic
523C2×C3×C5C22×SD1611yescharacteristic
524C2×C3×C5#57611yescharacteristic
525C3×D5—22no—
526C3×D5—42no—
527C3×D5—81no—
528C23×C3—21no—
529C23×C3—51no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3—202no—
533C23×C3—202no—
534C23×C3—202no—
535C23×C3—202no—
536C23×C3—401no—
537C23×C3—401no—
538C23×C3D4×D511yescharacteristic
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—42no—
542C3×D4—54no—
543C3×D4—52no—
544C3×D4—101no—
545C3×D4—101no—
546C3×D4—101no—
547C3×D4—202no—
548C3×D4—202no—
549C3×D4—202no—
550C3×D4—202no—
551C3×D4—401no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—51no—
556C2×C3×C4—51no—
557C2×C3×C4—51no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4—202no—
561C2×C3×C4D4×D511yescharacteristic
562C2×C3×C4C23×D511yescharacteristic
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—81no—
566C2×Dic3—101no—
567C2×Dic3—101no—
568C2×Dic3—401no—
569Dic6—101no—
570Dic6—101no—
571Dic6—401no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5—41no—
581C22×C5C2×#21412yes—
582C22×C5C22×#6711yescharacteristic
583C2×D5—21no—
584C2×D5—21no—
585C2×D5—22no—
586C2×D5—41no—
587C2×D5—41no—
588C2×D5—41no—
589C2×D5—41no—
590C2×D5—41no—
591C2×D5—84no—
592C2×D5—84no—
593C2×D5C2×#21412yes—
594C4×C5—21no—
595C4×C5—41no—
596C4×C5—121no—
597C4×C5—121no—
598C4×C5C2×#23711yescharacteristic
599C4×C5#100411yescharacteristic
600Dic5—21no—
601Dic5—21no—
602Dic5—121no—
603Dic5—121no—
604Dic5C2×#21412yes—
605C24—101no—
606C24—101no—
607C2×Q8—151no—
608C2×Q8—301no—
609C2×D4—21no—
610C2×D4—51no—
611C2×D4—51no—
612C2×D4—51no—
613C2×D4—102no—
614C2×D4—101no—
615C2×D4—101no—
616C2×D4—101no—
617C2×D4—101no—
618C2×D4—102no—
619C2×D4—101no—
620C2×D4—201no—
621C2×D4—201no—
622C2×D4—204no—
623C2×D4C2×D3×D511yescharacteristic
624C22×C4—51no—
625C22×C4—61no—
626C22×C4—101no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—302no—
630SD16—601no—
631SD16—601no—
632C2×C8—31no—
633C2×C8—31no—
634C2×C8—151no—
635C2×C8—151no—
636C2×C8—601no—
637C2×C8—601no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—51no—
641C4⋊C4—61no—
642C4⋊C4—151no—
643C4⋊C4—301no—
644C4⋊C4—301no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4C2×D3×D511yescharacteristic
649C22⋊C4—21no—
650C22⋊C4—51no—
651C22⋊C4—51no—
652C22⋊C4—101no—
653C22⋊C4—101no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—51no—
657C42—301no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—52no—
665C22×C3—101no—
666C22×C3—101no—
667C22×C3—102no—
668C22×C3—201no—
669C22×C3—201no—
670C22×C3—201no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3—404no—
674C22×C3—404no—
675C22×C3D5×SD1612yes—
676C22×C3C2×D4×D511yescharacteristic
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—52no—
680C3×C4—101no—
681C3×C4—101no—
682C3×C4D5×#4111yescharacteristic
683C3×C4#414911yescharacteristic
684Dic3—41no—
685Dic3—41no—
686Dic3—201no—
687Dic3—201no—
688C2×C5—22no—
689C2×C5—81no—
690C2×C5C22×#21411yescharacteristic
691C2×C5#580611yescharacteristic
692C2×C5#583511yescharacteristic
693D5—22no—
694D5—42no—
695D5—81no—
696C23—21no—
697C23—51no—
698C23—101no—
699C23—101no—
700C23—202no—
701C23—202no—
702C23—202no—
703C23—202no—
704C23—401no—
705C23—401no—
706C23D5×#6711yescharacteristic
707Q8—301no—
708Q8—301no—
709Q8—1201no—
710D4—21no—
711D4—21no—
712D4—42no—
713D4—54no—
714D4—52no—
715D4—101no—
716D4—101no—
717D4—101no—
718D4—202no—
719D4—202no—
720D4—202no—
721D4—202no—
722D4—401no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—51no—
727C2×C4—51no—
728C2×C4—51no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—202no—
734C2×C4—241no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—1201no—
738C2×C4D5×#6711yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—61no—
741C8—61no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—81no—
746C2×C3—102no—
747C2×C3—202no—
748C2×C3—401no—
749C2×C3#6598811yescharacteristic
750C2×C3C2×D5×SD1611yescharacteristic
751C2×C3#6610811yescharacteristic
752C5#8348311yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—52no—
759C22—101no—
760C22—101no—
761C22—102no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—201no—
767C22—404no—
768C22—404no—
769C22D5×#21412yes—
770C22C2×D5×#6711yescharacteristic
771C4—21no—
772C4—41no—
773C4—52no—
774C4—101no—
775C4—101no—
776C4—121no—
777C4—121no—
778C4—601no—
779C4—601no—
780C4D5×#23711yescharacteristic
781C4#9202611yescharacteristic
782C3#1061307311yescharacteristic, complemented, Sylow
783C2—22no—
784C2—81no—
785C2—102no—
786C2—202no—
787C2—401no—
788C2C2×D5×#21411yescharacteristic
789C2#1175478911yescharacteristic
790C2#1175531611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
prime radicalC3×#65943C2
hypercenter#121D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11754500C2semidirect
3. #11751142C2semidirect
4. C5×#5034C2semidirect
5. #11749102C2semidirect
6. #11749045C2semidirect
7. #11749000C2semidirect
8. D5×#832C2semidirect
9. #11748530C2semidirect
10. #11748493C2semidirect
11. C2×#90964C2semidirect
12. #11747444C2semidirect
13. #11747415C2semidirect
14. #11747268C2semidirect
15. #11747195C2semidirect
21. C2×#6716C22semidirect
22. #91813C22semidirect
23. C22×C3⋊#168C22semidirect
24. C2×C5×C4⋊Dic3C22semidirect
34. #91468C22semidirect
36. D5×C4⋊Dic3C22semidirect
37. #91360C22semidirect
39. #91333C22semidirect
41. C2×#6657C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91116C22semidirect
44. #91094C22semidirect
45. #91092C22semidirect
46. C5×#832C22semidirect
47. C5×#832C22semidirect
48. C5×#830C22semidirect
49. C5×#808C22semidirect
50. C5×#808C22semidirect
51. #90982C22semidirect
53. #90965C22semidirect
56. #90964C22semidirect
57. #90964C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
140. #5034D5semidirect
217. C3×C22⋊D5SD16semidirect
252. C2×C4⋊Dic3C2×D5semidirect
269. #832C2×D5semidirect
270. #832C2×D5semidirect
272. #830C2×D5semidirect
275. #808C2×D5semidirect
276. #808C2×D5semidirect
454. C22⋊D5#214semidirect
658. C3×C5#3295semidirect
752. C5#83483semidirect
782. C3#10613073semidirect

Maximal subgroups

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

subgroupindex
C3×#659432
#117545002
#117511422
C5×#50342
#117491022
#117490452
#117490002
D5×#8322
#117485302
#117484932
C2×#909642
#117474442
#117474152
#117472682
#117471952
#106130733
#834835