Finite Group Databasebeta

← #14458497

Subgroups — #14458497

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×D4×#67C211yesmaximal, characteristic
2#11754494C211yesmaximal, characteristic, complemented
3#11751319C211yesmaximal, characteristic, complemented
4C2×C3×#3964C211yesmaximal, characteristic, complemented
5#11749113C211yesmaximal, characteristic, complemented
6#11749056C211yesmaximal, characteristic, complemented
7#11749055C211yesmaximal, characteristic, complemented
8#11749013C211yesmaximal, characteristic, complemented
9#11749011C211yesmaximal, characteristic, complemented
10#11748956C211yesmaximal, characteristic, complemented
11D3×#3964C211yesmaximal, characteristic, complemented
12#11748941C211yesmaximal, characteristic, complemented
13#11748533C211yesmaximal, characteristic, complemented
14#67×#168C211yesmaximal, characteristic, complemented
15#11748385C211yesmaximal, characteristic, complemented
16#10615214—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C5×#67—21no—
19C2×C5×D3×D4C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C2×#6716C2211yescharacteristic, complemented
22#91813C2211yescharacteristic, complemented
23C5×#953—21no—
24C5×#940C2211yescharacteristic
25C5×#939—21no—
26C5×#938C2211yescharacteristic
27C5×#937—21no—
28C5×D4×Dic3C2211yescharacteristic
29C5×#930C2211yescharacteristic
30C4×C5×#67C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
32C22×C3×#168C2211yescharacteristic, complemented
33#91574—21no—
34Dic5×#67—21no—
35#91469C2211yescharacteristic, complemented
36#91436—21no—
37D3×C4⋊Dic5C2211yescharacteristic, complemented
38#91365C2211yescharacteristic, complemented
39#91346—21no—
40#91340C2211yescharacteristic, complemented
41C2×#6659C2211yescharacteristic, complemented
42C2×D3×#168C2211yescharacteristic, complemented
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic, complemented
45#91114C2211yescharacteristic, complemented
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic, complemented
50#90986C2211yescharacteristic, complemented
51#90986C2211yescharacteristic, complemented
52#90985C2211yescharacteristic, complemented
53Dic3⋊#168C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90967C2211yescharacteristic, complemented
56#90966C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#78758—51nomaximal, Hall
61C5×D42—31no—
62#65877—31no—
63#65507—31no—
64#65507—31no—
65C2×#3964—31no—
66C2×#3964D311yescharacteristic, complemented
67#65364—31no—
68#65359—31no—
69#65330—31no—
70#65330—31no—
71#65323—31no—
72#65323—31no—
73C4×#687—31no—
74D4×#168—31no—
75#65297—31no—
76C24×C3×C5—21no—
77C23×C5×D3—21no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4—41no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×Dic30C2311yescharacteristic
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C2×C5×#67—21no—
88C2×C5×#67—21no—
89C2×C5×#67—21no—
90C2×C5×#67—44no—
91C2×C5×#67D411yescharacteristic
92C22×C5×Dic3—21no—
93C5×D3×D4—22no—
94C5×D3×D4—41no—
95C2×C5×D12C2311yescharacteristic
96C2×C4×C5×D3C2311yescharacteristic
97C22×C3×Dic5—21no—
98C2×#1204—21no—
99C2×D3×Dic5—21no—
100#6719—21no—
101#6716—22no—
102#6716—41no—
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#217—21no—
108C5×#217—21no—
109C5×#217D411yescharacteristic
110C5×(C2×D3)⋊C4—21no—
111C5×(C2×D3)⋊C4D411yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4D411yescharacteristic
114C4×C5×Dic3C2311yescharacteristic
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C2×C3×#168—41no—
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121Dic3⋊Dic5—21no—
122Dic3⋊Dic5—21no—
123#6669—21no—
124#6668—21no—
125(C2×D3)⋊Dic5—21no—
126Dic3×Dic5—21no—
127#6659—41no—
128D3×#168—41no—
129D4×#67D511yescharacteristic
130#5511—51no—
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—
144C22×C5×D4—31no—
145C22×C5×D4—61no—
146C22×C5×D4C2×D311yescharacteristic
147C5×#127—31no—
148C5×#121—31no—
149C5×#121—31no—
150C5×#121—61no—
151C5×#120—61no—
152C5×#120—61no—
153C4×C5×D4—31no—
154C4×C5×D4—31no—
155D4×Dic5—61no—
156C2×#687—31no—
157C2×#687—31no—
158C2×#687—31no—
159C2×C4⋊Dic5—31no—
160C2×C4⋊Dic5C2×D311yescharacteristic, complemented
161#4070—31no—
162#4070—31no—
163C22×#168—31no—
164C22×#168C2×D311yescharacteristic, complemented
165#4036—61no—
166#4024—61no—
167#4024—61no—
168#4015—31no—
169C4×Dic10—31no—
170#3964—31no—
171#3964—31no—
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964C2×D311yescharacteristic
176#3964C2×D311yescharacteristic
177#3964C2×D311yescharacteristic, complemented
178#3964C2×D311yescharacteristic, complemented
179C22⋊#168—31no—
180C22⋊#168—31no—
181#3942—31no—
182#3940—31no—
183#3940—31no—
184#3940—31no—
185C4⋊#168—31no—
186C4×#168—31no—
187#3295—151noSylow
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—42no—
191C23×C3×C5—42no—
192C23×C3×C5—81no—
193C23×C3×C5C2×D411yescharacteristic
194C22×C5×D3—21no—
195C22×C5×D3—42no—
196C22×C5×D3—42no—
197C22×C5×D3—81no—
198C22×C5×D3C2×D411yescharacteristic
199C3×C5×D4—21no—
200C3×C5×D4—21no—
201C3×C5×D4—21no—
202C3×C5×D4—42no—
203C3×C5×D4#4112yes—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208C2×Dic15—21no—
209C2×Dic15—21no—
210Dic30—21no—
211Dic30—21no—
212C5×#67—42no—
213C5×#67—42no—
214C5×#67—42no—
215C5×#67—42no—
216C5×#67—81no—
217C5×#67SD1614yescomplemented
218C2×C5×Dic3—21no—
219C2×C5×Dic3—42no—
220C2×C5×Dic3C2×D411yescharacteristic
221C2×C5×Dic3C2×D411yescharacteristic
222C2×C5×Dic3C2×D411yescharacteristic
223C5×D12—21no—
224C5×D12—21no—
225C4×C5×D3—21no—
226C4×C5×D3—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—81no—
230#1204—81no—
231D3×Dic5—81no—
232C3⋊#168—21no—
233C3⋊#168—21no—
234C3×#168—21no—
235C3×#168—21no—
236C22×C3×D4C2×D511yescharacteristic
237C22×#67—21no—
238C2×D3×D4C2×D511yescharacteristic
239C22×C3×C8—51no—
240C2×C3×C4⋊C4—51no—
241#953—21no—
242#940C2×D511yescharacteristic
243#939—21no—
244#938C2×D511yescharacteristic
245#937—21no—
246D4×Dic3C2×D511yescharacteristic
247C2×#214—51no—
248C2×#214—51no—
249#930C2×D511yescharacteristic
250C4×#67—101no—
251C4×#67C2×D511yescharacteristic
252#924—51no—
253#924—101no—
254C2×#204—51no—
255C2×D3×C8—51no—
256#897—51no—
257#896—101no—
258D3×C4⋊C4—51no—
259#889—101no—
260#888—51no—
261#887—51no—
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—
279C24×C5—21no—
280C24×C5—61no—
281C2×C5×D4—22no—
282C2×C5×D4—21no—
283C2×C5×D4—31no—
284C2×C5×D4—31no—
285C2×C5×D4—41no—
286C2×C5×D4—61no—
287C2×C5×D4—61no—
288C2×C5×D4—61no—
289C2×C5×D4—62no—
290C2×C5×D4—61no—
291C2×C5×D4—61no—
292C2×C5×D4—121no—
293C2×C5×D4—124no—
294C2×C5×D4C22×D311yescharacteristic
295C2×C5×D4C22×D311yescharacteristic
296C22×C4×C5—31no—
297C22×C4×C5—61no—
298C22×C4×C5C22×D311yescharacteristic
299C22×Dic5—21no—
300C22×Dic5—61no—
301C2×Dic10—31no—
302C2×Dic10—61no—
303C5×C4⋊C4—31no—
304C5×C4⋊C4—31no—
305C5×C22⋊C4—31no—
306C5×C22⋊C4—31no—
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C5×C22⋊C4—61no—
310C42×C5—31no—
311C22⋊Dic5—61no—
312C22⋊Dic5—61no—
313#687—62no—
314#687—121no—
315#687—121no—
316C4⋊Dic5—21no—
317C4⋊Dic5—31no—
318C4⋊Dic5—61no—
319C4⋊Dic5—61no—
320C4⋊Dic5C22×D311yescharacteristic
321C4⋊Dic5C22×D311yescharacteristic
322#683—61no—
323#683—61no—
324#683—61no—
325C4×Dic5—61no—
326C2×#168—31no—
327C2×#168—31no—
328C2×#168—41no—
329C2×#168—121no—
330C2×#168C22×D311yescharacteristic
331C2×#168C22×D311yescharacteristic
332#554—151no—
333D42—31no—
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×C5—22no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5—41no—
353C22×C3×C5—41no—
354C22×C3×C5—41no—
355C22×C3×C5—84no—
356C22×C3×C5C2×SD1612yes—
357C22×C3×C5C22×D411yescharacteristic
358C2×C5×D3—21no—
359C2×C5×D3—21no—
360C2×C5×D3—41no—
361C2×C5×D3—41no—
362C2×C5×D3—41no—
363C2×C5×D3—84no—
364C2×C5×D3C2×SD1612yes—
365C3×C4×C5—21no—
366C3×C4×C5C2×#4111yescharacteristic
367C3×C4×C5H(5,𝔽2)11yescharacteristic
368Dic15—41no—
369Dic15—41no—
370C3×Dic5—41no—
371C3×Dic5—41no—
372C5×Dic3—21no—
373C5×Dic3—21no—
374C5×Dic3—41no—
375C5×Dic3C2×SD1612yes—
376C24×C3—21no—
377C23×D3—21no—
378C2×C3×D4—22no—
379C2×C3×D4—21no—
380C2×C3×D4—41no—
381C2×C3×D4C22×D511yescharacteristic
382C2×C3×D4C22×D511yescharacteristic
383C22×C3×C4—101no—
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—21no—
386C2×#67—21no—
387C2×#67—21no—
388C2×#67—21no—
389C2×#67—21no—
390C2×#67—44no—
391C2×#67C22⋊D511yescharacteristic
392C22×Dic3—21no—
393D3×D4—22no—
394D3×D4—41no—
395C2×D12C22×D511yescharacteristic
396C2×C4×D3—101no—
397C2×C4×D3C22×D511yescharacteristic
398C2×Dic6—51no—
399C2×Dic6—101no—
400C2×C3×C8—51no—
401C2×C3×C8—51no—
402C2×C3×C8—201no—
403C3×C4⋊C4—51no—
404C3×C4⋊C4—51no—
405C3×C4⋊C4—101no—
406#217—21no—
407#217—21no—
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—51no—
416C4⋊Dic3—101no—
417C4⋊Dic3C22×D511yescharacteristic
418Dic3⋊C4—101no—
419Dic3⋊C4—101no—
420Dic3⋊C4—101no—
421Dic3⋊C4—101no—
422Dic3⋊C4C22⋊D511yescharacteristic
423C4×Dic3—101no—
424C4×Dic3C22×D511yescharacteristic
425C2×C3⋊C8—51no—
426C2×C3⋊C8—51no—
427#204—201no—
428D3×C8—201no—
429C23×C5—21no—
430C23×C5—21no—
431C23×C5—31no—
432C23×C5—42no—
433C23×C5—42no—
434C23×C5—61no—
435C23×C5—81no—
436C23×C5—122no—
437C23×C5—122no—
438C23×C5—241no—
439C23×C5D3×D411yescharacteristic
440C5×D4—21no—
441C5×D4—21no—
442C5×D4—21no—
443C5×D4—34no—
444C5×D4—42no—
445C5×D4—61no—
446C5×D4—61no—
447C5×D4—122no—
448C5×D4—122no—
449C5×D4—122no—
450C5×D4—122no—
451C5×D4—241no—
452C5×D4#23512yes—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—31no—
456C2×C4×C5—31no—
457C2×C4×C5—31no—
458C2×C4×C5—61no—
459C2×C4×C5—61no—
460C2×C4×C5—61no—
461C2×C4×C5—122no—
462C2×C4×C5D3×D411yescharacteristic
463C2×C4×C5C23×D311yescharacteristic
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—81no—
469C2×Dic5—241no—
470Dic10—61no—
471Dic10—61no—
472Dic10—241no—
473#168—21no—
474#168—21no—
475#168—61no—
476#168—61no—
477C22×D4—31no—
478C22×D4—61no—
479C22×D4D3×D511yescharacteristic
480C2×SD16—151no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—51no—
484C22×C8—151no—
485C4⋊Q8—151no—
486#127—31no—
487#125—301no—
488C22⋊Q8—151no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—31no—
493#121—31no—
494#121—61no—
495#120—61no—
496#120—61no—
497C4×Q8—151no—
498C4×D4—31no—
499C4×D4—31no—
500C4×D4—301no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—151no—
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—42no—
522C2×C3×C5—81no—
523C2×C3×C5#54611yescharacteristic
524C2×C3×C5C22×SD1611yescharacteristic
525C2×C3×C5#57611yescharacteristic
526C5×D3—22no—
527C5×D3—81no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—81no—
533C23×C3C2×C22⋊D511yescharacteristic
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—81no—
538C22×D3C2×C22⋊D511yescharacteristic
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—42no—
543C3×D4#71112yes—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—401no—
549C2×C3×C4C2×C22⋊D511yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551#67—42no—
552#67—42no—
553#67—42no—
554#67—42no—
555#67—81no—
556#67#68714yescomplemented
557C2×Dic3—21no—
558C2×Dic3—42no—
559C2×Dic3—101no—
560C2×Dic3—101no—
561C2×Dic3C2×C22⋊D511yescharacteristic
562C2×Dic3C2×C22⋊D511yescharacteristic
563C2×Dic3C2×C22⋊D511yescharacteristic
564D12—21no—
565D12—21no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—401no—
569Dic6—101no—
570Dic6—101no—
571Dic6—401no—
572C3×C8—101no—
573C3×C8—101no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—22no—
579C22×C5—32no—
580C22×C5—41no—
581C22×C5—41no—
582C22×C5—41no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—61no—
586C22×C5—61no—
587C22×C5—84no—
588C22×C5—121no—
589C22×C5—121no—
590C22×C5—121no—
591C22×C5—244no—
592C22×C5D3×SD1612yes—
593C22×C5C2×D3×D411yescharacteristic
594C4×C5—21no—
595C4×C5—32no—
596C4×C5—61no—
597C4×C5—61no—
598C4×C5—121no—
599C4×C5C2×#23511yescharacteristic
600C4×C5#100411yescharacteristic
601Dic5—41no—
602Dic5—41no—
603Dic5—121no—
604Dic5—121no—
605C24—21no—
606C24—61no—
607C2×Q8—151no—
608C2×Q8—301no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—41no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—62no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—121no—
621C2×D4—124no—
622C2×D4C2×D3×D511yescharacteristic
623C2×D4C2×D3×D511yescharacteristic
624C22×C4—31no—
625C22×C4—61no—
626C22×C4—101no—
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—31no—
639C4⋊C4—31no—
640C4⋊C4—51no—
641C4⋊C4—51no—
642C4⋊C4—101no—
643C4⋊C4—151no—
644C4⋊C4—301no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C22⋊C4—31no—
650C22⋊C4—31no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—31no—
657C42—301no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—22no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—84no—
668C22×C3C2×#68712yes—
669C22×C3C22×C22⋊D511yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—84no—
676C2×D3C2×#68712yes—
677C3×C4—21no—
678C3×C4—201no—
679C3×C4—201no—
680C3×C4C2×#71111yescharacteristic
681C3×C4#414411yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—201no—
686Dic3—201no—
687Dic3C2×#68712yes—
688C2×C5—22no—
689C2×C5—42no—
690C2×C5—62no—
691C2×C5—81no—
692C2×C5—241no—
693C2×C5#549011yescharacteristic
694C2×C5#575711yescharacteristic
695C2×C5C2×D3×SD1611yescharacteristic
696C23—21no—
697C23—21no—
698C23—31no—
699C23—42no—
700C23—42no—
701C23—61no—
702C23—81no—
703C23—122no—
704C23—122no—
705C23—241no—
706C23D3×C22⋊D511yescharacteristic
707Q8—301no—
708Q8—301no—
709Q8—1201no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—34no—
714D4—42no—
715D4—61no—
716D4—61no—
717D4—122no—
718D4—122no—
719D4—122no—
720D4—122no—
721D4—241no—
722D4#678212yes—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—122no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—401no—
737C2×C4—1201no—
738C2×C4D3×C22⋊D511yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—101no—
741C8—101no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—42no—
746C2×C3—81no—
747C2×C3C22×#68711yescharacteristic
748C2×C3#6614011yescharacteristic
749C2×C3#6616911yescharacteristic
750D3—22no—
751D3—81no—
752C5#7875811yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—22no—
756C22—32no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—84no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—244no—
769C22D3×#68712yes—
770C22C2×D3×C22⋊D511yescharacteristic
771C4—21no—
772C4—32no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—201no—
777C4—201no—
778C4—601no—
779C4—601no—
780C4C2×#678211yescharacteristic
781C4#9204911yescharacteristic
782C3#1061521411yescharacteristic, complemented, Sylow
783C2—22no—
784C2—42no—
785C2—62no—
786C2—81no—
787C2—241no—
788C2#1175469711yescharacteristic
789C2C2×D3×#68711yescharacteristic
790C2#1175539311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×D4×#67C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11754494C2semidirect
3. #11751319C2semidirect
4. C2×C3×#3964C2semidirect
5. #11749113C2semidirect
6. #11749056C2semidirect
7. #11749055C2semidirect
8. #11749013C2semidirect
9. #11749011C2semidirect
10. #11748956C2semidirect
11. D3×#3964C2semidirect
12. #11748941C2semidirect
13. #11748533C2semidirect
14. #67×#168C2semidirect
15. #11748385C2semidirect
21. C2×#6716C22semidirect
22. #91813C22semidirect
31. C2×C3×C4⋊Dic5C22semidirect
32. C22×C3×#168C22semidirect
35. #91469C22semidirect
37. D3×C4⋊Dic5C22semidirect
38. #91365C22semidirect
40. #91340C22semidirect
41. C2×#6659C22semidirect
42. C2×D3×#168C22semidirect
44. #91116C22semidirect
45. #91114C22semidirect
48. C3×#3964C22semidirect
49. C3×#3964C22semidirect
50. #90986C22semidirect
51. #90986C22semidirect
52. #90985C22semidirect
53. Dic3⋊#168C22semidirect
54. #90975C22semidirect
55. #90967C22semidirect
56. #90966C22semidirect
57. #90966C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
66. C2×#3964D3semidirect
160. C2×C4⋊Dic5C2×D3semidirect
164. C22×#168C2×D3semidirect
177. #3964C2×D3semidirect
178. #3964C2×D3semidirect
217. C5×#67SD16semidirect
556. #67#687semidirect
658. C3×C5#3295semidirect
752. C5#78758semidirect
782. C3#10615214semidirect

Maximal subgroups

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

subgroupindex
C5×D4×#672
#117544942
#117513192
C2×C3×#39642
#117491132
#117490562
#117490552
#117490132
#117490112
#117489562
D3×#39642
#117489412
#117485332
#67×#1682
#117483852
#106152143
#787585