Finite Group Databasebeta

← #14458521

Subgroups — #14458521

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×#5609C211yesmaximal, characteristic
2#11754514C211yesmaximal, characteristic, complemented
3#11751135C211yesmaximal, characteristic, complemented
4C3×#65330C211yesmaximal, characteristic, complemented
5#11749058C211yesmaximal, characteristic, complemented
6#11749005C211yesmaximal, characteristic, complemented
7D3×#3964C211yesmaximal, characteristic, complemented
8#11748941C211yesmaximal, characteristic, complemented
9#11748537C211yesmaximal, characteristic, complemented
10#67×#168C211yesmaximal, characteristic, complemented
11C2×#90967C211yesmaximal, characteristic, complemented
12#11747419C211yesmaximal, characteristic, complemented
13#11747352C211yesmaximal, characteristic, complemented
14#11747264C211yesmaximal, characteristic, complemented
15#11747199C211yesmaximal, characteristic, complemented
16#10615214—31nomaximal, Hall
17C2×C5×D3×D4—21no—
18C2×C5×D3×D4C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C5×#940C2211yescharacteristic
23C5×#937—21no—
24C4×C5×#67C2211yescharacteristic
25C5×#895C2211yescharacteristic
26C5×#893C2211yescharacteristic
27C5×#884—21no—
28C5×#882—21no—
29C2×C3×#687C2211yescharacteristic, complemented
30C3×#4070C2211yescharacteristic, complemented
31C22×C3×#168C2211yescharacteristic, complemented
32#91576—21no—
33#67⋊Dic5—21no—
34#91469C2211yescharacteristic, complemented
35D3×C4⋊Dic5C2211yescharacteristic, complemented
36#91417—21no—
37#91369C2211yescharacteristic, complemented
38#91343—21no—
39Dic3×Dic10C2211yescharacteristic, complemented
40C2×#6656C2211yescharacteristic
41C2×#6656C2211yescharacteristic, complemented
42C2×D3×#168C2211yescharacteristic, complemented
43#91116C2211yescharacteristic, complemented
44#91116C2211yescharacteristic, complemented
45#91114C2211yescharacteristic, complemented
46#91092C2211yescharacteristic, complemented
47#91092C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic, complemented
49C3×#3942C2211yescharacteristic, complemented
50C3×#3940C2211yescharacteristic, complemented
51Dic3⋊#168C2211yescharacteristic, complemented
52#90967C2211yescharacteristic
53#90967C2211yescharacteristic
54#90967C2211yescharacteristic, complemented
55#90967C2211yescharacteristic, complemented
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#80680—51nomaximal, Hall
61C5×D42—31no—
62#65877—31no—
63#65507—31no—
64#65507—31no—
65C2×#3964—31no—
66C2×#3964—31no—
67#65364—31no—
68#65359—31no—
69#65330—31no—
70#65330D311yescharacteristic, complemented
71#65323—31no—
72#65323—31no—
73C4×#687—31no—
74D4×#168—31no—
75#65297—31no—
76C23×C5×D3—21no—
77C23×C5×D3—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×Dic15—21no—
82C2×C5×#67—21no—
83C2×C5×#67—21no—
84C2×C5×#67—21no—
85C2×C5×#67D411yescharacteristic
86C5×D3×D4—22no—
87C5×D3×D4—41no—
88C5×D3×D4—44no—
89C2×C5×D12—22no—
90C2×C5×D12—21no—
91C2×C5×D12—21no—
92C2×C5×D12—41no—
93C2×C5×D12C2311yescharacteristic
94C2×C5×D12C2311yescharacteristic
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3C2311yescharacteristic
97C2×C3×Dic10C2311yescharacteristic
98C2×#1204—21no—
99C2×D3×Dic5—21no—
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C22⋊C4—21no—
102C4⋊Dic15—21no—
103C4⋊Dic15C2311yescharacteristic
104C4⋊Dic15C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#217D411yescharacteristic
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×Dic3⋊C4D411yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C3×C22⋊Dic5—21no—
114C3×#687—41no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C2×C3×#168—41no—
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120Dic3⋊Dic5—21no—
121Dic3⋊Dic5—21no—
122#6669—21no—
123#6668—21no—
124(C2×D3)⋊Dic5—21no—
125Dic3×Dic5—21no—
126#6656—22no—
127#6656—41no—
128D3×#168—41no—
129#5635—51no—
130#5609D511yescharacteristic
131C3×#465—51no—
132#5169—51no—
133#5163—51no—
134C2×#821—51no—
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×C5×D4—31no—
146C22×C5×D4—61no—
147C5×#127—31no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#121C2×D311yescharacteristic
151C5×#120—61no—
152C5×#120—61no—
153C4×C5×D4—31no—
154C4×C5×D4—31no—
155D4×Dic5—61no—
156C2×#687—31no—
157C2×#687—31no—
158C2×#687C2×D311yescharacteristic, complemented
159C2×C4⋊Dic5—31no—
160C2×C4⋊Dic5—31no—
161#4070—31no—
162#4070C2×D311yescharacteristic, complemented
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#3964—31no—
176#3964—31no—
177#3964—31no—
178#3964C2×D311yescharacteristic, complemented
179C22⋊#168—31no—
180C22⋊#168—31no—
181#3942C2×D311yescharacteristic, complemented
182#3940—31no—
183#3940—31no—
184#3940C2×D311yescharacteristic, complemented
185C4⋊#168—31no—
186C4×#168—31no—
187#3295—151noSylow
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—42no—
193C22×C5×D3—42no—
194C22×C5×D3—42no—
195C22×C5×D3—42no—
196C22×C5×D3—81no—
197C22×C5×D3—81no—
198C22×C5×D3C2×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—
209C2×Dic15—81no—
210C5×#67—42no—
211C5×#67—42no—
212C5×#67—81no—
213C5×#67SD1614yescomplemented
214C2×C5×Dic3C2×D411yescharacteristic
215C2×C5×Dic3C2×D411yescharacteristic
216C2×C5×Dic3C2×D411yescharacteristic
217C5×D12—21no—
218C5×D12—21no—
219C5×D12—21no—
220C5×D12—42no—
221C5×D12—42no—
222C5×D12#4112yes—
223C4×C5×D3—21no—
224C4×C5×D3—21no—
225C4×C5×D3—42no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C3×Dic10—21no—
229C3×Dic10—21no—
230#1204—81no—
231D3×Dic5—81no—
232C3⋊#168—21no—
233C3⋊#168—21no—
234C3×#168—21no—
235C3×#168—21no—
236C2×D3×D4—21no—
237C2×D3×D4C2×D511yescharacteristic
238C22×D12C2×D511yescharacteristic
239C2×C3×SD16—51no—
240C22×C3×C8—51no—
241C3×C22⋊Q8—51no—
242C3×#121C2×D511yescharacteristic
243#946—51no—
244Q8×Dic3—51no—
245C2×#215—51no—
246C2×#215—51no—
247#940C2×D511yescharacteristic
248#937—21no—
249C4×#67C2×D511yescharacteristic
250C2×C4⋊Dic3—51no—
251C2×D3×C8—51no—
252#897—101no—
253#895C2×D511yescharacteristic
254#893C2×D511yescharacteristic
255D3×C4⋊C4—51no—
256#889—101no—
257#888—51no—
258#884—21no—
259#882—21no—
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#821—51no—
269#821—51no—
270#821—51no—
271#821—51no—
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—
280C24×C5—61no—
281C2×C5×D4—21no—
282C2×C5×D4—31no—
283C2×C5×D4—31no—
284C2×C5×D4—31no—
285C2×C5×D4—62no—
286C2×C5×D4—61no—
287C2×C5×D4—61no—
288C2×C5×D4—61no—
289C2×C5×D4—61no—
290C2×C5×D4—62no—
291C2×C5×D4—61no—
292C2×C5×D4—121no—
293C2×C5×D4—121no—
294C2×C5×D4—124no—
295C2×C5×D4C22×D311yescharacteristic
296C22×C4×C5—31no—
297C22×C4×C5—61no—
298C22×C4×C5C22×D311yescharacteristic
299C22×Dic5—61no—
300C22×Dic5—61no—
301C2×Dic10—61no—
302C2×Dic10C22×D311yescharacteristic
303C5×C4⋊C4—31no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C22⋊C4—21no—
306C5×C22⋊C4—31no—
307C5×C22⋊C4—31no—
308C5×C22⋊C4—61no—
309C5×C22⋊C4—61no—
310C42×C5—31no—
311C22⋊Dic5—21no—
312C22⋊Dic5—61no—
313#687—41no—
314#687—62no—
315#687—121no—
316C4⋊Dic5—31no—
317C4⋊Dic5—31no—
318C4⋊Dic5—61no—
319C4⋊Dic5—61no—
320C4⋊Dic5—61no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—21no—
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—51no—
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×C5×D3—21no—
355C2×C5×D3—21no—
356C2×C5×D3—22no—
357C2×C5×D3—41no—
358C2×C5×D3—41no—
359C2×C5×D3—41no—
360C2×C5×D3—41no—
361C2×C5×D3—41no—
362C2×C5×D3—84no—
363C2×C5×D3—84no—
364C2×C5×D3C2×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—41no—
372C3×Dic5—41no—
373C5×Dic3—21no—
374C5×Dic3—21no—
375C5×Dic3C2×SD1612yes—
376C23×D3—21no—
377C23×D3—21no—
378C2×C3×Q8—51no—
379C2×C3×D4—21no—
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—21no—
383C2×#67—21no—
384C2×#67—21no—
385C2×#67C22⋊D511yescharacteristic
386C22×Dic3—101no—
387D3×D4—22no—
388D3×D4—41no—
389D3×D4—44no—
390C2×D12—22no—
391C2×D12—21no—
392C2×D12—21no—
393C2×D12—41no—
394C2×D12C22×D511yescharacteristic
395C2×D12C22×D511yescharacteristic
396C2×C4×D3—21no—
397C2×C4×D3—101no—
398C2×C4×D3C22×D511yescharacteristic
399C2×Dic6—101no—
400C3×SD16—201no—
401C2×C3×C8—51no—
402C2×C3×C8—51no—
403C2×C3×C8—201no—
404C3×C4⋊C4—51no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4C22×D511yescharacteristic
407C3×C22⋊C4—21no—
408C3×C22⋊C4—101no—
409#217C22⋊D511yescharacteristic
410#215—102no—
411#215—201no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—101no—
415(C2×D3)⋊C4C22⋊D511yescharacteristic
416C4⋊Dic3—51no—
417C4⋊Dic3—51no—
418C4⋊Dic3—101no—
419C4⋊Dic3—101no—
420Dic3⋊C4—101no—
421Dic3⋊C4—101no—
422Dic3⋊C4—101no—
423Dic3⋊C4C22⋊D511yescharacteristic
424C4×Dic3—101no—
425C4×Dic3C22×D511yescharacteristic
426C2×C3⋊C8—51no—
427C2×C3⋊C8—51no—
428D3×C8—201no—
429C23×C5—21no—
430C23×C5—31no—
431C23×C5—61no—
432C23×C5—61no—
433C23×C5—122no—
434C23×C5—122no—
435C23×C5—122no—
436C23×C5—122no—
437C23×C5—241no—
438C23×C5—241no—
439C23×C5D3×D411yescharacteristic
440C5×D4—21no—
441C5×D4—21no—
442C5×D4—34no—
443C5×D4—32no—
444C5×D4—42no—
445C5×D4—61no—
446C5×D4—61no—
447C5×D4—61no—
448C5×D4—122no—
449C5×D4—122no—
450C5×D4—122no—
451C5×D4—122no—
452C5×D4—241no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—31no—
457C2×C4×C5—31no—
458C2×C4×C5—31no—
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—241no—
469C2×Dic5—241no—
470Dic10—21no—
471Dic10—21no—
472Dic10—241no—
473#168—21no—
474#168—21no—
475#168—61no—
476#168—61no—
477C22×D4—31no—
478C22×D4—31no—
479C22×D4—61no—
480C2×SD16—51no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—51no—
484C22×C8—151no—
485C4⋊Q8—151no—
486#127—31no—
487#125—301no—
488C22⋊Q8—51no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—31no—
493#121—61no—
494#121D3×D511yescharacteristic
495#120—61no—
496#120—61no—
497C4×Q8—151no—
498C4×D4—31no—
499C4×D4—31no—
500C4×D4—301no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503#106—51no—
504#106—151no—
505#106—151no—
506C4⋊C8—151no—
507#103—51no—
508#102—51no—
509#102—151no—
510#102—151no—
511#102—151no—
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—81no—
522C2×C3×C5#54611yescharacteristic
523C2×C3×C5C22×SD1611yescharacteristic
524C2×C3×C5#57611yescharacteristic
525C5×D3—22no—
526C5×D3—42no—
527C5×D3—81no—
528C23×C3—21no—
529C23×C3C2×C22⋊D511yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3—81no—
537C22×D3—81no—
538C22×D3C2×C22⋊D511yescharacteristic
539C3×Q8—101no—
540C3×Q8—101no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—42no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4C2×C22⋊D511yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551#67—42no—
552#67—42no—
553#67—81no—
554#67#68714yescomplemented
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—401no—
558C2×Dic3C2×C22⋊D511yescharacteristic
559C2×Dic3C2×C22⋊D511yescharacteristic
560C2×Dic3C2×C22⋊D511yescharacteristic
561D12—21no—
562D12—21no—
563D12—21no—
564D12—42no—
565D12—42no—
566D12#71112yes—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—42no—
570C4×D3—401no—
571Dic6—401no—
572C3×C8—101no—
573C3×C8—101no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—32no—
579C22×C5—41no—
580C22×C5—41no—
581C22×C5—41no—
582C22×C5—61no—
583C22×C5—61no—
584C22×C5—62no—
585C22×C5—121no—
586C22×C5—121no—
587C22×C5—121no—
588C22×C5—121no—
589C22×C5—121no—
590C22×C5—244no—
591C22×C5—244no—
592C22×C5D3×SD1612yes—
593C22×C5C2×D3×D411yescharacteristic
594C4×C5—21no—
595C4×C5—32no—
596C4×C5—41no—
597C4×C5—61no—
598C4×C5—61no—
599C4×C5#100411yescharacteristic
600C4×C5D3×#4111yescharacteristic
601Dic5—41no—
602Dic5—41no—
603Dic5—121no—
604Dic5—121no—
605C24—61no—
606C24—61no—
607C2×Q8—51no—
608C2×Q8—301no—
609C2×D4—21no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—62no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—62no—
619C2×D4—61no—
620C2×D4—121no—
621C2×D4—121no—
622C2×D4—124no—
623C2×D4C2×D3×D511yescharacteristic
624C22×C4—31no—
625C22×C4—61no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—201no—
630SD16—302no—
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—51no—
640C4⋊C4—101no—
641C4⋊C4—151no—
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—31no—
651C22⋊C4—31no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—101no—
655C22⋊C4—301no—
656C42—31no—
657C42—301no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3C2×#68712yes—
665C22×C3C22×C22⋊D511yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—84no—
675C2×D3—84no—
676C2×D3C2×#68712yes—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—201no—
680C3×C4—201no—
681C3×C4C2×#71111yescharacteristic
682C3×C4#414411yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—201no—
686Dic3—201no—
687Dic3C2×#68712yes—
688C2×C5—22no—
689C2×C5—62no—
690C2×C5—81no—
691C2×C5—122no—
692C2×C5—241no—
693C2×C5#561011yescharacteristic
694C2×C5C2×D3×SD1611yescharacteristic
695C2×C5#576911yescharacteristic
696C23—21no—
697C23—31no—
698C23—61no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—241no—
705C23—241no—
706C23D3×C22⋊D511yescharacteristic
707Q8—101no—
708Q8—101no—
709Q8—1201no—
710D4—21no—
711D4—21no—
712D4—34no—
713D4—32no—
714D4—42no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—122no—
719D4—122no—
720D4—122no—
721D4—122no—
722D4—241no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—122no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—1201no—
737C2×C4—1201no—
738C2×C4D3×C22⋊D511yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—101no—
741C8—101no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—81no—
746C2×C3C22×#68711yescharacteristic
747C2×C3#6614011yescharacteristic
748C2×C3#6616911yescharacteristic
749D3—22no—
750D3—42no—
751D3—81no—
752C5#8068011yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—61no—
760C22—61no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22—244no—
769C22D3×#68712yes—
770C22C2×D3×C22⋊D511yescharacteristic
771C4—21no—
772C4—32no—
773C4—41no—
774C4—61no—
775C4—61no—
776C4—201no—
777C4—201no—
778C4—601no—
779C4—601no—
780C4D3×#71111yescharacteristic
781C4#9202511yescharacteristic
782C3#1061521411yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—81no—
786C2—122no—
787C2—241no—
788C2C2×D3×#68711yescharacteristic
789C2#1175494211yescharacteristic
790C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
prime radicalC5×#5609C2
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. #11754514C2semidirect
3. #11751135C2semidirect
4. C3×#65330C2semidirect
5. #11749058C2semidirect
6. #11749005C2semidirect
7. D3×#3964C2semidirect
8. #11748941C2semidirect
9. #11748537C2semidirect
10. #67×#168C2semidirect
11. C2×#90967C2semidirect
12. #11747419C2semidirect
13. #11747352C2semidirect
14. #11747264C2semidirect
15. #11747199C2semidirect
21. C2×C4⋊Dic15C22semidirect
29. C2×C3×#687C22semidirect
30. C3×#4070C22semidirect
31. C22×C3×#168C22semidirect
34. #91469C22semidirect
35. D3×C4⋊Dic5C22semidirect
37. #91369C22semidirect
39. Dic3×Dic10C22semidirect
41. C2×#6656C22semidirect
42. C2×D3×#168C22semidirect
43. #91116C22semidirect
44. #91116C22semidirect
45. #91114C22semidirect
46. #91092C22semidirect
47. #91092C22semidirect
48. C3×#3964C22semidirect
49. C3×#3942C22semidirect
50. C3×#3940C22semidirect
51. Dic3⋊#168C22semidirect
54. #90967C22semidirect
55. #90967C22semidirect
57. #90966C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
70. #65330D3semidirect
158. C2×#687C2×D3semidirect
162. #4070C2×D3semidirect
164. C22×#168C2×D3semidirect
178. #3964C2×D3semidirect
181. #3942C2×D3semidirect
184. #3940C2×D3semidirect
213. C5×#67SD16semidirect
554. #67#687semidirect
658. C3×C5#3295semidirect
752. C5#80680semidirect
782. C3#10615214semidirect

Maximal subgroups

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

subgroupindex
C5×#56092
#117545142
#117511352
C3×#653302
#117490582
#117490052
D3×#39642
#117489412
#117485372
#67×#1682
C2×#909672
#117474192
#117473522
#117472642
#117471992
#106152143
#806805