Finite Group Databasebeta

← #14459019

Subgroups — #14459019

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5695C211yesmaximal, characteristic, complemented
2#11752749C211yesmaximal, characteristic, complemented
3#11751167C211yesmaximal, characteristic, complemented
4C3×#65357C211yesmaximal, characteristic, complemented
5#11747517C211yesmaximal, characteristic, complemented
6#11747504C211yesmaximal, characteristic, complemented
7#11747482C211yesmaximal, characteristic, complemented
8D3×#3941C211yesmaximal, characteristic, complemented
9#11747352C211yesmaximal, characteristic, complemented
10#11747349C211yesmaximal, characteristic, complemented
11#11747325C211yesmaximal, characteristic, complemented
12#11747319C211yesmaximal, characteristic, complemented
13#11747034C211yesmaximal, characteristic, complemented
14C4×#6654C211yesmaximal, characteristic, complemented
15D12×#168C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C2×D3×D20C2211yescharacteristic
18C2×#6769C2211yescharacteristic
19C3×C5×#125C2211yescharacteristic, complemented
20C4×D60C2211yescharacteristic
21C5×#898—21no—
22C5×#895—21no—
23C5×#895C2211yescharacteristic
24C5×#895C2211yescharacteristic, complemented
25C5×#894—21no—
26C5×#893—21no—
27C5×#892C2211yescharacteristic, complemented
28C5×D3×C4⋊C4C2211yescharacteristic
29C4×C5×D12C2211yescharacteristic
30C4×C5×D12C2211yescharacteristic, complemented
31C3×#4021C2211yescharacteristic
32#91475—21no—
33#91473—21no—
34#91461—21no—
35#91456C2211yescharacteristic
36#91369C2211yescharacteristic
37#91356—21no—
38C2×#6656C2211yescharacteristic, complemented
39C2×#6654C2211yescharacteristic
40C2×#6652C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91093C2211yescharacteristic
44#91093C2211yescharacteristic
45#91092C2211yescharacteristic, complemented
46#91091C2211yescharacteristic, complemented
47C4⋊(C3⋊#168)C2211yescharacteristic, complemented
48C3×#3942C2211yescharacteristic, complemented
49C3×#3942C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52C3×C4×#168C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90970C2211yescharacteristic, complemented
55#90969C2211yescharacteristic
56#90967C2211yescharacteristic, complemented
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60#81653—51nomaximal, Hall
61C5×#553—31no—
62#65884—31no—
63#65357D311yescharacteristic, complemented
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326—31no—
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65259—31no—
75C2×#3941—31no—
76C22×D3×D5—21no—
77C2×D60C2311yescharacteristic
78C2×C4×D15—21no—
79C2×C5×D12—21no—
80C2×C5×D12—21no—
81C2×C5×D12D411yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3C2311yescharacteristic
86C2×C4×C5×D3C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×C3×Dic10C2311yescharacteristic
89C2×#1203—21no—
90C2×#1202—21no—
91C2×#1201—21no—
92C2×#1200—21no—
93D3×D20—22no—
94D3×D20—41no—
95#6769—22no—
96#6769—41no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C42×C5C2311yescharacteristic
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×(C2×D3)⋊C4D411yescharacteristic
112C5×C4⋊Dic3D411yescharacteristic
113C5×C4⋊Dic3C2311yescharacteristic
114C5×Dic3⋊C4—21no—
115C4×C5×Dic3—21no—
116C3×#685—21no—
117C3×#685—21no—
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6669—21no—
121(C2×D3)⋊Dic5—21no—
122#6665—21no—
123#6656—41no—
124#6654—22no—
125#6652—41no—
126D3×#168—41no—
127D3×#168—41no—
128#5695D511yescharacteristic, complemented
129#5676—51no—
130C3×#488—51no—
131#5066—51no—
132#5057—51no—
133#4811—51no—
134#4810—51no—
135#4807—51no—
136#4804—51no—
137#4784—51no—
138#4775—51no—
139#4773—51no—
140D3×#102—51no—
141C4×D24—51no—
142C8×D12—51no—
143C2×#709—31no—
144C22×D20—31no—
145C5×#126—61no—
146C5×#125C2×D311yescharacteristic, complemented
147C5×#123—61no—
148C5×#121—31no—
149C5×#121—31no—
150C5×#121—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C4×C5×D4—61no—
154C5×#117—31no—
155C2×C5×C4⋊C4—31no—
156#4083—61no—
157C2×#687—31no—
158C2×#686—31no—
159C2×#686—31no—
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021C2×D311yescharacteristic
168C4×D20—31no—
169#3964—31no—
170C22⋊#168—31no—
171C22⋊#168—31no—
172#3942—31no—
173#3942C2×D311yescharacteristic, complemented
174#3942C2×D311yescharacteristic, complemented
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941C2×D311yescharacteristic
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168C2×D311yescharacteristic, complemented
186#3297—151noSylow
187C22×D15—21no—
188C22×C5×D3—21no—
189C22×C5×D3C2×D411yescharacteristic
190C22×C5×D3C2×D411yescharacteristic
191C22×C3×D5—21no—
192C2×D3×D5—42no—
193C2×D3×D5—42no—
194C2×D3×D5—81no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C2×Dic15—21no—
201D60—21no—
202D60#4112yes—
203C4×D15—81no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C5×D12—22no—
208C5×D12—21no—
209C5×D12—21no—
210C5×D12—42no—
211C5×D12—81no—
212C4×C5×D3—21no—
213C4×C5×D3—21no—
214C4×C5×D3—21no—
215C4×C5×D3—21no—
216C4×C5×D3—81no—
217C4×C5×D3—81no—
218C2×C3×Dic5—21no—
219C3×D20—21no—
220C3×D20—21no—
221C3×Dic10—21no—
222C3×Dic10—21no—
223#1203—42no—
224#1202—42no—
225#1201—81no—
226#1200—42no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#239—51no—
232C2×D3×D4—51no—
233C3×#125C2×D511yescharacteristic, complemented
234C3×#124—51no—
235#946—51no—
236C2×#215—51no—
237#938—51no—
238C2×#213—51no—
239C2×D24—51no—
240C2×D3×C8—51no—
241C2×D3×C8—51no—
242#898—21no—
243#895—21no—
244#895C2×D511yescharacteristic
245#895C2×D511yescharacteristic, complemented
246#894—21no—
247#893—21no—
248#892C2×D511yescharacteristic, complemented
249D3×C4⋊C4C2×D511yescharacteristic
250#884—101no—
251#883—101no—
252#882—101no—
253D3×C22⋊C4—101no—
254C4×D12—51no—
255C4×D12C2×D511yescharacteristic
256C4×D12C2×D511yescharacteristic, complemented
257C3×#103—51no—
258C3×#103—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×C4×C8—51no—
262#835—51no—
263#832—51no—
264#821—51no—
265#821—51no—
266(C2×D3)⋊C8—51no—
267(C2×D3)⋊C8—51no—
268#818—51no—
269#809—51no—
270#809—51no—
271#808—51no—
272#807—51no—
273C4⋊(C3⋊C8)—51no—
274C23×D5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C22×C4×C5—31no—
280C22×C4×C5—31no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285#709—62no—
286#709—121no—
287C2×D20—31no—
288C2×D20—62no—
289C2×D20—61no—
290C2×D20—121no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10C22×D311yescharacteristic
295C5×C4⋊C4—21no—
296C5×C4⋊C4—21no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—31no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—31no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C5×C22⋊C4—61no—
308C42×C5—61no—
309C42×C5C22×D311yescharacteristic
310C22⋊Dic5—61no—
311#687—121no—
312#686—62no—
313#686—121no—
314#685—21no—
315#685—21no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319#683—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—31no—
327#546—151no—
328#488—51no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—22no—
343C2×D15—41no—
344C2×D15—41no—
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—21no—
348C2×C5×D3—21no—
349C2×C5×D3—21no—
350C2×C5×D3—41no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3#13512yes—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5—41no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364Dic15—41no—
365C3×Dic5—41no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C23×D3—101no—
370C2×C3×Q8—51no—
371C2×C3×D4—51no—
372C2×#67—101no—
373C2×#67—101no—
374#239—102no—
375#239—201no—
376D3×D4—102no—
377D3×D4—201no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—51no—
381C2×D12—101no—
382C2×D12C22⋊D511yescharacteristic
383C2×D12C22×D511yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—21no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3C22×D511yescharacteristic
389C2×C4×D3C22×D511yescharacteristic
390C2×C3×C8—51no—
391C2×C3×C8—51no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C42C22×D511yescharacteristic
399#217—101no—
400#215—201no—
401#213—201no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4C22⋊D511yescharacteristic
409(C2×D3)⋊C4C22⋊D511yescharacteristic
410C4⋊Dic3—51no—
411C4⋊Dic3C22⋊D511yescharacteristic
412C4⋊Dic3C22×D511yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—101no—
415C4×Dic3—21no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418D24—102no—
419D3×C8—201no—
420D3×C8—201no—
421C23×C5—31no—
422C23×C5—31no—
423C23×C5—61no—
424C22×D5—21no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×D4—62no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—122no—
433C5×D4—241no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—31no—
437C2×C4×C5—31no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5—241no—
444C2×C4×C5—241no—
445C2×C4×C5D3×D411yescharacteristic
446C2×C4×C5D3×D411yescharacteristic
447C2×C4×C5C23×D311yescharacteristic
448C22⋊D5—122no—
449C22⋊D5—241no—
450C2×Dic5—21no—
451C2×Dic5—61no—
452D20—21no—
453D20—21no—
454D20—32no—
455D20—61no—
456D20—122no—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—21no—
460Dic10—21no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—61no—
473#125D3×D511yescharacteristic, complemented
474#124—51no—
475#123—61no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—31no—
480#121—61no—
481#121—151no—
482#121—301no—
483#120—301no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—61no—
487C4×D4—151no—
488#117—31no—
489C2×C4⋊C4—31no—
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—51no—
496#103—51no—
497#103—151no—
498#102—51no—
499#102—51no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—51no—
508C2×C3×C5#54611yescharacteristic
509C2×C3×C5C2×#13511yescharacteristic
510C2×C3×C5#57611yescharacteristic
511D15—42no—
512C3×D5—81no—
513C5×D3—22no—
514C5×D3—41no—
515C5×D3—81no—
516C23×C3—101no—
517C22×D3—21no—
518C22×D3—101no—
519C22×D3—202no—
520C22×D3—202no—
521C22×D3—401no—
522C22×D3C2×C22⋊D511yescharacteristic
523C22×D3C2×C22⋊D511yescharacteristic
524C3×Q8—101no—
525C3×Q8—101no—
526C3×D4—101no—
527C3×D4—101no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—101no—
531C2×C3×C4C2×C22⋊D511yescharacteristic
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—202no—
535#67—401no—
536C2×Dic3—21no—
537C2×Dic3—101no—
538C2×Dic3C2×C22⋊D511yescharacteristic
539C2×Dic3C2×C22⋊D511yescharacteristic
540D12—22no—
541D12—21no—
542D12—21no—
543D12—42no—
544D12—52no—
545D12—81no—
546D12—101no—
547D12—202no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—81no—
553C4×D3—81no—
554C4×D3—202no—
555C4×D3—401no—
556C3×C8—101no—
557C3×C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—32no—
561C22×C5—61no—
562C22×C5—61no—
563C22×C5—61no—
564C22×C5—61no—
565C22×C5—61no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5C2×D3×D411yescharacteristic
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—62no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—41no—
580C4×C5—41no—
581C4×C5—61no—
582C4×C5—61no—
583C4×C5—121no—
584C4×C5D3×#4111yescharacteristic
585C4×C5#100911yescharacteristic
586Dic5—41no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—51no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—151no—
598C2×D4—301no—
599C2×D4—302no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4—601no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—301no—
608C22×C4—301no—
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—151no—
624C4⋊C4—301no—
625C4⋊C4C2×D3×D511yescharacteristic
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—61no—
639C42C2×D3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—201no—
642C22×C3—201no—
643C22×C3—201no—
644C22×C3C22×C22⋊D511yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—102no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—404no—
657C2×D3#409612yes—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—201no—
663C3×C4D5×#4111yescharacteristic
664C3×C4#414911yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—201no—
669C2×C5—62no—
670C2×C5—121no—
671C2×C5—241no—
672C2×C5#567611yescharacteristic
673C2×C5D3×#13511yescharacteristic
674C2×C5#576911yescharacteristic
675D5—81no—
676D5—122no—
677C23—31no—
678C23—31no—
679C23—61no—
680C23—101no—
681C23—301no—
682C23—602no—
683C23—602no—
684C23—1201no—
685Q8—101no—
686Q8—101no—
687D4—62no—
688D4—61no—
689D4—61no—
690D4—101no—
691D4—101no—
692D4—122no—
693D4—152no—
694D4—241no—
695D4—301no—
696D4—602no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—101no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—301no—
712C2×C4—602no—
713C2×C4—1201no—
714C2×C4D3×C22⋊D511yescharacteristic
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—401no—
722C2×C3C2×#409611yescharacteristic
723C2×C3#6616311yescharacteristic
724C2×C3#6616911yescharacteristic
725D3—22no—
726D3—41no—
727D3—81no—
728D3—202no—
729C5#8165311yescharacteristic, complemented, Sylow
730C22—32no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—302no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—41no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—201no—
755C4—601no—
756C4#9203411yescharacteristic
757C4#9203511yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—62no—
760C2—121no—
761C2—241no—
762C2—401no—
763C2—602no—
764C2#1175528011yescharacteristic
765C2D3×#409611yescharacteristic
766C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
hypercenter#125D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C5×#5695C2semidirect
2. #11752749C2semidirect
3. #11751167C2semidirect
4. C3×#65357C2semidirect
5. #11747517C2semidirect
6. #11747504C2semidirect
7. #11747482C2semidirect
8. D3×#3941C2semidirect
9. #11747352C2semidirect
10. #11747349C2semidirect
11. #11747325C2semidirect
12. #11747319C2semidirect
13. #11747034C2semidirect
14. C4×#6654C2semidirect
15. D12×#168C2semidirect
19. C3×C5×#125C22semidirect
24. C5×#895C22semidirect
27. C5×#892C22semidirect
30. C4×C5×D12C22semidirect
38. C2×#6656C22semidirect
42. C2×D3×#168C22semidirect
45. #91092C22semidirect
46. #91091C22semidirect
47. C4⋊(C3⋊#168)C22semidirect
48. C3×#3942C22semidirect
49. C3×#3942C22semidirect
52. C3×C4×#168C22semidirect
53. #90988C22semidirect
54. #90970C22semidirect
56. #90967C22semidirect
59. (C2×D3)⋊#168C22semidirect
63. #65357D3semidirect
128. #5695D5semidirect
146. C5×#125C2×D3semidirect
173. #3942C2×D3semidirect
174. #3942C2×D3semidirect
185. C4×#168C2×D3semidirect
233. C3×#125C2×D5semidirect
245. #895C2×D5semidirect
248. #892C2×D5semidirect
256. C4×D12C2×D5semidirect
473. #125D3×D5semidirect
640. C3×C5#3297semidirect
729. C5#81653semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
C5×#56952
#117527492
#117511672
C3×#653572
#117475172
#117475042
#117474822
D3×#39412
#117473522
#117473492
#117473252
#117473192
#117470342
C4×#66542
D12×#1682
#106153453
#816535