Finite Group Databasebeta

← #14417056

Subgroups — #14417056

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91253C211yesmaximal, characteristic
2#11752727C211yesmaximal, characteristic, complemented
3#11752527C211yesmaximal, characteristic, complemented
4C4×D120C211yesmaximal, characteristic, complemented
5C5×#4689C211yesmaximal, characteristic, complemented
6C3×C4×#677C211yesmaximal, characteristic, complemented
7D3×#3953C211yesmaximal, characteristic, complemented
8#11747830C211yesmaximal, characteristic, complemented
9#11747796C211yesmaximal, characteristic, complemented
10#11747795C211yesmaximal, characteristic, complemented
11#11747740C211yesmaximal, characteristic, complemented
12#11747643C211yesmaximal, characteristic, complemented
13#11747628C211yesmaximal, characteristic, complemented
14#11747054C211yesmaximal, characteristic, complemented
15#11747023C211yesmaximal, characteristic, complemented
16#10610291—31nomaximal, Hall
17C2×D3×D20C2211yescharacteristic
18C2×#6769C2211yescharacteristic
19C2×D120C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C4×D60C2211yescharacteristic, complemented
22C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C5×D3×C8C2211yescharacteristic
24C5×#872C2211yescharacteristic
25C2×C3×#677C2211yescharacteristic
26C3×C4×D20C2211yescharacteristic
27C3×C4×Dic10C2211yescharacteristic, complemented
28#91473—21no—
29D5×(C2×D3)⋊C4—21no—
30#91444—21no—
31#91428C2211yescharacteristic
32#91428C2211yescharacteristic, complemented
33D3×C4⋊Dic5C2211yescharacteristic
34Dic3×D20C2211yescharacteristic
35#91406—21no—
36#91405—21no—
37#91404—21no—
38#91402—21no—
39#91396—21no—
40#91338C2211yescharacteristic
41Dic3×Dic10C2211yescharacteristic, complemented
42C2×#6658C2211yescharacteristic
43C2×#6653C2211yescharacteristic
44#91253C418yescomplemented
45C3×C4×C5×C8C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91105C2211yescharacteristic, complemented
48#91102C2211yescharacteristic, complemented
49C5×#815C2211yescharacteristic, complemented
50C5×C8×Dic3C2211yescharacteristic, complemented
51C5×#803C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×#3949C2211yescharacteristic, complemented
54C3×#3948C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90971C2211yescharacteristic, complemented
58#90968C2211yescharacteristic
59#90968C2211yescharacteristic, complemented
60#90965C2211yescharacteristic
61#79647—51nomaximal, Hall
62C2×#4054—31no—
63#65857—31no—
64#65855—31no—
65C5×#405—31no—
66#65410—31no—
67#65402—31no—
68C2×#3953—31no—
69#65000—31no—
70#65000—31no—
71#64999—31no—
72#64999—31no—
73C4×D40—31no—
74C4×D40—31no—
75C4×#677—31no—
76C4×#677D311yescharacteristic, complemented
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C4×C5×D3C2311yescharacteristic
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×Dic10C2311yescharacteristic
86C2×#1203—21no—
87C2×#1202—21no—
88C2×#1200—21no—
89C2×#1200—21no—
90C2×#1200—21no—
91C2×D3×Dic5—21no—
92C2×D5×Dic3—21no—
93D3×D20—22no—
94D3×D20C2×C414yescomplemented
95#6769—22no—
96#6769C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C2×C3×C5×C8C2311yescharacteristic
99C3×C42×C5C2311yescharacteristic
100#6714—21no—
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104D120C2×C414yescomplemented
105C5×(C2×D3)⋊C4D411yescharacteristic
106C5×(C2×D3)⋊C4D411yescharacteristic
107C5×Dic3⋊C4D411yescharacteristic
108C5×Dic3⋊C4D411yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C2×C5×C3⋊C8C2311yescharacteristic
112C5×ΓL(1,𝔽25)C2×C414yescomplemented
113C5×D3×C8—22no—
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×C4×Dic5—21no—
119C3×#677C2×C414yescomplemented
120Dic3⋊Dic5—21no—
121#6668—21no—
122#6667—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126Dic3×Dic5—21no—
127Dic3×Dic5—21no—
128#6658C2×C414yescomplemented
129#6653C2×C414yescomplemented
130C2×#914—51no—
131#5574—51no—
132#5545—51no—
133C3×C4×SD16—51no—
134#5164—51no—
135#5026—51no—
136#5014—51no—
137#4869—51no—
138#4861—51no—
139#4804—51no—
140#4788—51no—
141D3×#102—51no—
142#4756—51no—
143C4×D24—51no—
144#4689D511yescharacteristic, complemented
145C2×#709—31no—
146C22×D20—31no—
147C2×C5×M16—31no—
148C22×C5×C8—31no—
149C5×#117—31no—
150#4072—31no—
151C2×C4⋊Dic5—31no—
152#4054—38no—
153C2×D40—31no—
154C2×D40—31no—
155C2×#677—31no—
156C2×#677C2×D311yescharacteristic
157#4039—61no—
158#4039—61no—
159#4038—61no—
160D5×C4⋊C4—61no—
161#4027—61no—
162#4027—61no—
163D5×C22⋊C4—61no—
164D5×C22⋊C4—61no—
165C4×D20—31no—
166C4×D20—31no—
167C4×D20—31no—
168C4×D20—31no—
169C4×D20—31no—
170C4×D20C2×D311yescharacteristic
171C4×Dic10—31no—
172C4×Dic10C2×D311yescharacteristic, complemented
173C5×#97—31no—
174C5×#97—31no—
175C4×C5×C8—31no—
176C4×C5×C8C2×D311yescharacteristic, complemented
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3953—31no—
181#3953—31no—
182#3953C2×D311yescharacteristic
183#3950—31no—
184#3950—31no—
185#3949—31no—
186#3949C2×D311yescharacteristic, complemented
187#3948—31no—
188#3948C2×D311yescharacteristic, complemented
189#2946—151noSylow
190C22×D15—21no—
191C22×D15—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C2×Dic15—21no—
201C2×Dic15—21no—
202D60—21no—
203D60—21no—
204D60C22×C412yes—
205D60C22×C412yes—
206C4×D15—81no—
207C4×D15—81no—
208C2×C5×Dic3C2×D411yescharacteristic
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C4×C5×D3C22×C412yes—
212C4×C5×D3#4112yes—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C3×D20—21no—
217C3×D20C22×C412yes—
218C3×C4×D5—81no—
219C3×Dic10—21no—
220C3×Dic10C22×C412yes—
221#1203—24no—
222#1202—24no—
223#1200—24no—
224#1200—81no—
225#1200—81no—
226D3×Dic5—81no—
227D5×Dic3—81no—
228C3×C5×C8—21no—
229C3×C5×C8C22×C412yes—
230C5×C3⋊C8—21no—
231C5×C3⋊C8C22×C412yes—
232C2×#239—51no—
233C2×D3×D4—51no—
234C2×C3×SD16—51no—
235C3×C4×Q8—51no—
236C3×C4×D4—51no—
237Q8×Dic3—51no—
238C2×#215—51no—
239D4×Dic3—51no—
240C2×#213—51no—
241C4×#67—101no—
242C2×(C2×D3)⋊C4—101no—
243#914—58no—
244C2×D24—51no—
245C2×ΓL(1,𝔽25)C2×D511yescharacteristic
246C2×D3×C8C2×D511yescharacteristic
247#893—51no—
248#893—51no—
249#893—101no—
250#892—51no—
251D3×C4⋊C4—51no—
252D3×C4⋊C4—101no—
253#67⋊C4—101no—
254D3×C22⋊C4—101no—
255C4×D12—51no—
256C4×D12—51no—
257C4×D12—101no—
258#872—101no—
259#872C2×D511yescharacteristic
260C3×#106—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×C4×C8C2×D511yescharacteristic, complemented
264#835—51no—
265#832—51no—
266#821—51no—
267#821—51no—
268#818—51no—
269#815C2×D511yescharacteristic, complemented
270C8×Dic3C2×D511yescharacteristic, complemented
271#809—51no—
272#809—51no—
273#808—51no—
274#807—51no—
275#803C2×D511yescharacteristic, complemented
276C23×D5—61no—
277C22×C4×C5—31no—
278C2×C22⋊D5—61no—
279C22×Dic5—61no—
280#709—34no—
281#709—62no—
282C2×D20—31no—
283C2×D20—31no—
284C2×D20—34no—
285C2×D20—62no—
286C2×D20—61no—
287C2×D20C22×D311yescharacteristic
288C2×C4×D5—21no—
289C2×C4×D5—61no—
290C2×C4×D5—61no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×Dic10C22×D311yescharacteristic
296C5×M16—34no—
297C2×C5×C8—31no—
298C2×C5×C8—31no—
299C2×C5×C8—62no—
300C2×C5×C8C22×D311yescharacteristic
301C2×C5×C8C22×D311yescharacteristic
302C5×C4⋊C4—31no—
303C5×C4⋊C4—31no—
304C5×C22⋊C4—31no—
305C5×C22⋊C4—31no—
306C42×C5—31no—
307C42×C5C22×D311yescharacteristic
308C22⋊Dic5—61no—
309#685—21no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—61no—
318C4⋊Dic5C22×D311yescharacteristic
319C4⋊Dic5C22×D311yescharacteristic
320#683—21no—
321#683—61no—
322C4×Dic5—21no—
323C4×Dic5—61no—
324C4×Dic5—61no—
325D40—34no—
326D40—34no—
327#677—34no—
328#677C4×D314yescomplemented
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—51no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—31no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—22no—
347C2×D15—41no—
348C2×D15—41no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—21no—
352C2×C5×D3—21no—
353C2×C5×D3C4×D412yes—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5C23×C411yescharacteristic
361C3×C4×C5C2×#4111yescharacteristic
362Dic15—41no—
363Dic15—41no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C5×Dic3—21no—
368C5×Dic3—21no—
369C5×Dic3C4×D412yes—
370C23×D3—101no—
371C2×C3×Q8—51no—
372C2×C3×D4—51no—
373C22×C3×C4—101no—
374C2×#67—101no—
375C22×Dic3—101no—
376#239—54no—
377#239—102no—
378D3×D4—54no—
379D3×D4—102no—
380C2×D12—51no—
381C2×D12—51no—
382C2×D12—101no—
383C2×C4×D3—101no—
384C2×C4×D3—101no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3C22×D511yescharacteristic
390C3×SD16—54no—
391C2×C3×C8C22×D511yescharacteristic
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C42—101no—
398C3×C42C22×D511yescharacteristic
399#217—101no—
400#215—54no—
401#213—54no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4D2011yescharacteristic
408(C2×D3)⋊C4D2011yescharacteristic
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4D2011yescharacteristic
414Dic3⋊C4D2011yescharacteristic
415C4×Dic3—101no—
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8C22×D511yescharacteristic
419C2×C3⋊C8C22×D511yescharacteristic
420D24—54no—
421ΓL(1,𝔽25)C4×D514yescomplemented
422D3×C8—22no—
423C23×C5—31no—
424C22×D5—21no—
425C22×D5—64no—
426C22×D5—61no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C2×C4×C5—31no—
431C2×C4×C5—32no—
432C2×C4×C5—32no—
433C2×C4×C5—31no—
434C2×C4×C5—31no—
435C2×C4×C5D3×D411yescharacteristic
436C2×C4×C5D3×D411yescharacteristic
437C2×C4×C5C23×D311yescharacteristic
438C22⋊D5—64no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—241no—
445D20—21no—
446D20—32no—
447D20—32no—
448D20—64no—
449D20—61no—
450D20—61no—
451D20C2×C4×D312yes—
452C4×D5—64no—
453C4×D5—81no—
454C4×D5—241no—
455C4×D5—241no—
456C4×D5—241no—
457C4×D5—241no—
458C4×D5—241no—
459Dic10—21no—
460Dic10C2×C4×D312yes—
461C5×C8—21no—
462C5×C8—32no—
463C5×C8—61no—
464C5×C8C2×C4×D312yes—
465C2×#41—151no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—51no—
469C2×SD16—151no—
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—31no—
473C22×C8—31no—
474C4×Q8—51no—
475C4×Q8—151no—
476C4×D4—51no—
477C4×D4—151no—
478C4×D4—151no—
479C4×D4—151no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—31no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—151no—
494#107—151no—
495#106—51no—
496#106—151no—
497#103—51no—
498#103—151no—
499#102—51no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—31no—
506#97—31no—
507C4×C8—31no—
508C4×C8D3×D511yescharacteristic, complemented
509C2×C3×C5C2×C4×D411yescharacteristic
510C2×C3×C5#57611yescharacteristic
511C2×C3×C5#57711yescharacteristic
512D15—42no—
513D15—42no—
514C3×D5—42no—
515C5×D3—22no—
516C23×C3—101no—
517C22×D3—101no—
518C22×D3—101no—
519C22×D3—104no—
520C22×D3—401no—
521C22×D3—401no—
522C22×D3C2×D2011yescharacteristic
523C3×Q8—52no—
524C3×Q8—101no—
525C3×D4—52no—
526C3×D4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—401no—
531C2×C3×C4C2×D2011yescharacteristic
532C2×C3×C4C2×D2011yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—104no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—401no—
538C2×Dic3C2×D2011yescharacteristic
539C2×Dic3C2×D2011yescharacteristic
540C2×Dic3C2×D2011yescharacteristic
541D12—52no—
542D12—52no—
543D12—104no—
544D12—101no—
545D12—101no—
546C4×D3—104no—
547C4×D3—401no—
548C4×D3—401no—
549C4×D3—401no—
550C4×D3—401no—
551C4×D3—401no—
552C4×D3C2×C4×D512yes—
553C4×D3#70912yes—
554C3×C8—21no—
555C3×C8C2×C4×D512yes—
556C3⋊C8—21no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—32no—
559C22×C5—61no—
560C22×C5—61no—
561C22×C5C2×D3×D411yescharacteristic
562C2×D5—22no—
563C2×D5—41no—
564C2×D5—41no—
565C2×D5—62no—
566C2×D5—62no—
567C2×D5—121no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—32no—
575C4×C5—61no—
576C4×C5—61no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5D3×#4111yescharacteristic
579Dic5—22no—
580Dic5—41no—
581Dic5—41no—
582Dic5—121no—
583Dic5—121no—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8—51no—
588C2×D4—51no—
589C2×D4—154no—
590C2×D4—151no—
591C2×D4—151no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4—301no—
595C22×C4—31no—
596C22×C4—101no—
597C22×C4—301no—
598C22×C4—301no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—54no—
605SD16—154no—
606D8—154no—
607D8—154no—
608M16—34no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—62no—
612C2×C8C2×D3×D511yescharacteristic
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—101no—
619C4⋊C4—151no—
620C4⋊C4—151no—
621C4⋊C4—301no—
622C4⋊C4—301no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—101no—
626C22⋊C4—301no—
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—101no—
634C42—301no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—102no—
639C22×C3—201no—
640C22×C3—201no—
641C22×C3C22×D2011yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—102no—
645C2×D3—102no—
646C2×D3—201no—
647C2×D3—201no—
648C2×D3—201no—
649C2×D3—201no—
650C2×D3—404no—
651C2×D3C4×D2012yes—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—102no—
655C3×C4—201no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4C2×#70911yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—201no—
662Dic3—201no—
663Dic3C4×D2012yes—
664C2×C5—62no—
665C2×C5C4×D3×D411yescharacteristic
666C2×C5#576211yescharacteristic
667C2×C5#576911yescharacteristic
668D5—42no—
669D5—122no—
670D5—122no—
671C23—31no—
672C23—101no—
673C23—304no—
674C23—301no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—52no—
679Q8—101no—
680D4—52no—
681D4—101no—
682D4—152no—
683D4—152no—
684D4—304no—
685D4—304no—
686D4—301no—
687D4—301no—
688C2×C4—31no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—101no—
694C2×C4—101no—
695C2×C4—101no—
696C2×C4—304no—
697C2×C4—301no—
698C2×C4—301no—
699C2×C4—401no—
700C2×C4—1201no—
701C2×C4—1201no—
702C2×C4—1201no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4D3×D2011yescharacteristic
707C2×C4D3×D2011yescharacteristic
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—32no—
711C8—61no—
712C8C4×D3×D512yes—
713C2×C3—202no—
714C2×C3C2×C4×D2011yescharacteristic
715C2×C3#6608511yescharacteristic
716C2×C3#6608611yescharacteristic
717D3—22no—
718D3—202no—
719D3—202no—
720C5#7964711yescharacteristic, complemented, Sylow
721C22—32no—
722C22—61no—
723C22—61no—
724C22—102no—
725C22—201no—
726C22—201no—
727C22—302no—
728C22—302no—
729C22—601no—
730C22—601no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22C2×D3×D2011yescharacteristic
735C4—21no—
736C4—21no—
737C4—32no—
738C4—61no—
739C4—61no—
740C4—102no—
741C4—201no—
742C4—201no—
743C4—601no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D3×#70911yescharacteristic
747C3#1061029111yescharacteristic, complemented, Sylow
748C2—62no—
749C2—202no—
750C2—602no—
751C2—602no—
752C2C4×D3×D2011yescharacteristic
753C2#1175397011yescharacteristic
754C2#1175397311yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91253C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752727C2semidirect
3. #11752527C2semidirect
4. C4×D120C2semidirect
5. C5×#4689C2semidirect
6. C3×C4×#677C2semidirect
7. D3×#3953C2semidirect
8. #11747830C2semidirect
9. #11747796C2semidirect
10. #11747795C2semidirect
11. #11747740C2semidirect
12. #11747643C2semidirect
13. #11747628C2semidirect
14. #11747054C2semidirect
15. #11747023C2semidirect
21. C4×D60C22semidirect
27. C3×C4×Dic10C22semidirect
32. #91428C22semidirect
41. Dic3×Dic10C22semidirect
44. #91253C4semidirect
45. C3×C4×C5×C8C22semidirect
47. #91105C22semidirect
48. #91102C22semidirect
49. C5×#815C22semidirect
50. C5×C8×Dic3C22semidirect
51. C5×#803C22semidirect
53. C3×#3949C22semidirect
54. C3×#3948C22semidirect
55. #90990C22semidirect
56. #90987C22semidirect
57. #90971C22semidirect
59. #90968C22semidirect
76. C4×#677D3semidirect
94. D3×D20C2×C4semidirect
96. #6769C2×C4semidirect
104. D120C2×C4semidirect
112. C5×ΓL(1,𝔽25)C2×C4semidirect
119. C3×#677C2×C4semidirect
128. #6658C2×C4semidirect
129. #6653C2×C4semidirect
144. #4689D5semidirect
172. C4×Dic10C2×D3semidirect
176. C4×C5×C8C2×D3semidirect
186. #3949C2×D3semidirect
188. #3948C2×D3semidirect
263. C3×C4×C8C2×D5semidirect
269. #815C2×D5semidirect
270. C8×Dic3C2×D5semidirect
275. #803C2×D5semidirect
328. #677C4×D3semidirect
421. ΓL(1,𝔽25)C4×D5semidirect
508. C4×C8D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79647semidirect
747. C3#10610291semidirect

Maximal subgroups

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

subgroupindex
C2×#912532
#117527272
#117525272
C4×D1202
C5×#46892
C3×C4×#6772
D3×#39532
#117478302
#117477962
#117477952
#117477402
#117476432
#117476282
#117470542
#117470232
#106102913
#796475