Finite Group Databasebeta

← #14417031

Subgroups — #14417031

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
1#11754914C211yesmaximal, characteristic, complemented
2C2×#91496C211yesmaximal, characteristic
3#11753337C211yesmaximal, characteristic, complemented
4#11750886C211yesmaximal, characteristic, complemented
5C5×D3×#102C211yesmaximal, characteristic, complemented
6C3×#65046C211yesmaximal, characteristic, complemented
7#11749017C211yesmaximal, characteristic, complemented
8#11748975C211yesmaximal, characteristic, complemented
9#11747746C211yesmaximal, characteristic, complemented
10#11747738C211yesmaximal, characteristic, complemented
11#11747665C211yesmaximal, characteristic, complemented
12#11747643C211yesmaximal, characteristic, complemented
13#11747454C211yesmaximal, characteristic, complemented
14#11747233C211yesmaximal, characteristic, complemented
15#11747218C211yesmaximal, characteristic, complemented
16#10610457—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×#6769C2211yescharacteristic
19D4×Dic15C2211yescharacteristic
20C2×#6715C2211yescharacteristic
21#91782C2211yescharacteristic, complemented
22C2×C5×D3×C8C2211yescharacteristic
23C5×D3×C4⋊C4C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×#4033C2211yescharacteristic, complemented
27#67⋊Dic5—21no—
28D3×C22⋊Dic5—21no—
29Dic5×#67—21no—
30C2×(C2×D3)⋊Dic5—21no—
31#91496C418yescomplemented
32#91446—21no—
33C4×#1203—21no—
34#91435C2211yescharacteristic
35#91418C2211yescharacteristic, complemented
36Dic5×D12C2211yescharacteristic
37#91404—21no—
38#91402—21no—
39#91371C2211yescharacteristic
40#91338C2211yescharacteristic
41#91331C2211yescharacteristic, complemented
42C2×#6656C2211yescharacteristic
43C2×#6654C2211yescharacteristic
44C2×#6650C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic
46#91105C2211yescharacteristic, complemented
47#91099C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic
50C5×#821C2211yescharacteristic
51C5×#809C2211yescharacteristic
52C3×#3948C2211yescharacteristic, complemented
53C3×#3947C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90971C2211yescharacteristic, complemented
58#90968C2211yescharacteristic, complemented
59#90951C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#79775—51nomaximal, Hall
62#66132—31no—
63C2×#4078—31no—
64#65838—31no—
65C2×C5×#102—31no—
66#65402—31no—
67#65390—31no—
68#65253—31no—
69#65074—31no—
70#65074—31no—
71#65047—31no—
72#65047—31no—
73#65046—31no—
74#65046D311yescharacteristic, complemented
75#65045—31no—
76#65045—31no—
77C23×C5×D3—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×Dic15—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C5×#67—21no—
83C5×D3×D4—22no—
84C5×D3×D4C2×C414yescomplemented
85C2×C5×D12C2311yescharacteristic
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3C2311yescharacteristic
88C22×C3×Dic5—21no—
89C2×C3×Dic10C2311yescharacteristic
90C2×#1203—21no—
91C2×#1200—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5—21no—
95#6769—22no—
96#6769C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99#6719—21no—
100#6715C2×C414yescomplemented
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C4×Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C2×C5×C3⋊C8C2311yescharacteristic
108C5×D3×C8—22no—
109C3×C22⋊Dic5—21no—
110C3×#687C2×C414yescomplemented
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116Dic3⋊Dic5D411yescharacteristic
117Dic3⋊Dic5D411yescharacteristic
118#6668—21no—
119#6667—21no—
120(C2×D3)⋊Dic5—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5D411yescharacteristic
124(C2×D3)⋊Dic5D411yescharacteristic
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6656C2×C414yescomplemented
128#6654C2×C414yescomplemented
129#6650C2×C414yescomplemented
130C2×#914—51no—
131#5574—51no—
132#5545—51no—
133C3×#440—51no—
134Dic3×SD16—51no—
135C4×#215—51no—
136C4×#213—51no—
137#4881—51no—
138#4872—51no—
139#4817—51no—
140#4804—51no—
141#4785—51no—
142D3×#102D511yescharacteristic, complemented
143#4711—51no—
144#4708—51no—
145C22×C5×D4—31no—
146C2×#709—31no—
147C22×C5×C8—31no—
148C2×C5×C4⋊C4—31no—
149C2×C22⋊Dic5—61no—
150C2×C22⋊Dic5—61no—
151D4×Dic5—31no—
152D4×Dic5—31no—
153D4×Dic5—31no—
154D4×Dic5—61no—
155D4×Dic5—61no—
156D4×Dic5C2×D311yescharacteristic
157C2×#687—31no—
158C2×#687C2×D311yescharacteristic
159#4078—38no—
160C2×#686—31no—
161C2×#686—31no—
162C4×C22⋊D5—61no—
163C4×C22⋊D5—61no—
164#4072—31no—
165#4072—31no—
166C2×#681—31no—
167#4039—31no—
168#4039—31no—
169#4038—61no—
170D5×C4⋊C4—61no—
171#4033—31no—
172#4033C2×D311yescharacteristic, complemented
173C5×#102—31no—
174C5×#102—31no—
175C5×#102—31no—
176C5×#102C2×D311yescharacteristic
177#3953—31no—
178#3953—31no—
179#3948—31no—
180#3948C2×D311yescharacteristic, complemented
181#3947—31no—
182#3947C2×D311yescharacteristic, complemented
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3940—31no—
186#3940—31no—
187#3939—31no—
188#3939C2×D311yescharacteristic, complemented
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C5×D3—24no—
194C22×C5×D3—81no—
195C22×C5×D3—81no—
196C22×C5×D3C2×D411yescharacteristic
197C3×C5×D4—21no—
198C3×C5×D4C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15—21no—
202C2×Dic15—81no—
203C2×Dic15C2×D411yescharacteristic
204C2×Dic15C2×D411yescharacteristic
205D60—21no—
206D60C22×C412yes—
207C4×D15—81no—
208C5×#67—24no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C2×D411yescharacteristic
211C5×D12—21no—
212C5×D12C22×C412yes—
213C4×C5×D3—81no—
214C4×C5×D3C22×C412yes—
215C4×C5×D3#4112yes—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—81no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×Dic10—21no—
222C3×Dic10C22×C412yes—
223#1203—24no—
224#1200—24no—
225#1200—81no—
226D3×Dic5—81no—
227D3×Dic5—81no—
228C3×C5×C8—21no—
229C3⋊#168C22×C412yes—
230C3×#168C22×C412yes—
231C5×C3⋊C8—21no—
232C2×#239—51no—
233C2×D3×D4C2×D511yescharacteristic
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)—51no—
246C2×D3×C8C2×D511yescharacteristic
247#893—51no—
248#893—51no—
249#893—101no—
250#892—51no—
251D3×C4⋊C4—101no—
252D3×C4⋊C4C2×D511yescharacteristic
253#67⋊C4—101no—
254D3×C22⋊C4—101no—
255C4×D12—51no—
256C4×D12—51no—
257C4×D12—101no—
258#872—51no—
259#872—101no—
260C3×#107—51no—
261C3×#103—51no—
262C3×#102C2×D511yescharacteristic
263C3×#97—51no—
264#835—51no—
265#832C2×D511yescharacteristic
266#821—51no—
267#821C2×D511yescharacteristic
268#817—51no—
269#815—51no—
270C8×Dic3—51no—
271#809—51no—
272#809C2×D511yescharacteristic
273#808—51no—
274#807—51no—
275C4×C3⋊C8—51no—
276C24×C5—61no—
277C2×C5×D4—34no—
278C2×C5×D4—31no—
279C2×C5×D4—62no—
280C2×C5×D4—61no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—31no—
283C22×C4×C5—61no—
284C2×C22⋊D5—61no—
285C22×Dic5—21no—
286C22×Dic5—61no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289#709—34no—
290#709—62no—
291C2×D20—31no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×Dic10C22×D311yescharacteristic
296C2×C5×C8—31no—
297C2×C5×C8—62no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4C22×D311yescharacteristic
302C22⋊Dic5—21no—
303C22⋊Dic5—31no—
304C22⋊Dic5—31no—
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307C22⋊Dic5—61no—
308C22⋊Dic5—61no—
309#687—34no—
310#687C4×D314yescomplemented
311#686—34no—
312#686—34no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—31no—
318C4⋊Dic5C22×D311yescharacteristic
319#683—21no—
320#683—61no—
321C4×Dic5—21no—
322C4×Dic5—31no—
323C4×Dic5—61no—
324C4×Dic5—61no—
325C4×Dic5C22×D311yescharacteristic
326#681—34no—
327C2×#168—31no—
328C2×#168C22×D311yescharacteristic
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—51no—
335#440—151no—
336C4×SD16—151no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—31no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—21no—
352C2×C5×D3—21no—
353C2×C5×D3—22no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C2×C5×D3—84no—
357C2×C5×D3C4×D412yes—
358C3×C4×C5—41no—
359C3×C4×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—21no—
362Dic15—21no—
363Dic15—41no—
364C3×Dic5—22no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C5×Dic3—41no—
369C5×Dic3C4×D412yes—
370C23×D3—21no—
371C2×C3×Q8—51no—
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—101no—
374C2×#67—21no—
375C22×Dic3—101no—
376#239—54no—
377#239—102no—
378D3×D4—22no—
379D3×D4C4×D514yescomplemented
380C2×D12—51no—
381C2×D12—101no—
382C2×D12C22×D511yescharacteristic
383C2×C4×D3—21no—
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×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—101no—
397C3×C42—51no—
398C3×C42—101no—
399#217—101no—
400#215—54no—
401#213—54no—
402(C2×D3)⋊C4—51no—
403(C2×D3)⋊C4—51no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—51no—
410C4⋊Dic3—101no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—51no—
414Dic3⋊C4—51no—
415C4×Dic3—51no—
416C4×Dic3—101no—
417C4×Dic3—101no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8C22×D511yescharacteristic
420D24—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—22no—
423C23×C5—21no—
424C23×C5—31no—
425C23×C5—64no—
426C23×C5—61no—
427C23×C5—241no—
428C23×C5—241no—
429C22×D5—61no—
430C5×D4—21no—
431C5×D4—32no—
432C5×D4—64no—
433C5×D4—61no—
434C5×D4C2×C4×D312yes—
435C2×C4×C5—21no—
436C2×C4×C5—31no—
437C2×C4×C5—32no—
438C2×C4×C5—32no—
439C2×C4×C5—61no—
440C2×C4×C5—241no—
441C2×C4×C5C23×D311yescharacteristic
442C22⋊D5—64no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—31no—
446C2×Dic5—31no—
447C2×Dic5—61no—
448C2×Dic5—81no—
449C2×Dic5—241no—
450C2×Dic5—241no—
451C2×Dic5—241no—
452C2×Dic5D3×D411yescharacteristic
453C2×Dic5D3×D411yescharacteristic
454D20—32no—
455D20—61no—
456C4×D5—64no—
457C4×D5—241no—
458C4×D5—241no—
459Dic10—21no—
460Dic10C2×C4×D312yes—
461C5×C8—21no—
462C5×C8—61no—
463#168—32no—
464#168C2×C4×D312yes—
465C2×#41—151no—
466C22×D4—31no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—51no—
469C2×SD16—151no—
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—151no—
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—151no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—51no—
494#107—151no—
495#106—151no—
496#106—151no—
497#103—51no—
498#103—151no—
499#102—31no—
500#102—31no—
501#102—31no—
502#102—151no—
503#102—151no—
504#102D3×D511yescharacteristic
505#97—51no—
506#97—151no—
507C4×C8—151no—
508C4×C8—151no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—42no—
514C5×D3—22no—
515C5×D3—42no—
516C23×C3—21no—
517C22×D3—21no—
518C22×D3—24no—
519C22×D3—81no—
520C22×D3—81no—
521C22×D3—101no—
522C22×D3D4×D511yescharacteristic
523C3×Q8—52no—
524C3×Q8—101no—
525C3×D4—21no—
526C3×D4C2×C4×D512yes—
527C2×C3×C4—21no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—401no—
533C2×C3×C4C23×D511yescharacteristic
534#67—24no—
535C2×Dic3—21no—
536C2×Dic3—51no—
537C2×Dic3—51no—
538C2×Dic3—101no—
539C2×Dic3—401no—
540C2×Dic3D4×D511yescharacteristic
541D12—21no—
542D12—52no—
543D12—104no—
544D12—101no—
545D12C2×C4×D512yes—
546C4×D3—81no—
547C4×D3—104no—
548C4×D3—401no—
549C4×D3—401no—
550C4×D3—401no—
551C4×D3—401no—
552C4×D3C2×C4×D512yes—
553C4×D3#71112yes—
554C3×C8—21no—
555C3×C8—52no—
556C3⋊C8—21no—
557C3⋊C8—52no—
558C22×C5—22no—
559C22×C5—32no—
560C22×C5—41no—
561C22×C5—41no—
562C22×C5—61no—
563C22×C5—61no—
564C22×C5—62no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5—244no—
568C22×C5C2×D3×D411yescharacteristic
569C2×D5—62no—
570C2×D5—121no—
571C2×D5—121no—
572C4×C5—32no—
573C4×C5—41no—
574C4×C5—121no—
575C4×C5C22×C4×D311yescharacteristic
576C4×C5D3×#4111yescharacteristic
577Dic5—21no—
578Dic5—21no—
579Dic5—22no—
580Dic5—41no—
581Dic5—61no—
582Dic5—61no—
583Dic5—121no—
584C24—61no—
585#41—154no—
586#41—302no—
587C2×Q8—51no—
588C2×D4—34no—
589C2×D4—31no—
590C2×D4—62no—
591C2×D4—61no—
592C2×D4—151no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—101no—
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—154no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—62no—
612C2×C8—151no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—51no—
616C4⋊C4—61no—
617C4⋊C4—101no—
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—151no—
621C4⋊C4—301no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—101no—
624C22⋊C4—151no—
625C22⋊C4—151no—
626C22⋊C4—301no—
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—51no—
633C42—101no—
634C42—151no—
635C42—301no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3C2×D4×D511yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—84no—
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3#402712yes—
652C3×C4—41no—
653C3×C4—102no—
654C3×C4—101no—
655C3×C4—101no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4C2×#71111yescharacteristic
659Dic3—41no—
660Dic3—101no—
661Dic3—101no—
662Dic3—201no—
663Dic3#402712yes—
664C2×C5—42no—
665C2×C5—62no—
666C2×C5—122no—
667C2×C5C4×D3×D411yescharacteristic
668C2×C5#577411yescharacteristic
669C2×C5#577811yescharacteristic
670D5—122no—
671C23—21no—
672C23—31no—
673C23—64no—
674C23—61no—
675C23—241no—
676C23—241no—
677C23—301no—
678Q8—52no—
679Q8—101no—
680D4—21no—
681D4—32no—
682D4—64no—
683D4—61no—
684D4—152no—
685D4—304no—
686D4—301no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—51no—
693C2×C4—51no—
694C2×C4—61no—
695C2×C4—101no—
696C2×C4—101no—
697C2×C4—151no—
698C2×C4—151no—
699C2×C4—241no—
700C2×C4—304no—
701C2×C4—301no—
702C2×C4—401no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—52no—
711C8—61no—
712C8—152no—
713C2×C3—42no—
714C2×C3C2×#402711yescharacteristic
715C2×C3#6609111yescharacteristic
716C2×C3#6609611yescharacteristic
717D3—22no—
718D3—42no—
719D3—202no—
720C5#7977511yescharacteristic, complemented, Sylow
721C22—22no—
722C22—32no—
723C22—41no—
724C22—41no—
725C22—61no—
726C22—61no—
727C22—62no—
728C22—121no—
729C22—121no—
730C22—244no—
731C22—302no—
732C22—601no—
733C22—601no—
734C22D3×D4×D511yescharacteristic
735C4—32no—
736C4—41no—
737C4—101no—
738C4—101no—
739C4—102no—
740C4—121no—
741C4—201no—
742C4—301no—
743C4—301no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D3×#71111yescharacteristic
747C3#1061045711yescharacteristic, complemented, Sylow
748C2—42no—
749C2—62no—
750C2—122no—
751C2—602no—
752C2D3×#402711yescharacteristic
753C2#1175405611yescharacteristic
754C2#1175408511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91496C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #11754914C2semidirect
3. #11753337C2semidirect
4. #11750886C2semidirect
5. C5×D3×#102C2semidirect
6. C3×#65046C2semidirect
7. #11749017C2semidirect
8. #11748975C2semidirect
9. #11747746C2semidirect
10. #11747738C2semidirect
11. #11747665C2semidirect
12. #11747643C2semidirect
13. #11747454C2semidirect
14. #11747233C2semidirect
15. #11747218C2semidirect
21. #91782C22semidirect
26. C3×#4033C22semidirect
31. #91496C4semidirect
35. #91418C22semidirect
41. #91331C22semidirect
46. #91105C22semidirect
47. #91099C22semidirect
48. #91092C22semidirect
52. C3×#3948C22semidirect
53. C3×#3947C22semidirect
54. C3×#3939C22semidirect
55. #90989C22semidirect
56. #90985C22semidirect
57. #90971C22semidirect
58. #90968C22semidirect
59. #90951C22semidirect
60. Dic5×C3⋊C8C22semidirect
74. #65046D3semidirect
84. C5×D3×D4C2×C4semidirect
96. #6769C2×C4semidirect
100. #6715C2×C4semidirect
110. C3×#687C2×C4semidirect
127. #6656C2×C4semidirect
128. #6654C2×C4semidirect
129. #6650C2×C4semidirect
142. D3×#102D5semidirect
172. #4033C2×D3semidirect
180. #3948C2×D3semidirect
182. #3947C2×D3semidirect
188. #3939C2×D3semidirect
310. #687C4×D3semidirect
379. D3×D4C4×D5semidirect
637. C3×C5#2946semidirect
720. C5#79775semidirect
747. C3#10610457semidirect

Maximal subgroups

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

subgroupindex
#117549142
C2×#914962
#117533372
#117508862
C5×D3×#1022
C3×#650462
#117490172
#117489752
#117477462
#117477382
#117476652
#117476432
#117474542
#117472332
#117472182
#106104573
#797755