Finite Group Databasebeta

← #14417451

Subgroups — #14417451

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5545C211yesmaximal, characteristic
2C2×D3×#687C211yesmaximal, characteristic
3#11752523C211yesmaximal, characteristic, complemented
4C4×#6716C211yesmaximal, characteristic, complemented
5C3×#65307C211yesmaximal, characteristic, complemented
6#11749011C211yesmaximal, characteristic, complemented
7#11749010C211yesmaximal, characteristic, complemented
8#11748967C211yesmaximal, characteristic
9#11747489C211yesmaximal, characteristic, complemented
10#11747473C211yesmaximal, characteristic, complemented
11#11747435C211yesmaximal, characteristic, complemented
12#11747264C211yesmaximal, characteristic, complemented
13#11747056C211yesmaximal, characteristic, complemented
14C4×#6656C211yesmaximal, characteristic, complemented
15#11746979C211yesmaximal, characteristic, complemented
16#10614274—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×D3×Dic10C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C4×Dic30C2211yescharacteristic, complemented
22C5×D4×Dic3C2211yescharacteristic
23C4×C5×#67—21no—
24C2×C5×(C2×D3)⋊C4—21no—
25C5×#893C2211yescharacteristic
26C5×#892C2211yescharacteristic
27C5×#67⋊C4—21no—
28C5×D3×C22⋊C4—21no—
29C4×C5×D12C2211yescharacteristic
30C5×#872C2211yescharacteristic
31C2×C3×#687C2211yescharacteristic
32C3×C4×Dic10C2211yescharacteristic, complemented
33D3×#687C418yescomplemented
34#91400—21no—
35#91398—21no—
36#91340C2211yescharacteristic, complemented
37#91338C2211yescharacteristic
38Dic3×Dic10C2211yescharacteristic, complemented
39#91325—21no—
40#91323—21no—
41C2×#6659C2211yescharacteristic
42C2×#6656C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×D3×#168C2211yescharacteristic
45#91116C2211yescharacteristic
46#91094C2211yescharacteristic, complemented
47#91092C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic
50C3×#3942C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52C3×#3935C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90975C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90967C2211yescharacteristic
58#90966C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79777—51nomaximal, Hall
62C5×#518—31no—
63C22×#687—31no—
64#65850—31no—
65#65504—31no—
66#65307—31no—
67#65307—31no—
68#65307—31no—
69#65307D311yescharacteristic, complemented
70C4×#687—31no—
71C4×#687—31no—
72C4×#687—31no—
73C4×#687—31no—
74#65293—31no—
75#65287—31no—
76#65286—31no—
77C23×C5×D3—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×Dic30C2311yescharacteristic
81C2×C5×#67—21no—
82C22×C5×Dic3—21no—
83C5×D3×D4—22no—
84C5×D3×D4C2×C414yes—
85C2×C5×D12C2311yescharacteristic
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3C2311yescharacteristic
89C2×C3×Dic10C2311yescharacteristic
90C2×#1204—21no—
91C2×D3×Dic5—21no—
92D3×Dic10—22no—
93D3×Dic10C2×C414yescomplemented
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C22⋊C4—21no—
96C3×C42×C5C2311yescharacteristic
97#6716C2×C414yescomplemented
98C4⋊Dic15C2311yescharacteristic
99#6712—21no—
100C4×Dic15—21no—
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#217—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4D411yescharacteristic
111C5×Dic3⋊C4D411yescharacteristic
112C4×C5×Dic3—21no—
113C4×C5×Dic3C2311yescharacteristic
114C3×#687C2×C414yescomplemented
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×C4×Dic5—21no—
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6669—21no—
121#6668—21no—
122(C2×D3)⋊Dic5—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126#6659C2×C414yescomplemented
127#6656C2×C414yescomplemented
128#6650—22no—
129D3×#168C2×C414yescomplemented
130C2×D3×SD16—51no—
131#5572—51no—
132#5545D511yescharacteristic
133C3×#440—51no—
134#5164—51no—
135C4×#215—51no—
136C4×#214—51no—
137#4889—51no—
138#4880—51no—
139#4802—51no—
140#4788—51no—
141#4770—51no—
142#4758—51no—
143#4710—51no—
144#4708—51no—
145C22×C5×D4—31no—
146C22×Dic10—31no—
147C4×C5×D4—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150C4×C5×D4—61no—
151C4×C5×D4—61no—
152C4×C5×D4C2×D311yescharacteristic
153C5×#117—31no—
154C5×#117—31no—
155C2×C5×C22⋊C4—61no—
156C2×C5×C22⋊C4—61no—
157C2×#687—31no—
158C2×#687—31no—
159C2×#687—38no—
160C2×#687—31no—
161C2×#687C2×D311yescharacteristic
162#4072—31no—
163C2×#681—31no—
164C22×#168—31no—
165#4033—61no—
166#4033—61no—
167#4023—61no—
168#4023—61no—
169C4×Dic10—31no—
170C4×Dic10—31no—
171C4×Dic10—31no—
172C4×Dic10C2×D311yescharacteristic, complemented
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964C2×D311yescharacteristic
177#3942—31no—
178#3942—31no—
179#3942—31no—
180#3942C2×D311yescharacteristic, complemented
181#3940—31no—
182#3940—31no—
183#3939—31no—
184#3939C2×D311yescharacteristic, complemented
185#3935—31no—
186#3935C2×D311yescharacteristic, complemented
187C4×#168—31no—
188C4×#168—31no—
189#2949—151noSylow
190C23×C3×C5—21no—
191C22×C5×D3—21no—
192C22×C5×D3—24no—
193C22×C5×D3—81no—
194C22×C5×D3—81no—
195C22×C5×D3C2×D411yescharacteristic
196C3×C5×D4—21no—
197C3×C5×D4C22×C412yes—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205Dic30—21no—
206Dic30C22×C412yes—
207C5×#67—24no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—81no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C5×D12—21no—
214C5×D12C22×C412yes—
215C4×C5×D3—81no—
216C4×C5×D3—81no—
217C4×C5×D3C22×C412yes—
218C4×C5×D3#4112yes—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C3×Dic10—21no—
222C3×Dic10C22×C412yes—
223#1204—24no—
224D3×Dic5—24no—
225C3⋊#168—21no—
226C3⋊#168C22×C412yes—
227C3×#168—21no—
228C3×#168C22×C412yes—
229C2×D3×Q8—51no—
230C2×D3×D4C2×D511yescharacteristic
231C2×C3×SD16—51no—
232C3×C4×Q8—51no—
233C3×C4×D4C2×D511yescharacteristic
234Q8×Dic3—51no—
235C2×#215—51no—
236D4×Dic3C2×D511yescharacteristic
237C2×#214—51no—
238C4×#67—21no—
239C2×(C2×D3)⋊C4—21no—
240D3×SD16—58no—
241C2×#204—51no—
242C2×ΓL(1,𝔽25)—51no—
243C2×D3×C8—51no—
244#893C2×D511yescharacteristic
245#892—51no—
246#892—101no—
247#892C2×D511yescharacteristic
248#887—51no—
249#887—101no—
250#67⋊C4—21no—
251D3×C22⋊C4—21no—
252C4×D12C2×D511yescharacteristic
253#872—101no—
254#872C2×D511yescharacteristic
255C4×Dic6—51no—
256C4×Dic6—101no—
257C3×#107—51no—
258C3×#103—51no—
259C3×#102—51no—
260C3×#97—51no—
261#835—51no—
262#832—51no—
263#821—51no—
264#818—51no—
265#816—51no—
266#815—51no—
267C8×Dic3—51no—
268#810—51no—
269#809—51no—
270#808—51no—
271#808—51no—
272C4×C3⋊C8—51no—
273C24×C5—61no—
274C2×C5×D4—34no—
275C2×C5×D4—31no—
276C2×C5×D4—62no—
277C2×C5×D4—61no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—21no—
280C22×C4×C5—31no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C22×C4×C5—61no—
284C22×Dic5—61no—
285C2×Dic10—31no—
286C2×Dic10—34no—
287C2×Dic10—62no—
288C2×Dic10—61no—
289C2×Dic10C22×D311yescharacteristic
290C5×C4⋊C4—31no—
291C5×C4⋊C4—31no—
292C5×C4⋊C4—31no—
293C5×C4⋊C4C22×D311yescharacteristic
294C5×C22⋊C4—21no—
295C5×C22⋊C4—31no—
296C5×C22⋊C4—31no—
297C5×C22⋊C4—61no—
298C5×C22⋊C4—61no—
299C5×C22⋊C4—61no—
300C5×C22⋊C4—61no—
301C42×C5—31no—
302C42×C5—61no—
303C42×C5C22×D311yescharacteristic
304C22⋊Dic5—61no—
305#687—34no—
306#687—34no—
307#687—34no—
308#687C4×D314yescomplemented
309C4⋊Dic5—31no—
310C4⋊Dic5C22×D311yescharacteristic
311#683—21no—
312#683—61no—
313#683—61no—
314#683—61no—
315C4×Dic5—21no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320#681—62no—
321C2×#168—31no—
322C2×#168—34no—
323C2×#168—31no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326C22×SD16—151no—
327#519—151no—
328#518—31no—
329#440—51no—
330#440—151no—
331#440—151no—
332#440—151no—
333C4×SD16—151no—
334C4×SD16—151no—
335C4×SD16—151no—
336C4×SD16—151no—
337#427—151no—
338#419—151no—
339#418—151no—
340#405—151no—
341C22×C3×C5—22no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—22no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—84no—
351C2×C5×D3C4×D412yes—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—41no—
355C3×C4×C5C23×C411yescharacteristic
356C3×C4×C5C2×#4111yescharacteristic
357Dic15—22no—
358Dic15—41no—
359C3×Dic5—22no—
360C3×Dic5—41no—
361C5×Dic3—21no—
362C5×Dic3—21no—
363C5×Dic3—41no—
364C5×Dic3C4×D412yes—
365C23×D3—21no—
366C2×C3×Q8—51no—
367C2×C3×D4C22×D511yescharacteristic
368C22×C3×C4—21no—
369C2×#67—21no—
370C22×Dic3—21no—
371D3×Q8—54no—
372D3×Q8—102no—
373D3×D4—22no—
374D3×D4C4×D514yes—
375C2×D12C22×D511yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—101no—
379C2×C4×D3C22×D511yescharacteristic
380C2×Dic6—51no—
381C2×Dic6—101no—
382C3×SD16—54no—
383C2×C3×C8—51no—
384C2×C3×C8—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4C22×D511yescharacteristic
388C3×C22⋊C4—21no—
389C3×C42—101no—
390C3×C42C22×D511yescharacteristic
391#217—21no—
392#215—54no—
393#214—54no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4C22⋊D511yescharacteristic
399(C2×D3)⋊C4C22⋊D511yescharacteristic
400C4⋊Dic3—51no—
401C4⋊Dic3—101no—
402C4⋊Dic3C22×D511yescharacteristic
403Dic3⋊C4—101no—
404Dic3⋊C4—101no—
405Dic3⋊C4C22⋊D511yescharacteristic
406Dic3⋊C4C22⋊D511yescharacteristic
407C4×Dic3—21no—
408C4×Dic3—101no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C4×Dic3—101no—
412C4×Dic3C22×D511yescharacteristic
413C2×C3⋊C8—51no—
414C2×C3⋊C8—51no—
415#204—54no—
416ΓL(1,𝔽25)—102no—
417D3×C8—54no—
418C23×C5—21no—
419C23×C5—31no—
420C23×C5—64no—
421C23×C5—61no—
422C23×C5—241no—
423C23×C5—241no—
424C5×D4—21no—
425C5×D4—32no—
426C5×D4—64no—
427C5×D4—61no—
428C5×D4C2×C4×D312yes—
429C2×C4×C5—21no—
430C2×C4×C5—31no—
431C2×C4×C5—32no—
432C2×C4×C5—32no—
433C2×C4×C5—31no—
434C2×C4×C5—31no—
435C2×C4×C5—61no—
436C2×C4×C5—81no—
437C2×C4×C5—241no—
438C2×C4×C5—241no—
439C2×C4×C5—241no—
440C2×C4×C5D3×D411yescharacteristic
441C2×C4×C5D3×D411yescharacteristic
442C2×C4×C5C23×D311yescharacteristic
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—64no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448Dic10—21no—
449Dic10—32no—
450Dic10—64no—
451Dic10—61no—
452Dic10C2×C4×D312yes—
453#168—21no—
454#168—32no—
455#168—61no—
456#168C2×C4×D312yes—
457C22×Q8—151no—
458C22×D4—31no—
459C2×SD16—51no—
460C2×SD16—151no—
461C2×SD16—158no—
462C2×SD16—151no—
463C2×SD16—151no—
464C2×M16—151no—
465C22×C8—151no—
466C4×Q8—51no—
467C4×Q8—151no—
468C4×Q8—151no—
469C4×Q8—151no—
470C4×Q8—301no—
471C4×Q8—301no—
472C4×D4—31no—
473C4×D4—31no—
474C4×D4—31no—
475C4×D4—61no—
476C4×D4—61no—
477C4×D4D3×D511yescharacteristic
478#117—31no—
479#117—31no—
480#117—151no—
481#117—301no—
482#117—301no—
483C2×C22⋊C4—61no—
484C2×C22⋊C4—61no—
485#107—51no—
486#107—151no—
487#106—151no—
488#106—151no—
489#103—51no—
490#103—151no—
491#103—151no—
492#103—151no—
493#102—51no—
494#102—151no—
495#102—151no—
496#102—151no—
497#97—51no—
498#97—151no—
499C4×C8—151no—
500C4×C8—151no—
501C2×C3×C5—42no—
502C2×C3×C5C2×C4×D411yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C5×D3—22no—
506C5×D3—42no—
507C23×C3—21no—
508C22×D3—21no—
509C22×D3—24no—
510C22×D3—81no—
511C22×D3—81no—
512C22×D3C2×C22⋊D511yescharacteristic
513C3×Q8—52no—
514C3×Q8—101no—
515C3×D4—21no—
516C3×D4C2×C4×D512yes—
517C2×C3×C4—21no—
518C2×C3×C4—81no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4C2×C22⋊D511yescharacteristic
522C2×C3×C4C2×C22⋊D511yescharacteristic
523C2×C3×C4C23×D511yescharacteristic
524#67—24no—
525C2×Dic3—21no—
526C2×Dic3—81no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3C2×C22⋊D511yescharacteristic
530C2×Dic3C2×C22⋊D511yescharacteristic
531C2×Dic3C2×C22⋊D511yescharacteristic
532D12—21no—
533D12C2×C4×D512yes—
534C4×D3—81no—
535C4×D3—81no—
536C4×D3—104no—
537C4×D3C2×C4×D512yes—
538C4×D3#70912yes—
539Dic6—52no—
540Dic6—101no—
541Dic6—104no—
542C3×C8—52no—
543C3×C8—101no—
544C3⋊C8—52no—
545C3⋊C8—101no—
546C22×C5—22no—
547C22×C5—32no—
548C22×C5—41no—
549C22×C5—41no—
550C22×C5—61no—
551C22×C5—61no—
552C22×C5—62no—
553C22×C5—121no—
554C22×C5—121no—
555C22×C5—244no—
556C22×C5C2×D3×D411yescharacteristic
557C4×C5—21no—
558C4×C5—21no—
559C4×C5—32no—
560C4×C5—41no—
561C4×C5—61no—
562C4×C5—61no—
563C4×C5—121no—
564C4×C5C22×C4×D311yescharacteristic
565C4×C5D3×#4111yescharacteristic
566Dic5—22no—
567Dic5—41no—
568Dic5—62no—
569Dic5—121no—
570C24—61no—
571C2×Q8—51no—
572C2×Q8—154no—
573C2×Q8—151no—
574C2×Q8—301no—
575C2×Q8—302no—
576C2×D4—34no—
577C2×D4—31no—
578C2×D4—62no—
579C2×D4—61no—
580C2×D4C2×D3×D511yescharacteristic
581C22×C4—21no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—301no—
587SD16—54no—
588SD16—154no—
589SD16—154no—
590SD16—154no—
591M16—302no—
592C2×C8—51no—
593C2×C8—51no—
594C2×C8—154no—
595C2×C8—151no—
596C2×C8—151no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—51no—
601C4⋊C4—101no—
602C4⋊C4—151no—
603C4⋊C4—301no—
604C4⋊C4—301no—
605C4⋊C4—301no—
606C4⋊C4C2×D3×D511yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—301no—
615C42—31no—
616C42—61no—
617C42—101no—
618C42—301no—
619C42—301no—
620C42—301no—
621C42—301no—
622C42C2×D3×D511yescharacteristic
623C3×C5#294911yescharacteristic, complemented, Hall
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3C22×C22⋊D511yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—84no—
634C2×D3C4×C22⋊D512yes—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—41no—
638C3×C4—102no—
639C3×C4—201no—
640C3×C4C22×C4×D511yescharacteristic
641C3×C4C2×#70911yescharacteristic
642Dic3—21no—
643Dic3—21no—
644Dic3—41no—
645Dic3—102no—
646Dic3—201no—
647Dic3C4×C22⋊D512yes—
648C2×C5—42no—
649C2×C5—62no—
650C2×C5—122no—
651C2×C5C4×D3×D411yescharacteristic
652C2×C5#577511yescharacteristic
653C2×C5#577811yescharacteristic
654C23—21no—
655C23—31no—
656C23—64no—
657C23—61no—
658C23—241no—
659C23—241no—
660Q8—52no—
661Q8—101no—
662Q8—152no—
663Q8—304no—
664Q8—301no—
665D4—21no—
666D4—32no—
667D4—64no—
668D4—61no—
669D4C4×D3×D512yes—
670C2×C4—21no—
671C2×C4—31no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—61no—
677C2×C4—81no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—241no—
681C2×C4—241no—
682C2×C4—241no—
683C2×C4—304no—
684C2×C4—301no—
685C2×C4—301no—
686C2×C4D3×C22⋊D511yescharacteristic
687C2×C4D3×C22⋊D511yescharacteristic
688C2×C4C22×D3×D511yescharacteristic
689C8—52no—
690C8—101no—
691C8—152no—
692C8—301no—
693C2×C3—42no—
694C2×C3C2×C4×C22⋊D511yescharacteristic
695C2×C3#6617011yescharacteristic
696C2×C3#6617011yescharacteristic
697D3—22no—
698D3—42no—
699C5#7977711yescharacteristic, complemented, Sylow
700C22—22no—
701C22—32no—
702C22—41no—
703C22—41no—
704C22—61no—
705C22—61no—
706C22—62no—
707C22—121no—
708C22—121no—
709C22—244no—
710C22C2×D3×C22⋊D511yescharacteristic
711C4—21no—
712C4—21no—
713C4—32no—
714C4—41no—
715C4—61no—
716C4—61no—
717C4—102no—
718C4—121no—
719C4—201no—
720C4—302no—
721C4—601no—
722C4C2×C4×D3×D511yescharacteristic
723C4D3×#70911yescharacteristic
724C3#1061427411yescharacteristic, complemented, Sylow
725C2—42no—
726C2—62no—
727C2—122no—
728C2C4×D3×C22⋊D511yescharacteristic
729C2#1175472011yescharacteristic
730C2#1175534011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D3×D4C22
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2949
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11752523C2semidirect
4. C4×#6716C2semidirect
5. C3×#65307C2semidirect
6. #11749011C2semidirect
7. #11749010C2semidirect
9. #11747489C2semidirect
10. #11747473C2semidirect
11. #11747435C2semidirect
12. #11747264C2semidirect
13. #11747056C2semidirect
14. C4×#6656C2semidirect
15. #11746979C2semidirect
21. C4×Dic30C22semidirect
32. C3×C4×Dic10C22semidirect
33. D3×#687C4semidirect
36. #91340C22semidirect
38. Dic3×Dic10C22semidirect
46. #91094C22semidirect
47. #91092C22semidirect
48. C4×C3⋊#168C22semidirect
50. C3×#3942C22semidirect
51. C3×#3939C22semidirect
52. C3×#3935C22semidirect
53. #90988C22semidirect
54. #90986C22semidirect
55. #90975C22semidirect
56. #90970C22semidirect
59. #90953C22semidirect
60. Dic3×#168C22semidirect
69. #65307D3semidirect
93. D3×Dic10C2×C4semidirect
97. #6716C2×C4semidirect
114. C3×#687C2×C4semidirect
126. #6659C2×C4semidirect
127. #6656C2×C4semidirect
129. D3×#168C2×C4semidirect
172. C4×Dic10C2×D3semidirect
180. #3942C2×D3semidirect
184. #3939C2×D3semidirect
186. #3935C2×D3semidirect
308. #687C4×D3semidirect
623. C3×C5#2949semidirect
699. C5#79777semidirect
724. C3#10614274semidirect

Maximal subgroups

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

subgroupindex
C5×#55452
C2×D3×#6872
#117525232
C4×#67162
C3×#653072
#117490112
#117490102
#117489672
#117474892
#117474732
#117474352
#117472642
#117470562
C4×#66562
#117469792
#106142743
#797775