Finite Group Databasebeta

← #14427613

Subgroups — #14427613

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91255C211yesmaximal, characteristic, complemented
2C2×D3×C8×D5C211yesmaximal, characteristic, complemented
3#11753884C211yesmaximal, characteristic, complemented
4#11753850C211yesmaximal, characteristic
5D15×#106C211yesmaximal, characteristic, complemented
6C5×#4864C211yesmaximal, characteristic, complemented
7C3×#65153C211yesmaximal, characteristic, complemented
8#11747912C211yesmaximal, characteristic, complemented
9#11747896C211yesmaximal, characteristic, complemented
10#11747490C211yesmaximal, characteristic, complemented
11#11747478C211yesmaximal, characteristic, complemented
12#11747352C211yesmaximal, characteristic, complemented
13#11747339C211yesmaximal, characteristic, complemented
14#11747321C211yesmaximal, characteristic, complemented
15#11747309C211yesmaximal, characteristic, complemented
16D5×#465—31nomaximal, Hall
17C2×#6777—21no—
18C2×#6777C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×D15⋊Q8C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22C4⋊C4×D15C2211yescharacteristic
23C4⋊C4×D15C2211yescharacteristic
24C2×C5×#204C2211yescharacteristic, complemented
25C2×C5×D3×C8C2211yescharacteristic, complemented
26C5×#897C2211yescharacteristic, complemented
27C5×#895C2211yescharacteristic
28C2×C3×#677C2211yescharacteristic, complemented
29C2×C3×C8×D5C2211yescharacteristic, complemented
30C3×#4043C2211yescharacteristic, complemented
31C3×#4041C2211yescharacteristic
32#91473—21no—
33#91473—21no—
34#91456C2211yescharacteristic
35#91453—21no—
36#91449C2211yescharacteristic
37#91437—21no—
38#91436—21no—
39#91430—21no—
40#91408—21no—
41#91369C2211yescharacteristic, complemented
42#91359C2211yescharacteristic, complemented
43C2×#6656C2211yescharacteristic, complemented
44C2×#6655C2211yescharacteristic, complemented
45C2×#6648C2211yescharacteristic
46C2×D3×#168C2211yescharacteristic, complemented
47C2×D5×C3⋊C8C2211yescharacteristic, complemented
48#91255—24no—
49D3×C8×D5—24no—
50C3×C5×#106C2211yescharacteristic, complemented
51#91101C2211yescharacteristic, complemented
52#91092C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54C5×#810C2211yescharacteristic, complemented
55C5×#809C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90967C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62D3×#465—51nomaximal, Hall
63C2×D5×SD16—31no—
64C22×C8×D5—31no—
65D5×C22⋊Q8—31no—
66D5×#121—31no—
67C5×#465—31no—
68#65460—31no—
69#65403—31no—
70#65337—31no—
71#65330—31no—
72#65153D311yescharacteristic, complemented
73D5×#106—31no—
74#65096—31no—
75D5×#103—31no—
76#65067—31no—
77D5×#102—31no—
78C22×D3×D5—21no—
79C22×D3×D5D411yescharacteristic
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C4×D15C2311yescharacteristic
83C2×C5×D12—21no—
84C2×C5×D12C2311yescharacteristic
85C2×C4×C5×D3C2311yescharacteristic
86C2×C5×Dic6C2311yescharacteristic
87C2×C3×D20—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×Dic10C2311yescharacteristic
91C2×#1204—21no—
92C2×#1201—21no—
93C2×#1201—21no—
94C2×#1201—21no—
95C2×#1200—21no—
96C2×#1200D411yescharacteristic
97C2×D3×Dic5D411yescharacteristic
98C2×D5×Dic3D411yescharacteristic
99#6777—22no—
100#6777—22no—
101#6777—44no—
102C4×D3×D5—22no—
103C4×D3×D5—22no—
104D15⋊Q8—22no—
105D15⋊Q8—22no—
106C2×C3×C5×C8C2311yescharacteristic
107C3×C5×C4⋊C4C2311yescharacteristic
108C3×C5×C4⋊C4C2311yescharacteristic
109C4⋊Dic15C2311yescharacteristic
110C4⋊Dic15C2311yescharacteristic
111#6712—21no—
112#6712—21no—
113C2×C3⋊#168C2311yescharacteristic
114C8×D15D414yescomplemented
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×C4⋊Dic3—21no—
118C2×C5×C3⋊C8C2311yescharacteristic
119C5×#204—22no—
120C5×D3×C8—22no—
121C3×#685—21no—
122C3×#685—21no—
123C3×C4⋊Dic5—21no—
124C2×C3×#168C2311yescharacteristic
125C3×#677—22no—
126C3×C8×D5—22no—
127#6669—21no—
128#6669—21no—
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131#6665—21no—
132#6665—21no—
133#6656—22no—
134#6655—22no—
135#6648—22no—
136D3×#168—22no—
137D5×C3⋊C8—22no—
138C2×D3×SD16—51no—
139C22×D3×C8—51no—
140D3×C22⋊Q8—51no—
141D3×#121—51no—
142C3×#465—51no—
143#5171—51no—
144#5114—51no—
145#5048—51no—
146#5041—51no—
147#4864D511yescharacteristic, complemented
148D3×#106—51no—
149#4807—51no—
150D3×#103—51no—
151#4778—51no—
152D3×#102—51no—
153C2×Q8×D5—31no—
154C2×D4×D5—31no—
155C2×D4×D5—61no—
156C22×C4×D5—31no—
157C2×C5×SD16—31no—
158C22×C5×C8—31no—
159C5×C22⋊Q8—31no—
160C5×#121—31no—
161#4092—31no—
162C2×#688—31no—
163#4085—61no—
164#4084—31no—
165C2×#687—31no—
166#4076—31no—
167#4070—31no—
168C22×#168—31no—
169D5×SD16—64no—
170C2×#677C2×D311yescharacteristic, complemented
171C2×C8×D5—31no—
172C2×C8×D5—31no—
173C2×C8×D5—31no—
174C2×C8×D5—64no—
175C2×C8×D5C2×D311yescharacteristic, complemented
176#4043C2×D311yescharacteristic, complemented
177#4042—61no—
178#4041C2×D311yescharacteristic
179D5×C4⋊C4—31no—
180D5×C4⋊C4—31no—
181D5×C4⋊C4—61no—
182#4030—61no—
183D5×C22⋊C4—61no—
184D5×C22⋊C4—61no—
185#4024—61no—
186C5×#106C2×D311yescharacteristic, complemented
187C5×#103—31no—
188C5×#102—31no—
189#3967—31no—
190#3964—31no—
191#3953—31no—
192#3949—31no—
193#3948—31no—
194#3942C2×D311yescharacteristic, complemented
195#3941C2×D311yescharacteristic, complemented
196#3940—31no—
197#3940—31no—
198C2×#465—151noSylow
199C22×D15C2×D411yescharacteristic
200C22×C5×D3—21no—
201C22×C5×D3C2×D411yescharacteristic
202C22×C3×D5—21no—
203C22×C3×D5C2×D411yescharacteristic
204C2×D3×D5—22no—
205C2×D3×D5—22no—
206C2×D3×D5—42no—
207C2×D3×D5—42no—
208C2×D3×D5—42no—
209C2×D3×D5SD1614yescomplemented
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5C2411yescharacteristic
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15C2×D411yescharacteristic
216C4×D15—42no—
217C4×D15—42no—
218C4×D15C2×D412yes—
219C4×D15#4112yes—
220C2×C5×Dic3—21no—
221C2×C5×Dic3C2×D411yescharacteristic
222C5×D12—21no—
223C5×D12—21no—
224C5×D12—42no—
225C4×C5×D3—21no—
226C4×C5×D3—21no—
227C5×Dic6—21no—
228C5×Dic6—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5C2×D411yescharacteristic
231C3×D20—21no—
232C3×D20—21no—
233C3×D20—42no—
234C3×C4×D5—21no—
235C3×C4×D5—21no—
236C3×Dic10—21no—
237C3×Dic10—21no—
238#1204—42no—
239#1201—42no—
240#1201—42no—
241#1201—42no—
242#1200—22no—
243#1200—42no—
244D3×Dic5—22no—
245D5×Dic3—22no—
246C3×C5×C8C2×D412yescomplemented
247C3⋊#168C2×D412yescomplemented
248C3×#168—21no—
249C5×C3⋊C8—21no—
250C2×D3×Q8—51no—
251C2×D3×D4—51no—
252C2×D3×D4—101no—
253C22×C4×D3—51no—
254C2×C3×SD16—51no—
255C22×C3×C8—51no—
256C3×C22⋊Q8—51no—
257C3×#121—51no—
258#946—51no—
259C2×#215—51no—
260#939—101no—
261#938—51no—
262C2×#214—51no—
263#930—51no—
264#924—51no—
265C22×C3⋊C8—51no—
266D3×SD16—104no—
267C2×#204C2×D511yescharacteristic, complemented
268C2×D3×C8—51no—
269C2×D3×C8—51no—
270C2×D3×C8—51no—
271C2×D3×C8—104no—
272C2×D3×C8C2×D511yescharacteristic, complemented
273#897C2×D511yescharacteristic, complemented
274#896—101no—
275#895C2×D511yescharacteristic
276D3×C4⋊C4—51no—
277D3×C4⋊C4—51no—
278D3×C4⋊C4—101no—
279#884—101no—
280D3×C22⋊C4—101no—
281D3×C22⋊C4—101no—
282#878—101no—
283C3×#106C2×D511yescharacteristic, complemented
284C3×#103—51no—
285C3×#102—51no—
286#835—51no—
287#832—51no—
288#821—51no—
289#817—51no—
290#816—51no—
291#810C2×D511yescharacteristic, complemented
292#809C2×D511yescharacteristic, complemented
293#808—51no—
294#808—51no—
295C23×D5—31no—
296C23×D5—61no—
297C2×C5×Q8—31no—
298C2×C5×D4—31no—
299C2×C5×D4—61no—
300C22×C4×C5—31no—
301C2×C22⋊D5—61no—
302C2×C22⋊D5—61no—
303C2×C22⋊D5—61no—
304C22×Dic5—31no—
305Q8×D5—62no—
306Q8×D5—62no—
307D4×D5—62no—
308D4×D5—62no—
309D4×D5—124no—
310C2×D20—21no—
311C2×D20C22×D311yescharacteristic
312C2×C4×D5—31no—
313C2×C4×D5—31no—
314C2×C4×D5—31no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—61no—
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×C4×D5C22×D311yescharacteristic
321C2×Dic10—61no—
322C2×Dic10C22×D311yescharacteristic
323C5×SD16—62no—
324C2×C5×C8—31no—
325C2×C5×C8—62no—
326C2×C5×C8C22×D311yescharacteristic
327C5×C4⋊C4—61no—
328C5×C4⋊C4C22×D311yescharacteristic
329C5×C4⋊C4C22×D311yescharacteristic
330C5×C22⋊C4—61no—
331C5×C22⋊C4—61no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#688—62no—
335#687—62no—
336#685—21no—
337#685—21no—
338#685—61no—
339#685—61no—
340C4⋊Dic5—21no—
341C4⋊Dic5—31no—
342C4⋊Dic5—31no—
343#683—61no—
344#683—61no—
345#683—61no—
346#683—61no—
347C2×#168—31no—
348C2×#168—62no—
349C2×#168C22×D311yescharacteristic
350#677—22no—
351C8×D5—22no—
352C8×D5—34no—
353C8×D5—62no—
354C8×D5—62no—
355C22×SD16—151no—
356C23×C8—151no—
357C2×C22⋊Q8—151no—
358C2×#121—151no—
359#465—31no—
360#465—51no—
361#465—151no—
362#465—151no—
363#465—151no—
364#465—151no—
365#465—151no—
366#465—151no—
367C2×#106—151no—
368C2×#103—151no—
369C2×#102—151no—
370C22×C3×C5C22×D411yescharacteristic
371C2×D15#12112yes—
372C2×D15C2×SD1612yes—
373C2×D15#13512yes—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3—41no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3C2×SD1612yescomplemented
380C2×C3×D5—21no—
381C2×C3×D5—21no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5C2×SD1612yescomplemented
386D3×D5—28no—
387D3×D5—84no—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390C3×C4×C5C22×D411yescharacteristic
391C3×C4×C5C2×#4111yescharacteristic
392Dic15—41no—
393Dic15—41no—
394Dic15#12112yes—
395C3×Dic5—21no—
396C3×Dic5—41no—
397C5×Dic3—21no—
398C5×Dic3—41no—
399C23×D3—51no—
400C23×D3—101no—
401C2×C3×Q8—51no—
402C2×C3×D4—51no—
403C2×C3×D4—101no—
404C22×C3×C4—51no—
405C2×#67—101no—
406C2×#67—101no—
407C2×#67—101no—
408C22×Dic3—51no—
409D3×Q8—102no—
410D3×Q8—102no—
411D3×D4—102no—
412D3×D4—102no—
413D3×D4—204no—
414C2×D12—21no—
415C2×D12C22×D511yescharacteristic
416C2×C4×D3—51no—
417C2×C4×D3—51no—
418C2×C4×D3—51no—
419C2×C4×D3—102no—
420C2×C4×D3—102no—
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×C4×D3—101no—
424C2×C4×D3C22×D511yescharacteristic
425C2×Dic6—101no—
426C2×Dic6C22×D511yescharacteristic
427C3×SD16—102no—
428C2×C3×C8—51no—
429C2×C3×C8—102no—
430C2×C3×C8C22×D511yescharacteristic
431C3×C4⋊C4—101no—
432C3×C4⋊C4C22×D511yescharacteristic
433C3×C4⋊C4C22×D511yescharacteristic
434C3×C22⋊C4—101no—
435C3×C22⋊C4—101no—
436#217—101no—
437#217—101no—
438#215—102no—
439#214—102no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444C4⋊Dic3—21no—
445C4⋊Dic3—51no—
446C4⋊Dic3—51no—
447Dic3⋊C4—101no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451C2×C3⋊C8—51no—
452C2×C3⋊C8—102no—
453C2×C3⋊C8C22×D511yescharacteristic
454#204—22no—
455D3×C8—22no—
456D3×C8—54no—
457D3×C8—102no—
458D3×C8—102no—
459C23×C5—31no—
460C23×C5—61no—
461C22×D5—21no—
462C22×D5—31no—
463C22×D5—34no—
464C22×D5—62no—
465C22×D5—62no—
466C22×D5—122no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5D3×D411yescharacteristic
470C5×Q8—61no—
471C5×Q8—61no—
472C5×D4—61no—
473C5×D4—61no—
474C5×D4—122no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—31no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5C23×D311yescharacteristic
482C22⋊D5—122no—
483C22⋊D5—122no—
484C22⋊D5—122no—
485C2×Dic5—21no—
486C2×Dic5—31no—
487C2×Dic5—62no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5D3×D411yescharacteristic
491D20—21no—
492D20—21no—
493D20—42no—
494C4×D5—21no—
495C4×D5—21no—
496C4×D5—32no—
497C4×D5—32no—
498C4×D5—62no—
499C4×D5—62no—
500C4×D5—122no—
501C4×D5—122no—
502C4×D5—122no—
503Dic10—21no—
504Dic10—21no—
505Dic10—122no—
506C5×C8—61no—
507C5×C8D3×D412yescomplemented
508#168—21no—
509#168—32no—
510C22×Q8—151no—
511C22×D4—151no—
512C22×D4—301no—
513C23×C4—151no—
514C2×SD16—31no—
515C2×SD16—51no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—304no—
519C22×C8—31no—
520C22×C8—51no—
521C22×C8—151no—
522C22×C8—151no—
523C22×C8—151no—
524C22×C8—151no—
525C22×C8—304no—
526C22⋊Q8—31no—
527C22⋊Q8—51no—
528C22⋊Q8—151no—
529C22⋊Q8—151no—
530C22⋊Q8—301no—
531C22⋊Q8—301no—
532#121—31no—
533#121—51no—
534#121—151no—
535#121—151no—
536#121—301no—
537#121—301no—
538C2×C4⋊C4—151no—
539C2×C4⋊C4—151no—
540C2×C4⋊C4—301no—
541C2×C22⋊C4—301no—
542C2×C22⋊C4—301no—
543#106—151no—
544#106—151no—
545#106—151no—
546#106D3×D511yescharacteristic, complemented
547#103—31no—
548#103—51no—
549#103—151no—
550#103—151no—
551#102—31no—
552#102—51no—
553#102—151no—
554#102—151no—
555C2×C3×C5C2×#12111yescharacteristic
556C2×C3×C5C22×SD1611yescharacteristic
557C2×C3×C5C2×#13511yescharacteristic
558D15#46514yescomplemented
559C3×D5—22no—
560C3×D5—81no—
561C5×D3—22no—
562C5×D3—81no—
563C23×C3—51no—
564C23×C3—101no—
565C22×D3—21no—
566C22×D3—51no—
567C22×D3—54no—
568C22×D3—102no—
569C22×D3—102no—
570C22×D3—202no—
571C22×D3—202no—
572C22×D3—202no—
573C22×D3D4×D511yescharacteristic
574C3×Q8—101no—
575C3×Q8—101no—
576C3×D4—101no—
577C3×D4—101no—
578C3×D4—202no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—51no—
582C2×C3×C4—101no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4C23×D511yescharacteristic
586#67—202no—
587#67—202no—
588#67—202no—
589C2×Dic3—21no—
590C2×Dic3—51no—
591C2×Dic3—102no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3D4×D511yescharacteristic
595D12—21no—
596D12—21no—
597D12—42no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—52no—
601C4×D3—52no—
602C4×D3—102no—
603C4×D3—102no—
604C4×D3—202no—
605C4×D3—202no—
606C4×D3—202no—
607Dic6—21no—
608Dic6—21no—
609Dic6—202no—
610C3×C8—101no—
611C3×C8D4×D512yescomplemented
612C3⋊C8—21no—
613C3⋊C8—52no—
614C22×C5—32no—
615C22×C5—61no—
616C22×C5—61no—
617C22×C5—121no—
618C22×C5—121no—
619C22×C5—121no—
620C22×C5C2×D3×D411yescharacteristic
621C2×D5—21no—
622C2×D5—21no—
623C2×D5—32no—
624C2×D5—32no—
625C2×D5—32no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—68no—
630C2×D5—244no—
631C2×D5D3×SD1612yescomplemented
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—61no—
635C4×C5—121no—
636C4×C5C2×D3×D411yescharacteristic
637C4×C5D3×#4111yescharacteristic
638Dic5—21no—
639Dic5—32no—
640Dic5—41no—
641Dic5—121no—
642Dic5—121no—
643C24—151no—
644C24—301no—
645C2×Q8—31no—
646C2×Q8—51no—
647C2×Q8—301no—
648C2×Q8—302no—
649C2×Q8—302no—
650C2×D4—31no—
651C2×D4—51no—
652C2×D4—61no—
653C2×D4—101no—
654C2×D4—302no—
655C2×D4—302no—
656C2×D4—301no—
657C2×D4—301no—
658C2×D4—301no—
659C2×D4—604no—
660C22×C4—31no—
661C22×C4—51no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—301no—
667C22×C4—301no—
668C22×C4—302no—
669C22×C4—302no—
670C22×C4—301no—
671SD16—62no—
672SD16—102no—
673SD16—302no—
674SD16—302no—
675C2×C8—31no—
676C2×C8—51no—
677C2×C8—62no—
678C2×C8—102no—
679C2×C8—151no—
680C2×C8—154no—
681C2×C8—302no—
682C2×C8—302no—
683C2×C8—302no—
684C2×C8C2×D3×D511yescharacteristic
685C4⋊C4—61no—
686C4⋊C4—101no—
687C4⋊C4—151no—
688C4⋊C4—151no—
689C4⋊C4—301no—
690C4⋊C4—301no—
691C4⋊C4—301no—
692C4⋊C4—301no—
693C4⋊C4C2×D3×D511yescharacteristic
694C4⋊C4C2×D3×D511yescharacteristic
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—301no—
700C22⋊C4—301no—
701C22⋊C4—301no—
702C22⋊C4—301no—
703C3×C5C2×#46511yescharacteristic, complemented, Hall
704C22×C3—52no—
705C22×C3—101no—
706C22×C3—101no—
707C22×C3—201no—
708C22×C3—201no—
709C22×C3—201no—
710C22×C3C2×D4×D511yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—52no—
717C2×D3—52no—
718C2×D3—52no—
719C2×D3—108no—
720C2×D3—404no—
721C2×D3D5×SD1612yescomplemented
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—101no—
725C3×C4—201no—
726C3×C4C2×D4×D511yescharacteristic
727C3×C4D5×#4111yescharacteristic
728Dic3—21no—
729Dic3—41no—
730Dic3—52no—
731Dic3—201no—
732Dic3—201no—
733C2×C5—62no—
734C2×C5—241no—
735C2×C5D3×#12111yescharacteristic
736C2×C5C2×D3×SD1611yescharacteristic
737C2×C5D3×#13511yescharacteristic
738D5—22no—
739D5—34no—
740D5—81no—
741C23—31no—
742C23—51no—
743C23—61no—
744C23—101no—
745C23—154no—
746C23—151no—
747C23—302no—
748C23—302no—
749C23—602no—
750C23—602no—
751C23—602no—
752Q8—61no—
753Q8—61no—
754Q8—101no—
755Q8—101no—
756Q8—602no—
757D4—61no—
758D4—61no—
759D4—101no—
760D4—101no—
761D4—122no—
762D4—202no—
763D4—602no—
764D4—602no—
765D4—602no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—51no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—151no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—301no—
783C2×C4—301no—
784C2×C4—602no—
785C2×C4—602no—
786C2×C4—602no—
787C2×C4C22×D3×D511yescharacteristic
788C8—61no—
789C8—101no—
790C8—152no—
791C8#677712yescomplemented
792C2×C3—102no—
793C2×C3—401no—
794C2×C3D5×#12111yescharacteristic
795C2×C3C2×D5×SD1611yescharacteristic
796C2×C3D5×#13511yescharacteristic
797D3—22no—
798D3—54no—
799D3—81no—
800C5D3×#46511yescharacteristic, complemented, Sylow
801C22—32no—
802C22—52no—
803C22—61no—
804C22—61no—
805C22—101no—
806C22—101no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—152no—
811C22—152no—
812C22—152no—
813C22—201no—
814C22—201no—
815C22—201no—
816C22—308no—
817C22—1204no—
818C22D3×D4×D511yescharacteristic
819C4—41no—
820C4—41no—
821C4—61no—
822C4—101no—
823C4—121no—
824C4—152no—
825C4—201no—
826C4—601no—
827C4—601no—
828C4C2×#677711yescharacteristic
829C4#9203411yescharacteristic
830C3D5×#46511yescharacteristic, complemented, Sylow
831C2—62no—
832C2—102no—
833C2—154no—
834C2—241no—
835C2—401no—
836C2#1175385011yescharacteristic
837C2D3×D5×SD1611yescharacteristic
838C2#1175407911yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radical#11753850C2
hypercenter#106D3×D5
hypocenterC3×C5C2×#465
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#91255C2semidirect
2. C2×D3×C8×D5C2semidirect
3. #11753884C2semidirect
5. D15×#106C2semidirect
6. C5×#4864C2semidirect
7. C3×#65153C2semidirect
8. #11747912C2semidirect
9. #11747896C2semidirect
10. #11747490C2semidirect
11. #11747478C2semidirect
12. #11747352C2semidirect
13. #11747339C2semidirect
14. #11747321C2semidirect
15. #11747309C2semidirect
24. C2×C5×#204C22semidirect
25. C2×C5×D3×C8C22semidirect
26. C5×#897C22semidirect
28. C2×C3×#677C22semidirect
29. C2×C3×C8×D5C22semidirect
30. C3×#4043C22semidirect
41. #91369C22semidirect
42. #91359C22semidirect
43. C2×#6656C22semidirect
44. C2×#6655C22semidirect
46. C2×D3×#168C22semidirect
47. C2×D5×C3⋊C8C22semidirect
50. C3×C5×#106C22semidirect
51. #91101C22semidirect
52. #91092C22semidirect
53. #91092C22semidirect
54. C5×#810C22semidirect
55. C5×#809C22semidirect
56. C3×#3942C22semidirect
57. C3×#3941C22semidirect
58. #90973C22semidirect
59. #90971C22semidirect
60. #90967C22semidirect
61. #90965C22semidirect
72. #65153D3semidirect
114. C8×D15D4semidirect
147. #4864D5semidirect
170. C2×#677C2×D3semidirect
175. C2×C8×D5C2×D3semidirect
176. #4043C2×D3semidirect
186. C5×#106C2×D3semidirect
194. #3942C2×D3semidirect
195. #3941C2×D3semidirect
209. C2×D3×D5SD16semidirect
246. C3×C5×C8C2×D4semidirect
247. C3⋊#168C2×D4semidirect
267. C2×#204C2×D5semidirect
272. C2×D3×C8C2×D5semidirect
273. #897C2×D5semidirect
283. C3×#106C2×D5semidirect
291. #810C2×D5semidirect
292. #809C2×D5semidirect
379. C2×C5×D3C2×SD16semidirect
385. C2×C3×D5C2×SD16semidirect
507. C5×C8D3×D4semidirect
546. #106D3×D5semidirect
558. D15#465semidirect
611. C3×C8D4×D5semidirect
631. C2×D5D3×SD16semidirect
703. C3×C5C2×#465semidirect
721. C2×D3D5×SD16semidirect
791. C8#6777semidirect
800. C5D3×#465semidirect
830. C3D5×#465semidirect

Maximal subgroups

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

subgroupindex
C2×#912552
C2×D3×C8×D52
#117538842
#117538502
D15×#1062
C5×#48642
C3×#651532
#117479122
#117478962
#117474902
#117474782
#117473522
#117473392
#117473212
#117473092
D5×#4653
D3×#4655