Finite Group Databasebeta

← #14458637

Subgroups — #14458637

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5639C211yesmaximal, characteristic, complemented
2#11754638C211yesmaximal, characteristic
3#11751149C211yesmaximal, characteristic, complemented
4C3×#65336C211yesmaximal, characteristic, complemented
5#11749398C211yesmaximal, characteristic, complemented
6#11749326C211yesmaximal, characteristic, complemented
7#11749296C211yesmaximal, characteristic, complemented
8Dic3×#688C211yesmaximal, characteristic, complemented
9#67⋊#168C211yesmaximal, characteristic, complemented
10#11748373C211yesmaximal, characteristic, complemented
11#11748364C211yesmaximal, characteristic, complemented
12D3×#3941C211yesmaximal, characteristic, complemented
13#11747379C211yesmaximal, characteristic, complemented
14#11747348C211yesmaximal, characteristic, complemented
15#11747251C211yesmaximal, characteristic, complemented
16#10615329—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic, complemented
20C2×#6717C2211yescharacteristic
21#91819C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic, complemented
23C5×#946C2211yescharacteristic
24C5×Q8×Dic3C2211yescharacteristic, complemented
25C4×C5×#67C2211yescharacteristic
26C5×#926C2211yescharacteristic, complemented
27C5×#892—21no—
28C5×D3×C4⋊C4C2211yescharacteristic
29C5×#890C2211yescharacteristic, complemented
30C5×#889—21no—
31C5×#883—21no—
32C5×#879—21no—
33C2×C3×#689C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic
35#91577—21no—
36#91550—21no—
37D5×(C2×D3)⋊C4—21no—
38Dic3×D20C2211yescharacteristic
39#91374C2211yescharacteristic
40#91369C2211yescharacteristic
41#91348—21no—
42C2×D3×#168C2211yescharacteristic
43#91119C2211yescharacteristic, complemented
44#91093C2211yescharacteristic
45#91092C2211yescharacteristic, complemented
46C3×C22⋊#168C2211yescharacteristic, complemented
47C3×#3942C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic
49#90988C2211yescharacteristic, complemented
50#90985C2211yescharacteristic, complemented
51Dic3⋊#168C2211yescharacteristic, complemented
52#90970C2211yescharacteristic, complemented
53#90970C2211yescharacteristic, complemented
54#90969C2211yescharacteristic
55#90969C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic, complemented
60#80246—51nomaximal, Hall
61C5×#552—31no—
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65340—31no—
66#65337—31no—
67#65336D311yescharacteristic, complemented
68#65335—31no—
69#65317—31no—
70C4×#688—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65260—31no—
75C2×#3941—31no—
76C22×D3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80C2×D60C2311yescharacteristic
81C2×C5×#67D411yescharacteristic
82C2×C4×C5×D3—21no—
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×C22⋊D5—21no—
85C3×#709—22no—
86C3×#709—41no—
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×Dic10C2311yescharacteristic
90C2×#1202—21no—
91C2×D5×Dic3—21no—
92D3×D20—22no—
93D3×D20—41no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97#6717—41no—
98#6714—21no—
99C4⋊Dic15C2311yescharacteristic
100C2×C3⋊#168—41no—
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#217—21no—
104C5×#217D411yescharacteristic
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4D411yescharacteristic
107C5×C4⋊Dic3—21no—
108C5×C4⋊Dic3—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C5×C4⋊Dic3C2311yescharacteristic
111C5×Dic3⋊C4—21no—
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3—21no—
116C4×C5×Dic3—21no—
117C4×C5×Dic3C2311yescharacteristic
118C3×#689—41no—
119C3×#688—22no—
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6669—21no—
123#6667—21no—
124#6667—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127D3×#168—41no—
128#5829—51no—
129#5639D511yescharacteristic, complemented
130C3×#452—51no—
131#5233—51no—
132#5188—51no—
133#5185—51no—
134#5169—51no—
135Dic3×SD16—51no—
136#5048—51no—
137#4805—51no—
138#4800—51no—
139D3×#102—51no—
140#4766—51no—
141#4737—51no—
142#67⋊C8—51no—
143C2×#709C2×D311yescharacteristic
144C22×D20—31no—
145C5×#126—61no—
146C5×#125—31no—
147C5×#125—61no—
148C5×#123—61no—
149C5×C22⋊Q8—31no—
150C5×C22⋊Q8C2×D311yescharacteristic, complemented
151C4×C5×Q8—31no—
152C4×C5×D4—31no—
153C5×#117—31no—
154C5×#117—61no—
155C2×C5×C4⋊C4—31no—
156C2×#689C2×D311yescharacteristic, complemented
157C2×#688—31no—
158C2×#688C2×D311yescharacteristic
159#4083—61no—
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3967—31no—
170C22⋊#168—31no—
171C22⋊#168C2×D311yescharacteristic, complemented
172#3942—31no—
173#3942—31no—
174#3942C2×D311yescharacteristic, complemented
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3296—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×D15—21no—
189C22×C5×D3C2×D411yescharacteristic
190C22×C3×D5—21no—
191C2×D3×D5—42no—
192C2×D3×D5—42no—
193C2×D3×D5—81no—
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202#1220—81no—
203C2×Dic15—21no—
204D60—21no—
205D60—21no—
206C5×#67—22no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C4×C5×D3—21no—
213C4×C5×D3—21no—
214C4×C5×D3—42no—
215C3×C22⋊D5—42no—
216C2×C3×Dic5—21no—
217C3×D20—21no—
218C3×D20#4112yes—
219C3×C4×D5—42no—
220C3×Dic10—21no—
221C3×Dic10—21no—
222#1202—42no—
223D5×Dic3—81no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×C3×#41—51no—
229C2×D3×D4—51no—
230C2×C3×Q16—51no—
231C2×C3×SD16—51no—
232C3×C22⋊Q8C2×D511yescharacteristic, complemented
233#947—51no—
234#946—51no—
235#946C2×D511yescharacteristic
236Q8×Dic3C2×D511yescharacteristic, complemented
237C2×#215—51no—
238#939—101no—
239#937—101no—
240D4×Dic3—51no—
241#930—51no—
242#929—101no—
243C4×#67C2×D511yescharacteristic
244C2×(C2×D3)⋊C4—101no—
245#926C2×D511yescharacteristic, complemented
246C22×C3⋊C8—51no—
247C2×D3×C8—51no—
248#892—21no—
249D3×C4⋊C4C2×D511yescharacteristic
250#890C2×D511yescharacteristic, complemented
251#889—21no—
252#883—21no—
253#879—21no—
254C3×#103—51no—
255C3×#102—51no—
256C3×C22⋊C8—51no—
257#835—51no—
258#835—51no—
259#835—51no—
260#832—51no—
261#832—51no—
262#821—51no—
263#821—51no—
264(C2×D3)⋊C8—51no—
265#818—51no—
266#817—51no—
267Dic3⋊C8—51no—
268C8×Dic3—51no—
269#809—51no—
270#808—51no—
271C23×D5—61no—
272C2×C5×Q8C22×D311yescharacteristic
273C2×C5×D4—31no—
274C22×C4×C5—31no—
275C22×C4×C5—61no—
276C22×C4×C5C22×D311yescharacteristic
277C2×C22⋊D5—21no—
278C2×C22⋊D5—61no—
279#709—22no—
280#709—41no—
281C2×D20—31no—
282C2×D20—62no—
283C2×D20—61no—
284C2×D20—121no—
285C2×D20C22×D311yescharacteristic
286C2×C4×D5—21no—
287C2×C4×D5—61no—
288C2×Dic10C22×D311yescharacteristic
289C5×C4⋊C4—21no—
290C5×C4⋊C4—31no—
291C5×C4⋊C4—31no—
292C5×C4⋊C4—31no—
293C5×C4⋊C4—61no—
294C5×C4⋊C4—61no—
295C5×C4⋊C4—61no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4—61no—
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C22⋊C4—21no—
300C5×C22⋊C4—31no—
301C5×C22⋊C4—31no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C42×C5—31no—
305C42×C5—61no—
306C42×C5—61no—
307C22⋊Dic5—61no—
308#689—41no—
309#688—22no—
310#688—121no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316#683—61no—
317C2×#168—31no—
318C2×#168—31no—
319C2×#168—121no—
320C2×#168—121no—
321C2×#168C22×D311yescharacteristic
322C2×#168C22×D311yescharacteristic
323#552—31no—
324#546—151no—
325#488—151no—
326#483—151no—
327#482—151no—
328#478—151no—
329#467—151no—
330#465—151no—
331#464—151no—
332#452—51no—
333#450—151no—
334C4×SD16—151no—
335C8×D4—151no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—41no—
343C2×D15—41no—
344C2×D15—41no—
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3#13512yes—
348C2×C3×D5—22no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351D3×D5—84no—
352C3×C4×C5—21no—
353C3×C4×C5—41no—
354C3×C4×C5—41no—
355C3×C4×C5C2×#4111yescharacteristic
356C3×C4×C5H(5,𝔽2)11yescharacteristic
357Dic15—41no—
358C3×Dic5—41no—
359C5×Dic3—21no—
360C5×Dic3—21no—
361C5×Dic3—21no—
362C5×Dic3—41no—
363C5×Dic3—41no—
364C23×D3—101no—
365C3×#41—102no—
366C3×#41—201no—
367C2×C3×Q8—51no—
368C2×C3×Q8C22×D511yescharacteristic
369C2×C3×D4—51no—
370C2×C3×D4—101no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—101no—
374C2×#67—101no—
375C2×#67C22⋊D511yescharacteristic
376C22×Dic3—101no—
377D3×D4—102no—
378D3×D4—201no—
379C2×D12—51no—
380C2×C4×D3—21no—
381C2×C4×D3C22×D511yescharacteristic
382C3×Q16—201no—
383C3×SD16—102no—
384C2×C3×C8—51no—
385C2×C3×C8—51no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4C22×D511yescharacteristic
388C3×C22⋊C4—21no—
389#217—21no—
390#217—101no—
391#217C22⋊D511yescharacteristic
392#215—201no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—101no—
395(C2×D3)⋊C4—101no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4C22⋊D511yescharacteristic
399C4⋊Dic3—21no—
400C4⋊Dic3—21no—
401C4⋊Dic3—51no—
402C4⋊Dic3C22×D511yescharacteristic
403C4⋊Dic3C22×D511yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407Dic3⋊C4—101no—
408Dic3⋊C4C22⋊D511yescharacteristic
409C4×Dic3—21no—
410C4×Dic3—21no—
411C4×Dic3C22×D511yescharacteristic
412C2×C3⋊C8—51no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—201no—
415D3×C8—201no—
416C23×C5—31no—
417C23×C5D3×D411yescharacteristic
418C22×D5—21no—
419C22×D5—61no—
420C22×D5—122no—
421C22×D5—122no—
422C22×D5—241no—
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—62no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—31no—
431C2×C4×C5—31no—
432C2×C4×C5—31no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—122no—
438C2×C4×C5D3×D411yescharacteristic
439C2×C4×C5C23×D311yescharacteristic
440C22⋊D5—42no—
441C22⋊D5—241no—
442C2×Dic5—21no—
443C2×Dic5—61no—
444D20—21no—
445D20—61no—
446D20—61no—
447D20—122no—
448D20#23712yes—
449C4×D5—42no—
450C4×D5—241no—
451Dic10—21no—
452Dic10—21no—
453#168—21no—
454#168—21no—
455#168—61no—
456#168—61no—
457C2×#41—51no—
458C22×D4—151no—
459C2×Q16—51no—
460C2×SD16—51no—
461C2×SD16—151no—
462C22×C8—151no—
463C22×C8—151no—
464#126—61no—
465#125—31no—
466#125—61no—
467#124—151no—
468#123—61no—
469#123—301no—
470C22⋊Q8—31no—
471C22⋊Q8—151no—
472C22⋊Q8D3×D511yescharacteristic, complemented
473#121—151no—
474#121—301no—
475#120—301no—
476C4×Q8—31no—
477C4×D4—31no—
478C4×D4—151no—
479#117—31no—
480#117—61no—
481C2×C4⋊C4—31no—
482C2×C22⋊C4—301no—
483#107—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—151no—
487#103—51no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—51no—
492#102—151no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—51no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5—41no—
501C2×C3×C5#54611yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5#57711yescharacteristic
504D15—81no—
505C3×D5—42no—
506C5×D3—22no—
507C23×C3—101no—
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—101no—
510C22×D3—202no—
511C22×D3—202no—
512C22×D3—401no—
513C22×D3C2×C22⋊D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—101no—
517C3×Q8—101no—
518C3×D4—52no—
519C3×D4—101no—
520C3×D4—202no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—101no—
526C2×C3×C4—202no—
527C2×C3×C4C2×C22⋊D511yescharacteristic
528C2×C3×C4C23×D511yescharacteristic
529#67—22no—
530#67—202no—
531#67—401no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—101no—
535C2×Dic3—401no—
536C2×Dic3C2×C22⋊D511yescharacteristic
537C2×Dic3C2×C22⋊D511yescharacteristic
538C2×Dic3C2×C22⋊D511yescharacteristic
539D12—101no—
540D12—101no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—42no—
544C3×C8—101no—
545C3×C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—32no—
552C22×C5—61no—
553C22×C5—61no—
554C22×C5C2×D3×D411yescharacteristic
555C2×D5—22no—
556C2×D5—41no—
557C2×D5—41no—
558C2×D5—121no—
559C2×D5—121no—
560C2×D5—121no—
561C2×D5—244no—
562C4×C5—21no—
563C4×C5—41no—
564C4×C5—41no—
565C4×C5—61no—
566C4×C5—61no—
567C4×C5—61no—
568C4×C5—121no—
569C4×C5—121no—
570C4×C5C2×#23711yescharacteristic
571C4×C5#100411yescharacteristic
572Dic5—41no—
573Dic5—121no—
574C24—301no—
575#41—102no—
576#41—201no—
577C2×Q8—51no—
578C2×Q8C2×D3×D511yescharacteristic
579C2×D4—31no—
580C2×D4—51no—
581C2×D4—101no—
582C2×D4—151no—
583C2×D4—301no—
584C2×D4—302no—
585C2×D4—301no—
586C2×D4—601no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—101no—
590C22×C4—301no—
591C22×C4C2×D3×D511yescharacteristic
592Q16—201no—
593SD16—102no—
594SD16—601no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—151no—
598C2×C8—151no—
599C2×C8—601no—
600C2×C8—601no—
601C4⋊C4—21no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—151no—
611C4⋊C4—301no—
612C4⋊C4C2×D3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—301no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C42—31no—
624C42—61no—
625C42—61no—
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—102no—
631C22×C3—201no—
632C22×C3—201no—
633C22×C3C22×C22⋊D511yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—201no—
637C2×D3—201no—
638C2×D3—201no—
639C2×D3—404no—
640C2×D3#409612yes—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—201no—
645C3×C4D5×#4111yescharacteristic
646C3×C4#414911yescharacteristic
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—41no—
651Dic3—41no—
652Dic3—201no—
653C2×C5—41no—
654C2×C5—62no—
655C2×C5#559111yescharacteristic
656C2×C5D3×#13511yescharacteristic
657C2×C5#577811yescharacteristic
658D5—42no—
659D5—241no—
660C23—31no—
661C23—101no—
662C23—301no—
663C23—602no—
664C23—602no—
665C23—1201no—
666C23D3×C22⋊D511yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—101no—
670Q8—101no—
671D4—52no—
672D4—62no—
673D4—101no—
674D4—202no—
675D4—301no—
676D4—301no—
677D4—602no—
678D4—1201no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—101no—
691C2×C4—122no—
692C2×C4—202no—
693C2×C4—301no—
694C2×C4—1201no—
695C2×C4D3×C22⋊D511yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—301no—
700C8—301no—
701C2×C3—41no—
702C2×C3—202no—
703C2×C3C2×#409611yescharacteristic
704C2×C3#6616311yescharacteristic
705C2×C3#6617111yescharacteristic
706D3—22no—
707D3—401no—
708C5#8024611yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—32no—
713C22—61no—
714C22—61no—
715C22—102no—
716C22—201no—
717C22—201no—
718C22—601no—
719C22—601no—
720C22—601no—
721C22—1204no—
722C22C2×D3×C22⋊D511yescharacteristic
723C4—21no—
724C4—41no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—201no—
732C4—601no—
733C4D5×#23711yescharacteristic
734C4#9202611yescharacteristic
735C3#1061532911yescharacteristic, complemented, Sylow
736C2—41no—
737C2—62no—
738C2—202no—
739C2—1201no—
740C2#1175506611yescharacteristic
741C2#1175509211yescharacteristic
742C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754638C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5639C2semidirect
3. #11751149C2semidirect
4. C3×#65336C2semidirect
5. #11749398C2semidirect
6. #11749326C2semidirect
7. #11749296C2semidirect
8. Dic3×#688C2semidirect
9. #67⋊#168C2semidirect
10. #11748373C2semidirect
11. #11748364C2semidirect
12. D3×#3941C2semidirect
13. #11747379C2semidirect
14. #11747348C2semidirect
15. #11747251C2semidirect
19. C3×C5×C22⋊Q8C22semidirect
22. C22×C3⋊#168C22semidirect
24. C5×Q8×Dic3C22semidirect
26. C5×#926C22semidirect
29. C5×#890C22semidirect
33. C2×C3×#689C22semidirect
43. #91119C22semidirect
45. #91092C22semidirect
46. C3×C22⋊#168C22semidirect
47. C3×#3942C22semidirect
49. #90988C22semidirect
50. #90985C22semidirect
51. Dic3⋊#168C22semidirect
52. #90970C22semidirect
53. #90970C22semidirect
59. Dic3×#168C22semidirect
67. #65336D3semidirect
129. #5639D5semidirect
150. C5×C22⋊Q8C2×D3semidirect
156. C2×#689C2×D3semidirect
171. C22⋊#168C2×D3semidirect
174. #3942C2×D3semidirect
232. C3×C22⋊Q8C2×D5semidirect
236. Q8×Dic3C2×D5semidirect
245. #926C2×D5semidirect
250. #890C2×D5semidirect
472. C22⋊Q8D3×D5semidirect
626. C3×C5#3296semidirect
708. C5#80246semidirect
735. C3#10615329semidirect

Maximal subgroups

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

subgroupindex
C5×#56392
#117546382
#117511492
C3×#653362
#117493982
#117493262
#117492962
Dic3×#6882
#67⋊#1682
#117483732
#117483642
D3×#39412
#117473792
#117473482
#117472512
#106153293
#802465