Finite Group Databasebeta

← #14458763

Subgroups — #14458763

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×#5694C211yesmaximal, characteristic, complemented
2#11752736C211yesmaximal, characteristic
3#11751169C211yesmaximal, characteristic, complemented
4C3×#65355C211yesmaximal, characteristic, complemented
5#11747514C211yesmaximal, characteristic, complemented
6#11747502C211yesmaximal, characteristic, complemented
7#11747483C211yesmaximal, characteristic, complemented
8D3×#3941C211yesmaximal, characteristic, complemented
9#11747449C211yesmaximal, characteristic, complemented
10#11747447C211yesmaximal, characteristic, complemented
11#11747179C211yesmaximal, characteristic, complemented
12#11747174C211yesmaximal, characteristic, complemented
13#11747102C211yesmaximal, characteristic, complemented
14C4×#6655C211yesmaximal, characteristic, complemented
15#11746998C211yesmaximal, characteristic, complemented
16#10615329—31nomaximal, Hall
17C2×D3×D20C2211yescharacteristic
18C2×#6765C2211yescharacteristic
19C3×C5×#125C2211yescharacteristic, complemented
20#91764C2211yescharacteristic
21C5×#898—21no—
22C5×#897C2211yescharacteristic
23C5×#897C2211yescharacteristic, complemented
24C5×#894—21no—
25C5×#892—21no—
26C5×#892C2211yescharacteristic, complemented
27C5×D3×C4⋊C4C2211yescharacteristic
28C5×#890—21no—
29C4×C5×D12C2211yescharacteristic
30C4×C5×Dic6C2211yescharacteristic, complemented
31C3×C4×D20C2211yescharacteristic
32#91475—21no—
33D5×(C2×D3)⋊C4—21no—
34#91460C2211yescharacteristic
35#91448—21no—
36#91413—21no—
37#91365C2211yescharacteristic
38C2×#6663C2211yescharacteristic, complemented
39C2×#6660C2211yescharacteristic
40C2×#6655C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91094C2211yescharacteristic, complemented
44#91094C2211yescharacteristic, complemented
45#91093C2211yescharacteristic
46#91093C2211yescharacteristic
47C4×C3⋊#168C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50C3×#3940C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52C3×C4⋊#168C2211yescharacteristic, complemented
53#90986C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90972C2211yescharacteristic, complemented
56#90969C2211yescharacteristic
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60#81186—51nomaximal, Hall
61C5×#552—31no—
62#65884—31no—
63#65357—31no—
64#65355D311yescharacteristic, complemented
65#65340—31no—
66#65337—31no—
67#65336—31no—
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×D60C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×D12D411yescharacteristic
80C2×C4×C5×D3—21no—
81C2×C4×C5×D3C2311yescharacteristic
82C2×C4×C5×D3C2311yescharacteristic
83C2×C5×Dic6C2311yescharacteristic
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×#1203—21no—
87C2×#1202—21no—
88C2×#1201—21no—
89C2×D5×Dic3—21no—
90D3×D20—22no—
91D3×D20—41no—
92#6765—22no—
93#6765—41no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C42×C5C2311yescharacteristic
99#6714—21no—
100#6714—21no—
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×(C2×D3)⋊C4—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4D411yescharacteristic
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×C4⋊Dic3—21no—
109C5×C4⋊Dic3—21no—
110C5×C4⋊Dic3D411yescharacteristic
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4—21no—
114C4×C5×Dic3—21no—
115C4×C5×Dic3—21no—
116C3×#685—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6668—21no—
121#6667—21no—
122(C2×D3)⋊Dic5—21no—
123#6663—41no—
124#6660—41no—
125#6655—22no—
126D3×#168—41no—
127D3×#168—41no—
128#5694D511yescharacteristic, complemented
129#5554—51no—
130C3×#478—51no—
131#5068—51no—
132C4×#214—51no—
133#4887—51no—
134#4885—51no—
135#4864—51no—
136#4862—51no—
137#4845—51no—
138#4834—51no—
139#4783—51no—
140#4776—51no—
141#4772—51no—
142D3×#102—51no—
143C2×#709—31no—
144C22×D20—31no—
145C5×#126—61no—
146C5×#125—61no—
147C5×#125C2×D311yescharacteristic, complemented
148C5×#123—61no—
149C5×C22⋊Q8—31no—
150C5×C22⋊Q8—31no—
151C4×C5×Q8—31no—
152C4×C5×D4—31no—
153C5×#117—31no—
154C5×#117—61no—
155C2×C5×C4⋊C4—31no—
156C2×#689—31no—
157C2×#688—31no—
158C2×#688—31no—
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×D20C2×D311yescharacteristic
169#3967—31no—
170C22⋊#168—31no—
171C22⋊#168—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941C2×D311yescharacteristic
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940C2×D311yescharacteristic, complemented
183#3939C2×D311yescharacteristic, complemented
184C4⋊#168C2×D311yescharacteristic, complemented
185C4×#168—31no—
186#3296—151noSylow
187C22×D15—21no—
188C22×C5×D3C2×D411yescharacteristic
189C22×C5×D3C2×D411yescharacteristic
190C22×C3×D5—21no—
191C2×D3×D5—42no—
192C2×D3×D5—42no—
193C2×D3×D5—81no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200D60—21no—
201D60—21no—
202Dic30—21no—
203Dic30—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3C2×D411yescharacteristic
207C2×C5×Dic3C2×D411yescharacteristic
208C5×D12—22no—
209C4×C5×D3—21no—
210C4×C5×D3—21no—
211C4×C5×D3—21no—
212C4×C5×D3—21no—
213C4×C5×D3—42no—
214C5×Dic6—21no—
215C5×Dic6—21no—
216C2×C3×Dic5—21no—
217C3×D20—21no—
218C3×D20#4112yes—
219C3×C4×D5—81no—
220#1203—81no—
221#1202—42no—
222#1201—42no—
223D5×Dic3—42no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×#237—51no—
229C2×D3×D4—51no—
230C3×#125C2×D511yescharacteristic, complemented
231C3×C4×D4—51no—
232C2×#214—51no—
233#930—101no—
234C2×(C2×D3)⋊C4—101no—
235C2×Dic12—51no—
236C2×#204—51no—
237C2×D3×C8—51no—
238C2×D3×C8—51no—
239#898—21no—
240#897—51no—
241#897C2×D511yescharacteristic
242#897C2×D511yescharacteristic, complemented
243#895—51no—
244#894—21no—
245#892—21no—
246#892C2×D511yescharacteristic, complemented
247D3×C4⋊C4C2×D511yescharacteristic
248#890—21no—
249#886—101no—
250#882—101no—
251#875—51no—
252C4×D12C2×D511yescharacteristic
253C4×Dic6C2×D511yescharacteristic, complemented
254C3×#107—51no—
255C3×#106—51no—
256C3×C4⋊C8—51no—
257C3×#102—51no—
258C3×#102—51no—
259#832—51no—
260#821—51no—
261(C2×D3)⋊C8—51no—
262(C2×D3)⋊C8—51no—
263#816—51no—
264#810—51no—
265#810—51no—
266#810—51no—
267#809—51no—
268#809—51no—
269#808—51no—
270C4×C3⋊C8—51no—
271C23×D5—61no—
272C2×C5×Q8—31no—
273C2×C5×D4—31no—
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5—61no—
277C2×C22⋊D5—61no—
278C2×C22⋊D5—61no—
279#709—62no—
280#709—121no—
281C2×D20—31no—
282C2×D20—62no—
283C2×D20—61no—
284C2×D20—121no—
285C2×D20C22×D311yescharacteristic
286C2×C4×D5—21no—
287C2×C4×D5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
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⋊C4C22×D311yescharacteristic
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C22⋊C4—31no—
300C5×C22⋊C4—31no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C42×C5—61no—
305C42×C5—61no—
306C42×C5C22×D311yescharacteristic
307C22⋊Dic5—61no—
308#689—121no—
309#688—62no—
310#688—121no—
311#685—21no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5C22×D311yescharacteristic
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—51no—
329#467—151no—
330#465—151no—
331#464—151no—
332#452—151no—
333#450—151no—
334C4×SD16—151no—
335C8×D4—151no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5C22×D411yescharacteristic
339C2×D15—41no—
340C2×D15—41no—
341C2×D15—41no—
342C2×C5×D3—21no—
343C2×C5×D3—21no—
344C2×C5×D3—21no—
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—21no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358Dic15—41no—
359C3×Dic5—41no—
360C5×Dic3—21no—
361C5×Dic3—21no—
362C5×Dic3—41no—
363C5×Dic3—41no—
364C23×D3—101no—
365C2×C3×D4—51no—
366C22×C3×C4—101no—
367C2×#67—101no—
368C2×#67—101no—
369C22×Dic3—101no—
370#237—102no—
371#237—201no—
372D3×D4—102no—
373D3×D4—201no—
374C2×D12—51no—
375C2×D12—101no—
376C2×D12C22⋊D511yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3C22×D511yescharacteristic
379C2×C4×D3C22×D511yescharacteristic
380C2×Dic6—51no—
381C2×Dic6C22×D511yescharacteristic
382C2×C3×C8—51no—
383C2×C3×C8—51no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—51no—
387C3×C4⋊C4C22×D511yescharacteristic
388C3×C4⋊C4C22×D511yescharacteristic
389C3×C22⋊C4—101no—
390C3×C42C22×D511yescharacteristic
391#214—102no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—101no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4—101no—
399(C2×D3)⋊C4C22⋊D511yescharacteristic
400(C2×D3)⋊C4C22⋊D511yescharacteristic
401C4⋊Dic3—21no—
402C4⋊Dic3—21no—
403C4⋊Dic3—101no—
404C4⋊Dic3C22⋊D511yescharacteristic
405C4⋊Dic3C22×D511yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408C4×Dic3—21no—
409C4×Dic3—21no—
410C2×C3⋊C8—51no—
411C2×C3⋊C8—51no—
412Dic12—201no—
413#204—201no—
414D3×C8—201no—
415D3×C8—201no—
416C23×C5—31no—
417C23×C5—31no—
418C22×D5—21no—
419C22×D5—61no—
420C22×D5—122no—
421C22×D5—122no—
422C22×D5—241no—
423C5×Q8—61no—
424C5×Q8—61no—
425C5×D4—62no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—31no—
429C2×C4×C5—31no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—122no—
437C2×C4×C5D3×D411yescharacteristic
438C2×C4×C5D3×D411yescharacteristic
439C2×C4×C5C23×D311yescharacteristic
440C22⋊D5—122no—
441C22⋊D5—241no—
442C2×Dic5—21no—
443C2×Dic5—61no—
444D20—21no—
445D20—61no—
446D20—61no—
447D20—122no—
448D20#23912yes—
449C4×D5—81no—
450C4×D5—122no—
451Dic10—61no—
452Dic10—61no—
453#168—21no—
454#168—21no—
455#168—61no—
456#168—61no—
457C2×#41—151no—
458C22×D4—151no—
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—151no—
463C22×C8—151no—
464#126—61no—
465#125—61no—
466#125D3×D511yescharacteristic, complemented
467#124—151no—
468#123—61no—
469#123—301no—
470C22⋊Q8—31no—
471C22⋊Q8—31no—
472C22⋊Q8—151no—
473#121—151no—
474#121—301no—
475#120—301no—
476C4×Q8—31no—
477C4×D4—31no—
478C4×D4—51no—
479#117—31no—
480#117—61no—
481C2×C4⋊C4—31no—
482C2×C22⋊C4—301no—
483#107—51no—
484#106—51no—
485#106—151no—
486C4⋊C8—51no—
487#103—151no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—51no—
492#102—51no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—151no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5#54611yescharacteristic
501C2×C3×C5C2×#13511yescharacteristic
502C2×C3×C5#57711yescharacteristic
503D15—81no—
504C3×D5—42no—
505C5×D3—22no—
506C5×D3—41no—
507C23×C3—101no—
508C22×D3—101no—
509C22×D3—202no—
510C22×D3—202no—
511C22×D3—401no—
512C22×D3C2×C22⋊D511yescharacteristic
513C22×D3C2×C22⋊D511yescharacteristic
514C3×D4—52no—
515C3×D4—101no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—101no—
519C2×C3×C4—401no—
520C2×C3×C4C2×C22⋊D511yescharacteristic
521C2×C3×C4C2×C22⋊D511yescharacteristic
522C2×C3×C4C23×D511yescharacteristic
523#67—202no—
524#67—202no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—101no—
528C2×Dic3—202no—
529C2×Dic3C2×C22⋊D511yescharacteristic
530C2×Dic3C2×C22⋊D511yescharacteristic
531D12—22no—
532D12—101no—
533D12—101no—
534D12—401no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540Dic6—21no—
541Dic6—21no—
542Dic6—101no—
543Dic6—101no—
544C3×C8—101no—
545C3×C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—32no—
549C22×C5—61no—
550C22×C5—61no—
551C22×C5—61no—
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—21no—
564C4×C5—41no—
565C4×C5—41no—
566C4×C5—61no—
567C4×C5—61no—
568C4×C5—121no—
569C4×C5—121no—
570C4×C5C2×#23911yescharacteristic
571C4×C5#100911yescharacteristic
572Dic5—41no—
573Dic5—121no—
574C24—301no—
575#41—302no—
576#41—601no—
577C2×Q8—31no—
578C2×Q8—151no—
579C2×D4—31no—
580C2×D4—51no—
581C2×D4—151no—
582C2×D4—301no—
583C2×D4—302no—
584C2×D4—301no—
585C2×D4—301no—
586C2×D4—601no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—101no—
591C22×C4—301no—
592Q16—601no—
593SD16—302no—
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—21no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—51no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—301no—
611C4⋊C4C2×D3×D511yescharacteristic
612C4⋊C4C2×D3×D511yescharacteristic
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—101no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C42—61no—
624C42—61no—
625C42C2×D3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—102no—
628C22×C3—201no—
629C22×C3—201no—
630C22×C3C22×C22⋊D511yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
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—21no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—201no—
646C3×C4D5×#4111yescharacteristic
647C3×C4#414911yescharacteristic
648Dic3—21no—
649Dic3—21no—
650Dic3—41no—
651Dic3—41no—
652Dic3—201no—
653C2×C5—62no—
654C2×C5—121no—
655C2×C5#563011yescharacteristic
656C2×C5D3×#13511yescharacteristic
657C2×C5#577511yescharacteristic
658D5—42no—
659D5—241no—
660C23—31no—
661C23—31no—
662C23—101no—
663C23—301no—
664C23—602no—
665C23—602no—
666C23—1201no—
667Q8—61no—
668Q8—61no—
669Q8—301no—
670Q8—301no—
671D4—52no—
672D4—62no—
673D4—101no—
674D4—301no—
675D4—301no—
676D4—602no—
677D4—602no—
678D4—1201no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—101no—
690C2×C4—122no—
691C2×C4—301no—
692C2×C4—401no—
693C2×C4—602no—
694C2×C4D3×C22⋊D511yescharacteristic
695C2×C4D3×C22⋊D511yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—301no—
700C8—301no—
701C2×C3—202no—
702C2×C3C2×#409611yescharacteristic
703C2×C3#6616311yescharacteristic
704C2×C3#6617111yescharacteristic
705D3—22no—
706D3—41no—
707D3—401no—
708C5#8118611yescharacteristic, complemented, Sylow
709C22—32no—
710C22—61no—
711C22—61no—
712C22—61no—
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—21no—
725C4—41no—
726C4—41no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—201no—
732C4—601no—
733C4D5×#23911yescharacteristic
734C4#9203511yescharacteristic
735C3#1061532911yescharacteristic, complemented, Sylow
736C2—62no—
737C2—121no—
738C2—202no—
739C2—1201no—
740C2#1175527711yescharacteristic
741C2D3×#409611yescharacteristic
742C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radical#11752736C2
hypercenter#125D3×D5
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C5×#5694C2semidirect
3. #11751169C2semidirect
4. C3×#65355C2semidirect
5. #11747514C2semidirect
6. #11747502C2semidirect
7. #11747483C2semidirect
8. D3×#3941C2semidirect
9. #11747449C2semidirect
10. #11747447C2semidirect
11. #11747179C2semidirect
12. #11747174C2semidirect
13. #11747102C2semidirect
14. C4×#6655C2semidirect
15. #11746998C2semidirect
19. C3×C5×#125C22semidirect
23. C5×#897C22semidirect
26. C5×#892C22semidirect
30. C4×C5×Dic6C22semidirect
38. C2×#6663C22semidirect
42. C2×D3×#168C22semidirect
43. #91094C22semidirect
44. #91094C22semidirect
47. C4×C3⋊#168C22semidirect
50. C3×#3940C22semidirect
51. C3×#3939C22semidirect
52. C3×C4⋊#168C22semidirect
53. #90986C22semidirect
54. #90975C22semidirect
55. #90972C22semidirect
59. (C2×D3)⋊#168C22semidirect
64. #65355D3semidirect
128. #5694D5semidirect
147. C5×#125C2×D3semidirect
182. #3940C2×D3semidirect
183. #3939C2×D3semidirect
184. C4⋊#168C2×D3semidirect
230. C3×#125C2×D5semidirect
242. #897C2×D5semidirect
246. #892C2×D5semidirect
253. C4×Dic6C2×D5semidirect
466. #125D3×D5semidirect
626. C3×C5#3296semidirect
708. C5#81186semidirect
735. C3#10615329semidirect

Maximal subgroups

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

subgroupindex
C5×#56942
#117527362
#117511692
C3×#653552
#117475142
#117475022
#117474832
D3×#39412
#117474492
#117474472
#117471792
#117471742
#117471022
C4×#66552
#117469982
#106153293
#811865