Finite Group Databasebeta

← #14459148

Subgroups — #14459148

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5507C211yesmaximal, characteristic
2#11754377C211yesmaximal, characteristic, complemented
3C2×#91094C211yesmaximal, characteristic, complemented
4C3×#65260C211yesmaximal, characteristic, complemented
5#11748553C211yesmaximal, characteristic, complemented
6#11748547C211yesmaximal, characteristic, complemented
7#67⋊#168C211yesmaximal, characteristic, complemented
8#11747494C211yesmaximal, characteristic, complemented
9D3×#3942C211yesmaximal, characteristic, complemented
10#11747448C211yesmaximal, characteristic, complemented
11#11747422C211yesmaximal, characteristic, complemented
12#11747420C211yesmaximal, characteristic, complemented
13#11747297C211yesmaximal, characteristic, complemented
14#11747277C211yesmaximal, characteristic, complemented
15#11747179C211yesmaximal, characteristic, complemented
16#10615262—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C2×C5×#235—21no—
19C2×D3×Dic10C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C5×#930C2211yescharacteristic
23C5×#929—21no—
24C4×C5×#67C2211yescharacteristic
25C5×#896—21no—
26C5×#895C2211yescharacteristic
27C5×#894—21no—
28C5×#893C2211yescharacteristic
29C5×D3×C4⋊C4C2211yescharacteristic
30C5×#888C2211yescharacteristic
31C3×#4070C2211yescharacteristic
32#91576—21no—
33#67⋊Dic5—21no—
34#91432—21no—
35#91389C2211yescharacteristic
36#91365C2211yescharacteristic
37#91340C2211yescharacteristic
38#91328—21no—
39C2×#6659C2211yescharacteristic
40C2×#6659C2211yescharacteristic
41C2×#6656C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic
43#91094C2211yescharacteristic
44#91094C2211yescharacteristic
45#91094C2211yescharacteristic
46#91094C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3942C2211yescharacteristic
50C3×#3940C2211yescharacteristic
51C3×#3940C2211yescharacteristic
52#90986C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90975C2211yescharacteristic
56#90970C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81450—51nomaximal, Hall
61C5×#547—31no—
62D4×Dic10—31no—
63#65383—31no—
64#65382—31no—
65#65330—31no—
66#65330—31no—
67#65329—31no—
68#65329—31no—
69#65308—31no—
70C4×#687—31no—
71D4×#168—31no—
72#65260—31no—
73#65260D311yescharacteristic, complemented
74C2×#3942—31no—
75C2×#3942—31no—
76C22×C3×C4×C5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—21no—
79C2×Dic30—22no—
80C2×Dic30—21no—
81C2×Dic30—41no—
82C2×Dic30C2311yescharacteristic
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67D411yescharacteristic
86C5×#235—44no—
87C2×C5×D12—21no—
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3C2311yescharacteristic
92C2×C5×Dic6—21no—
93C2×C3×Dic10C2311yescharacteristic
94C2×#1204—21no—
95C2×D3×Dic5—21no—
96D3×Dic10—22no—
97D3×Dic10—41no—
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C2×C3⋊#168—41no—
102C2×C3⋊#168C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C5×#217D411yescharacteristic
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C5×Dic3⋊C4—21no—
112C5×Dic3⋊C4D411yescharacteristic
113C4×C5×Dic3C2311yescharacteristic
114C3×C22⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119Dic3⋊Dic5—21no—
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123(C2×D3)⋊Dic5—21no—
124Dic3×Dic5—21no—
125#6659—22no—
126#6659—41no—
127#6656—41no—
128D3×#168—41no—
129#5632—51no—
130#5507D511yescharacteristic
131C3×#483—51no—
132#5048—51no—
133C2×#810—51no—
134#4864—51no—
135#4862—51no—
136#4854—51no—
137#4852—51no—
138#4818—51no—
139#4806—51no—
140D3×#103—51no—
141#4792—51no—
142#4738—51no—
143#67⋊C8—51no—
144C2×C5×#41—61no—
145C22×Dic10—31no—
146C22×Dic10—31no—
147C5×C4⋊Q8—31no—
148C5×#123—61no—
149C5×#123—61no—
150C5×C22⋊Q8—61no—
151C5×#121—31no—
152C5×#121—31no—
153C4×C5×D4—31no—
154C4×C5×D4—31no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4C2×D311yescharacteristic
157D4×Dic5—61no—
158C2×#687—31no—
159C2×#687—31no—
160C2×#687—31no—
161#4070—31no—
162#4070C2×D311yescharacteristic
163C22×#168—31no—
164C22×#168—31no—
165#4034—61no—
166#4024—61no—
167#4024—61no—
168#4015—31no—
169C4×Dic10—31no—
170#3964—31no—
171C22⋊#168—31no—
172C22⋊#168C2×D311yescharacteristic
173#3942—31no—
174#3942—31no—
175#3942—31no—
176#3942—31no—
177#3942—31no—
178#3942—31no—
179#3942—31no—
180#3942C2×D311yescharacteristic
181#3942C2×D311yescharacteristic
182#3940—31no—
183#3940C2×D311yescharacteristic
184#3940C2×D311yescharacteristic
185C4⋊#168—31no—
186C4×#168—31no—
187#3298—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×C5×D3—21no—
190C22×C5×D3C2×D411yescharacteristic
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—42no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2411yescharacteristic
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—42no—
201Dic30—21no—
202Dic30—21no—
203Dic30—21no—
204Dic30—42no—
205Dic30#4112yescomplemented
206C5×#67—42no—
207C5×#67SD1614yescomplemented
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—42no—
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C4×C5×D3—42no—
218C4×C5×D3—42no—
219C5×Dic6—42no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224#1204—42no—
225D3×Dic5—42no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C2×D3×Q8—51no—
231C2×#235—21no—
232C22×Dic6—51no—
233C3×C22⋊Q8—51no—
234C2×C3×C4⋊C4C2×D511yescharacteristic
235#944—51no—
236C2×#215—51no—
237#930C2×D511yescharacteristic
238#929—21no—
239C4×#67C2×D511yescharacteristic
240C22×C3⋊C8—51no—
241C2×#204—51no—
242C2×#204—51no—
243C2×D3×C8—51no—
244#897—51no—
245#896—21no—
246#896—101no—
247#895C2×D511yescharacteristic
248#894—21no—
249#893C2×D511yescharacteristic
250D3×C4⋊C4C2×D511yescharacteristic
251#888—101no—
252#888C2×D511yescharacteristic
253#887—51no—
254#67⋊C4—101no—
255#878—101no—
256C3×#106—51no—
257C3×#106—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×C22⋊C8—51no—
261#835—51no—
262(C2×D3)⋊C8—51no—
263#816—51no—
264#816—51no—
265Dic3⋊C8—51no—
266C8×Dic3—51no—
267#810—51no—
268#810—51no—
269#810—51no—
270#810—51no—
271#809—51no—
272#808—51no—
273C5×#41—124no—
274C2×C5×Q8—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C22×C4×C5—21no—
280C22×C4×C5—31no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C22×C4×C5C22×D311yescharacteristic
284C22×Dic5—61no—
285C22×Dic5—61no—
286C2×Dic10—31no—
287C2×Dic10—31no—
288C2×Dic10—62no—
289C2×Dic10—62no—
290C2×Dic10—61no—
291C2×Dic10—61no—
292C2×Dic10—121no—
293C2×Dic10—121no—
294C2×Dic10C22×D311yescharacteristic
295C5×C4⋊C4—21no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—31no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C42×C5—31no—
308C22⋊Dic5—21no—
309C22⋊Dic5—61no—
310#687—62no—
311#687—121no—
312#687—121no—
313C4⋊Dic5—61no—
314C4⋊Dic5—61no—
315C4⋊Dic5C22×D311yescharacteristic
316#683—21no—
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326D4×Q8—151no—
327#547—31no—
328#487—151no—
329#483—51no—
330#483—151no—
331#475—151no—
332#465—151no—
333#465—151no—
334#461—151no—
335#448—151no—
336#448—151no—
337C4×SD16—151no—
338C8×D4—151no—
339C2×#103—151no—
340C2×#103—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5C2×SD1612yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3C2×SD1612yes—
351C3×C4×C5—21no—
352C3×C4×C5—41no—
353C3×C4×C5—41no—
354C3×C4×C5C2×#4111yescharacteristic
355C3×C4×C5H(5,𝔽2)11yescharacteristic
356Dic15—22no—
357Dic15—41no—
358C3×Dic5—41no—
359C3×Dic5—41no—
360C5×Dic3—21no—
361C5×Dic3—21no—
362C5×Dic3—41no—
363C5×Dic3C2×SD1612yes—
364C2×C3×Q8—51no—
365C22×C3×C4—21no—
366C22×C3×C4C22×D511yescharacteristic
367C2×#67—21no—
368C2×#67C22⋊D511yescharacteristic
369C22×Dic3—101no—
370D3×Q8—102no—
371D3×Q8—201no—
372#235—44no—
373C2×D12—21no—
374C2×D12C22×D511yescharacteristic
375C2×C4×D3—21no—
376C2×C4×D3—21no—
377C2×C4×D3—101no—
378C2×C4×D3C22×D511yescharacteristic
379C2×Dic6—21no—
380C2×Dic6—51no—
381C2×Dic6—51no—
382C2×Dic6—102no—
383C2×Dic6—101no—
384C2×Dic6—101no—
385C2×Dic6—201no—
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—51no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4C22×D511yescharacteristic
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—101no—
394#217C22⋊D511yescharacteristic
395#215—201no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—101no—
400(C2×D3)⋊C4C22⋊D511yescharacteristic
401C4⋊Dic3—101no—
402C4⋊Dic3C22×D511yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—101no—
406Dic3⋊C4—101no—
407Dic3⋊C4—101no—
408Dic3⋊C4C22⋊D511yescharacteristic
409C4×Dic3—101no—
410C4×Dic3C22×D511yescharacteristic
411C2×C3⋊C8—51no—
412C2×C3⋊C8—51no—
413C2×C3⋊C8—201no—
414#204—102no—
415#204—201no—
416D3×C8—201no—
417C23×C5—31no—
418C23×C5—61no—
419C23×C5D3×D411yescharacteristic
420C5×Q8—122no—
421C5×D4—34no—
422C5×D4—61no—
423C5×D4—61no—
424C5×D4—122no—
425C5×D4—122no—
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—42no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—122no—
438C2×C4×C5—122no—
439C2×C4×C5D3×D411yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—122no—
446C2×Dic5—122no—
447Dic10—21no—
448Dic10—21no—
449Dic10—32no—
450Dic10—61no—
451Dic10—61no—
452Dic10—61no—
453Dic10—122no—
454Dic10—122no—
455#168—21no—
456#168—21no—
457#168—61no—
458#168—61no—
459C2×#41—61no—
460C22×Q8—151no—
461C22×Q8—151no—
462C2×SD16—151no—
463C2×SD16—151no—
464C2×SD16—151no—
465C22×C8—151no—
466C22×C8—151no—
467C4⋊Q8—31no—
468C4⋊Q8—151no—
469C4⋊Q8—301no—
470#123—61no—
471#123—61no—
472C22⋊Q8—51no—
473C22⋊Q8—61no—
474C22⋊Q8—151no—
475C22⋊Q8—301no—
476C22⋊Q8—301no—
477#121—31no—
478#121—31no—
479C4×Q8—151no—
480C4×D4—31no—
481C4×D4—31no—
482C4×D4—301no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4D3×D511yescharacteristic
485#106—51no—
486#106—51no—
487#106—151no—
488C4⋊C8—151no—
489#103—51no—
490#103—51no—
491#103—151no—
492#103—151no—
493#103—151no—
494#103—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499C22⋊C8—51no—
500C22⋊C8—151no—
501C4×C8—151no—
502C2×C3×C5—22no—
503C2×C3×C5#54611yescharacteristic
504C2×C3×C5C22×SD1611yescharacteristic
505C2×C3×C5#57811yescharacteristic
506C5×D3—22no—
507C5×D3—81no—
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—21no—
510C22×D3C2×C22⋊D511yescharacteristic
511C3×Q8—101no—
512C3×Q8—101no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—42no—
518C2×C3×C4—101no—
519C2×C3×C4—101no—
520C2×C3×C4C2×C22⋊D511yescharacteristic
521C2×C3×C4C23×D511yescharacteristic
522#67—42no—
523#67#68714yescomplemented
524C2×Dic3—21no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—202no—
528C2×Dic3C2×C22⋊D511yescharacteristic
529C2×Dic3C2×C22⋊D511yescharacteristic
530C2×Dic3C2×C22⋊D511yescharacteristic
531D12—21no—
532D12—21no—
533D12—42no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—42no—
537C4×D3—42no—
538C4×D3—202no—
539Dic6—42no—
540Dic6—52no—
541Dic6—101no—
542Dic6—101no—
543Dic6—101no—
544Dic6—202no—
545Dic6—202no—
546C3×C8—101no—
547C3×C8—101no—
548C3⋊C8—101no—
549C3⋊C8—101no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—32no—
553C22×C5—61no—
554C22×C5—61no—
555C22×C5—121no—
556C22×C5—121no—
557C22×C5—121no—
558C22×C5D3×SD1612yes—
559C22×C5C2×D3×D411yescharacteristic
560C4×C5—21no—
561C4×C5—32no—
562C4×C5—41no—
563C4×C5—41no—
564C4×C5—61no—
565C4×C5—61no—
566C4×C5—121no—
567C4×C5D3×#4111yescharacteristic
568C4×C5#100911yescharacteristic
569Dic5—41no—
570Dic5—41no—
571Dic5—62no—
572Dic5—121no—
573#41—124no—
574C2×Q8—51no—
575C2×Q8—61no—
576C2×Q8—151no—
577C2×Q8—151no—
578C2×Q8—302no—
579C2×Q8—301no—
580C2×Q8—302no—
581C2×Q8—301no—
582C2×Q8—601no—
583C2×Q8—601no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—301no—
593C22×C4—301no—
594C22×C4C2×D3×D511yescharacteristic
595SD16—302no—
596SD16—601no—
597SD16—601no—
598C2×C8—51no—
599C2×C8—51no—
600C2×C8—151no—
601C2×C8—151no—
602C2×C8—601no—
603C2×C8—601no—
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—51no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—101no—
611C4⋊C4—301no—
612C4⋊C4—301no—
613C4⋊C4—301no—
614C4⋊C4—301no—
615C4⋊C4C2×D3×D511yescharacteristic
616C4⋊C4C2×D3×D511yescharacteristic
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—101no—
623C22⋊C4—301no—
624C42—31no—
625C42—301no—
626C3×C5#329811yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3C2×#68712yes—
630C22×C3C22×C22⋊D511yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3C2×#68712yes—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—201no—
641C3×C4—201no—
642C3×C4D5×#4111yescharacteristic
643C3×C4#414911yescharacteristic
644Dic3—21no—
645Dic3—21no—
646Dic3—41no—
647Dic3—102no—
648Dic3—201no—
649Dic3C2×#68712yes—
650C2×C5—22no—
651C2×C5—62no—
652C2×C5—241no—
653C2×C5#565411yescharacteristic
654C2×C5C2×D3×SD1611yescharacteristic
655C2×C5#577911yescharacteristic
656C23—31no—
657C23—61no—
658C23D3×C22⋊D511yescharacteristic
659Q8—101no—
660Q8—101no—
661Q8—122no—
662Q8—152no—
663Q8—301no—
664Q8—301no—
665Q8—301no—
666Q8—602no—
667Q8—602no—
668D4—34no—
669D4—61no—
670D4—61no—
671D4—122no—
672D4—122no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—42no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—602no—
691C2×C4—602no—
692C2×C4D3×C22⋊D511yescharacteristic
693C2×C4C22×D3×D511yescharacteristic
694C8—101no—
695C8—101no—
696C8—301no—
697C8—301no—
698C2×C3—22no—
699C2×C3C22×#68711yescharacteristic
700C2×C3#6616311yescharacteristic
701C2×C3#6617211yescharacteristic
702D3—22no—
703D3—81no—
704C5#8145011yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—32no—
708C22—61no—
709C22—61no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22D3×#68712yes—
714C22C2×D3×C22⋊D511yescharacteristic
715C4—21no—
716C4—32no—
717C4—41no—
718C4—41no—
719C4—61no—
720C4—61no—
721C4—121no—
722C4—201no—
723C4—201no—
724C4—302no—
725C4—601no—
726C4#9201611yescharacteristic
727C4#9201911yescharacteristic
728C3#1061526211yescharacteristic, complemented, Sylow
729C2—22no—
730C2—62no—
731C2—241no—
732C2#1175465611yescharacteristic
733C2C2×D3×#68711yescharacteristic
734C2#1175511411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5507C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754377C2semidirect
3. C2×#91094C2semidirect
4. C3×#65260C2semidirect
5. #11748553C2semidirect
6. #11748547C2semidirect
7. #67⋊#168C2semidirect
8. #11747494C2semidirect
9. D3×#3942C2semidirect
10. #11747448C2semidirect
11. #11747422C2semidirect
12. #11747420C2semidirect
13. #11747297C2semidirect
14. #11747277C2semidirect
15. #11747179C2semidirect
73. #65260D3semidirect
205. Dic30#41semidirect
207. C5×#67SD16semidirect
523. #67#687semidirect
626. C3×C5#3298semidirect
704. C5#81450semidirect
728. C3#10615262semidirect

Maximal subgroups

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

subgroupindex
C5×#55072
#117543772
C2×#910942
C3×#652602
#117485532
#117485472
#67⋊#1682
#117474942
D3×#39422
#117474482
#117474222
#117474202
#117472972
#117472772
#117471792
#106152623
#814505