Finite Group Databasebeta

← #14412605

Subgroups — #14412605

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C2×C3×D5×M16C211yesmaximal, characteristic, complemented
3C2×#91358C211yesmaximal, characteristic, complemented
4#11751234C211yesmaximal, characteristic, complemented
5C5×#5133C211yesmaximal, characteristic, complemented
6#11748394C211yesmaximal, characteristic, complemented
7#11748390C211yesmaximal, characteristic, complemented
8#11748135C212yesmaximal, complemented
9#11748122C212yesmaximal, complemented
10#11748105C212yesmaximal, complemented
11#11747642C212yesmaximal, complemented
12#10610612—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×D5×#67—21no—
17C2×#6782—21no—
18D5×#235—24no—
19D5×#235C418yescomplemented
20C2×D5×D12C2211yescharacteristic
21C2×C4×D3×D5—21no—
22C2×#6773C2211yescharacteristic
23C2×#6772C2211yescharacteristic
24C2×#6771—21no—
25C2×D5×Dic6C2211yescharacteristic
26C2×C3×C5×M16C2211yescharacteristic, complemented
27C2×C4⋊Dic15C2211yescharacteristic, complemented
28C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#681C2211yescharacteristic, complemented
30C3×D5×M16—24no—
31C2×C3×#676C2212yes—
32C2×C3×C8×D5C2212yescomplemented
33C2×#6665—21no—
34C2×Dic3×Dic5—21no—
35#91358—21no—
36#91358—21no—
37#91358C2212yes—
38#91358C2212yescomplemented
39#91105C2212yescomplemented
40#91100C2212yescomplemented
41C5×#821C2212yescomplemented
42C5×#816C2212yescomplemented
43#90975C2212yescomplemented
44#90973C2212yescomplemented
45#90969C2212yescomplemented
46#90967C2212yescomplemented
47#83768—51nomaximal, Hall
48C2×D5×#41—31no—
49C2×D5×M16D311yescharacteristic, complemented
50C2×#4038—31no—
51C5×#417—31no—
52#65521—31no—
53#65422—31no—
54#65255—31no—
55#65093—32no—
56#65091—32no—
57#65061—32no—
58#65059—32no—
59C23×C3×D5D411yescharacteristic
60C22×D3×D5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63C22×Dic15—21no—
64#6817—22no—
65#6817C2×C414yes—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×#67—21no—
70C22×C5×Dic3—21no—
71C5×#235—22no—
72C5×#235C2×C414yes—
73C2×C5×D12C2311yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C5×Dic6C2311yescharacteristic
76C22×C3×Dic5D411yescharacteristic
77C2×C3×C4×D5C2×C414yes—
78C2×C3×C4×D5D411yescharacteristic
79C2×C3×C4×D5D411yescharacteristic
80C2×C3×C4×D5D414yes—
81C2×C3×C4×D5C2311yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83D5×#67—28no—
84C2×#1204—21no—
85C2×#1203—21no—
86C2×#1202—21no—
87C2×#1201—21no—
88C2×#1200—21no—
89#6782—28no—
90C2×D3×Dic5—21no—
91C2×D5×Dic3—21no—
92D5×D12—22no—
93D5×D12C2×C414yescomplemented
94C4×D3×D5—28no—
95#6773—22no—
96#6773C2×C414yescomplemented
97#6772—22no—
98#6772C2×C414yescomplemented
99#6771—28no—
100D5×Dic6—22no—
101D5×Dic6C2×C414yescomplemented
102C3×C5×M16—22no—
103C2×C3×C5×C8C2312yes—
104C4⋊Dic15—21no—
105C4⋊Dic15C2312yes—
106C5×C4⋊Dic3—21no—
107C5×C4⋊Dic3C2312yes—
108C3×#681—22no—
109C2×C3×#168C2312yes—
110C3×#676—24no—
111C3×C8×D5—24no—
112#6665—22no—
113#6665—22no—
114Dic3×Dic5—22no—
115Dic3×Dic5—22no—
116C22×#235—51no—
117C22×C3×M16—51no—
118C2×#926—51no—
119#5133—51no—
120#5133—51no—
121#5133—51no—
122#5133D511yescharacteristic, complemented
123#5131—52no—
124#5120—52no—
125#5113—52no—
126#5113—52no—
127C2×C5×#41—31no—
128D5×#41—38no—
129D5×#41—64no—
130C2×#713—31no—
131C2×Q8×D5—31no—
132C2×#711—31no—
133C2×#711—61no—
134C2×D4×D5—31no—
135C2×D4×D5—61no—
136C2×#709—31no—
137C2×#709—61no—
138C22×C4×D5—61no—
139C22×C4×D5C2×D311yescharacteristic
140C2×C5×M16C2×D311yescharacteristic, complemented
141C2×C5×C4⋊C4—31no—
142C2×#685—61no—
143C2×C4⋊Dic5—31no—
144C2×C4×Dic5—61no—
145C2×#681C2×D311yescharacteristic, complemented
146D5×M16—24no—
147C2×#676C2×D312yes—
148C2×C8×D5C2×D312yescomplemented
149#4038—32no—
150#4038—32no—
151#4038—61no—
152#4038—61no—
153C5×#103—32no—
154C5×#102—32no—
155#3967—32no—
156#3964—32no—
157#3953—32no—
158#3948—32no—
159#3942—32no—
160#3941—32no—
161#2896—151noSylow
162C23×C3×C5C2×D411yescharacteristic
163C22×D15—21no—
164C22×C5×D3—21no—
165C22×C3×D5—41no—
166C22×C3×D5—41no—
167C22×C3×D5C22⋊C414yes—
168C22×C3×D5C2×D411yescharacteristic
169C22×C3×D5C2×D411yescharacteristic
170C2×D3×D5—24no—
171C2×D3×D5—42no—
172C2×D3×D5—42no—
173C2×C3×C4×C5C22×C412yes—
174C2×C3×C4×C5C2×D411yescharacteristic
175C2×C3×C4×C5C2×D412yes—
176C2×C3×C4×C5C2411yescharacteristic
177#1220—24no—
178C2×Dic15—21no—
179C2×Dic15—22no—
180C2×Dic15—42no—
181D60—21no—
182D60C22×C412yes—
183C4×D15—24no—
184Dic30—21no—
185Dic30C22×C412yes—
186C5×#67—24no—
187C2×C5×Dic3—21no—
188C2×C5×Dic3—22no—
189C2×C5×Dic3—42no—
190C5×D12—21no—
191C5×D12C22×C412yes—
192C4×C5×D3—24no—
193C5×Dic6—21no—
194C5×Dic6C22×C412yes—
195C2×C3×Dic5C22⋊C414yes—
196C2×C3×Dic5C2×D411yescharacteristic
197C2×C3×Dic5C2×D411yescharacteristic
198C3×C4×D5C22⋊C414yes—
199C3×C4×D5C22⋊C414yes—
200C3×C4×D5C22×C412yes—
201C3×C4×D5C22×C412yes—
202C3×C4×D5C2×D412yes—
203C3×C4×D5C2×D412yes—
204#1204—24no—
205#1203—24no—
206#1202—24no—
207#1201—24no—
208#1200—24no—
209D3×Dic5—24no—
210D5×Dic3—24no—
211C3×C5×C8—22no—
212C3×#168—22no—
213C23×C3×C4—51no—
214C22×#67—101no—
215C2×#235—51no—
216C2×#235—58no—
217C2×#235—51no—
218C2×#235—51no—
219C2×#235—101no—
220C2×#235—104no—
221C2×#235—101no—
222C2×#235C2×D511yescharacteristic
223C22×D12—51no—
224C22×C4×D3—101no—
225C22×Dic6—51no—
226C2×C3×M16—51no—
227C2×C3×M16—52no—
228C2×C3×M16—104no—
229C2×C3×M16C2×D511yescharacteristic, complemented
230C22×C3×C8—52no—
231C2×#217—101no—
232#926—52no—
233#926—52no—
234#926—101no—
235#926—101no—
236C2×C4⋊Dic3—51no—
237C2×C4⋊Dic3C2×D511yescharacteristic, complemented
238C2×C4×Dic3—101no—
239#821—52no—
240#821—52no—
241#821—52no—
242#821C2×D512yescomplemented
243#816—52no—
244#816—52no—
245#816—52no—
246#816C2×D512yescomplemented
247C23×D5—61no—
248C23×D5D1211yescharacteristic
249C5×#41—34no—
250C5×#41—62no—
251C2×C5×Q8—31no—
252C2×C5×D4—31no—
253C2×C5×D4—61no—
254C22×C4×C5—61no—
255C22×C4×C5—61no—
256C22×C4×C5C22×D311yescharacteristic
257C2×C22⋊D5—61no—
258C2×C22⋊D5—61no—
259C2×C22⋊D5—61no—
260C22×Dic5—61no—
261C22×Dic5—61no—
262C22×Dic5D1211yescharacteristic
263#713—34no—
264#713—62no—
265Q8×D5—34no—
266Q8×D5—62no—
267#711—34no—
268#711—68no—
269#711—62no—
270D4×D5—34no—
271D4×D5—68no—
272D4×D5—62no—
273#709—34no—
274#709—62no—
275#709—68no—
276C2×D20—31no—
277C2×D20—61no—
278C2×C4×D5—61no—
279C2×C4×D5—61no—
280C2×C4×D5—61no—
281C2×C4×D5—68no—
282C2×C4×D5C4×D314yes—
283C2×C4×D5D1211yescharacteristic
284C2×C4×D5D1211yescharacteristic
285C2×C4×D5#6714yes—
286C2×C4×D5C22×D311yescharacteristic
287C2×C4×D5C22×D311yescharacteristic
288C2×Dic10—31no—
289C2×Dic10—61no—
290C5×M16—22no—
291C2×C5×C8C22×D312yes—
292C5×C4⋊C4—32no—
293C5×C4⋊C4—61no—
294#685—62no—
295#685—62no—
296C4⋊Dic5—32no—
297C4⋊Dic5—61no—
298C4×Dic5—62no—
299C4×Dic5—62no—
300#681—22no—
301C2×#168C22×D312yes—
302#676—24no—
303C8×D5—24no—
304C22×#41—151no—
305C22×M16—51no—
306C2×#117—151no—
307#419—152no—
308#418—152no—
309#417—31no—
310#417—151no—
311#417—151no—
312#417—151no—
313#416—152no—
314#416—152no—
315C22×C3×C5—21no—
316C22×C3×C5—21no—
317C22×C3×C5C2×C22⋊C412yes—
318C22×C3×C5C22×D411yescharacteristic
319C2×D15—22no—
320C2×D15—41no—
321C2×D15—41no—
322C2×C5×D3—22no—
323C2×C5×D3—41no—
324C2×C5×D3—41no—
325C2×C3×D5—21no—
326C2×C3×D5—21no—
327C2×C3×D5—21no—
328C2×C3×D5—21no—
329C2×C3×D5—44no—
330C2×C3×D5C2×C22⋊C412yes—
331C2×C3×D5C2×C22⋊C412yes—
332D3×D5—48no—
333C3×C4×C5C2×C22⋊C412yes—
334C3×C4×C5C23×C411yescharacteristic
335C3×C4×C5C22×D411yescharacteristic
336Dic15—22no—
337Dic15—42no—
338C3×Dic5C2×C22⋊C412yes—
339C3×Dic5C2×C22⋊C412yes—
340C5×Dic3—22no—
341C5×Dic3—42no—
342C24×C3—51no—
343C23×D3—101no—
344C22×C3×C4—51no—
345C22×C3×C4—54no—
346C22×C3×C4—51no—
347C22×C3×C4—51no—
348C22×C3×C4—54no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4C22×D511yescharacteristic
352C2×#67—21no—
353C2×#67—101no—
354C2×#67—108no—
355C2×#67—101no—
356C2×#67—101no—
357C22×Dic3—21no—
358C22×Dic3—101no—
359C22×Dic3—101no—
360#235—22no—
361#235—54no—
362#235—54no—
363#235—54no—
364#235—102no—
365#235—108no—
366#235—102no—
367#235—108no—
368#235—102no—
369#235C4×D514yes—
370C2×D12—51no—
371C2×D12—54no—
372C2×D12—102no—
373C2×D12—101no—
374C2×D12C22×D511yescharacteristic
375C2×C4×D3—21no—
376C2×C4×D3—108no—
377C2×C4×D3—101no—
378C2×C4×D3—101no—
379C2×C4×D3—101no—
380C2×Dic6—51no—
381C2×Dic6—54no—
382C2×Dic6—102no—
383C2×Dic6—101no—
384C2×Dic6C22×D511yescharacteristic
385C3×M16—22no—
386C3×M16—104no—
387C3×M16—102no—
388C2×C3×C8—52no—
389C2×C3×C8—104no—
390C2×C3×C8C22×D512yes—
391#217—102no—
392#217—102no—
393C4⋊Dic3—21no—
394C4⋊Dic3—52no—
395C4⋊Dic3—101no—
396C4⋊Dic3C22×D512yes—
397C4×Dic3—102no—
398C4×Dic3—102no—
399C23×C5—61no—
400C23×C5C2×D1211yescharacteristic
401C22×D5—41no—
402C22×D5—41no—
403C22×D5—61no—
404C22×D5—64no—
405C22×D5—122no—
406C22×D5—122no—
407C22×D5(C2×D3)⋊C414yes—
408C22×D5C2×D1211yescharacteristic
409C22×D5C2×D1211yescharacteristic
410C5×Q8—32no—
411C5×Q8—61no—
412C5×D4—32no—
413C5×D4—64no—
414C5×D4—61no—
415C2×C4×C5—61no—
416C2×C4×C5—64no—
417C2×C4×C5—62no—
418C2×C4×C5—122no—
419C2×C4×C5C2×C4×D312yes—
420C2×C4×C5C2×D1211yescharacteristic
421C2×C4×C5C2×#6712yes—
422C2×C4×C5C23×D311yescharacteristic
423C22⋊D5—64no—
424C22⋊D5—64no—
425C22⋊D5—64no—
426C2×Dic5—61no—
427C2×Dic5—64no—
428C2×Dic5—62no—
429C2×Dic5—122no—
430C2×Dic5(C2×D3)⋊C414yes—
431C2×Dic5C2×D1211yescharacteristic
432C2×Dic5C2×D1211yescharacteristic
433D20—32no—
434D20—64no—
435D20—61no—
436C4×D5—64no—
437C4×D5—64no—
438C4×D5—64no—
439C4×D5(C2×D3)⋊C414yes—
440C4×D5(C2×D3)⋊C414yes—
441C4×D5C2×C4×D312yes—
442C4×D5C2×C4×D312yes—
443C4×D5C2×#6712yes—
444C4×D5C2×#6712yes—
445Dic10—32no—
446Dic10—61no—
447Dic10—64no—
448C5×C8—22no—
449#168—22no—
450C2×#41—31no—
451C2×#41—151no—
452C2×#41—151no—
453C2×#41—158no—
454C2×#41—151no—
455C2×#41—301no—
456C2×#41—301no—
457C2×#41—304no—
458C22×Q8—151no—
459C22×D4—151no—
460C22×D4—301no—
461C23×C4—51no—
462C23×C4—301no—
463C2×M16—51no—
464C2×M16—52no—
465C2×M16—104no—
466C2×M16D3×D511yescharacteristic, complemented
467C22×C8—52no—
468#117—152no—
469#117—152no—
470#117—301no—
471#117—301no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—151no—
474C2×C22⋊C4—301no—
475C2×C42—301no—
476#103—32no—
477#103—152no—
478#103—152no—
479#103—152no—
480#102—32no—
481#102—152no—
482#102—152no—
483#102—152no—
484C2×C3×C5—22no—
485C2×C3×C5C22×C22⋊C411yescharacteristic
486C2×C3×C5#57511yescharacteristic
487C2×C3×C5#57511yescharacteristic
488D15—42no—
489C3×D5—22no—
490C3×D5—22no—
491C5×D3—42no—
492C23×C3—51no—
493C23×C3—51no—
494C23×C3—54no—
495C23×C3—201no—
496C23×C3—201no—
497C23×C3D4×D511yescharacteristic
498C22×D3—21no—
499C22×D3—104no—
500C22×D3—101no—
501C22×D3—202no—
502C22×D3—202no—
503C2×C3×C4—51no—
504C2×C3×C4—51no—
505C2×C3×C4—54no—
506C2×C3×C4—52no—
507C2×C3×C4—52no—
508C2×C3×C4—52no—
509C2×C3×C4—52no—
510C2×C3×C4—54no—
511C2×C3×C4—54no—
512C2×C3×C4C2×C4×D512yes—
513C2×C3×C4D4×D511yescharacteristic
514C2×C3×C4D4×D512yes—
515C2×C3×C4C23×D511yescharacteristic
516#67—24no—
517#67—104no—
518#67—104no—
519#67—104no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—42no—
523C2×Dic3—104no—
524C2×Dic3—101no—
525C2×Dic3—102no—
526C2×Dic3—202no—
527D12—21no—
528D12—52no—
529D12—104no—
530D12—101no—
531D12C2×C4×D512yes—
532C4×D3—24no—
533C4×D3—104no—
534C4×D3—104no—
535C4×D3—104no—
536Dic6—21no—
537Dic6—52no—
538Dic6—104no—
539Dic6—101no—
540Dic6C2×C4×D512yes—
541C3×C8—22no—
542C3×C8—102no—
543C22×C5—21no—
544C22×C5—21no—
545C22×C5—62no—
546C22×C5—121no—
547C22×C5—121no—
548C22×C5C2×(C2×D3)⋊C412yes—
549C22×C5C22×D1211yescharacteristic
550C2×D5—21no—
551C2×D5—21no—
552C2×D5—21no—
553C2×D5—21no—
554C2×D5—44no—
555C2×D5—62no—
556C2×D5—128no—
557C2×D5—121no—
558C2×D5—121no—
559C2×D5C2×(C2×D3)⋊C412yes—
560C2×D5C2×(C2×D3)⋊C412yes—
561C4×C5—62no—
562C4×C5—122no—
563C4×C5C2×(C2×D3)⋊C412yes—
564C4×C5C22×C4×D311yescharacteristic
565C4×C5C22×#6711yescharacteristic
566Dic5—62no—
567Dic5—122no—
568Dic5C2×(C2×D3)⋊C412yes—
569Dic5C2×(C2×D3)⋊C412yes—
570C24—51no—
571C24—301no—
572#41—34no—
573#41—62no—
574#41—154no—
575#41—154no—
576#41—154no—
577#41—308no—
578#41—308no—
579#41—302no—
580#41—302no—
581#41—302no—
582C2×Q8—31no—
583C2×Q8—154no—
584C2×Q8—151no—
585C2×Q8—301no—
586C2×Q8—302no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—154no—
590C2×D4—151no—
591C2×D4—302no—
592C2×D4—301no—
593C2×D4—301no—
594C2×D4—308no—
595C2×D4—301no—
596C2×D4—301no—
597C22×C4—51no—
598C22×C4—54no—
599C22×C4—51no—
600C22×C4—51no—
601C22×C4—54no—
602C22×C4—51no—
603C22×C4—51no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—301no—
607C22×C4—308no—
608C22×C4—301no—
609C22×C4—301no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4C2×D3×D511yescharacteristic
613M16—22no—
614M16—104no—
615M16—102no—
616C2×C8—52no—
617C2×C8—104no—
618C2×C8C2×D3×D512yes—
619C4⋊C4—32no—
620C4⋊C4—61no—
621C4⋊C4—152no—
622C4⋊C4—301no—
623C22⋊C4—302no—
624C22⋊C4—302no—
625C42—302no—
626C42—302no—
627C3×C5#289611yescharacteristic, complemented, Hall
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—52no—
631C22×C3—52no—
632C22×C3—101no—
633C22×C3—101no—
634C22×C3—101no—
635C22×C3—101no—
636C22×C3—204no—
637C22×C3D5×C22⋊C412yes—
638C22×C3C2×D4×D511yescharacteristic
639C2×D3—22no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—102no—
643C2×D3—208no—
644C2×D3—201no—
645C2×D3—201no—
646C3×C4—52no—
647C3×C4—52no—
648C3×C4D5×C22⋊C412yes—
649C3×C4C22×C4×D511yescharacteristic
650C3×C4C2×D4×D511yescharacteristic
651Dic3—22no—
652Dic3—42no—
653Dic3—102no—
654Dic3—202no—
655C2×C5—22no—
656C2×C5—122no—
657C2×C5#574811yescharacteristic
658C2×C5#574811yescharacteristic
659C2×C5C22×(C2×D3)⋊C411yescharacteristic
660D5—22no—
661D5—22no—
662D5—122no—
663C23—51no—
664C23—51no—
665C23—54no—
666C23—61no—
667C23—201no—
668C23—201no—
669C23—304no—
670C23—301no—
671C23—602no—
672C23—602no—
673C23D5×D1211yescharacteristic
674Q8—32no—
675Q8—61no—
676Q8—152no—
677Q8—304no—
678Q8—301no—
679D4—32no—
680D4—64no—
681D4—61no—
682D4—152no—
683D4—304no—
684D4—304no—
685D4—304no—
686D4—304no—
687D4—301no—
688C2×C4—54no—
689C2×C4—51no—
690C2×C4—51no—
691C2×C4—54no—
692C2×C4—54no—
693C2×C4—52no—
694C2×C4—52no—
695C2×C4—52no—
696C2×C4—52no—
697C2×C4—61no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—122no—
701C2×C4—304no—
702C2×C4—304no—
703C2×C4—304no—
704C2×C4—301no—
705C2×C4—304no—
706C2×C4—302no—
707C2×C4—602no—
708C2×C4C4×D3×D512yes—
709C2×C4D5×D1211yescharacteristic
710C2×C4D5×#6712yes—
711C2×C4C22×D3×D511yescharacteristic
712C8—22no—
713C8—102no—
714C2×C3—22no—
715C2×C3—102no—
716C2×C3—102no—
717C2×C3C2×D5×C22⋊C411yescharacteristic
718C2×C3#6610711yescharacteristic
719C2×C3#6611111yescharacteristic
720D3—42no—
721D3—202no—
722C5#8376811yescharacteristic, complemented, Sylow
723C22—21no—
724C22—21no—
725C22—52no—
726C22—52no—
727C22—62no—
728C22—101no—
729C22—101no—
730C22—101no—
731C22—101no—
732C22—121no—
733C22—121no—
734C22—204no—
735C22—302no—
736C22—608no—
737C22—601no—
738C22—601no—
739C22D5×(C2×D3)⋊C412yes—
740C22C2×D5×D1211yescharacteristic
741C4—52no—
742C4—52no—
743C4—62no—
744C4—122no—
745C4—302no—
746C4—602no—
747C4D5×(C2×D3)⋊C412yes—
748C4C2×C4×D3×D511yescharacteristic
749C4C2×D5×#6711yescharacteristic
750C3#1061061211yescharacteristic, complemented, Sylow
751C2—22no—
752C2—102no—
753C2—102no—
754C2—122no—
755C2—602no—
756C2#1175402111yescharacteristic
757C2#1175402211yescharacteristic
758C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×#235C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2896
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×M16C2semidirect
3. C2×#91358C2semidirect
4. #11751234C2semidirect
5. C5×#5133C2semidirect
6. #11748394C2semidirect
7. #11748390C2semidirect
8. #11748135C2semidirect
9. #11748122C2semidirect
10. #11748105C2semidirect
11. #11747642C2semidirect
19. D5×#235C4semidirect
26. C2×C3×C5×M16C22semidirect
27. C2×C4⋊Dic15C22semidirect
28. C2×C5×C4⋊Dic3C22semidirect
29. C2×C3×#681C22semidirect
32. C2×C3×C8×D5C22semidirect
38. #91358C22semidirect
39. #91105C22semidirect
40. #91100C22semidirect
41. C5×#821C22semidirect
42. C5×#816C22semidirect
43. #90975C22semidirect
44. #90973C22semidirect
45. #90969C22semidirect
46. #90967C22semidirect
49. C2×D5×M16D3semidirect
93. D5×D12C2×C4semidirect
96. #6773C2×C4semidirect
98. #6772C2×C4semidirect
101. D5×Dic6C2×C4semidirect
122. #5133D5semidirect
140. C2×C5×M16C2×D3semidirect
145. C2×#681C2×D3semidirect
148. C2×C8×D5C2×D3semidirect
229. C2×C3×M16C2×D5semidirect
237. C2×C4⋊Dic3C2×D5semidirect
242. #821C2×D5semidirect
246. #816C2×D5semidirect
466. C2×M16D3×D5semidirect
627. C3×C5#2896semidirect
722. C5#83768semidirect
750. C3#10610612semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C2×C3×D5×M162
C2×#913582
#117512342
C5×#51332
#117483942
#117483902
#117481352
#117481222
#117481052
#117476422
#106106123
#837685