Finite Group Databasebeta

← C4×#91492 #14416243

Subgroups — C4×#91492 #14416243

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#711C211yesmaximal, characteristic, complemented
2C2×#91492C211yesmaximal, characteristic
3C4×#6773C211yesmaximal, characteristic, complemented
4C4×#6715C211yesmaximal, characteristic, complemented
5C4×C5×#214C211yesmaximal, characteristic, complemented
6Dic5×#214C211yesmaximal, characteristic, complemented
7#11748975C211yesmaximal, characteristic, complemented
8#11748961C211yesmaximal, characteristic, complemented
9#11747501C211yesmaximal, characteristic, complemented
10#11747433C211yesmaximal, characteristic, complemented
11#11747263C211yesmaximal, characteristic, complemented
12#11747225C211yesmaximal, characteristic, complemented
13C4×#6661C211yesmaximal, characteristic, complemented
14C4×#6658C211yesmaximal, characteristic, complemented
15C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
16C4×#4062—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18C2×#6773C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C2×#6715C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C2×C5×#214C2211yescharacteristic
23C4×C5×Dic6C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C3×C4×C22⋊D5—21no—
26C2×C3×C4×Dic5—21no—
27C3×#4038C2211yescharacteristic
28C3×#4033C2211yescharacteristic
29C3×#4027—21no—
30C3×#4023—21no—
31C3×C42×D5C2211yescharacteristic
32C3×C4×Dic10C2211yescharacteristic
33#91492C418yesdirect product factor
34#91444—21no—
35C4×#1202—21no—
36#91418C2211yescharacteristic
37#91402—21no—
38C4×#1200—21no—
39#91358C2211yescharacteristic
40Dic5×Dic6C2211yescharacteristic
41C2×#6661C2211yescharacteristic
42C2×#6658C2211yescharacteristic
43C2×D5×C3⋊C8C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91116C2211yescharacteristic
46#91093C2211yescharacteristic
47#91091C2211yescharacteristic
48C4×C3⋊#168C2211yescharacteristic
49C5×#832C2211yescharacteristic
50C5×#810C2211yescharacteristic
51C5×#808C2211yescharacteristic
52C4×C5×C3⋊C8C2211yescharacteristic
53#90989C2211yescharacteristic
54#90987C2211yescharacteristic
55#90972C2211yescharacteristic
56#90971C2211yescharacteristic
57#90970C2211yescharacteristic
58#90968C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60Dic5×C3⋊C8C2211yescharacteristic
61C4×#950—51nomaximal, Hall
62C2×#4062—31no—
63C4×#713—31no—
64C4×#711D311yescharacteristic, complemented
65C4×C5×SD16—31no—
66SD16×Dic5—31no—
67C4×#689—31no—
68C4×#686—31no—
69#65149—31no—
70#65141—31no—
71#65093—31no—
72#65079—31no—
73#65061—31no—
74#65045—31no—
75C4×#677—31no—
76C4×C8×D5—31no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C5×Dic6C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C22×C3×Dic5—21no—
84C22×C3×Dic5—21no—
85C3×#711—22no—
86C3×#711C2×C414yescomplemented
87C2×C3×C4×D5D411yescharacteristic
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×Dic10C2311yescharacteristic
91C2×#1202—21no—
92C2×#1200—21no—
93C2×#1200—21no—
94#6773—22no—
95#6773C2×C414yescomplemented
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C22⋊C4—21no—
98C3×C42×C5C2311yescharacteristic
99#6715C2×C414yescomplemented
100#6714—21no—
101C4⋊Dic15C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C5×#214C2×C414yescomplemented
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C4×C5×Dic3—21no—
108C2×C5×C3⋊C8C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C3×C22⋊Dic5—21no—
111C3×#685—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C3×C4×Dic5—21no—
116C3×C4×Dic5—21no—
117C3×C4×Dic5—21no—
118C3×C4×Dic5D411yescharacteristic
119C3×C4×Dic5D411yescharacteristic
120C3×C4×Dic5C2311yescharacteristic
121Dic3⋊Dic5—21no—
122#6667—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126#6661C2×C414yescomplemented
127#6658C2×C414yescomplemented
128D5×C3⋊C8—22no—
129D5×C3⋊C8C2×C414yescomplemented
130C3×C4×#41—51no—
131C2×#950—51no—
132C4×#235—51no—
133#5233—51no—
134C4×#216—51no—
135C4×#216—51no—
136C4×#215—51no—
137C4×#215—51no—
138C4×#214—51no—
139C4×#214D511yescharacteristic, complemented
140C4×#213—51no—
141C4×#213—51no—
142#5002—51no—
143#4998—51no—
144C2×C4×C3⋊C8—51no—
145C2×#713—31no—
146C2×#711C2×D311yescharacteristic
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4C2×D311yescharacteristic
150Q8×Dic5—31no—
151C2×#689—31no—
152D4×Dic5C2×D311yescharacteristic
153C2×#686—31no—
154C4×C22⋊D5—21no—
155C2×C4×Dic5—21no—
156#4062—38no—
157C2×#677—31no—
158C2×C8×D5—31no—
159C2×C8×D5—31no—
160#4039—31no—
161#4039—61no—
162#4038—31no—
163#4038—61no—
164#4038C2×D311yescharacteristic
165#4033C2×D311yescharacteristic
166#4027—21no—
167#4023—21no—
168C4×D20—31no—
169C4×D20—61no—
170C42×D5—61no—
171C42×D5C2×D311yescharacteristic
172C4×Dic10C2×D311yescharacteristic
173C5×#106—31no—
174C5×#103—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3949—31no—
181#3948—31no—
182C8×Dic5—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3941—31no—
186#3939—31no—
187#3939—31no—
188C4×#168—31no—
189C4×#135—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C3×D5C2×D411yescharacteristic
193C3×C5×D4—21no—
194C3×C5×D4C22×C412yes—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—42no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C2×Dic15—21no—
201D60—21no—
202D60C22×C412yes—
203C4×D15—42no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C5×Dic6—21no—
207C5×Dic6C22×C412yes—
208C3×C22⋊D5—24no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—24no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—42no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×C4×D5—22no—
217C3×C4×D5—22no—
218C3×C4×D5C22×C412yes—
219C3×C4×D5#4112yes—
220C3×Dic10—21no—
221C3×Dic10C22×C412yes—
222#1202—24no—
223#1200—24no—
224#1200—42no—
225C3⋊#168—21no—
226C3⋊#168C22×C412yes—
227C5×C3⋊C8—21no—
228C5×C3⋊C8C22×C412yes—
229C2×C3×#41—51no—
230C2×#235—51no—
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×D4—51no—
234C3×C4×D4—101no—
235C3×C4×D4—101no—
236C3×C4×D4C2×D511yescharacteristic
237C3×#117—51no—
238C3×#117—101no—
239C2×C3×C42—51no—
240C2×C3×C42—101no—
241#950—58no—
242C2×#216—51no—
243C2×#215—51no—
244C2×#214C2×D511yescharacteristic
245C2×#213—51no—
246C4×#67—101no—
247C4×#67—101no—
248#926—51no—
249C22×C3⋊C8—51no—
250C22×C3⋊C8—51no—
251C4×D12—51no—
252C4×D12—51no—
253#872—101no—
254C42×D3—101no—
255C4×Dic6—51no—
256C4×Dic6C2×D511yescharacteristic
257#835—51no—
258#835—51no—
259#832—51no—
260#832C2×D511yescharacteristic
261#810—51no—
262#810C2×D511yescharacteristic
263#809—51no—
264#809—51no—
265#808—51no—
266#808C2×D511yescharacteristic
267#807—51no—
268#807—51no—
269C4×C3⋊C8—51no—
270C4×C3⋊C8—51no—
271C4×C3⋊C8—51no—
272C4×C3⋊C8C2×D511yescharacteristic
273C2×C5×Q8—31no—
274C2×C5×D4C22×D311yescharacteristic
275C22×C4×C5—21no—
276C2×C22⋊D5—21no—
277C22×Dic5—21no—
278C22×Dic5—21no—
279#713—34no—
280#713—62no—
281#711—22no—
282#711C4×D314yescomplemented
283C2×D20—31no—
284C2×D20—61no—
285C2×C4×D5—61no—
286C2×C4×D5—61no—
287C2×C4×D5—61no—
288C2×C4×D5#6711yescharacteristic
289C2×C4×D5#6711yescharacteristic
290C2×C4×D5C22×D311yescharacteristic
291C2×Dic10C22×D311yescharacteristic
292C5×SD16—34no—
293C2×C5×C8—31no—
294C2×C5×C8—31no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C22⋊C4—21no—
299C42×C5—61no—
300C42×C5C22×D311yescharacteristic
301C22⋊Dic5—21no—
302#689—34no—
303#686—34no—
304#685—21no—
305#685—61no—
306#685—61no—
307#685—61no—
308C4⋊Dic5—31no—
309C4⋊Dic5—61no—
310C4⋊Dic5C22×D311yescharacteristic
311#683—21no—
312#683—21no—
313C4×Dic5—21no—
314C4×Dic5—21no—
315C4×Dic5—21no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C4×Dic5#6711yescharacteristic
319C4×Dic5#6711yescharacteristic
320C4×Dic5C22×D311yescharacteristic
321C2×#168—31no—
322C2×#168—31no—
323#677—34no—
324C8×D5—34no—
325C8×D5—62no—
326C2×#135—151no—
327C4×#41—51no—
328C4×#41—151no—
329C4×Q16—151no—
330C4×Q16—151no—
331C4×SD16—31no—
332C4×SD16—151no—
333C4×SD16—151no—
334C4×SD16—151no—
335C4×D8—151no—
336C4×D8—151no—
337#427—151no—
338#416—151no—
339#416—151no—
340C2×C4×C8—151no—
341C22×C3×C5—22no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5C4×D412yes—
351C3×C4×C5—21no—
352C3×C4×C5—41no—
353C3×C4×C5#13512yescomplemented
354C3×C4×C5C23×C411yescharacteristic
355C3×C4×C5C2×#4111yescharacteristic
356Dic15—41no—
357C3×Dic5—22no—
358C3×Dic5—21no—
359C3×Dic5—41no—
360C3×Dic5C4×D412yes—
361C3×Dic5#13512yescomplemented
362C5×Dic3—22no—
363C5×Dic3—41no—
364C3×#41—54no—
365C3×#41—102no—
366C2×C3×Q8—51no—
367C2×C3×D4—101no—
368C2×C3×D4C22×D511yescharacteristic
369C22×C3×C4—21no—
370C22×C3×C4—51no—
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—101no—
374C22×C3×C4—101no—
375C2×#67—101no—
376#235—54no—
377#235—102no—
378C2×D12—51no—
379C2×C4×D3—101no—
380C2×C4×D3—101no—
381C2×C4×D3—101no—
382C2×Dic6C22×D511yescharacteristic
383C3×C4⋊C4—51no—
384C3×C4⋊C4—101no—
385C3×C4⋊C4—101no—
386C3×C4⋊C4C22×D511yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—101no—
389C3×C22⋊C4—101no—
390C3×C42—51no—
391C3×C42—51no—
392C3×C42—51no—
393C3×C42—101no—
394C3×C42—101no—
395C3×C42—101no—
396C3×C42C22×D511yescharacteristic
397#217—101no—
398#216—54no—
399#215—54no—
400#214C4×D514yescomplemented
401#213—54no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404C4⋊Dic3—51no—
405C4⋊Dic3C22×D511yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—101no—
408C4×Dic3—21no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C2×C3⋊C8—51no—
412C2×C3⋊C8—54no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—102no—
415C2×C3⋊C8C22×D511yescharacteristic
416C2×C3⋊C8C22×D511yescharacteristic
417C23×C5—21no—
418C22×D5—61no—
419C22×D5C2×#6711yescharacteristic
420C5×Q8—32no—
421C5×Q8—61no—
422C5×D4—21no—
423C5×D4C2×C4×D312yes—
424C2×C4×C5—21no—
425C2×C4×C5—42no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5C2×#6711yescharacteristic
429C2×C4×C5C2×#6711yescharacteristic
430C2×C4×C5C23×D311yescharacteristic
431C22⋊D5—24no—
432C2×Dic5—21no—
433C2×Dic5—24no—
434C2×Dic5—21no—
435C2×Dic5—42no—
436C2×Dic5—61no—
437C2×Dic5C2×#6711yescharacteristic
438C2×Dic5C2×#6711yescharacteristic
439C2×Dic5C2×#6711yescharacteristic
440D20—32no—
441D20—64no—
442D20—61no—
443C4×D5—22no—
444C4×D5—22no—
445C4×D5—64no—
446C4×D5—122no—
447C4×D5—122no—
448C4×D5C2×C4×D312yes—
449C4×D5#23512yes—
450Dic10—21no—
451Dic10C2×C4×D312yes—
452C5×C8—32no—
453C5×C8—61no—
454#168—32no—
455#168—61no—
456C2×#41—51no—
457C2×#41—151no—
458#135—158no—
459C2×Q16—151no—
460C2×SD16—31no—
461C2×SD16—151no—
462C2×D8—151no—
463C22×C8—151no—
464C22×C8—151no—
465C4×Q8—31no—
466C4×Q8—51no—
467C4×Q8—51no—
468C4×Q8—151no—
469C4×D4—51no—
470C4×D4—101no—
471C4×D4—101no—
472C4×D4—151no—
473C4×D4—151no—
474C4×D4—301no—
475C4×D4—301no—
476C4×D4D3×D511yescharacteristic
477#117—51no—
478#117—101no—
479#117—151no—
480#117—301no—
481C2×C42—51no—
482C2×C42—101no—
483C2×C42—301no—
484#107—151no—
485#107—151no—
486#106—31no—
487#106—151no—
488#103—31no—
489#103—151no—
490#103—151no—
491#103—151no—
492#102—31no—
493#102—151no—
494#102—151no—
495#102—151no—
496C4×C8—31no—
497C4×C8—151no—
498C4×C8—151no—
499C4×C8—151no—
500C2×C3×C5—42no—
501C2×C3×C5C2×C4×D411yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504D15—42no—
505C3×D5—22no—
506C23×C3—21no—
507C23×C3—51no—
508C22×D3—101no—
509C3×Q8—52no—
510C3×Q8—101no—
511C3×D4—21no—
512C3×D4—104no—
513C3×D4C2×C4×D512yes—
514C2×C3×C4—21no—
515C2×C3×C4—42no—
516C2×C3×C4—51no—
517C2×C3×C4—51no—
518C2×C3×C4—52no—
519C2×C3×C4—52no—
520C2×C3×C4—51no—
521C2×C3×C4—102no—
522C2×C3×C4—104no—
523C2×C3×C4—101no—
524C2×C3×C4—102no—
525C2×C3×C4—101no—
526C2×C3×C4—202no—
527C2×C3×C4D4×D511yescharacteristic
528C2×C3×C4D4×D511yescharacteristic
529C2×C3×C4C23×D511yescharacteristic
530#67—104no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—101no—
534D12—52no—
535D12—101no—
536C4×D3—104no—
537C4×D3—202no—
538C4×D3—202no—
539Dic6—21no—
540Dic6C2×C4×D512yes—
541C3⋊C8—21no—
542C3⋊C8—52no—
543C3⋊C8—101no—
544C3⋊C8C2×C4×D512yes—
545C22×C5—22no—
546C22×C5—41no—
547C22×C5—41no—
548C22×C5C22×#6711yescharacteristic
549C2×D5—21no—
550C2×D5—21no—
551C2×D5—62no—
552C2×D5—121no—
553C2×D5—121no—
554C2×D5C4×#6712yes—
555C4×C5—21no—
556C4×C5—41no—
557C4×C5—62no—
558C4×C5—121no—
559C4×C5#95012yescomplemented
560C4×C5C22×C4×D311yescharacteristic
561C4×C5C2×#23511yescharacteristic
562Dic5—22no—
563Dic5—21no—
564Dic5—41no—
565Dic5—121no—
566Dic5C4×#6712yes—
567Dic5#95012yescomplemented
568#41—54no—
569#41—102no—
570#41—154no—
571#41—302no—
572C2×Q8—31no—
573C2×Q8—51no—
574C2×D4—101no—
575C2×D4—151no—
576C2×D4—301no—
577C2×D4C2×D3×D511yescharacteristic
578C22×C4—21no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—51no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—301no—
585C22×C4—301no—
586C22×C4—301no—
587Q16—154no—
588SD16—34no—
589SD16—154no—
590D8—154no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—154no—
594C2×C8—151no—
595C2×C8—151no—
596C2×C8—302no—
597C4⋊C4—31no—
598C4⋊C4—51no—
599C4⋊C4—61no—
600C4⋊C4—101no—
601C4⋊C4—101no—
602C4⋊C4—151no—
603C4⋊C4—301no—
604C4⋊C4C2×D3×D511yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—101no—
607C22⋊C4—101no—
608C22⋊C4—301no—
609C22⋊C4—301no—
610C22⋊C4—301no—
611C42—51no—
612C42—51no—
613C42—51no—
614C42—61no—
615C42—101no—
616C42—101no—
617C42—101no—
618C42—301no—
619C42—301no—
620C42C2×D3×D511yescharacteristic
621C3×C5C4×#13511yescharacteristic, complemented, Hall
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—52no—
626C22×C3—101no—
627C22×C3—101no—
628C22×C3C2×D4×D511yescharacteristic
629C2×D3—102no—
630C2×D3—201no—
631C2×D3—201no—
632C3×C4—21no—
633C3×C4—41no—
634C3×C4—52no—
635C3×C4—52no—
636C3×C4—101no—
637C3×C4—102no—
638C3×C4—201no—
639C3×C4#406212yescomplemented
640C3×C4C22×C4×D511yescharacteristic
641C3×C4D5×#4111yescharacteristic
642Dic3—22no—
643Dic3—41no—
644Dic3—201no—
645C2×C5—42no—
646C2×C5C2×C4×#6711yescharacteristic
647C2×C5C2×#95011yescharacteristic
648C2×C5C2×#95011yescharacteristic
649D5—22no—
650D5—122no—
651C23—21no—
652C23—51no—
653C23—301no—
654Q8—32no—
655Q8—52no—
656Q8—61no—
657Q8—101no—
658D4—21no—
659D4—104no—
660D4—152no—
661D4—304no—
662D4—301no—
663D4C4×D3×D512yes—
664C2×C4—21no—
665C2×C4—42no—
666C2×C4—51no—
667C2×C4—51no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—51no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—102no—
674C2×C4—104no—
675C2×C4—101no—
676C2×C4—102no—
677C2×C4—101no—
678C2×C4—202no—
679C2×C4—304no—
680C2×C4—301no—
681C2×C4—602no—
682C2×C4—602no—
683C2×C4D5×#6711yescharacteristic
684C2×C4D5×#6711yescharacteristic
685C2×C4C22×D3×D511yescharacteristic
686C8—32no—
687C8—61no—
688C8—152no—
689C8—301no—
690C2×C3—42no—
691C2×C3—102no—
692C2×C3C4×D4×D511yescharacteristic
693C2×C3C2×#406211yescharacteristic
694C2×C3D5×#13511yescharacteristic
695D3—202no—
696C5C4×#95011yescharacteristic, complemented, Sylow
697C22—22no—
698C22—41no—
699C22—41no—
700C22—52no—
701C22—101no—
702C22—101no—
703C22—302no—
704C22—601no—
705C22—601no—
706C22C2×D5×#6711yescharacteristic
707C4—21no—
708C4—41no—
709C4—52no—
710C4—52no—
711C4—62no—
712C4—102no—
713C4—101no—
714C4—121no—
715C4—201no—
716C4—601no—
717C4#9149212yesdirect product factor
718C4C2×C4×D3×D511yescharacteristic
719C4D5×#23511yescharacteristic
720C3C4×#406211yescharacteristic, complemented, Sylow
721C2—42no—
722C2—102no—
723C2—602no—
724C2C4×D5×#6711yescharacteristic
725C2C2×#9149211yescharacteristic
726C2D5×#95011yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91492C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×#711C2semidirect
3. C4×#6773C2semidirect
4. C4×#6715C2semidirect
5. C4×C5×#214C2semidirect
6. Dic5×#214C2semidirect
7. #11748975C2semidirect
8. #11748961C2semidirect
9. #11747501C2semidirect
10. #11747433C2semidirect
11. #11747263C2semidirect
12. #11747225C2semidirect
13. C4×#6661C2semidirect
14. C4×#6658C2semidirect
15. C4×D5×C3⋊C8C2semidirect
33. #91492C4direct (N × H)
64. C4×#711D3semidirect
86. C3×#711C2×C4semidirect
95. #6773C2×C4semidirect
99. #6715C2×C4semidirect
104. C5×#214C2×C4semidirect
126. #6661C2×C4semidirect
127. #6658C2×C4semidirect
129. D5×C3⋊C8C2×C4semidirect
139. C4×#214D5semidirect
282. #711C4×D3semidirect
353. C3×C4×C5#135semidirect
361. C3×Dic5#135semidirect
400. #214C4×D5semidirect
559. C4×C5#950semidirect
567. Dic5#950semidirect
621. C3×C5C4×#135semidirect
639. C3×C4#4062semidirect
696. C5C4×#950semidirect
717. C4#91492direct (N × H)
720. C3C4×#4062semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7112
C2×#914922
C4×#67732
C4×#67152
C4×C5×#2142
Dic5×#2142
#117489752
#117489612
#117475012
#117474332
#117472632
#117472252
C4×#66612
C4×#66582
C4×D5×C3⋊C82
C4×#40623
C4×#9505