Finite Group Databasebeta

← #14296992

Subgroups — #14296992

Order 1920.

1696 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
1C22×D3×D20C211yesmaximal, characteristic
2C2×#91093C211yesmaximal, characteristic, complemented
3C5×#4987C211yesmaximal, characteristic, complemented
4C2×C3×#3941C211yesmaximal, characteristic, complemented
5C2×#90969C211yesmaximal, characteristic, complemented
6C2×#90964C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊#168C211yesmaximal, characteristic, complemented
8#10600314—31nomaximal, Hall
9C23×D3×D5—21no—
10C22×D60C2211yescharacteristic
11C22×C4×C5×D3C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13C22×#1202—21no—
14C2×D3×D20—22no—
15C2×D3×D20—22no—
16C2×D3×D20—22no—
17C2×D3×D20—22no—
18C2×D3×D20—22no—
19C2×D3×D20C414yescomplemented
20C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
21C22×C3⋊#168C2211yescharacteristic, complemented
22C2×C5×(C2×D3)⋊C4—21no—
23C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
24C22×C3×#168C2211yescharacteristic, complemented
25#91093—22no—
26C5×C3⋊#95—21no—
27C3×#3941—22no—
28#90969—22no—
29#90964—22no—
30(C2×D3)⋊#168—22no—
31#70198—51nomaximal, Hall
32C23×D20—31no—
33C5×#380—31no—
34C2×C22⋊#168—31no—
35C2×#3941—31no—
36C2×#3941—31no—
37C2×#3941—31no—
38C2×#3941D311yescharacteristic, complemented
39C23×D15—21no—
40C23×C5×D3D411yescharacteristic
41C23×C3×D5—21no—
42C22×D3×D5—24no—
43C22×D3×D5—24no—
44C22×D3×D5—24no—
45C22×D3×D5—42no—
46C22×D3×D5—42no—
47C22×D3×D5—42no—
48C22×D3×D5—42no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×D60—21no—
52C2×D60—21no—
53C2×D60—21no—
54C2×D60C2×C412yes—
55C2×D60D412yes—
56C2×D60D412yes—
57C22×C5×Dic3—21no—
58C22×C5×Dic3D411yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C4×C5×D3—21no—
61C2×C4×C5×D3—21no—
62C2×C4×C5×D3—21no—
63C2×C4×C5×D3C2×C412yes—
64C2×C4×C5×D3D412yes—
65C2×C3×D20—21no—
66C2×C3×D20—21no—
67C2×C3×D20—21no—
68C2×C3×D20C2×C412yes—
69C2×C3×D20D412yes—
70C2×C3×D20D412yes—
71C2×#1202—24no—
72C2×#1202—24no—
73C2×#1202—24no—
74D3×D20—28no—
75D3×D20—28no—
76D3×D20—28no—
77D3×D20—28no—
78C3×C5×C4⋊C4—21no—
79C3×C5×C4⋊C4—21no—
80C2×C3⋊#168—21no—
81C2×C3⋊#168—21no—
82C2×C3⋊#168—21no—
83C5×(C2×D3)⋊C4—42no—
84C5×C4⋊Dic3—21no—
85C5×C4⋊Dic3—21no—
86C2×C3×#168—21no—
87C2×C3×#168—21no—
88C2×C3×#168—21no—
89C22×D3×D4—51no—
90C2×C3×#102—51no—
91C2×#832—51no—
92C2×#821—51no—
93C2×(C2×D3)⋊C8—51no—
94#4987D511yescharacteristic, complemented
95C2×#809—51no—
96C24×D5—61no—
97C23×C4×C5—31no—
98C22×D20—31no—
99C22×D20—34no—
100C22×D20—62no—
101C22×D20—62no—
102C22×D20—62no—
103C22×D20—61no—
104C22×D20—62no—
105C22×D20—62no—
106C22×D20C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
109C2×C5×C22⋊C4—61no—
110C22×#168—31no—
111C22×#168C2×D311yescharacteristic, complemented
112C5×#95—61no—
113C22⋊#168—62no—
114#3941—22no—
115#3941—62no—
116#3941—62no—
117#3941—62no—
118#1786—151noSylow
119C23×C3×C5C2×D411yescharacteristic
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—41no—
124C22×D15—41no—
125C22×D15—41no—
126C22×D15—41no—
127C22×C5×D3—21no—
128C22×C5×D3—21no—
129C22×C5×D3—21no—
130C22×C5×D3—21no—
131C22×C5×D3C22⋊C412yes—
132C22×C5×D3D812yes—
133C22×C5×D3SD1612yes—
134C22×C3×D5—22no—
135C22×C3×D5—22no—
136C22×C3×D5—22no—
137C22×C3×D5—41no—
138C22×C3×D5—41no—
139C22×C3×D5—41no—
140C22×C3×D5—41no—
141C2×D3×D5—216no—
142C2×D3×D5—48no—
143C2×D3×D5—48no—
144C2×D3×D5—48no—
145C2×D3×D5—48no—
146C2×D3×D5—48no—
147C2×D3×D5—48no—
148C2×C3×C4×C5—41no—
149C2×C3×C4×C5—41no—
150C2×C3×C4×C5—41no—
151C2×C3×C4×C5C22×C411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D411yescharacteristic
157D60—22no—
158D60—22no—
159D60—22no—
160D60C22⋊C414yescomplemented
161C2×C5×Dic3—21no—
162C2×C5×Dic3—21no—
163C2×C5×Dic3—41no—
164C2×C5×Dic3—41no—
165C2×C5×Dic3—41no—
166C2×C5×Dic3C22⋊C412yes—
167C4×C5×D3—22no—
168C4×C5×D3—22no—
169C4×C5×D3—22no—
170C4×C5×D3—22no—
171C3×D20—22no—
172C3×D20—22no—
173C3×D20—22no—
174C3×D20C22⋊C414yescomplemented
175#1202—216no—
176C3⋊#168—41no—
177C3×#168—41no—
178C24×D3—101no—
179C22×C3×D4—51no—
180C22×#67—101no—
181C2×D3×D4—54no—
182C2×D3×D4—102no—
183C2×D3×D4—102no—
184C2×D3×D4—102no—
185C2×D3×D4—102no—
186C2×D3×D4—102no—
187C22×D12—51no—
188C22×C4×D3C2×D511yescharacteristic
189C22×C3×C8—51no—
190C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
191C2×(C2×D3)⋊C4—21no—
192C2×C4⋊Dic3C2×D511yescharacteristic, complemented
193C22×C3⋊C8—51no—
194C3×#102—102no—
195#832—102no—
196C3⋊#95—21no—
197#821—102no—
198(C2×D3)⋊C8—102no—
199#809—102no—
200C24×C5—31no—
201C23×D5—21no—
202C23×D5—64no—
203C23×D5—64no—
204C23×D5—64no—
205C23×D5—61no—
206C23×D5—122no—
207C23×D5—122no—
208C23×D5—122no—
209C23×D5—122no—
210C22×C4×C5—21no—
211C22×C4×C5—31no—
212C22×C4×C5—32no—
213C22×C4×C5—32no—
214C22×C4×C5—61no—
215C22×C4×C5—61no—
216C22×C4×C5—61no—
217C22×C4×C5—61no—
218C22×C4×C5—61no—
219C22×C4×C5C22×D311yescharacteristic
220C2×D20—21no—
221C2×D20—21no—
222C2×D20—21no—
223C2×D20—32no—
224C2×D20—32no—
225C2×D20—32no—
226C2×D20—68no—
227C2×D20—68no—
228C2×D20—68no—
229C2×D20—64no—
230C2×D20—64no—
231C2×D20—64no—
232C2×D20—61no—
233C2×D20—61no—
234C2×D20—61no—
235C2×D20—68no—
236C2×D20C4×D312yes—
237C2×D20D1212yes—
238C2×D20#6712yes—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—61no—
242C5×C4⋊C4—61no—
243C5×C22⋊C4—122no—
244C2×#168—21no—
245C2×#168—21no—
246C2×#168—21no—
247C2×#168—61no—
248C2×#168—61no—
249C2×#168—61no—
250C23×D4—151no—
251C2×#102—51no—
252C2×#102—151no—
253C2×#102—151no—
254C2×#102—151no—
255C2×C22⋊C8—151no—
256#380—31no—
257C22×C3×C5C2×C22⋊C411yescharacteristic
258C22×C3×C5#12011yescharacteristic
259C22×C3×C5#12011yescharacteristic
260C22×C3×C5C2×D811yescharacteristic
261C22×C3×C5C2×SD1611yescharacteristic
262C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
263C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
264C2×D15—24no—
265C2×D15—42no—
266C2×D15—42no—
267C2×D15—42no—
268C2×D15—42no—
269C2×D15—42no—
270C2×D15—42no—
271C2×C5×D3—22no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3—22no—
275C2×C5×D3—22no—
276C2×C5×D3—22no—
277C2×C5×D3#10214yescomplemented
278C2×C3×D5—24no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285D3×D5—432no—
286C3×C4×C5—81no—
287C3×C4×C5C2×C22⋊C411yescharacteristic
288C3×C4×C5C2×C22⋊C411yescharacteristic
289C3×C4×C5#12011yescharacteristic
290C3×C4×C5#12011yescharacteristic
291C5×Dic3—22no—
292C5×Dic3—81no—
293C24×C3—101no—
294C23×D3—104no—
295C23×D3—104no—
296C23×D3—101no—
297C23×D3—104no—
298C23×D3—202no—
299C23×D3—202no—
300C23×D3—202no—
301C23×D3—202no—
302C23×D3C22⋊D511yescharacteristic
303C2×C3×D4—52no—
304C2×C3×D4—52no—
305C2×C3×D4—52no—
306C2×C3×D4—101no—
307C2×C3×D4—101no—
308C2×C3×D4—101no—
309C22×C3×C4—21no—
310C22×C3×C4C22×D511yescharacteristic
311C2×#67—104no—
312C2×#67—104no—
313C2×#67—104no—
314C22×Dic3—21no—
315C22×Dic3C22⋊D511yescharacteristic
316D3×D4—108no—
317D3×D4—108no—
318D3×D4—108no—
319D3×D4—108no—
320C2×D12—52no—
321C2×D12—52no—
322C2×D12—52no—
323C2×D12—101no—
324C2×D12—101no—
325C2×D12—101no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3C4×D512yes—
331C2×C4×D3D2012yes—
332C2×C3×C8—101no—
333C2×C3×C8—101no—
334C2×C3×C8—101no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337(C2×D3)⋊C4—42no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C2×C3⋊C8—101no—
341C2×C3⋊C8—101no—
342C2×C3⋊C8—101no—
343C23×C5—32no—
344C23×C5—32no—
345C23×C5—32no—
346C23×C5—61no—
347C23×C5—61no—
348C23×C5—61no—
349C23×C5—61no—
350C23×C5D3×D411yescharacteristic
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—41no—
355C22×D5—41no—
356C22×D5—41no—
357C22×D5—41no—
358C22×D5—616no—
359C22×D5—62no—
360C22×D5—62no—
361C22×D5—62no—
362C22×D5—128no—
363C22×D5—128no—
364C22×D5—128no—
365C22×D5—128no—
366C22×D5—128no—
367C22×D5—128no—
368C22×D5—121no—
369C22×D5—121no—
370C22×D5—121no—
371C22×D5—121no—
372C2×C4×C5—32no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—61no—
377C2×C4×C5—61no—
378C2×C4×C5—62no—
379C2×C4×C5—62no—
380C2×C4×C5—62no—
381C2×C4×C5—62no—
382C2×C4×C5—121no—
383C2×C4×C5—121no—
384C2×C4×C5—121no—
385C2×C4×C5C2×C4×D311yescharacteristic
386C2×C4×C5C2×D1211yescharacteristic
387C2×C4×C5D3×D411yescharacteristic
388C2×C4×C5D3×D411yescharacteristic
389C2×C4×C5D3×D411yescharacteristic
390C2×C4×C5C2×#6711yescharacteristic
391D20—22no—
392D20—22no—
393D20—22no—
394D20—34no—
395D20—616no—
396D20—62no—
397D20—62no—
398D20—62no—
399D20(C2×D3)⋊C414yescomplemented
400#168—41no—
401#168—121no—
402C25—301no—
403C22×D4—51no—
404C22×D4—154no—
405C22×D4—151no—
406C22×D4—302no—
407C22×D4—301no—
408C22×D4—302no—
409C22×D4—302no—
410C22×D4—302no—
411C22×D4—302no—
412C23×C4—31no—
413C22×C8—51no—
414C22×C8—151no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4D3×D511yescharacteristic, complemented
417C2×C22⋊C4—61no—
418#102—102no—
419#102—302no—
420#102—302no—
421#102—302no—
422C22⋊C8—302no—
423#95—61no—
424C2×C3×C5#37911yescharacteristic
425C2×C3×C5C2×#10211yescharacteristic
426C2×C3×C5#41811yescharacteristic
427C2×C3×C5#44711yescharacteristic
428C2×C3×C5#44711yescharacteristic
429C2×C3×C5#45011yescharacteristic
430C2×C3×C5#45011yescharacteristic
431D15—44no—
432C3×D5—44no—
433C5×D3—24no—
434C23×C3—102no—
435C23×C3—102no—
436C23×C3—102no—
437C23×C3—201no—
438C23×C3—201no—
439C23×C3—201no—
440C23×C3—201no—
441C23×C3C2×C22⋊D511yescharacteristic
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—1016no—
447C22×D3—102no—
448C22×D3—102no—
449C22×D3—102no—
450C22×D3—208no—
451C22×D3—208no—
452C22×D3—208no—
453C22×D3—208no—
454C22×D3—208no—
455C22×D3—201no—
456C22×D3—201no—
457C22×D3—201no—
458C22×D3—201no—
459C22×D3—208no—
460C22×D3#68512yes—
461C22×D3#68612yes—
462C22×D3#68812yes—
463C3×D4—54no—
464C3×D4—102no—
465C3×D4—102no—
466C3×D4—102no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4C2×C4×D511yescharacteristic
471C2×C3×C4C2×D2011yescharacteristic
472C2×C3×C4D4×D511yescharacteristic
473C2×C3×C4D4×D511yescharacteristic
474C2×C3×C4D4×D511yescharacteristic
475C2×C3×C4D4×D511yescharacteristic
476#67—1016no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3#68512yes—
483D12—54no—
484D12—102no—
485D12—102no—
486D12—102no—
487C4×D3—22no—
488C4×D3—22no—
489C4×D3—22no—
490C4×D3—22no—
491C3×C8—201no—
492C3⋊C8—201no—
493C22×C5—34no—
494C22×C5—62no—
495C22×C5—62no—
496C22×C5—62no—
497C22×C5—62no—
498C22×C5—62no—
499C22×C5—62no—
500C22×C5D3×C22⋊C411yescharacteristic
501C22×C5#88211yescharacteristic
502C22×C5D3×D811yescharacteristic
503C22×C5#91111yescharacteristic
504C22×C5D3×SD1611yescharacteristic
505C22×C5#91411yescharacteristic
506C22×C5#93711yescharacteristic
507C2×D5—24no—
508C2×D5—42no—
509C2×D5—42no—
510C2×D5—42no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—64no—
515C2×D5—1232no—
516C2×D5—122no—
517C2×D5—122no—
518C2×D5—122no—
519C2×D5—122no—
520C2×D5—122no—
521C2×D5—122no—
522C4×C5—62no—
523C4×C5—81no—
524C4×C5—241no—
525C4×C5D3×C22⋊C411yescharacteristic
526C4×C5#88211yescharacteristic
527C4×C5C2×(C2×D3)⋊C411yescharacteristic
528C4×C5#93711yescharacteristic
529C24—31no—
530C24—101no—
531C24—304no—
532C24—304no—
533C24—304no—
534C24—301no—
535C24—602no—
536C24—602no—
537C24—602no—
538C24—602no—
539C2×D4—52no—
540C2×D4—52no—
541C2×D4—52no—
542C2×D4—101no—
543C2×D4—101no—
544C2×D4—101no—
545C2×D4—152no—
546C2×D4—152no—
547C2×D4—152no—
548C2×D4—304no—
549C2×D4—308no—
550C2×D4—308no—
551C2×D4—308no—
552C2×D4—308no—
553C2×D4—304no—
554C2×D4—304no—
555C2×D4—301no—
556C2×D4—301no—
557C2×D4—301no—
558C22×C4—21no—
559C22×C4—31no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4C2×D3×D511yescharacteristic
568C2×C8—101no—
569C2×C8—101no—
570C2×C8—101no—
571C2×C8—301no—
572C2×C8—301no—
573C2×C8—301no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C22⋊C4—122no—
579C3×C5#178611yescharacteristic, complemented, Hall
580C22×C3—104no—
581C22×C3—202no—
582C22×C3—202no—
583C22×C3—202no—
584C22×C3—202no—
585C22×C3—202no—
586C22×C3—202no—
587C22×C3C2×#68511yescharacteristic
588C22×C3C2×#68611yescharacteristic
589C22×C3#408311yescharacteristic
590C22×C3#408311yescharacteristic
591C22×C3C2×#68811yescharacteristic
592C22×C3#409511yescharacteristic
593C22×C3#409511yescharacteristic
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—104no—
601C2×D3—2032no—
602C2×D3—202no—
603C2×D3—202no—
604C2×D3—202no—
605C2×D3—202no—
606C2×D3—202no—
607C2×D3—202no—
608C2×D3#394114yescomplemented
609C3×C4—81no—
610C3×C4D5×C22⋊C411yescharacteristic
611C3×C4D5×C22⋊C411yescharacteristic
612C3×C4#402811yescharacteristic
613C3×C4#402811yescharacteristic
614Dic3—22no—
615Dic3—81no—
616C2×C5—64no—
617C2×C5D3×#10211yescharacteristic
618C2×C5#477011yescharacteristic
619C2×C5#477311yescharacteristic
620C2×C5#477611yescharacteristic
621C2×C5#495511yescharacteristic
622C2×C5#515611yescharacteristic
623C2×C5#516911yescharacteristic
624D5—44no—
625D5—124no—
626C23—32no—
627C23—32no—
628C23—32no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—201no—
637C23—201no—
638C23—201no—
639C23—201no—
640C23—3016no—
641C23—302no—
642C23—302no—
643C23—302no—
644C23—608no—
645C23—608no—
646C23—608no—
647C23—608no—
648C23—608no—
649C23—608no—
650C23—601no—
651C23—601no—
652C23—601no—
653C23—601no—
654C23D3×C22⋊D511yescharacteristic
655D4—54no—
656D4—102no—
657D4—102no—
658D4—102no—
659D4—154no—
660D4—3016no—
661D4—302no—
662D4—302no—
663D4—302no—
664C2×C4—32no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4C4×D3×D511yescharacteristic
678C2×C4D5×D1211yescharacteristic
679C2×C4D3×D2011yescharacteristic
680C2×C4#677711yescharacteristic
681C2×C4D5×#6711yescharacteristic
682C2×C4#679011yescharacteristic
683C8—201no—
684C8—601no—
685C2×C3—204no—
686C2×C3#6524411yescharacteristic
687C2×C3C2×#394111yescharacteristic
688C2×C3#6529011yescharacteristic
689C2×C3#6532511yescharacteristic
690C2×C3#6532511yescharacteristic
691C2×C3#6533511yescharacteristic
692C2×C3#6533511yescharacteristic
693D3—24no—
694D3—204no—
695C5#7019811yescharacteristic, complemented, Sylow
696C22—34no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—62no—
701C22—62no—
702C22—62no—
703C22—104no—
704C22—202no—
705C22—202no—
706C22—202no—
707C22—202no—
708C22—202no—
709C22—202no—
710C22—304no—
711C22—6032no—
712C22—602no—
713C22—602no—
714C22—602no—
715C22—602no—
716C22—602no—
717C22—602no—
718C22D3×#68511yescharacteristic
719C22#9147511yescharacteristic
720C22D3×#68611yescharacteristic
721C22#9148011yescharacteristic
722C22D3×#68811yescharacteristic
723C22#9150411yescharacteristic
724C22#9157711yescharacteristic
725C4—62no—
726C4—81no—
727C4—241no—
728C4D5×(C2×D3)⋊C411yescharacteristic
729C4#9147311yescharacteristic
730C4#9147411yescharacteristic
731C4#9147611yescharacteristic
732C3#1060031411yescharacteristic, complemented, Sylow
733C2—64no—
734C2—204no—
735C2—604no—
736C2D3×#394111yescharacteristic
737C2#1174747711yescharacteristic
738C2#1174748211yescharacteristic
739C2#1174748311yescharacteristic
740C2#1174894011yescharacteristic
741C2#1174915211yescharacteristic
742C2#1174939811yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×D3×D20C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1786
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91093C2semidirect
3. C5×#4987C2semidirect
4. C2×C3×#3941C2semidirect
5. C2×#90969C2semidirect
6. C2×#90964C2semidirect
7. C2×(C2×D3)⋊#168C2semidirect
19. C2×D3×D20C4semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
21. C22×C3⋊#168C22semidirect
23. C2×C5×C4⋊Dic3C22semidirect
24. C22×C3×#168C22semidirect
38. C2×#3941D3semidirect
94. #4987D5semidirect
108. C2×C5×C4⋊C4C2×D3semidirect
111. C22×#168C2×D3semidirect
160. D60C22⋊C4semidirect
174. C3×D20C22⋊C4semidirect
190. C2×C3×C4⋊C4C2×D5semidirect
192. C2×C4⋊Dic3C2×D5semidirect
277. C2×C5×D3#102semidirect
399. D20(C2×D3)⋊C4semidirect
416. C2×C4⋊C4D3×D5semidirect
579. C3×C5#1786semidirect
608. C2×D3#3941semidirect
695. C5#70198semidirect
732. C3#10600314semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D202
C2×#910932
C5×#49872
C2×C3×#39412
C2×#909692
C2×#909642
C2×(C2×D3)⋊#1682
#106003143
#701985