Finite Group Databasebeta

← #14296993

Subgroups — #14296993

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×C3×D4×D5C211yesmaximal, characteristic
2C2×#91116C211yesmaximal, characteristic, complemented
3C2×C5×#832C211yesmaximal, characteristic, complemented
4#11748759C211yesmaximal, characteristic, complemented
5C2×#90965C211yesmaximal, characteristic, complemented
6C2×#90964C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#10600991—31nomaximal, Hall
9C24×C3×D5—21no—
10C22×C3×C5×D4C2211yescharacteristic
11C22×C3×C22⋊D5—21no—
12C2×C3×D4×D5—22no—
13C2×C3×D4×D5—22no—
14C2×C3×D4×D5—22no—
15C2×C3×D4×D5—22no—
16C2×C3×D4×D5—22no—
17C2×C3×D4×D5C414yescomplemented
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic, complemented
21C22×C3⋊#168C2211yescharacteristic, complemented
22C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2211yescharacteristic, complemented
24C2×#6665—21no—
25#91116—22no—
26C5×#832—22no—
27#90994—21no—
28#90965—22no—
29#90964—22no—
30#90955—22no—
31#72128—51nomaximal, Hall
32C22×D4×D5D311yescharacteristic
33C2×C5×#102—31no—
34C2×#3964—31no—
35C2×#3953—31no—
36C2×#3952—31no—
37#65276—31no—
38C2×#3941—31no—
39C24×C3×C5—21no—
40C23×C3×D5—24no—
41C23×C3×D5—24no—
42C23×C3×D5—21no—
43C23×C3×D5—24no—
44C23×C3×D5—42no—
45C23×C3×D5—42no—
46C23×C3×D5—42no—
47C23×C3×D5—42no—
48C23×C3×D5D411yescharacteristic
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2×C412yes—
53C2×C3×C5×D4D412yes—
54C2×C3×C5×D4D412yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C22×C5×Dic3—21no—
58C2×C3×C22⋊D5—24no—
59C2×C3×C22⋊D5—24no—
60C2×C3×C22⋊D5—24no—
61C22×C3×Dic5D411yescharacteristic
62C3×D4×D5—28no—
63C3×D4×D5—28no—
64C3×D4×D5—28no—
65C3×D4×D5—28no—
66C2×C3×D20—21no—
67C2×C3×D20—21no—
68C2×C3×D20—21no—
69C2×C3×D20C2×C412yes—
70C2×C3×D20D412yes—
71C2×C3×D20D412yes—
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—21no—
76C2×C3×C4×D5C2×C412yes—
77C2×C3×C4×D5D412yes—
78C4⋊Dic15—21no—
79C4⋊Dic15—21no—
80C2×C3⋊#168—21no—
81C2×C3⋊#168—21no—
82C2×C3⋊#168—21no—
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3—21no—
85C2×C5×C3⋊C8—21no—
86C2×C5×C3⋊C8—21no—
87C2×C5×C3⋊C8—21no—
88#6665—42no—
89C23×C3×D4—51no—
90C2×#832—51no—
91C2×#832—51no—
92C2×#832—51no—
93C2×#832D511yescharacteristic, complemented
94#5212—51no—
95C2×#830—51no—
96C24×D5—21no—
97C22×C5×D4C2×D311yescharacteristic
98C22×C22⋊D5—21no—
99C2×D4×D5—22no—
100C2×D4×D5—22no—
101C2×D4×D5—22no—
102C2×D4×D5—22no—
103C2×D4×D5—22no—
104C2×D4×D5Dic314yescomplemented
105C22×D20C2×D311yescharacteristic
106C22×C4×D5C2×D311yescharacteristic
107C22×C5×C8—31no—
108C2×C5×C4⋊C4—31no—
109C2×#685—61no—
110C2×C4⋊Dic5—31no—
111C22×#168—31no—
112C5×#102—62no—
113#3964—62no—
114#3963—61no—
115#3953—62no—
116#3952—62no—
117#3941—62no—
118#1786—151noSylow
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—22no—
122C23×C3×C5—41no—
123C23×C3×C5—41no—
124C23×C3×C5—41no—
125C23×C3×C5—41no—
126C23×C3×C5C2×D411yescharacteristic
127C22×C3×D5—21no—
128C22×C3×D5—21no—
129C22×C3×D5—21no—
130C22×C3×D5—21no—
131C22×C3×D5—216no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5—48no—
136C22×C3×D5—48no—
137C22×C3×D5—48no—
138C22×C3×D5—48no—
139C22×C3×D5—48no—
140C22×C3×D5—41no—
141C22×C3×D5—41no—
142C22×C3×D5—41no—
143C22×C3×D5—41no—
144C22×C3×D5—48no—
145C22×C3×D5C22⋊C412yes—
146C22×C3×D5D812yes—
147C22×C3×D5SD1612yes—
148C3×C5×D4—22no—
149C3×C5×D4—22no—
150C3×C5×D4—22no—
151C3×C5×D4C22⋊C414yescomplemented
152C2×C3×C4×C5C22×C411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×Dic15—41no—
159C2×Dic15—41no—
160C2×Dic15—41no—
161C2×C5×Dic3—41no—
162C2×C5×Dic3—41no—
163C2×C5×Dic3—41no—
164C3×C22⋊D5—216no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5C22⋊C412yes—
168C3×D20—22no—
169C3×D20—22no—
170C3×D20—22no—
171C3×D20C22⋊C414yescomplemented
172C3×C4×D5—22no—
173C3×C4×D5—22no—
174C3×C4×D5—22no—
175C3×C4×D5—22no—
176C3⋊#168—41no—
177C5×C3⋊C8—41no—
178C25×C3—101no—
179C22×C3×D4—54no—
180C22×C3×D4—51no—
181C22×C3×D4—102no—
182C22×C3×D4—101no—
183C22×C3×D4—102no—
184C22×C3×D4—102no—
185C22×C3×D4—102no—
186C22×C3×D4—102no—
187C22×C3×D4C2×D511yescharacteristic
188C23×C3×C4—51no—
189C2×#217—101no—
190C2×C4⋊Dic3—51no—
191C2×C4⋊Dic3C2×D511yescharacteristic, complemented
192C22×C3⋊C8—51no—
193C22×C3⋊C8C2×D511yescharacteristic, complemented
194#832—22no—
195#832—102no—
196#832—102no—
197#832—102no—
198C3⋊#95—101no—
199#830—102no—
200C24×C5—21no—
201C23×D5—24no—
202C23×D5—24no—
203C23×D5—21no—
204C23×D5—24no—
205C23×D5—42no—
206C23×D5—42no—
207C23×D5—42no—
208C23×D5—42no—
209C23×D5#6711yescharacteristic
210C2×C5×D4—21no—
211C2×C5×D4—21no—
212C2×C5×D4—21no—
213C2×C5×D4C2×Dic312yes—
214C2×C5×D4#6712yes—
215C2×C5×D4#6712yes—
216C22×C4×C5—61no—
217C22×C4×C5C22×D311yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C22×Dic5—61no—
222C22×Dic5#6711yescharacteristic
223D4×D5—28no—
224D4×D5—28no—
225D4×D5—28no—
226D4×D5—28no—
227C2×D20—21no—
228C2×D20—21no—
229C2×D20—21no—
230C2×D20C2×Dic312yes—
231C2×D20#6712yes—
232C2×D20#6712yes—
233C2×C4×D5—21no—
234C2×C4×D5—21no—
235C2×C4×D5—21no—
236C2×C4×D5—21no—
237C2×C4×D5C2×Dic312yes—
238C2×C4×D5#6712yes—
239C2×C5×C8—61no—
240C2×C5×C8—61no—
241C2×C5×C8—61no—
242C5×C4⋊C4—61no—
243C5×C4⋊C4—61no—
244#685—122no—
245C4⋊Dic5—61no—
246C4⋊Dic5—61no—
247C2×#168—61no—
248C2×#168—61no—
249C2×#168—61no—
250C23×D4—51no—
251C2×#102—31no—
252C2×#102—151no—
253C2×#102—151no—
254C2×#102—151no—
255C2×C22⋊C8—151no—
256#380—151no—
257C22×C3×C5—24no—
258C22×C3×C5—42no—
259C22×C3×C5—42no—
260C22×C3×C5—42no—
261C22×C3×C5—42no—
262C22×C3×C5—42no—
263C22×C3×C5—42no—
264C22×C3×C5C2×C22⋊C411yescharacteristic
265C22×C3×C5#12011yescharacteristic
266C22×C3×C5#12011yescharacteristic
267C22×C3×C5C2×D811yescharacteristic
268C22×C3×C5C2×SD1611yescharacteristic
269C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
270C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
271C2×C3×D5—22no—
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—22no—
276C2×C3×D5—22no—
277C2×C3×D5—24no—
278C2×C3×D5—432no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285C2×C3×D5#10214yescomplemented
286C3×C4×C5C2×C22⋊C411yescharacteristic
287C3×C4×C5C2×C22⋊C411yescharacteristic
288C3×C4×C5#12011yescharacteristic
289C3×C4×C5#12011yescharacteristic
290Dic15—81no—
291C3×Dic5—22no—
292C5×Dic3—81no—
293C24×C3—21no—
294C24×C3—51no—
295C24×C3—104no—
296C24×C3—104no—
297C24×C3—104no—
298C24×C3—101no—
299C24×C3—202no—
300C24×C3—202no—
301C24×C3—202no—
302C24×C3—202no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—52no—
307C2×C3×D4—52no—
308C2×C3×D4—52no—
309C2×C3×D4—104no—
310C2×C3×D4—108no—
311C2×C3×D4—108no—
312C2×C3×D4—108no—
313C2×C3×D4—104no—
314C2×C3×D4—104no—
315C2×C3×D4—108no—
316C2×C3×D4—101no—
317C2×C3×D4—101no—
318C2×C3×D4—101no—
319C2×C3×D4C4×D512yes—
320C2×C3×D4D2012yes—
321C2×C3×D4C22⋊D512yes—
322C22×C3×C4—51no—
323C22×C3×C4—52no—
324C22×C3×C4—52no—
325C22×C3×C4—101no—
326C22×C3×C4—101no—
327C22×C3×C4—101no—
328C22×C3×C4—101no—
329C22×C3×C4C22×D511yescharacteristic
330C22×Dic3—21no—
331C22×Dic3—101no—
332#217—202no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—101no—
336C4⋊Dic3—101no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—101no—
341C2×C3⋊C8—101no—
342C2×C3⋊C8—101no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5—41no—
349C23×C5—41no—
350C23×C5C2×#6711yescharacteristic
351C22×D5—21no—
352C22×D5—21no—
353C22×D5—21no—
354C22×D5—21no—
355C22×D5—216no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—48no—
360C22×D5—48no—
361C22×D5—48no—
362C22×D5—48no—
363C22×D5—48no—
364C22×D5—41no—
365C22×D5—41no—
366C22×D5—41no—
367C22×D5—41no—
368C22×D5—48no—
369C22×D5#21312yes—
370C22×D5#21412yes—
371C22×D5#21712yes—
372C5×D4—22no—
373C5×D4—22no—
374C5×D4—22no—
375C5×D4#21714yescomplemented
376C2×C4×C5—121no—
377C2×C4×C5—121no—
378C2×C4×C5—121no—
379C2×C4×C5C22×Dic311yescharacteristic
380C2×C4×C5C2×#6711yescharacteristic
381C2×C4×C5C2×#6711yescharacteristic
382C2×C4×C5C2×#6711yescharacteristic
383C2×C4×C5C2×#6711yescharacteristic
384C2×C4×C5C2×#6711yescharacteristic
385C22⋊D5—216no—
386C2×Dic5—21no—
387C2×Dic5—21no—
388C2×Dic5—121no—
389C2×Dic5—121no—
390C2×Dic5—121no—
391C2×Dic5#21712yes—
392D20—22no—
393D20—22no—
394D20—22no—
395D20#21714yescomplemented
396C4×D5—22no—
397C4×D5—22no—
398C4×D5—22no—
399C4×D5—22no—
400C5×C8—121no—
401#168—121no—
402C25—101no—
403C22×D4—54no—
404C22×D4—51no—
405C22×D4—102no—
406C22×D4—101no—
407C22×D4—102no—
408C22×D4—102no—
409C22×D4—102no—
410C22×D4—102no—
411C22×D4D3×D511yescharacteristic
412C23×C4—51no—
413C22×C8—31no—
414C22×C8—151no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—151no—
417C2×C22⋊C4—301no—
418#102—62no—
419#102—302no—
420#102—302no—
421#102—302no—
422C22⋊C8—302no—
423#95—301no—
424C2×C3×C5—44no—
425C2×C3×C5#37911yescharacteristic
426C2×C3×C5C2×#10211yescharacteristic
427C2×C3×C5#41811yescharacteristic
428C2×C3×C5#44711yescharacteristic
429C2×C3×C5#44711yescharacteristic
430C2×C3×C5#45011yescharacteristic
431C2×C3×C5#45011yescharacteristic
432C3×D5—24no—
433C3×D5—44no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—52no—
442C23×C3—52no—
443C23×C3—52no—
444C23×C3—1016no—
445C23×C3—101no—
446C23×C3—101no—
447C23×C3—101no—
448C23×C3—101no—
449C23×C3—102no—
450C23×C3—102no—
451C23×C3—102no—
452C23×C3—208no—
453C23×C3—208no—
454C23×C3—208no—
455C23×C3—208no—
456C23×C3—208no—
457C23×C3—208no—
458C23×C3—201no—
459C23×C3—201no—
460C23×C3—201no—
461C23×C3—201no—
462C23×C3D4×D511yescharacteristic
463C3×D4—22no—
464C3×D4—22no—
465C3×D4—22no—
466C3×D4—54no—
467C3×D4—1016no—
468C3×D4—102no—
469C3×D4—102no—
470C3×D4—102no—
471C3×D4#68514yescomplemented
472C2×C3×C4—52no—
473C2×C3×C4—101no—
474C2×C3×C4—101no—
475C2×C3×C4—102no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4C2×C4×D511yescharacteristic
480C2×C3×C4C2×D2011yescharacteristic
481C2×C3×C4D4×D511yescharacteristic
482C2×C3×C4D4×D511yescharacteristic
483C2×C3×C4D4×D511yescharacteristic
484C2×C3×C4C2×C22⋊D511yescharacteristic
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—201no—
489C2×Dic3—201no—
490C2×Dic3—201no—
491C3⋊C8—41no—
492C3⋊C8—201no—
493C22×C5—24no—
494C22×C5—42no—
495C22×C5—42no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5C2×#21311yescharacteristic
501C22×C5#93211yescharacteristic
502C22×C5#93211yescharacteristic
503C22×C5C2×#21411yescharacteristic
504C22×C5C2×#21711yescharacteristic
505C22×C5#95311yescharacteristic
506C22×C5#95311yescharacteristic
507C2×D5—22no—
508C2×D5—22no—
509C2×D5—22no—
510C2×D5—22no—
511C2×D5—22no—
512C2×D5—22no—
513C2×D5—24no—
514C2×D5—432no—
515C2×D5—42no—
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5#83214yescomplemented
522C4×C5—241no—
523C4×C5C2×#21711yescharacteristic
524C4×C5C2×#21711yescharacteristic
525C4×C5#95311yescharacteristic
526C4×C5#95311yescharacteristic
527Dic5—22no—
528Dic5—241no—
529C24—21no—
530C24—51no—
531C24—104no—
532C24—104no—
533C24—104no—
534C24—101no—
535C24—202no—
536C24—202no—
537C24—202no—
538C24—202no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—52no—
543C2×D4—52no—
544C2×D4—52no—
545C2×D4—104no—
546C2×D4—108no—
547C2×D4—108no—
548C2×D4—108no—
549C2×D4—104no—
550C2×D4—104no—
551C2×D4—108no—
552C2×D4—101no—
553C2×D4—101no—
554C2×D4—101no—
555C2×D4D5×Dic312yes—
556C2×D4#120112yes—
557C2×D4#120212yes—
558C22×C4—51no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—61no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—101no—
565C22×C4—101no—
566C22×C4—301no—
567C22×C4C2×D3×D511yescharacteristic
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—301no—
572C2×C8—301no—
573C2×C8—301no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—301no—
577C4⋊C4—301no—
578C22⋊C4—602no—
579C3×C5#178611yescharacteristic, complemented, Hall
580C22×C3—24no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—54no—
588C22×C3—102no—
589C22×C3—102no—
590C22×C3—102no—
591C22×C3—102no—
592C22×C3—102no—
593C22×C3—102no—
594C22×C3—104no—
595C22×C3—2032no—
596C22×C3—202no—
597C22×C3—202no—
598C22×C3—202no—
599C22×C3—202no—
600C22×C3—202no—
601C22×C3—202no—
602C22×C3D5×C22⋊C411yescharacteristic
603C22×C3#402811yescharacteristic
604C22×C3D5×D811yescharacteristic
605C22×C3#405711yescharacteristic
606C22×C3D5×SD1611yescharacteristic
607C22×C3#406011yescharacteristic
608C22×C3#408311yescharacteristic
609C3×C4—102no—
610C3×C4D5×C22⋊C411yescharacteristic
611C3×C4#402811yescharacteristic
612C3×C4C2×#68511yescharacteristic
613C3×C4#408311yescharacteristic
614Dic3—81no—
615Dic3—401no—
616C2×C5—44no—
617C2×C5C2×#83211yescharacteristic
618C2×C5#521511yescharacteristic
619C2×C5#521711yescharacteristic
620C2×C5#521711yescharacteristic
621C2×C5#521811yescharacteristic
622C2×C5#521811yescharacteristic
623C2×C5#524711yescharacteristic
624D5—24no—
625D5—44no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—52no—
634C23—52no—
635C23—52no—
636C23—1016no—
637C23—101no—
638C23—101no—
639C23—101no—
640C23—101no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—208no—
645C23—208no—
646C23—208no—
647C23—208no—
648C23—208no—
649C23—208no—
650C23—201no—
651C23—201no—
652C23—201no—
653C23—201no—
654C23D5×#6711yescharacteristic
655D4—22no—
656D4—22no—
657D4—22no—
658D4—54no—
659D4—1016no—
660D4—102no—
661D4—102no—
662D4—102no—
663D4#666514yescomplemented
664C2×C4—52no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—601no—
675C2×C4—601no—
676C2×C4—601no—
677C2×C4C2×D5×Dic311yescharacteristic
678C2×C4C2×#120111yescharacteristic
679C2×C4C2×#120211yescharacteristic
680C2×C4D5×#6711yescharacteristic
681C2×C4D5×#6711yescharacteristic
682C2×C4D5×#6711yescharacteristic
683C8—121no—
684C8—601no—
685C2×C3—44no—
686C2×C3—104no—
687C2×C3—204no—
688C2×C3D5×#10211yescharacteristic
689C2×C3#6505911yescharacteristic
690C2×C3#6506211yescharacteristic
691C2×C3#6506511yescharacteristic
692C2×C3#6524411yescharacteristic
693C2×C3#6544511yescharacteristic
694C2×C3#6545811yescharacteristic
695C5#7212811yescharacteristic, complemented, Sylow
696C22—24no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—54no—
704C22—102no—
705C22—102no—
706C22—102no—
707C22—102no—
708C22—102no—
709C22—102no—
710C22—104no—
711C22—2032no—
712C22—202no—
713C22—202no—
714C22—202no—
715C22—202no—
716C22—202no—
717C22—202no—
718C22D5×#21311yescharacteristic
719C22D5×#21411yescharacteristic
720C22#9148911yescharacteristic
721C22#9149111yescharacteristic
722C22D5×#21711yescharacteristic
723C22#9156311yescharacteristic
724C22#9156411yescharacteristic
725C4—102no—
726C4—241no—
727C4—1201no—
728C4C2×#666511yescharacteristic
729C4D5×#21711yescharacteristic
730C4#9156311yescharacteristic
731C4#9156411yescharacteristic
732C3#1060099111yescharacteristic, complemented, Sylow
733C2—44no—
734C2—104no—
735C2—204no—
736C2D5×#83211yescharacteristic
737C2#1174896211yescharacteristic
738C2#1174902111yescharacteristic
739C2#1174902211yescharacteristic
740C2#1174904411yescharacteristic
741C2#1174904511yescharacteristic
742C2#1174948811yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D4×D5C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1786
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91116C2semidirect
3. C2×C5×#832C2semidirect
4. #11748759C2semidirect
5. C2×#90965C2semidirect
6. C2×#90964C2semidirect
7. C2×#90955C2semidirect
17. C2×C3×D4×D5C4semidirect
20. C2×C4⋊Dic15C22semidirect
21. C22×C3⋊#168C22semidirect
22. C2×C5×C4⋊Dic3C22semidirect
23. C22×C5×C3⋊C8C22semidirect
93. C2×#832D5semidirect
104. C2×D4×D5Dic3semidirect
151. C3×C5×D4C22⋊C4semidirect
171. C3×D20C22⋊C4semidirect
191. C2×C4⋊Dic3C2×D5semidirect
193. C22×C3⋊C8C2×D5semidirect
285. C2×C3×D5#102semidirect
375. C5×D4#217semidirect
395. D20#217semidirect
471. C3×D4#685semidirect
521. C2×D5#832semidirect
579. C3×C5#1786semidirect
663. D4#6665semidirect
695. C5#72128semidirect
732. C3#10600991semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×#911162
C2×C5×#8322
#117487592
C2×#909652
C2×#909642
C2×#909552
#106009913
#721285