Finite Group Databasebeta

← #14306100

Subgroups — #14306100

Order 1920.

816 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
1C2×C3×#4085C211yesmaximal, characteristic
2C2×#91118C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4#11749506C211yesmaximal, characteristic, complemented
5Dic5×#217C211yesmaximal, characteristic, complemented
6C2×#90995C211yesmaximal, characteristic, complemented
7C2×#90995C211yesmaximal, characteristic, complemented
8#10600823—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C22⋊D5C411yescharacteristic, complemented
11C22×C3×C22⋊D5C2211yescharacteristic
12C23×C3×Dic5C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C5×#217C2211yescharacteristic
17C2×C3×C22⋊Dic5C411yescharacteristic, complemented
18C3×#4085—21no—
19C3×#4085—21no—
20C3×#4085—21no—
21C3×#4085—21no—
22C2×C3×#685C411yescharacteristic, complemented
23C2×C3×#683C411yescharacteristic, complemented
24C2×#6668—21no—
25C2×Dic3×Dic5—21no—
26#91118—22no—
27C5×#834—22no—
28#90995—22no—
29#90995—22no—
30#90994—21no—
31#90994—21no—
32#71686—51nomaximal, Hall
33C2×#4085D311yescharacteristic
34C2×C5×#99—31no—
35C2×#3966—31no—
36C2×#3938—31no—
37C2×#3938—31no—
38#65231—31no—
39C22⋊C4×Dic5—31no—
40C24×C3×C5C2×C411yescharacteristic
41C24×C3×C5C2311yescharacteristic
42C23×C3×D5C2×C411yescharacteristic
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C22×C3×C4×C5C2×C411yescharacteristic
50C22×Dic15—21no—
51C22×Dic15—21no—
52C22×C5×Dic3—21no—
53C22×C5×Dic3—21no—
54C2×C3×C22⋊D5—21no—
55C2×C3×C22⋊D5—21no—
56C2×C3×C22⋊D5—21no—
57C2×C3×C22⋊D5—21no—
58C2×C3×C22⋊D5—21no—
59C2×C3×C22⋊D5—21no—
60C2×C3×C22⋊D5—21no—
61C2×C3×C22⋊D5—21no—
62C2×C3×C22⋊D5—42no—
63C22×C3×Dic5—42no—
64C22×C3×Dic5C2×C411yescharacteristic
65C22×C3×Dic5C2×C411yescharacteristic
66C22×C3×Dic5C2×C411yescharacteristic
67C22×C3×Dic5D411yescharacteristic
68C22×C3×Dic5D411yescharacteristic
69C22×C3×Dic5D411yescharacteristic
70C22×C3×Dic5D411yescharacteristic
71#6719—21no—
72#6719—21no—
73#6719—21no—
74#6719D412yescomplemented
75C5×#217—21no—
76C5×#217—21no—
77C5×#217—21no—
78C5×#217D412yescomplemented
79C3×C22⋊Dic5—21no—
80C3×C22⋊Dic5—21no—
81C3×#685—21no—
82C3×#685—21no—
83C3×#683—21no—
84C3×#683—21no—
85#6668—42no—
86Dic3×Dic5—42no—
87C2×C3×#121—51no—
88C2×#834—51no—
89C2×#834—51no—
90C2×#834—51no—
91C2×#834D511yescharacteristic, complemented
92#5212—51no—
93C4×#217—51no—
94C22×C5×D4C2×D311yescharacteristic
95C22×C22⋊D5Dic311yescharacteristic, complemented
96C22×C22⋊D5C2×D311yescharacteristic
97C23×Dic5C2×D311yescharacteristic
98C2×C5×C22⋊C4—31no—
99C2×C5×C22⋊C4—31no—
100C2×C22⋊Dic5—31no—
101C2×C22⋊Dic5—31no—
102C2×C22⋊Dic5Dic311yescharacteristic, complemented
103#4085—21no—
104#4085—21no—
105#4085—21no—
106#4085—21no—
107C2×#685Dic311yescharacteristic, complemented
108C2×#683—61no—
109C2×#683Dic311yescharacteristic, complemented
110C2×C4×Dic5—61no—
111C5×#99—62no—
112#3966—62no—
113#3963—61no—
114#3963—61no—
115#3938—62no—
116#3938—62no—
117#1964—151noSylow
118C23×C3×C5—21no—
119C23×C3×C5—21no—
120C23×C3×C5—21no—
121C23×C3×C5—41no—
122C23×C3×C5—41no—
123C23×C3×C5—41no—
124C23×C3×C5—41no—
125C23×C3×C5C22×C411yescharacteristic
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C23×C3×C5C2×D411yescharacteristic
130C23×C3×C5#4111yescharacteristic
131C23×C3×C5#4111yescharacteristic
132C22×C3×D5—21no—
133C22×C3×D5—21no—
134C22×C3×D5—21no—
135C22×C3×D5—41no—
136C22×C3×D5—41no—
137C3×C5×D4—41no—
138C3×C5×D4—41no—
139C3×C5×D4—41no—
140C3×C5×D4—41no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×Dic15—22no—
145C2×Dic15—41no—
146C2×Dic15—41no—
147C2×Dic15—41no—
148C2×Dic15—41no—
149C2×Dic15—41no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—41no—
152C2×C5×Dic3—41no—
153C2×C5×Dic3—41no—
154C2×C5×Dic3—41no—
155C2×C5×Dic3—41no—
156C3×C22⋊D5—42no—
157C3×C22⋊D5—41no—
158C3×C22⋊D5—41no—
159C3×C22⋊D5—41no—
160C3×C22⋊D5—41no—
161C3×C22⋊D5—42no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—41no—
169C2×C3×Dic5—41no—
170C2×C3×Dic5—41no—
171C2×C3×Dic5C22⋊C411yescharacteristic
172C2×C3×Dic5C22⋊C411yescharacteristic
173C2×C3×Dic5C22⋊C411yescharacteristic
174C2×C3×Dic5C22⋊C411yescharacteristic
175C22×C3×D4—51no—
176C22×C3×D4—51no—
177C22×C3×D4C2×D511yescharacteristic
178C23×C3×C4—51no—
179C3×#121—101no—
180C3×#121—101no—
181C3×#121—101no—
182C3×#121—101no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C22⋊C4—51no—
185C2×C3×C22⋊C4—51no—
186C2×#217—51no—
187C2×#217—51no—
188C2×#217C2×D511yescharacteristic
189C2×#217C2×D511yescharacteristic
190C2×C4⋊Dic3—101no—
191C2×C4×Dic3—101no—
192#834—22no—
193#834—102no—
194#834—102no—
195#834—102no—
196C3⋊#95—101no—
197C3⋊#95—101no—
198C24×C5C2×Dic311yescharacteristic
199C24×C5C22×D311yescharacteristic
200C23×D5C2×Dic311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C22×C4×C5—61no—
208C22×C4×C5—61no—
209C22×C4×C5C2×Dic311yescharacteristic
210C2×C22⋊D5—21no—
211C2×C22⋊D5—21no—
212C2×C22⋊D5—21no—
213C2×C22⋊D5—21no—
214C2×C22⋊D5—21no—
215C2×C22⋊D5—21no—
216C2×C22⋊D5—21no—
217C2×C22⋊D5—21no—
218C2×C22⋊D5—42no—
219C22×Dic5—42no—
220C22×Dic5—61no—
221C22×Dic5—61no—
222C22×Dic5C2×Dic311yescharacteristic
223C22×Dic5C2×Dic311yescharacteristic
224C22×Dic5C2×Dic311yescharacteristic
225C22×Dic5#6711yescharacteristic
226C22×Dic5#6711yescharacteristic
227C22×Dic5#6711yescharacteristic
228C22×Dic5#6711yescharacteristic
229C5×C22⋊C4—32no—
230C5×C22⋊C4—61no—
231C5×C22⋊C4—61no—
232C5×C22⋊C4—61no—
233C22⋊Dic5—21no—
234C22⋊Dic5—21no—
235C22⋊Dic5—32no—
236C22⋊Dic5—61no—
237C22⋊Dic5—61no—
238C22⋊Dic5—61no—
239#685—21no—
240#685—21no—
241#683—21no—
242#683—21no—
243#683—122no—
244C4×Dic5—122no—
245C2×#121—51no—
246C2×#99—31no—
247C2×#99—151no—
248C2×#99—151no—
249C2×#99—151no—
250#380—151no—
251C4×C22⋊C4—151no—
252C22×C3×C5—21no—
253C22×C3×C5—21no—
254C22×C3×C5—21no—
255C22×C3×C5—21no—
256C22×C3×C5—21no—
257C22×C3×C5—21no—
258C22×C3×C5—41no—
259C22×C3×C5—41no—
260C22×C3×C5—41no—
261C22×C3×C5—41no—
262C22×C3×C5—41no—
263C22×C3×C5—41no—
264C22×C3×C5—41no—
265C22×C3×C5—81no—
266C22×C3×C5—81no—
267C22×C3×C5C2×C22⋊C411yescharacteristic
268C22×C3×C5C4×D411yescharacteristic
269C22×C3×C5C4×D411yescharacteristic
270C22×C3×C5#12111yescharacteristic
271C22×C3×C5#12111yescharacteristic
272C22×C3×C5#12411yescharacteristic
273C22×C3×C5#12711yescharacteristic
274C2×C3×D5—41no—
275C2×C3×D5—41no—
276C2×C3×D5—41no—
277C2×C3×D5—81no—
278C2×C3×D5—81no—
279C3×C4×C5—41no—
280Dic15—42no—
281Dic15—81no—
282C3×Dic5—21no—
283C3×Dic5—21no—
284C3×Dic5—21no—
285C3×Dic5—41no—
286C3×Dic5#9912yescomplemented
287C5×Dic3—42no—
288C5×Dic3—81no—
289C24×C3—51no—
290C24×C3C4×D511yescharacteristic
291C24×C3C22×D511yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—101no—
299C2×C3×D4—101no—
300C2×C3×D4—101no—
301C2×C3×D4—101no—
302C2×C3×D4—101no—
303C2×C3×D4—101no—
304C2×C3×D4—101no—
305C2×C3×D4—101no—
306C2×C3×D4—202no—
307C22×C3×C4—51no—
308C22×C3×C4—51no—
309C22×C3×C4—51no—
310C22×C3×C4—51no—
311C22×C3×C4—51no—
312C22×C3×C4—51no—
313C22×C3×C4—51no—
314C22×C3×C4—202no—
315C22×C3×C4C4×D511yescharacteristic
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—101no—
319C22×Dic3—101no—
320C3×C4⋊C4—101no—
321C3×C4⋊C4—101no—
322C3×C22⋊C4—101no—
323C3×C22⋊C4—101no—
324C3×C22⋊C4—101no—
325C3×C22⋊C4—101no—
326#217—21no—
327#217—21no—
328#217—21no—
329#217—52no—
330#217—101no—
331#217—101no—
332#217—101no—
333#217C22⋊D512yescomplemented
334C4⋊Dic3—202no—
335C4×Dic3—202no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5D3×D411yescharacteristic
344C23×C5D3×D411yescharacteristic
345C23×C5#23711yescharacteristic
346C23×C5#23711yescharacteristic
347C23×C5C22×Dic311yescharacteristic
348C23×C5C2×#6711yescharacteristic
349C23×C5C2×#6711yescharacteristic
350C22×D5—21no—
351C22×D5—21no—
352C22×D5—21no—
353C22×D5—41no—
354C22×D5—41no—
355C5×D4—41no—
356C5×D4—41no—
357C5×D4—41no—
358C5×D4—41no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—21no—
362C2×C4×C5—62no—
363C2×C4×C5—121no—
364C2×C4×C5—121no—
365C2×C4×C5—121no—
366C2×C4×C5—121no—
367C2×C4×C5—121no—
368C22⋊D5—42no—
369C22⋊D5—41no—
370C22⋊D5—41no—
371C22⋊D5—41no—
372C22⋊D5—41no—
373C22⋊D5—42no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—21no—
378C2×Dic5—21no—
379C2×Dic5—21no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—62no—
384C2×Dic5—121no—
385C2×Dic5—121no—
386C2×Dic5—121no—
387C2×Dic5—121no—
388C2×Dic5—121no—
389C2×Dic5#21711yescharacteristic
390C2×Dic5#21711yescharacteristic
391C2×Dic5#21711yescharacteristic
392C2×Dic5#21711yescharacteristic
393C22×D4—51no—
394C22×D4—51no—
395C22×D4D3×D511yescharacteristic
396C23×C4—51no—
397#121—101no—
398#121—101no—
399#121—101no—
400#121—101no—
401C2×C4⋊C4—51no—
402C2×C4⋊C4—301no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—51no—
406C2×C22⋊C4—51no—
407C2×C22⋊C4—151no—
408C2×C22⋊C4—151no—
409C2×C42—301no—
410#99—62no—
411#99—302no—
412#99—302no—
413#99—302no—
414#95—301no—
415#95—301no—
416C2×C3×C5—21no—
417C2×C3×C5—21no—
418C2×C3×C5—21no—
419C2×C3×C5—21no—
420C2×C3×C5—21no—
421C2×C3×C5—21no—
422C2×C3×C5—81no—
423C2×C3×C5#39011yescharacteristic
424C2×C3×C5C2×#9911yescharacteristic
425C2×C3×C5#41011yescharacteristic
426C3×D5—81no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—101no—
435C23×C3—101no—
436C23×C3—101no—
437C23×C3—201no—
438C23×C3—201no—
439C23×C3C2×C4×D511yescharacteristic
440C23×C3#70911yescharacteristic
441C23×C3D4×D511yescharacteristic
442C23×C3D4×D511yescharacteristic
443C23×C3D4×D511yescharacteristic
444C23×C3#71111yescharacteristic
445C23×C3C2×C22⋊D511yescharacteristic
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—202no—
451C3×D4—202no—
452C3×D4—201no—
453C3×D4—201no—
454C3×D4—201no—
455C3×D4—201no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—51no—
460C2×C3×C4—51no—
461C2×C3×C4—51no—
462C2×C3×C4—51no—
463C2×C3×C4—102no—
464C2×C3×C4—102no—
465C2×C3×C4—102no—
466C2×C3×C4—101no—
467C2×C3×C4—101no—
468C2×C3×C4—101no—
469C2×C3×C4—201no—
470C2×C3×C4—201no—
471C2×C3×C4—201no—
472C2×Dic3—22no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—102no—
479C2×Dic3—201no—
480C2×Dic3—201no—
481C2×Dic3—201no—
482C2×Dic3—201no—
483C2×Dic3—201no—
484C22×C5—21no—
485C22×C5—21no—
486C22×C5—21no—
487C22×C5—21no—
488C22×C5—21no—
489C22×C5—21no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5—41no—
496C22×C5—41no—
497C22×C5—81no—
498C22×C5—81no—
499C22×C5D4×Dic311yescharacteristic
500C22×C5D4×Dic311yescharacteristic
501C22×C5#93611yescharacteristic
502C22×C5#93811yescharacteristic
503C22×C5#93811yescharacteristic
504C22×C5#94011yescharacteristic
505C22×C5C2×#21711yescharacteristic
506C2×D5—41no—
507C2×D5—41no—
508C2×D5—41no—
509C2×D5—81no—
510C2×D5—81no—
511C4×C5—41no—
512C4×C5—122no—
513C4×C5—241no—
514Dic5—21no—
515Dic5—21no—
516Dic5—21no—
517Dic5—41no—
518Dic5—122no—
519Dic5—241no—
520Dic5#83412yescomplemented
521C24—51no—
522C24D5×Dic311yescharacteristic
523C24C2×D3×D511yescharacteristic
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—101no—
531C2×D4—101no—
532C2×D4—101no—
533C2×D4—101no—
534C2×D4—101no—
535C2×D4—101no—
536C2×D4—101no—
537C2×D4—101no—
538C2×D4—202no—
539C22×C4—51no—
540C22×C4—51no—
541C22×C4—51no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—202no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4D5×Dic311yescharacteristic
552C4⋊C4—101no—
553C4⋊C4—101no—
554C4⋊C4—602no—
555C22⋊C4—32no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—101no—
560C22⋊C4—101no—
561C22⋊C4—101no—
562C22⋊C4—101no—
563C22⋊C4—152no—
564C22⋊C4—301no—
565C22⋊C4—301no—
566C22⋊C4—301no—
567C42—602no—
568C3×C5#196411yescharacteristic, complemented, Hall
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—201no—
585C22×C3—201no—
586C22×C3—201no—
587C22×C3—401no—
588C22×C3—401no—
589C22×C3D5×C22⋊C411yescharacteristic
590C22×C3#402711yescharacteristic
591C22×C3#403011yescharacteristic
592C22×C3#403111yescharacteristic
593C22×C3C4×C22⋊D511yescharacteristic
594C22×C3#408511yescharacteristic
595C22×C3#408611yescharacteristic
596C3×C4—41no—
597C3×C4—52no—
598C3×C4—101no—
599C3×C4—101no—
600C3×C4—101no—
601C3×C4—201no—
602Dic3—42no—
603Dic3—81no—
604Dic3—202no—
605Dic3—401no—
606C2×C5—21no—
607C2×C5—21no—
608C2×C5—21no—
609C2×C5—21no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—81no—
613C2×C5C2×#83411yescharacteristic
614C2×C5#522111yescharacteristic
615C2×C5#524011yescharacteristic
616D5—81no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—101no—
625C23—101no—
626C23—101no—
627C23—201no—
628C23—201no—
629C23C2×D5×Dic311yescharacteristic
630C23#677911yescharacteristic
631C23#678011yescharacteristic
632C23D5×#6711yescharacteristic
633C23D5×#6711yescharacteristic
634C23D3×C22⋊D511yescharacteristic
635C23#679011yescharacteristic
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—202no—
641D4—202no—
642D4—201no—
643D4—201no—
644D4—201no—
645D4—201no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—51no—
650C2×C4—51no—
651C2×C4—51no—
652C2×C4—51no—
653C2×C4—62no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—201no—
666C2×C4—201no—
667C2×C4—201no—
668C2×C4—302no—
669C2×C4—601no—
670C2×C4—601no—
671C2×C4—601no—
672C2×C4—601no—
673C2×C4—601no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—81no—
681C2×C3—401no—
682C2×C3#6502911yescharacteristic
683C2×C3D5×#9911yescharacteristic
684C2×C3#6524611yescharacteristic
685C5#7168611yescharacteristic, complemented, Sylow
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—81no—
700C22—81no—
701C22—201no—
702C22—201no—
703C22—201no—
704C22—401no—
705C22—401no—
706C22#9153311yescharacteristic
707C22#9153411yescharacteristic
708C22D5×#21711yescharacteristic
709C22Dic3×C22⋊D511yescharacteristic
710C22#9155911yescharacteristic
711C22#9156511yescharacteristic
712C22#9156711yescharacteristic
713C4—41no—
714C4—52no—
715C4—101no—
716C4—101no—
717C4—101no—
718C4—122no—
719C4—201no—
720C4—241no—
721C4—602no—
722C4—1201no—
723C3#1060082311yescharacteristic, complemented, Sylow
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—81no—
731C2—401no—
732C2D5×#83411yescharacteristic
733C2#1174917211yescharacteristic
734C2#1174948911yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4085C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1964
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91118C2semidirect
3. C2×C5×#834C2semidirect
4. #11749506C2semidirect
5. Dic5×#217C2semidirect
6. C2×#90995C2semidirect
7. C2×#90995C2semidirect
10. C22×C3×C22⋊D5C4semidirect
17. C2×C3×C22⋊Dic5C4semidirect
22. C2×C3×#685C4semidirect
23. C2×C3×#683C4semidirect
74. #6719D4semidirect
78. C5×#217D4semidirect
91. C2×#834D5semidirect
95. C22×C22⋊D5Dic3semidirect
102. C2×C22⋊Dic5Dic3semidirect
107. C2×#685Dic3semidirect
109. C2×#683Dic3semidirect
286. C3×Dic5#99semidirect
333. #217C22⋊D5semidirect
520. Dic5#834semidirect
568. C3×C5#1964semidirect
685. C5#71686semidirect
723. C3#10600823semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40852
C2×#911182
C2×C5×#8342
#117495062
Dic5×#2172
C2×#909952
#106008233
#716865