Finite Group Databasebeta

← C5×#71546 #14280057

Subgroups — C5×#71546 #14280057

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
2C22×C5×#217C212yesmaximal
3C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×C5×C3⋊#95C212yesmaximal, complemented
6C5×#1439—31nomaximal, Hall
7C25×C3×C5C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic
9C23×C3×C4×C5C2211yescharacteristic
10C23×C5×Dic3C2212yes—
11C23×C5×Dic3C2212yes—
12C2×C3×C5×C22⋊C4—22no—
13C2×C3×C5×C22⋊C4—22no—
14C2×C3×C5×C22⋊C4C414yescomplemented
15C2×C5×#217—24no—
16C2×C5×#217—24no—
17C2×C5×#217—24no—
18C2×C5×C4⋊Dic3—22no—
19C2×C5×C4⋊Dic3—24no—
20C5×C3⋊#95—22no—
21C5×C3⋊#95—24no—
22#71546C511yesmaximal, characteristic, direct product factor, Hall
23C22×C5×C4⋊C4—31no—
24C22×C5×C22⋊C4—32no—
25C22×C5×C22⋊C4D311yescharacteristic
26C2×C5×#95—31no—
27C2×C5×#95—32no—
28C24×C3×C5—22no—
29C24×C3×C5—22no—
30C24×C3×C5—21no—
31C24×C3×C5—21no—
32C24×C3×C5—21no—
33C24×C3×C5—21no—
34C24×C3×C5—22no—
35C24×C3×C5—22no—
36C24×C3×C5C2×C412yes—
37C24×C3×C5D412yes—
38C24×C3×C5Q812yes—
39C24×C3×C5C2311yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—22no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5C2×C412yes—
47C22×C3×C4×C5C2×C412yes—
48C22×C3×C4×C5D412yes—
49C22×C3×C4×C5D412yes—
50C22×C5×Dic3—22no—
51C22×C5×Dic3—22no—
52C22×C5×Dic3—22no—
53C22×C5×Dic3—22no—
54C22×C5×Dic3—22no—
55C22×C5×Dic3—22no—
56C22×C5×Dic3—22no—
57C22×C5×Dic3—22no—
58C22×C5×Dic3—22no—
59C22×C5×Dic3—22no—
60C22×C5×Dic3—22no—
61C22×C5×Dic3—22no—
62C22×C5×Dic3D414yes—
63C22×C5×Dic3D414yes—
64C3×C5×C22⋊C4—28no—
65C5×#217—216no—
66C5×C4⋊Dic3—28no—
67C22×C3×C22⋊C4C2×C511yescharacteristic
68C22×#217C2×C512yes—
69C22×C4⋊Dic3C2×C511yescharacteristic, complemented
70C2×C3⋊#95C2×C511yescharacteristic, complemented
71C2×C3⋊#95C2×C512yescomplemented
72C25×C5C2×D311yescharacteristic
73C23×C4×C5—32no—
74C23×C4×C5—32no—
75C23×C4×C5C2×D311yescharacteristic
76C23×C4×C5C2×D311yescharacteristic
77C2×C5×C4⋊C4—64no—
78C2×C5×C4⋊C4—62no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—64no—
82C2×C5×C22⋊C4—64no—
83C2×C5×C22⋊C4—64no—
84C2×C5×C22⋊C4Dic314yescomplemented
85C5×#95—64no—
86C5×#95—62no—
87#1439—31noSylow
88C23×C3×C5—22no—
89C23×C3×C5—22no—
90C23×C3×C5—24no—
91C23×C3×C5—24no—
92C23×C3×C5—24no—
93C23×C3×C5—22no—
94C23×C3×C5—22no—
95C23×C3×C5—22no—
96C23×C3×C5—22no—
97C23×C3×C5—24no—
98C23×C3×C5—24no—
99C23×C3×C5—24no—
100C23×C3×C5—41no—
101C23×C3×C5—42no—
102C23×C3×C5—42no—
103C23×C3×C5—42no—
104C23×C3×C5—41no—
105C23×C3×C5—42no—
106C23×C3×C5—42no—
107C23×C3×C5—41no—
108C23×C3×C5—42no—
109C23×C3×C5—41no—
110C23×C3×C5C4⋊C414yescomplemented
111C23×C3×C5C22×C411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C23×C3×C5C2×D411yescharacteristic
114C23×C3×C5C2×D411yescharacteristic
115C23×C3×C5C2×D412yes—
116C23×C3×C5C2×D412yes—
117C23×C3×C5C2×Q811yescharacteristic
118C23×C3×C5#4111yescharacteristic
119C23×C3×C5#4111yescharacteristic
120C23×C3×C5#4112yes—
121C23×C3×C5#4112yes—
122C2×C3×C4×C5—24no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—24no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—24no—
128C2×C3×C4×C5—42no—
129C2×C3×C4×C5—41no—
130C2×C3×C4×C5—41no—
131C2×C3×C4×C5C22⋊C414yescomplemented
132C2×C5×Dic3—24no—
133C2×C5×Dic3—24no—
134C2×C5×Dic3—24no—
135C2×C5×Dic3—24no—
136C2×C5×Dic3—24no—
137C2×C5×Dic3—24no—
138C2×C5×Dic3—42no—
139C2×C5×Dic3—42no—
140C2×C5×Dic3—42no—
141C2×C5×Dic3—42no—
142C2×C5×Dic3—42no—
143C2×C5×Dic3—42no—
144C2×C5×Dic3—42no—
145C2×C5×Dic3—42no—
146C25×C3C22×C511yescharacteristic
147C23×C3×C4C22×C511yescharacteristic
148C23×C3×C4C22×C511yescharacteristic
149C23×Dic3C22×C512yes—
150C23×Dic3C22×C512yes—
151C2×C3×C22⋊C4—22no—
152C2×C3×C22⋊C4—22no—
153C2×C3×C22⋊C4C4×C514yescomplemented
154C2×#217—24no—
155C2×#217—24no—
156C2×#217—24no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—24no—
159C3⋊#95—22no—
160C3⋊#95—24no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5Dic612yes—
170C24×C5D1212yes—
171C24×C5C2×Dic312yes—
172C24×C5C22×D311yescharacteristic
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—34no—
180C22×C4×C5—34no—
181C22×C4×C5—62no—
182C22×C4×C5—62no—
183C22×C4×C5—62no—
184C22×C4×C5—62no—
185C22×C4×C5—62no—
186C22×C4×C5—62no—
187C22×C4×C5—62no—
188C22×C4×C5—62no—
189C22×C4×C5—62no—
190C22×C4×C5—62no—
191C22×C4×C5—62no—
192C22×C4×C5—62no—
193C22×C4×C5C2×Dic312yes—
194C22×C4×C5C2×Dic312yes—
195C22×C4×C5#6712yes—
196C22×C4×C5#6712yes—
197C5×C4⋊C4—68no—
198C5×C22⋊C4—28no—
199C5×C22⋊C4—616no—
200C22×C4⋊C4—31no—
201C22×C22⋊C4—32no—
202C22×C22⋊C4C5×D311yescharacteristic
203C2×#95—32no—
204C2×#95—31no—
205C22×C3×C5—24no—
206C22×C3×C5—28no—
207C22×C3×C5—42no—
208C22×C3×C5—44no—
209C22×C3×C5—42no—
210C22×C3×C5—42no—
211C22×C3×C5—42no—
212C22×C3×C5—44no—
213C22×C3×C5—44no—
214C22×C3×C5—42no—
215C22×C3×C5—42no—
216C22×C3×C5C2×C22⋊C411yescharacteristic
217C22×C3×C5C2×C4⋊C411yescharacteristic
218C22×C3×C5#11711yescharacteristic
219C22×C3×C5C4×D412yes—
220C22×C3×C5C4×D412yes—
221C22×C3×C5#12012yes—
222C22×C3×C5#12011yescharacteristic
223C22×C3×C5#12112yes—
224C22×C3×C5#12111yescharacteristic
225C22×C3×C5#12111yescharacteristic
226C22×C3×C5#12112yes—
227C22×C3×C5#12112yes—
228C22×C3×C5C22⋊Q812yes—
229C22×C3×C5C22⋊Q812yes—
230C22×C3×C5C22⋊Q811yescharacteristic
231C22×C3×C5C22⋊Q811yescharacteristic
232C22×C3×C5#12312yes—
233C22×C3×C5#12312yes—
234C22×C3×C5#12311yescharacteristic
235C22×C3×C5#12412yes—
236C22×C3×C5#12411yescharacteristic
237C22×C3×C5#12612yes—
238C22×C3×C5#12711yescharacteristic
239C3×C4×C5—24no—
240C3×C4×C5—42no—
241C5×Dic3—44no—
242C5×Dic3—44no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3C2×C4×C512yes—
252C24×C3C5×D412yes—
253C24×C3C5×Q812yes—
254C24×C3C23×C511yescharacteristic
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4C2×C4×C512yes—
262C22×C3×C4C2×C4×C512yes—
263C22×C3×C4C5×D412yes—
264C22×C3×C4C5×D412yes—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3C5×D414yes—
278C22×Dic3C5×D414yes—
279C3×C22⋊C4—28no—
280#217—216no—
281C4⋊Dic3—28no—
282C23×C5—24no—
283C23×C5—24no—
284C23×C5—24no—
285C23×C5—24no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—22no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5—42no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5—41no—
304C23×C5C4⋊Dic314yescomplemented
305C23×C5C2×Dic611yescharacteristic
306C23×C5C2×D1211yescharacteristic
307C23×C5#23511yescharacteristic
308C23×C5#23511yescharacteristic
309C23×C5D3×D412yes—
310C23×C5D3×D412yes—
311C23×C5#23712yes—
312C23×C5#23712yes—
313C23×C5C22×Dic311yescharacteristic
314C23×C5C2×#6711yescharacteristic
315C23×C5C2×#6711yescharacteristic
316C2×C4×C5—24no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—24no—
320C2×C4×C5—24no—
321C2×C4×C5—22no—
322C2×C4×C5—41no—
323C2×C4×C5—42no—
324C2×C4×C5—41no—
325C2×C4×C5—64no—
326C2×C4×C5—64no—
327C2×C4×C5—64no—
328C2×C4×C5—64no—
329C2×C4×C5—64no—
330C2×C4×C5—64no—
331C2×C4×C5—122no—
332C2×C4×C5—122no—
333C2×C4×C5—122no—
334C2×C4×C5—122no—
335C2×C4×C5—122no—
336C2×C4×C5—122no—
337C2×C4×C5—122no—
338C2×C4×C5—122no—
339C2×C4×C5#21714yescomplemented
340C25C2×C5×D311yescharacteristic
341C23×C4—32no—
342C23×C4—32no—
343C23×C4C2×C5×D311yescharacteristic
344C23×C4C2×C5×D311yescharacteristic
345C2×C4⋊C4—64no—
346C2×C4⋊C4—62no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4—64no—
351C2×C22⋊C4—64no—
352C2×C22⋊C4C5×Dic314yescomplemented
353#95—64no—
354#95—62no—
355C2×C3×C5—44no—
356C2×C3×C5#38011yescharacteristic
357C2×C3×C5#38512yes—
358C2×C3×C5#38611yescharacteristic
359C2×C3×C5#38812yes—
360C2×C3×C5#39011yescharacteristic
361C2×C3×C5#39211yescharacteristic
362C2×C3×C5#39311yescharacteristic
363C2×C3×C5#39412yes—
364C2×C3×C5#39612yes—
365C2×C3×C5#39711yescharacteristic
366C2×C3×C5#39911yescharacteristic
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—24no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—41no—
385C23×C3—42no—
386C23×C3—41no—
387C23×C3—42no—
388C23×C3—41no—
389C23×C3C5×C4⋊C414yescomplemented
390C23×C3C22×C4×C511yescharacteristic
391C23×C3C2×C5×D411yescharacteristic
392C23×C3C2×C5×D412yes—
393C23×C3C2×C5×D412yes—
394C23×C3C2×C5×D411yescharacteristic
395C23×C3C2×C5×D411yescharacteristic
396C23×C3C2×C5×Q811yescharacteristic
397C23×C3C5×#4111yescharacteristic
398C23×C3C5×#4111yescharacteristic
399C23×C3C5×#4112yes—
400C23×C3C5×#4112yes—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4C5×C22⋊C414yescomplemented
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C22×C5—28no—
426C22×C5—24no—
427C22×C5—42no—
428C22×C5—44no—
429C22×C5—42no—
430C22×C5—44no—
431C22×C5—42no—
432C22×C5—42no—
433C22×C5—44no—
434C22×C5—42no—
435C22×C5—42no—
436C22×C5#87812yes—
437C22×C5#87812yes—
438C22×C5#87912yes—
439C22×C5#88212yes—
440C22×C5#88312yes—
441C22×C5#88412yes—
442C22×C5#88512yes—
443C22×C5#88612yes—
444C22×C5#92411yescharacteristic
445C22×C5#92411yescharacteristic
446C22×C5C2×C4⋊Dic311yescharacteristic
447C22×C5#92611yescharacteristic
448C22×C5#93011yescharacteristic
449C22×C5#93011yescharacteristic
450C22×C5D4×Dic312yes—
451C22×C5D4×Dic312yes—
452C22×C5#93511yescharacteristic
453C22×C5#93611yescharacteristic
454C22×C5#93711yescharacteristic
455C22×C5#93812yes—
456C22×C5#93912yes—
457C22×C5#94011yescharacteristic
458C22×C5C2×#21711yescharacteristic
459C4×C5—24no—
460C4×C5—42no—
461C4×C5—124no—
462C4×C5—124no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24C5×Dic612yes—
472C24C5×D1212yes—
473C24C2×C5×Dic312yes—
474C24C22×C5×D311yescharacteristic
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—34no—
482C22×C4—34no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4C2×C5×Dic312yes—
496C22×C4C2×C5×Dic312yes—
497C22×C4C5×#6712yes—
498C22×C4C5×#6712yes—
499C4⋊C4—68no—
500C22⋊C4—28no—
501C22⋊C4—616no—
502C3×C5#143911yescharacteristic, complemented, Hall
503C22×C3—24no—
504C22×C3—28no—
505C22×C3—42no—
506C22×C3—44no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3C2×C5×C22⋊C411yescharacteristic
515C22×C3C2×C5×C4⋊C411yescharacteristic
516C22×C3C5×#11711yescharacteristic
517C22×C3C4×C5×D412yes—
518C22×C3C4×C5×D412yes—
519C22×C3C5×#12012yes—
520C22×C3C5×#12011yescharacteristic
521C22×C3C5×#12112yes—
522C22×C3C5×#12111yescharacteristic
523C22×C3C5×#12111yescharacteristic
524C22×C3C5×#12112yes—
525C22×C3C5×#12112yes—
526C22×C3C5×C22⋊Q812yes—
527C22×C3C5×C22⋊Q812yes—
528C22×C3C5×C22⋊Q811yescharacteristic
529C22×C3C5×C22⋊Q811yescharacteristic
530C22×C3C5×#12312yes—
531C22×C3C5×#12312yes—
532C22×C3C5×#12311yescharacteristic
533C22×C3C5×#12412yes—
534C22×C3C5×#12411yescharacteristic
535C22×C3C5×#12612yes—
536C22×C3C5×#12711yescharacteristic
537C3×C4—24no—
538C3×C4—42no—
539Dic3—44no—
540Dic3—44no—
541C2×C5—44no—
542C2×C5#494711yescharacteristic
543C2×C5#494812yes—
544C2×C5#494911yescharacteristic
545C2×C5#495012yes—
546C2×C5#495112yes—
547C2×C5#495311yescharacteristic
548C2×C5#496011yescharacteristic
549C2×C5#496112yes—
550C2×C5#521211yescharacteristic
551C2×C5#522011yescharacteristic
552C2×C5#522111yescharacteristic
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—22no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—42no—
573C23—42no—
574C23—41no—
575C23C5×C4⋊Dic314yescomplemented
576C23C2×C5×Dic611yescharacteristic
577C23C2×C5×D1211yescharacteristic
578C23C5×#23511yescharacteristic
579C23C5×#23511yescharacteristic
580C23C5×D3×D412yes—
581C23C5×D3×D412yes—
582C23C5×#23712yes—
583C23C5×#23712yes—
584C23C22×C5×Dic311yescharacteristic
585C23C2×C5×#6711yescharacteristic
586C23C2×C5×#6711yescharacteristic
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—64no—
597C2×C4—64no—
598C2×C4—64no—
599C2×C4—64no—
600C2×C4—64no—
601C2×C4—64no—
602C2×C4—122no—
603C2×C4—122no—
604C2×C4—122no—
605C2×C4—122no—
606C2×C4—122no—
607C2×C4—122no—
608C2×C4—122no—
609C2×C4—122no—
610C2×C4C5×#21714yescomplemented
611C2×C3—44no—
612C2×C3C5×#38011yescharacteristic
613C2×C3C5×#38512yes—
614C2×C3C5×#38611yescharacteristic
615C2×C3C5×#38812yes—
616C2×C3C5×#39011yescharacteristic
617C2×C3C5×#39211yescharacteristic
618C2×C3C5×#39311yescharacteristic
619C2×C3C5×#39412yes—
620C2×C3C5×#39612yes—
621C2×C3C5×#39711yescharacteristic
622C2×C3C5×#39911yescharacteristic
623C5#7154611yescharacteristic, direct product factor, Sylow
624C22—28no—
625C22—24no—
626C22—42no—
627C22—44no—
628C22—42no—
629C22—44no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22C5×#87812yes—
636C22C5×#87812yes—
637C22C5×#87912yes—
638C22C5×#88212yes—
639C22C5×#88312yes—
640C22C5×#88412yes—
641C22C5×#88512yes—
642C22C5×#88612yes—
643C22C5×#92411yescharacteristic
644C22C5×#92411yescharacteristic
645C22C2×C5×C4⋊Dic311yescharacteristic
646C22C5×#92611yescharacteristic
647C22C5×#93011yescharacteristic
648C22C5×#93011yescharacteristic
649C22C5×D4×Dic312yes—
650C22C5×D4×Dic312yes—
651C22C5×#93511yescharacteristic
652C22C5×#93611yescharacteristic
653C22C5×#93711yescharacteristic
654C22C5×#93812yes—
655C22C5×#93912yes—
656C22C5×#94011yescharacteristic
657C22C2×C5×#21711yescharacteristic
658C4—24no—
659C4—42no—
660C4—124no—
661C4—124no—
662C3C5×#143911yescharacteristic, complemented, Sylow
663C2—44no—
664C2C5×#494711yescharacteristic
665C2C5×#494812yes—
666C2C5×#494911yescharacteristic
667C2C5×#495012yes—
668C2C5×#495112yes—
669C2C5×#495311yescharacteristic
670C2C5×#496011yescharacteristic
671C2C5×#496112yes—
672C2C5×#521211yescharacteristic
673C2C5×#522011yescharacteristic
674C2C5×#522111yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC25×C3×C5C22
cosocleC24×C3C23×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C5×#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C5×C4⋊Dic3C2semidirect
4. C2×C5×C3⋊#95C2semidirect
5. C2×C5×C3⋊#95C2semidirect
14. C2×C3×C5×C22⋊C4C4semidirect
22. #71546C5direct (N × H)
69. C22×C4⋊Dic3C2×C5semidirect
70. C2×C3⋊#95C2×C5semidirect
71. C2×C3⋊#95C2×C5semidirect
84. C2×C5×C22⋊C4Dic3semidirect
110. C23×C3×C5C4⋊C4semidirect
131. C2×C3×C4×C5C22⋊C4semidirect
153. C2×C3×C22⋊C4C4×C5semidirect
304. C23×C5C4⋊Dic3semidirect
339. C2×C4×C5#217semidirect
352. C2×C22⋊C4C5×Dic3semidirect
389. C23×C3C5×C4⋊C4semidirect
410. C2×C3×C4C5×C22⋊C4semidirect
502. C3×C5#1439semidirect
575. C23C5×C4⋊Dic3semidirect
610. C2×C4C5×#217semidirect
623. C5#71546direct (N × H)
662. C3C5×#1439semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C22×C5×#2172
C22×C5×C4⋊Dic32
C2×C5×C3⋊#952
C5×#14393
#715465