Finite Group Databasebeta

← C5×#24337 #11947057

Subgroups — C5×#24337 #11947057

Order 1280.

1070 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
1C2×C5×#554C211yesmaximal, characteristic
2C2×C5×#479C211yesmaximal, characteristic, complemented
3C2×C4×C5×SD16C211yesmaximal, characteristic
4C5×#2581C211yesmaximal, characteristic, complemented
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#2026C211yesmaximal, characteristic, complemented
8C5×#2024C211yesmaximal, characteristic, complemented
9C5×#1991C211yesmaximal, characteristic, complemented
10C5×#1984C211yesmaximal, characteristic, complemented
11C5×#1877C211yesmaximal, characteristic
12C5×#1877C211yesmaximal, characteristic
13C5×#1864C211yesmaximal, characteristic
14C5×#1862C211yesmaximal, characteristic
15C5×#1804C211yesmaximal, characteristic
16C22×C5×SD16C2211yescharacteristic
17C5×#554—24no—
18C5×#554—24no—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#125C2211yescharacteristic
21C2×C5×#125C2211yescharacteristic
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C22×C5×C4⋊C4—21no—
31C5×#479—24no—
32C4×C5×SD16—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#106C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×C4⋊C8C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C4×C5×C8C2211yescharacteristic
44C5×#400—21no—
45C5×#395—21no—
46C5×#391C2211yescharacteristic
47C5×#391C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#387—21no—
51C5×#387—21no—
52C5×#382C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24337C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8D411yescharacteristic
66C22×C5×Q8C2311yescharacteristic
67C22×C5×D4C2311yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C2×C5×SD16—22no—
72C2×C5×SD16—22no—
73C2×C5×SD16Q814yescomplemented
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C5×C4⋊Q8—22no—
79C5×C4⋊Q8—22no—
80C5×#125—22no—
81C5×#125—22no—
82C5×#125—22no—
83C5×#125D414yes—
84C5×C22⋊Q8—28no—
85C5×C22⋊Q8—28no—
86C5×C22⋊Q8—28no—
87C4×C5×Q8—22no—
88C4×C5×Q8—22no—
89C4×C5×Q8—22no—
90C4×C5×Q8—22no—
91C4×C5×D4—22no—
92C4×C5×D4—22no—
93C4×C5×D4—22no—
94C4×C5×D4—22no—
95C4×C5×D4—22no—
96C4×C5×D4D414yes—
97C2×C5×C4⋊C4—28no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4D411yescharacteristic
107C2×C5×C4⋊C4D411yescharacteristic
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C42×C5—21no—
119C2×C42×C5C2311yescharacteristic
120C2×C42×C5C2311yescharacteristic
121C2×C42×C5C2311yescharacteristic
122C5×#107—22no—
123C5×#106—22no—
124C5×#106—22no—
125C5×C4⋊C8—22no—
126C5×#103—22no—
127C5×#103—22no—
128C5×#103—22no—
129C5×#102—22no—
130C5×#102—22no—
131C5×#102—22no—
132C4×C5×C8—22no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C2×#554C2×C511yescharacteristic
142C2×#479C2×C511yescharacteristic, complemented
143C2×C4×SD16C2×C511yescharacteristic
144#2581C2×C511yescharacteristic, complemented
145#2059C2×C511yescharacteristic, complemented
146#2058C2×C511yescharacteristic, complemented
147#2026C2×C511yescharacteristic, complemented
148#2024C2×C511yescharacteristic, complemented
149#1991C2×C511yescharacteristic, complemented
150#1984C2×C511yescharacteristic, complemented
151#1877C2×C511yescharacteristic
152#1877C2×C511yescharacteristic
153#1864C2×C511yescharacteristic
154#1862C2×C511yescharacteristic
155#1804C2×C511yescharacteristic
156C24×C5—21no—
157C2×C5×Q8—24no—
158C2×C5×Q8—22no—
159C2×C5×Q8—22no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—41no—
166C2×C5×Q8—81no—
167C2×C5×Q8—81no—
168C2×C5×Q8C2×Q812yes—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4C2×D412yes—
173C2×C5×D4C2×Q812yes—
174C2×C5×D4#4112yes—
175C22×C4×C5—24no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—24no—
181C22×C4×C5—24no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—81no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5—81no—
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2411yescharacteristic
198C5×SD16—28no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8C2×Q812yes—
211C5×C4⋊C4—24no—
212C5×C4⋊C4—24no—
213C5×C4⋊C4—24no—
214C5×C4⋊C4—22no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—22no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—42no—
229C5×C4⋊C4—42no—
230C5×C4⋊C4—42no—
231C5×C4⋊C4C2×D412yes—
232C5×C4⋊C4C2×D412yes—
233C5×C4⋊C4C2×D412yes—
234C5×C22⋊C4—24no—
235C5×C22⋊C4—24no—
236C5×C22⋊C4—24no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—42no—
242C42×C5C2×D412yes—
243C42×C5C2×D412yes—
244C22×SD16C22×C511yescharacteristic
245#554—24no—
246#554—24no—
247C2×C4⋊Q8C22×C511yescharacteristic
248C2×#125C22×C511yescharacteristic
249C2×#125C22×C511yescharacteristic
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—21no—
253C2×C4×Q8C22×C511yescharacteristic
254C2×C4×Q8C22×C511yescharacteristic
255C2×C4×D4C22×C511yescharacteristic
256C2×C4×D4C22×C511yescharacteristic
257C2×C4×D4C22×C511yescharacteristic
258C22×C4⋊C4—21no—
259#479—24no—
260C4×SD16—24no—
261C2×#107C22×C511yescharacteristic
262C2×#106C22×C511yescharacteristic
263C2×#106C22×C511yescharacteristic
264C2×C4⋊C8C22×C511yescharacteristic
265C2×#103C22×C511yescharacteristic
266C2×#103C22×C511yescharacteristic
267C2×#103C22×C511yescharacteristic
268C2×#102C22×C511yescharacteristic
269C2×#102C22×C511yescharacteristic
270C2×#102C22×C511yescharacteristic
271C2×C4×C8C22×C511yescharacteristic
272#400—21no—
273#395—21no—
274#391C22×C511yescharacteristic
275#391C22×C511yescharacteristic
276#389C22×C511yescharacteristic
277#389C22×C511yescharacteristic
278#387—21no—
279#387—21no—
280#382C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#336C22×C511yescharacteristic
288#336C22×C511yescharacteristic
289#336C22×C511yescharacteristic
290#336C22×C511yescharacteristic
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5C22×D411yescharacteristic
299C5×Q8—22no—
300C5×Q8—22no—
301C5×Q8—44no—
302C5×Q8—41no—
303C5×Q8—41no—
304C5×Q8—84no—
305C5×D4—22no—
306C5×D4—22no—
307C5×D4—22no—
308C5×D4C22⋊Q814yes—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—48no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—84no—
347C2×C4×C5—84no—
348C2×C4×C5#12012yes—
349C2×C4×C5#12012yes—
350C2×C4×C5#13512yes—
351C2×C4×C5C22×D411yescharacteristic
352C2×C4×C5C22×D411yescharacteristic
353C2×C4×C5C22×Q811yescharacteristic
354C2×C4×C5C2×#4111yescharacteristic
355C2×C4×C52−1+411yescharacteristic
356C2×C4×C52−1+411yescharacteristic
357C5×C8—22no—
358C5×C8—41no—
359C5×C8—41no—
360C5×C8—41no—
361C22×Q8—21no—
362C22×Q8C5×D411yescharacteristic
363C22×Q8C23×C511yescharacteristic
364C22×D4C23×C511yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16C5×Q814yescomplemented
371C22×C8C23×C511yescharacteristic
372C22×C8C23×C511yescharacteristic
373C22×C8C23×C511yescharacteristic
374C22×C8C23×C511yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#125—22no—
378#125—22no—
379#125—22no—
380#125C5×D414yes—
381C22⋊Q8—28no—
382C22⋊Q8—28no—
383C22⋊Q8—28no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4C5×D414yes—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4C5×D411yescharacteristic
404C2×C4⋊C4C5×D411yescharacteristic
405C2×C4⋊C4C5×D411yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
407C2×C4⋊C4C23×C511yescharacteristic
408C2×C4⋊C4C23×C511yescharacteristic
409C2×C4⋊C4C23×C511yescharacteristic
410C2×C4⋊C4C23×C511yescharacteristic
411C2×C4⋊C4C23×C511yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C42—21no—
416C2×C42C23×C511yescharacteristic
417C2×C42C23×C511yescharacteristic
418C2×C42C23×C511yescharacteristic
419#107—22no—
420#106—22no—
421#106—22no—
422C4⋊C8—22no—
423#103—22no—
424#103—22no—
425#103—22no—
426#102—22no—
427#102—22no—
428#102—22no—
429C4×C8—22no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438C22×C5—24no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5C2×#12011yescharacteristic
446C22×C5#54811yescharacteristic
447C22×C5D4×Q811yescharacteristic
448C22×C5C2×#13511yescharacteristic
449C22×C5#57511yescharacteristic
450C22×C5#57711yescharacteristic
451C22×C5#57711yescharacteristic
452C4×C5—22no—
453C4×C5—22no—
454C4×C5—22no—
455C4×C5—42no—
456C4×C5—41no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5—41no—
460C4×C5—42no—
461C4×C5—42no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5C2×C22⋊Q811yescharacteristic
466C4×C5#53611yescharacteristic
467C4×C5#54811yescharacteristic
468C4×C5D4×Q811yescharacteristic
469C24—21no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—41no—
479C2×Q8—81no—
480C2×Q8—81no—
481C2×Q8C2×C5×Q812yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C2×C5×D412yes—
486C2×D4C2×C5×Q812yes—
487C2×D4C5×#4112yes—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4C2×C5×D411yescharacteristic
505C22×C4C2×C5×D411yescharacteristic
506C22×C4C2×C5×D411yescharacteristic
507C22×C4C2×C5×D411yescharacteristic
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C24×C511yescharacteristic
511SD16—28no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8C2×C5×Q812yes—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4C2×C5×D412yes—
545C4⋊C4C2×C5×D412yes—
546C4⋊C4C2×C5×D412yes—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42C2×C5×D412yes—
556C42C2×C5×D412yes—
557C2×C5—44no—
558C2×C5#240911yescharacteristic
559C2×C5#300211yescharacteristic
560C2×C5#300911yescharacteristic
561C2×C5#336011yescharacteristic
562C2×C5#337611yescharacteristic
563C2×C5#338111yescharacteristic
564C2×C5#338811yescharacteristic
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×C5×D411yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—44no—
576Q8—41no—
577Q8—41no—
578Q8—84no—
579D4—22no—
580D4—22no—
581D4—22no—
582D4C5×C22⋊Q814yes—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—48no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—84no—
621C2×C4—84no—
622C2×C4C5×#12012yes—
623C2×C4C5×#12012yes—
624C2×C4C5×#13512yes—
625C2×C4C22×C5×D411yescharacteristic
626C2×C4C22×C5×D411yescharacteristic
627C2×C4C22×C5×Q811yescharacteristic
628C2×C4C2×C5×#4111yescharacteristic
629C2×C4C5×2−1+411yescharacteristic
630C2×C4C5×2−1+411yescharacteristic
631C8—22no—
632C8—41no—
633C8—41no—
634C8—41no—
635C5#2433711yescharacteristic, direct product factor, Sylow
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22C2×C5×#12011yescharacteristic
644C22C5×#54811yescharacteristic
645C22C5×D4×Q811yescharacteristic
646C22C2×C5×#13511yescharacteristic
647C22C5×#57511yescharacteristic
648C22C5×#57711yescharacteristic
649C22C5×#57711yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4C2×C5×C22⋊Q811yescharacteristic
664C4C5×#53611yescharacteristic
665C4C5×#54811yescharacteristic
666C4C5×D4×Q811yescharacteristic
667C2—44no—
668C2C5×#240911yescharacteristic
669C2C5×#300211yescharacteristic
670C2C5×#300911yescharacteristic
671C2C5×#336011yescharacteristic
672C2C5×#337611yescharacteristic
673C2C5×#338111yescharacteristic
674C2C5×#338811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#479C2semidirect
4. C5×#2581C2semidirect
5. C5×#2059C2semidirect
6. C5×#2058C2semidirect
7. C5×#2026C2semidirect
8. C5×#2024C2semidirect
9. C5×#1991C2semidirect
10. C5×#1984C2semidirect
63. #24337C5direct (N × H)
73. C2×C5×SD16Q8semidirect
142. C2×#479C2×C5semidirect
144. #2581C2×C5semidirect
145. #2059C2×C5semidirect
146. #2058C2×C5semidirect
147. #2026C2×C5semidirect
148. #2024C2×C5semidirect
149. #1991C2×C5semidirect
150. #1984C2×C5semidirect
370. C2×SD16C5×Q8semidirect
635. C5#24337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×C5×#4792
C2×C4×C5×SD162
C5×#25812
C5×#20592
C5×#20582
C5×#20262
C5×#20242
C5×#19912
C5×#19842
C5×#18772
C5×#18642
C5×#18622
C5×#18042
#243375