Finite Group Databasebeta

← C5×#26786 #11949506

Subgroups — C5×#26786 #11949506

Order 1280.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#483C211yesmaximal, characteristic, complemented
2C2×C5×#476C211yesmaximal, characteristic, complemented
3C5×#2492C211yesmaximal, characteristic, complemented
4C5×#2361C211yesmaximal, characteristic
5C5×#2066C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#2034C211yesmaximal, characteristic
8C5×#2000C211yesmaximal, characteristic
9C5×#1968C211yesmaximal, characteristic, complemented
10C5×#1927C211yesmaximal, characteristic, complemented
11C5×#1926C211yesmaximal, characteristic, complemented
12C5×#1923C211yesmaximal, characteristic, complemented
13C5×#1877C211yesmaximal, characteristic, complemented
14C5×#1853C211yesmaximal, characteristic, complemented
15C4×C5×#106C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#483—24no—
24C5×#476—24no—
25C2×C5×#106C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C4×C5×C8C2211yescharacteristic
40C5×#400—21no—
41C5×#393—21no—
42C5×#391—21no—
43C5×#391C2211yescharacteristic
44C5×#391C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#388—21no—
48C5×#388—21no—
49C5×#386—21no—
50C5×#385—21no—
51C5×#380C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C22⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26786C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8—21no—
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4—21no—
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C2×C5×SD16—22no—
70C2×C5×SD16—22no—
71C2×C5×SD16—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8—41no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8—41no—
80C5×#121—22no—
81C5×#121—22no—
82C4×C5×D4—22no—
83C4×C5×D4—41no—
84C4×C5×D4—44no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4D411yescharacteristic
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C42×C5—21no—
106C2×C42×C5—21no—
107C2×C42×C5C2311yescharacteristic
108C2×C42×C5C2311yescharacteristic
109C5×#106—22no—
110C5×#106—22no—
111C5×#106—22no—
112C5×#106—41no—
113C5×#106D414yescomplemented
114C5×C4⋊C8—22no—
115C5×#103—22no—
116C5×#103—22no—
117C5×#103—22no—
118C5×#102—22no—
119C5×#102—22no—
120C5×#102—22no—
121C5×C22⋊C8—22no—
122C5×C22⋊C8—22no—
123C4×C5×C8—22no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95D411yescharacteristic
133C5×#95D411yescharacteristic
134C2×#483C2×C511yescharacteristic, complemented
135C2×#476C2×C511yescharacteristic, complemented
136#2492C2×C511yescharacteristic, complemented
137#2361C2×C511yescharacteristic
138#2066C2×C511yescharacteristic, complemented
139#2058C2×C511yescharacteristic, complemented
140#2034C2×C511yescharacteristic
141#2000C2×C511yescharacteristic
142#1968C2×C511yescharacteristic, complemented
143#1927C2×C511yescharacteristic, complemented
144#1926C2×C511yescharacteristic, complemented
145#1923C2×C511yescharacteristic, complemented
146#1877C2×C511yescharacteristic, complemented
147#1853C2×C511yescharacteristic, complemented
148C4×#106C2×C511yescharacteristic, complemented
149C24×C5—21no—
150C24×C5C2×D411yescharacteristic
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—42no—
158C2×C5×Q8—42no—
159C2×C5×Q8—81no—
160C2×C5×D4—24no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—42no—
167C2×C5×D4—42no—
168C2×C5×D4#4112yes—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—42no—
185C22×C4×C5—42no—
186C22×C4×C5—81no—
187C22×C4×C5—81no—
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2411yescharacteristic
194C5×SD16—44no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
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×C8C2×D412yes—
206C2×C5×C8#4112yes—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—42no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4C2×D412yes—
221C5×C4⋊C4C2×D412yes—
222C5×C4⋊C4#4112yes—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—41no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—81no—
229C5×C22⋊C4—81no—
230C5×C22⋊C4SD1614yescomplemented
231C42×C5—21no—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—42no—
236C42×C5—81no—
237C22×SD16C22×C511yescharacteristic
238C2×C4⋊Q8C22×C511yescharacteristic
239C2×C22⋊Q8C22×C511yescharacteristic
240C2×#121C22×C511yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C22×C511yescharacteristic
243C22×C4⋊C4C22×C511yescharacteristic
244#483—24no—
245#476—24no—
246C2×#106C22×C511yescharacteristic
247C2×#106C22×C511yescharacteristic
248C2×#106C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×C4⋊C8C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×#103C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×C22⋊C8C22×C511yescharacteristic
259C2×C22⋊C8C22×C511yescharacteristic
260C2×C4×C8C22×C511yescharacteristic
261#400—21no—
262#393—21no—
263#391—21no—
264#391C22×C511yescharacteristic
265#391C22×C511yescharacteristic
266#390C22×C511yescharacteristic
267#389C22×C511yescharacteristic
268#388—21no—
269#388—21no—
270#386—21no—
271#385—21no—
272#380C22×C511yescharacteristic
273C4×C4⋊C4C22×C511yescharacteristic
274C4×C4⋊C4C22×C511yescharacteristic
275C4×C22⋊C4C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#336C22×C511yescharacteristic
281#336C22×C511yescharacteristic
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—22no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5C2×SD1612yes—
296C23×C5C22×D411yescharacteristic
297C5×Q8—41no—
298C5×Q8—41no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—84no—
302C5×D4—22no—
303C5×D4—22no—
304C5×D4—48no—
305C5×D4—41no—
306C5×D4—41no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
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—84no—
346C2×C4×C5—84no—
347C2×C4×C5C2×SD1612yes—
348C2×C4×C5C2×SD1612yes—
349C2×C4×C5C22×D411yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5C2×#4111yescharacteristic
352C2×C4×C5C2×#4111yescharacteristic
353C2×C4×C5H(5,𝔽2)11yescharacteristic
354C2×C4×C52−1+411yescharacteristic
355C5×C8—22no—
356C5×C8—22no—
357C5×C8—41no—
358C5×C8—41no—
359C22×Q8—21no—
360C22×Q8C23×C511yescharacteristic
361C22×D4—21no—
362C22×D4C23×C511yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4C23×C511yescharacteristic
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—41no—
369C22×C8C23×C511yescharacteristic
370C22×C8C23×C511yescharacteristic
371C22×C8C23×C511yescharacteristic
372C22×C8C23×C511yescharacteristic
373C4⋊Q8—22no—
374C4⋊Q8—41no—
375C22⋊Q8—22no—
376C22⋊Q8—41no—
377#121—22no—
378#121—22no—
379C4×D4—22no—
380C4×D4—41no—
381C4×D4—44no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4C5×D411yescharacteristic
401C2×C22⋊C4C5×D411yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C23×C511yescharacteristic
405C2×C42C23×C511yescharacteristic
406#106—22no—
407#106—22no—
408#106—22no—
409#106—41no—
410#106C5×D414yescomplemented
411C4⋊C8—22no—
412#103—22no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417#102—22no—
418C22⋊C8—22no—
419C22⋊C8—22no—
420C4×C8—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95C5×D411yescharacteristic
430#95C5×D411yescharacteristic
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—42no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—81no—
442C22×C5—81no—
443C22×C5—81no—
444C22×C5—81no—
445C22×C5#52511yescharacteristic
446C22×C5D4211yescharacteristic
447C22×C5#54711yescharacteristic
448C22×C5C22×SD1611yescharacteristic
449C22×C5#57511yescharacteristic
450C22×C5#57711yescharacteristic
451C22×C5#57711yescharacteristic
452C4×C5—22no—
453C4×C5—22no—
454C4×C5—41no—
455C4×C5—42no—
456C4×C5—41no—
457C4×C5—41no—
458C4×C5—42no—
459C4×C5—42no—
460C4×C5—81no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5#53211yescharacteristic
465C4×C5#54211yescharacteristic
466C4×C5#54811yescharacteristic
467C4×C5#55111yescharacteristic
468C24—21no—
469C24C2×C5×D411yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—81no—
479C2×D4—24no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4C5×#4112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4C2×C5×D411yescharacteristic
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C2×C5×D411yescharacteristic
511C22×C4C2×C5×D411yescharacteristic
512C22×C4C24×C511yescharacteristic
513SD16—44no—
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×C8—21no—
524C2×C8C2×C5×D412yes—
525C2×C8C5×#4112yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4C2×C5×D412yes—
540C4⋊C4C2×C5×D412yes—
541C4⋊C4C5×#4112yes—
542C22⋊C4—24no—
543C22⋊C4—41no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4C5×SD1614yescomplemented
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42—81no—
556C2×C5—42no—
557C2×C5—82no—
558C2×C5#246111yescharacteristic
559C2×C5#310111yescharacteristic
560C2×C5#312511yescharacteristic
561C2×C5#327511yescharacteristic
562C2×C5D4×SD1611yescharacteristic
563C2×C5#333511yescharacteristic
564C2×C5#335011yescharacteristic
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×C5×SD1612yes—
579C23C22×C5×D411yescharacteristic
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—84no—
585D4—22no—
586D4—22no—
587D4—48no—
588D4—41no—
589D4—41no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
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—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—84no—
629C2×C4—84no—
630C2×C4C2×C5×SD1612yes—
631C2×C4C2×C5×SD1612yes—
632C2×C4C22×C5×D411yescharacteristic
633C2×C4C2×C5×#4111yescharacteristic
634C2×C4C2×C5×#4111yescharacteristic
635C2×C4C2×C5×#4111yescharacteristic
636C2×C4C5×H(5,𝔽2)11yescharacteristic
637C2×C4C5×2−1+411yescharacteristic
638C8—22no—
639C8—22no—
640C8—41no—
641C8—41no—
642C5#2678611yescharacteristic, direct product factor, Sylow
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22C5×#52511yescharacteristic
658C22C5×D4211yescharacteristic
659C22C5×#54711yescharacteristic
660C22C22×C5×SD1611yescharacteristic
661C22C5×#57511yescharacteristic
662C22C5×#57711yescharacteristic
663C22C5×#57711yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—42no—
668C4—42no—
669C4—41no—
670C4—42no—
671C4—41no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4C5×#53211yescharacteristic
677C4C5×#54211yescharacteristic
678C4C5×#54811yescharacteristic
679C4C5×#55111yescharacteristic
680C2—42no—
681C2—82no—
682C2C5×#246111yescharacteristic
683C2C5×#310111yescharacteristic
684C2C5×#312511yescharacteristic
685C2C5×#327511yescharacteristic
686C2C5×D4×SD1611yescharacteristic
687C2C5×#333511yescharacteristic
688C2C5×#335011yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#483C2semidirect
2. C2×C5×#476C2semidirect
3. C5×#2492C2semidirect
5. C5×#2066C2semidirect
6. C5×#2058C2semidirect
9. C5×#1968C2semidirect
10. C5×#1927C2semidirect
11. C5×#1926C2semidirect
12. C5×#1923C2semidirect
13. C5×#1877C2semidirect
14. C5×#1853C2semidirect
15. C4×C5×#106C2semidirect
61. #26786C5direct (N × H)
113. C5×#106D4semidirect
134. C2×#483C2×C5semidirect
135. C2×#476C2×C5semidirect
136. #2492C2×C5semidirect
138. #2066C2×C5semidirect
139. #2058C2×C5semidirect
142. #1968C2×C5semidirect
143. #1927C2×C5semidirect
144. #1926C2×C5semidirect
145. #1923C2×C5semidirect
146. #1877C2×C5semidirect
147. #1853C2×C5semidirect
148. C4×#106C2×C5semidirect
230. C5×C22⋊C4SD16semidirect
410. #106C5×D4semidirect
549. C22⋊C4C5×SD16semidirect
642. C5#26786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4832
C2×C5×#4762
C5×#24922
C5×#23612
C5×#20662
C5×#20582
C5×#20342
C5×#20002
C5×#19682
C5×#19272
C5×#19262
C5×#19232
C5×#18772
C5×#18532
C4×C5×#1062
#267865