Finite Group Databasebeta

← C5×#24310 #11947030

Subgroups — C5×#24310 #11947030

Order 1280.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#544C211yesmaximal, characteristic
2C2×C5×#479C211yesmaximal, characteristic, complemented
3C2×C5×#475C211yesmaximal, characteristic, complemented
4C5×#2323C211yesmaximal, characteristic
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#2026C211yesmaximal, characteristic, complemented
8C5×#2024C211yesmaximal, characteristic, complemented
9C5×#1989C211yesmaximal, characteristic, complemented
10C5×#1987C211yesmaximal, characteristic, complemented
11C5×#1873C211yesmaximal, characteristic
12C5×#1872C211yesmaximal, characteristic
13C5×#1854C211yesmaximal, characteristic
14C5×#1853C211yesmaximal, characteristic
15C5×#1798C211yesmaximal, characteristic
16C5×#544—24no—
17C5×#544—24no—
18C2×C5×C4⋊Q8—21no—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#125—21no—
22C2×C5×#125C2211yescharacteristic
23C2×C5×#125C2211yescharacteristic
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8—21no—
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#479—24no—
32C5×#475—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#106C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×C4⋊C8C2211yescharacteristic
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#103C2211yescharacteristic
43C2×C5×C22⋊C8C2211yescharacteristic
44C2×C5×C22⋊C8C2211yescharacteristic
45C5×#391C2211yescharacteristic
46C5×#389—21no—
47C5×#389C2211yescharacteristic
48C5×#388—21no—
49C5×#388—21no—
50C5×#387—21no—
51C5×#380C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24310C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8—21no—
66C22×C5×Q8C2311yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C5×C4⋊Q8—28no—
74C5×C4⋊Q8—22no—
75C5×C4⋊Q8—22no—
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8D414yes—
78C5×#125—28no—
79C5×#125—22no—
80C5×#125—22no—
81C5×#125—22no—
82C5×#125D414yes—
83C5×C22⋊Q8—28no—
84C5×C22⋊Q8—28no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8Q814yescomplemented
87C4×C5×Q8—22no—
88C4×C5×Q8—22no—
89C5×#117—22no—
90C5×#117—22no—
91C5×#117—22no—
92C5×#117—22no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4D411yescharacteristic
106C2×C5×C4⋊C4D411yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C5×C22⋊C4D411yescharacteristic
119C2×C42×C5—21no—
120C2×C42×C5—21no—
121C2×C42×C5—21no—
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124C5×#107—22no—
125C5×#106—22no—
126C5×#106—22no—
127C5×#106—22no—
128C5×C4⋊C8—22no—
129C5×C4⋊C8—22no—
130C5×#103—22no—
131C5×#103—22no—
132C5×#103—22no—
133C5×#103—22no—
134C5×C22⋊C8—22no—
135C5×C22⋊C8—22no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C2×#544C2×C511yescharacteristic
142C2×#479C2×C511yescharacteristic, complemented
143C2×#475C2×C511yescharacteristic, complemented
144#2323C2×C511yescharacteristic
145#2059C2×C511yescharacteristic, complemented
146#2058C2×C511yescharacteristic, complemented
147#2026C2×C511yescharacteristic, complemented
148#2024C2×C511yescharacteristic, complemented
149#1989C2×C511yescharacteristic, complemented
150#1987C2×C511yescharacteristic, complemented
151#1873C2×C511yescharacteristic
152#1872C2×C511yescharacteristic
153#1854C2×C511yescharacteristic
154#1853C2×C511yescharacteristic
155#1798C2×C511yescharacteristic
156C24×C5C2×D411yescharacteristic
157C2×C5×Q8—24no—
158C2×C5×Q8—24no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—81no—
165C2×C5×Q8—81no—
166C2×C5×Q8—81no—
167C2×C5×Q8—81no—
168C2×C5×Q8C2×Q812yes—
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—24no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—81no—
183C22×C4×C5—81no—
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×Q812yes—
190C22×C4×C5#4112yes—
191C22×C4×C5C2411yescharacteristic
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
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—
204C5×C4⋊C4—24no—
205C5×C4⋊C4—24no—
206C5×C4⋊C4—24no—
207C5×C4⋊C4—24no—
208C5×C4⋊C4—24no—
209C5×C4⋊C4—24no—
210C5×C4⋊C4—24no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—24no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—81no—
225C5×C4⋊C4C2×D412yes—
226C5×C4⋊C4C2×D412yes—
227C5×C4⋊C4C2×D412yes—
228C5×C4⋊C4C2×D412yes—
229C5×C4⋊C4C2×Q812yes—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—24no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4—81no—
235C42×C5—24no—
236C42×C5—21no—
237C42×C5—21no—
238C42×C5—42no—
239C42×C5—81no—
240C42×C5C2×D412yes—
241C42×C5C2×D412yes—
242#544—24no—
243#544—24no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8C22×C511yescharacteristic
246C2×C4⋊Q8C22×C511yescharacteristic
247C2×#125—21no—
248C2×#125C22×C511yescharacteristic
249C2×#125C22×C511yescharacteristic
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8C22×C511yescharacteristic
253C2×C4×Q8C22×C511yescharacteristic
254C2×#117C22×C511yescharacteristic
255C2×#117C22×C511yescharacteristic
256C22×C4⋊C4C22×C511yescharacteristic
257#479—24no—
258#475—24no—
259C2×#107C22×C511yescharacteristic
260C2×#106C22×C511yescharacteristic
261C2×#106C22×C511yescharacteristic
262C2×#106C22×C511yescharacteristic
263C2×C4⋊C8C22×C511yescharacteristic
264C2×C4⋊C8C22×C511yescharacteristic
265C2×#103C22×C511yescharacteristic
266C2×#103C22×C511yescharacteristic
267C2×#103C22×C511yescharacteristic
268C2×#103C22×C511yescharacteristic
269C2×C22⋊C8C22×C511yescharacteristic
270C2×C22⋊C8C22×C511yescharacteristic
271#391C22×C511yescharacteristic
272#389—21no—
273#389C22×C511yescharacteristic
274#388—21no—
275#388—21no—
276#387—21no—
277#380C22×C511yescharacteristic
278C4×C4⋊C4C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×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
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5C22⋊Q812yes—
296C23×C5C22×D411yescharacteristic
297C5×Q8—22no—
298C5×Q8—22no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—84no—
302C5×Q8—84no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
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—84no—
344C2×C4×C5#12012yes—
345C2×C4×C5#12012yes—
346C2×C4×C5C22⋊Q812yes—
347C2×C4×C5C22×D411yescharacteristic
348C2×C4×C5C22×D411yescharacteristic
349C2×C4×C5C22×Q811yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C52−1+411yescharacteristic
352C2×C4×C52−1+411yescharacteristic
353C5×C8—41no—
354C5×C8—41no—
355C5×C8—41no—
356C5×C8—41no—
357C22×Q8—21no—
358C22×Q8—21no—
359C22×Q8C23×C511yescharacteristic
360C23×C4—21no—
361C23×C4C23×C511yescharacteristic
362C22×C8C23×C511yescharacteristic
363C22×C8C23×C511yescharacteristic
364C22×C8C23×C511yescharacteristic
365C22×C8C23×C511yescharacteristic
366C4⋊Q8—28no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8C5×D414yes—
371#125—28no—
372#125—22no—
373#125—22no—
374#125—22no—
375#125C5×D414yes—
376C22⋊Q8—28no—
377C22⋊Q8—28no—
378C22⋊Q8—22no—
379C22⋊Q8C5×Q814yescomplemented
380C4×Q8—22no—
381C4×Q8—22no—
382#117—22no—
383#117—22no—
384#117—22no—
385#117—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4C5×D411yescharacteristic
399C2×C4⋊C4C5×D411yescharacteristic
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4C5×D411yescharacteristic
411C2×C22⋊C4C5×D411yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C511yescharacteristic
416C2×C42C23×C511yescharacteristic
417#107—22no—
418#106—22no—
419#106—22no—
420#106—22no—
421C4⋊C8—22no—
422C4⋊C8—22no—
423#103—22no—
424#103—22no—
425#103—22no—
426#103—22no—
427C22⋊C8—22no—
428C22⋊C8—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5C2×#12011yescharacteristic
442C22×C5C2×C22⋊Q811yescharacteristic
443C22×C5#53611yescharacteristic
444C22×C5#57711yescharacteristic
445C22×C5#57711yescharacteristic
446C22×C5#57711yescharacteristic
447C22×C5#57811yescharacteristic
448C4×C5—22no—
449C4×C5—22no—
450C4×C5—22no—
451C4×C5—42no—
452C4×C5—42no—
453C4×C5—41no—
454C4×C5—42no—
455C4×C5—42no—
456C4×C5—42no—
457C4×C5—41no—
458C4×C5—42no—
459C4×C5—81no—
460C4×C5—81no—
461C4×C5#54811yescharacteristic
462C4×C5#54811yescharacteristic
463C4×C5D4×Q811yescharacteristic
464C4×C5D4×Q811yescharacteristic
465C24C2×C5×D411yescharacteristic
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—81no—
474C2×Q8—81no—
475C2×Q8—81no—
476C2×Q8—81no—
477C2×Q8C2×C5×Q812yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—81no—
492C22×C4—81no—
493C22×C4C2×C5×D411yescharacteristic
494C22×C4C2×C5×D411yescharacteristic
495C22×C4C2×C5×D411yescharacteristic
496C22×C4C2×C5×D411yescharacteristic
497C22×C4C2×C5×D411yescharacteristic
498C22×C4C2×C5×Q812yes—
499C22×C4C5×#4112yes—
500C22×C4C24×C511yescharacteristic
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C4⋊C4—24no—
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4C2×C5×D412yes—
535C4⋊C4C2×C5×D412yes—
536C4⋊C4C2×C5×D412yes—
537C4⋊C4C2×C5×D412yes—
538C4⋊C4C2×C5×Q812yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—81no—
544C42—24no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—81no—
549C42C2×C5×D412yes—
550C42C2×C5×D412yes—
551C2×C5—42no—
552C2×C5#240911yescharacteristic
553C2×C5#300911yescharacteristic
554C2×C5#301311yescharacteristic
555C2×C5#308211yescharacteristic
556C2×C5#308411yescharacteristic
557C2×C5#324211yescharacteristic
558C2×C5#324411yescharacteristic
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23C5×C22⋊Q812yes—
566C23C22×C5×D411yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8—84no—
572Q8—84no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
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—84no—
614C2×C4C5×#12012yes—
615C2×C4C5×#12012yes—
616C2×C4C5×C22⋊Q812yes—
617C2×C4C22×C5×D411yescharacteristic
618C2×C4C22×C5×D411yescharacteristic
619C2×C4C22×C5×Q811yescharacteristic
620C2×C4C2×C5×#4111yescharacteristic
621C2×C4C5×2−1+411yescharacteristic
622C2×C4C5×2−1+411yescharacteristic
623C8—41no—
624C8—41no—
625C8—41no—
626C8—41no—
627C5#2431011yescharacteristic, direct product factor, Sylow
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C5×#12011yescharacteristic
636C22C2×C5×C22⋊Q811yescharacteristic
637C22C5×#53611yescharacteristic
638C22C5×#57711yescharacteristic
639C22C5×#57711yescharacteristic
640C22C5×#57711yescharacteristic
641C22C5×#57811yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4C5×#54811yescharacteristic
656C4C5×#54811yescharacteristic
657C4C5×D4×Q811yescharacteristic
658C4C5×D4×Q811yescharacteristic
659C2—42no—
660C2C5×#240911yescharacteristic
661C2C5×#300911yescharacteristic
662C2C5×#301311yescharacteristic
663C2C5×#308211yescharacteristic
664C2C5×#308411yescharacteristic
665C2C5×#324211yescharacteristic
666C2C5×#324411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#479C2semidirect
3. C2×C5×#475C2semidirect
5. C5×#2059C2semidirect
6. C5×#2058C2semidirect
7. C5×#2026C2semidirect
8. C5×#2024C2semidirect
9. C5×#1989C2semidirect
10. C5×#1987C2semidirect
63. #24310C5direct (N × H)
86. C5×C22⋊Q8Q8semidirect
142. C2×#479C2×C5semidirect
143. C2×#475C2×C5semidirect
145. #2059C2×C5semidirect
146. #2058C2×C5semidirect
147. #2026C2×C5semidirect
148. #2024C2×C5semidirect
149. #1989C2×C5semidirect
150. #1987C2×C5semidirect
379. C22⋊Q8C5×Q8semidirect
627. C5#24310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5442
C2×C5×#4792
C2×C5×#4752
C5×#23232
C5×#20592
C5×#20582
C5×#20262
C5×#20242
C5×#19892
C5×#19872
C5×#18732
C5×#18722
C5×#18542
C5×#18532
C5×#17982
#243105