Finite Group Databasebeta

← C5×#24349 #11947069

Subgroups — C5×#24349 #11947069

Order 1280.

1072 conjugacy classes of subgroups.

The subgroup lattice has 680 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×C5×#440C211yesmaximal, characteristic
4C5×#2582C211yesmaximal, characteristic, complemented
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2057C211yesmaximal, characteristic, complemented
7C5×#2026C211yesmaximal, characteristic, complemented
8C5×#2024C211yesmaximal, characteristic, complemented
9C5×#1992C211yesmaximal, characteristic, complemented
10C5×#1985C211yesmaximal, characteristic, complemented
11C5×#1877C211yesmaximal, characteristic
12C5×#1877C211yesmaximal, characteristic
13C5×#1864C211yesmaximal, characteristic
14C5×#1862C211yesmaximal, characteristic
15C5×#1802C211yesmaximal, 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—
32C5×#440—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#107C2211yescharacteristic
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×C5×#97C2211yescharacteristic
44C5×#398—21no—
45C5×#398—21no—
46C5×#391—21no—
47C5×#391C2211yescharacteristic
48C5×#391C2211yescharacteristic
49C5×#389—21no—
50C5×#389C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#384C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24349C511yesmaximal, 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⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C42×C5—21no—
121C2×C42×C5C2311yescharacteristic
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124C5×#107—22no—
125C5×#107—22no—
126C5×#106—22no—
127C5×C4⋊C8—22no—
128C5×#103—22no—
129C5×#103—22no—
130C5×#103—22no—
131C5×#102—22no—
132C5×#102—22no—
133C5×#102—22no—
134C5×#97—22no—
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×#440C2×C511yescharacteristic
144#2582C2×C511yescharacteristic, complemented
145#2059C2×C511yescharacteristic, complemented
146#2057C2×C511yescharacteristic, complemented
147#2026C2×C511yescharacteristic, complemented
148#2024C2×C511yescharacteristic, complemented
149#1992C2×C511yescharacteristic, complemented
150#1985C2×C511yescharacteristic, complemented
151#1877C2×C511yescharacteristic
152#1877C2×C511yescharacteristic
153#1864C2×C511yescharacteristic
154#1862C2×C511yescharacteristic
155#1802C2×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—81no—
231C5×C4⋊C4—81no—
232C5×C4⋊C4—81no—
233C5×C4⋊C4C2×D412yes—
234C5×C4⋊C4C2×D412yes—
235C5×C4⋊C4C2×D412yes—
236C5×C22⋊C4—24no—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—24no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—42no—
244C42×C5C2×D412yes—
245C42×C5C2×D412yes—
246C22×SD16C22×C511yescharacteristic
247#554—24no—
248#554—24no—
249C2×C4⋊Q8C22×C511yescharacteristic
250C2×#125C22×C511yescharacteristic
251C2×#125C22×C511yescharacteristic
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×C4×Q8C22×C511yescharacteristic
256C2×C4×Q8C22×C511yescharacteristic
257C2×C4×D4C22×C511yescharacteristic
258C2×C4×D4C22×C511yescharacteristic
259C2×C4×D4C22×C511yescharacteristic
260C22×C4⋊C4—21no—
261#479—24no—
262#440—24no—
263C2×#107C22×C511yescharacteristic
264C2×#107C22×C511yescharacteristic
265C2×#106C22×C511yescharacteristic
266C2×C4⋊C8C22×C511yescharacteristic
267C2×#103C22×C511yescharacteristic
268C2×#103C22×C511yescharacteristic
269C2×#103C22×C511yescharacteristic
270C2×#102C22×C511yescharacteristic
271C2×#102C22×C511yescharacteristic
272C2×#102C22×C511yescharacteristic
273C2×#97C22×C511yescharacteristic
274#398—21no—
275#398—21no—
276#391—21no—
277#391C22×C511yescharacteristic
278#391C22×C511yescharacteristic
279#389—21no—
280#389C22×C511yescharacteristic
281#389C22×C511yescharacteristic
282#384C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#336C22×C511yescharacteristic
290#336C22×C511yescharacteristic
291#336C22×C511yescharacteristic
292#336C22×C511yescharacteristic
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5C22×D411yescharacteristic
301C5×Q8—22no—
302C5×Q8—22no—
303C5×Q8—44no—
304C5×Q8—41no—
305C5×Q8—41no—
306C5×Q8—84no—
307C5×D4—22no—
308C5×D4—22no—
309C5×D4—22no—
310C5×D4C22⋊Q814yes—
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—21no—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—48no—
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—41no—
347C2×C4×C5—41no—
348C2×C4×C5—84no—
349C2×C4×C5—84no—
350C2×C4×C5#12012yes—
351C2×C4×C5#12012yes—
352C2×C4×C5#13712yes—
353C2×C4×C5C22×D411yescharacteristic
354C2×C4×C5C22×D411yescharacteristic
355C2×C4×C5C22×Q811yescharacteristic
356C2×C4×C5C2×#4111yescharacteristic
357C2×C4×C52−1+411yescharacteristic
358C2×C4×C52−1+411yescharacteristic
359C5×C8—22no—
360C5×C8—41no—
361C5×C8—41no—
362C5×C8—41no—
363C22×Q8—21no—
364C22×Q8C5×D411yescharacteristic
365C22×Q8C23×C511yescharacteristic
366C22×D4C23×C511yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C2×SD16—22no—
371C2×SD16—22no—
372C2×SD16C5×Q814yescomplemented
373C22×C8C23×C511yescharacteristic
374C22×C8C23×C511yescharacteristic
375C22×C8C23×C511yescharacteristic
376C22×C8C23×C511yescharacteristic
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379#125—22no—
380#125—22no—
381#125—22no—
382#125C5×D414yes—
383C22⋊Q8—28no—
384C22⋊Q8—28no—
385C22⋊Q8—28no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4C5×D414yes—
396C2×C4⋊C4—28no—
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⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C5×D411yescharacteristic
408C2×C4⋊C4C5×D411yescharacteristic
409C2×C4⋊C4C5×D411yescharacteristic
410C2×C4⋊C4C23×C511yescharacteristic
411C2×C4⋊C4C23×C511yescharacteristic
412C2×C4⋊C4C23×C511yescharacteristic
413C2×C4⋊C4C23×C511yescharacteristic
414C2×C4⋊C4C23×C511yescharacteristic
415C2×C4⋊C4C23×C511yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—21no—
420C2×C42C23×C511yescharacteristic
421C2×C42C23×C511yescharacteristic
422C2×C42C23×C511yescharacteristic
423#107—22no—
424#107—22no—
425#106—22no—
426C4⋊C8—22no—
427#103—22no—
428#103—22no—
429#103—22no—
430#102—22no—
431#102—22no—
432#102—22no—
433#97—22no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440C22×C5—24no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5C2×#12011yescharacteristic
448C22×C5#54811yescharacteristic
449C22×C5D4×Q811yescharacteristic
450C22×C5C2×#13711yescharacteristic
451C22×C5#57511yescharacteristic
452C22×C5#57611yescharacteristic
453C22×C5#57711yescharacteristic
454C4×C5—22no—
455C4×C5—22no—
456C4×C5—22no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5—42no—
460C4×C5—41no—
461C4×C5—41no—
462C4×C5—42no—
463C4×C5—42no—
464C4×C5—81no—
465C4×C5—81no—
466C4×C5—81no—
467C4×C5C2×C22⋊Q811yescharacteristic
468C4×C5#53611yescharacteristic
469C4×C5#54811yescharacteristic
470C4×C5D4×Q811yescharacteristic
471C24—21no—
472C2×Q8—24no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—41no—
481C2×Q8—81no—
482C2×Q8—81no—
483C2×Q8C2×C5×Q812yes—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×C5×D412yes—
488C2×D4C2×C5×Q812yes—
489C2×D4C5×#4112yes—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4C2×C5×D411yescharacteristic
507C22×C4C2×C5×D411yescharacteristic
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C2×C5×D411yescharacteristic
511C22×C4C2×C5×D411yescharacteristic
512C22×C4C24×C511yescharacteristic
513SD16—28no—
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×C8—21no—
525C2×C8C2×C5×Q812yes—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C4⋊C4C2×C5×D412yes—
549C4⋊C4C2×C5×D412yes—
550C4⋊C4C2×C5×D412yes—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42C2×C5×D412yes—
560C42C2×C5×D412yes—
561C2×C5—44no—
562C2×C5#240911yescharacteristic
563C2×C5#300711yescharacteristic
564C2×C5#301211yescharacteristic
565C2×C5#337011yescharacteristic
566C2×C5#337211yescharacteristic
567C2×C5#338511yescharacteristic
568C2×C5#338811yescharacteristic
569C23—22no—
570C23—22no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23C22×C5×D411yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—44no—
580Q8—41no—
581Q8—41no—
582Q8—84no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4C5×C22⋊Q814yes—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—48no—
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—84no—
625C2×C4—84no—
626C2×C4C5×#12012yes—
627C2×C4C5×#12012yes—
628C2×C4C5×#13712yes—
629C2×C4C22×C5×D411yescharacteristic
630C2×C4C22×C5×D411yescharacteristic
631C2×C4C22×C5×Q811yescharacteristic
632C2×C4C2×C5×#4111yescharacteristic
633C2×C4C5×2−1+411yescharacteristic
634C2×C4C5×2−1+411yescharacteristic
635C8—22no—
636C8—41no—
637C8—41no—
638C8—41no—
639C5#2434911yescharacteristic, direct product factor, Sylow
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22C2×C5×#12011yescharacteristic
648C22C5×#54811yescharacteristic
649C22C5×D4×Q811yescharacteristic
650C22C2×C5×#13711yescharacteristic
651C22C5×#57511yescharacteristic
652C22C5×#57611yescharacteristic
653C22C5×#57711yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4C2×C5×C22⋊Q811yescharacteristic
668C4C5×#53611yescharacteristic
669C4C5×#54811yescharacteristic
670C4C5×D4×Q811yescharacteristic
671C2—44no—
672C2C5×#240911yescharacteristic
673C2C5×#300711yescharacteristic
674C2C5×#301211yescharacteristic
675C2C5×#337011yescharacteristic
676C2C5×#337211yescharacteristic
677C2C5×#338511yescharacteristic
678C2C5×#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×#2582C2semidirect
5. C5×#2059C2semidirect
6. C5×#2057C2semidirect
7. C5×#2026C2semidirect
8. C5×#2024C2semidirect
9. C5×#1992C2semidirect
10. C5×#1985C2semidirect
63. #24349C5direct (N × H)
73. C2×C5×SD16Q8semidirect
142. C2×#479C2×C5semidirect
144. #2582C2×C5semidirect
145. #2059C2×C5semidirect
146. #2057C2×C5semidirect
147. #2026C2×C5semidirect
148. #2024C2×C5semidirect
149. #1992C2×C5semidirect
150. #1985C2×C5semidirect
372. C2×SD16C5×Q8semidirect
639. C5#24349direct (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×C5×#4402
C5×#25822
C5×#20592
C5×#20572
C5×#20262
C5×#20242
C5×#19922
C5×#19852
C5×#18772
C5×#18642
C5×#18622
C5×#18022
#243495