Finite Group Databasebeta

← C5×#26932 #11949652

Subgroups — C5×#26932 #11949652

Order 1280.

864 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×#484C211yesmaximal, characteristic
2C2×C5×#462C211yesmaximal, characteristic, complemented
3C5×#2429C211yesmaximal, characteristic
4C5×#2360C211yesmaximal, characteristic
5C5×#2087C211yesmaximal, characteristic, complemented
6C5×#2043C211yesmaximal, characteristic, complemented
7C5×#2001C211yesmaximal, characteristic
8C5×#2001C211yesmaximal, characteristic
9C5×#1969C211yesmaximal, characteristic, complemented
10C5×#1928C211yesmaximal, characteristic, complemented
11C5×#1923C211yesmaximal, characteristic
12C5×#1878C211yesmaximal, characteristic, complemented
13C5×#1872C211yesmaximal, characteristic
14C5×#1863C211yesmaximal, characteristic, complemented
15C4×C5×#103C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C22×C5×Q16C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×Q8C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C5×#484—24no—
26C5×#462—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C4×C5×C8C2211yescharacteristic
41C5×#398—21no—
42C5×#396—21no—
43C5×#391C2211yescharacteristic
44C5×#391C2211yescharacteristic
45C5×#389—21no—
46C5×#389—21no—
47C5×#389C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#388—21no—
50C5×#387—21no—
51C5×#385—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C22⋊C4—21no—
54C4×C5×C22⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26932C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C22×C5×Q8C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5C2311yescharacteristic
67C2×C5×Q16—22no—
68C2×C5×Q16—22no—
69C2×C5×Q16—22no—
70C2×C5×Q16—22no—
71C2×C5×Q16—41no—
72C2×C5×Q16—41no—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×C4⋊Q8—22no—
78C5×C4⋊Q8—41no—
79C5×C22⋊Q8—22no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—41no—
84C5×C22⋊Q8—41no—
85C4×C5×Q8—22no—
86C4×C5×Q8—22no—
87C4×C5×Q8—41no—
88C4×C5×Q8—41no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
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—41no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4D411yescharacteristic
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C42×C5—21no—
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C5×#107—22no—
117C5×#107—22no—
118C5×C4⋊C8—22no—
119C5×#103—22no—
120C5×#103—22no—
121C5×#103—22no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#103—41no—
125C5×#103—41no—
126C5×#103D414yes—
127C5×C22⋊C8—22no—
128C5×C22⋊C8—41no—
129C4×C5×C8—41no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95D411yescharacteristic
138C5×#95D411yescharacteristic
139C2×#484C2×C511yescharacteristic
140C2×#462C2×C511yescharacteristic, complemented
141#2429C2×C511yescharacteristic
142#2360C2×C511yescharacteristic
143#2087C2×C511yescharacteristic, complemented
144#2043C2×C511yescharacteristic, complemented
145#2001C2×C511yescharacteristic
146#2001C2×C511yescharacteristic
147#1969C2×C511yescharacteristic, complemented
148#1928C2×C511yescharacteristic, complemented
149#1923C2×C511yescharacteristic
150#1878C2×C511yescharacteristic, complemented
151#1872C2×C511yescharacteristic
152#1863C2×C511yescharacteristic, complemented
153C4×#103C2×C511yescharacteristic, complemented
154C24×C5C2×D411yescharacteristic
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8C2×D412yes—
172C2×C5×Q8#4112yes—
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—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—42no—
188C22×C4×C5—42no—
189C22×C4×C5—81no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2411yescharacteristic
196C5×Q16—44no—
197C5×Q16—44no—
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×C8—21no—
206C2×C5×C8—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8C2×D412yes—
210C5×C4⋊C4—24no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—81no—
227C5×C4⋊C4C2×D412yes—
228C5×C4⋊C4#4112yes—
229C5×C4⋊C4#4112yes—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—41no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4Q1614yescomplemented
235C42×C5—21no—
236C42×C5—21no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—42no—
240C42×C5—42no—
241C42×C5—81no—
242C22×Q16C22×C511yescharacteristic
243C22×Q16C22×C511yescharacteristic
244C2×C4⋊Q8C22×C511yescharacteristic
245C2×C22⋊Q8C22×C511yescharacteristic
246C2×C22⋊Q8C22×C511yescharacteristic
247C2×C22⋊Q8C22×C511yescharacteristic
248C2×C4×Q8C22×C511yescharacteristic
249C2×C4×Q8C22×C511yescharacteristic
250C22×C4⋊C4C22×C511yescharacteristic
251#484—24no—
252#462—24no—
253C2×#107C22×C511yescharacteristic
254C2×#107C22×C511yescharacteristic
255C2×C4⋊C8C22×C511yescharacteristic
256C2×#103C22×C511yescharacteristic
257C2×#103C22×C511yescharacteristic
258C2×#103C22×C511yescharacteristic
259C2×#103C22×C511yescharacteristic
260C2×#103C22×C511yescharacteristic
261C2×#103C22×C511yescharacteristic
262C2×#103C22×C511yescharacteristic
263C2×#103C22×C511yescharacteristic
264C2×C22⋊C8C22×C511yescharacteristic
265C2×C22⋊C8C22×C511yescharacteristic
266C2×C4×C8C22×C511yescharacteristic
267#398—21no—
268#396—21no—
269#391C22×C511yescharacteristic
270#391C22×C511yescharacteristic
271#389—21no—
272#389—21no—
273#389C22×C511yescharacteristic
274#389C22×C511yescharacteristic
275#388—21no—
276#387—21no—
277#385—21no—
278C4×C4⋊C4C22×C511yescharacteristic
279C4×C22⋊C4—21no—
280C4×C22⋊C4C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#336C22×C511yescharacteristic
286#336C22×C511yescharacteristic
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5C2×Q1612yes—
294C23×C5C22×D411yescharacteristic
295C5×Q8—22no—
296C5×Q8—22no—
297C5×Q8—22no—
298C5×Q8—22no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—41no—
302C5×Q8—41no—
303C5×Q8—41no—
304C5×Q8—41no—
305C5×Q8—41no—
306C5×Q8—41no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
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—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—84no—
349C2×C4×C5C2×Q1612yes—
350C2×C4×C5C2×Q1612yes—
351C2×C4×C5C22×D411yescharacteristic
352C2×C4×C5C2×#4111yescharacteristic
353C2×C4×C5C2×#4111yescharacteristic
354C2×C4×C5C2×#4111yescharacteristic
355C2×C4×C5H(5,𝔽2)11yescharacteristic
356C2×C4×C5H(5,𝔽2)11yescharacteristic
357C5×C8—22no—
358C5×C8—41no—
359C5×C8—41no—
360C5×C8—41no—
361C22×Q8C23×C511yescharacteristic
362C22×Q8C23×C511yescharacteristic
363C22×Q8C23×C511yescharacteristic
364C23×C4—21no—
365C23×C4C23×C511yescharacteristic
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—41no—
371C2×Q16—41no—
372C22×C8C23×C511yescharacteristic
373C22×C8C23×C511yescharacteristic
374C22×C8C23×C511yescharacteristic
375C22×C8C23×C511yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—41no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4C5×D411yescharacteristic
409C2×C22⋊C4C5×D411yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C23×C511yescharacteristic
414C2×C42C23×C511yescharacteristic
415#107—22no—
416#107—22no—
417C4⋊C8—22no—
418#103—22no—
419#103—22no—
420#103—22no—
421#103—22no—
422#103—22no—
423#103—41no—
424#103—41no—
425#103C5×D414yes—
426C22⋊C8—22no—
427C22⋊C8—41no—
428C4×C8—41no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95C5×D411yescharacteristic
437#95C5×D411yescharacteristic
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5#52511yescharacteristic
446C22×C5D4211yescharacteristic
447C22×C5#54611yescharacteristic
448C22×C5C22×Q1611yescharacteristic
449C22×C5#57511yescharacteristic
450C22×C5#57711yescharacteristic
451C22×C5#57811yescharacteristic
452C4×C5—22no—
453C4×C5—22no—
454C4×C5—42no—
455C4×C5—41no—
456C4×C5—42no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5—42no—
460C4×C5—41no—
461C4×C5—42no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5#53211yescharacteristic
466C4×C5#54011yescharacteristic
467C4×C5#54611yescharacteristic
468C4×C5#55311yescharacteristic
469C24C2×C5×D411yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×C5×D412yes—
487C2×Q8C5×#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—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4C2×C5×D411yescharacteristic
506C22×C4C2×C5×D411yescharacteristic
507C22×C4C2×C5×D411yescharacteristic
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C24×C511yescharacteristic
511Q16—44no—
512Q16—44no—
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×C8—21no—
524C2×C8C2×C5×D412yes—
525C4⋊C4—24no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4C2×C5×D412yes—
543C4⋊C4C5×#4112yes—
544C4⋊C4C5×#4112yes—
545C22⋊C4—24no—
546C22⋊C4—41no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4C5×Q1614yescomplemented
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42—42no—
556C42—81no—
557C2×C5—42no—
558C2×C5#246411yescharacteristic
559C2×C5#310411yescharacteristic
560C2×C5#312011yescharacteristic
561C2×C5#327511yescharacteristic
562C2×C5D4×Q1611yescharacteristic
563C2×C5#329911yescharacteristic
564C2×C5#331511yescharacteristic
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23C2×C5×Q1612yes—
572C23C22×C5×D411yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
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—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—84no—
627C2×C4C2×C5×Q1612yes—
628C2×C4C2×C5×Q1612yes—
629C2×C4C22×C5×D411yescharacteristic
630C2×C4C2×C5×#4111yescharacteristic
631C2×C4C2×C5×#4111yescharacteristic
632C2×C4C2×C5×#4111yescharacteristic
633C2×C4C5×H(5,𝔽2)11yescharacteristic
634C2×C4C5×H(5,𝔽2)11yescharacteristic
635C8—22no—
636C8—41no—
637C8—41no—
638C8—41no—
639C5#2693211yescharacteristic, direct product factor, Sylow
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C5×#52511yescharacteristic
648C22C5×D4211yescharacteristic
649C22C5×#54611yescharacteristic
650C22C22×C5×Q1611yescharacteristic
651C22C5×#57511yescharacteristic
652C22C5×#57711yescharacteristic
653C22C5×#57811yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—42no—
661C4—41no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4C5×#53211yescharacteristic
668C4C5×#54011yescharacteristic
669C4C5×#54611yescharacteristic
670C4C5×#55311yescharacteristic
671C2—42no—
672C2C5×#246411yescharacteristic
673C2C5×#310411yescharacteristic
674C2C5×#312011yescharacteristic
675C2C5×#327511yescharacteristic
676C2C5×D4×Q1611yescharacteristic
677C2C5×#329911yescharacteristic
678C2C5×#331511yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
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
2. C2×C5×#462C2semidirect
5. C5×#2087C2semidirect
6. C5×#2043C2semidirect
9. C5×#1969C2semidirect
10. C5×#1928C2semidirect
12. C5×#1878C2semidirect
14. C5×#1863C2semidirect
15. C4×C5×#103C2semidirect
61. #26932C5direct (N × H)
140. C2×#462C2×C5semidirect
143. #2087C2×C5semidirect
144. #2043C2×C5semidirect
147. #1969C2×C5semidirect
148. #1928C2×C5semidirect
150. #1878C2×C5semidirect
152. #1863C2×C5semidirect
153. C4×#103C2×C5semidirect
234. C5×C22⋊C4Q16semidirect
549. C22⋊C4C5×Q16semidirect
639. C5#26932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4842
C2×C5×#4622
C5×#24292
C5×#23602
C5×#20872
C5×#20432
C5×#20012
C5×#19692
C5×#19282
C5×#19232
C5×#18782
C5×#18722
C5×#18632
C4×C5×#1032
#269325