Finite Group Databasebeta

← C5×#24977 #11947697

Subgroups — C5×#24977 #11947697

Order 1280.

892 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2535C211yesmaximal, characteristic
2C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C5×#2077C211yesmaximal, characteristic, complemented
4C5×#2076C211yesmaximal, characteristic, complemented
5C5×#2034C211yesmaximal, characteristic, complemented
6C5×#2033C211yesmaximal, characteristic, complemented
7C5×#1955C211yesmaximal, characteristic, complemented
8C5×#1949C211yesmaximal, characteristic, complemented
9C5×#1874C211yesmaximal, characteristic, complemented
10C5×#1874C211yesmaximal, characteristic, complemented
11C5×#1836C211yesmaximal, characteristic, complemented
12C5×#1824C211yesmaximal, characteristic, complemented
13C5×#1823C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C5×#1762C211yesmaximal, characteristic, complemented
16C2×C5×#121C2211yescharacteristic
17C2×C5×#121C2211yescharacteristic
18C2×C4×C5×D4—21no—
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C2×C5×#97C2211yescharacteristic
35C5×#397—21no—
36C5×#392—21no—
37C5×#389—21no—
38C5×#386—21no—
39C5×#386—21no—
40C5×#385—21no—
41C5×#385—21no—
42C5×#384C2211yescharacteristic
43C5×#382C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C5×#380C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C4×C5×C4⋊C4C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59#24977C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4—21no—
61C22×C5×D4—21no—
62C22×C5×D4D411yescharacteristic
63C22×C5×D4C2311yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C5×#121—22no—
74C5×#121—22no—
75C5×#121—41no—
76C5×#121—41no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C4×C5×D4—44no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—41no—
89C2×C5×C4⋊C4—41no—
90C2×C5×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C5×C22⋊C4D411yescharacteristic
107C2×C42×C5—21no—
108C2×C42×C5C2311yescharacteristic
109C5×#107—41no—
110C5×#106—41no—
111C5×C4⋊C8—22no—
112C5×#102—22no—
113C5×#102—22no—
114C5×#102—41no—
115C5×#102—41no—
116C5×C22⋊C8—41no—
117C5×C22⋊C8—41no—
118C5×C22⋊C8—41no—
119C5×C22⋊C8—41no—
120C5×#97—22no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128#2535C2×C511yescharacteristic
129D4×C4⋊C4C2×C511yescharacteristic, complemented
130#2077C2×C511yescharacteristic, complemented
131#2076C2×C511yescharacteristic, complemented
132#2034C2×C511yescharacteristic, complemented
133#2033C2×C511yescharacteristic, complemented
134#1955C2×C511yescharacteristic, complemented
135#1949C2×C511yescharacteristic, complemented
136#1874C2×C511yescharacteristic, complemented
137#1874C2×C511yescharacteristic, complemented
138#1836C2×C511yescharacteristic, complemented
139#1824C2×C511yescharacteristic, complemented
140#1823C2×C511yescharacteristic, complemented
141#1802C2×C511yescharacteristic, complemented
142#1762C2×C511yescharacteristic, complemented
143C24×C5—21no—
144C24×C5C2×D411yescharacteristic
145C24×C5C2×D411yescharacteristic
146C2×C5×D4—22no—
147C2×C5×D4—22no—
148C2×C5×D4—22no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—42no—
155C2×C5×D4—42no—
156C2×C5×D4—42no—
157C2×C5×D4—42no—
158C2×C5×D4—81no—
159C2×C5×D4—81no—
160C2×C5×D4#4112yes—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
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—42no—
181C22×C4×C5—42no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—42no—
185C22×C4×C5—81no—
186C22×C4×C5—81no—
187C22×C4×C5—81no—
188C22×C4×C5—81no—
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2411yescharacteristic
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—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C5×C4⋊C4—22no—
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—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—81no—
224C5×C4⋊C4#4112yes—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—81no—
233C5×C22⋊C4—81no—
234C42×C5—42no—
235C42×C5#4112yes—
236C42×C5#4112yes—
237C2×#121C22×C511yescharacteristic
238C2×#121C22×C511yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4C22×C511yescharacteristic
241C2×C4×D4C22×C511yescharacteristic
242C22×C4⋊C4C22×C511yescharacteristic
243C22×C4⋊C4C22×C511yescharacteristic
244C2×#107C22×C511yescharacteristic
245C2×#106C22×C511yescharacteristic
246C2×C4⋊C8C22×C511yescharacteristic
247C2×#102C22×C511yescharacteristic
248C2×#102C22×C511yescharacteristic
249C2×#102C22×C511yescharacteristic
250C2×#102C22×C511yescharacteristic
251C2×C22⋊C8C22×C511yescharacteristic
252C2×C22⋊C8C22×C511yescharacteristic
253C2×C22⋊C8C22×C511yescharacteristic
254C2×C22⋊C8C22×C511yescharacteristic
255C2×#97C22×C511yescharacteristic
256#397—21no—
257#392—21no—
258#389—21no—
259#386—21no—
260#386—21no—
261#385—21no—
262#385—21no—
263#384C22×C511yescharacteristic
264#382C22×C511yescharacteristic
265#380C22×C511yescharacteristic
266#380C22×C511yescharacteristic
267#380C22×C511yescharacteristic
268#380C22×C511yescharacteristic
269C4×C4⋊C4C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—22no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5AGL(1,ℤ/8)12yes—
300C23×C5#13712yes—
301C23×C5C22×D411yescharacteristic
302C5×D4—28no—
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—41no—
306C5×D4—41no—
307C5×D4—84no—
308C5×D4—84no—
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—22no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
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—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—84no—
349C2×C4×C5—84no—
350C2×C4×C5—84no—
351C2×C4×C5#12312yes—
352C2×C4×C5#12312yes—
353C2×C4×C5C2×#4111yescharacteristic
354C2×C4×C5C2×#4111yescharacteristic
355C2×C4×C5C2×#4111yescharacteristic
356C2×C4×C5C2×#4111yescharacteristic
357C2×C4×C5H(5,𝔽2)11yescharacteristic
358C2×C4×C5H(5,𝔽2)11yescharacteristic
359C5×C8—41no—
360C5×C8—41no—
361C5×C8—41no—
362C5×C8—41no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4C5×D411yescharacteristic
366C22×D4C23×C511yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4C23×C511yescharacteristic
371C23×C4C23×C511yescharacteristic
372C22×C8C23×C511yescharacteristic
373C22×C8C23×C511yescharacteristic
374C22×C8C23×C511yescharacteristic
375C22×C8C23×C511yescharacteristic
376#121—22no—
377#121—22no—
378#121—41no—
379#121—41no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—44no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4C5×D411yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C4⋊C4C23×C511yescharacteristic
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4C5×D411yescharacteristic
409C2×C22⋊C4C5×D411yescharacteristic
410C2×C42—21no—
411C2×C42C23×C511yescharacteristic
412#107—41no—
413#106—41no—
414C4⋊C8—22no—
415#102—22no—
416#102—22no—
417#102—41no—
418#102—41no—
419C22⋊C8—41no—
420C22⋊C8—41no—
421C22⋊C8—41no—
422C22⋊C8—41no—
423#97—22no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5C2×#12311yescharacteristic
453C22×C5#54611yescharacteristic
454C22×C5#54611yescharacteristic
455C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C5C2×#13711yescharacteristic
457C22×C5#57611yescharacteristic
458C22×C5#57711yescharacteristic
459C4×C5—22no—
460C4×C5—22no—
461C4×C5—41no—
462C4×C5—41no—
463C4×C5—42no—
464C4×C5—81no—
465C4×C5—81no—
466C4×C5—81no—
467C4×C5—81no—
468C4×C5—81no—
469C4×C5—81no—
470C4×C5#52911yescharacteristic
471C4×C5#54011yescharacteristic
472C4×C5#55311yescharacteristic
473C4×C5#55511yescharacteristic
474C24—21no—
475C24C2×C5×D411yescharacteristic
476C24C2×C5×D411yescharacteristic
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4C5×#4112yes—
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—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C24×C511yescharacteristic
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4C5×#4112yes—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C42—42no—
566C42C5×#4112yes—
567C42C5×#4112yes—
568C2×C5—42no—
569C2×C5—42no—
570C2×C5—82no—
571C2×C5#242011yescharacteristic
572C2×C5#309211yescharacteristic
573C2×C5#309611yescharacteristic
574C2×C5#330611yescharacteristic
575C2×C5#331411yescharacteristic
576C2×C5#331811yescharacteristic
577C2×C5#332011yescharacteristic
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C5×AGL(1,ℤ/8)12yes—
598C23C5×#13712yes—
599C23C22×C5×D411yescharacteristic
600D4—28no—
601D4—22no—
602D4—22no—
603D4—41no—
604D4—41no—
605D4—84no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
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—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4—84no—
649C2×C4C5×#12312yes—
650C2×C4C5×#12312yes—
651C2×C4C2×C5×#4111yescharacteristic
652C2×C4C2×C5×#4111yescharacteristic
653C2×C4C2×C5×#4111yescharacteristic
654C2×C4C2×C5×#4111yescharacteristic
655C2×C4C5×H(5,𝔽2)11yescharacteristic
656C2×C4C5×H(5,𝔽2)11yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C5#2497711yescharacteristic, direct product factor, Sylow
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×C5×#12311yescharacteristic
684C22C5×#54611yescharacteristic
685C22C5×#54611yescharacteristic
686C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
687C22C2×C5×#13711yescharacteristic
688C22C5×#57611yescharacteristic
689C22C5×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C5×#52911yescharacteristic
702C4C5×#54011yescharacteristic
703C4C5×#55311yescharacteristic
704C4C5×#55511yescharacteristic
705C2—42no—
706C2—42no—
707C2—82no—
708C2C5×#242011yescharacteristic
709C2C5×#309211yescharacteristic
710C2C5×#309611yescharacteristic
711C2C5×#330611yescharacteristic
712C2C5×#331411yescharacteristic
713C2C5×#331811yescharacteristic
714C2C5×#332011yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×D4×C4⋊C4C2semidirect
3. C5×#2077C2semidirect
4. C5×#2076C2semidirect
5. C5×#2034C2semidirect
6. C5×#2033C2semidirect
7. C5×#1955C2semidirect
8. C5×#1949C2semidirect
9. C5×#1874C2semidirect
10. C5×#1874C2semidirect
11. C5×#1836C2semidirect
12. C5×#1824C2semidirect
13. C5×#1823C2semidirect
14. C5×#1802C2semidirect
15. C5×#1762C2semidirect
59. #24977C5direct (N × H)
129. D4×C4⋊C4C2×C5semidirect
130. #2077C2×C5semidirect
131. #2076C2×C5semidirect
132. #2034C2×C5semidirect
133. #2033C2×C5semidirect
134. #1955C2×C5semidirect
135. #1949C2×C5semidirect
136. #1874C2×C5semidirect
137. #1874C2×C5semidirect
138. #1836C2×C5semidirect
139. #1824C2×C5semidirect
140. #1823C2×C5semidirect
141. #1802C2×C5semidirect
142. #1762C2×C5semidirect
661. C5#24977direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25352
C5×D4×C4⋊C42
C5×#20772
C5×#20762
C5×#20342
C5×#20332
C5×#19552
C5×#19492
C5×#18742
C5×#18362
C5×#18242
C5×#18232
C5×#18022
C5×#17622
#249775