Finite Group Databasebeta

← C5×#24982 #11947702

Subgroups — C5×#24982 #11947702

Order 1280.

862 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2537C211yesmaximal, characteristic
2C5×#2352C211yesmaximal, characteristic, complemented
3C5×#2077C211yesmaximal, characteristic, complemented
4C5×#2077C211yesmaximal, characteristic, complemented
5C5×#2034C211yesmaximal, characteristic, complemented
6C5×#2034C211yesmaximal, characteristic, complemented
7C5×#1955C211yesmaximal, characteristic, complemented
8C5×#1948C211yesmaximal, characteristic, complemented
9C5×#1875C211yesmaximal, characteristic, complemented
10C5×#1874C211yesmaximal, characteristic, complemented
11C5×#1836C211yesmaximal, characteristic, complemented
12C5×#1825C211yesmaximal, characteristic, complemented
13C5×#1823C211yesmaximal, characteristic, complemented
14C5×#1804C211yesmaximal, characteristic, complemented
15C5×#1762C211yesmaximal, characteristic, complemented
16C2×C5×#121—21no—
17C2×C5×#121C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
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×#394—21no—
36C5×#394—21no—
37C5×#388—21no—
38C5×#387—21no—
39C5×#386—21no—
40C5×#384C2211yescharacteristic
41C5×#382C2211yescharacteristic
42C5×#380—21no—
43C5×#380C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C5×#380C2211yescharacteristic
47C4×C5×C4⋊C4C2211yescharacteristic
48C4×C5×C22⋊C4—21no—
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59#24982C511yesmaximal, 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×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C5×#121—22no—
73C5×#121—22no—
74C5×#121—41no—
75C5×#121—41no—
76C5×#121—44no—
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C5×#117—22no—
82C5×#117—41no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4D411yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C22⋊C4—21no—
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⋊C4—21no—
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C42×C5—21no—
107C2×C42×C5—21no—
108C2×C42×C5C2311yescharacteristic
109C5×#106—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#2537C2×C511yescharacteristic
129#2352C2×C511yescharacteristic, complemented
130#2077C2×C511yescharacteristic, complemented
131#2077C2×C511yescharacteristic, complemented
132#2034C2×C511yescharacteristic, complemented
133#2034C2×C511yescharacteristic, complemented
134#1955C2×C511yescharacteristic, complemented
135#1948C2×C511yescharacteristic, complemented
136#1875C2×C511yescharacteristic, complemented
137#1874C2×C511yescharacteristic, complemented
138#1836C2×C511yescharacteristic, complemented
139#1825C2×C511yescharacteristic, complemented
140#1823C2×C511yescharacteristic, complemented
141#1804C2×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—21no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4—41no—
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×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2411yescharacteristic
191C2×C5×C8—21no—
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—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
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—42no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—81no—
220C5×C4⋊C4#4112yes—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—81no—
231C42×C5—42no—
232C42×C5—81no—
233C42×C5#4112yes—
234C42×C5#4112yes—
235C2×#121—21no—
236C2×#121C22×C511yescharacteristic
237C2×#121C22×C511yescharacteristic
238C2×C4×D4C22×C511yescharacteristic
239C2×C4×D4C22×C511yescharacteristic
240C2×#117C22×C511yescharacteristic
241C22×C4⋊C4C22×C511yescharacteristic
242C2×#106C22×C511yescharacteristic
243C2×#106C22×C511yescharacteristic
244C2×C4⋊C8C22×C511yescharacteristic
245C2×#102C22×C511yescharacteristic
246C2×#102C22×C511yescharacteristic
247C2×#102C22×C511yescharacteristic
248C2×#102C22×C511yescharacteristic
249C2×C22⋊C8C22×C511yescharacteristic
250C2×C22⋊C8C22×C511yescharacteristic
251C2×C22⋊C8C22×C511yescharacteristic
252C2×C22⋊C8C22×C511yescharacteristic
253C2×#97C22×C511yescharacteristic
254#394—21no—
255#394—21no—
256#388—21no—
257#387—21no—
258#386—21no—
259#384C22×C511yescharacteristic
260#382C22×C511yescharacteristic
261#380—21no—
262#380C22×C511yescharacteristic
263#380C22×C511yescharacteristic
264#380C22×C511yescharacteristic
265#380C22×C511yescharacteristic
266C4×C4⋊C4C22×C511yescharacteristic
267C4×C22⋊C4—21no—
268#340C22×C511yescharacteristic
269#340C22×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
278C23×C5—21no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—22no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5AGL(1,ℤ/8)12yes—
299C23×C5C22×D411yescharacteristic
300C5×D4—22no—
301C5×D4—22no—
302C5×D4—44no—
303C5×D4—41no—
304C5×D4—41no—
305C5×D4—84no—
306C5×D4—84no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
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—84no—
347C2×C4×C5—84no—
348C2×C4×C5#12312yes—
349C2×C4×C5#12312yes—
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5C2×#4111yescharacteristic
352C2×C4×C5C2×#4111yescharacteristic
353C2×C4×C5C2×#4111yescharacteristic
354C2×C4×C5H(5,𝔽2)11yescharacteristic
355C2×C4×C5H(5,𝔽2)11yescharacteristic
356C5×C8—41no—
357C5×C8—41no—
358C5×C8—41no—
359C5×C8—41no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4C5×D411yescharacteristic
363C22×D4C23×C511yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C23×C511yescharacteristic
367C23×C4C23×C511yescharacteristic
368C22×C8C23×C511yescharacteristic
369C22×C8C23×C511yescharacteristic
370C22×C8C23×C511yescharacteristic
371C22×C8C23×C511yescharacteristic
372#121—22no—
373#121—22no—
374#121—41no—
375#121—41no—
376#121—44no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381#117—22no—
382#117—41no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4C5×D411yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4C5×D411yescharacteristic
405C2×C22⋊C4C5×D411yescharacteristic
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C23×C511yescharacteristic
409#106—41no—
410#106—41no—
411C4⋊C8—22no—
412#102—22no—
413#102—22no—
414#102—41no—
415#102—41no—
416C22⋊C8—41no—
417C22⋊C8—41no—
418C22⋊C8—41no—
419C22⋊C8—41no—
420#97—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—42no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—42no—
442C22×C5—41no—
443C22×C5—42no—
444C22×C5—41no—
445C22×C5—81no—
446C22×C5—81no—
447C22×C5—81no—
448C22×C5—81no—
449C22×C5C2×#12311yescharacteristic
450C22×C5#54611yescharacteristic
451C22×C5#54611yescharacteristic
452C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C5#57511yescharacteristic
454C22×C5#57711yescharacteristic
455C22×C5#57711yescharacteristic
456C4×C5—22no—
457C4×C5—22no—
458C4×C5—41no—
459C4×C5—41no—
460C4×C5—42no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5—81no—
466C4×C5—81no—
467C4×C5#52911yescharacteristic
468C4×C5#54011yescharacteristic
469C4×C5#55311yescharacteristic
470C4×C5#55511yescharacteristic
471C24—21no—
472C24C2×C5×D411yescharacteristic
473C24C2×C5×D411yescharacteristic
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4C5×#4112yes—
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—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4C2×C5×D411yescharacteristic
515C22×C4C2×C5×D411yescharacteristic
516C22×C4C2×C5×D411yescharacteristic
517C22×C4C2×C5×D411yescharacteristic
518C22×C4C24×C511yescharacteristic
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
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—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4C5×#4112yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C42—42no—
560C42—81no—
561C42C5×#4112yes—
562C42C5×#4112yes—
563C2×C5—42no—
564C2×C5—81no—
565C2×C5—82no—
566C2×C5#242011yescharacteristic
567C2×C5#309411yescharacteristic
568C2×C5#309911yescharacteristic
569C2×C5#330611yescharacteristic
570C2×C5#330711yescharacteristic
571C2×C5#331011yescharacteristic
572C2×C5#332111yescharacteristic
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—22no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C5×AGL(1,ℤ/8)12yes—
594C23C22×C5×D411yescharacteristic
595D4—22no—
596D4—22no—
597D4—44no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—84no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
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—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—84no—
642C2×C4—84no—
643C2×C4C5×#12312yes—
644C2×C4C5×#12312yes—
645C2×C4C2×C5×#4111yescharacteristic
646C2×C4C2×C5×#4111yescharacteristic
647C2×C4C2×C5×#4111yescharacteristic
648C2×C4C2×C5×#4111yescharacteristic
649C2×C4C5×H(5,𝔽2)11yescharacteristic
650C2×C4C5×H(5,𝔽2)11yescharacteristic
651C8—41no—
652C8—41no—
653C8—41no—
654C8—41no—
655C5#2498211yescharacteristic, direct product factor, Sylow
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×C5×#12311yescharacteristic
678C22C5×#54611yescharacteristic
679C22C5×#54611yescharacteristic
680C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
681C22C5×#57511yescharacteristic
682C22C5×#57711yescharacteristic
683C22C5×#57711yescharacteristic
684C4—22no—
685C4—22no—
686C4—42no—
687C4—41no—
688C4—41no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C5×#52911yescharacteristic
696C4C5×#54011yescharacteristic
697C4C5×#55311yescharacteristic
698C4C5×#55511yescharacteristic
699C2—42no—
700C2—81no—
701C2—82no—
702C2C5×#242011yescharacteristic
703C2C5×#309411yescharacteristic
704C2C5×#309911yescharacteristic
705C2C5×#330611yescharacteristic
706C2C5×#330711yescharacteristic
707C2C5×#331011yescharacteristic
708C2C5×#332111yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2537C2
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×#2352C2semidirect
3. C5×#2077C2semidirect
4. C5×#2077C2semidirect
5. C5×#2034C2semidirect
6. C5×#2034C2semidirect
7. C5×#1955C2semidirect
8. C5×#1948C2semidirect
9. C5×#1875C2semidirect
10. C5×#1874C2semidirect
11. C5×#1836C2semidirect
12. C5×#1825C2semidirect
13. C5×#1823C2semidirect
14. C5×#1804C2semidirect
15. C5×#1762C2semidirect
59. #24982C5direct (N × H)
129. #2352C2×C5semidirect
130. #2077C2×C5semidirect
131. #2077C2×C5semidirect
132. #2034C2×C5semidirect
133. #2034C2×C5semidirect
134. #1955C2×C5semidirect
135. #1948C2×C5semidirect
136. #1875C2×C5semidirect
137. #1874C2×C5semidirect
138. #1836C2×C5semidirect
139. #1825C2×C5semidirect
140. #1823C2×C5semidirect
141. #1804C2×C5semidirect
142. #1762C2×C5semidirect
655. C5#24982direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25372
C5×#23522
C5×#20772
C5×#20342
C5×#19552
C5×#19482
C5×#18752
C5×#18742
C5×#18362
C5×#18252
C5×#18232
C5×#18042
C5×#17622
#249825