Finite Group Databasebeta

← C5×#26199 #11948919

Subgroups — C5×#26199 #11948919

Order 1280.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2414C211yesmaximal, characteristic
2C5×#2352C211yesmaximal, characteristic, complemented
3C5×#2101C211yesmaximal, characteristic, complemented
4C5×#2077C211yesmaximal, characteristic, complemented
5C5×#2073C211yesmaximal, characteristic, complemented
6C5×#2033C211yesmaximal, characteristic, complemented
7C5×#1926C211yesmaximal, characteristic, complemented
8C5×#1918C211yesmaximal, characteristic, complemented
9C5×#1893C211yesmaximal, characteristic, complemented
10C5×#1875C211yesmaximal, characteristic, complemented
11C5×#1874C211yesmaximal, characteristic, complemented
12C5×#1869C211yesmaximal, characteristic, complemented
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1824C211yesmaximal, characteristic, complemented
15C5×#1735C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C2×C5×#121C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×C22⋊C8C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C5×#394—21no—
33C5×#392—21no—
34C5×#390—21no—
35C5×#390C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#388—21no—
38C5×#388—21no—
39C5×#387—21no—
40C5×#386—21no—
41C5×#382C2211yescharacteristic
42C5×#380C2211yescharacteristic
43C5×#380C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C4×C5×C22⋊C4—21no—
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#26199C511yesmaximal, 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×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C22×C5×C8—22no—
68C22×C5×C8—41no—
69C22×C5×C8—41no—
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C5×#121—22no—
75C5×#121—22no—
76C5×#121—22no—
77C5×#121—41no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C5×#117—22no—
81C5×#117—22no—
82C5×#117—41no—
83C5×#117—41no—
84C2×C5×C4⋊C4—22no—
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⋊C4—21no—
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C5×C22⋊C4D411yescharacteristic
107C2×C42×C5—21no—
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5C2311yescharacteristic
111C5×#107—22no—
112C5×#106—41no—
113C5×#102—22no—
114C5×#102—41no—
115C5×#102—41no—
116C5×#102—41no—
117C5×C22⋊C8—22no—
118C5×C22⋊C8—41no—
119C5×C22⋊C8—41no—
120C5×#95—21no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127#2414C2×C511yescharacteristic
128#2352C2×C511yescharacteristic, complemented
129#2101C2×C511yescharacteristic, complemented
130#2077C2×C511yescharacteristic, complemented
131#2073C2×C511yescharacteristic, complemented
132#2033C2×C511yescharacteristic, complemented
133#1926C2×C511yescharacteristic, complemented
134#1918C2×C511yescharacteristic, complemented
135#1893C2×C511yescharacteristic, complemented
136#1875C2×C511yescharacteristic, complemented
137#1874C2×C511yescharacteristic, complemented
138#1869C2×C511yescharacteristic, complemented
139#1854C2×C511yescharacteristic, complemented
140#1824C2×C511yescharacteristic, complemented
141#1735C2×C511yescharacteristic, complemented
142C24×C5—21no—
143C24×C5C2×D411yescharacteristic
144C24×C5C2×D411yescharacteristic
145C2×C5×D4—22no—
146C2×C5×D4—22no—
147C2×C5×D4—21no—
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—81no—
158C2×C5×D4—81no—
159C2×C5×D4—81no—
160C22×C4×C5—21no—
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—42no—
178C22×C4×C5—42no—
179C22×C4×C5—81no—
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5#4112yes—
185C22×C4×C5#4112yes—
186C22×C4×C5C2411yescharacteristic
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
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—44no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
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—42no—
214C5×C4⋊C4—81no—
215C5×C4⋊C4#4112yes—
216C5×C4⋊C4#4112yes—
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—42no—
220C5×C22⋊C4—42no—
221C5×C22⋊C4—42no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—81no—
226C5×C22⋊C4—81no—
227C5×C22⋊C4—81no—
228C42×C5—21no—
229C42×C5—21no—
230C42×C5—42no—
231C42×C5—42no—
232C42×C5—81no—
233C23×C8C22×C511yescharacteristic
234C2×#121C22×C511yescharacteristic
235C2×#121C22×C511yescharacteristic
236C2×C4×D4C22×C511yescharacteristic
237C2×#117C22×C511yescharacteristic
238C2×#117C22×C511yescharacteristic
239C22×C4⋊C4C22×C511yescharacteristic
240C2×#107C22×C511yescharacteristic
241C2×#106C22×C511yescharacteristic
242C2×#102C22×C511yescharacteristic
243C2×#102C22×C511yescharacteristic
244C2×#102C22×C511yescharacteristic
245C2×#102C22×C511yescharacteristic
246C2×C22⋊C8C22×C511yescharacteristic
247C2×C22⋊C8C22×C511yescharacteristic
248C2×C22⋊C8C22×C511yescharacteristic
249#394—21no—
250#392—21no—
251#390—21no—
252#390C22×C511yescharacteristic
253#389C22×C511yescharacteristic
254#388—21no—
255#388—21no—
256#387—21no—
257#386—21no—
258#382C22×C511yescharacteristic
259#380C22×C511yescharacteristic
260#380C22×C511yescharacteristic
261#380C22×C511yescharacteristic
262C4×C4⋊C4C22×C511yescharacteristic
263C4×C22⋊C4—21no—
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#336C22×C511yescharacteristic
275#336C22×C511yescharacteristic
276C23×C5—21no—
277C23×C5—21no—
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—21no—
287C23×C5—21no—
288C23×C5—41no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5#12312yes—
296C23×C5#13512yes—
297C23×C5C22×D411yescharacteristic
298C5×D4—44no—
299C5×D4—41no—
300C5×D4—41no—
301C5×D4—41no—
302C5×D4—41no—
303C5×D4—84no—
304C5×D4—84no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
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—84no—
346C2×C4×C5#12312yes—
347C2×C4×C5C2×#4111yescharacteristic
348C2×C4×C5C2×#4111yescharacteristic
349C2×C4×C5C2×#4111yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5H(5,𝔽2)11yescharacteristic
352C2×C4×C5H(5,𝔽2)11yescharacteristic
353C5×C8—41no—
354C5×C8—41no—
355C5×C8—41no—
356C5×C8—41no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C5×D411yescharacteristic
360C22×D4C23×C511yescharacteristic
361C23×C4—21no—
362C23×C4C23×C511yescharacteristic
363C23×C4C23×C511yescharacteristic
364C22×C8—22no—
365C22×C8—41no—
366C22×C8—41no—
367C22×C8C23×C511yescharacteristic
368C22×C8C23×C511yescharacteristic
369C22×C8C23×C511yescharacteristic
370C22×C8C23×C511yescharacteristic
371#121—22no—
372#121—22no—
373#121—22no—
374#121—41no—
375C4×D4—22no—
376C4×D4—22no—
377#117—22no—
378#117—22no—
379#117—41no—
380#117—41no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4C5×D411yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
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⋊C4C5×D411yescharacteristic
403C2×C22⋊C4C5×D411yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42C23×C511yescharacteristic
408#107—22no—
409#106—41no—
410#102—22no—
411#102—41no—
412#102—41no—
413#102—41no—
414C22⋊C8—22no—
415C22⋊C8—41no—
416C22⋊C8—41no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—81no—
439C22×C5—81no—
440C22×C5—81no—
441C22×C5—81no—
442C22×C5—81no—
443C22×C5—81no—
444C22×C5—81no—
445C22×C5C2×#12311yescharacteristic
446C22×C5#54611yescharacteristic
447C22×C5#54611yescharacteristic
448C22×C5C2×#13511yescharacteristic
449C22×C5#57511yescharacteristic
450C22×C5#57611yescharacteristic
451C22×C5#57711yescharacteristic
452C4×C5—22no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—41no—
456C4×C5—42no—
457C4×C5—42no—
458C4×C5—81no—
459C4×C5—81no—
460C4×C5—81no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5#52911yescharacteristic
464C4×C5#53811yescharacteristic
465C4×C5#55311yescharacteristic
466C4×C5#55311yescharacteristic
467C24—21no—
468C24C2×C5×D411yescharacteristic
469C24C2×C5×D411yescharacteristic
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—81no—
483C2×D4—81no—
484C2×D4—81no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
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×C4C5×#4112yes—
510C22×C4C5×#4112yes—
511C22×C4C24×C511yescharacteristic
512C2×C8—21no—
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×C8—44no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4C5×#4112yes—
541C4⋊C4C5×#4112yes—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—42no—
557C42—81no—
558C2×C5—42no—
559C2×C5—42no—
560C2×C5—161no—
561C2×C5#244411yescharacteristic
562C2×C5#309111yescharacteristic
563C2×C5#309611yescharacteristic
564C2×C5#329711yescharacteristic
565C2×C5#330111yescharacteristic
566C2×C5#331711yescharacteristic
567C2×C5#331911yescharacteristic
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C5×#12312yes—
588C23C5×#13512yes—
589C23C22×C5×D411yescharacteristic
590D4—44no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—84no—
596D4—84no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
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—84no—
638C2×C4C5×#12312yes—
639C2×C4C2×C5×#4111yescharacteristic
640C2×C4C2×C5×#4111yescharacteristic
641C2×C4C2×C5×#4111yescharacteristic
642C2×C4C2×C5×#4111yescharacteristic
643C2×C4C5×H(5,𝔽2)11yescharacteristic
644C2×C4C5×H(5,𝔽2)11yescharacteristic
645C8—41no—
646C8—41no—
647C8—41no—
648C8—41no—
649C5#2619911yescharacteristic, direct product factor, Sylow
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22C2×C5×#12311yescharacteristic
672C22C5×#54611yescharacteristic
673C22C5×#54611yescharacteristic
674C22C2×C5×#13511yescharacteristic
675C22C5×#57511yescharacteristic
676C22C5×#57611yescharacteristic
677C22C5×#57711yescharacteristic
678C4—22no—
679C4—42no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4C5×#52911yescharacteristic
690C4C5×#53811yescharacteristic
691C4C5×#55311yescharacteristic
692C4C5×#55311yescharacteristic
693C2—42no—
694C2—42no—
695C2—161no—
696C2C5×#244411yescharacteristic
697C2C5×#309111yescharacteristic
698C2C5×#309611yescharacteristic
699C2C5×#329711yescharacteristic
700C2C5×#330111yescharacteristic
701C2C5×#331711yescharacteristic
702C2C5×#331911yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2414C2
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×#2101C2semidirect
4. C5×#2077C2semidirect
5. C5×#2073C2semidirect
6. C5×#2033C2semidirect
7. C5×#1926C2semidirect
8. C5×#1918C2semidirect
9. C5×#1893C2semidirect
10. C5×#1875C2semidirect
11. C5×#1874C2semidirect
12. C5×#1869C2semidirect
13. C5×#1854C2semidirect
14. C5×#1824C2semidirect
15. C5×#1735C2semidirect
59. #26199C5direct (N × H)
128. #2352C2×C5semidirect
129. #2101C2×C5semidirect
130. #2077C2×C5semidirect
131. #2073C2×C5semidirect
132. #2033C2×C5semidirect
133. #1926C2×C5semidirect
134. #1918C2×C5semidirect
135. #1893C2×C5semidirect
136. #1875C2×C5semidirect
137. #1874C2×C5semidirect
138. #1869C2×C5semidirect
139. #1854C2×C5semidirect
140. #1824C2×C5semidirect
141. #1735C2×C5semidirect
649. C5#26199direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24142
C5×#23522
C5×#21012
C5×#20772
C5×#20732
C5×#20332
C5×#19262
C5×#19182
C5×#18932
C5×#18752
C5×#18742
C5×#18692
C5×#18542
C5×#18242
C5×#17352
#261995