Finite Group Databasebeta

← C5×#26016 #11948736

Subgroups — C5×#26016 #11948736

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2441C211yesmaximal, characteristic
2C5×#2345C211yesmaximal, characteristic
3C5×#2099C211yesmaximal, characteristic, complemented
4C5×#2088C211yesmaximal, characteristic, complemented
5C5×#2087C211yesmaximal, characteristic, complemented
6C5×#2059C211yesmaximal, characteristic, complemented
7C5×#1989C211yesmaximal, characteristic, complemented
8C5×#1948C211yesmaximal, characteristic, complemented
9C5×#1921C211yesmaximal, characteristic, complemented
10C5×#1918C211yesmaximal, characteristic, complemented
11C5×#1854C211yesmaximal, characteristic
12C5×#1851C211yesmaximal, characteristic
13C5×#1823C211yesmaximal, characteristic
14C5×#1809C211yesmaximal, characteristic
15C5×#1736C211yesmaximal, characteristic
16C22×C5×M16C2211yescharacteristic
17C2×C5×#125C2211yescharacteristic
18C2×C5×#117C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×#106C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×C22⋊C8C2211yescharacteristic
27C5×#399—21no—
28C5×#396—21no—
29C5×#389—21no—
30C5×#389C2211yescharacteristic
31C5×#389C2211yescharacteristic
32C5×#389C2211yescharacteristic
33C5×#389C2211yescharacteristic
34C5×#387—21no—
35C5×#387—21no—
36C5×#387—21no—
37C5×#384C2211yescharacteristic
38C5×#380—21no—
39C5×#380C2211yescharacteristic
40C5×#380C2211yescharacteristic
41C4×C5×C4⋊C4C2211yescharacteristic
42C4×C5×C4⋊C4C2211yescharacteristic
43C4×C5×C22⋊C4—21no—
44C4×C5×C22⋊C4C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
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#26016C511yesmaximal, characteristic, direct product factor, Sylow
60C23×C4×C5—21no—
61C23×C4×C5C2311yescharacteristic
62C2×C5×M16—22no—
63C2×C5×M16—22no—
64C2×C5×M16—41no—
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C5×#125—22no—
70C5×#125—41no—
71C5×#117—22no—
72C5×#117—41no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4Q814yes—
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4D411yescharacteristic
96C2×C5×C22⋊C4D411yescharacteristic
97C2×C42×C5—21no—
98C2×C42×C5—21no—
99C2×C42×C5—21no—
100C2×C42×C5C2311yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C5×#107—22no—
103C5×#107—22no—
104C5×#106—41no—
105C5×#106—41no—
106C5×C4⋊C8—22no—
107C5×C4⋊C8—41no—
108C5×C22⋊C8—22no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95—21no—
112C5×#95—21no—
113C5×#95—21no—
114C5×#95—21no—
115C5×#95—21no—
116C5×#95—21no—
117C5×#95D411yescharacteristic
118C5×#95D411yescharacteristic
119#2441C2×C511yescharacteristic
120#2345C2×C511yescharacteristic
121#2099C2×C511yescharacteristic, complemented
122#2088C2×C511yescharacteristic, complemented
123#2087C2×C511yescharacteristic, complemented
124#2059C2×C511yescharacteristic, complemented
125#1989C2×C511yescharacteristic, complemented
126#1948C2×C511yescharacteristic, complemented
127#1921C2×C511yescharacteristic, complemented
128#1918C2×C511yescharacteristic, complemented
129#1854C2×C511yescharacteristic
130#1851C2×C511yescharacteristic
131#1823C2×C511yescharacteristic
132#1809C2×C511yescharacteristic
133#1736C2×C511yescharacteristic
134C24×C5C2×D411yescharacteristic
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—24no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—81no—
149C22×C4×C5—81no—
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×Q812yes—
156C22×C4×C5#4112yes—
157C22×C4×C5C2411yescharacteristic
158C5×M16—44no—
159C2×C5×C8—21no—
160C2×C5×C8—21no—
161C2×C5×C8—21no—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8#4112yes—
171C5×C4⋊C4—24no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—42no—
186C5×C4⋊C4—42no—
187C5×C4⋊C4—42no—
188C5×C4⋊C4—42no—
189C5×C4⋊C4—81no—
190C5×C4⋊C4—81no—
191C5×C4⋊C4—81no—
192C5×C4⋊C4—81no—
193C5×C4⋊C4C2×Q812yes—
194C5×C4⋊C4C2×Q812yes—
195C5×C4⋊C4#4112yes—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—41no—
198C5×C22⋊C4—42no—
199C5×C22⋊C4—42no—
200C5×C22⋊C4—81no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—42no—
206C42×C5—81no—
207C42×C5—81no—
208C22×M16C22×C511yescharacteristic
209C2×#125C22×C511yescharacteristic
210C2×#117C22×C511yescharacteristic
211C22×C4⋊C4C22×C511yescharacteristic
212C2×#107C22×C511yescharacteristic
213C2×#107C22×C511yescharacteristic
214C2×#106C22×C511yescharacteristic
215C2×#106C22×C511yescharacteristic
216C2×C4⋊C8C22×C511yescharacteristic
217C2×C4⋊C8C22×C511yescharacteristic
218C2×C22⋊C8C22×C511yescharacteristic
219#399—21no—
220#396—21no—
221#389—21no—
222#389C22×C511yescharacteristic
223#389C22×C511yescharacteristic
224#389C22×C511yescharacteristic
225#389C22×C511yescharacteristic
226#387—21no—
227#387—21no—
228#387—21no—
229#384C22×C511yescharacteristic
230#380—21no—
231#380C22×C511yescharacteristic
232#380C22×C511yescharacteristic
233C4×C4⋊C4C22×C511yescharacteristic
234C4×C4⋊C4C22×C511yescharacteristic
235C4×C22⋊C4—21no—
236C4×C22⋊C4C22×C511yescharacteristic
237#340C22×C511yescharacteristic
238#340C22×C511yescharacteristic
239#340C22×C511yescharacteristic
240#340C22×C511yescharacteristic
241#340C22×C511yescharacteristic
242#340C22×C511yescharacteristic
243#340C22×C511yescharacteristic
244#340C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249#336C22×C511yescharacteristic
250#336C22×C511yescharacteristic
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—21no—
257C23×C5C22⋊Q812yes—
258C23×C5C22×D411yescharacteristic
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—22no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—84no—
301C2×C4×C5C22⋊Q812yes—
302C2×C4×C5#13712yes—
303C2×C4×C5C22×Q811yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×C4×C5C2×#4111yescharacteristic
307C2×C4×C5H(5,𝔽2)11yescharacteristic
308C2×C4×C52−1+411yescharacteristic
309C5×C8—22no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—41no—
313C23×C4—21no—
314C23×C4C23×C511yescharacteristic
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—41no—
318C22×C8C23×C511yescharacteristic
319C22×C8C23×C511yescharacteristic
320C22×C8C23×C511yescharacteristic
321C22×C8C23×C511yescharacteristic
322#125—22no—
323#125—41no—
324#117—22no—
325#117—41no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C5×Q814yes—
337C2×C4⋊C4C23×C511yescharacteristic
338C2×C4⋊C4C23×C511yescharacteristic
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C4⋊C4C23×C511yescharacteristic
342C2×C4⋊C4C23×C511yescharacteristic
343C2×C4⋊C4C23×C511yescharacteristic
344C2×C4⋊C4C23×C511yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4C5×D411yescharacteristic
349C2×C22⋊C4C5×D411yescharacteristic
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42C23×C511yescharacteristic
354C2×C42C23×C511yescharacteristic
355#107—22no—
356#107—22no—
357#106—41no—
358#106—41no—
359C4⋊C8—22no—
360C4⋊C8—41no—
361C22⋊C8—22no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95C5×D411yescharacteristic
371#95C5×D411yescharacteristic
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5—41no—
379C22×C5C2×C22⋊Q811yescharacteristic
380C22×C5#54611yescharacteristic
381C22×C5#54711yescharacteristic
382C22×C5C2×#13711yescharacteristic
383C22×C5#57511yescharacteristic
384C22×C5#57611yescharacteristic
385C22×C5#57711yescharacteristic
386C4×C5—22no—
387C4×C5—22no—
388C4×C5—41no—
389C4×C5—42no—
390C4×C5—42no—
391C4×C5—41no—
392C4×C5—41no—
393C4×C5—42no—
394C4×C5—81no—
395C4×C5—81no—
396C4×C5—81no—
397C4×C5—81no—
398C4×C5—81no—
399C4×C5#53311yescharacteristic
400C4×C5#54411yescharacteristic
401C4×C5#55111yescharacteristic
402C4×C5#55211yescharacteristic
403C24C2×C5×D411yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—81no—
418C22×C4—81no—
419C22×C4C2×C5×D411yescharacteristic
420C22×C4C2×C5×D411yescharacteristic
421C22×C4C2×C5×D411yescharacteristic
422C22×C4C2×C5×D411yescharacteristic
423C22×C4C2×C5×D411yescharacteristic
424C22×C4C2×C5×Q812yes—
425C22×C4C5×#4112yes—
426C22×C4C24×C511yescharacteristic
427M16—44no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8C5×#4112yes—
440C4⋊C4—24no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4C2×C5×Q812yes—
463C4⋊C4C2×C5×Q812yes—
464C4⋊C4C5×#4112yes—
465C22⋊C4—22no—
466C22⋊C4—41no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—42no—
475C42—81no—
476C42—81no—
477C2×C5—42no—
478C2×C5#243811yescharacteristic
479C2×C5#307811yescharacteristic
480C2×C5#308111yescharacteristic
481C2×C5#330711yescharacteristic
482C2×C5#333311yescharacteristic
483C2×C5#334411yescharacteristic
484C2×C5#335511yescharacteristic
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23C5×C22⋊Q812yes—
492C23C22×C5×D411yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—84no—
535C2×C4C5×C22⋊Q812yes—
536C2×C4C5×#13712yes—
537C2×C4C22×C5×Q811yescharacteristic
538C2×C4C2×C5×#4111yescharacteristic
539C2×C4C2×C5×#4111yescharacteristic
540C2×C4C2×C5×#4111yescharacteristic
541C2×C4C5×H(5,𝔽2)11yescharacteristic
542C2×C4C5×2−1+411yescharacteristic
543C8—22no—
544C8—41no—
545C8—41no—
546C8—41no—
547C5#2601611yescharacteristic, direct product factor, Sylow
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×C5×C22⋊Q811yescharacteristic
556C22C5×#54611yescharacteristic
557C22C5×#54711yescharacteristic
558C22C2×C5×#13711yescharacteristic
559C22C5×#57511yescharacteristic
560C22C5×#57611yescharacteristic
561C22C5×#57711yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C5×#53311yescharacteristic
576C4C5×#54411yescharacteristic
577C4C5×#55111yescharacteristic
578C4C5×#55211yescharacteristic
579C2—42no—
580C2C5×#243811yescharacteristic
581C2C5×#307811yescharacteristic
582C2C5×#308111yescharacteristic
583C2C5×#330711yescharacteristic
584C2C5×#333311yescharacteristic
585C2C5×#334411yescharacteristic
586C2C5×#335511yescharacteristic
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
3. C5×#2099C2semidirect
4. C5×#2088C2semidirect
5. C5×#2087C2semidirect
6. C5×#2059C2semidirect
7. C5×#1989C2semidirect
8. C5×#1948C2semidirect
9. C5×#1921C2semidirect
10. C5×#1918C2semidirect
59. #26016C5direct (N × H)
121. #2099C2×C5semidirect
122. #2088C2×C5semidirect
123. #2087C2×C5semidirect
124. #2059C2×C5semidirect
125. #1989C2×C5semidirect
126. #1948C2×C5semidirect
127. #1921C2×C5semidirect
128. #1918C2×C5semidirect
547. C5#26016direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24412
C5×#23452
C5×#20992
C5×#20882
C5×#20872
C5×#20592
C5×#19892
C5×#19482
C5×#19212
C5×#19182
C5×#18542
C5×#18512
C5×#18232
C5×#18092
C5×#17362
#260165