Finite Group Databasebeta

← C5×#26125 #11948845

Subgroups — C5×#26125 #11948845

Order 1280.

728 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2571C211yesmaximal, characteristic, complemented
2C5×#2349C211yesmaximal, characteristic
3C5×#2101C211yesmaximal, characteristic, complemented
4C5×#2101C211yesmaximal, characteristic, complemented
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2086C211yesmaximal, characteristic, complemented
7C5×#1949C211yesmaximal, characteristic, complemented
8C5×#1940C211yesmaximal, characteristic, complemented
9C5×#1864C211yesmaximal, characteristic
10C5×#1862C211yesmaximal, characteristic
11C5×#1836C211yesmaximal, characteristic, complemented
12C5×#1804C211yesmaximal, characteristic
13C5×#1804C211yesmaximal, characteristic
14C5×#1802C211yesmaximal, characteristic
15C5×#1762C211yesmaximal, characteristic
16C2×C4×C5×D4C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#97C2211yescharacteristic
29C5×#400—21no—
30C5×#400—21no—
31C5×#389—21no—
32C5×#389C2211yescharacteristic
33C5×#389C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#385—21no—
37C5×#385—21no—
38C5×#384C2211yescharacteristic
39C5×#382—21no—
40C5×#382C2211yescharacteristic
41C5×#382C2211yescharacteristic
42C5×#382C2211yescharacteristic
43C5×#380—21no—
44C4×C5×C4⋊C4C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C2×C5×#95—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#26125C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4C2311yescharacteristic
61C23×C4×C5—21no—
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C4×C5×D4—22no—
69C4×C5×D4—22no—
70C4×C5×D4—22no—
71C4×C5×D4—41no—
72C4×C5×D4—41no—
73C4×C5×D4Q814yes—
74C2×C5×C4⋊C4—21no—
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⋊C4D411yescharacteristic
81C2×C5×C4⋊C4D411yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C42×C5—21no—
93C2×C42×C5C2311yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C5×#107—41no—
97C5×#106—41no—
98C5×C4⋊C8—22no—
99C5×C4⋊C8—41no—
100C5×C4⋊C8—41no—
101C5×#102—22no—
102C5×#102—22no—
103C5×#102—22no—
104C5×#102—22no—
105C5×#97—22no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
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#2571C2×C511yescharacteristic, complemented
120#2349C2×C511yescharacteristic
121#2101C2×C511yescharacteristic, complemented
122#2101C2×C511yescharacteristic, complemented
123#2088C2×C511yescharacteristic, complemented
124#2086C2×C511yescharacteristic, complemented
125#1949C2×C511yescharacteristic, complemented
126#1940C2×C511yescharacteristic, complemented
127#1864C2×C511yescharacteristic
128#1862C2×C511yescharacteristic
129#1836C2×C511yescharacteristic, complemented
130#1804C2×C511yescharacteristic
131#1804C2×C511yescharacteristic
132#1802C2×C511yescharacteristic
133#1762C2×C511yescharacteristic
134C24×C5—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4C2×Q812yes—
139C2×C5×D4#4112yes—
140C2×C5×D4#4112yes—
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—21no—
149C22×C4×C5—42no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5—42no—
153C22×C4×C5—81no—
154C22×C4×C5—81no—
155C22×C4×C5—81no—
156C22×C4×C5—81no—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2411yescharacteristic
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—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—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—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—41no—
190C5×C4⋊C4—41no—
191C5×C4⋊C4—42no—
192C5×C4⋊C4—81no—
193C5×C4⋊C4—81no—
194C5×C4⋊C4—81no—
195C5×C4⋊C4—81no—
196C5×C4⋊C4—81no—
197C5×C4⋊C4C2×Q812yes—
198C5×C22⋊C4—24no—
199C5×C22⋊C4—42no—
200C5×C22⋊C4—42no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—42no—
206C42×C5C2×Q812yes—
207C42×C5#4112yes—
208C2×C4×D4C22×C511yescharacteristic
209C2×C4×D4C22×C511yescharacteristic
210C2×C4×D4C22×C511yescharacteristic
211C2×#107C22×C511yescharacteristic
212C2×#106C22×C511yescharacteristic
213C2×C4⋊C8C22×C511yescharacteristic
214C2×C4⋊C8C22×C511yescharacteristic
215C2×C4⋊C8C22×C511yescharacteristic
216C2×#102C22×C511yescharacteristic
217C2×#102C22×C511yescharacteristic
218C2×#102C22×C511yescharacteristic
219C2×#102C22×C511yescharacteristic
220C2×#97C22×C511yescharacteristic
221#400—21no—
222#400—21no—
223#389—21no—
224#389C22×C511yescharacteristic
225#389C22×C511yescharacteristic
226#389C22×C511yescharacteristic
227#389C22×C511yescharacteristic
228#385—21no—
229#385—21no—
230#384C22×C511yescharacteristic
231#382—21no—
232#382C22×C511yescharacteristic
233#382C22×C511yescharacteristic
234#382C22×C511yescharacteristic
235#380—21no—
236C4×C4⋊C4C22×C511yescharacteristic
237C4×C4⋊C4C22×C511yescharacteristic
238C2×#95—21no—
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—22no—
252C23×C5—22no—
253C23×C5—22no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5C22×D411yescharacteristic
259C5×D4—22no—
260C5×D4—22no—
261C5×D4—22no—
262C5×D4#12514yes—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
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—21no—
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×C5—84no—
302C2×C4×C5—84no—
303C2×C4×C5C22⋊Q812yes—
304C2×C4×C5C22⋊Q812yes—
305C2×C4×C5C22×Q811yescharacteristic
306C2×C4×C5C2×#4111yescharacteristic
307C2×C4×C5C2×#4111yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C2×C4×C5H(5,𝔽2)11yescharacteristic
310C2×C4×C52−1+411yescharacteristic
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315C22×D4C23×C511yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C22×C8C23×C511yescharacteristic
320C22×C8C23×C511yescharacteristic
321C22×C8C23×C511yescharacteristic
322C22×C8C23×C511yescharacteristic
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—41no—
327C4×D4—41no—
328C4×D4C5×Q814yes—
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⋊C4C5×D411yescharacteristic
336C2×C4⋊C4C5×D411yescharacteristic
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×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42C23×C511yescharacteristic
349C2×C42C23×C511yescharacteristic
350C2×C42C23×C511yescharacteristic
351#107—41no—
352#106—41no—
353C4⋊C8—22no—
354C4⋊C8—41no—
355C4⋊C8—41no—
356#102—22no—
357#102—22no—
358#102—22no—
359#102—22no—
360#97—22no—
361#95—21no—
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#95—21no—
371#95—21no—
372#95C5×D411yescharacteristic
373#95C5×D411yescharacteristic
374C22×C5—24no—
375C22×C5—42no—
376C22×C5—42no—
377C22×C5—42no—
378C22×C5—42no—
379C22×C5—42no—
380C22×C5—42no—
381C22×C5C2×C22⋊Q811yescharacteristic
382C22×C5#54611yescharacteristic
383C22×C5#54811yescharacteristic
384C22×C5#57511yescharacteristic
385C22×C5#57511yescharacteristic
386C22×C5#57611yescharacteristic
387C22×C5#57711yescharacteristic
388C4×C5—22no—
389C4×C5—22no—
390C4×C5—42no—
391C4×C5—41no—
392C4×C5—41no—
393C4×C5—41no—
394C4×C5—41no—
395C4×C5—81no—
396C4×C5—81no—
397C4×C5—81no—
398C4×C5—81no—
399C4×C5—81no—
400C4×C5—81no—
401C4×C5C2×#12511yescharacteristic
402C4×C5#54411yescharacteristic
403C4×C5#55211yescharacteristic
404C4×C5#55311yescharacteristic
405C24—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4C2×C5×Q812yes—
410C2×D4C5×#4112yes—
411C2×D4C5×#4112yes—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—81no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4C2×C5×D411yescharacteristic
429C22×C4C2×C5×D411yescharacteristic
430C22×C4C2×C5×D411yescharacteristic
431C22×C4C2×C5×D411yescharacteristic
432C22×C4C2×C5×D411yescharacteristic
433C22×C4C2×C5×D411yescharacteristic
434C22×C4C24×C511yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4C2×C5×Q812yes—
469C22⋊C4—24no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42C2×C5×Q812yes—
478C42C5×#4112yes—
479C2×C5—44no—
480C2×C5#244211yescharacteristic
481C2×C5#308011yescharacteristic
482C2×C5#308111yescharacteristic
483C2×C5#331111yescharacteristic
484C2×C5#331911yescharacteristic
485C2×C5#337011yescharacteristic
486C2×C5#337611yescharacteristic
487C23—22no—
488C23—22no—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×C5×D411yescharacteristic
495D4—22no—
496D4—22no—
497D4—22no—
498D4C5×#12514yes—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
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—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4C5×C22⋊Q812yes—
540C2×C4C5×C22⋊Q812yes—
541C2×C4C22×C5×Q811yescharacteristic
542C2×C4C2×C5×#4111yescharacteristic
543C2×C4C2×C5×#4111yescharacteristic
544C2×C4C2×C5×#4111yescharacteristic
545C2×C4C5×H(5,𝔽2)11yescharacteristic
546C2×C4C5×2−1+411yescharacteristic
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C5#2612511yescharacteristic, direct product factor, Sylow
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22C2×C5×C22⋊Q811yescharacteristic
560C22C5×#54611yescharacteristic
561C22C5×#54811yescharacteristic
562C22C5×#57511yescharacteristic
563C22C5×#57511yescharacteristic
564C22C5×#57611yescharacteristic
565C22C5×#57711yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×C5×#12511yescharacteristic
580C4C5×#54411yescharacteristic
581C4C5×#55211yescharacteristic
582C4C5×#55311yescharacteristic
583C2—44no—
584C2C5×#244211yescharacteristic
585C2C5×#308011yescharacteristic
586C2C5×#308111yescharacteristic
587C2C5×#331111yescharacteristic
588C2C5×#331911yescharacteristic
589C2C5×#337011yescharacteristic
590C2C5×#337611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2571C2semidirect
3. C5×#2101C2semidirect
4. C5×#2101C2semidirect
5. C5×#2088C2semidirect
6. C5×#2086C2semidirect
7. C5×#1949C2semidirect
8. C5×#1940C2semidirect
11. C5×#1836C2semidirect
59. #26125C5direct (N × H)
119. #2571C2×C5semidirect
121. #2101C2×C5semidirect
122. #2101C2×C5semidirect
123. #2088C2×C5semidirect
124. #2086C2×C5semidirect
125. #1949C2×C5semidirect
126. #1940C2×C5semidirect
129. #1836C2×C5semidirect
551. C5#26125direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25712
C5×#23492
C5×#21012
C5×#20882
C5×#20862
C5×#19492
C5×#19402
C5×#18642
C5×#18622
C5×#18362
C5×#18042
C5×#18022
C5×#17622
#261255