Finite Group Databasebeta

← C5×#25002 #11947722

Subgroups — C5×#25002 #11947722

Order 1280.

716 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×#2580C211yesmaximal, characteristic
2C5×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2099C211yesmaximal, characteristic, complemented
5C5×#2071C211yesmaximal, characteristic
6C5×#2071C211yesmaximal, characteristic
7C5×#1985C211yesmaximal, characteristic, complemented
8C5×#1949C211yesmaximal, characteristic, complemented
9C5×#1926C211yesmaximal, characteristic
10C5×#1925C211yesmaximal, characteristic
11C5×#1921C211yesmaximal, characteristic, complemented
12C5×#1920C211yesmaximal, characteristic, complemented
13C5×#1836C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic
15C5×#1762C211yesmaximal, characteristic
16C2×C4×C5×Q8—21no—
17C2×C4×C5×Q8C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×#102C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C2×C5×#97C2211yescharacteristic
27C5×#399—21no—
28C5×#393—21no—
29C5×#390C2211yescharacteristic
30C5×#390C2211yescharacteristic
31C5×#389—21no—
32C5×#389—21no—
33C5×#389—21no—
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#385—21no—
37C5×#385—21no—
38C5×#384C2211yescharacteristic
39C5×#384C2211yescharacteristic
40C5×#384C2211yescharacteristic
41C5×#382C2211yescharacteristic
42C4×C5×C4⋊C4C2211yescharacteristic
43C4×C5×C4⋊C4C2211yescharacteristic
44C4×C5×C4⋊C4C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#336C2211yescharacteristic
56C5×#336C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#25002C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8D411yescharacteristic
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C4×C5×Q8—22no—
68C4×C5×Q8—22no—
69C4×C5×Q8—44no—
70C4×C5×D4—22no—
71C4×C5×D4—22no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
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⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C42×C5—21no—
96C2×C42×C5—21no—
97C2×C42×C5—21no—
98C2×C42×C5C2311yescharacteristic
99C2×C42×C5C2311yescharacteristic
100C2×C42×C5C2311yescharacteristic
101C5×#107—22no—
102C5×#106—22no—
103C5×C4⋊C8—22no—
104C5×#102—22no—
105C5×#102—22no—
106C5×#102—22no—
107C5×#102—22no—
108C5×#97—22no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95—21no—
112C5×#95—21no—
113C5×#95—21no—
114C5×#95—21no—
115C5×#95—21no—
116#2580C2×C511yescharacteristic
117Q8×C4⋊C4C2×C511yescharacteristic, complemented
118#2100C2×C511yescharacteristic, complemented
119#2099C2×C511yescharacteristic, complemented
120#2071C2×C511yescharacteristic
121#2071C2×C511yescharacteristic
122#1985C2×C511yescharacteristic, complemented
123#1949C2×C511yescharacteristic, complemented
124#1926C2×C511yescharacteristic
125#1925C2×C511yescharacteristic
126#1921C2×C511yescharacteristic, complemented
127#1920C2×C511yescharacteristic, complemented
128#1836C2×C511yescharacteristic, complemented
129#1802C2×C511yescharacteristic
130#1762C2×C511yescharacteristic
131C24×C5—21no—
132C2×C5×Q8—22no—
133C2×C5×Q8—22no—
134C2×C5×Q8—22no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4#4112yes—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—42no—
149C22×C4×C5—81no—
150C22×C4×C5—81no—
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2411yescharacteristic
158C2×C5×C8—21no—
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—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
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—21no—
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⋊C4—81no—
194C5×C4⋊C4#4112yes—
195C5×C22⋊C4—42no—
196C5×C22⋊C4—42no—
197C5×C22⋊C4—42no—
198C5×C22⋊C4—81no—
199C5×C22⋊C4—81no—
200C42×C5—21no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—42no—
205C42×C5—42no—
206C42×C5—42no—
207C42×C5#4112yes—
208C42×C5#4112yes—
209C2×C4×Q8—21no—
210C2×C4×Q8C22×C511yescharacteristic
211C2×C4×D4C22×C511yescharacteristic
212C2×#107C22×C511yescharacteristic
213C2×#106C22×C511yescharacteristic
214C2×C4⋊C8C22×C511yescharacteristic
215C2×#102C22×C511yescharacteristic
216C2×#102C22×C511yescharacteristic
217C2×#102C22×C511yescharacteristic
218C2×#102C22×C511yescharacteristic
219C2×#97C22×C511yescharacteristic
220#399—21no—
221#393—21no—
222#390C22×C511yescharacteristic
223#390C22×C511yescharacteristic
224#389—21no—
225#389—21no—
226#389—21no—
227#389C22×C511yescharacteristic
228#389C22×C511yescharacteristic
229#385—21no—
230#385—21no—
231#384C22×C511yescharacteristic
232#384C22×C511yescharacteristic
233#384C22×C511yescharacteristic
234#382C22×C511yescharacteristic
235C4×C4⋊C4C22×C511yescharacteristic
236C4×C4⋊C4C22×C511yescharacteristic
237C4×C4⋊C4C22×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#336C22×C511yescharacteristic
249#336C22×C511yescharacteristic
250#336C22×C511yescharacteristic
251#336C22×C511yescharacteristic
252C23×C5—22no—
253C23×C5—41no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5C22×D411yescharacteristic
260C5×Q8—28no—
261C5×D4—22no—
262C5×D4—22no—
263C5×D4—41no—
264C5×D4—41no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
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—22no—
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#12312yes—
302C2×C4×C5#12312yes—
303C2×C4×C5AGL(1,ℤ/8)12yes—
304C2×C4×C5#13712yes—
305C2×C4×C5C2×#4111yescharacteristic
306C2×C4×C5C2×#4111yescharacteristic
307C2×C4×C5C2×#4111yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C2×C4×C52−1+411yescharacteristic
310C2×C4×C52−1+411yescharacteristic
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315C22×Q8C5×D411yescharacteristic
316C22×D4C23×C511yescharacteristic
317C23×C4—21no—
318C22×C8C23×C511yescharacteristic
319C22×C8C23×C511yescharacteristic
320C22×C8C23×C511yescharacteristic
321C22×C8C23×C511yescharacteristic
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—44no—
325C4×D4—22no—
326C4×D4—22no—
327C2×C4⋊C4—21no—
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⋊C4C5×D411yescharacteristic
336C2×C4⋊C4C5×D411yescharacteristic
337C2×C4⋊C4C5×D411yescharacteristic
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⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42C23×C511yescharacteristic
354C2×C42C23×C511yescharacteristic
355C2×C42C23×C511yescharacteristic
356#107—22no—
357#106—22no—
358C4⋊C8—22no—
359#102—22no—
360#102—22no—
361#102—22no—
362#102—22no—
363#97—22no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371C22×C5—42no—
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—81no—
375C22×C5—81no—
376C22×C5—81no—
377C22×C5—81no—
378C22×C5C2×#12311yescharacteristic
379C22×C5#54811yescharacteristic
380C22×C5#54811yescharacteristic
381C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C5C2×#13711yescharacteristic
383C22×C5#57611yescharacteristic
384C22×C5#57711yescharacteristic
385C4×C5—22no—
386C4×C5—22no—
387C4×C5—22no—
388C4×C5—22no—
389C4×C5—41no—
390C4×C5—41no—
391C4×C5—42no—
392C4×C5—81no—
393C4×C5—81no—
394C4×C5—81no—
395C4×C5—81no—
396C4×C5—81no—
397C4×C5—81no—
398C4×C5#52911yescharacteristic
399C4×C5#54111yescharacteristic
400C4×C5#55211yescharacteristic
401C4×C5#55611yescharacteristic
402C24—21no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4C5×#4112yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4C2×C5×D411yescharacteristic
423C22×C4C2×C5×D411yescharacteristic
424C22×C4C2×C5×D411yescharacteristic
425C22×C4C2×C5×D411yescharacteristic
426C22×C4C2×C5×D411yescharacteristic
427C22×C4C2×C5×D411yescharacteristic
428C22×C4C24×C511yescharacteristic
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×C8—21no—
440C2×C8—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
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—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4C5×#4112yes—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—42no—
476C42—42no—
477C42—42no—
478C42C5×#4112yes—
479C42C5×#4112yes—
480C2×C5—82no—
481C2×C5#242111yescharacteristic
482C2×C5#309211yescharacteristic
483C2×C5#309611yescharacteristic
484C2×C5#336611yescharacteristic
485C2×C5#337211yescharacteristic
486C2×C5#337311yescharacteristic
487C2×C5#337511yescharacteristic
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C22×C5×D411yescharacteristic
496Q8—28no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
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×C4C5×#12312yes—
538C2×C4C5×#12312yes—
539C2×C4C5×AGL(1,ℤ/8)12yes—
540C2×C4C5×#13712yes—
541C2×C4C2×C5×#4111yescharacteristic
542C2×C4C2×C5×#4111yescharacteristic
543C2×C4C2×C5×#4111yescharacteristic
544C2×C4C2×C5×#4111yescharacteristic
545C2×C4C5×2−1+411yescharacteristic
546C2×C4C5×2−1+411yescharacteristic
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C5#2500211yescharacteristic, direct product factor, Sylow
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×C5×#12311yescharacteristic
560C22C5×#54811yescharacteristic
561C22C5×#54811yescharacteristic
562C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
563C22C2×C5×#13711yescharacteristic
564C22C5×#57611yescharacteristic
565C22C5×#57711yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C5×#52911yescharacteristic
580C4C5×#54111yescharacteristic
581C4C5×#55211yescharacteristic
582C4C5×#55611yescharacteristic
583C2—82no—
584C2C5×#242111yescharacteristic
585C2C5×#309211yescharacteristic
586C2C5×#309611yescharacteristic
587C2C5×#336611yescharacteristic
588C2C5×#337211yescharacteristic
589C2C5×#337311yescharacteristic
590C2C5×#337511yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×Q8×C4⋊C4C2semidirect
3. C5×#2100C2semidirect
4. C5×#2099C2semidirect
7. C5×#1985C2semidirect
8. C5×#1949C2semidirect
11. C5×#1921C2semidirect
12. C5×#1920C2semidirect
13. C5×#1836C2semidirect
59. #25002C5direct (N × H)
117. Q8×C4⋊C4C2×C5semidirect
118. #2100C2×C5semidirect
119. #2099C2×C5semidirect
122. #1985C2×C5semidirect
123. #1949C2×C5semidirect
126. #1921C2×C5semidirect
127. #1920C2×C5semidirect
128. #1836C2×C5semidirect
551. C5#25002direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25802
C5×Q8×C4⋊C42
C5×#21002
C5×#20992
C5×#20712
C5×#19852
C5×#19492
C5×#19262
C5×#19252
C5×#19212
C5×#19202
C5×#18362
C5×#18022
C5×#17622
#250025