Finite Group Databasebeta

← C5×#10404 #11933124

Subgroups — C5×#10404 #11933124

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2639C211yesmaximal, characteristic
2C5×#1874C211yesmaximal, characteristic
3C5×#1872C211yesmaximal, characteristic, complemented
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×C5×#327C211yesmaximal, characteristic
6C5×#1442C211yesmaximal, characteristic, complemented
7C5×#1280C211yesmaximal, characteristic, complemented
8C2×C5×C22⋊Q8C2211yescharacteristic
9C2×C5×#121C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C2×C5×#103—21no—
12C2×C5×#102—21no—
13C2×C5×C22⋊C8C2211yescharacteristic
14C2×C5×C22⋊C8C2211yescharacteristic
15C5×#400—21no—
16C5×#397—21no—
17C5×#394—21no—
18C5×#393—21no—
19C5×#386—21no—
20C5×#386—21no—
21C2×C5×#95—21no—
22C2×C5×#95—21no—
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
25C5×#340—21no—
26C5×#340—21no—
27C5×#328—22no—
28C5×#327—22no—
29#10404C511yesmaximal, characteristic, direct product factor, Sylow
30C22×C5×Q8D411yescharacteristic
31C22×C5×D4—21no—
32C22×C5×D4D411yescharacteristic
33C23×C4×C5—21no—
34C23×C4×C5—21no—
35C23×C4×C5D411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C22×C5×C8—21no—
39C22×C5×C8—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×#121—21no—
45C5×#121—21no—
46C5×#121—21no—
47C5×#121—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—42no—
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C4⋊C4D411yescharacteristic
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C5×#103—42no—
61C5×#102—42no—
62C5×C22⋊C8—21no—
63C5×C22⋊C8—21no—
64C5×C22⋊C8—21no—
65C5×C22⋊C8—21no—
66C5×#95—21no—
67C5×#95—21no—
68C5×#95—21no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—42no—
74C5×#95—42no—
75C5×#95D412yes—
76#2639C2×C511yescharacteristic
77#1874C2×C511yescharacteristic
78#1872C2×C511yescharacteristic, complemented
79C2×#328C2×C511yescharacteristic, complemented
80C2×#327C2×C511yescharacteristic
81#1442C2×C511yescharacteristic, complemented
82#1280C2×C511yescharacteristic, complemented
83C24×C5—21no—
84C24×C5C2×D411yescharacteristic
85C2×C5×Q8—21no—
86C2×C5×Q8—21no—
87C2×C5×Q8—41no—
88C2×C5×Q8—41no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—41no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C22×C4×C5—22no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5—41no—
113C22×C4×C5—41no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—41no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—41no—
123C22×C4×C5—41no—
124C22×C4×C5—41no—
125C22×C4×C5—41no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5C2×D411yescharacteristic
129C22×C4×C5C2×D411yescharacteristic
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5#4111yescharacteristic
132C22×C4×C5#4111yescharacteristic
133C22×C4×C5#4111yescharacteristic
134C2×C5×C8—41no—
135C2×C5×C8—41no—
136C2×C5×C8—41no—
137C2×C5×C8—41no—
138C2×C5×C8—41no—
139C2×C5×C8—41no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4—22no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—41no—
147C5×C4⋊C4—41no—
148C5×C4⋊C4—41no—
149C5×C4⋊C4—41no—
150C5×C22⋊C4—41no—
151C5×C22⋊C4—41no—
152C5×C22⋊C4—41no—
153C5×C22⋊C4—41no—
154C5×C22⋊C4—81no—
155C5×C22⋊C4—81no—
156C5×C22⋊C4—81no—
157C5×C22⋊C4—81no—
158C2×C22⋊Q8C22×C511yescharacteristic
159C2×#121C22×C511yescharacteristic
160C22×C4⋊C4C22×C511yescharacteristic
161C2×#103—21no—
162C2×#102—21no—
163C2×C22⋊C8C22×C511yescharacteristic
164C2×C22⋊C8C22×C511yescharacteristic
165#400—21no—
166#397—21no—
167#394—21no—
168#393—21no—
169#386—21no—
170#386—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95C22×C511yescharacteristic
174C2×#95C22×C511yescharacteristic
175#340—21no—
176#340—21no—
177#328—22no—
178#327—22no—
179C23×C5—21no—
180C23×C5—21no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5—41no—
186C23×C5—41no—
187C23×C5—41no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5#12011yescharacteristic
191C23×C5#12111yescharacteristic
192C23×C5#12411yescharacteristic
193C23×C5#13511yescharacteristic
194C23×C5#13511yescharacteristic
195C23×C5AGL(1,ℤ/8)11yescharacteristic
196C23×C5#13711yescharacteristic
197C5×Q8—42no—
198C5×Q8—81no—
199C5×D4—42no—
200C5×D4—81no—
201C5×D4—81no—
202C5×D4—81no—
203C5×D4—81no—
204C5×D4—81no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—42no—
214C2×C4×C5—42no—
215C2×C4×C5—42no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5—42no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—42no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—42no—
236C2×C4×C5—81no—
237C2×C4×C5—81no—
238C2×C4×C5—81no—
239C2×C4×C5—81no—
240C2×C4×C5—81no—
241C2×C4×C5—81no—
242C2×C4×C5—81no—
243C2×C4×C5—81no—
244C2×C4×C5—81no—
245C2×C4×C5—81no—
246C2×C4×C5#12111yescharacteristic
247C2×C4×C5#12111yescharacteristic
248C2×C4×C5#12311yescharacteristic
249C2×C4×C5#12311yescharacteristic
250C5×C8—81no—
251C5×C8—81no—
252C22×Q8C5×D411yescharacteristic
253C22×D4—21no—
254C22×D4C5×D411yescharacteristic
255C23×C4—21no—
256C23×C4—21no—
257C23×C4C5×D411yescharacteristic
258C23×C4C5×D411yescharacteristic
259C23×C4C23×C511yescharacteristic
260C22×C8—21no—
261C22×C8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4C5×D411yescharacteristic
275C2×C4⋊C4C5×D411yescharacteristic
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282#103—42no—
283#102—42no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—42no—
296#95—42no—
297#95C5×D412yes—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—81no—
311C22×C5—81no—
312C22×C5—81no—
313C22×C5—81no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5#39411yescharacteristic
318C22×C5#44911yescharacteristic
319C22×C5#45211yescharacteristic
320C22×C5#45411yescharacteristic
321C22×C5#45511yescharacteristic
322C22×C5B(4,𝔽2)11yescharacteristic
323C22×C5#45811yescharacteristic
324C22×C5#46311yescharacteristic
325C22×C5#46411yescharacteristic
326C22×C5#48811yescharacteristic
327C22×C5#48911yescharacteristic
328C4×C5—21no—
329C4×C5—21no—
330C4×C5—21no—
331C4×C5—21no—
332C4×C5—82no—
333C4×C5—82no—
334C4×C5—81no—
335C4×C5—81no—
336C4×C5—81no—
337C4×C5—81no—
338C4×C5—81no—
339C24—21no—
340C24C2×C5×D411yescharacteristic
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4C2×C5×D411yescharacteristic
385C22×C4C2×C5×D411yescharacteristic
386C22×C4C2×C5×D411yescharacteristic
387C22×C4C5×#4111yescharacteristic
388C22×C4C5×#4111yescharacteristic
389C22×C4C5×#4111yescharacteristic
390C2×C8—41no—
391C2×C8—41no—
392C2×C8—41no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—81no—
411C22⋊C4—81no—
412C22⋊C4—81no—
413C22⋊C4—81no—
414C2×C5—21no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—21no—
418C2×C5—161no—
419C2×C5#159711yescharacteristic
420C2×C5#160611yescharacteristic
421C2×C5#161211yescharacteristic
422C2×C5#161511yescharacteristic
423C2×C5#204011yescharacteristic
424C2×C5#204211yescharacteristic
425C2×C5#204411yescharacteristic
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C5×#12011yescharacteristic
438C23C5×#12111yescharacteristic
439C23C5×#12411yescharacteristic
440C23C5×#13511yescharacteristic
441C23C5×#13511yescharacteristic
442C23C5×AGL(1,ℤ/8)11yescharacteristic
443C23C5×#13711yescharacteristic
444Q8—42no—
445Q8—81no—
446D4—42no—
447D4—81no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4C5×#12111yescharacteristic
494C2×C4C5×#12111yescharacteristic
495C2×C4C5×#12311yescharacteristic
496C2×C4C5×#12311yescharacteristic
497C8—81no—
498C8—81no—
499C5#1040411yescharacteristic, direct product factor, Sylow
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22C5×#39411yescharacteristic
520C22C5×#44911yescharacteristic
521C22C5×#45211yescharacteristic
522C22C5×#45411yescharacteristic
523C22C5×#45511yescharacteristic
524C22C5×B(4,𝔽2)11yescharacteristic
525C22C5×#45811yescharacteristic
526C22C5×#46311yescharacteristic
527C22C5×#46411yescharacteristic
528C22C5×#48811yescharacteristic
529C22C5×#48911yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C4—81no—
540C4—81no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—161no—
546C2C5×#159711yescharacteristic
547C2C5×#160611yescharacteristic
548C2C5×#161211yescharacteristic
549C2C5×#161511yescharacteristic
550C2C5×#204011yescharacteristic
551C2C5×#204211yescharacteristic
552C2C5×#204411yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1872C2semidirect
4. C2×C5×#328C2semidirect
6. C5×#1442C2semidirect
7. C5×#1280C2semidirect
29. #10404C5direct (N × H)
78. #1872C2×C5semidirect
79. C2×#328C2×C5semidirect
81. #1442C2×C5semidirect
82. #1280C2×C5semidirect
499. C5#10404direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26392
C5×#18742
C5×#18722
C2×C5×#3282
C2×C5×#3272
C5×#14422
C5×#12802
#104045