Finite Group Databasebeta

← C5×#10405 #11933125

Subgroups — C5×#10405 #11933125

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 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×#1444C211yesmaximal, characteristic, complemented
7C5×#1280C211yesmaximal, characteristic, complemented
8C2×C5×C22⋊Q8C2211yescharacteristic
9C2×C5×#121C2211yescharacteristic
10C22×C5×C4⋊C4—21no—
11C22×C5×C4⋊C4C2211yescharacteristic
12C2×C5×#103—21no—
13C2×C5×#102—21no—
14C2×C5×C22⋊C8C2211yescharacteristic
15C2×C5×C22⋊C8C2211yescharacteristic
16C5×#400—21no—
17C5×#397—21no—
18C5×#394—21no—
19C5×#393—21no—
20C5×#386—21no—
21C5×#386—21no—
22C2×C5×#95—21no—
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
25C5×#340—21no—
26C5×#340—21no—
27C5×#328—22no—
28C5×#327—22no—
29#10405C511yesmaximal, 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⋊C4—42no—
53C2×C5×C4⋊C4—42no—
54C2×C5×C4⋊C4—42no—
55C2×C5×C4⋊C4D411yescharacteristic
56C2×C5×C4⋊C4D411yescharacteristic
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C5×#103—42no—
64C5×#102—42no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8—21no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—21no—
74C5×#95—21no—
75C5×#95—21no—
76C5×#95—42no—
77C5×#95D412yes—
78#2639C2×C511yescharacteristic
79#1874C2×C511yescharacteristic
80#1872C2×C511yescharacteristic, complemented
81C2×#328C2×C511yescharacteristic, complemented
82C2×#327C2×C511yescharacteristic
83#1444C2×C511yescharacteristic, complemented
84#1280C2×C511yescharacteristic, complemented
85C24×C5—21no—
86C24×C5C2×D411yescharacteristic
87C2×C5×Q8—21no—
88C2×C5×Q8—21no—
89C2×C5×Q8—41no—
90C2×C5×Q8—41no—
91C2×C5×D4—21no—
92C2×C5×D4—21no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—21no—
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×C5—41no—
129C22×C4×C5—41no—
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5C2×D411yescharacteristic
132C22×C4×C5C2×D411yescharacteristic
133C22×C4×C5#4111yescharacteristic
134C22×C4×C5#4111yescharacteristic
135C22×C4×C5#4111yescharacteristic
136C2×C5×C8—41no—
137C2×C5×C8—41no—
138C2×C5×C8—41no—
139C2×C5×C8—41no—
140C2×C5×C8—41no—
141C2×C5×C8—41no—
142C5×C4⋊C4—22no—
143C5×C4⋊C4—22no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—41no—
149C5×C4⋊C4—41no—
150C5×C4⋊C4—48no—
151C5×C4⋊C4—41no—
152C5×C4⋊C4—41no—
153C5×C22⋊C4—41no—
154C5×C22⋊C4—41no—
155C5×C22⋊C4—41no—
156C5×C22⋊C4—41no—
157C5×C22⋊C4—81no—
158C5×C22⋊C4—81no—
159C5×C22⋊C4—81no—
160C5×C22⋊C4—81no—
161C2×C22⋊Q8C22×C511yescharacteristic
162C2×#121C22×C511yescharacteristic
163C22×C4⋊C4—21no—
164C22×C4⋊C4C22×C511yescharacteristic
165C2×#103—21no—
166C2×#102—21no—
167C2×C22⋊C8C22×C511yescharacteristic
168C2×C22⋊C8C22×C511yescharacteristic
169#400—21no—
170#397—21no—
171#394—21no—
172#393—21no—
173#386—21no—
174#386—21no—
175C2×#95—21no—
176C2×#95C22×C511yescharacteristic
177C2×#95C22×C511yescharacteristic
178#340—21no—
179#340—21no—
180#328—22no—
181#327—22no—
182C23×C5—21no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—21no—
186C23×C5—41no—
187C23×C5—41no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5#12011yescharacteristic
194C23×C5#12111yescharacteristic
195C23×C5#12411yescharacteristic
196C23×C5#13511yescharacteristic
197C23×C5#13511yescharacteristic
198C23×C5AGL(1,ℤ/8)11yescharacteristic
199C23×C5#13711yescharacteristic
200C5×Q8—42no—
201C5×Q8—81no—
202C5×D4—42no—
203C5×D4—81no—
204C5×D4—81no—
205C5×D4—81no—
206C5×D4—81no—
207C5×D4—81no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—24no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—42no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—42no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—42no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—81no—
244C2×C4×C5—81no—
245C2×C4×C5—81no—
246C2×C4×C5—81no—
247C2×C4×C5—81no—
248C2×C4×C5—81no—
249C2×C4×C5#12111yescharacteristic
250C2×C4×C5#12111yescharacteristic
251C2×C4×C5#12311yescharacteristic
252C2×C4×C5#12311yescharacteristic
253C5×C8—81no—
254C5×C8—81no—
255C22×Q8C5×D411yescharacteristic
256C22×D4—21no—
257C22×D4C5×D411yescharacteristic
258C23×C4—21no—
259C23×C4—21no—
260C23×C4C5×D411yescharacteristic
261C23×C4C5×D411yescharacteristic
262C23×C4C23×C511yescharacteristic
263C22×C8—21no—
264C22×C8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4C5×D411yescharacteristic
281C2×C4⋊C4C5×D411yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288#103—42no—
289#102—42no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—42no—
302#95C5×D412yes—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5—81no—
320C22×C5—81no—
321C22×C5—81no—
322C22×C5#39411yescharacteristic
323C22×C5#44911yescharacteristic
324C22×C5#45211yescharacteristic
325C22×C5#45311yescharacteristic
326C22×C5#45611yescharacteristic
327C22×C5B(4,𝔽2)11yescharacteristic
328C22×C5#45811yescharacteristic
329C22×C5#46311yescharacteristic
330C22×C5#46411yescharacteristic
331C22×C5#48811yescharacteristic
332C22×C5#48911yescharacteristic
333C4×C5—21no—
334C4×C5—21no—
335C4×C5—21no—
336C4×C5—21no—
337C4×C5—44no—
338C4×C5—81no—
339C4×C5—82no—
340C4×C5—81no—
341C4×C5—81no—
342C4×C5—81no—
343C4×C5—81no—
344C24—21no—
345C24C2×C5×D411yescharacteristic
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
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×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4C2×C5×D411yescharacteristic
390C22×C4C2×C5×D411yescharacteristic
391C22×C4C2×C5×D411yescharacteristic
392C22×C4C5×#4111yescharacteristic
393C22×C4C5×#4111yescharacteristic
394C22×C4C5×#4111yescharacteristic
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—41no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—48no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—81no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C22⋊C4—81no—
420C2×C5—21no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—21no—
424C2×C5—161no—
425C2×C5#160011yescharacteristic
426C2×C5#160311yescharacteristic
427C2×C5#160911yescharacteristic
428C2×C5#161811yescharacteristic
429C2×C5#203911yescharacteristic
430C2×C5#204211yescharacteristic
431C2×C5#204411yescharacteristic
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C5×#12011yescharacteristic
444C23C5×#12111yescharacteristic
445C23C5×#12411yescharacteristic
446C23C5×#13511yescharacteristic
447C23C5×#13511yescharacteristic
448C23C5×AGL(1,ℤ/8)11yescharacteristic
449C23C5×#13711yescharacteristic
450Q8—42no—
451Q8—81no—
452D4—42no—
453D4—81no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4C5×#12111yescharacteristic
500C2×C4C5×#12111yescharacteristic
501C2×C4C5×#12311yescharacteristic
502C2×C4C5×#12311yescharacteristic
503C8—81no—
504C8—81no—
505C5#1040511yescharacteristic, direct product factor, Sylow
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22C5×#39411yescharacteristic
526C22C5×#44911yescharacteristic
527C22C5×#45211yescharacteristic
528C22C5×#45311yescharacteristic
529C22C5×#45611yescharacteristic
530C22C5×B(4,𝔽2)11yescharacteristic
531C22C5×#45811yescharacteristic
532C22C5×#46311yescharacteristic
533C22C5×#46411yescharacteristic
534C22C5×#48811yescharacteristic
535C22C5×#48911yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—44no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—82no—
546C4—81no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—161no—
552C2C5×#160011yescharacteristic
553C2C5×#160311yescharacteristic
554C2C5×#160911yescharacteristic
555C2C5×#161811yescharacteristic
556C2C5×#203911yescharacteristic
557C2C5×#204211yescharacteristic
558C2C5×#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×#1444C2semidirect
7. C5×#1280C2semidirect
29. #10405C5direct (N × H)
80. #1872C2×C5semidirect
81. C2×#328C2×C5semidirect
83. #1444C2×C5semidirect
84. #1280C2×C5semidirect
505. C5#10405direct (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×#14442
C5×#12802
#104055