Finite Group Databasebeta

← C5×#13084 #11935804

Subgroups — C5×#13084 #11935804

Order 1280.

894 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#99C211yesmaximal, characteristic
2C5×#2405C211yesmaximal, characteristic
3C2×C5×#352C212yesmaximal, complemented
4C5×#1783C211yesmaximal, characteristic
5C5×#1390C212yesmaximal, complemented
6C23×C5×D4C2211yescharacteristic
7C2×C5×#123C411yescharacteristic, complemented
8C2×C5×#123C2211yescharacteristic
9C22×C5×C22⋊C4—21no—
10C22×C5×C22⋊C4C411yescharacteristic, complemented
11C2×C5×#100—21no—
12C2×C5×#100C2212yes—
13C2×C5×#99—24no—
14C2×C5×#99—21no—
15C2×C5×#99C2212yes—
16C5×#407—21no—
17C5×#394—21no—
18C5×#394—21no—
19C5×#386C411yescharacteristic, complemented
20C5×#386C2211yescharacteristic
21C5×#385—21no—
22C5×#379—21no—
23C5×#379C411yescharacteristic, complemented
24C5×#352—24no—
25#13084C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5C2×C411yescharacteristic
27C25×C5D411yescharacteristic
28C22×C5×D4—22no—
29C22×C5×D4—22no—
30C22×C5×D4—41no—
31C22×C5×D4—41no—
32C22×C5×D4—42no—
33C22×C5×D4C2×C411yescharacteristic
34C22×C5×D4D411yescharacteristic
35C22×C5×D4D411yescharacteristic
36C22×C5×D4C2311yescharacteristic
37C23×C4×C5—41no—
38C23×C4×C5C2×C411yescharacteristic, complemented
39C23×C4×C5C2×C411yescharacteristic, complemented
40C23×C4×C5D411yescharacteristic
41C2×C5×M16—22no—
42C5×#123—22no—
43C5×#123—22no—
44C5×#123—42no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C22⋊C4—24no—
48C2×C5×C22⋊C4—22no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—41no—
58C2×C5×C22⋊C4—42no—
59C2×C5×C22⋊C4—41no—
60C2×C5×C22⋊C4—41no—
61C2×C5×C22⋊C4C2×C411yescharacteristic, complemented
62C2×C5×C22⋊C4C2×C411yescharacteristic, complemented
63C5×#100—22no—
64C5×#100—22no—
65C5×#100—42no—
66C5×#99—24no—
67C5×#99—22no—
68C5×#99D414yes—
69C5×C22⋊C8—41no—
70C5×C22⋊C8—41no—
71C5×#95—21no—
72C5×#95—21no—
73C22×#99C2×C511yescharacteristic
74#2405C2×C511yescharacteristic
75C2×#352C2×C512yescomplemented
76#1783C2×C511yescharacteristic
77#1390C2×C512yescomplemented
78C24×C5—21no—
79C24×C5—22no—
80C24×C5—21no—
81C24×C5—21no—
82C24×C5—21no—
83C24×C5—21no—
84C24×C5—21no—
85C24×C5—22no—
86C24×C5—41no—
87C24×C5—42no—
88C24×C5—42no—
89C24×C5—81no—
90C24×C5—81no—
91C24×C5C22⋊C411yescharacteristic
92C24×C5C22⋊C411yescharacteristic
93C24×C5C22⋊C411yescharacteristic
94C24×C5C22×C411yescharacteristic
95C24×C5C2×D411yescharacteristic
96C2×C5×D4—22no—
97C2×C5×D4—22no—
98C2×C5×D4—22no—
99C2×C5×D4—21no—
100C2×C5×D4—21no—
101C2×C5×D4—22no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4—41no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—44no—
109C2×C5×D4—44no—
110C2×C5×D4—44no—
111C2×C5×D4—44no—
112C2×C5×D4C2×D412yes—
113C2×C5×D4#4112yes—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—22no—
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—41no—
123C22×C4×C5—44no—
124C22×C4×C5—42no—
125C22×C4×C5—41no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5—81no—
129C22×C4×C5—82no—
130C22×C4×C5—82no—
131C22×C4×C5C22⋊C411yescharacteristic
132C22×C4×C5C2×D411yescharacteristic
133C5×M16—42no—
134C5×M16—42no—
135C2×C5×C8—42no—
136C5×C4⋊C4—42no—
137C5×C4⋊C4—42no—
138C5×C22⋊C4—22no—
139C5×C22⋊C4—24no—
140C5×C22⋊C4—42no—
141C5×C22⋊C4—44no—
142C5×C22⋊C4—42no—
143C5×C22⋊C4—42no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—41no—
146C5×C22⋊C4—42no—
147C5×C22⋊C4—41no—
148C5×C22⋊C4—41no—
149C5×C22⋊C4—41no—
150C5×C22⋊C4—81no—
151C5×C22⋊C4—81no—
152C5×C22⋊C4—81no—
153C23×D4C22×C511yescharacteristic
154C2×#123C4×C511yescharacteristic, complemented
155C2×#123C22×C511yescharacteristic
156C22×C22⋊C4—21no—
157C22×C22⋊C4C4×C511yescharacteristic, complemented
158C2×#100—21no—
159C2×#100C22×C512yes—
160C2×#99—21no—
161C2×#99—24no—
162C2×#99C22×C512yes—
163#407—21no—
164#394—21no—
165#394—21no—
166#386C4×C511yescharacteristic, complemented
167#386C22×C511yescharacteristic
168#385—21no—
169#379—21no—
170#379C4×C511yescharacteristic, complemented
171#352—24no—
172C23×C5—22no—
173C23×C5—22no—
174C23×C5—22no—
175C23×C5—22no—
176C23×C5—22no—
177C23×C5—21no—
178C23×C5—21no—
179C23×C5—21no—
180C23×C5—21no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—21no—
186C23×C5—21no—
187C23×C5—21no—
188C23×C5—41no—
189C23×C5—42no—
190C23×C5—42no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5—42no—
194C23×C5—41no—
195C23×C5—41no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5—42no—
199C23×C5—41no—
200C23×C5—41no—
201C23×C5—42no—
202C23×C5—42no—
203C23×C5—81no—
204C23×C5—81no—
205C23×C5—81no—
206C23×C5—81no—
207C23×C5—84no—
208C23×C5—82no—
209C23×C5—82no—
210C23×C5—84no—
211C23×C5—84no—
212C23×C5#9911yescharacteristic
213C23×C5#9911yescharacteristic
214C23×C5#9912yes—
215C23×C5C2×C22⋊C411yescharacteristic
216C23×C5C4×D412yes—
217C23×C5#12011yescharacteristic
218C23×C5#12311yescharacteristic
219C5×D4—42no—
220C5×D4—42no—
221C5×D4—44no—
222C5×D4—44no—
223C5×D4—42no—
224C5×D4—42no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—21no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—44no—
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—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—88no—
246C2×C4×C5—82no—
247C2×C4×C5—82no—
248C2×C4×C5—82no—
249C2×C4×C5—82no—
250C2×C4×C5#12112yes—
251C5×C8—82no—
252C25C2×C4×C511yescharacteristic
253C25C5×D411yescharacteristic
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—41no—
257C22×D4—41no—
258C22×D4—42no—
259C22×D4C2×C4×C511yescharacteristic
260C22×D4C5×D411yescharacteristic
261C22×D4C5×D411yescharacteristic
262C22×D4C23×C511yescharacteristic
263C23×C4—41no—
264C23×C4C2×C4×C511yescharacteristic, complemented
265C23×C4C2×C4×C511yescharacteristic, complemented
266C23×C4C5×D411yescharacteristic
267C2×M16—22no—
268#123—22no—
269#123—22no—
270#123—42no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4C2×C4×C511yescharacteristic, complemented
288C2×C22⋊C4C2×C4×C511yescharacteristic, complemented
289#100—22no—
290#100—22no—
291#100—42no—
292#99—24no—
293#99—22no—
294#99C5×D414yes—
295C22⋊C8—41no—
296C22⋊C8—41no—
297#95—21no—
298#95—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—22no—
308C22×C5—22no—
309C22×C5—21no—
310C22×C5—42no—
311C22×C5—42no—
312C22×C5—42no—
313C22×C5—42no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—44no—
317C22×C5—42no—
318C22×C5—44no—
319C22×C5—41no—
320C22×C5—41no—
321C22×C5—41no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—41no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—81no—
329C22×C5—81no—
330C22×C5—84no—
331C22×C5—81no—
332C22×C5—81no—
333C22×C5—82no—
334C22×C5—82no—
335C22×C5—84no—
336C22×C5#35212yescomplemented
337C22×C5#38611yescharacteristic
338C22×C5C2×#9911yescharacteristic
339C22×C5C2×#9911yescharacteristic
340C4×C5—22no—
341C4×C5—41no—
342C4×C5—81no—
343C4×C5—81no—
344C4×C5—84no—
345C4×C5—81no—
346C4×C5—81no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—22no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—41no—
356C24—42no—
357C24—42no—
358C24—81no—
359C24—81no—
360C24C5×C22⋊C411yescharacteristic
361C24C5×C22⋊C411yescharacteristic
362C24C5×C22⋊C411yescharacteristic
363C24C22×C4×C511yescharacteristic
364C24C2×C5×D411yescharacteristic
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4C2×C5×D412yes—
382C2×D4C5×#4112yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—41no—
392C22×C4—44no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—81no—
398C22×C4—82no—
399C22×C4—82no—
400C22×C4C5×C22⋊C411yescharacteristic
401C22×C4C2×C5×D411yescharacteristic
402M16—42no—
403M16—42no—
404C2×C8—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—44no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—81no—
420C22⋊C4—81no—
421C22⋊C4—81no—
422C2×C5—21no—
423C2×C5—21no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5—41no—
427C2×C5—42no—
428C2×C5—41no—
429C2×C5—42no—
430C2×C5—81no—
431C2×C5#189811yescharacteristic
432C2×C5C2×#35211yescharacteristic
433C2×C5#212111yescharacteristic
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23—81no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—82no—
470C23—82no—
471C23—84no—
472C23—84no—
473C23—84no—
474C23C5×#9911yescharacteristic
475C23C5×#9911yescharacteristic
476C23C5×#9912yes—
477C23C2×C5×C22⋊C411yescharacteristic
478C23C4×C5×D412yes—
479C23C5×#12011yescharacteristic
480C23C5×#12311yescharacteristic
481D4—42no—
482D4—42no—
483D4—44no—
484D4—44no—
485D4—42no—
486D4—42no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—88no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4C5×#12112yes—
513C8—82no—
514C5#1308411yescharacteristic, direct product factor, Sylow
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—21no—
525C22—22no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—41no—
530C22—41no—
531C22—42no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22C5×#35212yescomplemented
553C22C5×#38611yescharacteristic
554C22C2×C5×#9911yescharacteristic
555C22C2×C5×#9911yescharacteristic
556C4—22no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—84no—
561C4—81no—
562C4—81no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—41no—
569C2—42no—
570C2—42no—
571C2—81no—
572C2C5×#189811yescharacteristic
573C2C2×C5×#35211yescharacteristic
574C2C5×#212111yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C23×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#352C2semidirect
5. C5×#1390C2semidirect
7. C2×C5×#123C4semidirect
10. C22×C5×C22⋊C4C4semidirect
19. C5×#386C4semidirect
23. C5×#379C4semidirect
25. #13084C5direct (N × H)
38. C23×C4×C5C2×C4semidirect
39. C23×C4×C5C2×C4semidirect
61. C2×C5×C22⋊C4C2×C4semidirect
62. C2×C5×C22⋊C4C2×C4semidirect
75. C2×#352C2×C5semidirect
77. #1390C2×C5semidirect
154. C2×#123C4×C5semidirect
157. C22×C22⋊C4C4×C5semidirect
166. #386C4×C5semidirect
170. #379C4×C5semidirect
264. C23×C4C2×C4×C5semidirect
265. C23×C4C2×C4×C5semidirect
287. C2×C22⋊C4C2×C4×C5semidirect
288. C2×C22⋊C4C2×C4×C5semidirect
336. C22×C5#352semidirect
514. C5#13084direct (N × H)
552. C22C5×#352semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#992
C5×#24052
C2×C5×#3522
C5×#17832
C5×#13902
#130845