Finite Group Databasebeta

← C5×#16605 #11939325

Subgroups — C5×#16605 #11939325

Order 1280.

1382 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#125C211yesmaximal, characteristic
2C2×C5×#398C212yesmaximal
3C2×C5×#387C211yesmaximal, characteristic
4C5×#1444C211yesmaximal, characteristic
5C5×#1442C212yesmaximal
6C5×#1442C211yesmaximal, characteristic
7C5×#1441C212yesmaximal
8C5×#1441C212yesmaximal
9C5×#1441C211yesmaximal, characteristic
10C5×#1441C211yesmaximal, characteristic
11C5×C4⋊#95C211yesmaximal, characteristic
12C2×C5×#125—28no—
13C2×C5×#125—24no—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C4⋊C4C2212yes—
20C22×C5×C4⋊C4C2212yes—
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C5×#398—28no—
24C5×#387—24no—
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39#16605C511yesmaximal, characteristic, direct product factor, Sylow
40C23×C4×C5C2311yescharacteristic
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C5×#125—232no—
52C2×C5×C4⋊C4—22no—
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—24no—
55C2×C5×C4⋊C4—24no—
56C2×C5×C4⋊C4—24no—
57C2×C5×C4⋊C4—24no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—24no—
61C2×C5×C4⋊C4—24no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—24no—
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—24no—
67C2×C5×C4⋊C4—24no—
68C2×C5×C4⋊C4—24no—
69C2×C5×C4⋊C4—42no—
70C2×C5×C4⋊C4—42no—
71C2×C5×C4⋊C4D418yes—
72C2×C5×C4⋊C4Q814yes—
73C2×C42×C5—24no—
74C2×C42×C5D414yes—
75C5×#95—22no—
76C5×#95—22no—
77C5×#95—22no—
78C5×#95—22no—
79C5×#95—24no—
80C5×#95—24no—
81C5×#95—24no—
82C5×#95—22no—
83C5×#95—24no—
84C5×#95—22no—
85C5×#95—42no—
86C5×#95—42no—
87C5×#95—42no—
88C5×#95—42no—
89C22×#125C2×C511yescharacteristic
90C2×#398C2×C512yes—
91C2×#387C2×C511yescharacteristic
92#1444C2×C511yescharacteristic
93#1442C2×C511yescharacteristic
94#1442C2×C512yes—
95#1441C2×C512yes—
96#1441C2×C511yescharacteristic
97#1441C2×C511yescharacteristic
98#1441C2×C512yes—
99C4⋊#95C2×C511yescharacteristic
100C24×C5C2411yescharacteristic
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—21no—
104C22×C4×C5—22no—
105C22×C4×C5—21no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—21no—
112C22×C4×C5—22no—
113C22×C4×C5—21no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—21no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—22no—
148C22×C4×C5—21no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D414yes—
157C22×C4×C5C2×D414yes—
158C22×C4×C5C2×D414yes—
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×Q812yes—
162C22×C4×C5C2×Q812yes—
163C22×C4×C5C2×Q812yes—
164C22×C4×C5#4114yes—
165C22×C4×C5#4112yes—
166C5×C4⋊C4—28no—
167C5×C4⋊C4—28no—
168C5×C4⋊C4—216no—
169C5×C4⋊C4—216no—
170C5×C4⋊C4—28no—
171C5×C4⋊C4—48no—
172C5×C4⋊C4—48no—
173C5×C4⋊C4—44no—
174C42×C5—28no—
175C2×#125—28no—
176C2×#125—24no—
177C22×C4⋊C4C22×C511yescharacteristic
178C22×C4⋊C4C22×C512yes—
179C22×C4⋊C4C22×C511yescharacteristic
180C22×C4⋊C4C22×C511yescharacteristic
181C22×C4⋊C4C22×C512yes—
182C22×C4⋊C4C22×C512yes—
183C22×C4⋊C4C22×C512yes—
184C22×C4⋊C4C22×C511yescharacteristic
185C22×C42C22×C511yescharacteristic
186#398—28no—
187#387—24no—
188C2×#95C22×C512yes—
189C2×#95C22×C512yes—
190C2×#95C22×C512yes—
191C2×#95C22×C511yescharacteristic
192C2×#95C22×C511yescharacteristic
193C2×#95C22×C511yescharacteristic
194C2×#95C22×C511yescharacteristic
195C2×#95C22×C512yes—
196C2×#95C22×C511yescharacteristic
197C2×#95C22×C511yescharacteristic
198C2×#95C22×C512yes—
199C2×#95C22×C512yes—
200C2×#95C22×C512yes—
201C2×#95C22×C512yes—
202C23×C5C22×D411yescharacteristic
203C23×C5C22×D412yes—
204C23×C5C22×Q811yescharacteristic
205C23×C5C2×#4111yescharacteristic
206C23×C5C2×#4112yes—
207C23×C5H(5,𝔽2)11yescharacteristic
208C23×C5H(5,𝔽2)11yescharacteristic
209C23×C52−1+411yescharacteristic
210C23×C52−1+412yes—
211C23×C52−1+412yes—
212C23×C52−1+411yescharacteristic
213C2×C4×C5—22no—
214C2×C4×C5—22no—
215C2×C4×C5—22no—
216C2×C4×C5—22no—
217C2×C4×C5—24no—
218C2×C4×C5—24no—
219C2×C4×C5—24no—
220C2×C4×C5—24no—
221C2×C4×C5—22no—
222C2×C4×C5—24no—
223C2×C4×C5—24no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—24no—
228C2×C4×C5—22no—
229C2×C4×C5—24no—
230C2×C4×C5—24no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—24no—
237C2×C4×C5—24no—
238C2×C4×C5—41no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—41no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5—41no—
252C2×C4×C5—42no—
253C2×C4×C5—41no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5#12014yes—
277C2×C4×C5C22⋊Q814yes—
278C23×C4C23×C511yescharacteristic
279C23×C4C23×C512yes—
280C23×C4C23×C511yescharacteristic
281C23×C4C23×C512yes—
282C23×C4C23×C512yes—
283C23×C4C23×C511yescharacteristic
284C23×C4C23×C511yescharacteristic
285C23×C4C23×C511yescharacteristic
286C23×C4C23×C512yes—
287C23×C4C23×C511yescharacteristic
288C23×C4C23×C511yescharacteristic
289#125—232no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4C5×D418yes—
310C2×C4⋊C4C5×Q814yes—
311C2×C42—24no—
312C2×C42C5×D414yes—
313#95—22no—
314#95—22no—
315#95—22no—
316#95—22no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—22no—
321#95—24no—
322#95—22no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327C22×C5C2×#12011yescharacteristic
328C22×C5C2×C22⋊Q811yescharacteristic
329C22×C5#53211yescharacteristic
330C22×C5#53611yescharacteristic
331C22×C5#53611yescharacteristic
332C22×C5#53612yes—
333C22×C5#53711yescharacteristic
334C22×C5#53711yescharacteristic
335C22×C5#53712yes—
336C22×C5#53912yes—
337C22×C5#54011yescharacteristic
338C22×C5#54111yescharacteristic
339C22×C5#54112yes—
340C22×C5#54411yescharacteristic
341C22×C5#54411yescharacteristic
342C22×C5#54612yes—
343C22×C5#54712yes—
344C22×C5#54812yes—
345C22×C5D4×Q812yes—
346C22×C5#55212yes—
347C22×C5#55712yes—
348C22×C5#56312yes—
349C22×C5#56412yes—
350C4×C5—24no—
351C4×C5—24no—
352C4×C5—42no—
353C4×C5—44no—
354C4×C5—42no—
355C4×C5—42no—
356C4×C5—44no—
357C4×C5—44no—
358C4×C5—81no—
359C4×C5—81no—
360C4×C5—82no—
361C24C24×C511yescharacteristic
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4C2×C5×D412yes—
417C22×C4C2×C5×D414yes—
418C22×C4C2×C5×D414yes—
419C22×C4C2×C5×D412yes—
420C22×C4C2×C5×D414yes—
421C22×C4C2×C5×D412yes—
422C22×C4C2×C5×Q812yes—
423C22×C4C2×C5×Q812yes—
424C22×C4C2×C5×Q812yes—
425C22×C4C5×#4114yes—
426C22×C4C5×#4112yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—216no—
430C4⋊C4—216no—
431C4⋊C4—28no—
432C4⋊C4—48no—
433C4⋊C4—48no—
434C4⋊C4—44no—
435C42—28no—
436C2×C5#240911yescharacteristic
437C2×C5#243011yescharacteristic
438C2×C5#256511yescharacteristic
439C2×C5#261611yescharacteristic
440C2×C5#262911yescharacteristic
441C2×C5#266411yescharacteristic
442C2×C5#270712yes—
443C2×C5#271312yes—
444C2×C5#271912yes—
445C2×C5#272612yes—
446C2×C5#282211yescharacteristic
447C23C22×C5×D411yescharacteristic
448C23C22×C5×D412yes—
449C23C22×C5×Q811yescharacteristic
450C23C2×C5×#4111yescharacteristic
451C23C2×C5×#4112yes—
452C23C5×H(5,𝔽2)11yescharacteristic
453C23C5×H(5,𝔽2)11yescharacteristic
454C23C5×2−1+411yescharacteristic
455C23C5×2−1+412yes—
456C23C5×2−1+412yes—
457C23C5×2−1+411yescharacteristic
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4C5×#12014yes—
522C2×C4C5×C22⋊Q814yes—
523C5#1660511yescharacteristic, direct product factor, Sylow
524C22C2×C5×#12011yescharacteristic
525C22C2×C5×C22⋊Q811yescharacteristic
526C22C5×#53211yescharacteristic
527C22C5×#53611yescharacteristic
528C22C5×#53611yescharacteristic
529C22C5×#53612yes—
530C22C5×#53712yes—
531C22C5×#53711yescharacteristic
532C22C5×#53711yescharacteristic
533C22C5×#53912yes—
534C22C5×#54011yescharacteristic
535C22C5×#54111yescharacteristic
536C22C5×#54112yes—
537C22C5×#54411yescharacteristic
538C22C5×#54411yescharacteristic
539C22C5×#54612yes—
540C22C5×#54712yes—
541C22C5×#54812yes—
542C22C5×D4×Q812yes—
543C22C5×#55212yes—
544C22C5×#55712yes—
545C22C5×#56312yes—
546C22C5×#56412yes—
547C4—24no—
548C4—24no—
549C4—42no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—44no—
554C4—44no—
555C4—81no—
556C4—81no—
557C4—82no—
558C2C5×#240911yescharacteristic
559C2C5×#243011yescharacteristic
560C2C5×#256511yescharacteristic
561C2C5×#261611yescharacteristic
562C2C5×#262911yescharacteristic
563C2C5×#266411yescharacteristic
564C2C5×#270712yes—
565C2C5×#271312yes—
566C2C5×#271912yes—
567C2C5×#272612yes—
568C2C5×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C24
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
39. #16605C5direct (N × H)
523. C5#16605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1252
C2×C5×#3982
C2×C5×#3872
C5×#14442
C5×#14422
C5×#14412
C5×C4⋊#952
#166055