Finite Group Databasebeta

← C5×#14308 #11937028

Subgroups — C5×#14308 #11937028

Order 1280.

1210 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic
3C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
4C5×#1445C212yesmaximal
5C5×#1445C211yesmaximal, characteristic
6C5×#1443C212yesmaximal
7C5×#1442C211yesmaximal, characteristic
8C5×#1441C211yesmaximal, characteristic
9C5×#1436C212yesmaximal
10C5×#1436C212yesmaximal
11C5×#1434C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2212yes—
17C22×C42×C5C2211yescharacteristic
18C22×C42×C5C2212yes—
19C5×#398C418yescomplemented
20C5×#387—24no—
21C4×C5×C4⋊C4—24no—
22C2×C5×#95C2212yes—
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2212yes—
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38#14308C511yesmaximal, characteristic, direct product factor, Sylow
39C23×C4×C5C2311yescharacteristic
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2312yes—
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—22no—
52C2×C5×C4⋊C4—22no—
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4—22no—
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4—24no—
58C2×C5×C4⋊C4—42no—
59C2×C5×C4⋊C4—42no—
60C2×C5×C4⋊C4C2×C414yes—
61C2×C5×C4⋊C4C2×C414yes—
62C2×C5×C4⋊C4C2×C418yes—
63C2×C42×C5—24no—
64C2×C42×C5—24no—
65C2×C42×C5—42no—
66C2×C42×C5—42no—
67C2×C42×C5D414yes—
68C5×#95—24no—
69C5×#95—22no—
70C5×#95—22no—
71C5×#95—22no—
72C5×#95—22no—
73C5×#95—24no—
74C5×#95—24no—
75C5×#95—24no—
76C5×#95—22no—
77C5×#95—42no—
78C5×#95—42no—
79C5×#95—42no—
80C5×#95—42no—
81C5×#95—42no—
82C5×#95C2×C418yes—
83C5×#95C2×C414yes—
84C2×#398C2×C511yescharacteristic
85C2×#387C2×C511yescharacteristic
86C2×C4×C4⋊C4C2×C511yescharacteristic
87#1445C2×C511yescharacteristic
88#1445C2×C512yes—
89#1443C2×C512yes—
90#1442C2×C511yescharacteristic
91#1441C2×C511yescharacteristic
92#1436C2×C512yes—
93#1436C2×C512yes—
94#1434C2×C511yescharacteristic
95C24×C5C2411yescharacteristic
96C22×C4×C5—22no—
97C22×C4×C5—22no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5—21no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—21no—
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—22no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C22×C414yes—
152C22×C4×C5C22×C412yes—
153C22×C4×C5C22×C414yes—
154C22×C4×C5C22×C412yes—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×D412yes—
158C22×C4×C5#4114yes—
159C22×C4×C5#4112yes—
160C22×C4×C5#4114yes—
161C5×C4⋊C4—28no—
162C5×C4⋊C4—28no—
163C5×C4⋊C4—28no—
164C5×C4⋊C4—48no—
165C5×C4⋊C4—44no—
166C42×C5—28no—
167C42×C5—48no—
168C22×C4⋊C4C22×C511yescharacteristic
169C22×C4⋊C4C22×C511yescharacteristic
170C22×C4⋊C4C22×C511yescharacteristic
171C22×C4⋊C4C22×C511yescharacteristic
172C22×C4⋊C4C22×C512yes—
173C22×C42C22×C511yescharacteristic
174C22×C42C22×C512yes—
175#398C4×C518yescomplemented
176#387—24no—
177C4×C4⋊C4—24no—
178C2×#95C22×C512yes—
179C2×#95C22×C511yescharacteristic
180C2×#95C22×C511yescharacteristic
181C2×#95C22×C512yes—
182C2×#95C22×C512yes—
183C2×#95C22×C511yescharacteristic
184C2×#95C22×C511yescharacteristic
185C2×#95C22×C512yes—
186C2×#95C22×C511yescharacteristic
187C2×#95C22×C512yes—
188C2×#95C22×C512yes—
189C2×#95C22×C512yes—
190C2×#95C22×C512yes—
191C2×#95C22×C512yes—
192C2×#95C22×C511yescharacteristic
193C2×#95C22×C512yes—
194C23×C5C23×C411yescharacteristic
195C23×C5C22×D411yescharacteristic
196C23×C5C2×#4111yescharacteristic
197C23×C5C2×#4112yes—
198C23×C5C2×#4112yes—
199C23×C5H(5,𝔽2)11yescharacteristic
200C23×C5H(5,𝔽2)11yescharacteristic
201C23×C5H(5,𝔽2)11yescharacteristic
202C23×C52−1+412yes—
203C23×C52−1+412yes—
204C23×C52−1+411yescharacteristic
205C2×C4×C5—24no—
206C2×C4×C5—22no—
207C2×C4×C5—22no—
208C2×C4×C5—24no—
209C2×C4×C5—22no—
210C2×C4×C5—22no—
211C2×C4×C5—24no—
212C2×C4×C5—24no—
213C2×C4×C5—24no—
214C2×C4×C5—22no—
215C2×C4×C5—22no—
216C2×C4×C5—24no—
217C2×C4×C5—24no—
218C2×C4×C5—22no—
219C2×C4×C5—24no—
220C2×C4×C5—24no—
221C2×C4×C5—24no—
222C2×C4×C5—24no—
223C2×C4×C5—22no—
224C2×C4×C5—22no—
225C2×C4×C5—24no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—24no—
229C2×C4×C5—24no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—41no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—41no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—41no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—41no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—42no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5C4×D414yes—
269C2×C4×C5#12314yes—
270C23×C4C23×C511yescharacteristic
271C23×C4C23×C511yescharacteristic
272C23×C4C23×C512yes—
273C23×C4C23×C511yescharacteristic
274C23×C4C23×C511yescharacteristic
275C23×C4C23×C512yes—
276C23×C4C23×C512yes—
277C23×C4C23×C511yescharacteristic
278C23×C4C23×C512yes—
279C23×C4C23×C511yescharacteristic
280C23×C4C23×C511yescharacteristic
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4C2×C4×C514yes—
292C2×C4⋊C4C2×C4×C514yes—
293C2×C4⋊C4C2×C4×C518yes—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42C5×D414yes—
299#95—24no—
300#95—22no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—24no—
305#95—24no—
306#95—24no—
307#95—22no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95—42no—
313#95C2×C4×C518yes—
314#95C2×C4×C514yes—
315C22×C5C2×C4×D411yescharacteristic
316C22×C5C4×#4112yes—
317C22×C5#51811yescharacteristic
318C22×C5#51912yes—
319C22×C5#52011yescharacteristic
320C22×C5C2×#12311yescharacteristic
321C22×C5#52511yescharacteristic
322C22×C5#52912yes—
323C22×C5#53511yescharacteristic
324C22×C5#53611yescharacteristic
325C22×C5#53611yescharacteristic
326C22×C5#53711yescharacteristic
327C22×C5#53912yes—
328C22×C5#53912yes—
329C22×C5#53912yes—
330C22×C5#53912yes—
331C22×C5#54011yescharacteristic
332C22×C5#54112yes—
333C22×C5#54112yes—
334C22×C5#54112yes—
335C22×C5#54211yescharacteristic
336C22×C5#54212yes—
337C22×C5#54212yes—
338C4×C5—24no—
339C4×C5—24no—
340C4×C5—42no—
341C4×C5—44no—
342C4×C5—44no—
343C4×C5—42no—
344C4×C5—44no—
345C4×C5—42no—
346C4×C5—81no—
347C4×C5—81no—
348C4×C5—82no—
349C24C24×C511yescharacteristic
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
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—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4C22×C4×C512yes—
405C22×C4C22×C4×C514yes—
406C22×C4C22×C4×C514yes—
407C22×C4C22×C4×C512yes—
408C22×C4C22×C4×C512yes—
409C22×C4C2×C5×D412yes—
410C22×C4C2×C5×D412yes—
411C22×C4C2×C5×D412yes—
412C22×C4C5×#4114yes—
413C22×C4C5×#4112yes—
414C22×C4C5×#4114yes—
415C4⋊C4—28no—
416C4⋊C4—28no—
417C4⋊C4—28no—
418C4⋊C4—48no—
419C4⋊C4—44no—
420C42—28no—
421C42—48no—
422C2×C5C4×#12311yescharacteristic
423C2×C5#232411yescharacteristic
424C2×C5#232711yescharacteristic
425C2×C5#233212yes—
426C2×C5#233612yes—
427C2×C5#262311yescharacteristic
428C2×C5#262511yescharacteristic
429C2×C5#263311yescharacteristic
430C2×C5#263711yescharacteristic
431C2×C5#265412yes—
432C2×C5#265512yes—
433C23C23×C4×C511yescharacteristic
434C23C22×C5×D411yescharacteristic
435C23C2×C5×#4111yescharacteristic
436C23C2×C5×#4112yes—
437C23C2×C5×#4112yes—
438C23C5×H(5,𝔽2)11yescharacteristic
439C23C5×H(5,𝔽2)11yescharacteristic
440C23C5×H(5,𝔽2)11yescharacteristic
441C23C5×2−1+412yes—
442C23C5×2−1+412yes—
443C23C5×2−1+411yescharacteristic
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4C4×C5×D414yes—
508C2×C4C5×#12314yes—
509C5#1430811yescharacteristic, direct product factor, Sylow
510C22C2×C4×C5×D411yescharacteristic
511C22C4×C5×#4112yes—
512C22C5×#51811yescharacteristic
513C22C5×#51912yes—
514C22C5×#52011yescharacteristic
515C22C2×C5×#12311yescharacteristic
516C22C5×#52511yescharacteristic
517C22C5×#52912yes—
518C22C5×#53511yescharacteristic
519C22C5×#53611yescharacteristic
520C22C5×#53611yescharacteristic
521C22C5×#53711yescharacteristic
522C22C5×#53912yes—
523C22C5×#53912yes—
524C22C5×#53912yes—
525C22C5×#53912yes—
526C22C5×#54011yescharacteristic
527C22C5×#54112yes—
528C22C5×#54112yes—
529C22C5×#54112yes—
530C22C5×#54211yescharacteristic
531C22C5×#54212yes—
532C22C5×#54212yes—
533C4—24no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—44no—
538C4—44no—
539C4—42no—
540C4—44no—
541C4—81no—
542C4—81no—
543C4—82no—
544C2C4×C5×#12311yescharacteristic
545C2C5×#232411yescharacteristic
546C2C5×#232711yescharacteristic
547C2C5×#233212yes—
548C2C5×#233612yes—
549C2C5×#262311yescharacteristic
550C2C5×#262511yescharacteristic
551C2C5×#263311yescharacteristic
552C2C5×#263711yescharacteristic
553C2C5×#265412yes—
554C2C5×#265512yes—
subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
19. C5×#398C4semidirect
38. #14308C5direct (N × H)
175. #398C4×C5semidirect
509. C5#14308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C2×C5×#3872
C2×C4×C5×C4⋊C42
C5×#14452
C5×#14432
C5×#14422
C5×#14412
C5×#14362
C5×#14342
#143085