Finite Group Databasebeta

← C5×#14314 #11937034

Subgroups — C5×#14314 #11937034

Order 1280.

1310 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
1C2×C5×#398C211yesmaximal, characteristic
2C2×C5×#389C211yesmaximal, characteristic
3C2×C5×#387C212yesmaximal
4C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
5C5×#1445C211yesmaximal, characteristic
6C5×#1443C212yesmaximal
7C5×#1442C211yesmaximal, characteristic
8C5×#1441C211yesmaximal, characteristic
9C5×#1441C212yesmaximal
10C5×#1436C212yesmaximal
11C5×#1434C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C5×#398C418yescomplemented
22C5×#389—24no—
23C5×#387—28no—
24C4×C5×C4⋊C4—24no—
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2212yes—
39#14314C511yesmaximal, characteristic, direct product factor, Sylow
40C23×C4×C5C2312yes—
41C23×C4×C5C2312yes—
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
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—22no—
58C2×C5×C4⋊C4—24no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—24no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—24no—
63C2×C5×C4⋊C4—24no—
64C2×C5×C4⋊C4—42no—
65C2×C5×C4⋊C4C2×C414yes—
66C2×C5×C4⋊C4C2×C418yes—
67C2×C5×C4⋊C4C2×C414yes—
68C2×C42×C5—22no—
69C2×C42×C5—22no—
70C2×C42×C5—22no—
71C2×C42×C5—42no—
72C2×C42×C5—42no—
73C2×C42×C5D414yes—
74C2×C42×C5D414yes—
75C5×#95—22no—
76C5×#95—22no—
77C5×#95—24no—
78C5×#95—24no—
79C5×#95—24no—
80C5×#95—24no—
81C5×#95—24no—
82C5×#95—24no—
83C5×#95—22no—
84C5×#95—42no—
85C5×#95—42no—
86C5×#95—42no—
87C5×#95C2×C418yes—
88C5×#95C2×C414yes—
89C2×#398C2×C511yescharacteristic
90C2×#389C2×C511yescharacteristic
91C2×#387C2×C512yes—
92C2×C4×C4⋊C4C2×C511yescharacteristic
93#1445C2×C511yescharacteristic
94#1443C2×C512yes—
95#1442C2×C511yescharacteristic
96#1441C2×C512yes—
97#1441C2×C511yescharacteristic
98#1436C2×C512yes—
99#1434C2×C511yescharacteristic
100C24×C5C2411yescharacteristic
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—22no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5C22×C414yes—
152C22×C4×C5C22×C414yes—
153C22×C4×C5C22×C412yes—
154C22×C4×C5C22×C412yes—
155C22×C4×C5C22×C412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×D412yes—
158C22×C4×C5C2×D412yes—
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5#4112yes—
163C22×C4×C5#4112yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C5×C4⋊C4—28no—
167C5×C4⋊C4—28no—
168C5×C4⋊C4—216no—
169C5×C4⋊C4—28no—
170C5×C4⋊C4—44no—
171C5×C4⋊C4—48no—
172C42×C5—28no—
173C42×C5—44no—
174C42×C5—44no—
175C22×C4⋊C4C22×C512yes—
176C22×C4⋊C4C22×C511yescharacteristic
177C22×C4⋊C4C22×C511yescharacteristic
178C22×C4⋊C4C22×C512yes—
179C22×C4⋊C4C22×C511yescharacteristic
180C22×C4⋊C4C22×C511yescharacteristic
181C22×C42C22×C511yescharacteristic
182C22×C42C22×C511yescharacteristic
183C22×C42C22×C511yescharacteristic
184#398C4×C518yescomplemented
185#389—24no—
186#387—28no—
187C4×C4⋊C4—24no—
188C2×#95C22×C512yes—
189C2×#95C22×C511yescharacteristic
190C2×#95C22×C512yes—
191C2×#95C22×C512yes—
192C2×#95C22×C512yes—
193C2×#95C22×C512yes—
194C2×#95C22×C511yescharacteristic
195C2×#95C22×C511yescharacteristic
196C2×#95C22×C512yes—
197C2×#95C22×C512yes—
198C2×#95C22×C512yes—
199C2×#95C22×C512yes—
200C2×#95C22×C511yescharacteristic
201C2×#95C22×C512yes—
202C23×C5C23×C411yescharacteristic
203C23×C5C22×D411yescharacteristic
204C23×C5C22×D411yescharacteristic
205C23×C5C2×#4111yescharacteristic
206C23×C5C2×#4111yescharacteristic
207C23×C5C2×#4111yescharacteristic
208C23×C5C2×#4111yescharacteristic
209C23×C5H(5,𝔽2)12yes—
210C23×C52−1+412yes—
211C23×C52−1+412yes—
212C23×C52−1+412yes—
213C2×C4×C5—22no—
214C2×C4×C5—22no—
215C2×C4×C5—24no—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—22no—
224C2×C4×C5—24no—
225C2×C4×C5—24no—
226C2×C4×C5—24no—
227C2×C4×C5—22no—
228C2×C4×C5—24no—
229C2×C4×C5—24no—
230C2×C4×C5—24no—
231C2×C4×C5—24no—
232C2×C4×C5—24no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—24no—
240C2×C4×C5—22no—
241C2×C4×C5—24no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—42no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
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×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×C5C4×D414yes—
276C2×C4×C5C4×D414yes—
277C2×C4×C5#12114yes—
278C23×C4C23×C512yes—
279C23×C4C23×C512yes—
280C23×C4C23×C512yes—
281C23×C4C23×C512yes—
282C23×C4C23×C511yescharacteristic
283C23×C4C23×C511yescharacteristic
284C23×C4C23×C511yescharacteristic
285C23×C4C23×C511yescharacteristic
286C23×C4C23×C511yescharacteristic
287C23×C4C23×C511yescharacteristic
288C23×C4C23×C511yescharacteristic
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4C2×C4×C518yes—
304C2×C4⋊C4C2×C4×C514yes—
305C2×C4⋊C4C2×C4×C514yes—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42C5×D414yes—
312C2×C42C5×D414yes—
313#95—22no—
314#95—22no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—22no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95C2×C4×C518yes—
326#95C2×C4×C514yes—
327C22×C5C2×C4×D411yescharacteristic
328C22×C5C2×C4×D411yescharacteristic
329C22×C5C4×#4111yescharacteristic
330C22×C5#51912yes—
331C22×C5#52012yes—
332C22×C5C2×#12111yescharacteristic
333C22×C5#52511yescharacteristic
334C22×C5#52911yescharacteristic
335C22×C5#53211yescharacteristic
336C22×C5#53411yescharacteristic
337C22×C5#53611yescharacteristic
338C22×C5#53612yes—
339C22×C5#53611yescharacteristic
340C22×C5#53611yescharacteristic
341C22×C5#53712yes—
342C22×C5#53912yes—
343C22×C5#53912yes—
344C22×C5#53912yes—
345C22×C5#54112yes—
346C22×C5#54112yes—
347C22×C5#54112yes—
348C22×C5#54112yes—
349C22×C5#54212yes—
350C4×C5—24no—
351C4×C5—24no—
352C4×C5—24no—
353C4×C5—42no—
354C4×C5—44no—
355C4×C5—42no—
356C4×C5—42no—
357C4×C5—42no—
358C4×C5—44no—
359C4×C5—82no—
360C4×C5—82no—
361C24C24×C511yescharacteristic
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4C22×C4×C514yes—
413C22×C4C22×C4×C512yes—
414C22×C4C22×C4×C514yes—
415C22×C4C22×C4×C512yes—
416C22×C4C22×C4×C512yes—
417C22×C4C2×C5×D412yes—
418C22×C4C2×C5×D412yes—
419C22×C4C2×C5×D412yes—
420C22×C4C2×C5×D412yes—
421C22×C4C2×C5×D412yes—
422C22×C4C2×C5×D412yes—
423C22×C4C5×#4112yes—
424C22×C4C5×#4112yes—
425C22×C4C5×#4112yes—
426C22×C4C5×#4112yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—216no—
430C4⋊C4—28no—
431C4⋊C4—44no—
432C4⋊C4—48no—
433C42—28no—
434C42—44no—
435C42—44no—
436C2×C5C4×#12111yescharacteristic
437C2×C5#232211yescharacteristic
438C2×C5#232312yes—
439C2×C5#232711yescharacteristic
440C2×C5#233612yes—
441C2×C5#261811yescharacteristic
442C2×C5#262111yescharacteristic
443C2×C5#263411yescharacteristic
444C2×C5#263811yescharacteristic
445C2×C5#265512yes—
446C2×C5#266412yes—
447C23C23×C4×C511yescharacteristic
448C23C22×C5×D411yescharacteristic
449C23C22×C5×D411yescharacteristic
450C23C2×C5×#4111yescharacteristic
451C23C2×C5×#4111yescharacteristic
452C23C2×C5×#4111yescharacteristic
453C23C2×C5×#4111yescharacteristic
454C23C5×H(5,𝔽2)12yes—
455C23C5×2−1+412yes—
456C23C5×2−1+412yes—
457C23C5×2−1+412yes—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
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×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
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×C4C4×C5×D414yes—
521C2×C4C4×C5×D414yes—
522C2×C4C5×#12114yes—
523C5#1431411yescharacteristic, direct product factor, Sylow
524C22C2×C4×C5×D411yescharacteristic
525C22C2×C4×C5×D411yescharacteristic
526C22C4×C5×#4111yescharacteristic
527C22C5×#51912yes—
528C22C5×#52012yes—
529C22C2×C5×#12111yescharacteristic
530C22C5×#52511yescharacteristic
531C22C5×#52911yescharacteristic
532C22C5×#53211yescharacteristic
533C22C5×#53411yescharacteristic
534C22C5×#53611yescharacteristic
535C22C5×#53612yes—
536C22C5×#53611yescharacteristic
537C22C5×#53611yescharacteristic
538C22C5×#53712yes—
539C22C5×#53912yes—
540C22C5×#53912yes—
541C22C5×#53912yes—
542C22C5×#54112yes—
543C22C5×#54112yes—
544C22C5×#54112yes—
545C22C5×#54112yes—
546C22C5×#54212yes—
547C4—24no—
548C4—24no—
549C4—24no—
550C4—44no—
551C4—42no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—82no—
557C4—82no—
558C2C4×C5×#12111yescharacteristic
559C2C5×#232211yescharacteristic
560C2C5×#232312yes—
561C2C5×#232711yescharacteristic
562C2C5×#233612yes—
563C2C5×#261811yescharacteristic
564C2C5×#262111yescharacteristic
565C2C5×#263411yescharacteristic
566C2C5×#263811yescharacteristic
567C2C5×#265512yes—
568C2C5×#266412yes—
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
21. C5×#398C4semidirect
39. #14314C5direct (N × H)
184. #398C4×C5semidirect
523. C5#14314direct (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×#3892
C2×C5×#3872
C2×C4×C5×C4⋊C42
C5×#14452
C5×#14432
C5×#14422
C5×#14412
C5×#14362
C5×#14342
#143145