Finite Group Databasebeta

← C5×#29529 #11952249

Subgroups — C5×#29529 #11952249

Order 1280.

626 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
1C5×#2644C211yesmaximal, characteristic
2C5×#2330C211yesmaximal, characteristic, complemented
3C5×#2099C211yesmaximal, characteristic, complemented
4C5×#2094C211yesmaximal, characteristic
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2025C211yesmaximal, characteristic
7C5×#1943C211yesmaximal, characteristic, complemented
8C5×#1941C211yesmaximal, characteristic, complemented
9C5×#1936C211yesmaximal, characteristic
10C5×#1934C211yesmaximal, characteristic
11C5×#1926C211yesmaximal, characteristic
12C5×#1925C211yesmaximal, characteristic
13C5×#1920C211yesmaximal, characteristic, complemented
14C5×#1919C211yesmaximal, characteristic, complemented
15C5×#1746C211yesmaximal, characteristic, complemented
16C2×C5×#125C2211yescharacteristic
17C2×C5×#107C2211yescharacteristic
18C2×C5×#106C2211yescharacteristic
19C2×C5×#106C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×#102C2211yescharacteristic
22C2×C5×#102C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#97C2211yescharacteristic
26C2×C4×C5×C8C2211yescharacteristic
27C5×#397—21no—
28C5×#397—21no—
29C5×#397—21no—
30C5×#396—21no—
31C5×#390C2211yescharacteristic
32C5×#390C2211yescharacteristic
33C5×#390C2211yescharacteristic
34C5×#389—21no—
35C5×#389—21no—
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#389C2211yescharacteristic
39C5×#389C2211yescharacteristic
40C5×#389C2211yescharacteristic
41C5×#387—21no—
42C5×#387—21no—
43C5×#384C2211yescharacteristic
44C4×C5×C4⋊C4C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C5×#376C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#336C2211yescharacteristic
56C5×#336C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#29529C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4C2311yescharacteristic
61C22×C5×C8C2311yescharacteristic
62C22×C5×C8C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C5×#125—22no—
66C5×#125—22no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4—21no—
89C2×C42×C5—21no—
90C2×C42×C5—21no—
91C2×C42×C5C2311yescharacteristic
92C2×C42×C5C2311yescharacteristic
93C2×C42×C5C2311yescharacteristic
94C5×#107—22no—
95C5×#106—22no—
96C5×#106—22no—
97C5×#106—22no—
98C5×#102—22no—
99C5×#102—22no—
100C5×#102—22no—
101C5×#102—22no—
102C5×#97—22no—
103C4×C5×C8—22no—
104C5×#95—21no—
105C5×#95—21no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95D411yescharacteristic
112C5×#95D411yescharacteristic
113C5×#95D411yescharacteristic
114C5×#95D411yescharacteristic
115#2644C2×C511yescharacteristic
116#2330C2×C511yescharacteristic, complemented
117#2099C2×C511yescharacteristic, complemented
118#2094C2×C511yescharacteristic
119#2059C2×C511yescharacteristic, complemented
120#2025C2×C511yescharacteristic
121#1943C2×C511yescharacteristic, complemented
122#1941C2×C511yescharacteristic, complemented
123#1936C2×C511yescharacteristic
124#1934C2×C511yescharacteristic
125#1926C2×C511yescharacteristic
126#1925C2×C511yescharacteristic
127#1920C2×C511yescharacteristic, complemented
128#1919C2×C511yescharacteristic, complemented
129#1746C2×C511yescharacteristic, complemented
130C24×C5—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2411yescharacteristic
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C2×C5×C8—21no—
155C2×C5×C8—21no—
156C2×C5×C8—21no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8—21no—
160C2×C5×C8—21no—
161C2×C5×C8#4112yes—
162C2×C5×C8#4112yes—
163C5×C4⋊C4—24no—
164C5×C4⋊C4—24no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—81no—
178C5×C4⋊C4—81no—
179C5×C4⋊C4—81no—
180C5×C4⋊C4—81no—
181C5×C4⋊C4—81no—
182C5×C4⋊C4—81no—
183C5×C4⋊C4—81no—
184C5×C4⋊C4#4112yes—
185C5×C4⋊C4#4112yes—
186C5×C22⋊C4—81no—
187C5×C22⋊C4—81no—
188C5×C22⋊C4—81no—
189C5×C22⋊C4—81no—
190C5×C22⋊C4—81no—
191C5×C22⋊C4—81no—
192C42×C5—21no—
193C42×C5—21no—
194C42×C5—21no—
195C42×C5—21no—
196C42×C5—21no—
197C42×C5—21no—
198C42×C5—81no—
199C42×C5—81no—
200C2×#125C22×C511yescharacteristic
201C2×#107C22×C511yescharacteristic
202C2×#106C22×C511yescharacteristic
203C2×#106C22×C511yescharacteristic
204C2×#106C22×C511yescharacteristic
205C2×#102C22×C511yescharacteristic
206C2×#102C22×C511yescharacteristic
207C2×#102C22×C511yescharacteristic
208C2×#102C22×C511yescharacteristic
209C2×#97C22×C511yescharacteristic
210C2×C4×C8C22×C511yescharacteristic
211#397—21no—
212#397—21no—
213#397—21no—
214#396—21no—
215#390C22×C511yescharacteristic
216#390C22×C511yescharacteristic
217#390C22×C511yescharacteristic
218#389—21no—
219#389—21no—
220#389C22×C511yescharacteristic
221#389C22×C511yescharacteristic
222#389C22×C511yescharacteristic
223#389C22×C511yescharacteristic
224#389C22×C511yescharacteristic
225#387—21no—
226#387—21no—
227#384C22×C511yescharacteristic
228C4×C4⋊C4C22×C511yescharacteristic
229C4×C4⋊C4C22×C511yescharacteristic
230#376C22×C511yescharacteristic
231#340C22×C511yescharacteristic
232#340C22×C511yescharacteristic
233#340C22×C511yescharacteristic
234#340C22×C511yescharacteristic
235#340C22×C511yescharacteristic
236#340C22×C511yescharacteristic
237#340C22×C511yescharacteristic
238#340C22×C511yescharacteristic
239#336C22×C511yescharacteristic
240#336C22×C511yescharacteristic
241#336C22×C511yescharacteristic
242#336C22×C511yescharacteristic
243C23×C5—41no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5—41no—
248C23×C5—41no—
249C23×C5—41no—
250C23×C5C22×D411yescharacteristic
251C5×D4—41no—
252C5×D4—41no—
253C5×D4—41no—
254C5×D4—41no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5C2×#4111yescharacteristic
295C2×C4×C5C2×#4111yescharacteristic
296C2×C4×C5C2×#4111yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×C4×C52−1+411yescharacteristic
299C2×C4×C52−1+411yescharacteristic
300C5×C8—22no—
301C5×C8—22no—
302C5×C8—41no—
303C5×C8—41no—
304C22×D4C23×C511yescharacteristic
305C22×C8C23×C511yescharacteristic
306C22×C8C23×C511yescharacteristic
307C22×C8C23×C511yescharacteristic
308C22×C8C23×C511yescharacteristic
309#125—22no—
310#125—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C23×C511yescharacteristic
321C2×C4⋊C4C23×C511yescharacteristic
322C2×C4⋊C4C23×C511yescharacteristic
323C2×C4⋊C4C23×C511yescharacteristic
324C2×C4⋊C4C23×C511yescharacteristic
325C2×C4⋊C4C23×C511yescharacteristic
326C2×C4⋊C4C23×C511yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42C23×C511yescharacteristic
336C2×C42C23×C511yescharacteristic
337C2×C42C23×C511yescharacteristic
338#107—22no—
339#106—22no—
340#106—22no—
341#106—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346#97—22no—
347C4×C8—22no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95C5×D411yescharacteristic
356#95C5×D411yescharacteristic
357#95C5×D411yescharacteristic
358#95C5×D411yescharacteristic
359C22×C5—81no—
360C22×C5—81no—
361C22×C5—81no—
362C22×C5—81no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5#52511yescharacteristic
367C22×C5#53211yescharacteristic
368C22×C5#53611yescharacteristic
369C22×C5#57611yescharacteristic
370C22×C5#57711yescharacteristic
371C22×C5#57711yescharacteristic
372C22×C5#57711yescharacteristic
373C4×C5—41no—
374C4×C5—42no—
375C4×C5—41no—
376C4×C5—42no—
377C4×C5—41no—
378C4×C5—41no—
379C4×C5—41no—
380C4×C5—41no—
381C4×C5—81no—
382C4×C5—81no—
383C4×C5—81no—
384C4×C5—81no—
385C4×C5—81no—
386C4×C5#55211yescharacteristic
387C4×C5#55211yescharacteristic
388C4×C5#55611yescharacteristic
389C4×C5#55611yescharacteristic
390C24—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4C2×C5×D411yescharacteristic
405C22×C4C2×C5×D411yescharacteristic
406C22×C4C2×C5×D411yescharacteristic
407C22×C4C2×C5×D411yescharacteristic
408C22×C4C2×C5×D411yescharacteristic
409C22×C4C2×C5×D411yescharacteristic
410C22×C4C24×C511yescharacteristic
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C5×#4112yes—
422C2×C8C5×#4112yes—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—81no—
438C4⋊C4—81no—
439C4⋊C4—81no—
440C4⋊C4—81no—
441C4⋊C4—81no—
442C4⋊C4—81no—
443C4⋊C4—81no—
444C4⋊C4C5×#4112yes—
445C4⋊C4C5×#4112yes—
446C22⋊C4—81no—
447C22⋊C4—81no—
448C22⋊C4—81no—
449C22⋊C4—81no—
450C22⋊C4—81no—
451C22⋊C4—81no—
452C42—21no—
453C42—21no—
454C42—21no—
455C42—21no—
456C42—21no—
457C42—21no—
458C42—81no—
459C42—81no—
460C2×C5—161no—
461C2×C5#260411yescharacteristic
462C2×C5#311911yescharacteristic
463C2×C5#312511yescharacteristic
464C2×C5#317411yescharacteristic
465C2×C5#317911yescharacteristic
466C2×C5#324111yescharacteristic
467C2×C5#324411yescharacteristic
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23C22×C5×D411yescharacteristic
476D4—41no—
477D4—41no—
478D4—41no—
479D4—41no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4C2×C5×#4111yescharacteristic
520C2×C4C2×C5×#4111yescharacteristic
521C2×C4C2×C5×#4111yescharacteristic
522C2×C4C2×C5×#4111yescharacteristic
523C2×C4C5×2−1+411yescharacteristic
524C2×C4C5×2−1+411yescharacteristic
525C8—22no—
526C8—22no—
527C8—41no—
528C8—41no—
529C5#2952911yescharacteristic, direct product factor, Sylow
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22C5×#52511yescharacteristic
538C22C5×#53211yescharacteristic
539C22C5×#53611yescharacteristic
540C22C5×#57611yescharacteristic
541C22C5×#57711yescharacteristic
542C22C5×#57711yescharacteristic
543C22C5×#57711yescharacteristic
544C4—41no—
545C4—41no—
546C4—41no—
547C4—42no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4C5×#55211yescharacteristic
558C4C5×#55211yescharacteristic
559C4C5×#55611yescharacteristic
560C4C5×#55611yescharacteristic
561C2—161no—
562C2C5×#260411yescharacteristic
563C2C5×#311911yescharacteristic
564C2C5×#312511yescharacteristic
565C2C5×#317411yescharacteristic
566C2C5×#317911yescharacteristic
567C2C5×#324111yescharacteristic
568C2C5×#324411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C5×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2330C2semidirect
3. C5×#2099C2semidirect
5. C5×#2059C2semidirect
7. C5×#1943C2semidirect
8. C5×#1941C2semidirect
13. C5×#1920C2semidirect
14. C5×#1919C2semidirect
15. C5×#1746C2semidirect
59. #29529C5direct (N × H)
116. #2330C2×C5semidirect
117. #2099C2×C5semidirect
119. #2059C2×C5semidirect
121. #1943C2×C5semidirect
122. #1941C2×C5semidirect
127. #1920C2×C5semidirect
128. #1919C2×C5semidirect
129. #1746C2×C5semidirect
529. C5#29529direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26442
C5×#23302
C5×#20992
C5×#20942
C5×#20592
C5×#20252
C5×#19432
C5×#19412
C5×#19362
C5×#19342
C5×#19262
C5×#19252
C5×#19202
C5×#19192
C5×#17462
#295295