Finite Group Databasebeta

← C5×#29584 #11952304

Subgroups — C5×#29584 #11952304

Order 1280.

644 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2647C211yesmaximal, characteristic, complemented
2C5×#2319C211yesmaximal, characteristic
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2093C211yesmaximal, characteristic
5C5×#2085C211yesmaximal, characteristic, complemented
6C5×#2073C211yesmaximal, characteristic
7C5×#1944C211yesmaximal, characteristic, complemented
8C5×#1942C211yesmaximal, characteristic, complemented
9C5×#1936C211yesmaximal, characteristic
10C5×#1934C211yesmaximal, characteristic
11C5×#1921C211yesmaximal, characteristic, complemented
12C5×#1918C211yesmaximal, characteristic, complemented
13C5×#1864C211yesmaximal, characteristic
14C5×#1862C211yesmaximal, characteristic
15C5×#1746C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×C5×#107C2211yescharacteristic
18C2×C5×#107C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×#102C2211yescharacteristic
22C2×C5×#102C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#97C2211yescharacteristic
26C2×C4×C5×C8C2211yescharacteristic
27C5×#400—21no—
28C5×#400—21no—
29C5×#398—21no—
30C5×#398—21no—
31C5×#390C2211yescharacteristic
32C5×#390C2211yescharacteristic
33C5×#389C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#389C2211yescharacteristic
39C5×#388—21no—
40C5×#388—21no—
41C5×#384C2211yescharacteristic
42C5×#382C2211yescharacteristic
43C5×#381—21no—
44C5×#380—21no—
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#29584C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4C2311yescharacteristic
61C23×C4×C5—21no—
62C22×C5×C8C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C4×C5×D4—22no—
67C4×C5×D4—22no—
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×C42×C5—21no—
89C2×C42×C5C2311yescharacteristic
90C2×C42×C5C2311yescharacteristic
91C2×C42×C5C2311yescharacteristic
92C5×#107—22no—
93C5×#107—22no—
94C5×#107—22no—
95C5×#106—22no—
96C5×#102—22no—
97C5×#102—22no—
98C5×#102—22no—
99C5×#102—22no—
100C5×#97—22no—
101C4×C5×C8—22no—
102C5×#95—21no—
103C5×#95—21no—
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#2647C2×C511yescharacteristic, complemented
116#2319C2×C511yescharacteristic
117#2100C2×C511yescharacteristic, complemented
118#2093C2×C511yescharacteristic
119#2085C2×C511yescharacteristic, complemented
120#2073C2×C511yescharacteristic
121#1944C2×C511yescharacteristic, complemented
122#1942C2×C511yescharacteristic, complemented
123#1936C2×C511yescharacteristic
124#1934C2×C511yescharacteristic
125#1921C2×C511yescharacteristic, complemented
126#1918C2×C511yescharacteristic, complemented
127#1864C2×C511yescharacteristic
128#1862C2×C511yescharacteristic
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#4112yes—
137C22×C4×C5—21no—
138C22×C4×C5—24no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—81no—
146C22×C4×C5—81no—
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2411yescharacteristic
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—21no—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8#4112yes—
165C2×C5×C8#4112yes—
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—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—81no—
180C5×C4⋊C4—81no—
181C5×C4⋊C4—81no—
182C5×C4⋊C4—81no—
183C5×C4⋊C4—81no—
184C5×C4⋊C4—81no—
185C5×C4⋊C4—81no—
186C5×C4⋊C4—81no—
187C5×C4⋊C4#4112yes—
188C5×C22⋊C4—24no—
189C5×C22⋊C4—81no—
190C5×C22⋊C4—81no—
191C5×C22⋊C4—81no—
192C5×C22⋊C4—81no—
193C42×C5—21no—
194C42×C5—21no—
195C42×C5—21no—
196C42×C5—21no—
197C42×C5—21no—
198C42×C5—21no—
199C42×C5—81no—
200C2×C4×D4C22×C511yescharacteristic
201C2×#107C22×C511yescharacteristic
202C2×#107C22×C511yescharacteristic
203C2×#107C22×C511yescharacteristic
204C2×#106C22×C511yescharacteristic
205C2×#102C22×C511yescharacteristic
206C2×#102C22×C511yescharacteristic
207C2×#102C22×C511yescharacteristic
208C2×#102C22×C511yescharacteristic
209C2×#97C22×C511yescharacteristic
210C2×C4×C8C22×C511yescharacteristic
211#400—21no—
212#400—21no—
213#398—21no—
214#398—21no—
215#390C22×C511yescharacteristic
216#390C22×C511yescharacteristic
217#389C22×C511yescharacteristic
218#389C22×C511yescharacteristic
219#389C22×C511yescharacteristic
220#389C22×C511yescharacteristic
221#389C22×C511yescharacteristic
222#389C22×C511yescharacteristic
223#388—21no—
224#388—21no—
225#384C22×C511yescharacteristic
226#382C22×C511yescharacteristic
227#381—21no—
228#380—21no—
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—22no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5—41no—
248C23×C5—41no—
249C23×C5—41no—
250C23×C5C22×D411yescharacteristic
251C5×D4—22no—
252C5×D4—22no—
253C5×D4—41no—
254C5×D4—41no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—22no—
258C2×C4×C5—21no—
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—41no—
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×C5—84no—
295C2×C4×C5C2×#4111yescharacteristic
296C2×C4×C5C2×#4111yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×C4×C5C2×#4111yescharacteristic
299C2×C4×C52−1+411yescharacteristic
300C2×C4×C52−1+411yescharacteristic
301C5×C8—22no—
302C5×C8—22no—
303C5×C8—41no—
304C5×C8—41no—
305C22×D4C23×C511yescharacteristic
306C23×C4—21no—
307C22×C8C23×C511yescharacteristic
308C22×C8C23×C511yescharacteristic
309C22×C8C23×C511yescharacteristic
310C22×C8C23×C511yescharacteristic
311C4×D4—22no—
312C4×D4—22no—
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⋊C4—21no—
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×C4⋊C4C23×C511yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42—21no—
334C2×C42C23×C511yescharacteristic
335C2×C42C23×C511yescharacteristic
336C2×C42C23×C511yescharacteristic
337#107—22no—
338#107—22no—
339#107—22no—
340#106—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345#97—22no—
346C4×C8—22no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95C5×D411yescharacteristic
357#95C5×D411yescharacteristic
358#95C5×D411yescharacteristic
359#95C5×D411yescharacteristic
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5#52511yescharacteristic
368C22×C5#53211yescharacteristic
369C22×C5#53611yescharacteristic
370C22×C5#57611yescharacteristic
371C22×C5#57611yescharacteristic
372C22×C5#57711yescharacteristic
373C22×C5#57811yescharacteristic
374C4×C5—41no—
375C4×C5—42no—
376C4×C5—41no—
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—81no—
387C4×C5#55211yescharacteristic
388C4×C5#55211yescharacteristic
389C4×C5#55211yescharacteristic
390C4×C5#55211yescharacteristic
391C24—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4C5×#4112yes—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—81no—
407C22×C4—81no—
408C22×C4C2×C5×D411yescharacteristic
409C22×C4C2×C5×D411yescharacteristic
410C22×C4C2×C5×D411yescharacteristic
411C22×C4C2×C5×D411yescharacteristic
412C22×C4C2×C5×D411yescharacteristic
413C22×C4C2×C5×D411yescharacteristic
414C22×C4C24×C511yescharacteristic
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8C5×#4112yes—
426C2×C8C5×#4112yes—
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—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—81no—
441C4⋊C4—81no—
442C4⋊C4—81no—
443C4⋊C4—81no—
444C4⋊C4—81no—
445C4⋊C4—81no—
446C4⋊C4—81no—
447C4⋊C4—81no—
448C4⋊C4C5×#4112yes—
449C22⋊C4—24no—
450C22⋊C4—81no—
451C22⋊C4—81no—
452C22⋊C4—81no—
453C22⋊C4—81no—
454C42—21no—
455C42—21no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—81no—
461C2×C5—82no—
462C2×C5#261111yescharacteristic
463C2×C5#311811yescharacteristic
464C2×C5#312411yescharacteristic
465C2×C5#317611yescharacteristic
466C2×C5#317811yescharacteristic
467C2×C5#324111yescharacteristic
468C2×C5#324311yescharacteristic
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C22×C5×D411yescharacteristic
477D4—22no—
478D4—22no—
479D4—41no—
480D4—41no—
481C2×C4—21no—
482C2×C4—21no—
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×C4—41no—
520C2×C4—84no—
521C2×C4C2×C5×#4111yescharacteristic
522C2×C4C2×C5×#4111yescharacteristic
523C2×C4C2×C5×#4111yescharacteristic
524C2×C4C2×C5×#4111yescharacteristic
525C2×C4C5×2−1+411yescharacteristic
526C2×C4C5×2−1+411yescharacteristic
527C8—22no—
528C8—22no—
529C8—41no—
530C8—41no—
531C5#2958411yescharacteristic, direct product factor, Sylow
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22C5×#52511yescharacteristic
540C22C5×#53211yescharacteristic
541C22C5×#53611yescharacteristic
542C22C5×#57611yescharacteristic
543C22C5×#57611yescharacteristic
544C22C5×#57711yescharacteristic
545C22C5×#57811yescharacteristic
546C4—41no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4C5×#55211yescharacteristic
560C4C5×#55211yescharacteristic
561C4C5×#55211yescharacteristic
562C4C5×#55211yescharacteristic
563C2—82no—
564C2C5×#261111yescharacteristic
565C2C5×#311811yescharacteristic
566C2C5×#312411yescharacteristic
567C2C5×#317611yescharacteristic
568C2C5×#317811yescharacteristic
569C2C5×#324111yescharacteristic
570C2C5×#324311yescharacteristic
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
1. C5×#2647C2semidirect
3. C5×#2100C2semidirect
5. C5×#2085C2semidirect
7. C5×#1944C2semidirect
8. C5×#1942C2semidirect
11. C5×#1921C2semidirect
12. C5×#1918C2semidirect
15. C5×#1746C2semidirect
59. #29584C5direct (N × H)
115. #2647C2×C5semidirect
117. #2100C2×C5semidirect
119. #2085C2×C5semidirect
121. #1944C2×C5semidirect
122. #1942C2×C5semidirect
125. #1921C2×C5semidirect
126. #1918C2×C5semidirect
129. #1746C2×C5semidirect
531. C5#29584direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26472
C5×#23192
C5×#21002
C5×#20932
C5×#20852
C5×#20732
C5×#19442
C5×#19422
C5×#19362
C5×#19342
C5×#19212
C5×#19182
C5×#18642
C5×#18622
C5×#17462
#295845