Finite Group Databasebeta

← C5×#29542 #11952262

Subgroups — C5×#29542 #11952262

Order 1280.

746 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2319C211yesmaximal, characteristic, complemented
2C5×#2319C211yesmaximal, characteristic, complemented
3C5×#2088C211yesmaximal, characteristic, complemented
4C5×#2067C211yesmaximal, characteristic, complemented
5C5×#2065C211yesmaximal, characteristic, complemented
6C5×#2054C211yesmaximal, characteristic
7C5×#1926C211yesmaximal, characteristic, complemented
8C5×#1926C211yesmaximal, characteristic, complemented
9C5×#1920C211yesmaximal, characteristic, complemented
10C5×#1918C211yesmaximal, characteristic, complemented
11C5×#1879C211yesmaximal, characteristic
12C5×#1879C211yesmaximal, characteristic
13C5×#1864C211yesmaximal, characteristic, complemented
14C5×#1862C211yesmaximal, characteristic, complemented
15C5×#1832C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C2×C5×#102C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C5×#390C2211yescharacteristic
31C5×#390C2211yescharacteristic
32C5×#390C2211yescharacteristic
33C5×#390C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#388—21no—
39C5×#388—21no—
40C5×#388—21no—
41C5×#388—21no—
42C5×#381—21no—
43C5×#381—21no—
44C5×#380—21no—
45C5×#380—21no—
46C4×C5×C4⋊C4C2211yescharacteristic
47C4×C5×C4⋊C4C2211yescharacteristic
48C5×#376C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#336C2211yescharacteristic
56C5×#336C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#29542C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4C2311yescharacteristic
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C2×C5×D8—22no—
65C2×C5×D8—22no—
66C2×C5×D8—41no—
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C4×C5×D4—22no—
72C4×C5×D4—22no—
73C4×C5×D4—22no—
74C4×C5×D4—22no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C42×C5—21no—
96C2×C42×C5—21no—
97C2×C42×C5C2311yescharacteristic
98C2×C42×C5C2311yescharacteristic
99C2×C42×C5C2311yescharacteristic
100C5×#107—22no—
101C5×#106—22no—
102C5×#106—41no—
103C5×C4⋊C8—41no—
104C5×C4⋊C8—41no—
105C5×#102—22no—
106C5×#102—22no—
107C5×#102—22no—
108C5×#102—22no—
109C5×#102—41no—
110C5×#102—41no—
111C5×#95—21no—
112C5×#95—21no—
113C5×#95—21no—
114C5×#95—21no—
115C5×#95—21no—
116C5×#95—21no—
117C5×#95D411yescharacteristic
118C5×#95D411yescharacteristic
119C5×#95D411yescharacteristic
120C5×#95D411yescharacteristic
121#2319C2×C511yescharacteristic, complemented
122#2319C2×C511yescharacteristic, complemented
123#2088C2×C511yescharacteristic, complemented
124#2067C2×C511yescharacteristic, complemented
125#2065C2×C511yescharacteristic, complemented
126#2054C2×C511yescharacteristic
127#1926C2×C511yescharacteristic, complemented
128#1926C2×C511yescharacteristic, complemented
129#1920C2×C511yescharacteristic, complemented
130#1918C2×C511yescharacteristic, complemented
131#1879C2×C511yescharacteristic
132#1879C2×C511yescharacteristic
133#1864C2×C511yescharacteristic, complemented
134#1862C2×C511yescharacteristic, complemented
135#1832C2×C511yescharacteristic, complemented
136C24×C5—21no—
137C24×C5—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4#4112yes—
149C2×C5×D4#4112yes—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—24no—
153C22×C4×C5—24no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—81no—
159C22×C4×C5—81no—
160C22×C4×C5—81no—
161C22×C4×C5—81no—
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2411yescharacteristic
169C5×D8—44no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—81no—
193C5×C4⋊C4—81no—
194C5×C4⋊C4—81no—
195C5×C4⋊C4—81no—
196C5×C4⋊C4#4112yes—
197C5×C4⋊C4#4112yes—
198C5×C22⋊C4—24no—
199C5×C22⋊C4—24no—
200C5×C22⋊C4—81no—
201C5×C22⋊C4—81no—
202C5×C22⋊C4—81no—
203C5×C22⋊C4—81no—
204C5×C22⋊C4—81no—
205C5×C22⋊C4—81no—
206C5×C22⋊C4—81no—
207C5×C22⋊C4—81no—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5—21no—
211C42×C5—21no—
212C42×C5—21no—
213C42×C5—21no—
214C42×C5—81no—
215C42×C5—81no—
216C22×D8C22×C511yescharacteristic
217C2×C4×D4C22×C511yescharacteristic
218C2×C4×D4C22×C511yescharacteristic
219C2×#107C22×C511yescharacteristic
220C2×#106C22×C511yescharacteristic
221C2×#106C22×C511yescharacteristic
222C2×C4⋊C8C22×C511yescharacteristic
223C2×C4⋊C8C22×C511yescharacteristic
224C2×#102C22×C511yescharacteristic
225C2×#102C22×C511yescharacteristic
226C2×#102C22×C511yescharacteristic
227C2×#102C22×C511yescharacteristic
228C2×#102C22×C511yescharacteristic
229C2×#102C22×C511yescharacteristic
230#390C22×C511yescharacteristic
231#390C22×C511yescharacteristic
232#390C22×C511yescharacteristic
233#390C22×C511yescharacteristic
234#389C22×C511yescharacteristic
235#389C22×C511yescharacteristic
236#389C22×C511yescharacteristic
237#389C22×C511yescharacteristic
238#388—21no—
239#388—21no—
240#388—21no—
241#388—21no—
242#381—21no—
243#381—21no—
244#380—21no—
245#380—21no—
246C4×C4⋊C4C22×C511yescharacteristic
247C4×C4⋊C4C22×C511yescharacteristic
248#376C22×C511yescharacteristic
249#340C22×C511yescharacteristic
250#340C22×C511yescharacteristic
251#340C22×C511yescharacteristic
252#340C22×C511yescharacteristic
253#340C22×C511yescharacteristic
254#340C22×C511yescharacteristic
255#336C22×C511yescharacteristic
256#336C22×C511yescharacteristic
257#336C22×C511yescharacteristic
258#336C22×C511yescharacteristic
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5C22×D411yescharacteristic
274C5×D4—22no—
275C5×D4—22no—
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—41no—
279C5×D4—41no—
280C5×D4—41no—
281C5×D4—41no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—84no—
319C2×C4×C5—84no—
320C2×C4×C5C2×#4111yescharacteristic
321C2×C4×C5C2×#4111yescharacteristic
322C2×C4×C5C2×#4111yescharacteristic
323C2×C4×C5C2×#4111yescharacteristic
324C2×C4×C5H(5,𝔽2)11yescharacteristic
325C2×C4×C52−1+411yescharacteristic
326C5×C8—41no—
327C5×C8—41no—
328C5×C8—41no—
329C5×C8—41no—
330C22×D4C23×C511yescharacteristic
331C22×D4C23×C511yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C2×D8—22no—
335C2×D8—22no—
336C2×D8—41no—
337C22×C8C23×C511yescharacteristic
338C22×C8C23×C511yescharacteristic
339C22×C8C23×C511yescharacteristic
340C22×C8C23×C511yescharacteristic
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C23×C511yescharacteristic
350C2×C4⋊C4C23×C511yescharacteristic
351C2×C4⋊C4C23×C511yescharacteristic
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C4⋊C4C23×C511yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42C23×C511yescharacteristic
368C2×C42C23×C511yescharacteristic
369C2×C42C23×C511yescharacteristic
370#107—22no—
371#106—22no—
372#106—41no—
373C4⋊C8—41no—
374C4⋊C8—41no—
375#102—22no—
376#102—22no—
377#102—22no—
378#102—22no—
379#102—41no—
380#102—41no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95C5×D411yescharacteristic
388#95C5×D411yescharacteristic
389#95C5×D411yescharacteristic
390#95C5×D411yescharacteristic
391C22×C5—42no—
392C22×C5—42no—
393C22×C5—42no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—81no—
398C22×C5—81no—
399C22×C5—81no—
400C22×C5—81no—
401C22×C5—81no—
402C22×C5—81no—
403C22×C5—81no—
404C22×C5—81no—
405C22×C5#52511yescharacteristic
406C22×C5#52511yescharacteristic
407C22×C5#53711yescharacteristic
408C22×C5#57611yescharacteristic
409C22×C5#57611yescharacteristic
410C22×C5#57711yescharacteristic
411C22×C5#57711yescharacteristic
412C4×C5—41no—
413C4×C5—42no—
414C4×C5—41no—
415C4×C5—41no—
416C4×C5—42no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5—41no—
420C4×C5—81no—
421C4×C5—81no—
422C4×C5—81no—
423C4×C5—81no—
424C4×C5#55111yescharacteristic
425C4×C5#55211yescharacteristic
426C4×C5#55211yescharacteristic
427C4×C5#55511yescharacteristic
428C24—21no—
429C24—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C5×#4112yes—
441C2×D4C5×#4112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4C2×C5×D411yescharacteristic
455C22×C4C2×C5×D411yescharacteristic
456C22×C4C2×C5×D411yescharacteristic
457C22×C4C2×C5×D411yescharacteristic
458C22×C4C2×C5×D411yescharacteristic
459C22×C4C2×C5×D411yescharacteristic
460C22×C4C24×C511yescharacteristic
461D8—44no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4C5×#4112yes—
489C4⋊C4C5×#4112yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—81no—
507C42—81no—
508C2×C5—82no—
509C2×C5—82no—
510C2×C5#260911yescharacteristic
511C2×C5#311811yescharacteristic
512C2×C5#311911yescharacteristic
513C2×C5#312211yescharacteristic
514C2×C5#312511yescharacteristic
515C2×C5#325711yescharacteristic
516C2×C5#325711yescharacteristic
517C23—22no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23C22×C5×D411yescharacteristic
532D4—22no—
533D4—22no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—84no—
578C2×C4C2×C5×#4111yescharacteristic
579C2×C4C2×C5×#4111yescharacteristic
580C2×C4C2×C5×#4111yescharacteristic
581C2×C4C2×C5×#4111yescharacteristic
582C2×C4C5×H(5,𝔽2)11yescharacteristic
583C2×C4C5×2−1+411yescharacteristic
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C5#2954211yescharacteristic, direct product factor, Sylow
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C5×#52511yescharacteristic
604C22C5×#52511yescharacteristic
605C22C5×#53711yescharacteristic
606C22C5×#57611yescharacteristic
607C22C5×#57611yescharacteristic
608C22C5×#57711yescharacteristic
609C22C5×#57711yescharacteristic
610C4—41no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4C5×#55111yescharacteristic
623C4C5×#55211yescharacteristic
624C4C5×#55211yescharacteristic
625C4C5×#55511yescharacteristic
626C2—82no—
627C2—82no—
628C2C5×#260911yescharacteristic
629C2C5×#311811yescharacteristic
630C2C5×#311911yescharacteristic
631C2C5×#312211yescharacteristic
632C2C5×#312511yescharacteristic
633C2C5×#325711yescharacteristic
634C2C5×#325711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D8C22
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×#2319C2semidirect
2. C5×#2319C2semidirect
3. C5×#2088C2semidirect
4. C5×#2067C2semidirect
5. C5×#2065C2semidirect
7. C5×#1926C2semidirect
8. C5×#1926C2semidirect
9. C5×#1920C2semidirect
10. C5×#1918C2semidirect
13. C5×#1864C2semidirect
14. C5×#1862C2semidirect
15. C5×#1832C2semidirect
59. #29542C5direct (N × H)
121. #2319C2×C5semidirect
122. #2319C2×C5semidirect
123. #2088C2×C5semidirect
124. #2067C2×C5semidirect
125. #2065C2×C5semidirect
127. #1926C2×C5semidirect
128. #1926C2×C5semidirect
129. #1920C2×C5semidirect
130. #1918C2×C5semidirect
133. #1864C2×C5semidirect
134. #1862C2×C5semidirect
135. #1832C2×C5semidirect
588. C5#29542direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23192
C5×#20882
C5×#20672
C5×#20652
C5×#20542
C5×#19262
C5×#19202
C5×#19182
C5×#18792
C5×#18642
C5×#18622
C5×#18322
#295425