Finite Group Databasebeta

← C5×#29547 #11952267

Subgroups — C5×#29547 #11952267

Order 1280.

698 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2320C211yesmaximal, characteristic, complemented
2C5×#2319C211yesmaximal, characteristic
3C5×#2088C211yesmaximal, characteristic, complemented
4C5×#2068C211yesmaximal, characteristic, complemented
5C5×#2067C211yesmaximal, characteristic
6C5×#2055C211yesmaximal, characteristic
7C5×#1927C211yesmaximal, characteristic, complemented
8C5×#1926C211yesmaximal, characteristic
9C5×#1921C211yesmaximal, characteristic, complemented
10C5×#1918C211yesmaximal, characteristic, complemented
11C5×#1880C211yesmaximal, characteristic
12C5×#1877C211yesmaximal, characteristic
13C5×#1863C211yesmaximal, characteristic, complemented
14C5×#1862C211yesmaximal, characteristic
15C5×#1832C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×#103C2211yescharacteristic
25C2×C5×#103C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C5×#391C2211yescharacteristic
31C5×#391C2211yescharacteristic
32C5×#390C2211yescharacteristic
33C5×#390C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#388—21no—
39C5×#388—21no—
40C5×#387—21no—
41C5×#387—21no—
42C5×#383—21no—
43C5×#382—21no—
44C5×#381—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#29547C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C2×C5×SD16—22no—
64C2×C5×SD16—22no—
65C2×C5×SD16—41no—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C4×C5×Q8—22no—
71C4×C5×Q8—22no—
72C4×C5×D4—22no—
73C4×C5×D4—22no—
74C2×C5×C4⋊C4—21no—
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×C42×C5—21no—
91C2×C42×C5—21no—
92C2×C42×C5—21no—
93C2×C42×C5C2311yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C5×#107—22no—
97C5×#107—22no—
98C5×#106—41no—
99C5×C4⋊C8—41no—
100C5×C4⋊C8—41no—
101C5×#103—22no—
102C5×#103—22no—
103C5×#103—41no—
104C5×#102—22no—
105C5×#102—22no—
106C5×#102—41no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110C5×#95—21no—
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#2320C2×C511yescharacteristic, complemented
122#2319C2×C511yescharacteristic
123#2088C2×C511yescharacteristic, complemented
124#2068C2×C511yescharacteristic, complemented
125#2067C2×C511yescharacteristic
126#2055C2×C511yescharacteristic
127#1927C2×C511yescharacteristic, complemented
128#1926C2×C511yescharacteristic
129#1921C2×C511yescharacteristic, complemented
130#1918C2×C511yescharacteristic, complemented
131#1880C2×C511yescharacteristic
132#1877C2×C511yescharacteristic
133#1863C2×C511yescharacteristic, complemented
134#1862C2×C511yescharacteristic
135#1832C2×C511yescharacteristic, complemented
136C24×C5—21no—
137C2×C5×Q8—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8#4112yes—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4#4112yes—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—24no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—81no—
158C22×C4×C5—81no—
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2411yescharacteristic
166C5×SD16—44no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
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—
179C5×C4⋊C4—24no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—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—81no—
191C5×C4⋊C4—81no—
192C5×C4⋊C4—81no—
193C5×C4⋊C4—81no—
194C5×C4⋊C4#4112yes—
195C5×C4⋊C4#4112yes—
196C5×C22⋊C4—24no—
197C5×C22⋊C4—81no—
198C5×C22⋊C4—81no—
199C5×C22⋊C4—81no—
200C5×C22⋊C4—81no—
201C42×C5—24no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—81no—
209C42×C5—81no—
210C22×SD16C22×C511yescharacteristic
211C2×C4×Q8C22×C511yescharacteristic
212C2×C4×D4C22×C511yescharacteristic
213C2×#107C22×C511yescharacteristic
214C2×#107C22×C511yescharacteristic
215C2×#106C22×C511yescharacteristic
216C2×C4⋊C8C22×C511yescharacteristic
217C2×C4⋊C8C22×C511yescharacteristic
218C2×#103C22×C511yescharacteristic
219C2×#103C22×C511yescharacteristic
220C2×#103C22×C511yescharacteristic
221C2×#102C22×C511yescharacteristic
222C2×#102C22×C511yescharacteristic
223C2×#102C22×C511yescharacteristic
224#391C22×C511yescharacteristic
225#391C22×C511yescharacteristic
226#390C22×C511yescharacteristic
227#390C22×C511yescharacteristic
228#389C22×C511yescharacteristic
229#389C22×C511yescharacteristic
230#389C22×C511yescharacteristic
231#389C22×C511yescharacteristic
232#388—21no—
233#388—21no—
234#387—21no—
235#387—21no—
236#383—21no—
237#382—21no—
238#381—21no—
239#380—21no—
240C4×C4⋊C4C22×C511yescharacteristic
241C4×C4⋊C4C22×C511yescharacteristic
242#376C22×C511yescharacteristic
243#340C22×C511yescharacteristic
244#340C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249#336C22×C511yescharacteristic
250#336C22×C511yescharacteristic
251#336C22×C511yescharacteristic
252#336C22×C511yescharacteristic
253C23×C5—22no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5C22×D411yescharacteristic
261C5×Q8—22no—
262C5×Q8—22no—
263C5×Q8—41no—
264C5×Q8—41no—
265C5×D4—22no—
266C5×D4—22no—
267C5×D4—41no—
268C5×D4—41no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
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—84no—
309C2×C4×C5C2×#4111yescharacteristic
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5H(5,𝔽2)11yescharacteristic
314C2×C4×C52−1+411yescharacteristic
315C5×C8—41no—
316C5×C8—41no—
317C5×C8—41no—
318C5×C8—41no—
319C22×Q8C23×C511yescharacteristic
320C22×D4C23×C511yescharacteristic
321C23×C4—21no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—41no—
325C22×C8C23×C511yescharacteristic
326C22×C8C23×C511yescharacteristic
327C22×C8C23×C511yescharacteristic
328C22×C8C23×C511yescharacteristic
329C4×Q8—22no—
330C4×Q8—22no—
331C4×D4—22no—
332C4×D4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C23×C511yescharacteristic
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C4⋊C4C23×C511yescharacteristic
342C2×C4⋊C4C23×C511yescharacteristic
343C2×C4⋊C4C23×C511yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42C23×C511yescharacteristic
353C2×C42C23×C511yescharacteristic
354C2×C42C23×C511yescharacteristic
355#107—22no—
356#107—22no—
357#106—41no—
358C4⋊C8—41no—
359C4⋊C8—41no—
360#103—22no—
361#103—22no—
362#103—41no—
363#102—22no—
364#102—22no—
365#102—41no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95C5×D411yescharacteristic
377#95C5×D411yescharacteristic
378#95C5×D411yescharacteristic
379#95C5×D411yescharacteristic
380C22×C5—42no—
381C22×C5—42no—
382C22×C5—42no—
383C22×C5—81no—
384C22×C5—81no—
385C22×C5—81no—
386C22×C5—81no—
387C22×C5#52511yescharacteristic
388C22×C5#52511yescharacteristic
389C22×C5#53711yescharacteristic
390C22×C5#57611yescharacteristic
391C22×C5#57711yescharacteristic
392C22×C5#57711yescharacteristic
393C22×C5#57811yescharacteristic
394C4×C5—41no—
395C4×C5—42no—
396C4×C5—41no—
397C4×C5—42no—
398C4×C5—41no—
399C4×C5—42no—
400C4×C5—41no—
401C4×C5—41no—
402C4×C5—41no—
403C4×C5—81no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5—81no—
407C4×C5#55111yescharacteristic
408C4×C5#55211yescharacteristic
409C4×C5#55211yescharacteristic
410C4×C5#55511yescharacteristic
411C24—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8C5×#4112yes—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4C5×#4112yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C2×C5×D411yescharacteristic
440C22×C4C24×C511yescharacteristic
441SD16—44no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4C5×#4112yes—
470C4⋊C4C5×#4112yes—
471C22⋊C4—24no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—24no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—81no—
485C2×C5—82no—
486C2×C5#260911yescharacteristic
487C2×C5#311811yescharacteristic
488C2×C5#311911yescharacteristic
489C2×C5#312011yescharacteristic
490C2×C5#312111yescharacteristic
491C2×C5#326011yescharacteristic
492C2×C5#326211yescharacteristic
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×C5×D411yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505D4—22no—
506D4—22no—
507D4—41no—
508D4—41no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4C2×C5×#4111yescharacteristic
550C2×C4C2×C5×#4111yescharacteristic
551C2×C4C2×C5×#4111yescharacteristic
552C2×C4C2×C5×#4111yescharacteristic
553C2×C4C5×H(5,𝔽2)11yescharacteristic
554C2×C4C5×2−1+411yescharacteristic
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C5#2954711yescharacteristic, direct product factor, Sylow
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C5×#52511yescharacteristic
568C22C5×#52511yescharacteristic
569C22C5×#53711yescharacteristic
570C22C5×#57611yescharacteristic
571C22C5×#57711yescharacteristic
572C22C5×#57711yescharacteristic
573C22C5×#57811yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C5×#55111yescharacteristic
588C4C5×#55211yescharacteristic
589C4C5×#55211yescharacteristic
590C4C5×#55511yescharacteristic
591C2—82no—
592C2C5×#260911yescharacteristic
593C2C5×#311811yescharacteristic
594C2C5×#311911yescharacteristic
595C2C5×#312011yescharacteristic
596C2C5×#312111yescharacteristic
597C2C5×#326011yescharacteristic
598C2C5×#326211yescharacteristic
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×#2320C2semidirect
3. C5×#2088C2semidirect
4. C5×#2068C2semidirect
7. C5×#1927C2semidirect
9. C5×#1921C2semidirect
10. C5×#1918C2semidirect
13. C5×#1863C2semidirect
15. C5×#1832C2semidirect
59. #29547C5direct (N × H)
121. #2320C2×C5semidirect
123. #2088C2×C5semidirect
124. #2068C2×C5semidirect
127. #1927C2×C5semidirect
129. #1921C2×C5semidirect
130. #1918C2×C5semidirect
133. #1863C2×C5semidirect
135. #1832C2×C5semidirect
559. C5#29547direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#23202
C5×#23192
C5×#20882
C5×#20682
C5×#20672
C5×#20552
C5×#19272
C5×#19262
C5×#19212
C5×#19182
C5×#18802
C5×#18772
C5×#18632
C5×#18622
C5×#18322
#295475