Finite Group Databasebeta

← C5×#32833 #11955553

Subgroups — C5×#32833 #11955553

Order 1280.

612 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2647C211yesmaximal, characteristic, complemented
2C5×#2640C211yesmaximal, characteristic
3C5×#2097C211yesmaximal, characteristic, complemented
4C5×#2092C211yesmaximal, characteristic
5C5×#2072C211yesmaximal, characteristic, complemented
6C5×#2071C211yesmaximal, characteristic
7C5×#2068C211yesmaximal, characteristic, complemented
8C5×#2067C211yesmaximal, characteristic
9C5×#2066C211yesmaximal, characteristic, complemented
10C5×#2065C211yesmaximal, characteristic
11C5×#2058C211yesmaximal, characteristic, complemented
12C5×#2057C211yesmaximal, characteristic, complemented
13C5×#2042C211yesmaximal, characteristic
14C5×#2042C211yesmaximal, characteristic
15C5×#1832C211yesmaximal, characteristic, complemented
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C5×#124C2211yescharacteristic
18C2×C5×#107C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×#103C2211yescharacteristic
25C2×C5×#103C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C5×#400—21no—
33C5×#400—21no—
34C5×#398—21no—
35C5×#398—21no—
36C5×#397—21no—
37C5×#397—21no—
38C5×#393—21no—
39C5×#393—21no—
40C5×#391C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#384C2211yescharacteristic
49C5×#382C2211yescharacteristic
50C5×#376C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#336C2211yescharacteristic
56C5×#336C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#32833C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C22×C5×Q8C2311yescharacteristic
62C22×C5×D4C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C5×C4⋊Q8—41no—
68C5×C4⋊Q8—41no—
69C5×#124—41no—
70C5×#124—41no—
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⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
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×C5×C22⋊C4—21no—
90C2×C42×C5C2311yescharacteristic
91C2×C42×C5C2311yescharacteristic
92C2×C42×C5C2311yescharacteristic
93C5×#107—41no—
94C5×#107—41no—
95C5×#106—41no—
96C5×#106—41no—
97C5×C4⋊C8—41no—
98C5×C4⋊C8—41no—
99C5×#103—41no—
100C5×#103—41no—
101C5×#103—41no—
102C5×#103—41no—
103C5×#102—41no—
104C5×#102—41no—
105C5×#102—41no—
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#2647C2×C511yescharacteristic, complemented
122#2640C2×C511yescharacteristic
123#2097C2×C511yescharacteristic, complemented
124#2092C2×C511yescharacteristic
125#2072C2×C511yescharacteristic, complemented
126#2071C2×C511yescharacteristic
127#2068C2×C511yescharacteristic, complemented
128#2067C2×C511yescharacteristic
129#2066C2×C511yescharacteristic, complemented
130#2065C2×C511yescharacteristic
131#2058C2×C511yescharacteristic, complemented
132#2057C2×C511yescharacteristic, complemented
133#2042C2×C511yescharacteristic
134#2042C2×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—21no—
143C2×C5×Q8—42no—
144C2×C5×Q8—81no—
145C2×C5×Q8—81no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
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
166C2×C5×C8—21no—
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—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
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—42no—
191C5×C4⋊C4—81no—
192C5×C4⋊C4—81no—
193C5×C4⋊C4—81no—
194C5×C4⋊C4—81no—
195C5×C4⋊C4—81no—
196C5×C4⋊C4—81no—
197C5×C22⋊C4—42no—
198C5×C22⋊C4—42no—
199C5×C22⋊C4—81no—
200C5×C22⋊C4—81no—
201C5×C22⋊C4—81no—
202C5×C22⋊C4—81no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C2×C4⋊Q8C22×C511yescharacteristic
210C2×#124C22×C511yescharacteristic
211C2×#107C22×C511yescharacteristic
212C2×#107C22×C511yescharacteristic
213C2×#106C22×C511yescharacteristic
214C2×#106C22×C511yescharacteristic
215C2×C4⋊C8C22×C511yescharacteristic
216C2×C4⋊C8C22×C511yescharacteristic
217C2×#103C22×C511yescharacteristic
218C2×#103C22×C511yescharacteristic
219C2×#103C22×C511yescharacteristic
220C2×#103C22×C511yescharacteristic
221C2×#102C22×C511yescharacteristic
222C2×#102C22×C511yescharacteristic
223C2×#102C22×C511yescharacteristic
224C2×#102C22×C511yescharacteristic
225#400—21no—
226#400—21no—
227#398—21no—
228#398—21no—
229#397—21no—
230#397—21no—
231#393—21no—
232#393—21no—
233#391C22×C511yescharacteristic
234#391C22×C511yescharacteristic
235#390C22×C511yescharacteristic
236#390C22×C511yescharacteristic
237#389C22×C511yescharacteristic
238#389C22×C511yescharacteristic
239#389C22×C511yescharacteristic
240#389C22×C511yescharacteristic
241#384C22×C511yescharacteristic
242#382C22×C511yescharacteristic
243#376C22×C511yescharacteristic
244#340C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#336C22×C511yescharacteristic
249#336C22×C511yescharacteristic
250#336C22×C511yescharacteristic
251#336C22×C511yescharacteristic
252C23×C5—41no—
253C23×C5—41no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5C22×D411yescharacteristic
260C5×Q8—41no—
261C5×Q8—41no—
262C5×Q8—41no—
263C5×Q8—41no—
264C5×Q8—84no—
265C5×D4—41no—
266C5×D4—41no—
267C5×D4—41no—
268C5×D4—41no—
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—21no—
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—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—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×C5H(5,𝔽2)11yescharacteristic
309C2×C4×C5H(5,𝔽2)11yescharacteristic
310C2×C4×C5H(5,𝔽2)11yescharacteristic
311C2×C4×C52−1+411yescharacteristic
312C2×C4×C52−1+411yescharacteristic
313C2×C4×C52−1+411yescharacteristic
314C5×C8—41no—
315C5×C8—41no—
316C5×C8—41no—
317C5×C8—41no—
318C22×Q8—21no—
319C22×Q8C23×C511yescharacteristic
320C22×D4C23×C511yescharacteristic
321C22×C8C23×C511yescharacteristic
322C22×C8C23×C511yescharacteristic
323C22×C8C23×C511yescharacteristic
324C22×C8C23×C511yescharacteristic
325C4⋊Q8—41no—
326C4⋊Q8—41no—
327#124—41no—
328#124—41no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C23×C511yescharacteristic
337C2×C4⋊C4C23×C511yescharacteristic
338C2×C4⋊C4C23×C511yescharacteristic
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C4⋊C4C23×C511yescharacteristic
341C2×C4⋊C4C23×C511yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42C23×C511yescharacteristic
349C2×C42C23×C511yescharacteristic
350C2×C42C23×C511yescharacteristic
351#107—41no—
352#107—41no—
353#106—41no—
354#106—41no—
355C4⋊C8—41no—
356C4⋊C8—41no—
357#103—41no—
358#103—41no—
359#103—41no—
360#103—41no—
361#102—41no—
362#102—41no—
363#102—41no—
364#102—41no—
365#95—21no—
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#95C5×D411yescharacteristic
376#95C5×D411yescharacteristic
377#95C5×D411yescharacteristic
378#95C5×D411yescharacteristic
379C22×C5—81no—
380C22×C5—81no—
381C22×C5—81no—
382C22×C5—81no—
383C22×C5—81no—
384C22×C5—81no—
385C22×C5—81no—
386C22×C5#53511yescharacteristic
387C22×C5#53611yescharacteristic
388C22×C5#53711yescharacteristic
389C22×C5#57611yescharacteristic
390C22×C5#57711yescharacteristic
391C22×C5#57711yescharacteristic
392C22×C5#57811yescharacteristic
393C4×C5—41no—
394C4×C5—41no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—41no—
398C4×C5—41no—
399C4×C5—81no—
400C4×C5—81no—
401C4×C5—81no—
402C4×C5—81no—
403C4×C5—81no—
404C4×C5—81no—
405C4×C5—81no—
406C4×C5#56211yescharacteristic
407C4×C5#56211yescharacteristic
408C4×C5#56311yescharacteristic
409C4×C5#56311yescharacteristic
410C24—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—42no—
418C2×Q8—81no—
419C2×Q8—81no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4C2×C5×D411yescharacteristic
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D411yescharacteristic
437C22×C4C2×C5×D411yescharacteristic
438C22×C4C2×C5×D411yescharacteristic
439C22×C4C24×C511yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
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—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
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—42no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C2×C5—161no—
484C2×C5#282011yescharacteristic
485C2×C5#322411yescharacteristic
486C2×C5#322511yescharacteristic
487C2×C5#324311yescharacteristic
488C2×C5#324411yescharacteristic
489C2×C5#325711yescharacteristic
490C2×C5#325811yescharacteristic
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C22×C5×D411yescharacteristic
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—84no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
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—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
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×C4C5×H(5,𝔽2)11yescharacteristic
548C2×C4C5×H(5,𝔽2)11yescharacteristic
549C2×C4C5×H(5,𝔽2)11yescharacteristic
550C2×C4C5×2−1+411yescharacteristic
551C2×C4C5×2−1+411yescharacteristic
552C2×C4C5×2−1+411yescharacteristic
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C5#3283311yescharacteristic, direct product factor, Sylow
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C5×#53511yescharacteristic
566C22C5×#53611yescharacteristic
567C22C5×#53711yescharacteristic
568C22C5×#57611yescharacteristic
569C22C5×#57711yescharacteristic
570C22C5×#57711yescharacteristic
571C22C5×#57811yescharacteristic
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C5×#56211yescharacteristic
586C4C5×#56211yescharacteristic
587C4C5×#56311yescharacteristic
588C4C5×#56311yescharacteristic
589C2—161no—
590C2C5×#282011yescharacteristic
591C2C5×#322411yescharacteristic
592C2C5×#322511yescharacteristic
593C2C5×#324311yescharacteristic
594C2C5×#324411yescharacteristic
595C2C5×#325711yescharacteristic
596C2C5×#325811yescharacteristic
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×#2097C2semidirect
5. C5×#2072C2semidirect
7. C5×#2068C2semidirect
9. C5×#2066C2semidirect
11. C5×#2058C2semidirect
12. C5×#2057C2semidirect
15. C5×#1832C2semidirect
59. #32833C5direct (N × H)
121. #2647C2×C5semidirect
123. #2097C2×C5semidirect
125. #2072C2×C5semidirect
127. #2068C2×C5semidirect
129. #2066C2×C5semidirect
131. #2058C2×C5semidirect
132. #2057C2×C5semidirect
135. #1832C2×C5semidirect
557. C5#32833direct (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×#26402
C5×#20972
C5×#20922
C5×#20722
C5×#20712
C5×#20682
C5×#20672
C5×#20662
C5×#20652
C5×#20582
C5×#20572
C5×#20422
C5×#18322
#328335