Finite Group Databasebeta

← C5×#32793 #11955513

Subgroups — C5×#32793 #11955513

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2629C211yesmaximal, characteristic
2C5×#2628C211yesmaximal, characteristic
3C5×#2101C211yesmaximal, characteristic, complemented
4C5×#2101C211yesmaximal, characteristic, complemented
5C5×#2100C211yesmaximal, characteristic, complemented
6C5×#2099C211yesmaximal, characteristic, complemented
7C5×#2077C211yesmaximal, characteristic
8C5×#2077C211yesmaximal, characteristic
9C5×#2076C211yesmaximal, characteristic
10C5×#2075C211yesmaximal, characteristic
11C5×#2059C211yesmaximal, characteristic, complemented
12C5×#2059C211yesmaximal, characteristic, complemented
13C5×#2058C211yesmaximal, characteristic, complemented
14C5×#2057C211yesmaximal, characteristic, complemented
15C5×#1818C211yesmaximal, characteristic
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C5×#125C2211yescharacteristic
18C2×C5×#117C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×C22⋊C8C2211yescharacteristic
24C2×C5×C22⋊C8C2211yescharacteristic
25C5×#400—21no—
26C5×#399—21no—
27C5×#398—21no—
28C5×#398—21no—
29C5×#396—21no—
30C5×#396—21no—
31C5×#395—21no—
32C5×#393—21no—
33C5×#389C2211yescharacteristic
34C5×#389C2211yescharacteristic
35C5×#389C2211yescharacteristic
36C5×#389C2211yescharacteristic
37C5×#384C2211yescharacteristic
38C5×#382C2211yescharacteristic
39C5×#380C2211yescharacteristic
40C5×#380C2211yescharacteristic
41C5×#380C2211yescharacteristic
42C5×#380C2211yescharacteristic
43C5×#340C2211yescharacteristic
44C5×#340C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
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#32793C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C23×C4×C5C2311yescharacteristic
62C22×C5×C8C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C5×C4⋊Q8—41no—
67C5×C4⋊Q8—41no—
68C5×#125—41no—
69C5×#125—41no—
70C5×#117—41no—
71C5×#117—41no—
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⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4D411yescharacteristic
82C2×C5×C4⋊C4D411yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C22⋊C4—21no—
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4D411yescharacteristic
96C2×C5×C22⋊C4D411yescharacteristic
97C2×C42×C5C2311yescharacteristic
98C2×C42×C5C2311yescharacteristic
99C5×#107—41no—
100C5×#107—41no—
101C5×#106—41no—
102C5×#106—41no—
103C5×C22⋊C8—41no—
104C5×C22⋊C8—41no—
105C5×#95—21no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110C5×#95—21no—
111C5×#95—21no—
112C5×#95—21no—
113C5×#95—21no—
114C5×#95—21no—
115#2629C2×C511yescharacteristic
116#2628C2×C511yescharacteristic
117#2101C2×C511yescharacteristic, complemented
118#2101C2×C511yescharacteristic, complemented
119#2100C2×C511yescharacteristic, complemented
120#2099C2×C511yescharacteristic, complemented
121#2077C2×C511yescharacteristic
122#2077C2×C511yescharacteristic
123#2076C2×C511yescharacteristic
124#2075C2×C511yescharacteristic
125#2059C2×C511yescharacteristic, complemented
126#2059C2×C511yescharacteristic, complemented
127#2058C2×C511yescharacteristic, complemented
128#2057C2×C511yescharacteristic, complemented
129#1818C2×C511yescharacteristic
130C24×C5C2×D411yescharacteristic
131C2×C5×Q8—42no—
132C2×C5×Q8—81no—
133C2×C5×Q8—81no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—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×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
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—21no—
165C2×C5×C8—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—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—41no—
183C5×C4⋊C4—41no—
184C5×C4⋊C4—42no—
185C5×C4⋊C4—42no—
186C5×C4⋊C4—42no—
187C5×C4⋊C4—81no—
188C5×C4⋊C4—81no—
189C5×C4⋊C4—81no—
190C5×C4⋊C4—81no—
191C5×C4⋊C4—81no—
192C5×C4⋊C4—81no—
193C5×C22⋊C4—41no—
194C5×C22⋊C4—41no—
195C5×C22⋊C4—81no—
196C5×C22⋊C4—81no—
197C5×C22⋊C4—81no—
198C5×C22⋊C4—81no—
199C42×C5—21no—
200C42×C5—21no—
201C42×C5—21no—
202C42×C5—21no—
203C2×C4⋊Q8C22×C511yescharacteristic
204C2×#125C22×C511yescharacteristic
205C2×#117C22×C511yescharacteristic
206C2×#107C22×C511yescharacteristic
207C2×#107C22×C511yescharacteristic
208C2×#106C22×C511yescharacteristic
209C2×#106C22×C511yescharacteristic
210C2×C22⋊C8C22×C511yescharacteristic
211C2×C22⋊C8C22×C511yescharacteristic
212#400—21no—
213#399—21no—
214#398—21no—
215#398—21no—
216#396—21no—
217#396—21no—
218#395—21no—
219#393—21no—
220#389C22×C511yescharacteristic
221#389C22×C511yescharacteristic
222#389C22×C511yescharacteristic
223#389C22×C511yescharacteristic
224#384C22×C511yescharacteristic
225#382C22×C511yescharacteristic
226#380C22×C511yescharacteristic
227#380C22×C511yescharacteristic
228#380C22×C511yescharacteristic
229#380C22×C511yescharacteristic
230#340C22×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#340C22×C511yescharacteristic
240#340C22×C511yescharacteristic
241#340C22×C511yescharacteristic
242#336C22×C511yescharacteristic
243#336C22×C511yescharacteristic
244#336C22×C511yescharacteristic
245#336C22×C511yescharacteristic
246C23×C5—21no—
247C23×C5—21no—
248C23×C5—21no—
249C23×C5—21no—
250C23×C5—21no—
251C23×C5—21no—
252C23×C5—21no—
253C23×C5C22×D411yescharacteristic
254C5×Q8—84no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
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—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
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—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5H(5,𝔽2)11yescharacteristic
299C2×C4×C5H(5,𝔽2)11yescharacteristic
300C2×C4×C52−1+411yescharacteristic
301C2×C4×C52−1+411yescharacteristic
302C2×C4×C52−1+411yescharacteristic
303C2×C4×C52−1+411yescharacteristic
304C5×C8—41no—
305C5×C8—41no—
306C5×C8—41no—
307C5×C8—41no—
308C22×Q8—21no—
309C23×C4C23×C511yescharacteristic
310C22×C8C23×C511yescharacteristic
311C22×C8C23×C511yescharacteristic
312C22×C8C23×C511yescharacteristic
313C22×C8C23×C511yescharacteristic
314C4⋊Q8—41no—
315C4⋊Q8—41no—
316#125—41no—
317#125—41no—
318#117—41no—
319#117—41no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4C5×D411yescharacteristic
330C2×C4⋊C4C5×D411yescharacteristic
331C2×C4⋊C4C23×C511yescharacteristic
332C2×C4⋊C4C23×C511yescharacteristic
333C2×C4⋊C4C23×C511yescharacteristic
334C2×C4⋊C4C23×C511yescharacteristic
335C2×C4⋊C4C23×C511yescharacteristic
336C2×C4⋊C4C23×C511yescharacteristic
337C2×C4⋊C4C23×C511yescharacteristic
338C2×C4⋊C4C23×C511yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4C5×D411yescharacteristic
344C2×C22⋊C4C5×D411yescharacteristic
345C2×C42C23×C511yescharacteristic
346C2×C42C23×C511yescharacteristic
347#107—41no—
348#107—41no—
349#106—41no—
350#106—41no—
351C22⋊C8—41no—
352C22⋊C8—41no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363C22×C5—41no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—41no—
367C22×C5—41no—
368C22×C5—41no—
369C22×C5—41no—
370C22×C5#53411yescharacteristic
371C22×C5#53611yescharacteristic
372C22×C5#53611yescharacteristic
373C22×C5#57611yescharacteristic
374C22×C5#57711yescharacteristic
375C22×C5#57711yescharacteristic
376C22×C5#57811yescharacteristic
377C4×C5—41no—
378C4×C5—41no—
379C4×C5—41no—
380C4×C5—41no—
381C4×C5—41no—
382C4×C5—81no—
383C4×C5—81no—
384C4×C5—81no—
385C4×C5—81no—
386C4×C5—81no—
387C4×C5—81no—
388C4×C5—81no—
389C4×C5—81no—
390C4×C5#56311yescharacteristic
391C4×C5#56311yescharacteristic
392C4×C5#56311yescharacteristic
393C4×C5#56311yescharacteristic
394C24C2×C5×D411yescharacteristic
395C2×Q8—42no—
396C2×Q8—81no—
397C2×Q8—81no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4C2×C5×D411yescharacteristic
413C22×C4C2×C5×D411yescharacteristic
414C22×C4C2×C5×D411yescharacteristic
415C22×C4C2×C5×D411yescharacteristic
416C22×C4C2×C5×D411yescharacteristic
417C22×C4C24×C511yescharacteristic
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—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—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—81no—
460C22⋊C4—81no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C2×C5—81no—
468C2×C5#281711yescharacteristic
469C2×C5#319811yescharacteristic
470C2×C5#320111yescharacteristic
471C2×C5#324111yescharacteristic
472C2×C5#324211yescharacteristic
473C2×C5#324311yescharacteristic
474C2×C5#324411yescharacteristic
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23C22×C5×D411yescharacteristic
483Q8—84no—
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—41no—
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—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4C5×H(5,𝔽2)11yescharacteristic
528C2×C4C5×H(5,𝔽2)11yescharacteristic
529C2×C4C5×2−1+411yescharacteristic
530C2×C4C5×2−1+411yescharacteristic
531C2×C4C5×2−1+411yescharacteristic
532C2×C4C5×2−1+411yescharacteristic
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C5#3279311yescharacteristic, direct product factor, Sylow
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22C5×#53411yescharacteristic
546C22C5×#53611yescharacteristic
547C22C5×#53611yescharacteristic
548C22C5×#57611yescharacteristic
549C22C5×#57711yescharacteristic
550C22C5×#57711yescharacteristic
551C22C5×#57811yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C5×#56311yescharacteristic
566C4C5×#56311yescharacteristic
567C4C5×#56311yescharacteristic
568C4C5×#56311yescharacteristic
569C2—81no—
570C2C5×#281711yescharacteristic
571C2C5×#319811yescharacteristic
572C2C5×#320111yescharacteristic
573C2C5×#324111yescharacteristic
574C2C5×#324211yescharacteristic
575C2C5×#324311yescharacteristic
576C2C5×#324411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2101C2semidirect
4. C5×#2101C2semidirect
5. C5×#2100C2semidirect
6. C5×#2099C2semidirect
11. C5×#2059C2semidirect
12. C5×#2059C2semidirect
13. C5×#2058C2semidirect
14. C5×#2057C2semidirect
59. #32793C5direct (N × H)
117. #2101C2×C5semidirect
118. #2101C2×C5semidirect
119. #2100C2×C5semidirect
120. #2099C2×C5semidirect
125. #2059C2×C5semidirect
126. #2059C2×C5semidirect
127. #2058C2×C5semidirect
128. #2057C2×C5semidirect
537. C5#32793direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26292
C5×#26282
C5×#21012
C5×#21002
C5×#20992
C5×#20772
C5×#20762
C5×#20752
C5×#20592
C5×#20582
C5×#20572
C5×#18182
#327935