Finite Group Databasebeta

← C5×#32844 #11955564

Subgroups — C5×#32844 #11955564

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2660C211yesmaximal, characteristic, complemented
2C5×#2644C211yesmaximal, characteristic
3C5×#2101C211yesmaximal, characteristic, complemented
4C5×#2099C211yesmaximal, characteristic, complemented
5C5×#2094C211yesmaximal, characteristic
6C5×#2092C211yesmaximal, characteristic
7C5×#2085C211yesmaximal, characteristic, complemented
8C5×#2084C211yesmaximal, characteristic, complemented
9C5×#2073C211yesmaximal, characteristic
10C5×#2071C211yesmaximal, characteristic
11C5×#2059C211yesmaximal, characteristic, complemented
12C5×#2058C211yesmaximal, characteristic, complemented
13C5×#2025C211yesmaximal, characteristic
14C5×#2023C211yesmaximal, characteristic
15C5×#1840C211yesmaximal, characteristic, complemented
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C5×#125C2211yescharacteristic
18C2×C5×#107C2211yescharacteristic
19C2×C5×#106C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×#102C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C5×#398—21no—
27C5×#398—21no—
28C5×#397—21no—
29C5×#397—21no—
30C5×#397—21no—
31C5×#396—21no—
32C5×#395—21no—
33C5×#395—21no—
34C5×#390C2211yescharacteristic
35C5×#390C2211yescharacteristic
36C5×#390C2211yescharacteristic
37C5×#389C2211yescharacteristic
38C5×#389C2211yescharacteristic
39C5×#389C2211yescharacteristic
40C5×#384C2211yescharacteristic
41C5×#384C2211yescharacteristic
42C5×#382C2211yescharacteristic
43C5×#382C2211yescharacteristic
44C5×#376C2211yescharacteristic
45C5×#340C2211yescharacteristic
46C5×#340C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#336C2211yescharacteristic
54C5×#336C2211yescharacteristic
55C5×#336C2211yescharacteristic
56C5×#336C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#32844C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C22×C5×D4C2311yescharacteristic
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—
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⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
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×C42×C5C2311yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C5×#107—41no—
97C5×#106—41no—
98C5×#106—41no—
99C5×#106—41no—
100C5×#102—41no—
101C5×#102—41no—
102C5×#102—41no—
103C5×#102—41no—
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#2660C2×C511yescharacteristic, complemented
116#2644C2×C511yescharacteristic
117#2101C2×C511yescharacteristic, complemented
118#2099C2×C511yescharacteristic, complemented
119#2094C2×C511yescharacteristic
120#2092C2×C511yescharacteristic
121#2085C2×C511yescharacteristic, complemented
122#2084C2×C511yescharacteristic, complemented
123#2073C2×C511yescharacteristic
124#2071C2×C511yescharacteristic
125#2059C2×C511yescharacteristic, complemented
126#2058C2×C511yescharacteristic, complemented
127#2025C2×C511yescharacteristic
128#2023C2×C511yescharacteristic
129#1840C2×C511yescharacteristic, complemented
130C24×C5—21no—
131C2×C5×Q8—42no—
132C2×C5×Q8—81no—
133C2×C5×Q8—81no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—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×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—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—42no—
181C5×C4⋊C4—42no—
182C5×C4⋊C4—42no—
183C5×C4⋊C4—81no—
184C5×C4⋊C4—81no—
185C5×C4⋊C4—81no—
186C5×C4⋊C4—81no—
187C5×C4⋊C4—81no—
188C5×C4⋊C4—81no—
189C5×C4⋊C4—81no—
190C5×C22⋊C4—81no—
191C5×C22⋊C4—81no—
192C5×C22⋊C4—81no—
193C5×C22⋊C4—81no—
194C5×C22⋊C4—81no—
195C5×C22⋊C4—81no—
196C42×C5—21no—
197C42×C5—21no—
198C42×C5—21no—
199C42×C5—21no—
200C42×C5—21no—
201C42×C5—21no—
202C2×C4⋊Q8C22×C511yescharacteristic
203C2×#125C22×C511yescharacteristic
204C2×#107C22×C511yescharacteristic
205C2×#106C22×C511yescharacteristic
206C2×#106C22×C511yescharacteristic
207C2×#106C22×C511yescharacteristic
208C2×#102C22×C511yescharacteristic
209C2×#102C22×C511yescharacteristic
210C2×#102C22×C511yescharacteristic
211C2×#102C22×C511yescharacteristic
212#398—21no—
213#398—21no—
214#397—21no—
215#397—21no—
216#397—21no—
217#396—21no—
218#395—21no—
219#395—21no—
220#390C22×C511yescharacteristic
221#390C22×C511yescharacteristic
222#390C22×C511yescharacteristic
223#389C22×C511yescharacteristic
224#389C22×C511yescharacteristic
225#389C22×C511yescharacteristic
226#384C22×C511yescharacteristic
227#384C22×C511yescharacteristic
228#382C22×C511yescharacteristic
229#382C22×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
243#336C22×C511yescharacteristic
244#336C22×C511yescharacteristic
245C23×C5—41no—
246C23×C5—41no—
247C23×C5—41no—
248C23×C5—41no—
249C23×C5—41no—
250C23×C5—41no—
251C23×C5—41no—
252C23×C5C22×D411yescharacteristic
253C5×Q8—84no—
254C5×D4—41no—
255C5×D4—41no—
256C5×D4—41no—
257C5×D4—41no—
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—21no—
275C2×C4×C5—21no—
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×C5H(5,𝔽2)11yescharacteristic
298C2×C4×C5H(5,𝔽2)11yescharacteristic
299C2×C4×C52−1+411yescharacteristic
300C2×C4×C52−1+411yescharacteristic
301C2×C4×C52−1+411yescharacteristic
302C2×C4×C52−1+411yescharacteristic
303C5×C8—41no—
304C5×C8—41no—
305C5×C8—41no—
306C5×C8—41no—
307C22×Q8—21no—
308C22×D4C23×C511yescharacteristic
309C22×C8C23×C511yescharacteristic
310C22×C8C23×C511yescharacteristic
311C22×C8C23×C511yescharacteristic
312C22×C8C23×C511yescharacteristic
313C4⋊Q8—41no—
314C4⋊Q8—41no—
315#125—41no—
316#125—41no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
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⋊C4C23×C511yescharacteristic
328C2×C4⋊C4C23×C511yescharacteristic
329C2×C4⋊C4C23×C511yescharacteristic
330C2×C4⋊C4C23×C511yescharacteristic
331C2×C4⋊C4C23×C511yescharacteristic
332C2×C4⋊C4C23×C511yescharacteristic
333C2×C4⋊C4C23×C511yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42C23×C511yescharacteristic
341C2×C42C23×C511yescharacteristic
342C2×C42C23×C511yescharacteristic
343#107—41no—
344#106—41no—
345#106—41no—
346#106—41no—
347#102—41no—
348#102—41no—
349#102—41no—
350#102—41no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95C5×D411yescharacteristic
359#95C5×D411yescharacteristic
360#95C5×D411yescharacteristic
361#95C5×D411yescharacteristic
362C22×C5—81no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5—81no—
368C22×C5—81no—
369C22×C5#53511yescharacteristic
370C22×C5#53611yescharacteristic
371C22×C5#53611yescharacteristic
372C22×C5#57611yescharacteristic
373C22×C5#57711yescharacteristic
374C22×C5#57711yescharacteristic
375C22×C5#57711yescharacteristic
376C4×C5—41no—
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#56311yescharacteristic
390C4×C5#56311yescharacteristic
391C4×C5#56311yescharacteristic
392C4×C5#56311yescharacteristic
393C24—21no—
394C2×Q8—42no—
395C2×Q8—81no—
396C2×Q8—81no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4C2×C5×D411yescharacteristic
411C22×C4C2×C5×D411yescharacteristic
412C22×C4C2×C5×D411yescharacteristic
413C22×C4C2×C5×D411yescharacteristic
414C22×C4C2×C5×D411yescharacteristic
415C22×C4C2×C5×D411yescharacteristic
416C22×C4C24×C511yescharacteristic
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×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—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—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—81no—
447C4⋊C4—81no—
448C4⋊C4—81no—
449C4⋊C4—81no—
450C4⋊C4—81no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C22⋊C4—81no—
454C22⋊C4—81no—
455C22⋊C4—81no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C22⋊C4—81no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—21no—
464C42—21no—
465C2×C5—161no—
466C2×C5#282111yescharacteristic
467C2×C5#322111yescharacteristic
468C2×C5#322411yescharacteristic
469C2×C5#324111yescharacteristic
470C2×C5#324111yescharacteristic
471C2×C5#324411yescharacteristic
472C2×C5#324411yescharacteristic
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23C22×C5×D411yescharacteristic
481Q8—84no—
482D4—41no—
483D4—41no—
484D4—41no—
485D4—41no—
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—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
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×C4C5×H(5,𝔽2)11yescharacteristic
526C2×C4C5×H(5,𝔽2)11yescharacteristic
527C2×C4C5×2−1+411yescharacteristic
528C2×C4C5×2−1+411yescharacteristic
529C2×C4C5×2−1+411yescharacteristic
530C2×C4C5×2−1+411yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C5#3284411yescharacteristic, direct product factor, Sylow
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C5×#53511yescharacteristic
544C22C5×#53611yescharacteristic
545C22C5×#53611yescharacteristic
546C22C5×#57611yescharacteristic
547C22C5×#57711yescharacteristic
548C22C5×#57711yescharacteristic
549C22C5×#57711yescharacteristic
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C5×#56311yescharacteristic
564C4C5×#56311yescharacteristic
565C4C5×#56311yescharacteristic
566C4C5×#56311yescharacteristic
567C2—161no—
568C2C5×#282111yescharacteristic
569C2C5×#322111yescharacteristic
570C2C5×#322411yescharacteristic
571C2C5×#324111yescharacteristic
572C2C5×#324111yescharacteristic
573C2C5×#324411yescharacteristic
574C2C5×#324411yescharacteristic
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×#2660C2semidirect
3. C5×#2101C2semidirect
4. C5×#2099C2semidirect
7. C5×#2085C2semidirect
8. C5×#2084C2semidirect
11. C5×#2059C2semidirect
12. C5×#2058C2semidirect
15. C5×#1840C2semidirect
59. #32844C5direct (N × H)
115. #2660C2×C5semidirect
117. #2101C2×C5semidirect
118. #2099C2×C5semidirect
121. #2085C2×C5semidirect
122. #2084C2×C5semidirect
125. #2059C2×C5semidirect
126. #2058C2×C5semidirect
129. #1840C2×C5semidirect
535. C5#32844direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26602
C5×#26442
C5×#21012
C5×#20992
C5×#20942
C5×#20922
C5×#20852
C5×#20842
C5×#20732
C5×#20712
C5×#20592
C5×#20582
C5×#20252
C5×#20232
C5×#18402
#328445