Finite Group Databasebeta

← C5×#32865 #11955585

Subgroups — C5×#32865 #11955585

Order 1280.

596 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2645C211yesmaximal, characteristic, complemented
2C5×#2644C211yesmaximal, characteristic
3C5×#2088C211yesmaximal, characteristic, complemented
4C5×#2087C211yesmaximal, characteristic, complemented
5C5×#2086C211yesmaximal, characteristic, complemented
6C5×#2068C211yesmaximal, characteristic, complemented
7C5×#2068C211yesmaximal, characteristic, complemented
8C5×#2067C211yesmaximal, characteristic
9C5×#2067C211yesmaximal, characteristic
10C5×#2066C211yesmaximal, characteristic, complemented
11C5×#2065C211yesmaximal, characteristic
12C5×#2055C211yesmaximal, characteristic
13C5×#2055C211yesmaximal, characteristic
14C5×#2055C211yesmaximal, characteristic
15C5×#1843C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C2×C5×#107C2211yescharacteristic
18C2×C5×#107C2211yescharacteristic
19C2×C5×#106C2211yescharacteristic
20C2×C5×C4⋊C8C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C5×#401—21no—
33C5×#400—21no—
34C5×#400—21no—
35C5×#400—21no—
36C5×#397—21no—
37C5×#397—21no—
38C5×#397—21no—
39C5×#396—21no—
40C5×#391C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#389C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#376C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59#32865C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4C2311yescharacteristic
62C2×C5×SD16—41no—
63C2×C5×SD16—41no—
64C2×C5×SD16—41no—
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C2×C5×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2311yescharacteristic
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4—21no—
87C2×C42×C5C2311yescharacteristic
88C2×C42×C5C2311yescharacteristic
89C2×C42×C5C2311yescharacteristic
90C5×#107—41no—
91C5×#107—41no—
92C5×#106—41no—
93C5×C4⋊C8—41no—
94C5×C4⋊C8—41no—
95C5×C4⋊C8—41no—
96C5×C4⋊C8—41no—
97C5×C4⋊C8—41no—
98C5×C4⋊C8—41no—
99C5×#103—41no—
100C5×#103—41no—
101C5×#103—41no—
102C5×#102—41no—
103C5×#102—41no—
104C5×#102—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—
115C5×#95—21no—
116C5×#95—21no—
117C5×#95D411yescharacteristic
118C5×#95D411yescharacteristic
119C5×#95D411yescharacteristic
120C5×#95D411yescharacteristic
121#2645C2×C511yescharacteristic, complemented
122#2644C2×C511yescharacteristic
123#2088C2×C511yescharacteristic, complemented
124#2087C2×C511yescharacteristic, complemented
125#2086C2×C511yescharacteristic, complemented
126#2068C2×C511yescharacteristic, complemented
127#2068C2×C511yescharacteristic, complemented
128#2067C2×C511yescharacteristic
129#2067C2×C511yescharacteristic
130#2066C2×C511yescharacteristic, complemented
131#2065C2×C511yescharacteristic
132#2055C2×C511yescharacteristic
133#2055C2×C511yescharacteristic
134#2055C2×C511yescharacteristic
135#1843C2×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×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2411yescharacteristic
163C5×SD16—44no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
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—
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—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—81no—
189C5×C4⋊C4—81no—
190C5×C4⋊C4—81no—
191C5×C4⋊C4—81no—
192C5×C4⋊C4—81no—
193C5×C4⋊C4—81no—
194C5×C22⋊C4—81no—
195C5×C22⋊C4—81no—
196C5×C22⋊C4—81no—
197C5×C22⋊C4—81no—
198C5×C22⋊C4—81no—
199C5×C22⋊C4—81no—
200C42×C5—21no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—21no—
206C22×SD16C22×C511yescharacteristic
207C2×#107C22×C511yescharacteristic
208C2×#107C22×C511yescharacteristic
209C2×#106C22×C511yescharacteristic
210C2×C4⋊C8C22×C511yescharacteristic
211C2×C4⋊C8C22×C511yescharacteristic
212C2×C4⋊C8C22×C511yescharacteristic
213C2×C4⋊C8C22×C511yescharacteristic
214C2×C4⋊C8C22×C511yescharacteristic
215C2×C4⋊C8C22×C511yescharacteristic
216C2×#103C22×C511yescharacteristic
217C2×#103C22×C511yescharacteristic
218C2×#103C22×C511yescharacteristic
219C2×#102C22×C511yescharacteristic
220C2×#102C22×C511yescharacteristic
221C2×#102C22×C511yescharacteristic
222#401—21no—
223#400—21no—
224#400—21no—
225#400—21no—
226#397—21no—
227#397—21no—
228#397—21no—
229#396—21no—
230#391C22×C511yescharacteristic
231#391C22×C511yescharacteristic
232#391C22×C511yescharacteristic
233#390C22×C511yescharacteristic
234#390C22×C511yescharacteristic
235#390C22×C511yescharacteristic
236#389C22×C511yescharacteristic
237#389C22×C511yescharacteristic
238#389C22×C511yescharacteristic
239#389C22×C511yescharacteristic
240#389C22×C511yescharacteristic
241#389C22×C511yescharacteristic
242#376C22×C511yescharacteristic
243#340C22×C511yescharacteristic
244#340C22×C511yescharacteristic
245#340C22×C511yescharacteristic
246#340C22×C511yescharacteristic
247#340C22×C511yescharacteristic
248#340C22×C511yescharacteristic
249C23×C5—41no—
250C23×C5—41no—
251C23×C5—41no—
252C23×C5—41no—
253C23×C5—41no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5C22×D411yescharacteristic
257C5×Q8—41no—
258C5×Q8—41no—
259C5×Q8—41no—
260C5×Q8—41no—
261C5×D4—41no—
262C5×D4—41no—
263C5×D4—41no—
264C5×D4—41no—
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—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—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×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5H(5,𝔽2)11yescharacteristic
305C2×C4×C5H(5,𝔽2)11yescharacteristic
306C2×C4×C5H(5,𝔽2)11yescharacteristic
307C2×C4×C52−1+411yescharacteristic
308C2×C4×C52−1+411yescharacteristic
309C2×C4×C52−1+411yescharacteristic
310C5×C8—41no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C22×Q8C23×C511yescharacteristic
315C22×D4C23×C511yescharacteristic
316C2×SD16—41no—
317C2×SD16—41no—
318C2×SD16—41no—
319C22×C8C23×C511yescharacteristic
320C22×C8C23×C511yescharacteristic
321C22×C8C23×C511yescharacteristic
322C22×C8C23×C511yescharacteristic
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⋊C4C23×C511yescharacteristic
330C2×C4⋊C4C23×C511yescharacteristic
331C2×C4⋊C4C23×C511yescharacteristic
332C2×C4⋊C4C23×C511yescharacteristic
333C2×C4⋊C4C23×C511yescharacteristic
334C2×C4⋊C4C23×C511yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C42C23×C511yescharacteristic
342C2×C42C23×C511yescharacteristic
343C2×C42C23×C511yescharacteristic
344#107—41no—
345#107—41no—
346#106—41no—
347C4⋊C8—41no—
348C4⋊C8—41no—
349C4⋊C8—41no—
350C4⋊C8—41no—
351C4⋊C8—41no—
352C4⋊C8—41no—
353#103—41no—
354#103—41no—
355#103—41no—
356#102—41no—
357#102—41no—
358#102—41no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95C5×D411yescharacteristic
372#95C5×D411yescharacteristic
373#95C5×D411yescharacteristic
374#95C5×D411yescharacteristic
375C22×C5—81no—
376C22×C5—81no—
377C22×C5—81no—
378C22×C5—81no—
379C22×C5—81no—
380C22×C5—81no—
381C22×C5—81no—
382C22×C5#53711yescharacteristic
383C22×C5#53711yescharacteristic
384C22×C5#53711yescharacteristic
385C22×C5#57611yescharacteristic
386C22×C5#57711yescharacteristic
387C22×C5#57711yescharacteristic
388C22×C5#57811yescharacteristic
389C4×C5—41no—
390C4×C5—41no—
391C4×C5—41no—
392C4×C5—41no—
393C4×C5—41no—
394C4×C5—41no—
395C4×C5—81no—
396C4×C5—81no—
397C4×C5—81no—
398C4×C5—81no—
399C4×C5—81no—
400C4×C5—81no—
401C4×C5—81no—
402C4×C5#56011yescharacteristic
403C4×C5#56311yescharacteristic
404C4×C5#56311yescharacteristic
405C4×C5#56311yescharacteristic
406C24—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4C2×C5×D411yescharacteristic
427C22×C4C2×C5×D411yescharacteristic
428C22×C4C2×C5×D411yescharacteristic
429C22×C4C2×C5×D411yescharacteristic
430C22×C4C2×C5×D411yescharacteristic
431C22×C4C2×C5×D411yescharacteristic
432C22×C4C24×C511yescharacteristic
433SD16—44no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C22⋊C4—81no—
467C22⋊C4—81no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C2×C5—161no—
477C2×C5#282311yescharacteristic
478C2×C5#325711yescharacteristic
479C2×C5#325711yescharacteristic
480C2×C5#325811yescharacteristic
481C2×C5#325811yescharacteristic
482C2×C5#326011yescharacteristic
483C2×C5#326211yescharacteristic
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×C5×D411yescharacteristic
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
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—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×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×C4C5×H(5,𝔽2)11yescharacteristic
540C2×C4C5×H(5,𝔽2)11yescharacteristic
541C2×C4C5×H(5,𝔽2)11yescharacteristic
542C2×C4C5×2−1+411yescharacteristic
543C2×C4C5×2−1+411yescharacteristic
544C2×C4C5×2−1+411yescharacteristic
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C5#3286511yescharacteristic, direct product factor, Sylow
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C5×#53711yescharacteristic
558C22C5×#53711yescharacteristic
559C22C5×#53711yescharacteristic
560C22C5×#57611yescharacteristic
561C22C5×#57711yescharacteristic
562C22C5×#57711yescharacteristic
563C22C5×#57811yescharacteristic
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C5×#56011yescharacteristic
578C4C5×#56311yescharacteristic
579C4C5×#56311yescharacteristic
580C4C5×#56311yescharacteristic
581C2—161no—
582C2C5×#282311yescharacteristic
583C2C5×#325711yescharacteristic
584C2C5×#325711yescharacteristic
585C2C5×#325811yescharacteristic
586C2C5×#325811yescharacteristic
587C2C5×#326011yescharacteristic
588C2C5×#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×#2645C2semidirect
3. C5×#2088C2semidirect
4. C5×#2087C2semidirect
5. C5×#2086C2semidirect
6. C5×#2068C2semidirect
7. C5×#2068C2semidirect
10. C5×#2066C2semidirect
15. C5×#1843C2semidirect
59. #32865C5direct (N × H)
121. #2645C2×C5semidirect
123. #2088C2×C5semidirect
124. #2087C2×C5semidirect
125. #2086C2×C5semidirect
126. #2068C2×C5semidirect
127. #2068C2×C5semidirect
130. #2066C2×C5semidirect
135. #1843C2×C5semidirect
549. C5#32865direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26452
C5×#26442
C5×#20882
C5×#20872
C5×#20862
C5×#20682
C5×#20672
C5×#20662
C5×#20652
C5×#20552
C5×#18432
#328655