Finite Group Databasebeta

← C5×#26399 #11949119

Subgroups — C5×#26399 #11949119

Order 1280.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#479C211yesmaximal, characteristic, complemented
2C2×C5×#440C211yesmaximal, characteristic
3C5×#2454C211yesmaximal, characteristic
4C5×#2351C211yesmaximal, characteristic, complemented
5C5×#2092C211yesmaximal, characteristic
6C5×#2085C211yesmaximal, characteristic, complemented
7C5×#2065C211yesmaximal, characteristic
8C5×#2059C211yesmaximal, characteristic, complemented
9C5×#1944C211yesmaximal, characteristic, complemented
10C5×#1917C211yesmaximal, characteristic, complemented
11C5×#1880C211yesmaximal, characteristic
12C5×#1880C211yesmaximal, characteristic
13C5×#1865C211yesmaximal, characteristic, complemented
14C5×#1865C211yesmaximal, characteristic, complemented
15C5×#1864C211yesmaximal, characteristic
16C22×C5×SD16C2211yescharacteristic
17C2×C5×#125C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C5×#479—24no—
23C5×#440—24no—
24C2×C5×#107C2211yescharacteristic
25C2×C5×#107C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#97C2211yescharacteristic
37C5×#399—21no—
38C5×#396—21no—
39C5×#390C2211yescharacteristic
40C5×#390C2211yescharacteristic
41C5×#389—21no—
42C5×#389—21no—
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#385—21no—
48C5×#382—21no—
49C5×#382C2211yescharacteristic
50C5×#380—21no—
51C4×C5×C4⋊C4—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26399C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×D4C2311yescharacteristic
64C23×C4×C5—21no—
65C2×C5×SD16—22no—
66C2×C5×SD16—22no—
67C2×C5×SD16Q814yes—
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C5×#125—22no—
73C5×#125—41no—
74C4×C5×Q8—22no—
75C4×C5×Q8—22no—
76C4×C5×Q8—22no—
77C4×C5×Q8—22no—
78C4×C5×Q8—41no—
79C4×C5×Q8—41no—
80C4×C5×D4—22no—
81C4×C5×D4—41no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4D411yescharacteristic
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C42×C5—21no—
105C2×C42×C5—21no—
106C2×C42×C5—21no—
107C2×C42×C5C2311yescharacteristic
108C2×C42×C5C2311yescharacteristic
109C2×C42×C5C2311yescharacteristic
110C5×#107—22no—
111C5×#107—22no—
112C5×#106—22no—
113C5×#106—22no—
114C5×#106—41no—
115C5×C4⋊C8—22no—
116C5×#103—22no—
117C5×#103—22no—
118C5×#103D414yes—
119C5×#102—22no—
120C5×#102—22no—
121C5×#102—41no—
122C5×#97—22no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95D411yescharacteristic
130C5×#95D411yescharacteristic
131C2×#479C2×C511yescharacteristic, complemented
132C2×#440C2×C511yescharacteristic
133#2454C2×C511yescharacteristic
134#2351C2×C511yescharacteristic, complemented
135#2092C2×C511yescharacteristic
136#2085C2×C511yescharacteristic, complemented
137#2065C2×C511yescharacteristic
138#2059C2×C511yescharacteristic, complemented
139#1944C2×C511yescharacteristic, complemented
140#1917C2×C511yescharacteristic, complemented
141#1880C2×C511yescharacteristic
142#1880C2×C511yescharacteristic
143#1865C2×C511yescharacteristic, complemented
144#1865C2×C511yescharacteristic, complemented
145#1864C2×C511yescharacteristic
146C24×C5—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8C2×D412yes—
151C2×C5×Q8C2×Q812yes—
152C2×C5×Q8#4112yes—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4C2×Q812yes—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—42no—
167C22×C4×C5—42no—
168C22×C4×C5—81no—
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2411yescharacteristic
176C5×SD16—28no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8C2×D412yes—
188C2×C5×C8C2×Q812yes—
189C5×C4⋊C4—24no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—41no—
201C5×C4⋊C4—41no—
202C5×C4⋊C4—42no—
203C5×C4⋊C4—42no—
204C5×C4⋊C4—42no—
205C5×C4⋊C4—42no—
206C5×C4⋊C4—42no—
207C5×C4⋊C4—42no—
208C5×C4⋊C4—81no—
209C5×C4⋊C4—81no—
210C5×C4⋊C4C2×D412yes—
211C5×C4⋊C4#4112yes—
212C5×C22⋊C4—42no—
213C5×C22⋊C4—42no—
214C5×C22⋊C4—81no—
215C5×C22⋊C4—81no—
216C5×C22⋊C4—81no—
217C42×C5—24no—
218C42×C5—21no—
219C42×C5—21no—
220C42×C5—21no—
221C42×C5—21no—
222C42×C5—21no—
223C42×C5—21no—
224C42×C5—42no—
225C42×C5—42no—
226C22×SD16C22×C511yescharacteristic
227C2×#125C22×C511yescharacteristic
228C2×C4×Q8C22×C511yescharacteristic
229C2×C4×Q8C22×C511yescharacteristic
230C2×C4×Q8C22×C511yescharacteristic
231C2×C4×D4C22×C511yescharacteristic
232#479—24no—
233#440—24no—
234C2×#107C22×C511yescharacteristic
235C2×#107C22×C511yescharacteristic
236C2×#106C22×C511yescharacteristic
237C2×#106C22×C511yescharacteristic
238C2×#106C22×C511yescharacteristic
239C2×C4⋊C8C22×C511yescharacteristic
240C2×#103C22×C511yescharacteristic
241C2×#103C22×C511yescharacteristic
242C2×#103C22×C511yescharacteristic
243C2×#102C22×C511yescharacteristic
244C2×#102C22×C511yescharacteristic
245C2×#102C22×C511yescharacteristic
246C2×#97C22×C511yescharacteristic
247#399—21no—
248#396—21no—
249#390C22×C511yescharacteristic
250#390C22×C511yescharacteristic
251#389—21no—
252#389—21no—
253#389C22×C511yescharacteristic
254#389C22×C511yescharacteristic
255#389C22×C511yescharacteristic
256#389C22×C511yescharacteristic
257#385—21no—
258#382—21no—
259#382C22×C511yescharacteristic
260#380—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4C22×C511yescharacteristic
263#340C22×C511yescharacteristic
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#336C22×C511yescharacteristic
268#336C22×C511yescharacteristic
269#336C22×C511yescharacteristic
270#336C22×C511yescharacteristic
271C23×C5—22no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5C22×D411yescharacteristic
279C5×Q8—22no—
280C5×Q8—22no—
281C5×Q8—22no—
282C5×Q8C22⋊Q814yes—
283C5×D4—22no—
284C5×D4—22no—
285C5×D4—41no—
286C5×D4—41no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—84no—
327C2×C4×C5C22×D411yescharacteristic
328C2×C4×C5C22×Q811yescharacteristic
329C2×C4×C5C2×#4111yescharacteristic
330C2×C4×C5C2×#4111yescharacteristic
331C2×C4×C5H(5,𝔽2)11yescharacteristic
332C2×C4×C52−1+411yescharacteristic
333C5×C8—22no—
334C5×C8—22no—
335C5×C8—41no—
336C5×C8—41no—
337C22×Q8C23×C511yescharacteristic
338C22×D4C23×C511yescharacteristic
339C23×C4—21no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16C5×Q814yes—
343C22×C8C23×C511yescharacteristic
344C22×C8C23×C511yescharacteristic
345C22×C8C23×C511yescharacteristic
346C22×C8C23×C511yescharacteristic
347#125—22no—
348#125—41no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—41no—
354C4×Q8—41no—
355C4×D4—22no—
356C4×D4—41no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C5×D411yescharacteristic
367C2×C4⋊C4C5×D411yescharacteristic
368C2×C4⋊C4C23×C511yescharacteristic
369C2×C4⋊C4C23×C511yescharacteristic
370C2×C4⋊C4C23×C511yescharacteristic
371C2×C4⋊C4C23×C511yescharacteristic
372C2×C4⋊C4C23×C511yescharacteristic
373C2×C4⋊C4C23×C511yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C23×C511yescharacteristic
383C2×C42C23×C511yescharacteristic
384C2×C42C23×C511yescharacteristic
385#107—22no—
386#107—22no—
387#106—22no—
388#106—22no—
389#106—41no—
390C4⋊C8—22no—
391#103—22no—
392#103—22no—
393#103C5×D414yes—
394#102—22no—
395#102—22no—
396#102—41no—
397#97—22no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95C5×D411yescharacteristic
405#95C5×D411yescharacteristic
406C22×C5—42no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—81no—
410C22×C5—81no—
411C22×C5—81no—
412C22×C5—81no—
413C22×C5#52511yescharacteristic
414C22×C5D4211yescharacteristic
415C22×C5D4×Q811yescharacteristic
416C22×C5#57511yescharacteristic
417C22×C5#57511yescharacteristic
418C22×C5#57711yescharacteristic
419C22×C5#57711yescharacteristic
420C4×C5—24no—
421C4×C5—41no—
422C4×C5—42no—
423C4×C5—41no—
424C4×C5—41no—
425C4×C5—41no—
426C4×C5—41no—
427C4×C5—41no—
428C4×C5—42no—
429C4×C5—81no—
430C4×C5—81no—
431C4×C5—81no—
432C4×C5—81no—
433C4×C5C2×C22⋊Q811yescharacteristic
434C4×C5#53911yescharacteristic
435C4×C5#54711yescharacteristic
436C4×C5#55411yescharacteristic
437C24—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C5×D412yes—
442C2×Q8C2×C5×Q812yes—
443C2×Q8C5×#4112yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×C5×Q812yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4C2×C5×D411yescharacteristic
461C22×C4C2×C5×D411yescharacteristic
462C22×C4C2×C5×D411yescharacteristic
463C22×C4C2×C5×D411yescharacteristic
464C22×C4C2×C5×D411yescharacteristic
465C22×C4C2×C5×D411yescharacteristic
466C22×C4C24×C511yescharacteristic
467SD16—28no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8C2×C5×D412yes—
479C2×C8C2×C5×Q812yes—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4C2×C5×D412yes—
502C4⋊C4C5×#4112yes—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C42—24no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—42no—
517C2×C5—82no—
518C2×C5#244911yescharacteristic
519C2×C5#311111yescharacteristic
520C2×C5#312611yescharacteristic
521C2×C5#327111yescharacteristic
522C2×C5#327511yescharacteristic
523C2×C5#338811yescharacteristic
524C2×C5#338811yescharacteristic
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×C5×D411yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8C5×C22⋊Q814yes—
537D4—22no—
538D4—22no—
539D4—41no—
540D4—41no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4C22×C5×D411yescharacteristic
582C2×C4C22×C5×Q811yescharacteristic
583C2×C4C2×C5×#4111yescharacteristic
584C2×C4C2×C5×#4111yescharacteristic
585C2×C4C5×H(5,𝔽2)11yescharacteristic
586C2×C4C5×2−1+411yescharacteristic
587C8—22no—
588C8—22no—
589C8—41no—
590C8—41no—
591C5#2639911yescharacteristic, direct product factor, Sylow
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22C5×#52511yescharacteristic
600C22C5×D4211yescharacteristic
601C22C5×D4×Q811yescharacteristic
602C22C5×#57511yescharacteristic
603C22C5×#57511yescharacteristic
604C22C5×#57711yescharacteristic
605C22C5×#57711yescharacteristic
606C4—24no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4C2×C5×C22⋊Q811yescharacteristic
620C4C5×#53911yescharacteristic
621C4C5×#54711yescharacteristic
622C4C5×#55411yescharacteristic
623C2—82no—
624C2C5×#244911yescharacteristic
625C2C5×#311111yescharacteristic
626C2C5×#312611yescharacteristic
627C2C5×#327111yescharacteristic
628C2C5×#327511yescharacteristic
629C2C5×#338811yescharacteristic
630C2C5×#338811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#479C2semidirect
4. C5×#2351C2semidirect
6. C5×#2085C2semidirect
8. C5×#2059C2semidirect
9. C5×#1944C2semidirect
10. C5×#1917C2semidirect
13. C5×#1865C2semidirect
14. C5×#1865C2semidirect
61. #26399C5direct (N × H)
131. C2×#479C2×C5semidirect
134. #2351C2×C5semidirect
136. #2085C2×C5semidirect
138. #2059C2×C5semidirect
139. #1944C2×C5semidirect
140. #1917C2×C5semidirect
143. #1865C2×C5semidirect
144. #1865C2×C5semidirect
591. C5#26399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4792
C2×C5×#4402
C5×#24542
C5×#23512
C5×#20922
C5×#20852
C5×#20652
C5×#20592
C5×#19442
C5×#19172
C5×#18802
C5×#18652
C5×#18642
#263995