Finite Group Databasebeta

← C5×#26079 #11948799

Subgroups — C5×#26079 #11948799

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#501C211yesmaximal, characteristic, complemented
2C2×C5×#428C211yesmaximal, characteristic
3C5×#2442C211yesmaximal, characteristic
4C5×#2439C211yesmaximal, characteristic
5C5×#2085C211yesmaximal, characteristic, complemented
6C5×#2085C211yesmaximal, characteristic, complemented
7C5×#2059C211yesmaximal, characteristic, complemented
8C5×#2057C211yesmaximal, characteristic, complemented
9C5×#1943C211yesmaximal, characteristic, complemented
10C5×#1942C211yesmaximal, characteristic, complemented
11C5×#1854C211yesmaximal, characteristic
12C5×#1852C211yesmaximal, characteristic
13C5×#1846C211yesmaximal, characteristic, complemented
14C5×#1809C211yesmaximal, characteristic
15C5×#1753C211yesmaximal, characteristic
16C22×C5×M16C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×#125C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C5×#501—24no—
22C5×#428—24no—
23C2×C5×#107C2211yescharacteristic
24C2×C5×#107C2211yescharacteristic
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×#106C2211yescharacteristic
32C2×C5×#106C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C2×C5×#97C2211yescharacteristic
35C2×C4×C5×C8C2211yescharacteristic
36C5×#400—21no—
37C5×#398—21no—
38C5×#396—21no—
39C5×#393—21no—
40C5×#391—21no—
41C5×#389C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#387—21no—
46C5×#385—21no—
47C5×#382C2211yescharacteristic
48C5×#382C2211yescharacteristic
49C5×#380—21no—
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26079C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8—21no—
63C23×C4×C5—21no—
64C23×C4×C5C2311yescharacteristic
65C2×C5×M16—22no—
66C2×C5×M16—22no—
67C2×C5×M16Q814yescomplemented
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C5×C4⋊Q8—22no—
73C5×C4⋊Q8—41no—
74C5×#125—22no—
75C5×#125—41no—
76C5×#117—22no—
77C5×#117—41no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
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—41no—
88C2×C5×C4⋊C4C2311yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4D411yescharacteristic
100C2×C5×C22⋊C4D411yescharacteristic
101C2×C42×C5—21no—
102C2×C42×C5C2311yescharacteristic
103C2×C42×C5C2311yescharacteristic
104C5×#107—22no—
105C5×#107—22no—
106C5×#107—22no—
107C5×#107—41no—
108C5×#107—41no—
109C5×#107D414yes—
110C5×#106—22no—
111C5×#106—22no—
112C5×#106—22no—
113C5×#106—22no—
114C5×C22⋊C8Q814yescomplemented
115C5×#97—22no—
116C4×C5×C8—22no—
117C5×#95—21no—
118C5×#95—21no—
119C5×#95—21no—
120C5×#95—21no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95D411yescharacteristic
128C5×#95D411yescharacteristic
129C2×#501C2×C511yescharacteristic, complemented
130C2×#428C2×C511yescharacteristic
131#2442C2×C511yescharacteristic
132#2439C2×C511yescharacteristic
133#2085C2×C511yescharacteristic, complemented
134#2085C2×C511yescharacteristic, complemented
135#2059C2×C511yescharacteristic, complemented
136#2057C2×C511yescharacteristic, complemented
137#1943C2×C511yescharacteristic, complemented
138#1942C2×C511yescharacteristic, complemented
139#1854C2×C511yescharacteristic
140#1852C2×C511yescharacteristic
141#1846C2×C511yescharacteristic, complemented
142#1809C2×C511yescharacteristic
143#1753C2×C511yescharacteristic
144C24×C5C2×D411yescharacteristic
145C2×C5×Q8—42no—
146C2×C5×Q8—42no—
147C2×C5×Q8—81no—
148C22×C4×C5—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×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—42no—
161C22×C4×C5—42no—
162C22×C4×C5—81no—
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×Q812yes—
169C22×C4×C5C2×Q812yes—
170C22×C4×C5C2411yescharacteristic
171C5×M16—28no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C2×D412yes—
179C2×C5×C8C2×Q812yes—
180C2×C5×C8C2×Q812yes—
181C2×C5×C8C2×Q812yes—
182C2×C5×C8C2×Q812yes—
183C2×C5×C8#4112yes—
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—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—42no—
199C5×C4⋊C4—42no—
200C5×C4⋊C4—42no—
201C5×C4⋊C4—42no—
202C5×C4⋊C4—42no—
203C5×C4⋊C4—81no—
204C5×C4⋊C4—81no—
205C5×C4⋊C4—81no—
206C5×C4⋊C4C2×D412yes—
207C5×C4⋊C4C2×D412yes—
208C5×C22⋊C4—41no—
209C5×C22⋊C4—41no—
210C5×C22⋊C4—42no—
211C5×C22⋊C4—42no—
212C5×C22⋊C4—81no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5—21no—
216C42×C5—21no—
217C42×C5—42no—
218C22×M16C22×C511yescharacteristic
219C2×C4⋊Q8C22×C511yescharacteristic
220C2×#125C22×C511yescharacteristic
221C2×#117C22×C511yescharacteristic
222C22×C4⋊C4C22×C511yescharacteristic
223#501—24no—
224#428—24no—
225C2×#107C22×C511yescharacteristic
226C2×#107C22×C511yescharacteristic
227C2×#107C22×C511yescharacteristic
228C2×#107C22×C511yescharacteristic
229C2×#107C22×C511yescharacteristic
230C2×#107C22×C511yescharacteristic
231C2×#106C22×C511yescharacteristic
232C2×#106C22×C511yescharacteristic
233C2×#106C22×C511yescharacteristic
234C2×#106C22×C511yescharacteristic
235C2×C22⋊C8C22×C511yescharacteristic
236C2×#97C22×C511yescharacteristic
237C2×C4×C8C22×C511yescharacteristic
238#400—21no—
239#398—21no—
240#396—21no—
241#393—21no—
242#391—21no—
243#389C22×C511yescharacteristic
244#389C22×C511yescharacteristic
245#389C22×C511yescharacteristic
246#389C22×C511yescharacteristic
247#387—21no—
248#385—21no—
249#382C22×C511yescharacteristic
250#382C22×C511yescharacteristic
251#380—21no—
252#380C22×C511yescharacteristic
253#380C22×C511yescharacteristic
254C4×C22⋊C4C22×C511yescharacteristic
255#340C22×C511yescharacteristic
256#340C22×C511yescharacteristic
257#340C22×C511yescharacteristic
258#340C22×C511yescharacteristic
259#340C22×C511yescharacteristic
260#340C22×C511yescharacteristic
261#336C22×C511yescharacteristic
262#336C22×C511yescharacteristic
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5C4⋊Q812yes—
270C23×C5C22×D411yescharacteristic
271C5×Q8—84no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
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×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—84no—
315C2×C4×C5C4⋊Q812yes—
316C2×C4×C5C22×D411yescharacteristic
317C2×C4×C5C22×Q811yescharacteristic
318C2×C4×C5C22×Q811yescharacteristic
319C2×C4×C5C2×#4111yescharacteristic
320C2×C4×C5H(5,𝔽2)11yescharacteristic
321C2×C4×C52−1+411yescharacteristic
322C5×C8—22no—
323C5×C8—22no—
324C5×C8—22no—
325C5×C8C22⋊Q814yes—
326C22×Q8—21no—
327C23×C4—21no—
328C23×C4C23×C511yescharacteristic
329C2×M16—22no—
330C2×M16—22no—
331C2×M16C5×Q814yescomplemented
332C22×C8C23×C511yescharacteristic
333C22×C8C23×C511yescharacteristic
334C22×C8C23×C511yescharacteristic
335C22×C8C23×C511yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—41no—
338#125—22no—
339#125—41no—
340#117—22no—
341#117—41no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4C23×C511yescharacteristic
353C2×C4⋊C4C23×C511yescharacteristic
354C2×C4⋊C4C23×C511yescharacteristic
355C2×C4⋊C4C23×C511yescharacteristic
356C2×C4⋊C4C23×C511yescharacteristic
357C2×C4⋊C4C23×C511yescharacteristic
358C2×C4⋊C4C23×C511yescharacteristic
359C2×C4⋊C4C23×C511yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4C5×D411yescharacteristic
364C2×C22⋊C4C5×D411yescharacteristic
365C2×C42—21no—
366C2×C42C23×C511yescharacteristic
367C2×C42C23×C511yescharacteristic
368#107—22no—
369#107—22no—
370#107—22no—
371#107—41no—
372#107—41no—
373#107C5×D414yes—
374#106—22no—
375#106—22no—
376#106—22no—
377#106—22no—
378C22⋊C8C5×Q814yescomplemented
379#97—22no—
380C4×C8—22no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95C5×D411yescharacteristic
392#95C5×D411yescharacteristic
393C22×C5—22no—
394C22×C5—22no—
395C22×C5—22no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×C4⋊Q811yescharacteristic
401C22×C5D4211yescharacteristic
402C22×C5#54711yescharacteristic
403C22×C5#57511yescharacteristic
404C22×C5#57511yescharacteristic
405C22×C5#57611yescharacteristic
406C22×C5#57811yescharacteristic
407C4×C5—22no—
408C4×C5—41no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—42no—
412C4×C5—42no—
413C4×C5—41no—
414C4×C5—81no—
415C4×C5—81no—
416C4×C5—81no—
417C4×C5—81no—
418C4×C5—81no—
419C4×C5—81no—
420C4×C5C2×C22⋊Q811yescharacteristic
421C4×C5#54411yescharacteristic
422C4×C5D4×Q811yescharacteristic
423C4×C5#55411yescharacteristic
424C24C2×C5×D411yescharacteristic
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—81no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—81no—
443C22×C4C2×C5×D411yescharacteristic
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C2×C5×D411yescharacteristic
447C22×C4C2×C5×D411yescharacteristic
448C22×C4C2×C5×Q812yes—
449C22×C4C2×C5×Q812yes—
450C22×C4C24×C511yescharacteristic
451M16—28no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×C5×D412yes—
459C2×C8C2×C5×Q812yes—
460C2×C8C2×C5×Q812yes—
461C2×C8C2×C5×Q812yes—
462C2×C8C2×C5×Q812yes—
463C2×C8C5×#4112yes—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4C2×C5×D412yes—
487C4⋊C4C2×C5×D412yes—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—81no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C2×C5—42no—
499C2×C5#244011yescharacteristic
500C2×C5#316411yescharacteristic
501C2×C5#316611yescharacteristic
502C2×C5#327311yescharacteristic
503C2×C5#327711yescharacteristic
504C2×C5#334711yescharacteristic
505C2×C5#334911yescharacteristic
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23C5×C4⋊Q812yes—
513C23C22×C5×D411yescharacteristic
514Q8—84no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
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×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4C5×C4⋊Q812yes—
559C2×C4C22×C5×D411yescharacteristic
560C2×C4C22×C5×Q811yescharacteristic
561C2×C4C22×C5×Q811yescharacteristic
562C2×C4C2×C5×#4111yescharacteristic
563C2×C4C5×H(5,𝔽2)11yescharacteristic
564C2×C4C5×2−1+411yescharacteristic
565C8—22no—
566C8—22no—
567C8—22no—
568C8C5×C22⋊Q814yes—
569C5#2607911yescharacteristic, direct product factor, Sylow
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×C5×C4⋊Q811yescharacteristic
578C22C5×D4211yescharacteristic
579C22C5×#54711yescharacteristic
580C22C5×#57511yescharacteristic
581C22C5×#57511yescharacteristic
582C22C5×#57611yescharacteristic
583C22C5×#57811yescharacteristic
584C4—22no—
585C4—41no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C2×C5×C22⋊Q811yescharacteristic
598C4C5×#54411yescharacteristic
599C4C5×D4×Q811yescharacteristic
600C4C5×#55411yescharacteristic
601C2—42no—
602C2C5×#244011yescharacteristic
603C2C5×#316411yescharacteristic
604C2C5×#316611yescharacteristic
605C2C5×#327311yescharacteristic
606C2C5×#327711yescharacteristic
607C2C5×#334711yescharacteristic
608C2C5×#334911yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#501C2semidirect
5. C5×#2085C2semidirect
6. C5×#2085C2semidirect
7. C5×#2059C2semidirect
8. C5×#2057C2semidirect
9. C5×#1943C2semidirect
10. C5×#1942C2semidirect
13. C5×#1846C2semidirect
61. #26079C5direct (N × H)
67. C2×C5×M16Q8semidirect
114. C5×C22⋊C8Q8semidirect
129. C2×#501C2×C5semidirect
133. #2085C2×C5semidirect
134. #2085C2×C5semidirect
135. #2059C2×C5semidirect
136. #2057C2×C5semidirect
137. #1943C2×C5semidirect
138. #1942C2×C5semidirect
141. #1846C2×C5semidirect
331. C2×M16C5×Q8semidirect
378. C22⋊C8C5×Q8semidirect
569. C5#26079direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5012
C2×C5×#4282
C5×#24422
C5×#24392
C5×#20852
C5×#20592
C5×#20572
C5×#19432
C5×#19422
C5×#18542
C5×#18522
C5×#18462
C5×#18092
C5×#17532
#260795