Finite Group Databasebeta

← C5×#26200 #11948920

Subgroups — C5×#26200 #11948920

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2417C211yesmaximal, characteristic
2C5×D4×C4⋊C4C211yesmaximal, characteristic
3C5×#2099C211yesmaximal, characteristic, complemented
4C5×#2077C211yesmaximal, characteristic, complemented
5C5×#2072C211yesmaximal, characteristic, complemented
6C5×#2035C211yesmaximal, characteristic, complemented
7C5×#1927C211yesmaximal, characteristic, complemented
8C5×#1920C211yesmaximal, characteristic, complemented
9C5×#1892C211yesmaximal, characteristic, complemented
10C5×#1872C211yesmaximal, characteristic, complemented
11C5×#1872C211yesmaximal, characteristic, complemented
12C5×#1869C211yesmaximal, characteristic
13C5×#1853C211yesmaximal, characteristic, complemented
14C5×#1823C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C2×C5×C22⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C4×C5×D4—21no—
20C2×C4×C5×D4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×#103C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C5×#398—21no—
34C5×#396—21no—
35C5×#391C2211yescharacteristic
36C5×#389—21no—
37C5×#389C2211yescharacteristic
38C5×#386—21no—
39C5×#385—21no—
40C5×#385—21no—
41C5×#384C2211yescharacteristic
42C5×#380—21no—
43C5×#380C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C4×C5×C4⋊C4C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#26200C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4D411yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C22×C5×C8—22no—
68C22×C5×C8—41no—
69C22×C5×C8—41no—
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C5×C22⋊Q8—22no—
75C5×C22⋊Q8—22no—
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—41no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C4×C5×D4—44no—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—22no—
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⋊C4—21no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4D411yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4D411yescharacteristic
109C2×C5×C22⋊C4D411yescharacteristic
110C2×C42×C5—21no—
111C2×C42×C5C2311yescharacteristic
112C5×#106—22no—
113C5×#106—41no—
114C5×#103—22no—
115C5×#103—41no—
116C5×#103—41no—
117C5×#103—41no—
118C5×C22⋊C8—22no—
119C5×C22⋊C8—41no—
120C5×C22⋊C8—41no—
121C5×#95—21no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128#2417C2×C511yescharacteristic
129D4×C4⋊C4C2×C511yescharacteristic
130#2099C2×C511yescharacteristic, complemented
131#2077C2×C511yescharacteristic, complemented
132#2072C2×C511yescharacteristic, complemented
133#2035C2×C511yescharacteristic, complemented
134#1927C2×C511yescharacteristic, complemented
135#1920C2×C511yescharacteristic, complemented
136#1892C2×C511yescharacteristic, complemented
137#1872C2×C511yescharacteristic, complemented
138#1872C2×C511yescharacteristic, complemented
139#1869C2×C511yescharacteristic
140#1853C2×C511yescharacteristic, complemented
141#1823C2×C511yescharacteristic, complemented
142C2×#340C2×C511yescharacteristic, complemented
143C24×C5C2×D411yescharacteristic
144C24×C5C2×D411yescharacteristic
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—21no—
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4SD1614yes—
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—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—42no—
173C22×C4×C5—42no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5—42no—
177C22×C4×C5—42no—
178C22×C4×C5—81no—
179C22×C4×C5—81no—
180C22×C4×C5—81no—
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5#4112yes—
186C22×C4×C5#4112yes—
187C22×C4×C5C2411yescharacteristic
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—44no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—42no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—81no—
221C5×C4⋊C4—81no—
222C5×C4⋊C4#4112yes—
223C5×C4⋊C4#4112yes—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—81no—
231C42×C5—21no—
232C42×C5—21no—
233C42×C5—42no—
234C23×C8C22×C511yescharacteristic
235C2×C22⋊Q8C22×C511yescharacteristic
236C2×C22⋊Q8C22×C511yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C22×C511yescharacteristic
239C22×C4⋊C4C22×C511yescharacteristic
240C22×C4⋊C4C22×C511yescharacteristic
241C22×C4⋊C4C22×C511yescharacteristic
242C2×#106C22×C511yescharacteristic
243C2×#106C22×C511yescharacteristic
244C2×#103C22×C511yescharacteristic
245C2×#103C22×C511yescharacteristic
246C2×#103C22×C511yescharacteristic
247C2×#103C22×C511yescharacteristic
248C2×C22⋊C8C22×C511yescharacteristic
249C2×C22⋊C8C22×C511yescharacteristic
250C2×C22⋊C8C22×C511yescharacteristic
251#398—21no—
252#396—21no—
253#391C22×C511yescharacteristic
254#389—21no—
255#389C22×C511yescharacteristic
256#386—21no—
257#385—21no—
258#385—21no—
259#384C22×C511yescharacteristic
260#380—21no—
261#380C22×C511yescharacteristic
262#380C22×C511yescharacteristic
263#380C22×C511yescharacteristic
264C4×C4⋊C4C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#336C22×C511yescharacteristic
276#336C22×C511yescharacteristic
277C23×C5—21no—
278C23×C5—21no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5#12312yes—
288C23×C5C2×SD1612yes—
289C23×C5C2×SD1612yes—
290C23×C5#13712yes—
291C23×C5C22×D411yescharacteristic
292C5×Q8—41no—
293C5×Q8—41no—
294C5×Q8—41no—
295C5×Q8—41no—
296C5×D4—28no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
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—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—84no—
340C2×C4×C5—84no—
341C2×C4×C5—84no—
342C2×C4×C5#12312yes—
343C2×C4×C5C2×SD1612yes—
344C2×C4×C5C2×#4111yescharacteristic
345C2×C4×C5C2×#4111yescharacteristic
346C2×C4×C5C2×#4111yescharacteristic
347C2×C4×C5C2×#4111yescharacteristic
348C2×C4×C5H(5,𝔽2)11yescharacteristic
349C2×C4×C5H(5,𝔽2)11yescharacteristic
350C5×C8—41no—
351C5×C8—41no—
352C5×C8—41no—
353C5×C8—41no—
354C22×Q8C23×C511yescharacteristic
355C22×D4C5×D411yescharacteristic
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4C23×C511yescharacteristic
360C23×C4C23×C511yescharacteristic
361C22×C8—22no—
362C22×C8—41no—
363C22×C8—41no—
364C22×C8C23×C511yescharacteristic
365C22×C8C23×C511yescharacteristic
366C22×C8C23×C511yescharacteristic
367C22×C8C23×C511yescharacteristic
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—41no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—44no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4C5×D411yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4C5×D411yescharacteristic
403C2×C22⋊C4C5×D411yescharacteristic
404C2×C42—21no—
405C2×C42C23×C511yescharacteristic
406#106—22no—
407#106—41no—
408#103—22no—
409#103—41no—
410#103—41no—
411#103—41no—
412C22⋊C8—22no—
413C22⋊C8—41no—
414C22⋊C8—41no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422C22×C5—22no—
423C22×C5—22no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5#48314yes—
436C22×C5C2×#12311yescharacteristic
437C22×C5#54611yescharacteristic
438C22×C5#54611yescharacteristic
439C22×C5C22×SD1611yescharacteristic
440C22×C5C2×#13711yescharacteristic
441C22×C5#57611yescharacteristic
442C22×C5#57811yescharacteristic
443C4×C5—22no—
444C4×C5—22no—
445C4×C5—41no—
446C4×C5—41no—
447C4×C5—42no—
448C4×C5—42no—
449C4×C5—81no—
450C4×C5—81no—
451C4×C5—81no—
452C4×C5—81no—
453C4×C5—81no—
454C4×C5—81no—
455C4×C5#52911yescharacteristic
456C4×C5#53811yescharacteristic
457C4×C5#55311yescharacteristic
458C4×C5#55311yescharacteristic
459C24C2×C5×D411yescharacteristic
460C24C2×C5×D411yescharacteristic
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4C5×SD1614yes—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4C2×C5×D411yescharacteristic
498C22×C4C2×C5×D411yescharacteristic
499C22×C4C2×C5×D411yescharacteristic
500C22×C4C2×C5×D411yescharacteristic
501C22×C4C5×#4112yes—
502C22×C4C5×#4112yes—
503C22×C4C24×C511yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—44no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4C5×#4112yes—
539C4⋊C4C5×#4112yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—42no—
550C2×C5—24no—
551C2×C5—42no—
552C2×C5#244411yescharacteristic
553C2×C5C2×#48311yescharacteristic
554C2×C5#309811yescharacteristic
555C2×C5#329511yescharacteristic
556C2×C5#329811yescharacteristic
557C2×C5#331211yescharacteristic
558C2×C5#331411yescharacteristic
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23C5×#12312yes—
570C23C2×C5×SD1612yes—
571C23C2×C5×SD1612yes—
572C23C5×#13712yes—
573C23C22×C5×D411yescharacteristic
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578D4—28no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4C5×#12312yes—
625C2×C4C2×C5×SD1612yes—
626C2×C4C2×C5×#4111yescharacteristic
627C2×C4C2×C5×#4111yescharacteristic
628C2×C4C2×C5×#4111yescharacteristic
629C2×C4C2×C5×#4111yescharacteristic
630C2×C4C5×H(5,𝔽2)11yescharacteristic
631C2×C4C5×H(5,𝔽2)11yescharacteristic
632C8—41no—
633C8—41no—
634C8—41no—
635C8—41no—
636C5#2620011yescharacteristic, direct product factor, Sylow
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22C5×#48314yes—
651C22C2×C5×#12311yescharacteristic
652C22C5×#54611yescharacteristic
653C22C5×#54611yescharacteristic
654C22C22×C5×SD1611yescharacteristic
655C22C2×C5×#13711yescharacteristic
656C22C5×#57611yescharacteristic
657C22C5×#57811yescharacteristic
658C4—22no—
659C4—22no—
660C4—42no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C5×#52911yescharacteristic
671C4C5×#53811yescharacteristic
672C4C5×#55311yescharacteristic
673C4C5×#55311yescharacteristic
674C2—24no—
675C2—42no—
676C2C5×#244411yescharacteristic
677C2C2×C5×#48311yescharacteristic
678C2C5×#309811yescharacteristic
679C2C5×#329511yescharacteristic
680C2C5×#329811yescharacteristic
681C2C5×#331211yescharacteristic
682C2C5×#331411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2099C2semidirect
4. C5×#2077C2semidirect
5. C5×#2072C2semidirect
6. C5×#2035C2semidirect
7. C5×#1927C2semidirect
8. C5×#1920C2semidirect
9. C5×#1892C2semidirect
10. C5×#1872C2semidirect
11. C5×#1872C2semidirect
13. C5×#1853C2semidirect
14. C5×#1823C2semidirect
15. C2×C5×#340C2semidirect
59. #26200C5direct (N × H)
130. #2099C2×C5semidirect
131. #2077C2×C5semidirect
132. #2072C2×C5semidirect
133. #2035C2×C5semidirect
134. #1927C2×C5semidirect
135. #1920C2×C5semidirect
136. #1892C2×C5semidirect
137. #1872C2×C5semidirect
138. #1872C2×C5semidirect
140. #1853C2×C5semidirect
141. #1823C2×C5semidirect
142. C2×#340C2×C5semidirect
636. C5#26200direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24172
C5×D4×C4⋊C42
C5×#20992
C5×#20772
C5×#20722
C5×#20352
C5×#19272
C5×#19202
C5×#18922
C5×#18722
C5×#18692
C5×#18532
C5×#18232
C2×C5×#3402
#262005