Finite Group Databasebeta

← C5×#25202 #11947922

Subgroups — C5×#25202 #11947922

Order 1280.

942 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#481C211yesmaximal, characteristic
2C2×C5×#465C211yesmaximal, characteristic
3C5×#2502C211yesmaximal, characteristic, complemented
4C5×#2361C211yesmaximal, characteristic
5C5×#2084C211yesmaximal, characteristic, complemented
6C5×#2071C211yesmaximal, characteristic, complemented
7C5×#2066C211yesmaximal, characteristic, complemented
8C5×#2055C211yesmaximal, characteristic, complemented
9C5×#1948C211yesmaximal, characteristic, complemented
10C5×#1927C211yesmaximal, characteristic, complemented
11C5×#1877C211yesmaximal, characteristic, complemented
12C5×#1872C211yesmaximal, characteristic, complemented
13C5×#1850C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#481—24no—
25C5×#465—24no—
26C2×C5×#106C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C5×#398—21no—
39C5×#398—21no—
40C5×#391C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#388—21no—
45C5×#386—21no—
46C5×#385—21no—
47C5×#385—21no—
48C5×#385—21no—
49C5×#384C2211yescharacteristic
50C5×#384C2211yescharacteristic
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25202C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×D4—21no—
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C2×C5×SD16—22no—
70C2×C5×SD16—22no—
71C2×C5×SD16—41no—
72C22×C5×C8—22no—
73C22×C5×C8—22no—
74C22×C5×C8—41no—
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C5×C22⋊Q8—22no—
80C5×C22⋊Q8—22no—
81C5×#121—22no—
82C5×#121D414yes—
83C4×C5×D4—22no—
84C4×C5×D4—41no—
85C4×C5×D4—44no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—41no—
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4D411yescharacteristic
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C42×C5—21no—
112C2×C42×C5C2311yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C5×#106—22no—
115C5×#106—22no—
116C5×#106—22no—
117C5×C4⋊C8—22no—
118C5×C4⋊C8—41no—
119C5×#103—22no—
120C5×#103—22no—
121C5×#103—41no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×C22⋊C8—22no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95D411yescharacteristic
133C5×#95D411yescharacteristic
134C2×#481C2×C511yescharacteristic
135C2×#465C2×C511yescharacteristic
136#2502C2×C511yescharacteristic, complemented
137#2361C2×C511yescharacteristic
138#2084C2×C511yescharacteristic, complemented
139#2071C2×C511yescharacteristic, complemented
140#2066C2×C511yescharacteristic, complemented
141#2055C2×C511yescharacteristic, complemented
142#1948C2×C511yescharacteristic, complemented
143#1927C2×C511yescharacteristic, complemented
144#1877C2×C511yescharacteristic, complemented
145#1872C2×C511yescharacteristic, complemented
146#1850C2×C511yescharacteristic, complemented
147#1802C2×C511yescharacteristic, complemented
148C2×#340C2×C511yescharacteristic, complemented
149C24×C5—21no—
150C24×C5C2×D411yescharacteristic
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×D4—24no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—42no—
164C2×C5×D4—42no—
165C2×C5×D4C2×D412yes—
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—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—42no—
180C22×C4×C5—42no—
181C22×C4×C5—42no—
182C22×C4×C5—81no—
183C22×C4×C5—81no—
184C22×C4×C5—81no—
185C22×C4×C5—81no—
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D412yes—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5#4112yes—
193C22×C4×C5C2411yescharacteristic
194C5×SD16—44no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—44no—
207C2×C5×C8#4112yes—
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—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—81no—
223C5×C4⋊C4—81no—
224C5×C4⋊C4—81no—
225C5×C4⋊C4—81no—
226C5×C4⋊C4C2×D412yes—
227C5×C4⋊C4#4112yes—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—24no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—81no—
234C5×C22⋊C4SD1614yescomplemented
235C42×C5—21no—
236C42×C5—21no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—42no—
240C22×SD16C22×C511yescharacteristic
241C23×C8C22×C511yescharacteristic
242C2×C22⋊Q8C22×C511yescharacteristic
243C2×#121C22×C511yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C22×C511yescharacteristic
246C22×C4⋊C4C22×C511yescharacteristic
247C22×C4⋊C4C22×C511yescharacteristic
248#481—24no—
249#465—24no—
250C2×#106C22×C511yescharacteristic
251C2×#106C22×C511yescharacteristic
252C2×#106C22×C511yescharacteristic
253C2×C4⋊C8C22×C511yescharacteristic
254C2×C4⋊C8C22×C511yescharacteristic
255C2×#103C22×C511yescharacteristic
256C2×#103C22×C511yescharacteristic
257C2×#103C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×C22⋊C8C22×C511yescharacteristic
262#398—21no—
263#398—21no—
264#391C22×C511yescharacteristic
265#391C22×C511yescharacteristic
266#390C22×C511yescharacteristic
267#389C22×C511yescharacteristic
268#388—21no—
269#386—21no—
270#385—21no—
271#385—21no—
272#385—21no—
273#384C22×C511yescharacteristic
274#384C22×C511yescharacteristic
275C4×C4⋊C4C22×C511yescharacteristic
276C4×C22⋊C4C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#336C22×C511yescharacteristic
284#336C22×C511yescharacteristic
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—22no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5#12112yes—
297C23×C5C2×SD1612yes—
298C23×C5#13712yes—
299C23×C5C22×D411yescharacteristic
300C5×Q8—41no—
301C5×Q8—41no—
302C5×Q8—41no—
303C5×Q8—41no—
304C5×D4—22no—
305C5×D4—22no—
306C5×D4—48no—
307C5×D4—41no—
308C5×D4—41no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—22no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
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—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—84no—
347C2×C4×C5—84no—
348C2×C4×C5—84no—
349C2×C4×C5#12112yes—
350C2×C4×C5C2×SD1612yes—
351C2×C4×C5C2×SD1612yes—
352C2×C4×C5C22×D411yescharacteristic
353C2×C4×C5C2×#4111yescharacteristic
354C2×C4×C5C2×#4111yescharacteristic
355C2×C4×C5C2×#4111yescharacteristic
356C2×C4×C5H(5,𝔽2)11yescharacteristic
357C2×C4×C52−1+411yescharacteristic
358C5×C8—22no—
359C5×C8—41no—
360C5×C8—41no—
361C5×C8—41no—
362C22×Q8C23×C511yescharacteristic
363C22×D4—21no—
364C22×D4C23×C511yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4C23×C511yescharacteristic
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—41no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—41no—
375C22×C8C23×C511yescharacteristic
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381#121—22no—
382#121C5×D414yes—
383C4×D4—22no—
384C4×D4—41no—
385C4×D4—44no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4C5×D411yescharacteristic
410C2×C22⋊C4C5×D411yescharacteristic
411C2×C42—21no—
412C2×C42C23×C511yescharacteristic
413C2×C42C23×C511yescharacteristic
414#106—22no—
415#106—22no—
416#106—22no—
417C4⋊C8—22no—
418C4⋊C8—41no—
419#103—22no—
420#103—22no—
421#103—41no—
422#102—22no—
423#102—22no—
424#102—22no—
425C22⋊C8—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95C5×D411yescharacteristic
433#95C5×D411yescharacteristic
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—81no—
444C22×C5—81no—
445C22×C5—81no—
446C22×C5—81no—
447C22×C5#46114yes—
448C22×C5C2×#12111yescharacteristic
449C22×C5#54611yescharacteristic
450C22×C5#54711yescharacteristic
451C22×C5C22×SD1611yescharacteristic
452C22×C5C2×#13711yescharacteristic
453C22×C5#57611yescharacteristic
454C22×C5#57711yescharacteristic
455C4×C5—22no—
456C4×C5—22no—
457C4×C5—22no—
458C4×C5—41no—
459C4×C5—42no—
460C4×C5—42no—
461C4×C5—41no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5—81no—
466C4×C5—81no—
467C4×C5#52911yescharacteristic
468C4×C5#53911yescharacteristic
469C4×C5#54611yescharacteristic
470C4×C5#54711yescharacteristic
471C24—21no—
472C24C2×C5×D411yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×D4—24no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4C2×C5×D412yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C2×C5×D411yescharacteristic
511C22×C4C2×C5×D412yes—
512C22×C4C2×C5×D411yescharacteristic
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C5×#4112yes—
515C22×C4C24×C511yescharacteristic
516SD16—44no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—44no—
529C2×C8C5×#4112yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C4⋊C4C2×C5×D412yes—
549C4⋊C4C5×#4112yes—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4C5×SD1614yescomplemented
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C2×C5—24no—
563C2×C5—82no—
564C2×C5#242511yescharacteristic
565C2×C5C2×#46111yescharacteristic
566C2×C5#304511yescharacteristic
567C2×C5#329511yescharacteristic
568C2×C5#331611yescharacteristic
569C2×C5#333511yescharacteristic
570C2×C5#334611yescharacteristic
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C5×#12112yes—
583C23C2×C5×SD1612yes—
584C23C5×#13712yes—
585C23C22×C5×D411yescharacteristic
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590D4—22no—
591D4—22no—
592D4—48no—
593D4—41no—
594D4—41no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
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—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4C5×#12112yes—
636C2×C4C2×C5×SD1612yes—
637C2×C4C2×C5×SD1612yes—
638C2×C4C22×C5×D411yescharacteristic
639C2×C4C2×C5×#4111yescharacteristic
640C2×C4C2×C5×#4111yescharacteristic
641C2×C4C2×C5×#4111yescharacteristic
642C2×C4C5×H(5,𝔽2)11yescharacteristic
643C2×C4C5×2−1+411yescharacteristic
644C8—22no—
645C8—41no—
646C8—41no—
647C8—41no—
648C5#2520211yescharacteristic, direct product factor, Sylow
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22C5×#46114yes—
663C22C2×C5×#12111yescharacteristic
664C22C5×#54611yescharacteristic
665C22C5×#54711yescharacteristic
666C22C22×C5×SD1611yescharacteristic
667C22C2×C5×#13711yescharacteristic
668C22C5×#57611yescharacteristic
669C22C5×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C5×#52911yescharacteristic
683C4C5×#53911yescharacteristic
684C4C5×#54611yescharacteristic
685C4C5×#54711yescharacteristic
686C2—24no—
687C2—82no—
688C2C5×#242511yescharacteristic
689C2C2×C5×#46111yescharacteristic
690C2C5×#304511yescharacteristic
691C2C5×#329511yescharacteristic
692C2C5×#331611yescharacteristic
693C2C5×#333511yescharacteristic
694C2C5×#334611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
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
3. C5×#2502C2semidirect
5. C5×#2084C2semidirect
6. C5×#2071C2semidirect
7. C5×#2066C2semidirect
8. C5×#2055C2semidirect
9. C5×#1948C2semidirect
10. C5×#1927C2semidirect
11. C5×#1877C2semidirect
12. C5×#1872C2semidirect
13. C5×#1850C2semidirect
14. C5×#1802C2semidirect
15. C2×C5×#340C2semidirect
61. #25202C5direct (N × H)
136. #2502C2×C5semidirect
138. #2084C2×C5semidirect
139. #2071C2×C5semidirect
140. #2066C2×C5semidirect
141. #2055C2×C5semidirect
142. #1948C2×C5semidirect
143. #1927C2×C5semidirect
144. #1877C2×C5semidirect
145. #1872C2×C5semidirect
146. #1850C2×C5semidirect
147. #1802C2×C5semidirect
148. C2×#340C2×C5semidirect
234. C5×C22⋊C4SD16semidirect
556. C22⋊C4C5×SD16semidirect
648. C5#25202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4812
C2×C5×#4652
C5×#25022
C5×#23612
C5×#20842
C5×#20712
C5×#20662
C5×#20552
C5×#19482
C5×#19272
C5×#18772
C5×#18722
C5×#18502
C5×#18022
C2×C5×#3402
#252025