Finite Group Databasebeta

← C5×#25200 #11947920

Subgroups — C5×#25200 #11947920

Order 1280.

1024 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#480C211yesmaximal, characteristic, complemented
2C2×C5×#466C211yesmaximal, characteristic
3C5×#2501C211yesmaximal, characteristic, complemented
4C5×#2361C211yesmaximal, characteristic, complemented
5C5×#2083C211yesmaximal, characteristic, complemented
6C5×#2071C211yesmaximal, characteristic, complemented
7C5×#2067C211yesmaximal, characteristic, complemented
8C5×#2054C211yesmaximal, characteristic, complemented
9C5×#1947C211yesmaximal, characteristic, complemented
10C5×#1925C211yesmaximal, characteristic, complemented
11C5×#1879C211yesmaximal, characteristic, complemented
12C5×#1874C211yesmaximal, characteristic, complemented
13C5×#1850C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×#123—21no—
19C2×C5×#123—21no—
20C2×C5×#121C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×D4—21no—
23C2×C4×C5×D4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C5×#480—24no—
27C5×#466—24no—
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
30C2×C5×#107C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×C4⋊C8C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C5×#399—21no—
41C5×#399—21no—
42C5×#390C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#388—21no—
47C5×#386—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#25200C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4C2311yescharacteristic
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5C2311yescharacteristic
70C2×C5×D8—22no—
71C2×C5×D8—22no—
72C2×C5×D8—41no—
73C22×C5×C8—22no—
74C22×C5×C8—22no—
75C22×C5×C8—41no—
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×#123—44no—
81C5×#123—44no—
82C5×#121—22no—
83C5×#121—22no—
84C5×#121—22no—
85C5×#121D414yes—
86C4×C5×D4—22no—
87C4×C5×D4—41no—
88C4×C5×D4—44no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
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—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—41no—
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4D411yescharacteristic
116C2×C5×C22⋊C4D411yescharacteristic
117C2×C42×C5—21no—
118C2×C42×C5C2311yescharacteristic
119C2×C42×C5C2311yescharacteristic
120C5×#107—22no—
121C5×#107—22no—
122C5×#107—22no—
123C5×C4⋊C8—22no—
124C5×C4⋊C8—41no—
125C5×#102—22no—
126C5×#102—22no—
127C5×#102—22no—
128C5×#102—22no—
129C5×#102—22no—
130C5×#102—41no—
131C5×C22⋊C8—22no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95D411yescharacteristic
135C5×#95D411yescharacteristic
136C2×#480C2×C511yescharacteristic, complemented
137C2×#466C2×C511yescharacteristic
138#2501C2×C511yescharacteristic, complemented
139#2361C2×C511yescharacteristic, complemented
140#2083C2×C511yescharacteristic, complemented
141#2071C2×C511yescharacteristic, complemented
142#2067C2×C511yescharacteristic, complemented
143#2054C2×C511yescharacteristic, complemented
144#1947C2×C511yescharacteristic, complemented
145#1925C2×C511yescharacteristic, complemented
146#1879C2×C511yescharacteristic, complemented
147#1874C2×C511yescharacteristic, complemented
148#1850C2×C511yescharacteristic, complemented
149#1802C2×C511yescharacteristic, complemented
150C2×#340C2×C511yescharacteristic, complemented
151C24×C5—21no—
152C24×C5—21no—
153C24×C5C2×D411yescharacteristic
154C2×C5×D4—24no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—42no—
167C2×C5×D4—42no—
168C2×C5×D4—42no—
169C2×C5×D4—42no—
170C2×C5×D4—42no—
171C2×C5×D4C2×D412yes—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—42no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—42no—
189C22×C4×C5—81no—
190C22×C4×C5—81no—
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D412yes—
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5#4112yes—
198C22×C4×C5C2411yescharacteristic
199C5×D8—44no—
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—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—44no—
212C2×C5×C8#4112yes—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—42no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4—42no—
229C5×C4⋊C4—42no—
230C5×C4⋊C4C2×D412yes—
231C5×C4⋊C4#4112yes—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—24no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—42no—
237C5×C22⋊C4—42no—
238C5×C22⋊C4—42no—
239C5×C22⋊C4—42no—
240C5×C22⋊C4—42no—
241C5×C22⋊C4—81no—
242C5×C22⋊C4D814yescomplemented
243C42×C5—21no—
244C42×C5—21no—
245C42×C5—21no—
246C42×C5—21no—
247C42×C5—42no—
248C22×D8C22×C511yescharacteristic
249C23×C8C22×C511yescharacteristic
250C2×#123—21no—
251C2×#123—21no—
252C2×#121C22×C511yescharacteristic
253C2×#121C22×C511yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4C22×C511yescharacteristic
256C22×C4⋊C4C22×C511yescharacteristic
257C22×C4⋊C4C22×C511yescharacteristic
258#480—24no—
259#466—24no—
260C2×#107C22×C511yescharacteristic
261C2×#107C22×C511yescharacteristic
262C2×#107C22×C511yescharacteristic
263C2×C4⋊C8C22×C511yescharacteristic
264C2×C4⋊C8C22×C511yescharacteristic
265C2×#102C22×C511yescharacteristic
266C2×#102C22×C511yescharacteristic
267C2×#102C22×C511yescharacteristic
268C2×#102C22×C511yescharacteristic
269C2×#102C22×C511yescharacteristic
270C2×#102C22×C511yescharacteristic
271C2×C22⋊C8C22×C511yescharacteristic
272#399—21no—
273#399—21no—
274#390C22×C511yescharacteristic
275#390C22×C511yescharacteristic
276#390C22×C511yescharacteristic
277#389C22×C511yescharacteristic
278#388—21no—
279#386—21no—
280#385—21no—
281#384C22×C511yescharacteristic
282#384C22×C511yescharacteristic
283C4×C4⋊C4C22×C511yescharacteristic
284C4×C22⋊C4C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#340C22×C511yescharacteristic
290#340C22×C511yescharacteristic
291#336C22×C511yescharacteristic
292#336C22×C511yescharacteristic
293C23×C5—21no—
294C23×C5—21no—
295C23×C5—21no—
296C23×C5—21no—
297C23×C5—22no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5#12112yes—
312C23×C5C2×D812yes—
313C23×C5AGL(1,ℤ/8)12yes—
314C23×C5C22×D411yescharacteristic
315C5×D4—22no—
316C5×D4—22no—
317C5×D4—48no—
318C5×D4—41no—
319C5×D4—41no—
320C5×D4—41no—
321C5×D4—41no—
322C5×D4—41no—
323C5×D4—41no—
324C5×D4—84no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—21no—
337C2×C4×C5—22no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—84no—
360C2×C4×C5—84no—
361C2×C4×C5—84no—
362C2×C4×C5#12112yes—
363C2×C4×C5C2×D812yes—
364C2×C4×C5C2×D812yes—
365C2×C4×C5C22×D411yescharacteristic
366C2×C4×C5C2×#4111yescharacteristic
367C2×C4×C5C2×#4111yescharacteristic
368C2×C4×C5C2×#4111yescharacteristic
369C2×C4×C5H(5,𝔽2)11yescharacteristic
370C2×C4×C52−1+411yescharacteristic
371C5×C8—22no—
372C5×C8—41no—
373C5×C8—41no—
374C5×C8—41no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4C23×C511yescharacteristic
378C22×D4C23×C511yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4C23×C511yescharacteristic
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—41no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—41no—
389C22×C8C23×C511yescharacteristic
390C22×C8C23×C511yescharacteristic
391C22×C8C23×C511yescharacteristic
392C22×C8C23×C511yescharacteristic
393#123—44no—
394#123—44no—
395#121—22no—
396#121—22no—
397#121—22no—
398#121C5×D414yes—
399C4×D4—22no—
400C4×D4—41no—
401C4×D4—44no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4C23×C511yescharacteristic
414C2×C4⋊C4C23×C511yescharacteristic
415C2×C4⋊C4C23×C511yescharacteristic
416C2×C4⋊C4C23×C511yescharacteristic
417C2×C4⋊C4C23×C511yescharacteristic
418C2×C4⋊C4C23×C511yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4C5×D411yescharacteristic
429C2×C22⋊C4C5×D411yescharacteristic
430C2×C42—21no—
431C2×C42C23×C511yescharacteristic
432C2×C42C23×C511yescharacteristic
433#107—22no—
434#107—22no—
435#107—22no—
436C4⋊C8—22no—
437C4⋊C8—41no—
438#102—22no—
439#102—22no—
440#102—22no—
441#102—22no—
442#102—22no—
443#102—41no—
444C22⋊C8—22no—
445#95—21no—
446#95—21no—
447#95C5×D411yescharacteristic
448#95C5×D411yescharacteristic
449C22×C5—22no—
450C22×C5—22no—
451C22×C5—22no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—42no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5—81no—
467C22×C5—81no—
468C22×C5—81no—
469C22×C5#45914yes—
470C22×C5C2×#12111yescharacteristic
471C22×C5#54611yescharacteristic
472C22×C5#54711yescharacteristic
473C22×C5C22×D811yescharacteristic
474C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
475C22×C5#57711yescharacteristic
476C22×C5#57811yescharacteristic
477C4×C5—22no—
478C4×C5—22no—
479C4×C5—22no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—42no—
483C4×C5—41no—
484C4×C5—81no—
485C4×C5—81no—
486C4×C5—81no—
487C4×C5—81no—
488C4×C5#52911yescharacteristic
489C4×C5#53911yescharacteristic
490C4×C5#54611yescharacteristic
491C4×C5#54711yescharacteristic
492C24—21no—
493C24—21no—
494C24C2×C5×D411yescharacteristic
495C2×D4—24no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4C2×C5×D412yes—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D411yescharacteristic
534C22×C4C2×C5×D411yescharacteristic
535C22×C4C2×C5×D412yes—
536C22×C4C2×C5×D411yescharacteristic
537C22×C4C2×C5×D411yescharacteristic
538C22×C4C5×#4112yes—
539C22×C4C24×C511yescharacteristic
540D8—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—44no—
553C2×C8C5×#4112yes—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4C2×C5×D412yes—
572C4⋊C4C5×#4112yes—
573C22⋊C4—22no—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4C5×D814yescomplemented
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C2×C5—24no—
590C2×C5—82no—
591C2×C5—161no—
592C2×C5#242511yescharacteristic
593C2×C5C2×#45911yescharacteristic
594C2×C5#304611yescharacteristic
595C2×C5#329411yescharacteristic
596C2×C5#330811yescharacteristic
597C2×C5#333411yescharacteristic
598C2×C5#334511yescharacteristic
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C5×#12112yes—
618C23C2×C5×D812yes—
619C23C5×AGL(1,ℤ/8)12yes—
620C23C22×C5×D411yescharacteristic
621D4—22no—
622D4—22no—
623D4—48no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—84no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4C5×#12112yes—
669C2×C4C2×C5×D812yes—
670C2×C4C2×C5×D812yes—
671C2×C4C22×C5×D411yescharacteristic
672C2×C4C2×C5×#4111yescharacteristic
673C2×C4C2×C5×#4111yescharacteristic
674C2×C4C2×C5×#4111yescharacteristic
675C2×C4C5×H(5,𝔽2)11yescharacteristic
676C2×C4C5×2−1+411yescharacteristic
677C8—22no—
678C8—41no—
679C8—41no—
680C8—41no—
681C5#2520011yescharacteristic, direct product factor, Sylow
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C5×#45914yes—
703C22C2×C5×#12111yescharacteristic
704C22C5×#54611yescharacteristic
705C22C5×#54711yescharacteristic
706C22C22×C5×D811yescharacteristic
707C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
708C22C5×#57711yescharacteristic
709C22C5×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4C5×#52911yescharacteristic
722C4C5×#53911yescharacteristic
723C4C5×#54611yescharacteristic
724C4C5×#54711yescharacteristic
725C2—24no—
726C2—82no—
727C2—161no—
728C2C5×#242511yescharacteristic
729C2C2×C5×#45911yescharacteristic
730C2C5×#304611yescharacteristic
731C2C5×#329411yescharacteristic
732C2C5×#330811yescharacteristic
733C2C5×#333411yescharacteristic
734C2C5×#334511yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#466C2
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×#480C2semidirect
3. C5×#2501C2semidirect
4. C5×#2361C2semidirect
5. C5×#2083C2semidirect
6. C5×#2071C2semidirect
7. C5×#2067C2semidirect
8. C5×#2054C2semidirect
9. C5×#1947C2semidirect
10. C5×#1925C2semidirect
11. C5×#1879C2semidirect
12. C5×#1874C2semidirect
13. C5×#1850C2semidirect
14. C5×#1802C2semidirect
15. C2×C5×#340C2semidirect
61. #25200C5direct (N × H)
136. C2×#480C2×C5semidirect
138. #2501C2×C5semidirect
139. #2361C2×C5semidirect
140. #2083C2×C5semidirect
141. #2071C2×C5semidirect
142. #2067C2×C5semidirect
143. #2054C2×C5semidirect
144. #1947C2×C5semidirect
145. #1925C2×C5semidirect
146. #1879C2×C5semidirect
147. #1874C2×C5semidirect
148. #1850C2×C5semidirect
149. #1802C2×C5semidirect
150. C2×#340C2×C5semidirect
242. C5×C22⋊C4D8semidirect
583. C22⋊C4C5×D8semidirect
681. C5#25200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4802
C2×C5×#4662
C5×#25012
C5×#23612
C5×#20832
C5×#20712
C5×#20672
C5×#20542
C5×#19472
C5×#19252
C5×#18792
C5×#18742
C5×#18502
C5×#18022
C2×C5×#3402
#252005