Finite Group Databasebeta

← C5×#25209 #11947929

Subgroups — C5×#25209 #11947929

Order 1280.

904 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#482C211yesmaximal, characteristic, complemented
2C2×C5×#466C211yesmaximal, characteristic
3C5×#2500C211yesmaximal, characteristic, complemented
4C5×#2363C211yesmaximal, characteristic, complemented
5C5×#2085C211yesmaximal, characteristic, complemented
6C5×#2071C211yesmaximal, characteristic, complemented
7C5×#2067C211yesmaximal, characteristic, complemented
8C5×#2054C211yesmaximal, characteristic, complemented
9C5×#1947C211yesmaximal, characteristic, complemented
10C5×#1926C211yesmaximal, characteristic, complemented
11C5×#1879C211yesmaximal, characteristic, complemented
12C5×#1875C211yesmaximal, characteristic, complemented
13C5×#1850C211yesmaximal, characteristic, complemented
14C5×#1804C211yesmaximal, characteristic, complemented
15C5×#1735C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C5×#482—24no—
24C5×#466—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#394—21no—
38C5×#394—21no—
39C5×#390—21no—
40C5×#390C2211yescharacteristic
41C5×#390C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#388—21no—
45C5×#388—21no—
46C5×#388—21no—
47C5×#386—21no—
48C5×#384C2211yescharacteristic
49C5×#382C2211yescharacteristic
50C4×C5×C4⋊C4C2211yescharacteristic
51C4×C5×C22⋊C4—21no—
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25209C511yesmaximal, 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×C5C2311yescharacteristic
68C2×C5×D8—22no—
69C2×C5×D8—22no—
70C2×C5×D8—41no—
71C22×C5×C8—22no—
72C22×C5×C8—22no—
73C22×C5×C8—41no—
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C5×#121—22no—
79C5×#121—22no—
80C5×#121—22no—
81C5×#121D414yes—
82C4×C5×D4—22no—
83C4×C5×D4—41no—
84C5×#117—22no—
85C5×#117—22no—
86C5×#117—22no—
87C5×#117—41no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
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×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×C5—21no—
112C2×C42×C5—21no—
113C2×C42×C5C2311yescharacteristic
114C2×C42×C5C2311yescharacteristic
115C5×#107—22no—
116C5×#107—22no—
117C5×#106—22no—
118C5×C4⋊C8—22no—
119C5×C4⋊C8—41no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×#102—41no—
126C5×C22⋊C8—22no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95D411yescharacteristic
132C5×#95D411yescharacteristic
133C2×#482C2×C511yescharacteristic, complemented
134C2×#466C2×C511yescharacteristic
135#2500C2×C511yescharacteristic, complemented
136#2363C2×C511yescharacteristic, complemented
137#2085C2×C511yescharacteristic, complemented
138#2071C2×C511yescharacteristic, complemented
139#2067C2×C511yescharacteristic, complemented
140#2054C2×C511yescharacteristic, complemented
141#1947C2×C511yescharacteristic, complemented
142#1926C2×C511yescharacteristic, complemented
143#1879C2×C511yescharacteristic, complemented
144#1875C2×C511yescharacteristic, complemented
145#1850C2×C511yescharacteristic, complemented
146#1804C2×C511yescharacteristic, complemented
147#1735C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5—21no—
150C24×C5C2×D411yescharacteristic
151C2×C5×D4—24no—
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
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—42no—
164C2×C5×D4—81no—
165C2×C5×D4—81no—
166C2×C5×D4—81no—
167C2×C5×D4—81no—
168C2×C5×D4C2×D412yes—
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—21no—
178C22×C4×C5—21no—
179C22×C4×C5—42no—
180C22×C4×C5—42no—
181C22×C4×C5—81no—
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D412yes—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5#4112yes—
189C22×C4×C5C2411yescharacteristic
190C5×D8—44no—
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—21no—
201C2×C5×C8—21no—
202C2×C5×C8—44no—
203C2×C5×C8#4112yes—
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—81no—
215C5×C4⋊C4—81no—
216C5×C4⋊C4—81no—
217C5×C4⋊C4C2×D412yes—
218C5×C4⋊C4#4112yes—
219C5×C22⋊C4—24no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—41no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—81no—
230C5×C22⋊C4—81no—
231C5×C22⋊C4—81no—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—42no—
237C42×C5—42no—
238C42×C5—81no—
239C22×D8C22×C511yescharacteristic
240C23×C8C22×C511yescharacteristic
241C2×#121C22×C511yescharacteristic
242C2×#121C22×C511yescharacteristic
243C2×C4×D4C22×C511yescharacteristic
244C2×#117C22×C511yescharacteristic
245C2×#117C22×C511yescharacteristic
246#482—24no—
247#466—24no—
248C2×#107C22×C511yescharacteristic
249C2×#107C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×C4⋊C8C22×C511yescharacteristic
252C2×C4⋊C8C22×C511yescharacteristic
253C2×#102C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×C22⋊C8C22×C511yescharacteristic
260#394—21no—
261#394—21no—
262#390—21no—
263#390C22×C511yescharacteristic
264#390C22×C511yescharacteristic
265#390C22×C511yescharacteristic
266#389C22×C511yescharacteristic
267#388—21no—
268#388—21no—
269#388—21no—
270#386—21no—
271#384C22×C511yescharacteristic
272#382C22×C511yescharacteristic
273C4×C4⋊C4C22×C511yescharacteristic
274C4×C22⋊C4—21no—
275C4×C22⋊C4C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#336C22×C511yescharacteristic
283#336C22×C511yescharacteristic
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—22no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5#12112yes—
305C23×C5C22×D411yescharacteristic
306C5×D4—22no—
307C5×D4—22no—
308C5×D4—41no—
309C5×D4—41no—
310C5×D4—41no—
311C5×D4—41no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—84no—
315C5×D4—84no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
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—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—84no—
352C2×C4×C5#12112yes—
353C2×C4×C5#13512yes—
354C2×C4×C5C22×D411yescharacteristic
355C2×C4×C5C2×#4111yescharacteristic
356C2×C4×C5C2×#4111yescharacteristic
357C2×C4×C5C2×#4111yescharacteristic
358C2×C4×C5H(5,𝔽2)11yescharacteristic
359C2×C4×C52−1+411yescharacteristic
360C5×C8—22no—
361C5×C8—41no—
362C5×C8—41no—
363C5×C8—41no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4C23×C511yescharacteristic
367C22×D4C23×C511yescharacteristic
368C23×C4—21no—
369C23×C4C23×C511yescharacteristic
370C2×D8—22no—
371C2×D8—22no—
372C2×D8—41no—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—41no—
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379C22×C8C23×C511yescharacteristic
380#121—22no—
381#121—22no—
382#121—22no—
383#121C5×D414yes—
384C4×D4—22no—
385C4×D4—41no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—41no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C4⋊C4C23×C511yescharacteristic
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4C5×D411yescharacteristic
411C2×C22⋊C4C5×D411yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C511yescharacteristic
416C2×C42C23×C511yescharacteristic
417#107—22no—
418#107—22no—
419#106—22no—
420C4⋊C8—22no—
421C4⋊C8—41no—
422#102—22no—
423#102—22no—
424#102—22no—
425#102—22no—
426#102—22no—
427#102—41no—
428C22⋊C8—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95C5×D411yescharacteristic
434#95C5×D411yescharacteristic
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—81no—
446C22×C5—81no—
447C22×C5—81no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5—81no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5C2×#12111yescharacteristic
457C22×C5#54611yescharacteristic
458C22×C5#54711yescharacteristic
459C22×C5C2×#13511yescharacteristic
460C22×C5#57511yescharacteristic
461C22×C5#57611yescharacteristic
462C22×C5#57611yescharacteristic
463C4×C5—22no—
464C4×C5—22no—
465C4×C5—41no—
466C4×C5—42no—
467C4×C5—41no—
468C4×C5—41no—
469C4×C5—42no—
470C4×C5—81no—
471C4×C5—81no—
472C4×C5—81no—
473C4×C5—81no—
474C4×C5#52911yescharacteristic
475C4×C5#53911yescharacteristic
476C4×C5#54611yescharacteristic
477C4×C5#54711yescharacteristic
478C24—21no—
479C24—21no—
480C24C2×C5×D411yescharacteristic
481C2×D4—24no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4C2×C5×D412yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4C2×C5×D411yescharacteristic
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C2×C5×D411yescharacteristic
515C22×C4C2×C5×D411yescharacteristic
516C22×C4C2×C5×D412yes—
517C22×C4C2×C5×D411yescharacteristic
518C22×C4C5×#4112yes—
519C22×C4C24×C511yescharacteristic
520D8—44no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—44no—
533C2×C8C5×#4112yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—81no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4C2×C5×D412yes—
548C4⋊C4C5×#4112yes—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C42—81no—
569C2×C5—42no—
570C2×C5—82no—
571C2×C5—161no—
572C2×C5#242511yescharacteristic
573C2×C5#303511yescharacteristic
574C2×C5#304111yescharacteristic
575C2×C5#330511yescharacteristic
576C2×C5#331911yescharacteristic
577C2×C5#333911yescharacteristic
578C2×C5#334711yescharacteristic
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23C5×#12112yes—
600C23C22×C5×D411yescharacteristic
601D4—22no—
602D4—22no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—84no—
610D4—84no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—84no—
647C2×C4C5×#12112yes—
648C2×C4C5×#13512yes—
649C2×C4C22×C5×D411yescharacteristic
650C2×C4C2×C5×#4111yescharacteristic
651C2×C4C2×C5×#4111yescharacteristic
652C2×C4C2×C5×#4111yescharacteristic
653C2×C4C5×H(5,𝔽2)11yescharacteristic
654C2×C4C5×2−1+411yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C5#2520911yescharacteristic, direct product factor, Sylow
660C22—22no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C5×#12111yescharacteristic
682C22C5×#54611yescharacteristic
683C22C5×#54711yescharacteristic
684C22C2×C5×#13511yescharacteristic
685C22C5×#57511yescharacteristic
686C22C5×#57611yescharacteristic
687C22C5×#57611yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4C5×#52911yescharacteristic
700C4C5×#53911yescharacteristic
701C4C5×#54611yescharacteristic
702C4C5×#54711yescharacteristic
703C2—42no—
704C2—82no—
705C2—161no—
706C2C5×#242511yescharacteristic
707C2C5×#303511yescharacteristic
708C2C5×#304111yescharacteristic
709C2C5×#330511yescharacteristic
710C2C5×#331911yescharacteristic
711C2C5×#333911yescharacteristic
712C2C5×#334711yescharacteristic
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×#482C2semidirect
3. C5×#2500C2semidirect
4. C5×#2363C2semidirect
5. C5×#2085C2semidirect
6. C5×#2071C2semidirect
7. C5×#2067C2semidirect
8. C5×#2054C2semidirect
9. C5×#1947C2semidirect
10. C5×#1926C2semidirect
11. C5×#1879C2semidirect
12. C5×#1875C2semidirect
13. C5×#1850C2semidirect
14. C5×#1804C2semidirect
15. C5×#1735C2semidirect
61. #25209C5direct (N × H)
133. C2×#482C2×C5semidirect
135. #2500C2×C5semidirect
136. #2363C2×C5semidirect
137. #2085C2×C5semidirect
138. #2071C2×C5semidirect
139. #2067C2×C5semidirect
140. #2054C2×C5semidirect
141. #1947C2×C5semidirect
142. #1926C2×C5semidirect
143. #1879C2×C5semidirect
144. #1875C2×C5semidirect
145. #1850C2×C5semidirect
146. #1804C2×C5semidirect
147. #1735C2×C5semidirect
659. C5#25209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4822
C2×C5×#4662
C5×#25002
C5×#23632
C5×#20852
C5×#20712
C5×#20672
C5×#20542
C5×#19472
C5×#19262
C5×#18792
C5×#18752
C5×#18502
C5×#18042
C5×#17352
#252095