Finite Group Databasebeta

← C5×#25237 #11947957

Subgroups — C5×#25237 #11947957

Order 1280.

904 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#482C211yesmaximal, characteristic, complemented
2C2×C5×C8×D4C211yesmaximal, characteristic, complemented
3C5×#2485C211yesmaximal, characteristic, complemented
4C5×#2414C211yesmaximal, characteristic
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2076C211yesmaximal, characteristic, complemented
7C5×#2065C211yesmaximal, characteristic, complemented
8C5×#2033C211yesmaximal, characteristic, complemented
9C5×#1942C211yesmaximal, characteristic, complemented
10C5×#1934C211yesmaximal, characteristic, complemented
11C5×#1893C211yesmaximal, characteristic, complemented
12C5×#1893C211yesmaximal, characteristic, complemented
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1807C211yesmaximal, characteristic, complemented
15C5×#1735C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C5×#482—24no—
24C5×C8×D4—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×C22⋊C8C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C4×C5×C8C2211yescharacteristic
37C5×#397—21no—
38C5×#394—21no—
39C5×#394—21no—
40C5×#392—21no—
41C5×#390—21no—
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#388—21no—
47C5×#388—21no—
48C5×#387—21no—
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61#25237C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4D411yescharacteristic
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C22×C5×C8—22no—
69C22×C5×C8—22no—
70C22×C5×C8—22no—
71C22×C5×C8—22no—
72C22×C5×C8—41no—
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×#121—41no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
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⋊C4D411yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
109C2×C5×C22⋊C4D411yescharacteristic
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C42×C5—21no—
112C2×C42×C5—21no—
113C2×C42×C5C2311yescharacteristic
114C5×#107—22no—
115C5×#107—22no—
116C5×#106—22no—
117C5×#106—41no—
118C5×C4⋊C8—22no—
119C5×#102—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—41no—
123C5×C22⋊C8—22no—
124C5×C22⋊C8D414yescomplemented
125C4×C5×C8—22no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C2×#482C2×C511yescharacteristic, complemented
134C2×C8×D4C2×C511yescharacteristic, complemented
135#2485C2×C511yescharacteristic, complemented
136#2414C2×C511yescharacteristic
137#2088C2×C511yescharacteristic, complemented
138#2076C2×C511yescharacteristic, complemented
139#2065C2×C511yescharacteristic, complemented
140#2033C2×C511yescharacteristic, complemented
141#1942C2×C511yescharacteristic, complemented
142#1934C2×C511yescharacteristic, complemented
143#1893C2×C511yescharacteristic, complemented
144#1893C2×C511yescharacteristic, complemented
145#1854C2×C511yescharacteristic, complemented
146#1807C2×C511yescharacteristic, complemented
147#1735C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5C2×D411yescharacteristic
150C24×C5C2×D411yescharacteristic
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4—22no—
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—42no—
161C2×C5×D4—42no—
162C2×C5×D4—42no—
163C2×C5×D4—81no—
164C2×C5×D4—81no—
165C2×C5×D4—81no—
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—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
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
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—44no—
200C2×C5×C8—44no—
201C2×C5×C8C2×D412yes—
202C2×C5×C8C2×D412yes—
203C2×C5×C8#4112yes—
204C5×C4⋊C4—22no—
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—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—81no—
220C5×C4⋊C4—81no—
221C5×C4⋊C4#4112yes—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—81no—
231C5×C22⋊C4—81no—
232C5×C22⋊C4—81no—
233C5×C22⋊C4—81no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—42no—
237C42×C5—42no—
238C23×C8C22×C511yescharacteristic
239C23×C8C22×C511yescharacteristic
240C2×#121C22×C511yescharacteristic
241C2×#121C22×C511yescharacteristic
242C2×C4×D4C22×C511yescharacteristic
243C2×#117C22×C511yescharacteristic
244C2×#117C22×C511yescharacteristic
245#482—24no—
246C8×D4—24no—
247C2×#107C22×C511yescharacteristic
248C2×#107C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×C4⋊C8C22×C511yescharacteristic
252C2×#102C22×C511yescharacteristic
253C2×#102C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×C22⋊C8C22×C511yescharacteristic
257C2×C22⋊C8C22×C511yescharacteristic
258C2×C4×C8C22×C511yescharacteristic
259#397—21no—
260#394—21no—
261#394—21no—
262#392—21no—
263#390—21no—
264#390C22×C511yescharacteristic
265#389C22×C511yescharacteristic
266#389C22×C511yescharacteristic
267#389C22×C511yescharacteristic
268#388—21no—
269#388—21no—
270#387—21no—
271#380C22×C511yescharacteristic
272#380C22×C511yescharacteristic
273#380C22×C511yescharacteristic
274#380C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5#12112yes—
303C23×C5#13512yes—
304C23×C5C22×D411yescharacteristic
305C5×D4—28no—
306C5×D4—41no—
307C5×D4—41no—
308C5×D4—41no—
309C5×D4—41no—
310C5×D4—84no—
311C5×D4—84no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—22no—
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—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5#12112yes—
352C2×C4×C5#13512yes—
353C2×C4×C5C22×D411yescharacteristic
354C2×C4×C5C2×#4111yescharacteristic
355C2×C4×C5C2×#4111yescharacteristic
356C2×C4×C5C2×#4111yescharacteristic
357C2×C4×C5H(5,𝔽2)11yescharacteristic
358C2×C4×C52−1+411yescharacteristic
359C5×C8—22no—
360C5×C8—22no—
361C5×C8—22no—
362C5×C8—41no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4C5×D411yescharacteristic
366C22×D4C23×C511yescharacteristic
367C23×C4C23×C511yescharacteristic
368C23×C4C23×C511yescharacteristic
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—41no—
374C22×C8—41no—
375C22×C8C23×C511yescharacteristic
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379#121—22no—
380#121—22no—
381#121—22no—
382#121—41no—
383C4×D4—22no—
384C4×D4—22no—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C5×D411yescharacteristic
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×C4⋊C4C23×C511yescharacteristic
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×C42C23×C511yescharacteristic
415#107—22no—
416#107—22no—
417#106—22no—
418#106—41no—
419C4⋊C8—22no—
420#102—22no—
421#102—22no—
422#102—22no—
423#102—41no—
424C22⋊C8—22no—
425C22⋊C8C5×D414yescomplemented
426C4×C8—22no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5—81no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5C2×#12111yescharacteristic
456C22×C5#54611yescharacteristic
457C22×C5#54711yescharacteristic
458C22×C5C2×#13511yescharacteristic
459C22×C5C2×#13511yescharacteristic
460C22×C5#57611yescharacteristic
461C22×C5#57711yescharacteristic
462C4×C5—22no—
463C4×C5—22no—
464C4×C5—41no—
465C4×C5—42no—
466C4×C5—41no—
467C4×C5—81no—
468C4×C5—81no—
469C4×C5—81no—
470C4×C5—81no—
471C4×C5—81no—
472C4×C5—81no—
473C4×C5#52911yescharacteristic
474C4×C5#53911yescharacteristic
475C4×C5#54611yescharacteristic
476C4×C5#54711yescharacteristic
477C24—21no—
478C24C2×C5×D411yescharacteristic
479C24C2×C5×D411yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4—81no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
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—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4C2×C5×D411yescharacteristic
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C2×C5×D411yescharacteristic
515C22×C4C2×C5×D412yes—
516C22×C4C2×C5×D411yescharacteristic
517C22×C4C5×#4112yes—
518C22×C4C24×C511yescharacteristic
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×C8—44no—
530C2×C8C2×C5×D412yes—
531C2×C8C2×C5×D412yes—
532C2×C8C5×#4112yes—
533C4⋊C4—22no—
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—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4C5×#4112yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
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—
562C22⋊C4—81no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C2×C5—42no—
568C2×C5—42no—
569C2×C5—161no—
570C2×C5#242511yescharacteristic
571C2×C5#305011yescharacteristic
572C2×C5#306211yescharacteristic
573C2×C5#329711yescharacteristic
574C2×C5#330411yescharacteristic
575C2×C5#333711yescharacteristic
576C2×C5#334111yescharacteristic
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23C5×#12112yes—
597C23C5×#13512yes—
598C23C22×C5×D411yescharacteristic
599D4—28no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605D4—84no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
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—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×C4C5×#12112yes—
646C2×C4C5×#13512yes—
647C2×C4C22×C5×D411yescharacteristic
648C2×C4C2×C5×#4111yescharacteristic
649C2×C4C2×C5×#4111yescharacteristic
650C2×C4C2×C5×#4111yescharacteristic
651C2×C4C5×H(5,𝔽2)11yescharacteristic
652C2×C4C5×2−1+411yescharacteristic
653C8—22no—
654C8—22no—
655C8—22no—
656C8—41no—
657C5#2523711yescharacteristic, direct product factor, Sylow
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C5×#12111yescharacteristic
680C22C5×#54611yescharacteristic
681C22C5×#54711yescharacteristic
682C22C2×C5×#13511yescharacteristic
683C22C2×C5×#13511yescharacteristic
684C22C5×#57611yescharacteristic
685C22C5×#57711yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C5×#52911yescharacteristic
698C4C5×#53911yescharacteristic
699C4C5×#54611yescharacteristic
700C4C5×#54711yescharacteristic
701C2—42no—
702C2—42no—
703C2—161no—
704C2C5×#242511yescharacteristic
705C2C5×#305011yescharacteristic
706C2C5×#306211yescharacteristic
707C2C5×#329711yescharacteristic
708C2C5×#330411yescharacteristic
709C2C5×#333711yescharacteristic
710C2C5×#334111yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2414C2
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
1. C2×C5×#482C2semidirect
2. C2×C5×C8×D4C2semidirect
3. C5×#2485C2semidirect
5. C5×#2088C2semidirect
6. C5×#2076C2semidirect
7. C5×#2065C2semidirect
8. C5×#2033C2semidirect
9. C5×#1942C2semidirect
10. C5×#1934C2semidirect
11. C5×#1893C2semidirect
12. C5×#1893C2semidirect
13. C5×#1854C2semidirect
14. C5×#1807C2semidirect
15. C5×#1735C2semidirect
61. #25237C5direct (N × H)
124. C5×C22⋊C8D4semidirect
133. C2×#482C2×C5semidirect
134. C2×C8×D4C2×C5semidirect
135. #2485C2×C5semidirect
137. #2088C2×C5semidirect
138. #2076C2×C5semidirect
139. #2065C2×C5semidirect
140. #2033C2×C5semidirect
141. #1942C2×C5semidirect
142. #1934C2×C5semidirect
143. #1893C2×C5semidirect
144. #1893C2×C5semidirect
145. #1854C2×C5semidirect
146. #1807C2×C5semidirect
147. #1735C2×C5semidirect
425. C22⋊C8C5×D4semidirect
657. C5#25237direct (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×C8×D42
C5×#24852
C5×#24142
C5×#20882
C5×#20762
C5×#20652
C5×#20332
C5×#19422
C5×#19342
C5×#18932
C5×#18542
C5×#18072
C5×#17352
#252375