Finite Group Databasebeta

← C5×#25937 #11948657

Subgroups — C5×#25937 #11948657

Order 1280.

1028 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#557C211yesmaximal, characteristic, complemented
2C2×C5×#488C211yesmaximal, characteristic
3C2×C5×#464C211yesmaximal, characteristic
4C5×#2592C211yesmaximal, characteristic
5C5×#2026C211yesmaximal, characteristic, complemented
6C5×#2025C211yesmaximal, characteristic
7C5×#2024C211yesmaximal, characteristic, complemented
8C5×#2023C211yesmaximal, characteristic
9C5×#1989C211yesmaximal, characteristic, complemented
10C5×#1984C211yesmaximal, characteristic, complemented
11C5×#1880C211yesmaximal, characteristic
12C5×#1880C211yesmaximal, characteristic
13C5×#1878C211yesmaximal, characteristic, complemented
14C5×#1878C211yesmaximal, characteristic, complemented
15C4×C5×#103C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C5×#557—24no—
19C5×#557—24no—
20C2×C5×C4⋊Q8—21no—
21C2×C5×C4⋊Q8C2211yescharacteristic
22C2×C5×#125—21no—
23C2×C5×#125—21no—
24C2×C5×#125C2211yescharacteristic
25C2×C5×#125C2211yescharacteristic
26C2×C5×#124C2211yescharacteristic
27C2×C4×C5×Q8—21no—
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C4×C5×Q8C2211yescharacteristic
30C2×C4×C5×Q8C2211yescharacteristic
31C2×C4×C5×Q8C2211yescharacteristic
32C5×#488—24no—
33C5×#464—24no—
34C2×C5×C4⋊C8C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C4×C5×C8C2211yescharacteristic
44C5×#397—21no—
45C5×#393—21no—
46C5×#391C2211yescharacteristic
47C5×#391C2211yescharacteristic
48C5×#390C2211yescharacteristic
49C5×#390C2211yescharacteristic
50C5×#388—21no—
51C5×#388—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#25937C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8D411yescharacteristic
66C22×C5×Q8C2311yescharacteristic
67C22×C5×Q8C2311yescharacteristic
68C22×C5×D4C2311yescharacteristic
69C2×C5×Q16—22no—
70C2×C5×Q16—22no—
71C2×C5×Q16—22no—
72C2×C5×SD16—22no—
73C2×C5×SD16—22no—
74C2×C5×SD16—22no—
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C5×C4⋊Q8—28no—
80C5×C4⋊Q8—22no—
81C5×C4⋊Q8—22no—
82C5×#125—28no—
83C5×#125—28no—
84C5×#125—22no—
85C5×#125—22no—
86C5×#125—22no—
87C5×#125D414yes—
88C5×#124—22no—
89C5×#124—22no—
90C4×C5×Q8—28no—
91C4×C5×Q8—22no—
92C4×C5×Q8—22no—
93C4×C5×Q8—22no—
94C4×C5×Q8—22no—
95C4×C5×Q8—22no—
96C4×C5×Q8—22no—
97C4×C5×Q8—22no—
98C4×C5×Q8D414yes—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4D411yescharacteristic
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C42×C5—21no—
122C2×C42×C5—21no—
123C2×C42×C5—21no—
124C2×C42×C5—21no—
125C2×C42×C5C2311yescharacteristic
126C2×C42×C5C2311yescharacteristic
127C2×C42×C5C2311yescharacteristic
128C5×C4⋊C8—22no—
129C5×#103—22no—
130C5×#103—22no—
131C5×#103—22no—
132C5×#103—22no—
133C5×#103—22no—
134C5×#102—22no—
135C5×#102—22no—
136C5×#102—22no—
137C4×C5×C8—22no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C2×#557C2×C511yescharacteristic, complemented
144C2×#488C2×C511yescharacteristic
145C2×#464C2×C511yescharacteristic
146#2592C2×C511yescharacteristic
147#2026C2×C511yescharacteristic, complemented
148#2025C2×C511yescharacteristic
149#2024C2×C511yescharacteristic, complemented
150#2023C2×C511yescharacteristic
151#1989C2×C511yescharacteristic, complemented
152#1984C2×C511yescharacteristic, complemented
153#1880C2×C511yescharacteristic
154#1880C2×C511yescharacteristic
155#1878C2×C511yescharacteristic, complemented
156#1878C2×C511yescharacteristic, complemented
157C4×#103C2×C511yescharacteristic, complemented
158C24×C5—21no—
159C2×C5×Q8—24no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—41no—
172C2×C5×Q8—42no—
173C2×C5×Q8—42no—
174C2×C5×Q8C2×D412yes—
175C2×C5×Q8#4112yes—
176C2×C5×Q8#4112yes—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2411yescharacteristic
197C5×Q16—44no—
198C5×SD16—44no—
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—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C5×C4⋊C4—24no—
212C5×C4⋊C4—24no—
213C5×C4⋊C4—24no—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—22no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4C2×D412yes—
230C5×C4⋊C4C2×D412yes—
231C5×C4⋊C4C2×D412yes—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—81no—
237C5×C22⋊C4—81no—
238C42×C5—24no—
239C42×C5—24no—
240C42×C5—24no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—21no—
244C42×C5—21no—
245C42×C5—81no—
246C42×C5C2×D412yes—
247C42×C5C2×D412yes—
248C22×Q16C22×C511yescharacteristic
249C22×SD16C22×C511yescharacteristic
250#557—24no—
251#557—24no—
252C2×C4⋊Q8—21no—
253C2×C4⋊Q8C22×C511yescharacteristic
254C2×#125—21no—
255C2×#125—21no—
256C2×#125C22×C511yescharacteristic
257C2×#125C22×C511yescharacteristic
258C2×#124C22×C511yescharacteristic
259C2×C4×Q8—21no—
260C2×C4×Q8C22×C511yescharacteristic
261C2×C4×Q8C22×C511yescharacteristic
262C2×C4×Q8C22×C511yescharacteristic
263C2×C4×Q8C22×C511yescharacteristic
264#488—24no—
265#464—24no—
266C2×C4⋊C8C22×C511yescharacteristic
267C2×#103C22×C511yescharacteristic
268C2×#103C22×C511yescharacteristic
269C2×#103C22×C511yescharacteristic
270C2×#103C22×C511yescharacteristic
271C2×#103C22×C511yescharacteristic
272C2×#102C22×C511yescharacteristic
273C2×#102C22×C511yescharacteristic
274C2×#102C22×C511yescharacteristic
275C2×C4×C8C22×C511yescharacteristic
276#397—21no—
277#393—21no—
278#391C22×C511yescharacteristic
279#391C22×C511yescharacteristic
280#390C22×C511yescharacteristic
281#390C22×C511yescharacteristic
282#388—21no—
283#388—21no—
284C4×C4⋊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
293#336C22×C511yescharacteristic
294#336C22×C511yescharacteristic
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5C22×D411yescharacteristic
303C5×Q8—22no—
304C5×Q8—22no—
305C5×Q8—22no—
306C5×Q8—44no—
307C5×Q8—48no—
308C5×Q8—41no—
309C5×Q8—41no—
310C5×Q8—41no—
311C5×Q8—41no—
312C5×Q8#12414yes—
313C5×D4—41no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—41no—
317C2×C4×C5—22no—
318C2×C4×C5—21no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
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—41no—
352C2×C4×C5—41no—
353C2×C4×C5#12012yes—
354C2×C4×C5#12012yes—
355C2×C4×C5#13512yes—
356C2×C4×C5C22×D411yescharacteristic
357C2×C4×C5C22×D411yescharacteristic
358C2×C4×C5C2×#4111yescharacteristic
359C2×C4×C5C2×#4111yescharacteristic
360C2×C4×C52−1+411yescharacteristic
361C2×C4×C52−1+411yescharacteristic
362C5×C8—41no—
363C5×C8—41no—
364C5×C8—41no—
365C5×C8—41no—
366C22×Q8—21no—
367C22×Q8C5×D411yescharacteristic
368C22×Q8C23×C511yescharacteristic
369C22×Q8C23×C511yescharacteristic
370C22×D4C23×C511yescharacteristic
371C2×Q16—22no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379C22×C8C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C4⋊Q8—28no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384#125—28no—
385#125—28no—
386#125—22no—
387#125—22no—
388#125—22no—
389#125C5×D414yes—
390#124—22no—
391#124—22no—
392C4×Q8—28no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8C5×D414yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C5×D411yescharacteristic
410C2×C4⋊C4C5×D411yescharacteristic
411C2×C4⋊C4C5×D411yescharacteristic
412C2×C4⋊C4C23×C511yescharacteristic
413C2×C4⋊C4C23×C511yescharacteristic
414C2×C4⋊C4C23×C511yescharacteristic
415C2×C4⋊C4C23×C511yescharacteristic
416C2×C4⋊C4C23×C511yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C23×C511yescharacteristic
428C2×C42C23×C511yescharacteristic
429C2×C42C23×C511yescharacteristic
430C4⋊C8—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—22no—
436#102—22no—
437#102—22no—
438#102—22no—
439C4×C8—22no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445C22×C5—81no—
446C22×C5—81no—
447C22×C5—81no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5C2×#12011yescharacteristic
453C22×C5#54811yescharacteristic
454C22×C5#54811yescharacteristic
455C22×C5C2×#13511yescharacteristic
456C22×C5#57511yescharacteristic
457C22×C5#57711yescharacteristic
458C22×C5#57811yescharacteristic
459C4×C5—24no—
460C4×C5—22no—
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—41no—
464C4×C5—42no—
465C4×C5—42no—
466C4×C5—41no—
467C4×C5—41no—
468C4×C5—42no—
469C4×C5—81no—
470C4×C5—81no—
471C4×C5—81no—
472C4×C5C2×#12411yescharacteristic
473C4×C5#53611yescharacteristic
474C4×C5#54811yescharacteristic
475C4×C5#54811yescharacteristic
476C24—21no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—41no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8C2×C5×D412yes—
493C2×Q8C5×#4112yes—
494C2×Q8C5×#4112yes—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4C2×C5×D411yescharacteristic
509C22×C4C2×C5×D411yescharacteristic
510C22×C4C2×C5×D411yescharacteristic
511C22×C4C2×C5×D411yescharacteristic
512C22×C4C2×C5×D411yescharacteristic
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C24×C511yescharacteristic
515Q16—44no—
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—21no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4C2×C5×D412yes—
548C4⋊C4C2×C5×D412yes—
549C4⋊C4C2×C5×D412yes—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C42—24no—
557C42—24no—
558C42—24no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—81no—
564C42C2×C5×D412yes—
565C42C2×C5×D412yes—
566C2×C5—161no—
567C2×C5#243611yescharacteristic
568C2×C5#300211yescharacteristic
569C2×C5#301311yescharacteristic
570C2×C5#336411yescharacteristic
571C2×C5#336511yescharacteristic
572C2×C5#337111yescharacteristic
573C2×C5#337711yescharacteristic
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23C22×C5×D411yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—44no—
586Q8—48no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8C5×#12414yes—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
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×C4C5×#12012yes—
633C2×C4C5×#12012yes—
634C2×C4C5×#13512yes—
635C2×C4C22×C5×D411yescharacteristic
636C2×C4C22×C5×D411yescharacteristic
637C2×C4C2×C5×#4111yescharacteristic
638C2×C4C2×C5×#4111yescharacteristic
639C2×C4C5×2−1+411yescharacteristic
640C2×C4C5×2−1+411yescharacteristic
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C5#2593711yescharacteristic, direct product factor, Sylow
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×C5×#12011yescharacteristic
654C22C5×#54811yescharacteristic
655C22C5×#54811yescharacteristic
656C22C2×C5×#13511yescharacteristic
657C22C5×#57511yescharacteristic
658C22C5×#57711yescharacteristic
659C22C5×#57811yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—24no—
664C4—41no—
665C4—42no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4C2×C5×#12411yescharacteristic
674C4C5×#53611yescharacteristic
675C4C5×#54811yescharacteristic
676C4C5×#54811yescharacteristic
677C2—161no—
678C2C5×#243611yescharacteristic
679C2C5×#300211yescharacteristic
680C2C5×#301311yescharacteristic
681C2C5×#336411yescharacteristic
682C2C5×#336511yescharacteristic
683C2C5×#337111yescharacteristic
684C2C5×#337711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#557C2semidirect
5. C5×#2026C2semidirect
7. C5×#2024C2semidirect
9. C5×#1989C2semidirect
10. C5×#1984C2semidirect
13. C5×#1878C2semidirect
14. C5×#1878C2semidirect
15. C4×C5×#103C2semidirect
63. #25937C5direct (N × H)
143. C2×#557C2×C5semidirect
147. #2026C2×C5semidirect
149. #2024C2×C5semidirect
151. #1989C2×C5semidirect
152. #1984C2×C5semidirect
155. #1878C2×C5semidirect
156. #1878C2×C5semidirect
157. C4×#103C2×C5semidirect
645. C5#25937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5572
C2×C5×#4882
C2×C5×#4642
C5×#25922
C5×#20262
C5×#20252
C5×#20242
C5×#20232
C5×#19892
C5×#19842
C5×#18802
C5×#18782
C4×C5×#1032
#259375