Finite Group Databasebeta

← C5×#26888 #11949608

Subgroups — C5×#26888 #11949608

Order 1280.

976 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#478C211yesmaximal, characteristic, complemented
2C2×C4×C5×D8C211yesmaximal, characteristic, complemented
3C5×#2454C211yesmaximal, characteristic, complemented
4C5×#2366C211yesmaximal, characteristic, complemented
5C5×#2054C211yesmaximal, characteristic, complemented
6C5×#2041C211yesmaximal, characteristic, complemented
7C5×#2025C211yesmaximal, characteristic, complemented
8C5×#2011C211yesmaximal, characteristic
9C5×#1934C211yesmaximal, characteristic, complemented
10C5×#1926C211yesmaximal, characteristic, complemented
11C5×#1921C211yesmaximal, characteristic, complemented
12C5×#1916C211yesmaximal, characteristic, complemented
13C5×#1879C211yesmaximal, characteristic, complemented
14C5×#1879C211yesmaximal, characteristic, complemented
15C5×#1864C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C2×C5×#127C2211yescharacteristic
19C2×C5×#125C2211yescharacteristic
20C2×C4×C5×D4—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C2×C4×C5×D4C2211yescharacteristic
24C5×#478—24no—
25C4×C5×D8—24no—
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C4×C5×C8C2211yescharacteristic
38C5×#399—21no—
39C5×#396—21no—
40C5×#390—21no—
41C5×#390C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#390C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#386—21no—
48C5×#386—21no—
49C5×#385—21no—
50C5×#380—21no—
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26888C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4C2311yescharacteristic
65C22×C5×D4C2311yescharacteristic
66C22×C5×D4C2311yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C2×C5×D8—22no—
71C2×C5×D8—22no—
72C2×C5×D8—22no—
73C2×C5×D8—22no—
74C2×C5×D8—22no—
75C2×C5×D8—41no—
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×#127—22no—
81C5×#127—22no—
82C5×#125—22no—
83C5×#125—41no—
84C4×C5×D4—22no—
85C4×C5×D4—22no—
86C4×C5×D4—22no—
87C4×C5×D4—41no—
88C4×C5×D4—41no—
89C4×C5×D4—41no—
90C4×C5×D4—44no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4D411yescharacteristic
96C2×C5×C4⋊C4D411yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C2×C42×C5C2311yescharacteristic
117C5×#107D414yescomplemented
118C5×#106—22no—
119C5×C4⋊C8—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×#102—22no—
126C5×#102—22no—
127C5×#102—41no—
128C4×C5×C8—22no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95D411yescharacteristic
133C5×#95D411yescharacteristic
134C2×#478C2×C511yescharacteristic, complemented
135C2×C4×D8C2×C511yescharacteristic, complemented
136#2454C2×C511yescharacteristic, complemented
137#2366C2×C511yescharacteristic, complemented
138#2054C2×C511yescharacteristic, complemented
139#2041C2×C511yescharacteristic, complemented
140#2025C2×C511yescharacteristic, complemented
141#2011C2×C511yescharacteristic
142#1934C2×C511yescharacteristic, complemented
143#1926C2×C511yescharacteristic, complemented
144#1921C2×C511yescharacteristic, complemented
145#1916C2×C511yescharacteristic, complemented
146#1879C2×C511yescharacteristic, complemented
147#1879C2×C511yescharacteristic, complemented
148#1864C2×C511yescharacteristic, complemented
149C24×C5—21no—
150C24×C5—21no—
151C24×C5—21no—
152C2×C5×D4—24no—
153C2×C5×D4—24no—
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—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—42no—
170C2×C5×D4—42no—
171C2×C5×D4—81no—
172C2×C5×D4—81no—
173C2×C5×D4#4112yes—
174C2×C5×D4#4112yes—
175C2×C5×D4#4112yes—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—42no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—42no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—81no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
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×D8—28no—
198C5×D8—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×C8C2×D412yes—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
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—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—81no—
224C5×C4⋊C4—81no—
225C5×C4⋊C4C2×D412yes—
226C5×C4⋊C4C2×D412yes—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—81no—
234C5×C22⋊C4—81no—
235C5×C22⋊C4—81no—
236C5×C22⋊C4—81no—
237C5×C22⋊C4—81no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—21no—
244C42×C5—42no—
245C22×D8C22×C511yescharacteristic
246C22×D8C22×C511yescharacteristic
247C2×#127C22×C511yescharacteristic
248C2×#125C22×C511yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4C22×C511yescharacteristic
251C2×C4×D4C22×C511yescharacteristic
252C2×C4×D4C22×C511yescharacteristic
253#478—24no—
254C4×D8—24no—
255C2×#107C22×C511yescharacteristic
256C2×#106C22×C511yescharacteristic
257C2×C4⋊C8C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×#102C22×C511yescharacteristic
263C2×#102C22×C511yescharacteristic
264C2×#102C22×C511yescharacteristic
265C2×#102C22×C511yescharacteristic
266C2×C4×C8C22×C511yescharacteristic
267#399—21no—
268#396—21no—
269#390—21no—
270#390C22×C511yescharacteristic
271#390C22×C511yescharacteristic
272#390C22×C511yescharacteristic
273#390C22×C511yescharacteristic
274#389C22×C511yescharacteristic
275#389C22×C511yescharacteristic
276#386—21no—
277#386—21no—
278#385—21no—
279#380—21no—
280C4×C4⋊C4C22×C511yescharacteristic
281C4×C4⋊C4C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#336C22×C511yescharacteristic
287#336C22×C511yescharacteristic
288#336C22×C511yescharacteristic
289#336C22×C511yescharacteristic
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—22no—
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—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5C22×D411yescharacteristic
312C5×D4—22no—
313C5×D4—22no—
314C5×D4—22no—
315C5×D4—22no—
316C5×D4—22no—
317C5×D4—22no—
318C5×D4—48no—
319C5×D4—41no—
320C5×D4—41no—
321C5×D4—41no—
322C5×D4—41no—
323C5×D4—41no—
324C5×D4—41no—
325C5×D4—84no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
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—22no—
335C2×C4×C5—22no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
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—84no—
358C2×C4×C5—84no—
359C2×C4×C5—84no—
360C2×C4×C5#13512yes—
361C2×C4×C5AGL(1,ℤ/8)12yes—
362C2×C4×C5C22×D411yescharacteristic
363C2×C4×C5C2×#4111yescharacteristic
364C2×C4×C5C2×#4111yescharacteristic
365C2×C4×C5C2×#4111yescharacteristic
366C2×C4×C5H(5,𝔽2)11yescharacteristic
367C2×C4×C52−1+411yescharacteristic
368C5×C8—22no—
369C5×C8—41no—
370C5×C8—41no—
371C5×C8—41no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4C23×C511yescharacteristic
375C22×D4C23×C511yescharacteristic
376C22×D4C23×C511yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—21no—
380C2×D8—22no—
381C2×D8—22no—
382C2×D8—22no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—41no—
386C22×C8C23×C511yescharacteristic
387C22×C8C23×C511yescharacteristic
388C22×C8C23×C511yescharacteristic
389C22×C8C23×C511yescharacteristic
390#127—22no—
391#127—22no—
392#125—22no—
393#125—41no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—41no—
398C4×D4—41no—
399C4×D4—41no—
400C4×D4—44no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4C5×D411yescharacteristic
406C2×C4⋊C4C5×D411yescharacteristic
407C2×C4⋊C4C23×C511yescharacteristic
408C2×C4⋊C4C23×C511yescharacteristic
409C2×C4⋊C4C23×C511yescharacteristic
410C2×C4⋊C4C23×C511yescharacteristic
411C2×C4⋊C4C23×C511yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
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×C42C23×C511yescharacteristic
425C2×C42C23×C511yescharacteristic
426C2×C42C23×C511yescharacteristic
427#107C5×D414yescomplemented
428#106—22no—
429C4⋊C8—22no—
430#102—22no—
431#102—22no—
432#102—22no—
433#102—22no—
434#102—22no—
435#102—22no—
436#102—22no—
437#102—41no—
438C4×C8—22no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95C5×D411yescharacteristic
443#95C5×D411yescharacteristic
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—42no—
451C22×C5—42no—
452C22×C5—42no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5#52511yescharacteristic
466C22×C5D4211yescharacteristic
467C22×C5#54811yescharacteristic
468C22×C5C2×#13511yescharacteristic
469C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C5#57611yescharacteristic
471C22×C5#57611yescharacteristic
472C4×C5—22no—
473C4×C5—22no—
474C4×C5—41no—
475C4×C5—41no—
476C4×C5—42no—
477C4×C5—42no—
478C4×C5—41no—
479C4×C5—41no—
480C4×C5—81no—
481C4×C5—81no—
482C4×C5—81no—
483C4×C5#52511yescharacteristic
484C4×C5#53911yescharacteristic
485C4×C5#54811yescharacteristic
486C4×C5#55111yescharacteristic
487C24—21no—
488C24—21no—
489C24—21no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
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—81no—
510C2×D4—81no—
511C2×D4C5×#4112yes—
512C2×D4C5×#4112yes—
513C2×D4C5×#4112yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D411yescharacteristic
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D411yescharacteristic
534C22×C4C24×C511yescharacteristic
535D8—28no—
536D8—44no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C2×C5×D412yes—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4C2×C5×D412yes—
564C4⋊C4C2×C5×D412yes—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C2×C5—82no—
584C2×C5—82no—
585C2×C5—82no—
586C2×C5#246311yescharacteristic
587C2×C5#310511yescharacteristic
588C2×C5#312211yescharacteristic
589C2×C5#326411yescharacteristic
590C2×C5#328711yescharacteristic
591C2×C5#336111yescharacteristic
592C2×C5#336611yescharacteristic
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C22×C5×D411yescharacteristic
615D4—22no—
616D4—22no—
617D4—22no—
618D4—22no—
619D4—22no—
620D4—22no—
621D4—48no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—84no—
629C2×C4—21no—
630C2×C4—21no—
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—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
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—84no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4C5×#13512yes—
664C2×C4C5×AGL(1,ℤ/8)12yes—
665C2×C4C22×C5×D411yescharacteristic
666C2×C4C2×C5×#4111yescharacteristic
667C2×C4C2×C5×#4111yescharacteristic
668C2×C4C2×C5×#4111yescharacteristic
669C2×C4C5×H(5,𝔽2)11yescharacteristic
670C2×C4C5×2−1+411yescharacteristic
671C8—22no—
672C8—41no—
673C8—41no—
674C8—41no—
675C5#2688811yescharacteristic, direct product factor, Sylow
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C5×#52511yescharacteristic
698C22C5×D4211yescharacteristic
699C22C5×#54811yescharacteristic
700C22C2×C5×#13511yescharacteristic
701C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
702C22C5×#57611yescharacteristic
703C22C5×#57611yescharacteristic
704C4—22no—
705C4—22no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4C5×#52511yescharacteristic
716C4C5×#53911yescharacteristic
717C4C5×#54811yescharacteristic
718C4C5×#55111yescharacteristic
719C2—82no—
720C2—82no—
721C2—82no—
722C2C5×#246311yescharacteristic
723C2C5×#310511yescharacteristic
724C2C5×#312211yescharacteristic
725C2C5×#326411yescharacteristic
726C2C5×#328711yescharacteristic
727C2C5×#336111yescharacteristic
728C2C5×#336611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#478C2semidirect
2. C2×C4×C5×D8C2semidirect
3. C5×#2454C2semidirect
4. C5×#2366C2semidirect
5. C5×#2054C2semidirect
6. C5×#2041C2semidirect
7. C5×#2025C2semidirect
9. C5×#1934C2semidirect
10. C5×#1926C2semidirect
11. C5×#1921C2semidirect
12. C5×#1916C2semidirect
13. C5×#1879C2semidirect
14. C5×#1879C2semidirect
15. C5×#1864C2semidirect
61. #26888C5direct (N × H)
117. C5×#107D4semidirect
134. C2×#478C2×C5semidirect
135. C2×C4×D8C2×C5semidirect
136. #2454C2×C5semidirect
137. #2366C2×C5semidirect
138. #2054C2×C5semidirect
139. #2041C2×C5semidirect
140. #2025C2×C5semidirect
142. #1934C2×C5semidirect
143. #1926C2×C5semidirect
144. #1921C2×C5semidirect
145. #1916C2×C5semidirect
146. #1879C2×C5semidirect
147. #1879C2×C5semidirect
148. #1864C2×C5semidirect
427. #107C5×D4semidirect
675. C5#26888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4782
C2×C4×C5×D82
C5×#24542
C5×#23662
C5×#20542
C5×#20412
C5×#20252
C5×#20112
C5×#19342
C5×#19262
C5×#19212
C5×#19162
C5×#18792
C5×#18642
#268885