Finite Group Databasebeta

← C5×#26827 #11949547

Subgroups — C5×#26827 #11949547

Order 1280.

924 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#490C211yesmaximal, characteristic, complemented
2C2×C4×C5×D8C211yesmaximal, characteristic, complemented
3C5×#2454C211yesmaximal, characteristic, complemented
4C5×#2445C211yesmaximal, characteristic, complemented
5C5×#2067C211yesmaximal, characteristic, complemented
6C5×#2059C211yesmaximal, characteristic, complemented
7C5×#2054C211yesmaximal, characteristic, complemented
8C5×#2011C211yesmaximal, characteristic
9C5×#1972C211yesmaximal, characteristic, complemented
10C5×#1936C211yesmaximal, characteristic, complemented
11C5×#1936C211yesmaximal, characteristic, complemented
12C5×#1934C211yesmaximal, characteristic, complemented
13C5×#1879C211yesmaximal, characteristic, complemented
14C5×#1864C211yesmaximal, characteristic, complemented
15C5×#1771C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C2×C5×#127C2211yescharacteristic
19C2×C5×#125C2211yescharacteristic
20C2×C5×#123—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C5×#490—24no—
24C4×C5×D8—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×C4⋊C8C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#97C2211yescharacteristic
37C2×C5×#97C2211yescharacteristic
38C2×C4×C5×C8C2211yescharacteristic
39C5×#399—21no—
40C5×#396—21no—
41C5×#394—21no—
42C5×#394—21no—
43C5×#390C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#390C2211yescharacteristic
47C5×#390C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#389C2211yescharacteristic
51C5×#386—21no—
52C5×#385—21no—
53C5×#380—21no—
54C4×C5×C4⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26827C511yesmaximal, 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—
69C2×C5×D8—22no—
70C2×C5×D8—22no—
71C2×C5×D8—22no—
72C2×C5×D8—22no—
73C2×C5×D8—22no—
74C2×C5×D8—41no—
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C5×#127—22no—
80C5×#127—41no—
81C5×#125—22no—
82C5×#125—41no—
83C5×#123—44no—
84C4×C5×D4—22no—
85C4×C5×D4—22no—
86C4×C5×D4—41no—
87C4×C5×D4—41no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4D411yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C42×C5C2311yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C2×C42×C5C2311yescharacteristic
115C5×#107—22no—
116C5×#106—41no—
117C5×C4⋊C8—22no—
118C5×#102—22no—
119C5×#102—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×#102D414yes—
126C5×#97—22no—
127C5×#97—22no—
128C4×C5×C8—22no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95D411yescharacteristic
133C5×#95D411yescharacteristic
134C2×#490C2×C511yescharacteristic, complemented
135C2×C4×D8C2×C511yescharacteristic, complemented
136#2454C2×C511yescharacteristic, complemented
137#2445C2×C511yescharacteristic, complemented
138#2067C2×C511yescharacteristic, complemented
139#2059C2×C511yescharacteristic, complemented
140#2054C2×C511yescharacteristic, complemented
141#2011C2×C511yescharacteristic
142#1972C2×C511yescharacteristic, complemented
143#1936C2×C511yescharacteristic, complemented
144#1936C2×C511yescharacteristic, complemented
145#1934C2×C511yescharacteristic, complemented
146#1879C2×C511yescharacteristic, complemented
147#1864C2×C511yescharacteristic, complemented
148#1771C2×C511yescharacteristic, complemented
149C24×C5—21no—
150C24×C5—21no—
151C24×C5—21no—
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—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—42no—
169C2×C5×D4—42no—
170C2×C5×D4—42no—
171C2×C5×D4—42no—
172C2×C5×D4—81no—
173C2×C5×D4—81no—
174C2×C5×D4C2×D412yes—
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—81no—
186C22×C4×C5—81no—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2411yescharacteristic
194C5×D8—28no—
195C5×D8—44no—
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—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8C2×D412yes—
206C2×C5×C8#4112yes—
207C2×C5×C8#4112yes—
208C5×C4⋊C4—22no—
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—41no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—81no—
223C5×C4⋊C4—81no—
224C5×C4⋊C4C2×D412yes—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—81no—
232C5×C22⋊C4—81no—
233C5×C22⋊C4—81no—
234C5×C22⋊C4—81no—
235C5×C22⋊C4—81no—
236C5×C22⋊C4—81no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—21no—
243C22×D8C22×C511yescharacteristic
244C22×D8C22×C511yescharacteristic
245C2×#127C22×C511yescharacteristic
246C2×#125C22×C511yescharacteristic
247C2×#123—21no—
248C2×C4×D4C22×C511yescharacteristic
249C2×C4×D4C22×C511yescharacteristic
250#490—24no—
251C4×D8—24no—
252C2×#107C22×C511yescharacteristic
253C2×#106C22×C511yescharacteristic
254C2×C4⋊C8C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×#102C22×C511yescharacteristic
263C2×#97C22×C511yescharacteristic
264C2×#97C22×C511yescharacteristic
265C2×C4×C8C22×C511yescharacteristic
266#399—21no—
267#396—21no—
268#394—21no—
269#394—21no—
270#390C22×C511yescharacteristic
271#390C22×C511yescharacteristic
272#390C22×C511yescharacteristic
273#390C22×C511yescharacteristic
274#390C22×C511yescharacteristic
275#389C22×C511yescharacteristic
276#389C22×C511yescharacteristic
277#389C22×C511yescharacteristic
278#386—21no—
279#385—21no—
280#380—21no—
281C4×C4⋊C4C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#336C22×C511yescharacteristic
287#336C22×C511yescharacteristic
288C23×C5—22no—
289C23×C5—22no—
290C23×C5—41no—
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—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5C22×D411yescharacteristic
310C5×D4—22no—
311C5×D4—22no—
312C5×D4—22no—
313C5×D4—22no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—41no—
317C5×D4—41no—
318C5×D4—41no—
319C5×D4—41no—
320C5×D4—41no—
321C5×D4—41no—
322C5×D4—84no—
323C5×D4—84no—
324C2×C4×C5—21no—
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—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
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—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—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—84no—
357C2×C4×C5—84no—
358C2×C4×C5AGL(1,ℤ/8)12yes—
359C2×C4×C5C22×D411yescharacteristic
360C2×C4×C5C2×#4111yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C2×C4×C5C2×#4111yescharacteristic
363C2×C4×C5H(5,𝔽2)11yescharacteristic
364C2×C4×C52−1+411yescharacteristic
365C5×C8—22no—
366C5×C8—22no—
367C5×C8—22no—
368C5×C8—41no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4C23×C511yescharacteristic
372C22×D4C23×C511yescharacteristic
373C22×D4C23×C511yescharacteristic
374C23×C4—21no—
375C23×C4—21no—
376C2×D8—22no—
377C2×D8—22no—
378C2×D8—22no—
379C2×D8—22no—
380C2×D8—22no—
381C2×D8—41no—
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386#127—22no—
387#127—41no—
388#125—22no—
389#125—41no—
390#123—44no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—41no—
394C4×D4—41no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C5×D411yescharacteristic
401C2×C4⋊C4C5×D411yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
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×C42C23×C511yescharacteristic
420C2×C42C23×C511yescharacteristic
421C2×C42C23×C511yescharacteristic
422#107—22no—
423#106—41no—
424C4⋊C8—22no—
425#102—22no—
426#102—22no—
427#102—22no—
428#102—22no—
429#102—22no—
430#102—22no—
431#102—22no—
432#102C5×D414yes—
433#97—22no—
434#97—22no—
435C4×C8—22no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95C5×D411yescharacteristic
440#95C5×D411yescharacteristic
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
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×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5#53211yescharacteristic
463C22×C5D4211yescharacteristic
464C22×C5#54811yescharacteristic
465C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
466C22×C5#57511yescharacteristic
467C22×C5#57611yescharacteristic
468C22×C5#57611yescharacteristic
469C4×C5—22no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5—41no—
473C4×C5—42no—
474C4×C5—41no—
475C4×C5—41no—
476C4×C5—81no—
477C4×C5—81no—
478C4×C5—81no—
479C4×C5—81no—
480C4×C5#52511yescharacteristic
481C4×C5#54211yescharacteristic
482C4×C5#54711yescharacteristic
483C4×C5#55111yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
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—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C2×C5×D412yes—
510C2×D4C5×#4112yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C24×C511yescharacteristic
529D8—28no—
530D8—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8C2×C5×D412yes—
541C2×C8C5×#4112yes—
542C2×C8C5×#4112yes—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—41no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4C2×C5×D412yes—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C2×C5—82no—
579C2×C5—82no—
580C2×C5—161no—
581C2×C5#246111yescharacteristic
582C2×C5#317111yescharacteristic
583C2×C5#317611yescharacteristic
584C2×C5#326411yescharacteristic
585C2×C5#326811yescharacteristic
586C2×C5#336611yescharacteristic
587C2×C5#337011yescharacteristic
588C23—22no—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
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—
609C23C22×C5×D411yescharacteristic
610D4—22no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—84no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
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—84no—
657C2×C4—84no—
658C2×C4C5×AGL(1,ℤ/8)12yes—
659C2×C4C22×C5×D411yescharacteristic
660C2×C4C2×C5×#4111yescharacteristic
661C2×C4C2×C5×#4111yescharacteristic
662C2×C4C2×C5×#4111yescharacteristic
663C2×C4C5×H(5,𝔽2)11yescharacteristic
664C2×C4C5×2−1+411yescharacteristic
665C8—22no—
666C8—22no—
667C8—22no—
668C8—41no—
669C5#2682711yescharacteristic, direct product factor, Sylow
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C5×#53211yescharacteristic
692C22C5×D4211yescharacteristic
693C22C5×#54811yescharacteristic
694C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
695C22C5×#57511yescharacteristic
696C22C5×#57611yescharacteristic
697C22C5×#57611yescharacteristic
698C4—22no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C5×#52511yescharacteristic
710C4C5×#54211yescharacteristic
711C4C5×#54711yescharacteristic
712C4C5×#55111yescharacteristic
713C2—82no—
714C2—82no—
715C2—161no—
716C2C5×#246111yescharacteristic
717C2C5×#317111yescharacteristic
718C2C5×#317611yescharacteristic
719C2C5×#326411yescharacteristic
720C2C5×#326811yescharacteristic
721C2C5×#336611yescharacteristic
722C2C5×#337011yescharacteristic
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×#490C2semidirect
2. C2×C4×C5×D8C2semidirect
3. C5×#2454C2semidirect
4. C5×#2445C2semidirect
5. C5×#2067C2semidirect
6. C5×#2059C2semidirect
7. C5×#2054C2semidirect
9. C5×#1972C2semidirect
10. C5×#1936C2semidirect
11. C5×#1936C2semidirect
12. C5×#1934C2semidirect
13. C5×#1879C2semidirect
14. C5×#1864C2semidirect
15. C5×#1771C2semidirect
61. #26827C5direct (N × H)
134. C2×#490C2×C5semidirect
135. C2×C4×D8C2×C5semidirect
136. #2454C2×C5semidirect
137. #2445C2×C5semidirect
138. #2067C2×C5semidirect
139. #2059C2×C5semidirect
140. #2054C2×C5semidirect
142. #1972C2×C5semidirect
143. #1936C2×C5semidirect
144. #1936C2×C5semidirect
145. #1934C2×C5semidirect
146. #1879C2×C5semidirect
147. #1864C2×C5semidirect
148. #1771C2×C5semidirect
669. C5#26827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4902
C2×C4×C5×D82
C5×#24542
C5×#24452
C5×#20672
C5×#20592
C5×#20542
C5×#20112
C5×#19722
C5×#19362
C5×#19342
C5×#18792
C5×#18642
C5×#17712
#268275