Finite Group Databasebeta

← C5×#26812 #11949532

Subgroups — C5×#26812 #11949532

Order 1280.

910 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#482C211yesmaximal, characteristic, complemented
2C2×C5×#474C211yesmaximal, characteristic, complemented
3C5×#2491C211yesmaximal, characteristic, complemented
4C5×#2363C211yesmaximal, characteristic, complemented
5C5×#2065C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#2034C211yesmaximal, characteristic, complemented
8C5×#1999C211yesmaximal, characteristic
9C5×#1972C211yesmaximal, characteristic, complemented
10C5×#1926C211yesmaximal, characteristic, complemented
11C5×#1925C211yesmaximal, characteristic, complemented
12C5×#1924C211yesmaximal, characteristic, complemented
13C5×#1879C211yesmaximal, characteristic, complemented
14C5×#1854C211yesmaximal, characteristic, complemented
15C5×#1776C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×#124—21no—
19C2×C5×#121C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C5×#482—24no—
24C5×#474—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×#97C2211yescharacteristic
40C5×#394—21no—
41C5×#393—21no—
42C5×#390—21no—
43C5×#390C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#388—21no—
48C5×#388—21no—
49C5×#386—21no—
50C5×#380C2211yescharacteristic
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C22⋊C4—21no—
54C4×C5×C22⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26812C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8—21no—
63C22×C5×D4—21no—
64C22×C5×D4—21no—
65C22×C5×D4C2311yescharacteristic
66C22×C5×D4C2311yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C2×C5×D8—22no—
70C2×C5×D8—22no—
71C2×C5×D8—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8—41no—
78C5×#124—44no—
79C5×#121—22no—
80C5×#121—22no—
81C5×#121—22no—
82C5×#121—41no—
83C4×C5×D4—22no—
84C4×C5×D4—41no—
85C5×#117—22no—
86C5×#117—41no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
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⋊C4D411yescharacteristic
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C5×#107—22no—
114C5×#107D414yescomplemented
115C5×#106—22no—
116C5×#106—22no—
117C5×#106—41no—
118C5×C4⋊C8—22no—
119C5×#102—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×C22⋊C8—22no—
126C5×C22⋊C8—22no—
127C5×#97—22no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95D411yescharacteristic
133C5×#95D411yescharacteristic
134C2×#482C2×C511yescharacteristic, complemented
135C2×#474C2×C511yescharacteristic, complemented
136#2491C2×C511yescharacteristic, complemented
137#2363C2×C511yescharacteristic, complemented
138#2065C2×C511yescharacteristic, complemented
139#2058C2×C511yescharacteristic, complemented
140#2034C2×C511yescharacteristic, complemented
141#1999C2×C511yescharacteristic
142#1972C2×C511yescharacteristic, complemented
143#1926C2×C511yescharacteristic, complemented
144#1925C2×C511yescharacteristic, complemented
145#1924C2×C511yescharacteristic, complemented
146#1879C2×C511yescharacteristic, complemented
147#1854C2×C511yescharacteristic, complemented
148#1776C2×C511yescharacteristic, complemented
149C24×C5—21no—
150C24×C5—21no—
151C24×C5C2×D411yescharacteristic
152C2×C5×Q8—42no—
153C2×C5×Q8—42no—
154C2×C5×Q8—81no—
155C2×C5×D4—24no—
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—42no—
168C2×C5×D4—42no—
169C2×C5×D4—81no—
170C2×C5×D4—81no—
171C2×C5×D4—81no—
172C2×C5×D4#4112yes—
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×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—81no—
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—44no—
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—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8C2×D412yes—
206C2×C5×C8#4112yes—
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—42no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4C2×D412yes—
219C5×C4⋊C4C2×D412yes—
220C5×C4⋊C4#4112yes—
221C5×C22⋊C4—24no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—41no—
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—42no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—81no—
233C5×C22⋊C4—81no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—21no—
237C42×C5—21no—
238C42×C5—42no—
239C42×C5—42no—
240C42×C5—81no—
241C22×D8C22×C511yescharacteristic
242C2×C4⋊Q8C22×C511yescharacteristic
243C2×#124—21no—
244C2×#121C22×C511yescharacteristic
245C2×#121C22×C511yescharacteristic
246C2×C4×D4C22×C511yescharacteristic
247C2×#117C22×C511yescharacteristic
248#482—24no—
249#474—24no—
250C2×#107C22×C511yescharacteristic
251C2×#107C22×C511yescharacteristic
252C2×#106C22×C511yescharacteristic
253C2×#106C22×C511yescharacteristic
254C2×#106C22×C511yescharacteristic
255C2×C4⋊C8C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×C22⋊C8C22×C511yescharacteristic
263C2×C22⋊C8C22×C511yescharacteristic
264C2×#97C22×C511yescharacteristic
265#394—21no—
266#393—21no—
267#390—21no—
268#390C22×C511yescharacteristic
269#390C22×C511yescharacteristic
270#390C22×C511yescharacteristic
271#389C22×C511yescharacteristic
272#388—21no—
273#388—21no—
274#386—21no—
275#380C22×C511yescharacteristic
276C4×C4⋊C4C22×C511yescharacteristic
277C4×C4⋊C4C22×C511yescharacteristic
278C4×C22⋊C4—21no—
279C4×C22⋊C4C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#336C22×C511yescharacteristic
285#336C22×C511yescharacteristic
286C23×C5—22no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
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×C5C22×D411yescharacteristic
308C5×Q8—84no—
309C5×D4—22no—
310C5×D4—22no—
311C5×D4—41no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—41no—
317C5×D4—84no—
318C5×D4—84no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—22no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
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—21no—
335C2×C4×C5—21no—
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—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—84no—
356C2×C4×C5AGL(1,ℤ/8)12yes—
357C2×C4×C5C22×D411yescharacteristic
358C2×C4×C5C2×#4111yescharacteristic
359C2×C4×C5C2×#4111yescharacteristic
360C2×C4×C5C2×#4111yescharacteristic
361C2×C4×C5H(5,𝔽2)11yescharacteristic
362C2×C4×C52−1+411yescharacteristic
363C5×C8—22no—
364C5×C8—22no—
365C5×C8—41no—
366C5×C8—41no—
367C22×Q8—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4C23×C511yescharacteristic
371C22×D4C23×C511yescharacteristic
372C23×C4—21no—
373C23×C4C23×C511yescharacteristic
374C2×D8—22no—
375C2×D8—22no—
376C2×D8—41no—
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379C22×C8C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C4⋊Q8—22no—
382C4⋊Q8—41no—
383#124—44no—
384#121—22no—
385#121—22no—
386#121—22no—
387#121—41no—
388C4×D4—22no—
389C4×D4—41no—
390#117—22no—
391#117—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
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⋊C4—21no—
411C2×C22⋊C4C5×D411yescharacteristic
412C2×C22⋊C4C5×D411yescharacteristic
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42C23×C511yescharacteristic
417C2×C42C23×C511yescharacteristic
418#107—22no—
419#107C5×D414yescomplemented
420#106—22no—
421#106—22no—
422#106—41no—
423C4⋊C8—22no—
424#102—22no—
425#102—22no—
426#102—22no—
427#102—22no—
428#102—22no—
429#102—22no—
430C22⋊C8—22no—
431C22⋊C8—22no—
432#97—22no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95C5×D411yescharacteristic
438#95C5×D411yescharacteristic
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—42no—
443C22×C5—41no—
444C22×C5—42no—
445C22×C5—41no—
446C22×C5—42no—
447C22×C5—41no—
448C22×C5—41no—
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#52511yescharacteristic
461C22×C5D4211yescharacteristic
462C22×C5#54711yescharacteristic
463C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
464C22×C5#57511yescharacteristic
465C22×C5#57611yescharacteristic
466C22×C5#57711yescharacteristic
467C4×C5—22no—
468C4×C5—41no—
469C4×C5—41no—
470C4×C5—42no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—42no—
474C4×C5—41no—
475C4×C5—81no—
476C4×C5—81no—
477C4×C5—81no—
478C4×C5#53211yescharacteristic
479C4×C5#54211yescharacteristic
480C4×C5#54811yescharacteristic
481C4×C5#55111yescharacteristic
482C24—21no—
483C24—21no—
484C24C2×C5×D411yescharacteristic
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—81no—
488C2×D4—24no—
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—42no—
501C2×D4—42no—
502C2×D4—81no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4C5×#4112yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C24×C511yescharacteristic
527D8—44no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8C2×C5×D412yes—
539C2×C8C5×#4112yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4C2×C5×D412yes—
552C4⋊C4C2×C5×D412yes—
553C4⋊C4C5×#4112yes—
554C22⋊C4—24no—
555C22⋊C4—22no—
556C22⋊C4—41no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—42no—
573C42—81no—
574C2×C5—81no—
575C2×C5—82no—
576C2×C5—161no—
577C2×C5#246111yescharacteristic
578C2×C5#311511yescharacteristic
579C2×C5#311811yescharacteristic
580C2×C5#326411yescharacteristic
581C2×C5#327111yescharacteristic
582C2×C5#334711yescharacteristic
583C2×C5#335411yescharacteristic
584C23—22no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
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—
605C23C22×C5×D411yescharacteristic
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—84no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
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—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—84no—
654C2×C4C5×AGL(1,ℤ/8)12yes—
655C2×C4C22×C5×D411yescharacteristic
656C2×C4C2×C5×#4111yescharacteristic
657C2×C4C2×C5×#4111yescharacteristic
658C2×C4C2×C5×#4111yescharacteristic
659C2×C4C5×H(5,𝔽2)11yescharacteristic
660C2×C4C5×2−1+411yescharacteristic
661C8—22no—
662C8—22no—
663C8—41no—
664C8—41no—
665C5#2681211yescharacteristic, direct product factor, Sylow
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—41no—
673C22—42no—
674C22—41no—
675C22—42no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C5×#52511yescharacteristic
688C22C5×D4211yescharacteristic
689C22C5×#54711yescharacteristic
690C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
691C22C5×#57511yescharacteristic
692C22C5×#57611yescharacteristic
693C22C5×#57711yescharacteristic
694C4—22no—
695C4—42no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4C5×#53211yescharacteristic
706C4C5×#54211yescharacteristic
707C4C5×#54811yescharacteristic
708C4C5×#55111yescharacteristic
709C2—81no—
710C2—82no—
711C2—161no—
712C2C5×#246111yescharacteristic
713C2C5×#311511yescharacteristic
714C2C5×#311811yescharacteristic
715C2C5×#326411yescharacteristic
716C2C5×#327111yescharacteristic
717C2C5×#334711yescharacteristic
718C2C5×#335411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#1999C2
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
2. C2×C5×#474C2semidirect
3. C5×#2491C2semidirect
4. C5×#2363C2semidirect
5. C5×#2065C2semidirect
6. C5×#2058C2semidirect
7. C5×#2034C2semidirect
9. C5×#1972C2semidirect
10. C5×#1926C2semidirect
11. C5×#1925C2semidirect
12. C5×#1924C2semidirect
13. C5×#1879C2semidirect
14. C5×#1854C2semidirect
15. C5×#1776C2semidirect
61. #26812C5direct (N × H)
114. C5×#107D4semidirect
134. C2×#482C2×C5semidirect
135. C2×#474C2×C5semidirect
136. #2491C2×C5semidirect
137. #2363C2×C5semidirect
138. #2065C2×C5semidirect
139. #2058C2×C5semidirect
140. #2034C2×C5semidirect
142. #1972C2×C5semidirect
143. #1926C2×C5semidirect
144. #1925C2×C5semidirect
145. #1924C2×C5semidirect
146. #1879C2×C5semidirect
147. #1854C2×C5semidirect
148. #1776C2×C5semidirect
419. #107C5×D4semidirect
665. C5#26812direct (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×#4742
C5×#24912
C5×#23632
C5×#20652
C5×#20582
C5×#20342
C5×#19992
C5×#19722
C5×#19262
C5×#19252
C5×#19242
C5×#18792
C5×#18542
C5×#17762
#268125