Finite Group Databasebeta

← C5×#26392 #11949112

Subgroups — C5×#26392 #11949112

Order 1280.

962 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×#476C211yesmaximal, characteristic, complemented
2C2×C5×#442C211yesmaximal, characteristic
3C5×#2452C211yesmaximal, characteristic, complemented
4C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#2094C211yesmaximal, characteristic, complemented
6C5×#2084C211yesmaximal, characteristic, complemented
7C5×#2067C211yesmaximal, characteristic, complemented
8C5×#2058C211yesmaximal, characteristic, complemented
9C5×#1943C211yesmaximal, characteristic, complemented
10C5×#1917C211yesmaximal, characteristic, complemented
11C5×#1879C211yesmaximal, characteristic
12C5×#1879C211yesmaximal, characteristic
13C5×#1864C211yesmaximal, characteristic, complemented
14C5×#1864C211yesmaximal, characteristic, complemented
15C5×#1862C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8—21no—
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic
23C22×C5×C4⋊C4—21no—
24C5×#476—24no—
25C5×#442—24no—
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×C4⋊C8C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#97C2211yescharacteristic
39C5×#396—21no—
40C5×#393—21no—
41C5×#390C2211yescharacteristic
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#385—21no—
48C5×#385—21no—
49C5×#385—21no—
50C5×#384C2211yescharacteristic
51C5×#380—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26392C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8—21no—
63C22×C5×D4C2311yescharacteristic
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5—21no—
69C2×C5×D8—22no—
70C2×C5×D8—22no—
71C2×C5×D8Q814yescomplemented
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8—41no—
78C5×C22⋊Q8—44no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C4×C5×D4—22no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
84C4×C5×D4—41no—
85C4×C5×D4—41no—
86C4×C5×D4—41no—
87C2×C5×C4⋊C4—21no—
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⋊C4—21no—
94C2×C5×C4⋊C4—44no—
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×C4⋊C4C2311yescharacteristic
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×C42×C5C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C5×#107—22no—
115C5×#106—22no—
116C5×#106—22no—
117C5×#106—22no—
118C5×#106—41no—
119C5×C4⋊C8—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—41no—
125C5×#102D414yes—
126C5×#97—22no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95D411yescharacteristic
132C5×#95D411yescharacteristic
133C2×#476C2×C511yescharacteristic, complemented
134C2×#442C2×C511yescharacteristic
135#2452C2×C511yescharacteristic, complemented
136D4×C4⋊C4C2×C511yescharacteristic, complemented
137#2094C2×C511yescharacteristic, complemented
138#2084C2×C511yescharacteristic, complemented
139#2067C2×C511yescharacteristic, complemented
140#2058C2×C511yescharacteristic, complemented
141#1943C2×C511yescharacteristic, complemented
142#1917C2×C511yescharacteristic, complemented
143#1879C2×C511yescharacteristic
144#1879C2×C511yescharacteristic
145#1864C2×C511yescharacteristic, complemented
146#1864C2×C511yescharacteristic, complemented
147#1862C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5—21no—
150C2×C5×Q8—42no—
151C2×C5×Q8—42no—
152C2×C5×Q8—81no—
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×D4C2×D412yes—
162C2×C5×D4C2×Q812yes—
163C2×C5×D4C2×Q812yes—
164C2×C5×D4#4112yes—
165C22×C4×C5—24no—
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—42no—
173C22×C4×C5—42no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5—42no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—42no—
180C22×C4×C5—81no—
181C22×C4×C5—81no—
182C22×C4×C5—81no—
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2411yescharacteristic
190C5×D8—28no—
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—21no—
200C2×C5×C8—21no—
201C2×C5×C8C2×D412yes—
202C2×C5×C8C2×Q812yes—
203C5×C4⋊C4—22no—
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—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—42no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—81no—
222C5×C4⋊C4C2×D412yes—
223C5×C4⋊C4#4112yes—
224C5×C22⋊C4—24no—
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—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—21no—
237C42×C5—21no—
238C22×D8C22×C511yescharacteristic
239C2×C4⋊Q8C22×C511yescharacteristic
240C2×C22⋊Q8—21no—
241C2×C4×D4C22×C511yescharacteristic
242C2×C4×D4C22×C511yescharacteristic
243C2×C4×D4C22×C511yescharacteristic
244C2×C4×D4C22×C511yescharacteristic
245C22×C4⋊C4—21no—
246#476—24no—
247#442—24no—
248C2×#107C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×#106C22×C511yescharacteristic
252C2×#106C22×C511yescharacteristic
253C2×C4⋊C8C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#97C22×C511yescharacteristic
261#396—21no—
262#393—21no—
263#390C22×C511yescharacteristic
264#390C22×C511yescharacteristic
265#389C22×C511yescharacteristic
266#389C22×C511yescharacteristic
267#389C22×C511yescharacteristic
268#389C22×C511yescharacteristic
269#385—21no—
270#385—21no—
271#385—21no—
272#384C22×C511yescharacteristic
273#380—21no—
274C4×C4⋊C4C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#336C22×C511yescharacteristic
280#336C22×C511yescharacteristic
281#336C22×C511yescharacteristic
282#336C22×C511yescharacteristic
283C23×C5—22no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—41no—
288C23×C5—41no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5C22×D411yescharacteristic
298C5×Q8—84no—
299C5×D4—22no—
300C5×D4—22no—
301C5×D4—22no—
302C5×D4—22no—
303C5×D4—22no—
304C5×D4—41no—
305C5×D4—41no—
306C5×D4C22⋊Q814yescomplemented
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—48no—
326C2×C4×C5—41no—
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—84no—
343C2×C4×C5—84no—
344C2×C4×C5—84no—
345C2×C4×C5AGL(1,ℤ/8)12yes—
346C2×C4×C5AGL(1,ℤ/8)12yes—
347C2×C4×C5C22×D411yescharacteristic
348C2×C4×C5C22×Q811yescharacteristic
349C2×C4×C5C2×#4111yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5H(5,𝔽2)11yescharacteristic
352C2×C4×C52−1+411yescharacteristic
353C5×C8—22no—
354C5×C8—22no—
355C5×C8—41no—
356C5×C8—41no—
357C22×Q8—21no—
358C22×D4C23×C511yescharacteristic
359C22×D4C23×C511yescharacteristic
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C2×D8—22no—
365C2×D8—22no—
366C2×D8C5×Q814yescomplemented
367C22×C8C23×C511yescharacteristic
368C22×C8C23×C511yescharacteristic
369C22×C8C23×C511yescharacteristic
370C22×C8C23×C511yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—41no—
373C22⋊Q8—44no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—41no—
380C4×D4—41no—
381C4×D4—41no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4C5×D411yescharacteristic
391C2×C4⋊C4C5×D411yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C4⋊C4C23×C511yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
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×C42C23×C511yescharacteristic
407C2×C42C23×C511yescharacteristic
408C2×C42C23×C511yescharacteristic
409#107—22no—
410#106—22no—
411#106—22no—
412#106—22no—
413#106—41no—
414C4⋊C8—22no—
415#102—22no—
416#102—22no—
417#102—22no—
418#102—22no—
419#102—41no—
420#102C5×D414yes—
421#97—22no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95C5×D411yescharacteristic
427#95C5×D411yescharacteristic
428C22×C5—24no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5—42no—
432C22×C5—42no—
433C22×C5—42no—
434C22×C5—42no—
435C22×C5—42no—
436C22×C5—42no—
437C22×C5—42no—
438C22×C5—81no—
439C22×C5—81no—
440C22×C5—81no—
441C22×C5—81no—
442C22×C5#52511yescharacteristic
443C22×C5D4211yescharacteristic
444C22×C5D4×Q811yescharacteristic
445C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
447C22×C5#57711yescharacteristic
448C22×C5#57711yescharacteristic
449C4×C5—22no—
450C4×C5—22no—
451C4×C5—42no—
452C4×C5—41no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—41no—
456C4×C5—42no—
457C4×C5—81no—
458C4×C5—81no—
459C4×C5—81no—
460C4×C5—81no—
461C4×C5C2×C22⋊Q811yescharacteristic
462C4×C5#53911yescharacteristic
463C4×C5#54711yescharacteristic
464C4×C5#55411yescharacteristic
465C24—21no—
466C24—21no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—81no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4C2×C5×D412yes—
479C2×D4C2×C5×Q812yes—
480C2×D4C2×C5×Q812yes—
481C2×D4C5×#4112yes—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4C2×C5×D411yescharacteristic
501C22×C4C2×C5×D411yescharacteristic
502C22×C4C2×C5×D411yescharacteristic
503C22×C4C2×C5×D411yescharacteristic
504C22×C4C2×C5×D411yescharacteristic
505C22×C4C2×C5×D411yescharacteristic
506C22×C4C24×C511yescharacteristic
507D8—28no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8C2×C5×D412yes—
519C2×C8C2×C5×Q812yes—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—81no—
539C4⋊C4C2×C5×D412yes—
540C4⋊C4C5×#4112yes—
541C22⋊C4—24no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C2×C5—44no—
556C2×C5—82no—
557C2×C5#244911yescharacteristic
558C2×C5#310911yescharacteristic
559C2×C5#312511yescharacteristic
560C2×C5#326511yescharacteristic
561C2×C5#327211yescharacteristic
562C2×C5#338411yescharacteristic
563C2×C5#338411yescharacteristic
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×C5×D411yescharacteristic
579Q8—84no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4C5×C22⋊Q814yescomplemented
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—48no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—84no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4C5×AGL(1,ℤ/8)12yes—
627C2×C4C5×AGL(1,ℤ/8)12yes—
628C2×C4C22×C5×D411yescharacteristic
629C2×C4C22×C5×Q811yescharacteristic
630C2×C4C2×C5×#4111yescharacteristic
631C2×C4C2×C5×#4111yescharacteristic
632C2×C4C5×H(5,𝔽2)11yescharacteristic
633C2×C4C5×2−1+411yescharacteristic
634C8—22no—
635C8—22no—
636C8—41no—
637C8—41no—
638C5#2639211yescharacteristic, direct product factor, Sylow
639C22—24no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C5×#52511yescharacteristic
654C22C5×D4211yescharacteristic
655C22C5×D4×Q811yescharacteristic
656C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
657C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
658C22C5×#57711yescharacteristic
659C22C5×#57711yescharacteristic
660C4—22no—
661C4—22no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—42no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C2×C5×C22⋊Q811yescharacteristic
673C4C5×#53911yescharacteristic
674C4C5×#54711yescharacteristic
675C4C5×#55411yescharacteristic
676C2—44no—
677C2—82no—
678C2C5×#244911yescharacteristic
679C2C5×#310911yescharacteristic
680C2C5×#312511yescharacteristic
681C2C5×#326511yescharacteristic
682C2C5×#327211yescharacteristic
683C2C5×#338411yescharacteristic
684C2C5×#338411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D8C22
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×#476C2semidirect
3. C5×#2452C2semidirect
4. C5×D4×C4⋊C4C2semidirect
5. C5×#2094C2semidirect
6. C5×#2084C2semidirect
7. C5×#2067C2semidirect
8. C5×#2058C2semidirect
9. C5×#1943C2semidirect
10. C5×#1917C2semidirect
13. C5×#1864C2semidirect
14. C5×#1864C2semidirect
15. C5×#1862C2semidirect
61. #26392C5direct (N × H)
71. C2×C5×D8Q8semidirect
133. C2×#476C2×C5semidirect
135. #2452C2×C5semidirect
136. D4×C4⋊C4C2×C5semidirect
137. #2094C2×C5semidirect
138. #2084C2×C5semidirect
139. #2067C2×C5semidirect
140. #2058C2×C5semidirect
141. #1943C2×C5semidirect
142. #1917C2×C5semidirect
145. #1864C2×C5semidirect
146. #1864C2×C5semidirect
147. #1862C2×C5semidirect
306. C5×D4C22⋊Q8semidirect
366. C2×D8C5×Q8semidirect
587. D4C5×C22⋊Q8semidirect
638. C5#26392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4762
C2×C5×#4422
C5×#24522
C5×D4×C4⋊C42
C5×#20942
C5×#20842
C5×#20672
C5×#20582
C5×#19432
C5×#19172
C5×#18792
C5×#18642
C5×#18622
#263925