Finite Group Databasebeta

← C5×#25223 #11947943

Subgroups — C5×#25223 #11947943

Order 1280.

880 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#480C211yesmaximal, characteristic
2C2×C5×#468C211yesmaximal, characteristic
3C5×#2502C211yesmaximal, characteristic, complemented
4C5×#2363C211yesmaximal, characteristic
5C5×#2083C211yesmaximal, characteristic, complemented
6C5×#2071C211yesmaximal, characteristic, complemented
7C5×#2068C211yesmaximal, characteristic, complemented
8C5×#2055C211yesmaximal, characteristic, complemented
9C5×#1947C211yesmaximal, characteristic, complemented
10C5×#1928C211yesmaximal, characteristic, complemented
11C5×#1877C211yesmaximal, characteristic, complemented
12C5×#1873C211yesmaximal, characteristic, complemented
13C5×#1851C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C5×#1736C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#480—24no—
24C5×#468—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#398—21no—
38C5×#398—21no—
39C5×#391C2211yescharacteristic
40C5×#391C2211yescharacteristic
41C5×#390—21no—
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#388—21no—
45C5×#386—21no—
46C5×#385—21no—
47C5×#385—21no—
48C5×#384C2211yescharacteristic
49C5×#384C2211yescharacteristic
50C4×C5×C4⋊C4C2211yescharacteristic
51C4×C5×C22⋊C4—21no—
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25223C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×D4—21no—
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5C2311yescharacteristic
68C2×C5×SD16—22no—
69C2×C5×SD16—22no—
70C2×C5×SD16—41no—
71C2×C5×M16—22no—
72C2×C5×M16—22no—
73C2×C5×M16—41no—
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8—22no—
80C5×#121—22no—
81C5×#121D414yes—
82C4×C5×D4—22no—
83C4×C5×D4—41no—
84C5×#117—22no—
85C5×#117—41no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
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—21no—
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
108C2×C5×C22⋊C4D411yescharacteristic
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C5×#107—22no—
114C5×#107—22no—
115C5×#107—22no—
116C5×C4⋊C8—22no—
117C5×C4⋊C8—41no—
118C5×#103—22no—
119C5×#103—22no—
120C5×#103—41no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—22no—
124C5×C22⋊C8—22no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95D411yescharacteristic
132C5×#95D411yescharacteristic
133C2×#480C2×C511yescharacteristic
134C2×#468C2×C511yescharacteristic
135#2502C2×C511yescharacteristic, complemented
136#2363C2×C511yescharacteristic
137#2083C2×C511yescharacteristic, complemented
138#2071C2×C511yescharacteristic, complemented
139#2068C2×C511yescharacteristic, complemented
140#2055C2×C511yescharacteristic, complemented
141#1947C2×C511yescharacteristic, complemented
142#1928C2×C511yescharacteristic, complemented
143#1877C2×C511yescharacteristic, complemented
144#1873C2×C511yescharacteristic, complemented
145#1851C2×C511yescharacteristic, complemented
146#1802C2×C511yescharacteristic, complemented
147#1736C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5C2×D411yescharacteristic
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×D4—24no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—81no—
163C2×C5×D4—81no—
164C2×C5×D4C2×D412yes—
165C22×C4×C5—21no—
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—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—42no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—81no—
180C22×C4×C5—81no—
181C22×C4×C5—81no—
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D412yes—
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5#4112yes—
189C22×C4×C5C2411yescharacteristic
190C5×SD16—44no—
191C5×M16—44no—
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×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8#4112yes—
204C5×C4⋊C4—21no—
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—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—81no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4—81no—
219C5×C4⋊C4—81no—
220C5×C4⋊C4—81no—
221C5×C4⋊C4C2×D412yes—
222C5×C4⋊C4#4112yes—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—81no—
231C42×C5—21no—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—42no—
236C42×C5—81no—
237C22×SD16C22×C511yescharacteristic
238C22×M16C22×C511yescharacteristic
239C2×C22⋊Q8C22×C511yescharacteristic
240C2×#121C22×C511yescharacteristic
241C2×C4×D4C22×C511yescharacteristic
242C2×#117C22×C511yescharacteristic
243C22×C4⋊C4C22×C511yescharacteristic
244#480—24no—
245#468—24no—
246C2×#107C22×C511yescharacteristic
247C2×#107C22×C511yescharacteristic
248C2×#107C22×C511yescharacteristic
249C2×C4⋊C8C22×C511yescharacteristic
250C2×C4⋊C8C22×C511yescharacteristic
251C2×#103C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×C22⋊C8C22×C511yescharacteristic
258#398—21no—
259#398—21no—
260#391C22×C511yescharacteristic
261#391C22×C511yescharacteristic
262#390—21no—
263#390C22×C511yescharacteristic
264#389C22×C511yescharacteristic
265#388—21no—
266#386—21no—
267#385—21no—
268#385—21no—
269#384C22×C511yescharacteristic
270#384C22×C511yescharacteristic
271C4×C4⋊C4C22×C511yescharacteristic
272C4×C22⋊C4—21no—
273C4×C22⋊C4C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#336C22×C511yescharacteristic
281#336C22×C511yescharacteristic
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—22no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5#12112yes—
296C23×C5C22×D411yescharacteristic
297C5×Q8—41no—
298C5×Q8—41no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×D4—22no—
302C5×D4—22no—
303C5×D4—41no—
304C5×D4—41no—
305C5×D4—84no—
306C2×C4×C5—21no—
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—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—21no—
318C2×C4×C5—22no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
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—41no—
343C2×C4×C5—84no—
344C2×C4×C5—84no—
345C2×C4×C5#12112yes—
346C2×C4×C5#13712yes—
347C2×C4×C5#13712yes—
348C2×C4×C5C22×D411yescharacteristic
349C2×C4×C5C2×#4111yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5C2×#4111yescharacteristic
352C2×C4×C5H(5,𝔽2)11yescharacteristic
353C2×C4×C52−1+411yescharacteristic
354C5×C8—22no—
355C5×C8—41no—
356C5×C8—41no—
357C5×C8—41no—
358C22×Q8C23×C511yescharacteristic
359C22×D4—21no—
360C22×D4C23×C511yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C23×C511yescharacteristic
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—41no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—41no—
370C22×C8C23×C511yescharacteristic
371C22×C8C23×C511yescharacteristic
372C22×C8C23×C511yescharacteristic
373C22×C8C23×C511yescharacteristic
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#121—22no—
377#121C5×D414yes—
378C4×D4—22no—
379C4×D4—41no—
380#117—22no—
381#117—41no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4C5×D411yescharacteristic
404C2×C22⋊C4C5×D411yescharacteristic
405C2×C42—21no—
406C2×C42—21no—
407C2×C42C23×C511yescharacteristic
408C2×C42C23×C511yescharacteristic
409#107—22no—
410#107—22no—
411#107—22no—
412C4⋊C8—22no—
413C4⋊C8—41no—
414#103—22no—
415#103—22no—
416#103—41no—
417#102—22no—
418#102—22no—
419#102—22no—
420C22⋊C8—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95C5×D411yescharacteristic
428#95C5×D411yescharacteristic
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—42no—
437C22×C5—42no—
438C22×C5—42no—
439C22×C5—81no—
440C22×C5—81no—
441C22×C5—81no—
442C22×C5—81no—
443C22×C5C2×#12111yescharacteristic
444C22×C5#54611yescharacteristic
445C22×C5#54711yescharacteristic
446C22×C5C2×#13711yescharacteristic
447C22×C5C2×#13711yescharacteristic
448C22×C5#57611yescharacteristic
449C22×C5#57611yescharacteristic
450C4×C5—22no—
451C4×C5—22no—
452C4×C5—22no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—42no—
456C4×C5—42no—
457C4×C5—81no—
458C4×C5—81no—
459C4×C5—81no—
460C4×C5—81no—
461C4×C5—81no—
462C4×C5#52911yescharacteristic
463C4×C5#53911yescharacteristic
464C4×C5#54611yescharacteristic
465C4×C5#54711yescharacteristic
466C24—21no—
467C24C2×C5×D411yescharacteristic
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×D4—24no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4C2×C5×D412yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
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×D412yes—
504C22×C4C2×C5×D411yescharacteristic
505C22×C4C2×C5×D411yescharacteristic
506C22×C4C5×#4112yes—
507C22×C4C24×C511yescharacteristic
508SD16—44no—
509M16—44no—
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×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8C5×#4112yes—
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—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4C2×C5×D412yes—
540C4⋊C4C5×#4112yes—
541C22⋊C4—24no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—81no—
555C2×C5—42no—
556C2×C5—82no—
557C2×C5#242511yescharacteristic
558C2×C5#303911yescharacteristic
559C2×C5#304111yescharacteristic
560C2×C5#331411yescharacteristic
561C2×C5#333311yescharacteristic
562C2×C5#334611yescharacteristic
563C2×C5#335711yescharacteristic
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C5×#12112yes—
578C23C22×C5×D411yescharacteristic
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—84no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
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—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—84no—
627C2×C4C5×#12112yes—
628C2×C4C5×#13712yes—
629C2×C4C5×#13712yes—
630C2×C4C22×C5×D411yescharacteristic
631C2×C4C2×C5×#4111yescharacteristic
632C2×C4C2×C5×#4111yescharacteristic
633C2×C4C2×C5×#4111yescharacteristic
634C2×C4C5×H(5,𝔽2)11yescharacteristic
635C2×C4C5×2−1+411yescharacteristic
636C8—22no—
637C8—41no—
638C8—41no—
639C8—41no—
640C5#2522311yescharacteristic, direct product factor, Sylow
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×C5×#12111yescharacteristic
656C22C5×#54611yescharacteristic
657C22C5×#54711yescharacteristic
658C22C2×C5×#13711yescharacteristic
659C22C2×C5×#13711yescharacteristic
660C22C5×#57611yescharacteristic
661C22C5×#57611yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C5×#52911yescharacteristic
675C4C5×#53911yescharacteristic
676C4C5×#54611yescharacteristic
677C4C5×#54711yescharacteristic
678C2—42no—
679C2—82no—
680C2C5×#242511yescharacteristic
681C2C5×#303911yescharacteristic
682C2C5×#304111yescharacteristic
683C2C5×#331411yescharacteristic
684C2C5×#333311yescharacteristic
685C2C5×#334611yescharacteristic
686C2C5×#335711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
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
3. C5×#2502C2semidirect
5. C5×#2083C2semidirect
6. C5×#2071C2semidirect
7. C5×#2068C2semidirect
8. C5×#2055C2semidirect
9. C5×#1947C2semidirect
10. C5×#1928C2semidirect
11. C5×#1877C2semidirect
12. C5×#1873C2semidirect
13. C5×#1851C2semidirect
14. C5×#1802C2semidirect
15. C5×#1736C2semidirect
61. #25223C5direct (N × H)
135. #2502C2×C5semidirect
137. #2083C2×C5semidirect
138. #2071C2×C5semidirect
139. #2068C2×C5semidirect
140. #2055C2×C5semidirect
141. #1947C2×C5semidirect
142. #1928C2×C5semidirect
143. #1877C2×C5semidirect
144. #1873C2×C5semidirect
145. #1851C2×C5semidirect
146. #1802C2×C5semidirect
147. #1736C2×C5semidirect
640. C5#25223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4802
C2×C5×#4682
C5×#25022
C5×#23632
C5×#20832
C5×#20712
C5×#20682
C5×#20552
C5×#19472
C5×#19282
C5×#18772
C5×#18732
C5×#18512
C5×#18022
C5×#17362
#252235