Finite Group Databasebeta

← C5×#62793 #11985513

Subgroups — C5×#62793 #11985513

Order 1280.

7190 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3524C218yesmaximal, complemented
2C5×#3518C214yesmaximal, complemented
3C5×#3517C214yesmaximal, complemented
4C5×#3506C216yesmaximal, complemented
5C5×#3502C211yesmaximal, characteristic, complemented
6C5×#3497C211yesmaximal, characteristic, complemented
7C5×#3493C216yesmaximal, complemented
8C5×#3487C212yesmaximal, complemented
9C5×#3483C214yesmaximal, complemented
10C5×#3482C214yesmaximal, complemented
11C5×#3480C218yesmaximal, complemented
12C5×#3460C216yesmaximal, complemented
13C5×#3444C216yesmaximal, complemented
14C4×C5×2−1+4C212yesmaximal, complemented
15C2×C4×C5×#41C211yesmaximal, characteristic, complemented
16C2×C5×2−1+4C2212yes—
17C22×C5×#41C2211yescharacteristic
18C5×#559C22124yescomplemented
19C5×Q82C2214yescomplemented
20C5×#557C2218yescomplemented
21C5×#557C2214yescomplemented
22C5×#556C22124yescomplemented
23C5×#556C22112yescomplemented
24C5×#555C22124yescomplemented
25C5×#555C22112yescomplemented
26C5×#553C22124yescomplemented
27C5×#553C22124yescomplemented
28C5×#552C22124yescomplemented
29C5×#550C2218yes—
30C5×#550C2218yes—
31C5×#550C2214yescomplemented
32C5×#550C22112yescomplemented
33C5×D4×Q8C2214yescomplemented
34C5×#548C2218yes—
35C5×#548C2218yes—
36C5×#548C2218yescomplemented
37C5×#547C22112yescomplemented
38C5×#544C2216yes—
39C5×#542C22124yescomplemented
40C5×#540C22124yescomplemented
41C5×#538C22124yes—
42C5×#537C2216yes—
43C5×#535C22112yes—
44C5×#533C2216yes—
45C5×#533C2216yescomplemented
46C5×#533C2216yescomplemented
47C5×#532C2216yes—
48C5×#532C2216yescomplemented
49C5×#532C2216yescomplemented
50C5×#532C22124yescomplemented
51C5×#529C2214yes—
52C5×#529C22112yes—
53C5×#529C22112yescomplemented
54C5×#529C22112yescomplemented
55C5×#529C22112yescomplemented
56C5×#529C22112yescomplemented
57C5×#529C22124yescomplemented
58C5×#525C22112yes—
59C5×#525C22112yes—
60C5×#525C22112yes—
61C5×#520C22112yes—
62C5×#520C2218yescomplemented
63C5×#519C2212yes—
64C5×#519C2218yescomplemented
65C4×C5×#41C2214yes—
66C4×C5×#41C2214yes—
67C4×C5×#41C2214yes—
68C4×C5×#41C2214yes—
69C4×C5×#41C22112yes—
70C4×C5×#41C2218yescomplemented
71C4×C5×#41C22112yescomplemented
72C4×C5×#41C22112yescomplemented
73C2×C4×C5×Q8C2211yescharacteristic
74C2×C4×C5×Q8C2211yescharacteristic
75C2×C4×C5×Q8C2218yescomplemented
76C2×C4×C5×D4C2213yes—
77C2×C4×C5×D4C2213yes—
78C2×C5×#117C2213yes—
79C22×C42×C5C2213yes—
80#62793C511yesmaximal, characteristic, direct product factor, Sylow
81C5×2−1+4—216no—
82C2×C5×#41—28no—
83C2×C5×#41C2314yes—
84C2×C5×#41C2314yes—
85C2×C5×#41C23112yes—
86C2×C5×#41C2318yes—
87C2×C5×#41C23112yes—
88C2×C5×#41C23112yes—
89C22×C5×Q8C2318yes—
90C22×C5×Q8C2311yescharacteristic
91C22×C5×D4C2313yes—
92C23×C4×C5C2313yes—
93C23×C4×C5C2313yes—
94C23×C4×C5C2313yes—
95C5×C4⋊Q8C2316yes—
96C5×C4⋊Q8C2316yes—
97C5×C4⋊Q8C2316yes—
98C5×C4⋊Q8C23124yes—
99C5×#127C2316yes—
100C5×#127C23124yes—
101C5×#126C2318yes—
102C5×#126C23124yes—
103C5×#126C23148yes—
104C5×#125C2314yes—
105C5×#125C23112yes—
106C5×#125C23112yes—
107C5×#125C23124yes—
108C5×#124C2314yes—
109C5×#124C23112yes—
110C5×#124C23112yes—
111C5×#124C23124yes—
112C5×#124C23148yes—
113C5×#123C2318yes—
114C5×#123C23124yes—
115C5×#123C23124yes—
116C5×#123C23148yes—
117C5×C22⋊Q8C2314yes—
118C5×C22⋊Q8C23112yes—
119C5×C22⋊Q8C23112yes—
120C5×C22⋊Q8C23112yes—
121C5×C22⋊Q8C23112yes—
122C5×C22⋊Q8C23112yes—
123C5×C22⋊Q8C23124yes—
124C5×#121C2314yes—
125C5×#121C23112yes—
126C5×#121C23112yes—
127C5×#121C23112yes—
128C5×#121C23112yes—
129C5×#121C23112yes—
130C5×#121C23124yes—
131C5×#121C23124yes—
132C5×#121C23124yes—
133C5×#121C23148yes—
134C5×#120C23124yes—
135C4×C5×Q8C2314yes—
136C4×C5×Q8C2314yes—
137C4×C5×Q8C2314yes—
138C4×C5×Q8C2314yes—
139C4×C5×Q8C23112yes—
140C4×C5×Q8C2318yes—
141C4×C5×Q8C23124yes—
142C4×C5×Q8C23112yes—
143C4×C5×Q8C2314yes—
144C4×C5×Q8C2318yes—
145C4×C5×Q8C23112yes—
146C4×C5×Q8C23112yes—
147C4×C5×Q8C23112yes—
148C4×C5×D4C23112yes—
149C4×C5×D4C23112yes—
150C4×C5×D4C23112yes—
151C4×C5×D4C23112yes—
152C4×C5×D4C2318yes—
153C4×C5×D4C23112yes—
154C4×C5×D4C23124yes—
155C4×C5×D4C23112yes—
156C4×C5×D4C2314yes—
157C4×C5×D4C23124yes—
158C4×C5×D4C23124yes—
159C4×C5×D4C23124yes—
160C4×C5×D4C23124yes—
161C4×C5×D4C23124yes—
162C4×C5×D4C23112yes—
163C4×C5×D4C23112yes—
164C4×C5×D4C23112yes—
165C5×#117C23112yes—
166C5×#117C23112yes—
167C5×#117C23112yes—
168C5×#117C23124yes—
169C5×#117C2318yes—
170C5×#117C23124yes—
171C5×#117C23112yes—
172C5×#117C23112yes—
173C5×#117C23124yes—
174C2×C5×C4⋊C4C2313yes—
175C2×C5×C4⋊C4C2313yes—
176C2×C5×C4⋊C4C23124yes—
177C2×C5×C22⋊C4C2316yes—
178C2×C42×C5C2311yescharacteristic
179C2×C42×C5C2313yes—
180C2×C42×C5C2313yes—
181C2×C42×C5C2313yes—
182C2×C42×C5C2316yes—
183C2×C42×C5C2316yes—
184C2×C42×C5C2316yes—
185C2×C42×C5C2316yes—
186C2×C42×C5C23124yes—
187#3524C2×C518yescomplemented
188#3518C2×C514yescomplemented
189#3517C2×C514yescomplemented
190#3506C2×C516yescomplemented
191#3502C2×C511yescharacteristic, complemented
192#3497C2×C511yescharacteristic, complemented
193#3493C2×C516yescomplemented
194#3487C2×C512yescomplemented
195#3483C2×C514yescomplemented
196#3482C2×C514yescomplemented
197#3480C2×C518yescomplemented
198#3460C2×C516yescomplemented
199#3444C2×C516yescomplemented
200C4×2−1+4C2×C512yescomplemented
201C2×C4×#41C2×C511yescharacteristic, complemented
202C24×C5C2413yes—
203C5×#41—216no—
204C5×#41—216no—
205C5×#41—232no—
206C5×#41—248no—
207C5×#41—424no—
208C5×#41—424no—
209C2×C5×Q8—232no—
210C2×C5×Q8#4118yescomplemented
211C2×C5×Q8C24112yes—
212C2×C5×Q8C2414yes—
213C2×C5×Q8C24112yes—
214C2×C5×Q8C2414yes—
215C2×C5×D4—212no—
216C2×C5×D4C2418yes—
217C2×C5×D4C24112yes—
218C2×C5×D4C24112yes—
219C2×C5×D4C2414yes—
220C2×C5×D4C24124yes—
221C2×C5×D4C24124yes—
222C2×C5×D4C24112yes—
223C22×C4×C5—212no—
224C22×C4×C5—46no—
225C22×C4×C5—46no—
226C22×C4×C5C2411yescharacteristic
227C22×C4×C5C2411yescharacteristic
228C22×C4×C5C2416yes—
229C22×C4×C5C2416yes—
230C22×C4×C5C2416yes—
231C22×C4×C5C24124yes—
232C22×C4×C5C2411yescharacteristic
233C22×C4×C5C2418yes—
234C22×C4×C5C2416yes—
235C22×C4×C5C2413yes—
236C22×C4×C5C2413yes—
237C22×C4×C5C2416yes—
238C22×C4×C5C2416yes—
239C22×C4×C5C24124yes—
240C22×C4×C5C2413yes—
241C5×C4⋊C4C24112yes—
242C5×C4⋊C4C24112yes—
243C5×C4⋊C4C24124yes—
244C5×C4⋊C4C24112yes—
245C5×C4⋊C4C2414yes—
246C5×C4⋊C4C2418yes—
247C5×C4⋊C4C24112yes—
248C5×C4⋊C4C2414yes—
249C5×C4⋊C4C2418yes—
250C5×C4⋊C4C2418yes—
251C5×C4⋊C4C2418yes—
252C5×C4⋊C4C24124yes—
253C5×C4⋊C4C24112yes—
254C5×C4⋊C4C24112yes—
255C5×C22⋊C4C24124yes—
256C5×C22⋊C4C2418yes—
257C5×C22⋊C4C2418yes—
258C5×C22⋊C4C24124yes—
259C5×C22⋊C4C2418yes—
260C5×C22⋊C4C2418yes—
261C5×C22⋊C4C2418yes—
262C5×C22⋊C4C24124yes—
263C5×C22⋊C4C24124yes—
264C5×C22⋊C4C24124yes—
265C42×C5C2411yescharacteristic
266C42×C5C2411yescharacteristic
267C42×C5C2416yes—
268C42×C5C2416yes—
269C42×C5C2416yes—
270C42×C5C2416yes—
271C42×C5C2416yes—
272C42×C5C24124yes—
273C42×C5C24124yes—
274C42×C5C2411yescharacteristic
275C42×C5C2416yes—
276C42×C5C2411yescharacteristic
277C42×C5C2418yes—
278C2×2−1+4C22×C512yes—
279C22×#41C22×C511yescharacteristic
280#559C22×C5124yescomplemented
281Q82C22×C514yescomplemented
282#557C22×C518yescomplemented
283#557C22×C514yescomplemented
284#556C22×C5124yescomplemented
285#556C22×C5112yescomplemented
286#555C22×C5124yescomplemented
287#555C22×C5112yescomplemented
288#553C22×C5124yescomplemented
289#553C22×C5124yescomplemented
290#552C22×C5124yescomplemented
291#550C22×C518yes—
292#550C22×C518yes—
293#550C22×C514yescomplemented
294#550C22×C5112yescomplemented
295D4×Q8C22×C514yescomplemented
296#548C22×C518yes—
297#548C22×C518yes—
298#548C22×C518yescomplemented
299#547C22×C5112yescomplemented
300#544C22×C516yes—
301#542C22×C5124yescomplemented
302#540C22×C5124yescomplemented
303#538C22×C5124yes—
304#537C22×C516yes—
305#535C22×C5112yes—
306#533C22×C516yes—
307#533C22×C516yescomplemented
308#533C22×C516yescomplemented
309#532C22×C516yes—
310#532C22×C516yescomplemented
311#532C22×C516yescomplemented
312#532C22×C5124yescomplemented
313#529C22×C514yes—
314#529C22×C5112yes—
315#529C22×C5112yescomplemented
316#529C22×C5112yescomplemented
317#529C22×C5112yescomplemented
318#529C22×C5112yescomplemented
319#529C22×C5124yescomplemented
320#525C22×C5112yes—
321#525C22×C5112yes—
322#525C22×C5112yes—
323#520C22×C5112yes—
324#520C22×C518yescomplemented
325#519C22×C512yes—
326#519C22×C518yescomplemented
327C4×#41C22×C514yes—
328C4×#41C22×C514yes—
329C4×#41C22×C514yes—
330C4×#41C22×C514yes—
331C4×#41C22×C5112yes—
332C4×#41C22×C518yescomplemented
333C4×#41C22×C5112yescomplemented
334C4×#41C22×C5112yescomplemented
335C2×C4×Q8C22×C511yescharacteristic
336C2×C4×Q8C22×C511yescharacteristic
337C2×C4×Q8C22×C518yescomplemented
338C2×C4×D4C22×C513yes—
339C2×C4×D4C22×C513yes—
340C2×#117C22×C513yes—
341C22×C42C22×C513yes—
342C23×C5—26no—
343C23×C5—43no—
344C23×C5—43no—
345C23×C5C2516yes—
346C23×C5C2518yes—
347C23×C5C2511yescharacteristic
348C5×Q8—224no—
349C5×Q8—28no—
350C5×Q8—412no—
351C5×Q8C2×#41116yes—
352C5×D4—216no—
353C5×D4—224no—
354C5×D4—224no—
355C5×D4—28no—
356C5×D4—412no—
357C5×D4—424no—
358C5×D4—424no—
359C2×C4×C5—22no—
360C2×C4×C5—212no—
361C2×C4×C5—212no—
362C2×C4×C5—248no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—212no—
366C2×C4×C5—212no—
367C2×C4×C5—216no—
368C2×C4×C5—43no—
369C2×C4×C5—46no—
370C2×C4×C5—46no—
371C2×C4×C5—43no—
372C2×C4×C5—424no—
373C2×C4×C5C2×#41112yes—
374C2×C4×C5C2511yescharacteristic
375C2×C4×C5C2511yescharacteristic
376C2×C4×C5C2511yescharacteristic
377C2×C4×C5C2511yescharacteristic
378C2×C4×C5C2516yes—
379C2×C4×C5C2518yes—
380C2×C4×C5C2518yes—
381C2×C4×C5C2516yes—
382C2×C4×C5C2518yes—
383C2×C4×C5C2516yes—
384C2×C4×C5C2511yescharacteristic
385C2×C4×C5C2511yescharacteristic
3862−1+4—216no—
387C2×#41—28no—
388C2×#41C23×C514yes—
389C2×#41C23×C514yes—
390C2×#41C23×C5112yes—
391C2×#41C23×C518yes—
392C2×#41C23×C5112yes—
393C2×#41C23×C5112yes—
394C22×Q8C23×C518yes—
395C22×Q8C23×C511yescharacteristic
396C22×D4C23×C513yes—
397C23×C4C23×C513yes—
398C23×C4C23×C513yes—
399C23×C4C23×C513yes—
400C4⋊Q8C23×C516yes—
401C4⋊Q8C23×C516yes—
402C4⋊Q8C23×C516yes—
403C4⋊Q8C23×C5124yes—
404#127C23×C516yes—
405#127C23×C5124yes—
406#126C23×C518yes—
407#126C23×C5124yes—
408#126C23×C5148yes—
409#125C23×C514yes—
410#125C23×C5112yes—
411#125C23×C5112yes—
412#125C23×C5124yes—
413#124C23×C514yes—
414#124C23×C5112yes—
415#124C23×C5112yes—
416#124C23×C5124yes—
417#124C23×C5148yes—
418#123C23×C518yes—
419#123C23×C5124yes—
420#123C23×C5124yes—
421#123C23×C5148yes—
422C22⋊Q8C23×C514yes—
423C22⋊Q8C23×C5112yes—
424C22⋊Q8C23×C5112yes—
425C22⋊Q8C23×C5112yes—
426C22⋊Q8C23×C5112yes—
427C22⋊Q8C23×C5112yes—
428C22⋊Q8C23×C5124yes—
429#121C23×C514yes—
430#121C23×C5112yes—
431#121C23×C5112yes—
432#121C23×C5112yes—
433#121C23×C5112yes—
434#121C23×C5112yes—
435#121C23×C5124yes—
436#121C23×C5124yes—
437#121C23×C5124yes—
438#121C23×C5148yes—
439#120C23×C5124yes—
440C4×Q8C23×C514yes—
441C4×Q8C23×C514yes—
442C4×Q8C23×C514yes—
443C4×Q8C23×C514yes—
444C4×Q8C23×C5112yes—
445C4×Q8C23×C518yes—
446C4×Q8C23×C5124yes—
447C4×Q8C23×C5112yes—
448C4×Q8C23×C514yes—
449C4×Q8C23×C518yes—
450C4×Q8C23×C5112yes—
451C4×Q8C23×C5112yes—
452C4×Q8C23×C5112yes—
453C4×D4C23×C5112yes—
454C4×D4C23×C5112yes—
455C4×D4C23×C5112yes—
456C4×D4C23×C5112yes—
457C4×D4C23×C518yes—
458C4×D4C23×C5112yes—
459C4×D4C23×C5124yes—
460C4×D4C23×C5112yes—
461C4×D4C23×C514yes—
462C4×D4C23×C5124yes—
463C4×D4C23×C5124yes—
464C4×D4C23×C5124yes—
465C4×D4C23×C5124yes—
466C4×D4C23×C5124yes—
467C4×D4C23×C5112yes—
468C4×D4C23×C5112yes—
469C4×D4C23×C5112yes—
470#117C23×C5112yes—
471#117C23×C5112yes—
472#117C23×C5112yes—
473#117C23×C5124yes—
474#117C23×C518yes—
475#117C23×C5124yes—
476#117C23×C5112yes—
477#117C23×C5112yes—
478#117C23×C5124yes—
479C2×C4⋊C4C23×C513yes—
480C2×C4⋊C4C23×C513yes—
481C2×C4⋊C4C23×C5124yes—
482C2×C22⋊C4C23×C516yes—
483C2×C42C23×C513yes—
484C2×C42C23×C513yes—
485C2×C42C23×C513yes—
486C2×C42C23×C5124yes—
487C2×C42C23×C516yes—
488C2×C42C23×C516yes—
489C2×C42C23×C516yes—
490C2×C42C23×C516yes—
491C2×C42C23×C511yescharacteristic
492C22×C5—21no—
493C22×C5—21no—
494C22×C5—28no—
495C22×C5—26no—
496C22×C5—26no—
497C22×C5—26no—
498C22×C5—28no—
499C22×C5—28no—
500C22×C5—412no—
501C22×C5C22×#4112yes—
502C22×C5C2611yescharacteristic
503C4×C5—21no—
504C4×C5—21no—
505C4×C5—28no—
506C4×C5—21no—
507C4×C5—21no—
508C4×C5—26no—
509C4×C5—26no—
510C4×C5—28no—
511C4×C5—28no—
512C4×C5C22×#41112yes—
513C4×C5#58512yes—
514C4×C5#58512yes—
515C24C24×C513yes—
516#41—216no—
517#41—216no—
518#41—232no—
519#41—248no—
520#41—424no—
521#41—424no—
522C2×Q8—232no—
523C2×Q8C5×#4118yescomplemented
524C2×Q8C24×C5112yes—
525C2×Q8C24×C514yes—
526C2×Q8C24×C5112yes—
527C2×Q8C24×C514yes—
528C2×D4—212no—
529C2×D4C24×C518yes—
530C2×D4C24×C5112yes—
531C2×D4C24×C5112yes—
532C2×D4C24×C514yes—
533C2×D4C24×C5124yes—
534C2×D4C24×C5124yes—
535C2×D4C24×C5112yes—
536C22×C4—212no—
537C22×C4—46no—
538C22×C4—46no—
539C22×C4C24×C511yescharacteristic
540C22×C4C24×C511yescharacteristic
541C22×C4C24×C511yescharacteristic
542C22×C4C24×C518yes—
543C22×C4C24×C516yes—
544C22×C4C24×C516yes—
545C22×C4C24×C516yes—
546C22×C4C24×C516yes—
547C22×C4C24×C5124yes—
548C22×C4C24×C513yes—
549C22×C4C24×C513yes—
550C22×C4C24×C516yes—
551C22×C4C24×C516yes—
552C22×C4C24×C5124yes—
553C22×C4C24×C513yes—
554C4⋊C4C24×C5112yes—
555C4⋊C4C24×C5112yes—
556C4⋊C4C24×C5124yes—
557C4⋊C4C24×C5112yes—
558C4⋊C4C24×C514yes—
559C4⋊C4C24×C518yes—
560C4⋊C4C24×C5112yes—
561C4⋊C4C24×C514yes—
562C4⋊C4C24×C518yes—
563C4⋊C4C24×C518yes—
564C4⋊C4C24×C518yes—
565C4⋊C4C24×C5124yes—
566C4⋊C4C24×C5112yes—
567C4⋊C4C24×C5112yes—
568C22⋊C4C24×C5124yes—
569C22⋊C4C24×C518yes—
570C22⋊C4C24×C518yes—
571C22⋊C4C24×C5124yes—
572C22⋊C4C24×C518yes—
573C22⋊C4C24×C518yes—
574C22⋊C4C24×C518yes—
575C22⋊C4C24×C5124yes—
576C22⋊C4C24×C5124yes—
577C22⋊C4C24×C5124yes—
578C42C24×C511yescharacteristic
579C42C24×C516yes—
580C42C24×C511yescharacteristic
581C42C24×C511yescharacteristic
582C42C24×C511yescharacteristic
583C42C24×C516yes—
584C42C24×C516yes—
585C42C24×C518yes—
586C42C24×C516yes—
587C42C24×C516yes—
588C42C24×C516yes—
589C42C24×C5124yes—
590C42C24×C5124yes—
591C2×C5—22no—
592C2×C5—48no—
593C2×C5—46no—
594C2×C5C23×#4111yescharacteristic
595C2×C5C2×#58511yescharacteristic
596C2×C5C2×#58511yescharacteristic
597C23—26no—
598C23—43no—
599C23—43no—
600C23C25×C516yes—
601C23C25×C518yes—
602C23C25×C511yescharacteristic
603Q8—224no—
604Q8—28no—
605Q8—412no—
606Q8C2×C5×#41116yes—
607D4—216no—
608D4—224no—
609D4—224no—
610D4—28no—
611D4—412no—
612D4—424no—
613D4—424no—
614C2×C4—22no—
615C2×C4—212no—
616C2×C4—212no—
617C2×C4—248no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—212no—
621C2×C4—212no—
622C2×C4—216no—
623C2×C4—43no—
624C2×C4—46no—
625C2×C4—46no—
626C2×C4—43no—
627C2×C4—424no—
628C2×C4C2×C5×#41112yes—
629C2×C4C25×C511yescharacteristic
630C2×C4C25×C511yescharacteristic
631C2×C4C25×C511yescharacteristic
632C2×C4C25×C516yes—
633C2×C4C25×C511yescharacteristic
634C2×C4C25×C518yes—
635C2×C4C25×C518yes—
636C2×C4C25×C516yes—
637C2×C4C25×C518yes—
638C2×C4C25×C516yes—
639C2×C4C25×C511yescharacteristic
640C2×C4C25×C511yescharacteristic
641C5#6279311yescharacteristic, direct product factor, Sylow
642C22—21no—
643C22—21no—
644C22—28no—
645C22—26no—
646C22—26no—
647C22—26no—
648C22—28no—
649C22—28no—
650C22—412no—
651C22C22×C5×#4112yes—
652C22C26×C511yescharacteristic
653C4—21no—
654C4—21no—
655C4—28no—
656C4—21no—
657C4—21no—
658C4—26no—
659C4—26no—
660C4—28no—
661C4—28no—
662C4C22×C5×#41112yes—
663C4C5×#58512yes—
664C4C5×#58512yes—
665C2—22no—
666C2—46no—
667C2—48no—
668C2C23×C5×#4111yescharacteristic
669C2C2×C5×#58511yescharacteristic
670C2C2×C5×#58511yescharacteristic
subgroupG/H
centerC2×C4×C5C25
commutator, Frattini, cosocleC22C26×C5
socleC22×C5C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3524C2semidirect
2. C5×#3518C2semidirect
3. C5×#3517C2semidirect
4. C5×#3506C2semidirect
5. C5×#3502C2semidirect
6. C5×#3497C2semidirect
7. C5×#3493C2semidirect
8. C5×#3487C2semidirect
9. C5×#3483C2semidirect
10. C5×#3482C2semidirect
11. C5×#3480C2semidirect
12. C5×#3460C2semidirect
13. C5×#3444C2semidirect
14. C4×C5×2−1+4C2semidirect
15. C2×C4×C5×#41C2semidirect
18. C5×#559C22semidirect
19. C5×Q82C22semidirect
20. C5×#557C22semidirect
21. C5×#557C22semidirect
22. C5×#556C22semidirect
23. C5×#556C22semidirect
24. C5×#555C22semidirect
25. C5×#555C22semidirect
26. C5×#553C22semidirect
27. C5×#553C22semidirect
28. C5×#552C22semidirect
31. C5×#550C22semidirect
32. C5×#550C22semidirect
33. C5×D4×Q8C22semidirect
36. C5×#548C22semidirect
37. C5×#547C22semidirect
39. C5×#542C22semidirect
40. C5×#540C22semidirect
45. C5×#533C22semidirect
46. C5×#533C22semidirect
48. C5×#532C22semidirect
49. C5×#532C22semidirect
50. C5×#532C22semidirect
53. C5×#529C22semidirect
54. C5×#529C22semidirect
55. C5×#529C22semidirect
56. C5×#529C22semidirect
57. C5×#529C22semidirect
62. C5×#520C22semidirect
64. C5×#519C22semidirect
70. C4×C5×#41C22semidirect
71. C4×C5×#41C22semidirect
72. C4×C5×#41C22semidirect
75. C2×C4×C5×Q8C22semidirect
80. #62793C5direct (N × H)
187. #3524C2×C5semidirect
188. #3518C2×C5semidirect
189. #3517C2×C5semidirect
190. #3506C2×C5semidirect
191. #3502C2×C5semidirect
192. #3497C2×C5semidirect
193. #3493C2×C5semidirect
194. #3487C2×C5semidirect
195. #3483C2×C5semidirect
196. #3482C2×C5semidirect
197. #3480C2×C5semidirect
198. #3460C2×C5semidirect
199. #3444C2×C5semidirect
200. C4×2−1+4C2×C5semidirect
201. C2×C4×#41C2×C5semidirect
210. C2×C5×Q8#41semidirect
280. #559C22×C5semidirect
281. Q82C22×C5semidirect
282. #557C22×C5semidirect
283. #557C22×C5semidirect
284. #556C22×C5semidirect
285. #556C22×C5semidirect
286. #555C22×C5semidirect
287. #555C22×C5semidirect
288. #553C22×C5semidirect
289. #553C22×C5semidirect
290. #552C22×C5semidirect
293. #550C22×C5semidirect
294. #550C22×C5semidirect
295. D4×Q8C22×C5semidirect
298. #548C22×C5semidirect
299. #547C22×C5semidirect
301. #542C22×C5semidirect
302. #540C22×C5semidirect
307. #533C22×C5semidirect
308. #533C22×C5semidirect
310. #532C22×C5semidirect
311. #532C22×C5semidirect
312. #532C22×C5semidirect
315. #529C22×C5semidirect
316. #529C22×C5semidirect
317. #529C22×C5semidirect
318. #529C22×C5semidirect
319. #529C22×C5semidirect
324. #520C22×C5semidirect
326. #519C22×C5semidirect
332. C4×#41C22×C5semidirect
333. C4×#41C22×C5semidirect
334. C4×#41C22×C5semidirect
337. C2×C4×Q8C22×C5semidirect
523. C2×Q8C5×#41semidirect
641. C5#62793direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35242
C5×#35182
C5×#35172
C5×#35062
C5×#35022
C5×#34972
C5×#34932
C5×#34872
C5×#34832
C5×#34822
C5×#34802
C5×#34602
C5×#34442
C4×C5×2−1+42
C2×C4×C5×#412
#627935