Finite Group Databasebeta

← C5×#26149 #11948869

Subgroups — C5×#26149 #11948869

Order 1280.

868 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#483C211yesmaximal, characteristic, complemented
2C2×C5×#428C211yesmaximal, characteristic, complemented
3C5×#2417C211yesmaximal, characteristic
4C5×#2352C211yesmaximal, characteristic
5C5×#2097C211yesmaximal, characteristic, complemented
6C5×#2085C211yesmaximal, characteristic, complemented
7C5×#2076C211yesmaximal, characteristic, complemented
8C5×#2036C211yesmaximal, characteristic, complemented
9C5×#1927C211yesmaximal, characteristic, complemented
10C5×#1919C211yesmaximal, characteristic, complemented
11C5×#1894C211yesmaximal, characteristic, complemented
12C5×#1873C211yesmaximal, characteristic, complemented
13C5×#1870C211yesmaximal, characteristic
14C5×#1853C211yesmaximal, characteristic, complemented
15C5×#1853C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×C5×C22⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#483—24no—
24C5×#428—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C5×#398—21no—
39C5×#396—21no—
40C5×#391C2211yescharacteristic
41C5×#389C2211yescharacteristic
42C5×#388—21no—
43C5×#387—21no—
44C5×#386—21no—
45C5×#386—21no—
46C5×#382C2211yescharacteristic
47C5×#380—21no—
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C22⋊C4—21no—
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26149C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×D4D411yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C2×C5×M16—22no—
69C2×C5×M16—22no—
70C2×C5×M16—22no—
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×C22⋊Q8—22no—
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—22no—
78C5×C22⋊Q8—41no—
79C4×C5×D4—22no—
80C4×C5×D4—22no—
81C5×#117—22no—
82C5×#117—41no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—41no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5C2311yescharacteristic
111C5×#107—22no—
112C5×#107—22no—
113C5×#106—22no—
114C5×#106—22no—
115C5×#106—41no—
116C5×#106D414yescomplemented
117C5×#103—22no—
118C5×#103—22no—
119C5×#103—22no—
120C5×#103—41no—
121C5×C22⋊C8—22no—
122C5×C22⋊C8—22no—
123C5×C22⋊C8—22no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C2×#483C2×C511yescharacteristic, complemented
134C2×#428C2×C511yescharacteristic, complemented
135#2417C2×C511yescharacteristic
136#2352C2×C511yescharacteristic
137#2097C2×C511yescharacteristic, complemented
138#2085C2×C511yescharacteristic, complemented
139#2076C2×C511yescharacteristic, complemented
140#2036C2×C511yescharacteristic, complemented
141#1927C2×C511yescharacteristic, complemented
142#1919C2×C511yescharacteristic, complemented
143#1894C2×C511yescharacteristic, complemented
144#1873C2×C511yescharacteristic, complemented
145#1870C2×C511yescharacteristic
146#1853C2×C511yescharacteristic, complemented
147#1853C2×C511yescharacteristic, complemented
148C24×C5C2×D411yescharacteristic
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—22no—
157C2×C5×D4—22no—
158C2×C5×D4—41no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
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—21no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—42no—
180C22×C4×C5—42no—
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×C5#4112yes—
188C22×C4×C5#4112yes—
189C22×C4×C5C2411yescharacteristic
190C5×M16—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×C8#4112yes—
203C5×C4⋊C4—22no—
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—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—42no—
218C5×C4⋊C4—42no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—81no—
221C5×C4⋊C4C2×D412yes—
222C5×C4⋊C4C2×D412yes—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—81no—
230C5×C22⋊C4—81no—
231C42×C5—21no—
232C42×C5—21no—
233C42×C5—42no—
234C42×C5—81no—
235C22×M16C22×C511yescharacteristic
236C2×C22⋊Q8C22×C511yescharacteristic
237C2×C22⋊Q8C22×C511yescharacteristic
238C2×C4×D4C22×C511yescharacteristic
239C2×#117C22×C511yescharacteristic
240C22×C4⋊C4C22×C511yescharacteristic
241C22×C4⋊C4C22×C511yescharacteristic
242#483—24no—
243#428—24no—
244C2×#107C22×C511yescharacteristic
245C2×#107C22×C511yescharacteristic
246C2×#106C22×C511yescharacteristic
247C2×#106C22×C511yescharacteristic
248C2×#106C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#103C22×C511yescharacteristic
251C2×#103C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×C22⋊C8C22×C511yescharacteristic
255C2×C22⋊C8C22×C511yescharacteristic
256C2×C22⋊C8C22×C511yescharacteristic
257#398—21no—
258#396—21no—
259#391C22×C511yescharacteristic
260#389C22×C511yescharacteristic
261#388—21no—
262#387—21no—
263#386—21no—
264#386—21no—
265#382C22×C511yescharacteristic
266#380—21no—
267#380C22×C511yescharacteristic
268#380C22×C511yescharacteristic
269#380C22×C511yescharacteristic
270C4×C4⋊C4C22×C511yescharacteristic
271C4×C22⋊C4—21no—
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#336C22×C511yescharacteristic
279#336C22×C511yescharacteristic
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5#12312yes—
293C23×C5#13712yes—
294C23×C5C22×D411yescharacteristic
295C5×Q8—41no—
296C5×Q8—41no—
297C5×Q8—41no—
298C5×Q8—41no—
299C5×D4—44no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
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#12312yes—
346C2×C4×C5C22×D411yescharacteristic
347C2×C4×C5C2×#4111yescharacteristic
348C2×C4×C5C2×#4111yescharacteristic
349C2×C4×C5C2×#4111yescharacteristic
350C2×C4×C5H(5,𝔽2)11yescharacteristic
351C2×C4×C52−1+411yescharacteristic
352C5×C8—22no—
353C5×C8—22no—
354C5×C8—41no—
355C5×C8—41no—
356C22×Q8C23×C511yescharacteristic
357C22×D4C5×D411yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C23×C511yescharacteristic
361C23×C4C23×C511yescharacteristic
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C22×C8C23×C511yescharacteristic
366C22×C8C23×C511yescharacteristic
367C22×C8C23×C511yescharacteristic
368C22×C8C23×C511yescharacteristic
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—41no—
373C4×D4—22no—
374C4×D4—22no—
375#117—22no—
376#117—41no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4C5×D411yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4C5×D411yescharacteristic
401C2×C22⋊C4C5×D411yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C23×C511yescharacteristic
405#107—22no—
406#107—22no—
407#106—22no—
408#106—22no—
409#106—41no—
410#106C5×D414yescomplemented
411#103—22no—
412#103—22no—
413#103—22no—
414#103—41no—
415C22⋊C8—22no—
416C22⋊C8—22no—
417C22⋊C8—22no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5C2×#12311yescharacteristic
442C22×C5D4211yescharacteristic
443C22×C5#54711yescharacteristic
444C22×C5C2×#13711yescharacteristic
445C22×C5#57511yescharacteristic
446C22×C5#57711yescharacteristic
447C22×C5#57711yescharacteristic
448C4×C5—22no—
449C4×C5—41no—
450C4×C5—41no—
451C4×C5—41no—
452C4×C5—42no—
453C4×C5—42no—
454C4×C5—81no—
455C4×C5—81no—
456C4×C5—81no—
457C4×C5—81no—
458C4×C5—81no—
459C4×C5—81no—
460C4×C5#52511yescharacteristic
461C4×C5#53911yescharacteristic
462C4×C5#54811yescharacteristic
463C4×C5#55311yescharacteristic
464C24C2×C5×D411yescharacteristic
465C24C2×C5×D411yescharacteristic
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—41no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
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—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4C2×C5×D411yescharacteristic
500C22×C4C2×C5×D411yescharacteristic
501C22×C4C2×C5×D411yescharacteristic
502C22×C4C2×C5×D411yescharacteristic
503C22×C4C5×#4112yes—
504C22×C4C5×#4112yes—
505C22×C4C24×C511yescharacteristic
506M16—28no—
507C2×C8—21no—
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×C8C2×C5×D412yes—
518C2×C8C5×#4112yes—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
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—81no—
537C4⋊C4C2×C5×D412yes—
538C4⋊C4C2×C5×D412yes—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—42no—
550C42—81no—
551C2×C5—42no—
552C2×C5—42no—
553C2×C5#244311yescharacteristic
554C2×C5#309511yescharacteristic
555C2×C5#309911yescharacteristic
556C2×C5#326611yescharacteristic
557C2×C5#327511yescharacteristic
558C2×C5#334411yescharacteristic
559C2×C5#335111yescharacteristic
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23C5×#12312yes—
573C23C5×#13712yes—
574C23C22×C5×D411yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
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—84no—
624C2×C4—84no—
625C2×C4C5×#12312yes—
626C2×C4C22×C5×D411yescharacteristic
627C2×C4C2×C5×#4111yescharacteristic
628C2×C4C2×C5×#4111yescharacteristic
629C2×C4C2×C5×#4111yescharacteristic
630C2×C4C5×H(5,𝔽2)11yescharacteristic
631C2×C4C5×2−1+411yescharacteristic
632C8—22no—
633C8—22no—
634C8—41no—
635C8—41no—
636C5#2614911yescharacteristic, direct product factor, Sylow
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×C5×#12311yescharacteristic
652C22C5×D4211yescharacteristic
653C22C5×#54711yescharacteristic
654C22C2×C5×#13711yescharacteristic
655C22C5×#57511yescharacteristic
656C22C5×#57711yescharacteristic
657C22C5×#57711yescharacteristic
658C4—22no—
659C4—42no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C5×#52511yescharacteristic
671C4C5×#53911yescharacteristic
672C4C5×#54811yescharacteristic
673C4C5×#55311yescharacteristic
674C2—42no—
675C2—42no—
676C2C5×#244311yescharacteristic
677C2C5×#309511yescharacteristic
678C2C5×#309911yescharacteristic
679C2C5×#326611yescharacteristic
680C2C5×#327511yescharacteristic
681C2C5×#334411yescharacteristic
682C2C5×#335111yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#483C2semidirect
2. C2×C5×#428C2semidirect
5. C5×#2097C2semidirect
6. C5×#2085C2semidirect
7. C5×#2076C2semidirect
8. C5×#2036C2semidirect
9. C5×#1927C2semidirect
10. C5×#1919C2semidirect
11. C5×#1894C2semidirect
12. C5×#1873C2semidirect
14. C5×#1853C2semidirect
15. C5×#1853C2semidirect
61. #26149C5direct (N × H)
116. C5×#106D4semidirect
133. C2×#483C2×C5semidirect
134. C2×#428C2×C5semidirect
137. #2097C2×C5semidirect
138. #2085C2×C5semidirect
139. #2076C2×C5semidirect
140. #2036C2×C5semidirect
141. #1927C2×C5semidirect
142. #1919C2×C5semidirect
143. #1894C2×C5semidirect
144. #1873C2×C5semidirect
146. #1853C2×C5semidirect
147. #1853C2×C5semidirect
410. #106C5×D4semidirect
636. C5#26149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4832
C2×C5×#4282
C5×#24172
C5×#23522
C5×#20972
C5×#20852
C5×#20762
C5×#20362
C5×#19272
C5×#19192
C5×#18942
C5×#18732
C5×#18702
C5×#18532
#261495