Finite Group Databasebeta

← C5×#24878 #11947598

Subgroups — C5×#24878 #11947598

Order 1280.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#481C211yesmaximal, characteristic, complemented
2C2×C5×#418C211yesmaximal, characteristic, complemented
3C5×#2408C211yesmaximal, characteristic
4C5×#2352C211yesmaximal, characteristic, complemented
5C5×#2092C211yesmaximal, characteristic, complemented
6C5×#2073C211yesmaximal, characteristic, complemented
7C5×#2033C211yesmaximal, characteristic, complemented
8C5×#2033C211yesmaximal, characteristic, complemented
9C5×#1926C211yesmaximal, characteristic, complemented
10C5×#1925C211yesmaximal, characteristic, complemented
11C5×#1874C211yesmaximal, characteristic, complemented
12C5×#1870C211yesmaximal, characteristic, complemented
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1809C211yesmaximal, characteristic, complemented
15C5×#1786C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C5×#120—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic, complemented
24C5×#481—24no—
25C2×C5×#107C2211yescharacteristic, complemented
26C2×C5×#107C2211yescharacteristic, complemented
27C2×C5×#106C2211yescharacteristic, complemented
28C2×C5×#106C2211yescharacteristic, complemented
29C5×#418—24no—
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic, complemented
40C2×C5×C22⋊C8C2211yescharacteristic, complemented
41C5×#394—21no—
42C5×#392—21no—
43C5×#390C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#388—21no—
46C5×#387—21no—
47C5×#386—21no—
48C5×#382C2211yescharacteristic, complemented
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic, complemented
52C5×#379—21no—
53C4×C5×C4⋊C4C2211yescharacteristic, complemented
54C4×C5×C22⋊C4—21no—
55C5×#340C2211yescharacteristic, complemented
56C5×#340C2211yescharacteristic, complemented
57C5×#340C2211yescharacteristic, complemented
58C5×#340C2211yescharacteristic, complemented
59C5×#336C2211yescharacteristic, complemented
60C5×#336C2211yescharacteristic, complemented
61#24878C511yesmaximal, characteristic, direct product factor, Sylow
62C25×C5—21no—
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—21no—
66C22×C5×D4—21no—
67C22×C5×D4—21no—
68C22×C5×D4—22no—
69C22×C5×D4—22no—
70C22×C5×D4—41no—
71C22×C5×D4—41no—
72C22×C5×D4D411yescharacteristic
73C22×C5×D4C2311yescharacteristic
74C22×C5×D4C2311yescharacteristic
75C23×C4×C5—21no—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C2×C5×M16—22no—
79C2×C5×M16—22no—
80C2×C5×M16—41no—
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C22×C5×C8C2311yescharacteristic
84C22×C5×C8C2311yescharacteristic
85C5×#121—22no—
86C5×#121—22no—
87C5×#121—41no—
88C5×#121—41no—
89C5×#120—44no—
90C4×C5×D4—22no—
91C4×C5×D4—22no—
92C5×#117—22no—
93C5×#117—41no—
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—41no—
97C2×C5×C4⋊C4D411yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
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×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4D411yescharacteristic
115C2×C5×C22⋊C4D411yescharacteristic
116C2×C42×C5—21no—
117C2×C42×C5—21no—
118C2×C42×C5C2311yescharacteristic
119C5×#107—41no—
120C5×#107—41no—
121C5×#106—22no—
122C5×#106—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×#102—22no—
126C5×#102—22no—
127C5×#102—22no—
128C5×#102—41no—
129C5×#102—41no—
130C5×#102D414yescomplemented
131C5×C22⋊C8—22no—
132C5×C22⋊C8—22no—
133C5×C22⋊C8—41no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140C2×#481C2×C511yescharacteristic, complemented
141C2×#418C2×C511yescharacteristic, complemented
142#2408C2×C511yescharacteristic
143#2352C2×C511yescharacteristic, complemented
144#2092C2×C511yescharacteristic, complemented
145#2073C2×C511yescharacteristic, complemented
146#2033C2×C511yescharacteristic, complemented
147#2033C2×C511yescharacteristic, complemented
148#1926C2×C511yescharacteristic, complemented
149#1925C2×C511yescharacteristic, complemented
150#1874C2×C511yescharacteristic, complemented
151#1870C2×C511yescharacteristic, complemented
152#1854C2×C511yescharacteristic, complemented
153#1809C2×C511yescharacteristic, complemented
154#1786C2×C511yescharacteristic, complemented
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—42no—
158C24×C5—42no—
159C24×C5—42no—
160C24×C5—42no—
161C24×C5—42no—
162C24×C5—81no—
163C24×C5—81no—
164C24×C5C2×D411yescharacteristic
165C24×C5C2×D411yescharacteristic
166C2×C5×D4—28no—
167C2×C5×D4—22no—
168C2×C5×D4—22no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4—44no—
180C2×C5×D4—44no—
181C2×C5×D4—41no—
182C2×C5×D4—42no—
183C2×C5×D4—42no—
184C2×C5×D4—44no—
185C2×C5×D4—42no—
186C2×C5×D4—42no—
187C2×C5×D4—42no—
188C2×C5×D4—42no—
189C2×C5×D4—42no—
190C2×C5×D4—81no—
191C2×C5×D4—81no—
192C2×C5×D4C2×D412yes—
193C2×C5×D4#4112yes—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—42no—
211C22×C4×C5—42no—
212C22×C4×C5—81no—
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5#4112yes—
218C22×C4×C5#4112yes—
219C22×C4×C5C2411yescharacteristic
220C5×M16—44no—
221C2×C5×C8—21no—
222C2×C5×C8—21no—
223C2×C5×C8—21no—
224C2×C5×C8—21no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8—21no—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C2×C5×C8—21no—
232C2×C5×C8C2×D412yes—
233C5×C4⋊C4—22no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4—42no—
246C5×C4⋊C4C2×D412yes—
247C5×C22⋊C4—22no—
248C5×C22⋊C4—22no—
249C5×C22⋊C4—42no—
250C5×C22⋊C4—42no—
251C5×C22⋊C4—42no—
252C5×C22⋊C4—42no—
253C5×C22⋊C4—42no—
254C5×C22⋊C4—42no—
255C5×C22⋊C4—42no—
256C5×C22⋊C4—81no—
257C5×C22⋊C4—81no—
258C5×C22⋊C4—81no—
259C42×C5—21no—
260C42×C5—21no—
261C42×C5—42no—
262C42×C5—81no—
263C23×D4C22×C511yescharacteristic
264C22×M16C22×C511yescharacteristic
265C2×#121C22×C511yescharacteristic
266C2×#121C22×C511yescharacteristic
267C2×#120—21no—
268C2×C4×D4C22×C511yescharacteristic
269C2×#117C22×C511yescharacteristic
270C22×C4⋊C4C22×C511yescharacteristic, complemented
271#481—24no—
272C2×#107C22×C511yescharacteristic, complemented
273C2×#107C22×C511yescharacteristic, complemented
274C2×#106C22×C511yescharacteristic, complemented
275C2×#106C22×C511yescharacteristic, complemented
276#418—24no—
277C2×#102C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×#102C22×C511yescharacteristic
280C2×#102C22×C511yescharacteristic
281C2×#102C22×C511yescharacteristic
282C2×#102C22×C511yescharacteristic
283C2×#102C22×C511yescharacteristic
284C2×#102C22×C511yescharacteristic
285C2×C22⋊C8C22×C511yescharacteristic
286C2×C22⋊C8C22×C511yescharacteristic, complemented
287C2×C22⋊C8C22×C511yescharacteristic, complemented
288#394—21no—
289#392—21no—
290#390C22×C511yescharacteristic
291#390C22×C511yescharacteristic
292#388—21no—
293#387—21no—
294#386—21no—
295#382C22×C511yescharacteristic, complemented
296#380C22×C511yescharacteristic
297#380C22×C511yescharacteristic
298#380C22×C511yescharacteristic, complemented
299#379—21no—
300C4×C4⋊C4C22×C511yescharacteristic, complemented
301C4×C22⋊C4—21no—
302#340C22×C511yescharacteristic, complemented
303#340C22×C511yescharacteristic, complemented
304#340C22×C511yescharacteristic, complemented
305#340C22×C511yescharacteristic, complemented
306#336C22×C511yescharacteristic, complemented
307#336C22×C511yescharacteristic, complemented
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—48no—
323C23×C5—41no—
324C23×C5—41no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—84no—
336C23×C5—84no—
337C23×C5—84no—
338C23×C5—84no—
339C23×C5—84no—
340C23×C5—84no—
341C23×C5#12312yes—
342C23×C5AGL(1,ℤ/8)12yes—
343C23×C5C22×D411yescharacteristic
344C5×D4—22no—
345C5×D4—22no—
346C5×D4—22no—
347C5×D4—22no—
348C5×D4—48no—
349C5×D4—44no—
350C5×D4—41no—
351C5×D4—41no—
352C5×D4—41no—
353C5×D4—41no—
354C5×D4—84no—
355C5×D4—84no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—22no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—21no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—84no—
394C2×C4×C5#12312yes—
395C2×C4×C5C22×D411yescharacteristic
396C2×C4×C5C2×#4111yescharacteristic
397C2×C4×C5C2×#4111yescharacteristic
398C2×C4×C5C2×#4111yescharacteristic
399C2×C4×C5H(5,𝔽2)11yescharacteristic
400C2×C4×C5H(5,𝔽2)11yescharacteristic
401C5×C8—22no—
402C5×C8—41no—
403C5×C8—41no—
404C5×C8—41no—
405C25—21no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—41no—
414C22×D4—41no—
415C22×D4C5×D411yescharacteristic
416C22×D4C23×C511yescharacteristic
417C22×D4C23×C511yescharacteristic
418C23×C4—21no—
419C23×C4C23×C511yescharacteristic
420C23×C4C23×C511yescharacteristic
421C2×M16—22no—
422C2×M16—22no—
423C2×M16—41no—
424C22×C8C23×C511yescharacteristic
425C22×C8C23×C511yescharacteristic
426C22×C8C23×C511yescharacteristic
427C22×C8C23×C511yescharacteristic
428#121—22no—
429#121—22no—
430#121—41no—
431#121—41no—
432#120—44no—
433C4×D4—22no—
434C4×D4—22no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4C5×D411yescharacteristic
441C2×C4⋊C4C23×C511yescharacteristic
442C2×C4⋊C4C23×C511yescharacteristic
443C2×C4⋊C4C23×C511yescharacteristic
444C2×C4⋊C4C23×C511yescharacteristic
445C2×C4⋊C4C23×C511yescharacteristic
446C2×C4⋊C4C23×C511yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4C5×D411yescharacteristic
458C2×C22⋊C4C5×D411yescharacteristic
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C511yescharacteristic
462#107—41no—
463#107—41no—
464#106—22no—
465#106—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—41no—
472#102—41no—
473#102C5×D414yescomplemented
474C22⋊C8—22no—
475C22⋊C8—22no—
476C22⋊C8—41no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483C22×C5—22no—
484C22×C5—22no—
485C22×C5—22no—
486C22×C5—22no—
487C22×C5—22no—
488C22×C5—22no—
489C22×C5—41no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5—41no—
496C22×C5—41no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—816no—
504C22×C5—81no—
505C22×C5—81no—
506C22×C5—81no—
507C22×C5—81no—
508C22×C5—81no—
509C22×C5—81no—
510C22×C5—81no—
511C22×C5—81no—
512C22×C5C2×#12311yescharacteristic
513C22×C5D4211yescharacteristic
514C22×C5#54611yescharacteristic
515C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C5#57511yescharacteristic
517C22×C5#57611yescharacteristic
518C22×C5#57711yescharacteristic
519C4×C5—22no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5—41no—
523C4×C5—42no—
524C4×C5—81no—
525C4×C5—81no—
526C4×C5—81no—
527C4×C5—81no—
528C4×C5—81no—
529C4×C5#52511yescharacteristic
530C4×C5#53811yescharacteristic
531C4×C5#54611yescharacteristic
532C4×C5#55111yescharacteristic
533C24—21no—
534C24—21no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24—42no—
539C24—42no—
540C24—81no—
541C24—81no—
542C24C2×C5×D411yescharacteristic
543C24C2×C5×D411yescharacteristic
544C2×D4—28no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×C5×D412yes—
571C2×D4C5×#4112yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4C2×C5×D411yescharacteristic
592C22×C4C2×C5×D411yescharacteristic
593C22×C4C2×C5×D411yescharacteristic
594C22×C4C2×C5×D411yescharacteristic
595C22×C4C5×#4112yes—
596C22×C4C5×#4112yes—
597C22×C4C24×C511yescharacteristic
598M16—44no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×C5×D412yes—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4C2×C5×D412yes—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C42—21no—
638C42—21no—
639C42—42no—
640C42—81no—
641C2×C5—42no—
642C2×C5—42no—
643C2×C5—82no—
644C2×C5—82no—
645C2×C5#241811yescharacteristic
646C2×C5#309411yescharacteristic
647C2×C5#309611yescharacteristic
648C2×C5#326511yescharacteristic
649C2×C5#327311yescharacteristic
650C2×C5#331811yescharacteristic
651C2×C5#332311yescharacteristic
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23C5×#12312yes—
686C23C5×AGL(1,ℤ/8)12yes—
687C23C22×C5×D411yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4C5×#12312yes—
739C2×C4C22×C5×D411yescharacteristic
740C2×C4C2×C5×#4111yescharacteristic
741C2×C4C2×C5×#4111yescharacteristic
742C2×C4C2×C5×#4111yescharacteristic
743C2×C4C5×H(5,𝔽2)11yescharacteristic
744C2×C4C5×H(5,𝔽2)11yescharacteristic
745C8—22no—
746C8—41no—
747C8—41no—
748C8—41no—
749C5#2487811yescharacteristic, direct product factor, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×C5×#12311yescharacteristic
780C22C5×D4211yescharacteristic
781C22C5×#54611yescharacteristic
782C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
783C22C5×#57511yescharacteristic
784C22C5×#57611yescharacteristic
785C22C5×#57711yescharacteristic
786C4—22no—
787C4—42no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C5×#52511yescharacteristic
797C4C5×#53811yescharacteristic
798C4C5×#54611yescharacteristic
799C4C5×#55111yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2C5×#241811yescharacteristic
805C2C5×#309411yescharacteristic
806C2C5×#309611yescharacteristic
807C2C5×#326511yescharacteristic
808C2C5×#327311yescharacteristic
809C2C5×#331811yescharacteristic
810C2C5×#332311yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2408C2
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×#481C2semidirect
2. C2×C5×#418C2semidirect
4. C5×#2352C2semidirect
5. C5×#2092C2semidirect
6. C5×#2073C2semidirect
7. C5×#2033C2semidirect
8. C5×#2033C2semidirect
9. C5×#1926C2semidirect
10. C5×#1925C2semidirect
11. C5×#1874C2semidirect
12. C5×#1870C2semidirect
13. C5×#1854C2semidirect
14. C5×#1809C2semidirect
15. C5×#1786C2semidirect
23. C22×C5×C4⋊C4C22semidirect
25. C2×C5×#107C22semidirect
26. C2×C5×#107C22semidirect
27. C2×C5×#106C22semidirect
28. C2×C5×#106C22semidirect
39. C2×C5×C22⋊C8C22semidirect
40. C2×C5×C22⋊C8C22semidirect
48. C5×#382C22semidirect
51. C5×#380C22semidirect
53. C4×C5×C4⋊C4C22semidirect
55. C5×#340C22semidirect
56. C5×#340C22semidirect
57. C5×#340C22semidirect
58. C5×#340C22semidirect
59. C5×#336C22semidirect
60. C5×#336C22semidirect
61. #24878C5direct (N × H)
130. C5×#102D4semidirect
140. C2×#481C2×C5semidirect
141. C2×#418C2×C5semidirect
143. #2352C2×C5semidirect
144. #2092C2×C5semidirect
145. #2073C2×C5semidirect
146. #2033C2×C5semidirect
147. #2033C2×C5semidirect
148. #1926C2×C5semidirect
149. #1925C2×C5semidirect
150. #1874C2×C5semidirect
151. #1870C2×C5semidirect
152. #1854C2×C5semidirect
153. #1809C2×C5semidirect
154. #1786C2×C5semidirect
270. C22×C4⋊C4C22×C5semidirect
272. C2×#107C22×C5semidirect
273. C2×#107C22×C5semidirect
274. C2×#106C22×C5semidirect
275. C2×#106C22×C5semidirect
286. C2×C22⋊C8C22×C5semidirect
287. C2×C22⋊C8C22×C5semidirect
295. #382C22×C5semidirect
298. #380C22×C5semidirect
300. C4×C4⋊C4C22×C5semidirect
302. #340C22×C5semidirect
303. #340C22×C5semidirect
304. #340C22×C5semidirect
305. #340C22×C5semidirect
306. #336C22×C5semidirect
307. #336C22×C5semidirect
473. #102C5×D4semidirect
749. C5#24878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4812
C2×C5×#4182
C5×#24082
C5×#23522
C5×#20922
C5×#20732
C5×#20332
C5×#19262
C5×#19252
C5×#18742
C5×#18702
C5×#18542
C5×#18092
C5×#17862
#248785