Finite Group Databasebeta

← C5×#25176 #11947896

Subgroups — C5×#25176 #11947896

Order 1280.

1262 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#461C211yesmaximal, characteristic, complemented
2C2×C5×#450C211yesmaximal, characteristic
3C2×C5×#450C211yesmaximal, characteristic
4C2×C5×#440C211yesmaximal, characteristic, complemented
5C5×#2429C211yesmaximal, characteristic, complemented
6C5×D4×C22⋊C4C211yesmaximal, characteristic
7C5×#2067C211yesmaximal, characteristic, complemented
8C5×#2036C211yesmaximal, characteristic, complemented
9C5×#2036C211yesmaximal, characteristic, complemented
10C5×#2013C211yesmaximal, characteristic, complemented
11C5×#1973C211yesmaximal, characteristic, complemented
12C5×#1924C211yesmaximal, characteristic, complemented
13C5×#1880C211yesmaximal, characteristic, complemented
14C5×#1877C211yesmaximal, characteristic, complemented
15C5×#1862C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C22×C5×SD16C2211yescharacteristic
21C2×C5×C4⋊Q8C2211yescharacteristic, complemented
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C4×C5×Q8C2211yescharacteristic, complemented
25C2×C4×C5×D4C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C22×C5×C22⋊C4—21no—
28C5×#461—24no—
29C5×#450—24no—
30C5×#450—24no—
31C5×#440—24no—
32C2×C5×#107C2211yescharacteristic, complemented
33C2×C5×#107C2211yescharacteristic, complemented
34C2×C5×C4⋊C8C2211yescharacteristic, complemented
35C2×C5×#103C2211yescharacteristic, complemented
36C2×C5×#103C2211yescharacteristic, complemented
37C2×C5×#103C2211yescharacteristic, complemented
38C2×C5×#103C2211yescharacteristic, complemented
39C2×C5×#102C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×C22⋊C8C2211yescharacteristic
44C2×C5×C22⋊C8C2211yescharacteristic
45C2×C5×#97C2211yescharacteristic, complemented
46C5×#398—21no—
47C5×#396—21no—
48C5×#391C2211yescharacteristic, complemented
49C5×#390C2211yescharacteristic
50C5×#390C2211yescharacteristic
51C5×#389—21no—
52C5×#389C2211yescharacteristic, complemented
53C5×#388—21no—
54C5×#386—21no—
55C5×#386—21no—
56C5×#380C2211yescharacteristic
57C5×#379—21no—
58C4×C5×C22⋊C4C2211yescharacteristic
59C5×#340C2211yescharacteristic, complemented
60C5×#340C2211yescharacteristic, complemented
61C5×#336C2211yescharacteristic, complemented
62C5×#336C2211yescharacteristic, complemented
63#25176C511yesmaximal, characteristic, direct product factor, Sylow
64C25×C5—21no—
65C22×C5×Q8C2311yescharacteristic
66C22×C5×Q8C2311yescharacteristic
67C22×C5×D4—22no—
68C22×C5×D4—22no—
69C22×C5×D4—22no—
70C22×C5×D4—22no—
71C22×C5×D4—21no—
72C22×C5×D4—41no—
73C22×C5×D4—41no—
74C22×C5×D4C2311yescharacteristic
75C22×C5×D4C2311yescharacteristic
76C23×C4×C5—21no—
77C23×C4×C5—21no—
78C23×C4×C5C2311yescharacteristic
79C2×C5×SD16—22no—
80C2×C5×SD16—22no—
81C2×C5×SD16—22no—
82C2×C5×SD16—22no—
83C2×C5×SD16—22no—
84C2×C5×SD16—22no—
85C2×C5×SD16—22no—
86C2×C5×SD16—22no—
87C2×C5×SD16—22no—
88C2×C5×SD16—41no—
89C2×C5×SD16—41no—
90C2×C5×SD16D414yes—
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C22×C5×C8C2311yescharacteristic
94C22×C5×C8C2311yescharacteristic
95C5×C4⋊Q8—22no—
96C5×C4⋊Q8—41no—
97C5×C22⋊Q8—22no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8—41no—
100C5×C22⋊Q8—41no—
101C4×C5×Q8—22no—
102C4×C5×Q8—41no—
103C4×C5×D4—22no—
104C4×C5×D4—22no—
105C4×C5×D4—41no—
106C4×C5×D4—41no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4—44no—
127C2×C5×C22⋊C4D411yescharacteristic
128C2×C5×C22⋊C4D411yescharacteristic
129C2×C42×C5—21no—
130C2×C42×C5C2311yescharacteristic
131C2×C42×C5C2311yescharacteristic
132C5×#107—22no—
133C5×#107—41no—
134C5×C4⋊C8—22no—
135C5×#103—22no—
136C5×#103—22no—
137C5×#103—22no—
138C5×#103—41no—
139C5×#102—22no—
140C5×#102—22no—
141C5×#102—22no—
142C5×#102D414yes—
143C5×C22⋊C8—22no—
144C5×C22⋊C8—22no—
145C5×#97—22no—
146C5×#95—21no—
147C5×#95—21no—
148C5×#95—21no—
149C5×#95—21no—
150C5×#95D411yescharacteristic
151C5×#95D411yescharacteristic
152C2×#461C2×C511yescharacteristic, complemented
153C2×#450C2×C511yescharacteristic
154C2×#450C2×C511yescharacteristic
155C2×#440C2×C511yescharacteristic, complemented
156#2429C2×C511yescharacteristic, complemented
157D4×C22⋊C4C2×C511yescharacteristic
158#2067C2×C511yescharacteristic, complemented
159#2036C2×C511yescharacteristic, complemented
160#2036C2×C511yescharacteristic, complemented
161#2013C2×C511yescharacteristic, complemented
162#1973C2×C511yescharacteristic, complemented
163#1924C2×C511yescharacteristic, complemented
164#1880C2×C511yescharacteristic, complemented
165#1877C2×C511yescharacteristic, complemented
166#1862C2×C511yescharacteristic, complemented
167C24×C5—21no—
168C24×C5—24no—
169C24×C5—21no—
170C24×C5—42no—
171C24×C5—42no—
172C24×C5—42no—
173C24×C5—42no—
174C24×C5—81no—
175C24×C5—81no—
176C24×C5C2×D411yescharacteristic
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8—21no—
180C2×C5×Q8—21no—
181C2×C5×Q8—21no—
182C2×C5×Q8—21no—
183C2×C5×Q8—21no—
184C2×C5×Q8—21no—
185C2×C5×Q8—21no—
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8C2×D412yes—
189C2×C5×D4—24no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—42no—
199C2×C5×D4—42no—
200C2×C5×D4—44no—
201C2×C5×D4—44no—
202C2×C5×D4—44no—
203C2×C5×D4—44no—
204C2×C5×D4C2×D412yes—
205C2×C5×D4C2×D412yes—
206C2×C5×D4#4112yes—
207C2×C5×D4#4112yes—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—42no—
221C22×C4×C5—42no—
222C22×C4×C5—42no—
223C22×C4×C5—42no—
224C22×C4×C5—81no—
225C22×C4×C5—81no—
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2411yescharacteristic
232C5×SD16—28no—
233C5×SD16—44no—
234C5×SD16—44no—
235C5×SD16—44no—
236C2×C5×C8—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—21no—
243C2×C5×C8—21no—
244C2×C5×C8—21no—
245C2×C5×C8—21no—
246C2×C5×C8C2×D412yes—
247C2×C5×C8C2×D412yes—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—42no—
256C5×C4⋊C4—42no—
257C5×C4⋊C4—42no—
258C5×C4⋊C4—42no—
259C5×C4⋊C4—42no—
260C5×C4⋊C4—42no—
261C5×C4⋊C4C2×D412yes—
262C5×C22⋊C4—22no—
263C5×C22⋊C4—22no—
264C5×C22⋊C4—42no—
265C5×C22⋊C4—42no—
266C5×C22⋊C4—42no—
267C5×C22⋊C4—42no—
268C5×C22⋊C4—42no—
269C5×C22⋊C4—42no—
270C5×C22⋊C4—42no—
271C5×C22⋊C4—81no—
272C5×C22⋊C4—81no—
273C42×C5—21no—
274C42×C5—21no—
275C42×C5—21no—
276C42×C5—21no—
277C42×C5—42no—
278C23×D4C22×C511yescharacteristic
279C22×SD16C22×C511yescharacteristic
280C22×SD16C22×C511yescharacteristic
281C22×SD16C22×C511yescharacteristic
282C22×SD16C22×C511yescharacteristic
283C2×C4⋊Q8C22×C511yescharacteristic, complemented
284C2×C22⋊Q8C22×C511yescharacteristic
285C2×C22⋊Q8C22×C511yescharacteristic
286C2×C4×Q8C22×C511yescharacteristic, complemented
287C2×C4×D4C22×C511yescharacteristic
288C2×C4×D4C22×C511yescharacteristic
289C22×C22⋊C4—21no—
290#461—24no—
291#450—24no—
292#450—24no—
293#440—24no—
294C2×#107C22×C511yescharacteristic, complemented
295C2×#107C22×C511yescharacteristic, complemented
296C2×C4⋊C8C22×C511yescharacteristic, complemented
297C2×#103C22×C511yescharacteristic, complemented
298C2×#103C22×C511yescharacteristic, complemented
299C2×#103C22×C511yescharacteristic, complemented
300C2×#103C22×C511yescharacteristic, complemented
301C2×#102C22×C511yescharacteristic
302C2×#102C22×C511yescharacteristic
303C2×#102C22×C511yescharacteristic
304C2×#102C22×C511yescharacteristic
305C2×C22⋊C8C22×C511yescharacteristic
306C2×C22⋊C8C22×C511yescharacteristic
307C2×#97C22×C511yescharacteristic, complemented
308#398—21no—
309#396—21no—
310#391C22×C511yescharacteristic, complemented
311#390C22×C511yescharacteristic
312#390C22×C511yescharacteristic
313#389—21no—
314#389C22×C511yescharacteristic, complemented
315#388—21no—
316#386—21no—
317#386—21no—
318#380C22×C511yescharacteristic
319#379—21no—
320C4×C22⋊C4C22×C511yescharacteristic
321#340C22×C511yescharacteristic, complemented
322#340C22×C511yescharacteristic, complemented
323#336C22×C511yescharacteristic, complemented
324#336C22×C511yescharacteristic, complemented
325C23×C5—21no—
326C23×C5—22no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—21no—
334C23×C5—22no—
335C23×C5—48no—
336C23×C5—48no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—84no—
348C23×C5—84no—
349C23×C5—84no—
350C23×C5—84no—
351C23×C5—84no—
352C23×C5#13712yes—
353C23×C5C22×D411yescharacteristic
354C5×Q8—22no—
355C5×Q8—22no—
356C5×Q8—41no—
357C5×Q8—41no—
358C5×Q8—41no—
359C5×Q8—41no—
360C5×Q8—41no—
361C5×Q8—41no—
362C5×D4—22no—
363C5×D4—22no—
364C5×D4—22no—
365C5×D4—22no—
366C5×D4—22no—
367C5×D4—48no—
368C5×D4—41no—
369C5×D4—41no—
370C5×D4#12114yes—
371C2×C4×C5—21no—
372C2×C4×C5—21no—
373C2×C4×C5—21no—
374C2×C4×C5—21no—
375C2×C4×C5—21no—
376C2×C4×C5—21no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
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—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—84no—
408C2×C4×C5—84no—
409C2×C4×C5AGL(1,ℤ/8)12yes—
410C2×C4×C5C22×D411yescharacteristic
411C2×C4×C5C22×D411yescharacteristic
412C2×C4×C5C2×#4111yescharacteristic
413C2×C4×C5C2×#4111yescharacteristic
414C2×C4×C5H(5,𝔽2)11yescharacteristic
415C2×C4×C5H(5,𝔽2)11yescharacteristic
416C5×C8—22no—
417C5×C8—22no—
418C5×C8—41no—
419C5×C8—41no—
420C25—21no—
421C22×Q8C23×C511yescharacteristic
422C22×Q8C23×C511yescharacteristic
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—21no—
428C22×D4—41no—
429C22×D4—41no—
430C22×D4C23×C511yescharacteristic
431C22×D4C23×C511yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C511yescharacteristic
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—41no—
445C2×SD16—41no—
446C2×SD16C5×D414yes—
447C22×C8C23×C511yescharacteristic
448C22×C8C23×C511yescharacteristic
449C22×C8C23×C511yescharacteristic
450C22×C8C23×C511yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8—41no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—41no—
456C22⋊Q8—41no—
457C4×Q8—22no—
458C4×Q8—41no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—41no—
462C4×D4—41no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4C23×C511yescharacteristic
470C2×C4⋊C4C23×C511yescharacteristic
471C2×C4⋊C4C23×C511yescharacteristic
472C2×C4⋊C4C23×C511yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—44no—
483C2×C22⋊C4C5×D411yescharacteristic
484C2×C22⋊C4C5×D411yescharacteristic
485C2×C42—21no—
486C2×C42C23×C511yescharacteristic
487C2×C42C23×C511yescharacteristic
488#107—22no—
489#107—41no—
490C4⋊C8—22no—
491#103—22no—
492#103—22no—
493#103—22no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102C5×D414yes—
499C22⋊C8—22no—
500C22⋊C8—22no—
501#97—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95C5×D411yescharacteristic
507#95C5×D411yescharacteristic
508C22×C5—22no—
509C22×C5—24no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—42no—
513C22×C5—41no—
514C22×C5—42no—
515C22×C5—41no—
516C22×C5—42no—
517C22×C5—41no—
518C22×C5—42no—
519C22×C5—42no—
520C22×C5—42no—
521C22×C5—41no—
522C22×C5—42no—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—816no—
526C22×C5—81no—
527C22×C5—81no—
528C22×C5—81no—
529C22×C5—81no—
530C22×C5#52511yescharacteristic
531C22×C5D4211yescharacteristic
532C22×C5D4211yescharacteristic
533C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
534C22×C5C2×#13711yescharacteristic
535C22×C5#57711yescharacteristic
536C22×C5#57711yescharacteristic
537C4×C5—22no—
538C4×C5—41no—
539C4×C5—42no—
540C4×C5—41no—
541C4×C5—41no—
542C4×C5—41no—
543C4×C5—42no—
544C4×C5—81no—
545C4×C5—81no—
546C4×C5—81no—
547C4×C5—81no—
548C4×C5C2×#12111yescharacteristic
549C4×C5#53811yescharacteristic
550C4×C5#54611yescharacteristic
551C4×C5#54611yescharacteristic
552C24—21no—
553C24—24no—
554C24—21no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×C5×D411yescharacteristic
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C2×C5×D412yes—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—44no—
589C2×D4C2×C5×D412yes—
590C2×D4C2×C5×D412yes—
591C2×D4C5×#4112yes—
592C2×D4C5×#4112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4C2×C5×D411yescharacteristic
612C22×C4C2×C5×D411yescharacteristic
613C22×C4C2×C5×D411yescharacteristic
614C22×C4C2×C5×D411yescharacteristic
615C22×C4C2×C5×D411yescharacteristic
616C22×C4C24×C511yescharacteristic
617SD16—28no—
618SD16—44no—
619SD16—44no—
620SD16—44no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8C2×C5×D412yes—
632C2×C8C2×C5×D412yes—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4C2×C5×D412yes—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—42no—
663C2×C5—42no—
664C2×C5—44no—
665C2×C5—82no—
666C2×C5#242411yescharacteristic
667C2×C5#311011yescharacteristic
668C2×C5#312311yescharacteristic
669C2×C5#326511yescharacteristic
670C2×C5#326611yescharacteristic
671C2×C5#326611yescharacteristic
672C2×C5#327211yescharacteristic
673C23—21no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—48no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23C5×#13712yes—
701C23C22×C5×D411yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—41no—
717D4—41no—
718D4C5×#12114yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C5×AGL(1,ℤ/8)12yes—
758C2×C4C22×C5×D411yescharacteristic
759C2×C4C22×C5×D411yescharacteristic
760C2×C4C2×C5×#4111yescharacteristic
761C2×C4C2×C5×#4111yescharacteristic
762C2×C4C5×H(5,𝔽2)11yescharacteristic
763C2×C4C5×H(5,𝔽2)11yescharacteristic
764C8—22no—
765C8—22no—
766C8—41no—
767C8—41no—
768C5#2517611yescharacteristic, direct product factor, Sylow
769C22—22no—
770C22—22no—
771C22—22no—
772C22—24no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—41no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C5×#52511yescharacteristic
792C22C5×D4211yescharacteristic
793C22C5×D4211yescharacteristic
794C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
795C22C2×C5×#13711yescharacteristic
796C22C5×#57711yescharacteristic
797C22C5×#57711yescharacteristic
798C4—22no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×C5×#12111yescharacteristic
810C4C5×#53811yescharacteristic
811C4C5×#54611yescharacteristic
812C4C5×#54611yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2C5×#242411yescharacteristic
817C2C5×#311011yescharacteristic
818C2C5×#312311yescharacteristic
819C2C5×#326511yescharacteristic
820C2C5×#326611yescharacteristic
821C2C5×#326611yescharacteristic
822C2C5×#327211yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC23×C5×D4C22
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
1. C2×C5×#461C2semidirect
4. C2×C5×#440C2semidirect
5. C5×#2429C2semidirect
7. C5×#2067C2semidirect
8. C5×#2036C2semidirect
9. C5×#2036C2semidirect
10. C5×#2013C2semidirect
11. C5×#1973C2semidirect
12. C5×#1924C2semidirect
13. C5×#1880C2semidirect
14. C5×#1877C2semidirect
15. C5×#1862C2semidirect
21. C2×C5×C4⋊Q8C22semidirect
24. C2×C4×C5×Q8C22semidirect
32. C2×C5×#107C22semidirect
33. C2×C5×#107C22semidirect
34. C2×C5×C4⋊C8C22semidirect
35. C2×C5×#103C22semidirect
36. C2×C5×#103C22semidirect
37. C2×C5×#103C22semidirect
38. C2×C5×#103C22semidirect
45. C2×C5×#97C22semidirect
48. C5×#391C22semidirect
52. C5×#389C22semidirect
59. C5×#340C22semidirect
60. C5×#340C22semidirect
61. C5×#336C22semidirect
62. C5×#336C22semidirect
63. #25176C5direct (N × H)
152. C2×#461C2×C5semidirect
155. C2×#440C2×C5semidirect
156. #2429C2×C5semidirect
158. #2067C2×C5semidirect
159. #2036C2×C5semidirect
160. #2036C2×C5semidirect
161. #2013C2×C5semidirect
162. #1973C2×C5semidirect
163. #1924C2×C5semidirect
164. #1880C2×C5semidirect
165. #1877C2×C5semidirect
166. #1862C2×C5semidirect
283. C2×C4⋊Q8C22×C5semidirect
286. C2×C4×Q8C22×C5semidirect
294. C2×#107C22×C5semidirect
295. C2×#107C22×C5semidirect
296. C2×C4⋊C8C22×C5semidirect
297. C2×#103C22×C5semidirect
298. C2×#103C22×C5semidirect
299. C2×#103C22×C5semidirect
300. C2×#103C22×C5semidirect
307. C2×#97C22×C5semidirect
310. #391C22×C5semidirect
314. #389C22×C5semidirect
321. #340C22×C5semidirect
322. #340C22×C5semidirect
323. #336C22×C5semidirect
324. #336C22×C5semidirect
768. C5#25176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4612
C2×C5×#4502
C2×C5×#4402
C5×#24292
C5×D4×C22⋊C42
C5×#20672
C5×#20362
C5×#20132
C5×#19732
C5×#19242
C5×#18802
C5×#18772
C5×#18622
#251765