Finite Group Databasebeta

← C2×C5×#1904 #11943716

Subgroups — C2×C5×#1904 #11943716

Order 1280.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C5×#518C211yesmaximal, characteristic, complemented
3C2×C5×#421C211yesmaximal, characteristic, complemented
4C2×C5×#418C211yesmaximal, characteristic, complemented
5C2×C5×#410C211yesmaximal, characteristic, complemented
6C5×#1904C218yesmaximal, direct product factor
7C2×C5×#344C211yesmaximal, characteristic, complemented
8C2×C5×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×C5×#41C2211yescharacteristic
10C23×C5×D4C2211yescharacteristic
11C2×C5×AGL(1,ℤ/8)—22no—
12C2×C5×AGL(1,ℤ/8)—22no—
13C2×C5×AGL(1,ℤ/8)—22no—
14C2×C5×AGL(1,ℤ/8)—22no—
15C2×C5×AGL(1,ℤ/8)C414yescomplemented
16C2×C5×AGL(1,ℤ/8)C2214yes—
17C22×C5×SD16C412yescomplemented
18C22×C5×D8C412yescomplemented
19C22×C5×M16C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic
21C5×#518—22no—
22C5×#518—22no—
23C5×#518—22no—
24C5×#518C2214yescomplemented
25C2×C4×C5×D4—22no—
26C2×C4×C5×D4—22no—
27C2×C5×#117C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C22⋊C4—22no—
31C5×#421—22no—
32C5×#421C2214yescomplemented
33C2×C5×#104—22no—
34C5×#418—22no—
35C5×#418C2214yescomplemented
36C2×C5×#102—22no—
37C5×#410—22no—
38C5×#410C2214yescomplemented
39C2×C5×#99—22no—
40C5×#344C2214yescomplemented
41C5×H(3,ℤ/4)C2214yescomplemented
42C2×#1904C511yesmaximal, characteristic, direct product factor, Sylow
43C25×C5—21no—
44C2×C5×#41—21no—
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41—21no—
50C2×C5×#41—21no—
51C2×C5×#41—21no—
52C2×C5×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41C2×C412yescomplemented
55C2×C5×#41C2312yes—
56C22×C5×Q8C2×C411yescharacteristic, complemented
57C22×C5×D4—21no—
58C22×C5×D4—21no—
59C22×C5×D4—21no—
60C22×C5×D4—21no—
61C22×C5×D4—21no—
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4—21no—
65C22×C5×D4C2×C412yes—
66C22×C5×D4C2×C412yes—
67C22×C5×D4C2×C411yescharacteristic, complemented
68C22×C5×D4D412yes—
69C22×C5×D4D412yes—
70C22×C5×D4D412yes—
71C22×C5×D4D412yes—
72C22×C5×D4C2312yes—
73C23×C4×C5—24no—
74C23×C4×C5—21no—
75C23×C4×C5C2311yescharacteristic
76C5×AGL(1,ℤ/8)—28no—
77C5×AGL(1,ℤ/8)—28no—
78C5×AGL(1,ℤ/8)—28no—
79C5×AGL(1,ℤ/8)—28no—
80C2×C5×SD16—24no—
81C2×C5×SD16—24no—
82C2×C5×SD16C2×C418yescomplemented
83C2×C5×D8—24no—
84C2×C5×D8—24no—
85C2×C5×D8C2×C418yescomplemented
86C2×C5×M16—21no—
87C2×C5×M16—21no—
88C2×C5×M16—21no—
89C2×C5×M16—21no—
90C2×C5×M16—21no—
91C2×C5×M16—21no—
92C2×C5×M16—21no—
93C2×C5×M16—21no—
94C2×C5×M16—21no—
95C2×C5×M16C2×C412yescomplemented
96C2×C5×M16C2312yes—
97C2×C5×M16C2312yes—
98C22×C5×C8—21no—
99C22×C5×C8C2×C412yescomplemented
100C4×C5×D4—28no—
101C4×C5×D4—28no—
102C4×C5×D4—28no—
103C4×C5×D4—28no—
104C5×#117—21no—
105C5×#117—21no—
106C5×#117—21no—
107C5×#117—21no—
108C5×#117—21no—
109C5×#117—21no—
110C5×#117—21no—
111C5×#117D412yes—
112C5×#117D412yes—
113C5×#117C2312yes—
114C5×#117C2312yes—
115C5×#117C2312yes—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4—21no—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4—28no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—28no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4D412yes—
125C2×C42×C5—21no—
126C2×C42×C5—21no—
127C2×C42×C5D412yes—
128C5×#104—28no—
129C5×#102—28no—
130C5×#99—28no—
131C22×AGL(1,ℤ/8)C2×C511yescharacteristic
132C2×#518C2×C511yescharacteristic, complemented
133C2×#421C2×C511yescharacteristic, complemented
134C2×#418C2×C511yescharacteristic, complemented
135C2×#410C2×C511yescharacteristic, complemented
136#1904C2×C518yesdirect product factor
137C2×#344C2×C511yescharacteristic, complemented
138C2×H(3,ℤ/4)C2×C511yescharacteristic, complemented
139C24×C5—22no—
140C24×C5—22no—
141C24×C5—22no—
142C24×C5—22no—
143C24×C5—22no—
144C24×C5—22no—
145C24×C5—22no—
146C24×C5—21no—
147C24×C5—84no—
148C24×C5C2×D411yescharacteristic
149C5×#41—22no—
150C5×#41—22no—
151C5×#41—22no—
152C5×#41—22no—
153C5×#41—22no—
154C5×#41—22no—
155C5×#41—22no—
156C5×#41—22no—
157C5×#41—41no—
158C5×#41—41no—
159C5×#41—41no—
160C5×#41—41no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—41no—
164C5×#41—41no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8C22×C412yescomplemented
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—22no—
176C2×C5×D4—22no—
177C2×C5×D4—22no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—22no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—22no—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4—22no—
188C2×C5×D4—22no—
189C2×C5×D4—22no—
190C2×C5×D4—22no—
191C2×C5×D4—22no—
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4—22no—
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—41no—
200C2×C5×D4—41no—
201C2×C5×D4—41no—
202C2×C5×D4—41no—
203C2×C5×D4C22⋊C414yes—
204C2×C5×D4C22⋊C414yes—
205C2×C5×D4C22⋊C414yes—
206C2×C5×D4C22⋊C414yes—
207C2×C5×D4C22×C414yes—
208C2×C5×D4C22×C412yescomplemented
209C2×C5×D4C2×D414yes—
210C2×C5×D4C2×D414yes—
211C22×C4×C5—21no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—216no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—41no—
218C22×C4×C5—41no—
219C22×C4×C5—41no—
220C22×C4×C5—41no—
221C22×C4×C5—41no—
222C22×C4×C5—88no—
223C22×C4×C5C22×C411yescharacteristic
224C22×C4×C5C22×C411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5#4111yescharacteristic
233C22×C4×C5#4111yescharacteristic
234C22×C4×C5#4111yescharacteristic
235C22×C4×C5#4111yescharacteristic
236C22×C4×C5C2411yescharacteristic
237C5×SD16—216no—
238C5×D8—216no—
239C5×M16—22no—
240C5×M16—22no—
241C5×M16—22no—
242C5×M16—22no—
243C5×M16—22no—
244C5×M16—22no—
245C5×M16—41no—
246C5×M16—41no—
247C2×C5×C8—22no—
248C2×C5×C8—22no—
249C2×C5×C8—22no—
250C2×C5×C8—41no—
251C2×C5×C8—41no—
252C2×C5×C8C22×C414yescomplemented
253C5×C4⋊C4—22no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—22no—
256C5×C4⋊C4—22no—
257C5×C4⋊C4—22no—
258C5×C4⋊C4—41no—
259C5×C22⋊C4—216no—
260C5×C22⋊C4—22no—
261C5×C22⋊C4—22no—
262C5×C22⋊C4—22no—
263C5×C22⋊C4—22no—
264C5×C22⋊C4—41no—
265C5×C22⋊C4C2×D414yes—
266C42×C5—22no—
267C42×C5—22no—
268C42×C5—22no—
269C42×C5—22no—
270C42×C5—41no—
271C42×C5C2×D414yes—
272C22×#41C22×C511yescharacteristic
273C23×D4C22×C511yescharacteristic
274C2×AGL(1,ℤ/8)—22no—
275C2×AGL(1,ℤ/8)—22no—
276C2×AGL(1,ℤ/8)—22no—
277C2×AGL(1,ℤ/8)—22no—
278C2×AGL(1,ℤ/8)C4×C514yescomplemented
279C2×AGL(1,ℤ/8)C22×C514yes—
280C22×SD16C4×C512yescomplemented
281C22×D8C4×C512yescomplemented
282C22×M16C22×C511yescharacteristic
283C22×M16C22×C511yescharacteristic
284#518—22no—
285#518—22no—
286#518—22no—
287#518C22×C514yescomplemented
288C2×C4×D4—22no—
289C2×C4×D4—22no—
290C2×#117C22×C511yescharacteristic
291C2×#117C22×C511yescharacteristic
292C2×#117C22×C511yescharacteristic
293C22×C22⋊C4—22no—
294#421—22no—
295#421C22×C514yescomplemented
296C2×#104—22no—
297#418—22no—
298#418C22×C514yescomplemented
299C2×#102—22no—
300#410—22no—
301#410C22×C514yescomplemented
302C2×#99—22no—
303#344C22×C514yescomplemented
304H(3,ℤ/4)C22×C514yescomplemented
305C23×C5—24no—
306C23×C5—24no—
307C23×C5—24no—
308C23×C5—24no—
309C23×C5—24no—
310C23×C5—24no—
311C23×C5—24no—
312C23×C5—22no—
313C23×C5—42no—
314C23×C5—48no—
315C23×C5—41no—
316C23×C5—41no—
317C23×C5—84no—
318C23×C5—84no—
319C23×C5—82no—
320C23×C5—84no—
321C23×C5—84no—
322C23×C5—84no—
323C23×C5—84no—
324C23×C5C4×D411yescharacteristic
325C23×C5C4×D411yescharacteristic
326C23×C5#12011yescharacteristic
327C23×C5#12011yescharacteristic
328C23×C5#12111yescharacteristic
329C23×C5#12111yescharacteristic
330C23×C5C22×D411yescharacteristic
331C5×Q8—22no—
332C5×Q8—22no—
333C5×Q8—41no—
334C5×Q8—41no—
335C5×D4—22no—
336C5×D4—24no—
337C5×D4—22no—
338C5×D4—24no—
339C5×D4—24no—
340C5×D4—24no—
341C5×D4—24no—
342C5×D4—24no—
343C5×D4—24no—
344C5×D4—42no—
345C5×D4—42no—
346C5×D4—42no—
347C5×D4—42no—
348C5×D4—41no—
349C5×D4—41no—
350C5×D4C2×C22⋊C418yes—
351C2×C4×C5—22no—
352C2×C4×C5—24no—
353C2×C4×C5—24no—
354C2×C4×C5—44no—
355C2×C4×C5—44no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—42no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5—42no—
363C2×C4×C5—816no—
364C2×C4×C5—82no—
365C2×C4×C5C2×C22⋊C411yescharacteristic
366C2×C4×C5C2×C22⋊C411yescharacteristic
367C2×C4×C5C2×C22⋊C411yescharacteristic
368C2×C4×C5C2×C22⋊C411yescharacteristic
369C2×C4×C5C4×D411yescharacteristic
370C2×C4×C5C4×D411yescharacteristic
371C2×C4×C5C4×D411yescharacteristic
372C2×C4×C5C4×D411yescharacteristic
373C2×C4×C5C4×D411yescharacteristic
374C2×C4×C5C4×D411yescharacteristic
375C2×C4×C5#12011yescharacteristic
376C2×C4×C5#12011yescharacteristic
377C2×C4×C5#12111yescharacteristic
378C2×C4×C5#12111yescharacteristic
379C2×C4×C5#12111yescharacteristic
380C2×C4×C5#12111yescharacteristic
381C2×C4×C5#12111yescharacteristic
382C2×C4×C5#12111yescharacteristic
383C2×C4×C5#12311yescharacteristic
384C2×C4×C5#12311yescharacteristic
385C2×C4×C5#12311yescharacteristic
386C2×C4×C5#12311yescharacteristic
387C2×C4×C5C23×C411yescharacteristic
388C2×C4×C5C22×D411yescharacteristic
389C2×C4×C5C22×D411yescharacteristic
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C2×#4111yescharacteristic
392C2×C4×C5C2×#4111yescharacteristic
393C5×C8—24no—
394C5×C8—42no—
395C25—21no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41—21no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41C2×C4×C512yescomplemented
407C2×#41C23×C512yes—
408C22×Q8C2×C4×C511yescharacteristic, complemented
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4C2×C4×C512yes—
418C22×D4C2×C4×C512yes—
419C22×D4C2×C4×C511yescharacteristic, complemented
420C22×D4C5×D412yes—
421C22×D4C5×D412yes—
422C22×D4C5×D412yes—
423C22×D4C5×D412yes—
424C22×D4C23×C512yes—
425C23×C4—24no—
426C23×C4—21no—
427C23×C4C23×C511yescharacteristic
428AGL(1,ℤ/8)—28no—
429AGL(1,ℤ/8)—28no—
430AGL(1,ℤ/8)—28no—
431AGL(1,ℤ/8)—28no—
432C2×SD16—24no—
433C2×SD16—24no—
434C2×SD16C2×C4×C518yescomplemented
435C2×D8—24no—
436C2×D8—24no—
437C2×D8C2×C4×C518yescomplemented
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16C2×C4×C512yescomplemented
448C2×M16C23×C512yes—
449C2×M16C23×C512yes—
450C22×C8—21no—
451C22×C8C2×C4×C512yescomplemented
452C4×D4—28no—
453C4×D4—28no—
454C4×D4—28no—
455C4×D4—28no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—21no—
462#117—21no—
463#117C5×D412yes—
464#117C5×D412yes—
465#117C23×C512yes—
466#117C23×C512yes—
467#117C23×C512yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4C5×D412yes—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C5×D412yes—
480#104—28no—
481#102—28no—
482#99—28no—
483C22×C5—22no—
484C22×C5—22no—
485C22×C5—22no—
486C22×C5—28no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5—41no—
491C22×C5—48no—
492C22×C5—48no—
493C22×C5—48no—
494C22×C5—42no—
495C22×C5—84no—
496C22×C5—84no—
497C22×C5—84no—
498C22×C5—84no—
499C22×C5—82no—
500C22×C5—82no—
501C22×C5—82no—
502C22×C5#38611yescharacteristic
503C22×C5#38611yescharacteristic
504C22×C5#38611yescharacteristic
505C22×C5#38611yescharacteristic
506C22×C5C2×C4×D411yescharacteristic
507C22×C5C2×#12011yescharacteristic
508C22×C5C2×#12111yescharacteristic
509C4×C5—44no—
510C4×C5—44no—
511C4×C5—42no—
512C4×C5—82no—
513C4×C5#38611yescharacteristic
514C4×C5#38611yescharacteristic
515C4×C5#38611yescharacteristic
516C4×C5#38611yescharacteristic
517C4×C5C22×C22⋊C411yescharacteristic
518C4×C5C2×C4×D411yescharacteristic
519C4×C5C2×#12111yescharacteristic
520C4×C5C2×#12311yescharacteristic
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—21no—
529C24—84no—
530C24C2×C5×D411yescharacteristic
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8C22×C4×C512yescomplemented
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4C5×C22⋊C414yes—
586C2×D4C5×C22⋊C414yes—
587C2×D4C5×C22⋊C414yes—
588C2×D4C5×C22⋊C414yes—
589C2×D4C22×C4×C514yes—
590C2×D4C22×C4×C512yescomplemented
591C2×D4C2×C5×D414yes—
592C2×D4C2×C5×D414yes—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—216no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—88no—
605C22×C4C22×C4×C511yescharacteristic
606C22×C4C22×C4×C511yescharacteristic
607C22×C4C2×C5×D411yescharacteristic
608C22×C4C2×C5×D411yescharacteristic
609C22×C4C2×C5×D411yescharacteristic
610C22×C4C2×C5×D411yescharacteristic
611C22×C4C2×C5×D411yescharacteristic
612C22×C4C2×C5×D411yescharacteristic
613C22×C4C2×C5×D411yescharacteristic
614C22×C4C5×#4111yescharacteristic
615C22×C4C5×#4111yescharacteristic
616C22×C4C5×#4111yescharacteristic
617C22×C4C5×#4111yescharacteristic
618C22×C4C24×C511yescharacteristic
619SD16—216no—
620D8—216no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—22no—
625M16—22no—
626M16—22no—
627M16—41no—
628M16—41no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8C22×C4×C514yescomplemented
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C22⋊C4—216no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—41no—
647C22⋊C4C2×C5×D414yes—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—41no—
653C42C2×C5×D414yes—
654C2×C5—21no—
655C2×C5—21no—
656C2×C5—21no—
657C2×C5—21no—
658C2×C5—21no—
659C2×C5—21no—
660C2×C5—48no—
661C2×C5—82no—
662C2×C5#190412yesdirect product factor
663C2×C5C2×#38611yescharacteristic
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—42no—
673C23—48no—
674C23—41no—
675C23—41no—
676C23—84no—
677C23—84no—
678C23—82no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23C4×C5×D411yescharacteristic
684C23C4×C5×D411yescharacteristic
685C23C5×#12011yescharacteristic
686C23C5×#12011yescharacteristic
687C23C5×#12111yescharacteristic
688C23C5×#12111yescharacteristic
689C23C22×C5×D411yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—41no—
693Q8—41no—
694D4—24no—
695D4—24no—
696D4—24no—
697D4—24no—
698D4—22no—
699D4—24no—
700D4—22no—
701D4—24no—
702D4—24no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4C2×C5×C22⋊C418yes—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—816no—
723C2×C4—82no—
724C2×C4C2×C5×C22⋊C411yescharacteristic
725C2×C4C2×C5×C22⋊C411yescharacteristic
726C2×C4C2×C5×C22⋊C411yescharacteristic
727C2×C4C2×C5×C22⋊C411yescharacteristic
728C2×C4C4×C5×D411yescharacteristic
729C2×C4C4×C5×D411yescharacteristic
730C2×C4C4×C5×D411yescharacteristic
731C2×C4C4×C5×D411yescharacteristic
732C2×C4C4×C5×D411yescharacteristic
733C2×C4C4×C5×D411yescharacteristic
734C2×C4C5×#12011yescharacteristic
735C2×C4C5×#12011yescharacteristic
736C2×C4C5×#12111yescharacteristic
737C2×C4C5×#12111yescharacteristic
738C2×C4C5×#12111yescharacteristic
739C2×C4C5×#12111yescharacteristic
740C2×C4C5×#12111yescharacteristic
741C2×C4C5×#12111yescharacteristic
742C2×C4C5×#12311yescharacteristic
743C2×C4C5×#12311yescharacteristic
744C2×C4C5×#12311yescharacteristic
745C2×C4C5×#12311yescharacteristic
746C2×C4C23×C4×C511yescharacteristic
747C2×C4C22×C5×D411yescharacteristic
748C2×C4C22×C5×D411yescharacteristic
749C2×C4C22×C5×D411yescharacteristic
750C2×C4C2×C5×#4111yescharacteristic
751C2×C4C2×C5×#4111yescharacteristic
752C8—24no—
753C8—42no—
754C5C2×#190411yescharacteristic, direct product factor, Sylow
755C22—22no—
756C22—22no—
757C22—22no—
758C22—28no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—48no—
764C22—48no—
765C22—48no—
766C22—42no—
767C22—84no—
768C22—84no—
769C22—84no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22C5×#38611yescharacteristic
775C22C5×#38611yescharacteristic
776C22C5×#38611yescharacteristic
777C22C5×#38611yescharacteristic
778C22C2×C4×C5×D411yescharacteristic
779C22C2×C5×#12011yescharacteristic
780C22C2×C5×#12111yescharacteristic
781C4—44no—
782C4—44no—
783C4—42no—
784C4—82no—
785C4C5×#38611yescharacteristic
786C4C5×#38611yescharacteristic
787C4C5×#38611yescharacteristic
788C4C5×#38611yescharacteristic
789C4C22×C5×C22⋊C411yescharacteristic
790C4C2×C4×C5×D411yescharacteristic
791C4C2×C5×#12111yescharacteristic
792C4C2×C5×#12311yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—48no—
800C2—82no—
801C2C5×#190412yesdirect product factor
802C2C2×C5×#38611yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×AGL(1,ℤ/8)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#518C2semidirect
3. C2×C5×#421C2semidirect
4. C2×C5×#418C2semidirect
5. C2×C5×#410C2semidirect
6. C5×#1904C2direct (N × H)
7. C2×C5×#344C2semidirect
8. C2×C5×H(3,ℤ/4)C2semidirect
15. C2×C5×AGL(1,ℤ/8)C4semidirect
17. C22×C5×SD16C4semidirect
18. C22×C5×D8C4semidirect
24. C5×#518C22semidirect
32. C5×#421C22semidirect
35. C5×#418C22semidirect
38. C5×#410C22semidirect
40. C5×#344C22semidirect
41. C5×H(3,ℤ/4)C22semidirect
42. C2×#1904C5direct (N × H)
54. C2×C5×#41C2×C4semidirect
56. C22×C5×Q8C2×C4semidirect
67. C22×C5×D4C2×C4semidirect
82. C2×C5×SD16C2×C4semidirect
85. C2×C5×D8C2×C4semidirect
95. C2×C5×M16C2×C4semidirect
99. C22×C5×C8C2×C4semidirect
132. C2×#518C2×C5semidirect
133. C2×#421C2×C5semidirect
134. C2×#418C2×C5semidirect
135. C2×#410C2×C5semidirect
136. #1904C2×C5direct (N × H)
137. C2×#344C2×C5semidirect
138. C2×H(3,ℤ/4)C2×C5semidirect
170. C2×C5×Q8C22×C4semidirect
208. C2×C5×D4C22×C4semidirect
252. C2×C5×C8C22×C4semidirect
278. C2×AGL(1,ℤ/8)C4×C5semidirect
280. C22×SD16C4×C5semidirect
281. C22×D8C4×C5semidirect
287. #518C22×C5semidirect
295. #421C22×C5semidirect
298. #418C22×C5semidirect
301. #410C22×C5semidirect
303. #344C22×C5semidirect
304. H(3,ℤ/4)C22×C5semidirect
406. C2×#41C2×C4×C5semidirect
408. C22×Q8C2×C4×C5semidirect
419. C22×D4C2×C4×C5semidirect
434. C2×SD16C2×C4×C5semidirect
437. C2×D8C2×C4×C5semidirect
447. C2×M16C2×C4×C5semidirect
451. C22×C8C2×C4×C5semidirect
552. C2×Q8C22×C4×C5semidirect
590. C2×D4C22×C4×C5semidirect
634. C2×C8C22×C4×C5semidirect
662. C2×C5#1904direct (N × H)
754. C5C2×#1904direct (N × H)
801. C2C5×#1904direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×AGL(1,ℤ/8)2
C2×C5×#5182
C2×C5×#4212
C2×C5×#4182
C2×C5×#4102
C5×#19042
C2×C5×#3442
C2×C5×H(3,ℤ/4)2
C2×#19045