Finite Group Databasebeta

← C5×#83953 #14453430

Subgroups — C5×#83953 #14453430

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C5×#5831C211yesmaximal, characteristic, complemented
3C5×D4×#67C211yesmaximal, characteristic, complemented
4C2×C5×D3×SD16C211yesmaximal, characteristic, complemented
5C5×#5238C211yesmaximal, characteristic, complemented
6C5×#5218C211yesmaximal, characteristic, complemented
7C5×#5170C211yesmaximal, characteristic, complemented
8C5×#5164C211yesmaximal, characteristic, complemented
9C5×#5163C211yesmaximal, characteristic, complemented
10C5×#5157C211yesmaximal, characteristic, complemented
11C5×#5156C211yesmaximal, characteristic, complemented
12C5×#5154C211yesmaximal, characteristic, complemented
13C5×#5153C211yesmaximal, characteristic, complemented
14C5×#5134C211yesmaximal, characteristic, complemented
15C5×#5127C211yesmaximal, characteristic, complemented
16C5×#3265—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic
19C22×C5×#67—21no—
20C2×C5×D3×Q8C2211yescharacteristic, complemented
21C2×C5×D3×D4C2211yescharacteristic
22C3×C5×AGL(1,ℤ/8)—24no—
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×SD16C2211yescharacteristic, complemented
25C2×C3×C5×D8C2211yescharacteristic
26C2×C3×C5×D8C2211yescharacteristic, complemented
27C2×C3×C5×M16C2211yescharacteristic, complemented
28C5×#953—21no—
29C5×Q8×Dic3C2211yescharacteristic, complemented
30C2×C5×#215C2211yescharacteristic, complemented
31C5×#940C2211yescharacteristic
32C5×#939—21no—
33C5×#938—21no—
34C5×#938C2211yescharacteristic
35C5×#938C2211yescharacteristic, complemented
36C5×#937—21no—
37C5×#936—21no—
38C5×#936C2211yescharacteristic, complemented
39C5×D4×Dic3C2211yescharacteristic
40C2×C5×#214C2211yescharacteristic
41C2×C5×#214C2211yescharacteristic, complemented
42C2×C5×#213C2211yescharacteristic, complemented
43C5×#930C2211yescharacteristic
44C4×C5×#67—21no—
45C4×C5×#67C2211yescharacteristic
46C5×#924—21no—
47C5×#924C2211yescharacteristic, complemented
48C5×D3×SD16—24no—
49C2×C5×#204C2211yescharacteristic, complemented
50C2×C5×D3×C8C2211yescharacteristic, complemented
51C5×#835C2211yescharacteristic, complemented
52C5×#832C2211yescharacteristic
53C5×#832C2211yescharacteristic, complemented
54C5×#832C2211yescharacteristic, complemented
55C5×#830C2211yescharacteristic, complemented
56C5×#821C2211yescharacteristic, complemented
57C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C5×#818C2211yescharacteristic, complemented
59C5×#816C2211yescharacteristic, complemented
60C5×#815C2211yescharacteristic, complemented
61C5×Dic3⋊C8C2211yescharacteristic, complemented
62#83953C511yesmaximal, characteristic, direct product factor, Hall
63C2×C5×AGL(1,ℤ/8)D311yescharacteristic, complemented
64C22×C5×SD16—31no—
65C5×#548—31no—
66C5×D42—31no—
67C5×#496—31no—
68C5×#468—31no—
69C5×#466—31no—
70C5×#463—31no—
71C5×#460—31no—
72C5×#450—31no—
73C5×#449—31no—
74C5×#448—31no—
75C5×#447—31no—
76C5×#440—31no—
77C5×#435—31no—
78C24×C3×C5—21no—
79C23×C5×D3—21no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—22no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×#67—21no—
94C2×C5×#67—21no—
95C2×C5×#67—21no—
96C2×C5×#67—21no—
97C2×C5×#67—21no—
98C2×C5×#67—44no—
99C2×C5×#67D411yescharacteristic
100C22×C5×Dic3—21no—
101C5×D3×Q8—22no—
102C5×D3×Q8—41no—
103C5×D3×D4—22no—
104C5×D3×D4—41no—
105C2×C5×D12C2311yescharacteristic
106C2×C4×C5×D3—21no—
107C2×C4×C5×D3C2311yescharacteristic
108C2×C5×Dic6—21no—
109C2×C5×Dic6C2311yescharacteristic
110C3×C5×SD16—22no—
111C3×C5×SD16D414yescomplemented
112C3×C5×D8—22no—
113C3×C5×D8—22no—
114C3×C5×M16—22no—
115C2×C3×C5×C8C2311yescharacteristic
116C2×C3×C5×C8C2311yescharacteristic
117C5×#217—21no—
118C5×#217—21no—
119C5×#217—21no—
120C5×#217—21no—
121C5×#217—21no—
122C5×#217—21no—
123C5×#217D411yescharacteristic
124C5×#215—22no—
125C5×#214—22no—
126C5×#214—41no—
127C5×#213—41no—
128C5×(C2×D3)⋊C4—21no—
129C5×(C2×D3)⋊C4D411yescharacteristic
130C5×C4⋊Dic3—21no—
131C5×C4⋊Dic3C2311yescharacteristic
132C5×C4⋊Dic3C2311yescharacteristic
133C5×Dic3⋊C4—21no—
134C5×Dic3⋊C4D411yescharacteristic
135C4×C5×Dic3—21no—
136C4×C5×Dic3C2311yescharacteristic
137C2×C5×C3⋊C8C2311yescharacteristic
138C2×C5×C3⋊C8C2311yescharacteristic
139C5×#204—22no—
140C5×D3×C8—22no—
141C2×C3×AGL(1,ℤ/8)C2×C511yescharacteristic, complemented
142#5831C2×C511yescharacteristic, complemented
143D4×#67C2×C511yescharacteristic, complemented
144C2×D3×SD16C2×C511yescharacteristic, complemented
145#5238C2×C511yescharacteristic, complemented
146#5218C2×C511yescharacteristic, complemented
147#5170C2×C511yescharacteristic, complemented
148#5164C2×C511yescharacteristic, complemented
149#5163C2×C511yescharacteristic, complemented
150#5157C2×C511yescharacteristic, complemented
151#5156C2×C511yescharacteristic, complemented
152#5154C2×C511yescharacteristic, complemented
153#5153C2×C511yescharacteristic, complemented
154#5134C2×C511yescharacteristic, complemented
155#5127C2×C511yescharacteristic, complemented
156C2×C5×#41C2×D311yescharacteristic, complemented
157C22×C5×Q8—31no—
158C22×C5×D4—31no—
159C22×C5×D4—61no—
160C22×C5×D4C2×D311yescharacteristic
161C5×AGL(1,ℤ/8)—24no—
162C2×C5×SD16—31no—
163C2×C5×SD16—31no—
164C2×C5×SD16—31no—
165C2×C5×SD16—31no—
166C2×C5×SD16—64no—
167C2×C5×SD16C2×D311yescharacteristic
168C2×C5×SD16C2×D311yescharacteristic, complemented
169C2×C5×D8—31no—
170C2×C5×D8C2×D311yescharacteristic
171C2×C5×D8C2×D311yescharacteristic, complemented
172C2×C5×M16C2×D311yescharacteristic, complemented
173C22×C5×C8—31no—
174C5×#127—31no—
175C5×#124—31no—
176C5×#124—61no—
177C5×C22⋊Q8—31no—
178C5×C22⋊Q8—61no—
179C5×#121—31no—
180C5×#121—31no—
181C5×#121—31no—
182C5×#121—61no—
183C5×#121—61no—
184C5×#120—61no—
185C5×#120—61no—
186C4×C5×Q8—31no—
187C4×C5×D4—31no—
188C4×C5×D4—31no—
189C4×C5×D4—61no—
190C5×#107—31no—
191C5×C4⋊C8—31no—
192C5×#103—31no—
193C5×#103—31no—
194C5×#102—31no—
195C5×#102—31no—
196C5×#102—31no—
197C5×#102—31no—
198C5×C22⋊C8—31no—
199C5×C22⋊C8—31no—
200C5×#97—31no—
201#3265—31noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—42no—
206C23×C3×C5—42no—
207C23×C3×C5—81no—
208C23×C3×C5C2×D411yescharacteristic
209C22×C5×D3—21no—
210C22×C5×D3—42no—
211C22×C5×D3—42no—
212C22×C5×D3—81no—
213C22×C5×D3C2×D411yescharacteristic
214C3×C5×Q8—21no—
215C3×C5×Q8C2×D412yescomplemented
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4—42no—
223C3×C5×D4C2×D412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—42no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2411yescharacteristic
230C5×#67—22no—
231C5×#67—42no—
232C5×#67—42no—
233C5×#67—42no—
234C5×#67—42no—
235C5×#67—42no—
236C5×#67—81no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—42no—
241C2×C5×Dic3C2×D411yescharacteristic
242C2×C5×Dic3C2×D411yescharacteristic
243C2×C5×Dic3C2×D411yescharacteristic
244C5×D12—21no—
245C5×D12—21no—
246C4×C5×D3—21no—
247C4×C5×D3—21no—
248C4×C5×D3—42no—
249C5×Dic6—21no—
250C5×Dic6—21no—
251C5×Dic6—42no—
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C5×C3⋊C8—21no—
255C5×C3⋊C8—21no—
256C2×C3×#41C22×C511yescharacteristic, complemented
257C22×C3×D4C22×C511yescharacteristic
258C22×#67—21no—
259C2×D3×Q8C22×C511yescharacteristic, complemented
260C2×D3×D4C22×C511yescharacteristic
261C3×AGL(1,ℤ/8)—24no—
262C2×C3×SD16C22×C511yescharacteristic
263C2×C3×SD16C22×C511yescharacteristic, complemented
264C2×C3×D8C22×C511yescharacteristic
265C2×C3×D8C22×C511yescharacteristic, complemented
266C2×C3×M16C22×C511yescharacteristic, complemented
267#953—21no—
268Q8×Dic3C22×C511yescharacteristic, complemented
269C2×#215C22×C511yescharacteristic, complemented
270#940C22×C511yescharacteristic
271#939—21no—
272#938—21no—
273#938C22×C511yescharacteristic
274#938C22×C511yescharacteristic, complemented
275#937—21no—
276#936—21no—
277#936C22×C511yescharacteristic, complemented
278D4×Dic3C22×C511yescharacteristic
279C2×#214C22×C511yescharacteristic
280C2×#214C22×C511yescharacteristic, complemented
281C2×#213C22×C511yescharacteristic, complemented
282#930C22×C511yescharacteristic
283C4×#67—21no—
284C4×#67C22×C511yescharacteristic
285#924—21no—
286#924C22×C511yescharacteristic, complemented
287D3×SD16—24no—
288C2×#204C22×C511yescharacteristic, complemented
289C2×D3×C8C22×C511yescharacteristic, complemented
290#835C22×C511yescharacteristic, complemented
291#832C22×C511yescharacteristic
292#832C22×C511yescharacteristic, complemented
293#832C22×C511yescharacteristic, complemented
294#830C22×C511yescharacteristic, complemented
295#821C22×C511yescharacteristic, complemented
296(C2×D3)⋊C8C22×C511yescharacteristic, complemented
297#818C22×C511yescharacteristic, complemented
298#816C22×C511yescharacteristic, complemented
299#815C22×C511yescharacteristic, complemented
300Dic3⋊C8C22×C511yescharacteristic, complemented
301C24×C5—21no—
302C24×C5—61no—
303C5×#41—22no—
304C5×#41—41no—
305C2×C5×Q8—31no—
306C2×C5×Q8—61no—
307C2×C5×Q8—62no—
308C2×C5×Q8—121no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—22no—
311C2×C5×D4—21no—
312C2×C5×D4—21no—
313C2×C5×D4—31no—
314C2×C5×D4—31no—
315C2×C5×D4—41no—
316C2×C5×D4—61no—
317C2×C5×D4—61no—
318C2×C5×D4—61no—
319C2×C5×D4—62no—
320C2×C5×D4—61no—
321C2×C5×D4—61no—
322C2×C5×D4—61no—
323C2×C5×D4—121no—
324C2×C5×D4—124no—
325C2×C5×D4C22×D311yescharacteristic
326C2×C5×D4C22×D311yescharacteristic
327C2×C5×D4C22×D311yescharacteristic
328C22×C4×C5—21no—
329C22×C4×C5—31no—
330C22×C4×C5—61no—
331C22×C4×C5—61no—
332C22×C4×C5C22×D311yescharacteristic
333C5×SD16—22no—
334C5×SD16—62no—
335C5×SD16—62no—
336C5×SD16—62no—
337C5×SD16—121no—
338C5×SD16#6714yescomplemented
339C5×D8—22no—
340C5×D8—22no—
341C5×D8—121no—
342C5×M16—22no—
343C2×C5×C8—31no—
344C2×C5×C8—31no—
345C2×C5×C8—62no—
346C2×C5×C8C22×D311yescharacteristic
347C2×C5×C8C22×D311yescharacteristic
348C5×C4⋊C4—31no—
349C5×C4⋊C4—31no—
350C5×C4⋊C4—31no—
351C5×C4⋊C4—61no—
352C5×C4⋊C4—61no—
353C5×C22⋊C4—31no—
354C5×C22⋊C4—31no—
355C5×C22⋊C4—61no—
356C5×C22⋊C4—61no—
357C5×C22⋊C4—61no—
358C5×C22⋊C4—61no—
359C5×C22⋊C4—61no—
360C5×C22⋊C4—61no—
361C5×C22⋊C4—61no—
362C42×C5—31no—
363C42×C5—61no—
364C2×AGL(1,ℤ/8)C5×D311yescharacteristic, complemented
365C22×SD16—31no—
366#548—31no—
367D42—31no—
368#496—31no—
369#468—31no—
370#466—31no—
371#463—31no—
372#460—31no—
373#450—31no—
374#449—31no—
375#448—31no—
376#447—31no—
377#440—31no—
378#435—31no—
379C22×C3×C5—22no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—84no—
392C22×C3×C5C22×D411yescharacteristic
393C2×C5×D3—21no—
394C2×C5×D3—21no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—84no—
399C2×C5×D3AGL(1,ℤ/8)12yescomplemented
400C3×C4×C5—22no—
401C3×C4×C5—21no—
402C3×C4×C5C22×D411yescharacteristic
403C3×C4×C5H(5,𝔽2)11yescharacteristic
404C5×Dic3—21no—
405C5×Dic3—21no—
406C5×Dic3—21no—
407C5×Dic3—41no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C24×C3—21no—
411C23×D3—21no—
412C3×#41—22no—
413C3×#41—41no—
414C2×C3×Q8C23×C511yescharacteristic
415C2×C3×D4—22no—
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4—41no—
419C2×C3×D4C23×C511yescharacteristic
420C2×C3×D4C23×C511yescharacteristic
421C2×C3×D4C23×C511yescharacteristic
422C22×C3×C4—21no—
423C22×C3×C4C23×C511yescharacteristic
424C2×#67—21no—
425C2×#67—21no—
426C2×#67—21no—
427C2×#67—21no—
428C2×#67—21no—
429C2×#67—21no—
430C2×#67—44no—
431C2×#67C5×D411yescharacteristic
432C22×Dic3—21no—
433D3×Q8—22no—
434D3×Q8—41no—
435D3×D4—22no—
436D3×D4—41no—
437C2×D12C23×C511yescharacteristic
438C2×C4×D3—21no—
439C2×C4×D3C23×C511yescharacteristic
440C2×Dic6—21no—
441C2×Dic6C23×C511yescharacteristic
442C3×SD16—22no—
443C3×SD16C5×D414yescomplemented
444C3×D8—22no—
445C3×D8—22no—
446C3×M16—22no—
447C2×C3×C8C23×C511yescharacteristic
448C2×C3×C8C23×C511yescharacteristic
449#217—21no—
450#217—21no—
451#217—21no—
452#217—21no—
453#217—21no—
454#217—21no—
455#217C5×D411yescharacteristic
456#215—22no—
457#214—22no—
458#214—41no—
459#213—41no—
460(C2×D3)⋊C4—21no—
461(C2×D3)⋊C4C5×D411yescharacteristic
462C4⋊Dic3—21no—
463C4⋊Dic3C23×C511yescharacteristic
464C4⋊Dic3C23×C511yescharacteristic
465Dic3⋊C4—21no—
466Dic3⋊C4C5×D411yescharacteristic
467C4×Dic3—21no—
468C4×Dic3C23×C511yescharacteristic
469C2×C3⋊C8C23×C511yescharacteristic
470C2×C3⋊C8C23×C511yescharacteristic
471#204—22no—
472D3×C8—22no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—31no—
477C23×C5—42no—
478C23×C5—42no—
479C23×C5—61no—
480C23×C5—81no—
481C23×C5—122no—
482C23×C5—122no—
483C23×C5—241no—
484C23×C5D3×D411yescharacteristic
485C5×Q8—21no—
486C5×Q8—61no—
487C5×Q8—61no—
488C5×Q8—122no—
489C5×Q8C2×#6712yescomplemented
490C5×D4—21no—
491C5×D4—21no—
492C5×D4—21no—
493C5×D4—21no—
494C5×D4—21no—
495C5×D4—42no—
496C5×D4—42no—
497C5×D4—62no—
498C5×D4—61no—
499C5×D4—61no—
500C5×D4—122no—
501C5×D4—122no—
502C5×D4—122no—
503C5×D4—122no—
504C5×D4—122no—
505C5×D4—241no—
506C5×D4C2×#6712yes—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—31no—
511C2×C4×C5—31no—
512C2×C4×C5—31no—
513C2×C4×C5—42no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5—61no—
519C2×C4×C5—122no—
520C2×C4×C5—122no—
521C2×C4×C5D3×D411yescharacteristic
522C2×C4×C5C23×D311yescharacteristic
523C5×C8—21no—
524C5×C8—61no—
525C5×C8—61no—
526C5×C8C2×#6712yescomplemented
527C2×#41C2×C5×D311yescharacteristic, complemented
528C22×Q8—31no—
529C22×D4—31no—
530C22×D4—61no—
531C22×D4C2×C5×D311yescharacteristic
532AGL(1,ℤ/8)—24no—
533C2×SD16—31no—
534C2×SD16—31no—
535C2×SD16—31no—
536C2×SD16—31no—
537C2×SD16—64no—
538C2×SD16C2×C5×D311yescharacteristic
539C2×SD16C2×C5×D311yescharacteristic, complemented
540C2×D8—31no—
541C2×D8C2×C5×D311yescharacteristic
542C2×D8C2×C5×D311yescharacteristic, complemented
543C2×M16C2×C5×D311yescharacteristic, complemented
544C22×C8—31no—
545#127—31no—
546#124—31no—
547#124—61no—
548C22⋊Q8—31no—
549C22⋊Q8—61no—
550#121—31no—
551#121—31no—
552#121—31no—
553#121—61no—
554#121—61no—
555#120—61no—
556#120—61no—
557C4×Q8—31no—
558C4×D4—31no—
559C4×D4—31no—
560C4×D4—61no—
561#107—31no—
562C4⋊C8—31no—
563#103—31no—
564#103—31no—
565#102—31no—
566#102—31no—
567#102—31no—
568#102—31no—
569C22⋊C8—31no—
570C22⋊C8—31no—
571#97—31no—
572C2×C3×C5—42no—
573C2×C3×C5—41no—
574C2×C3×C5—81no—
575C2×C3×C5—81no—
576C2×C3×C5D4211yescharacteristic
577C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
578C2×C3×C5#57711yescharacteristic
579C5×D3—22no—
580C5×D3—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—81no—
587C23×C3C2×C5×D411yescharacteristic
588C22×D3—21no—
589C22×D3—42no—
590C22×D3—42no—
591C22×D3—81no—
592C22×D3C2×C5×D411yescharacteristic
593C3×Q8—21no—
594C3×Q8C2×C5×D412yescomplemented
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—42no—
601C3×D4—42no—
602C3×D4C2×C5×D412yes—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—42no—
607C2×C3×C4C2×C5×D411yescharacteristic
608C2×C3×C4C24×C511yescharacteristic
609#67—22no—
610#67—42no—
611#67—42no—
612#67—42no—
613#67—42no—
614#67—42no—
615#67—81no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—42no—
620C2×Dic3C2×C5×D411yescharacteristic
621C2×Dic3C2×C5×D411yescharacteristic
622C2×Dic3C2×C5×D411yescharacteristic
623D12—21no—
624D12—21no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—42no—
628Dic6—21no—
629Dic6—21no—
630Dic6—42no—
631C3×C8—21no—
632C3×C8C2×C5×D412yescomplemented
633C3⋊C8—21no—
634C3⋊C8—21no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—22no—
639C22×C5—32no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—61no—
649C22×C5—61no—
650C22×C5—84no—
651C22×C5—121no—
652C22×C5—121no—
653C22×C5—121no—
654C22×C5—244no—
655C22×C5C2×D3×D411yescharacteristic
656C4×C5—21no—
657C4×C5—22no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5—61no—
661C4×C5—121no—
662C4×C5—121no—
663C4×C5—121no—
664C4×C5#100411yescharacteristic
665C4×C5C22×#6711yescharacteristic
666C24—21no—
667C24—61no—
668#41—22no—
669#41—41no—
670C2×Q8—31no—
671C2×Q8—61no—
672C2×Q8—62no—
673C2×Q8—121no—
674C2×Q8C22×C5×D311yescharacteristic
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—41no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—62no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—121no—
689C2×D4—124no—
690C2×D4C22×C5×D311yescharacteristic
691C2×D4C22×C5×D311yescharacteristic
692C2×D4C22×C5×D311yescharacteristic
693C22×C4—21no—
694C22×C4—31no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4C22×C5×D311yescharacteristic
698SD16—22no—
699SD16—62no—
700SD16—62no—
701SD16—62no—
702SD16—121no—
703SD16C5×#6714yescomplemented
704D8—22no—
705D8—22no—
706D8—121no—
707M16—22no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8C22×C5×D311yescharacteristic
712C2×C8C22×C5×D311yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—61no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C42—31no—
728C42—61no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—84no—
743C22×C3C22×C5×D411yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—84no—
750C2×D3C5×AGL(1,ℤ/8)12yescomplemented
751C3×C4—22no—
752C3×C4—21no—
753C3×C4C22×C5×D411yescharacteristic
754C3×C4C5×H(5,𝔽2)11yescharacteristic
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—41no—
759Dic3—41no—
760Dic3—41no—
761C2×C5—41no—
762C2×C5—42no—
763C2×C5—62no—
764C2×C5—81no—
765C2×C5—81no—
766C2×C5—241no—
767C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
768C2×C5#577511yescharacteristic
769C2×C5D4×#6711yescharacteristic
770C23—21no—
771C23—21no—
772C23—21no—
773C23—31no—
774C23—42no—
775C23—42no—
776C23—61no—
777C23—81no—
778C23—122no—
779C23—122no—
780C23—241no—
781C23C5×D3×D411yescharacteristic
782Q8—21no—
783Q8—61no—
784Q8—61no—
785Q8—122no—
786Q8C2×C5×#6712yescomplemented
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—42no—
793D4—42no—
794D4—62no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—122no—
799D4—122no—
800D4—122no—
801D4—122no—
802D4—241no—
803D4C2×C5×#6712yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—42no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4C5×D3×D411yescharacteristic
819C2×C4C23×C5×D311yescharacteristic
820C8—21no—
821C8—61no—
822C8—61no—
823C8C2×C5×#6712yescomplemented
824C2×C3—42no—
825C2×C3—41no—
826C2×C3—81no—
827C2×C3—81no—
828C2×C3C5×D4211yescharacteristic
829C2×C3C2×C5×AGL(1,ℤ/8)11yescharacteristic
830C2×C3C5×#57711yescharacteristic
831D3—22no—
832D3—81no—
833C5#8395311yescharacteristic, direct product factor, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—22no—
838C22—32no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—61no—
848C22—61no—
849C22—84no—
850C22—121no—
851C22—121no—
852C22—121no—
853C22—244no—
854C22C2×C5×D3×D411yescharacteristic
855C4—21no—
856C4—22no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—121no—
861C4—121no—
862C4—121no—
863C4C5×#100411yescharacteristic
864C4C22×C5×#6711yescharacteristic
865C3C5×#326511yescharacteristic, complemented, Sylow
866C2—41no—
867C2—42no—
868C2—62no—
869C2—81no—
870C2—81no—
871C2—241no—
872C2C5×D3×AGL(1,ℤ/8)11yescharacteristic
873C2C5×#577511yescharacteristic
874C2C5×D4×#6711yescharacteristic
subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
hypercenterC2×C5×AGL(1,ℤ/8)D3
hypocenterC3C5×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
2. C5×#5831C2semidirect
3. C5×D4×#67C2semidirect
4. C2×C5×D3×SD16C2semidirect
5. C5×#5238C2semidirect
6. C5×#5218C2semidirect
7. C5×#5170C2semidirect
8. C5×#5164C2semidirect
9. C5×#5163C2semidirect
10. C5×#5157C2semidirect
11. C5×#5156C2semidirect
12. C5×#5154C2semidirect
13. C5×#5153C2semidirect
14. C5×#5134C2semidirect
15. C5×#5127C2semidirect
17. C2×C3×C5×#41C22semidirect
20. C2×C5×D3×Q8C22semidirect
24. C2×C3×C5×SD16C22semidirect
26. C2×C3×C5×D8C22semidirect
27. C2×C3×C5×M16C22semidirect
29. C5×Q8×Dic3C22semidirect
30. C2×C5×#215C22semidirect
35. C5×#938C22semidirect
38. C5×#936C22semidirect
41. C2×C5×#214C22semidirect
42. C2×C5×#213C22semidirect
47. C5×#924C22semidirect
49. C2×C5×#204C22semidirect
50. C2×C5×D3×C8C22semidirect
51. C5×#835C22semidirect
53. C5×#832C22semidirect
54. C5×#832C22semidirect
55. C5×#830C22semidirect
56. C5×#821C22semidirect
57. C5×(C2×D3)⋊C8C22semidirect
58. C5×#818C22semidirect
59. C5×#816C22semidirect
60. C5×#815C22semidirect
61. C5×Dic3⋊C8C22semidirect
62. #83953C5direct (N × H)
63. C2×C5×AGL(1,ℤ/8)D3semidirect
111. C3×C5×SD16D4semidirect
141. C2×C3×AGL(1,ℤ/8)C2×C5semidirect
142. #5831C2×C5semidirect
143. D4×#67C2×C5semidirect
144. C2×D3×SD16C2×C5semidirect
145. #5238C2×C5semidirect
146. #5218C2×C5semidirect
147. #5170C2×C5semidirect
148. #5164C2×C5semidirect
149. #5163C2×C5semidirect
150. #5157C2×C5semidirect
151. #5156C2×C5semidirect
152. #5154C2×C5semidirect
153. #5153C2×C5semidirect
154. #5134C2×C5semidirect
155. #5127C2×C5semidirect
156. C2×C5×#41C2×D3semidirect
168. C2×C5×SD16C2×D3semidirect
171. C2×C5×D8C2×D3semidirect
172. C2×C5×M16C2×D3semidirect
215. C3×C5×Q8C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
256. C2×C3×#41C22×C5semidirect
259. C2×D3×Q8C22×C5semidirect
263. C2×C3×SD16C22×C5semidirect
265. C2×C3×D8C22×C5semidirect
266. C2×C3×M16C22×C5semidirect
268. Q8×Dic3C22×C5semidirect
269. C2×#215C22×C5semidirect
274. #938C22×C5semidirect
277. #936C22×C5semidirect
280. C2×#214C22×C5semidirect
281. C2×#213C22×C5semidirect
286. #924C22×C5semidirect
288. C2×#204C22×C5semidirect
289. C2×D3×C8C22×C5semidirect
290. #835C22×C5semidirect
292. #832C22×C5semidirect
293. #832C22×C5semidirect
294. #830C22×C5semidirect
295. #821C22×C5semidirect
296. (C2×D3)⋊C8C22×C5semidirect
297. #818C22×C5semidirect
298. #816C22×C5semidirect
299. #815C22×C5semidirect
300. Dic3⋊C8C22×C5semidirect
338. C5×SD16#67semidirect
364. C2×AGL(1,ℤ/8)C5×D3semidirect
399. C2×C5×D3AGL(1,ℤ/8)semidirect
443. C3×SD16C5×D4semidirect
489. C5×Q8C2×#67semidirect
526. C5×C8C2×#67semidirect
527. C2×#41C2×C5×D3semidirect
539. C2×SD16C2×C5×D3semidirect
542. C2×D8C2×C5×D3semidirect
543. C2×M16C2×C5×D3semidirect
594. C3×Q8C2×C5×D4semidirect
632. C3×C8C2×C5×D4semidirect
703. SD16C5×#67semidirect
729. C3×C5#3265semidirect
750. C2×D3C5×AGL(1,ℤ/8)semidirect
786. Q8C2×C5×#67semidirect
823. C8C2×C5×#67semidirect
833. C5#83953direct (N × H)
865. C3C5×#3265semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×AGL(1,ℤ/8)2
C5×#58312
C5×D4×#672
C2×C5×D3×SD162
C5×#52382
C5×#52182
C5×#51702
C5×#51642
C5×#51632
C5×#51572
C5×#51562
C5×#51542
C5×#51532
C5×#51342
C5×#51272
C5×#32653
#839535