Finite Group Databasebeta

← C2×C5×#5239 #14423499

Subgroups — C2×C5×#5239 #14423499

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic
2C22×C5×#216C211yesmaximal, characteristic, complemented
3C22×C5×#214C211yesmaximal, characteristic, complemented
4C2×C5×#924C211yesmaximal, characteristic, complemented
5C5×#5239C218yesmaximal, direct product factor
6C2×C5×#835C211yesmaximal, characteristic, complemented
7C2×C5×#832C211yesmaximal, characteristic, complemented
8C2×C5×#830C211yesmaximal, characteristic, complemented
9C2×C5×#452—31nomaximal, Hall
10C2×C3×C5×#41—24no—
11C2×C3×C5×#41—24no—
12C2×C3×C5×#41—22no—
13C2×C3×C5×#41C2214yes—
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C3×C5×D4—21no—
16C22×C3×C5×D4C2211yescharacteristic
17C23×C3×C4×C5—21no—
18C23×C3×C4×C5C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C2×C5×#217—21no—
21C2×C5×#216—24no—
22C2×C5×#216C2214yescomplemented
23C2×C5×#214—24no—
24C2×C5×#214C2214yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C5×#924—22no—
27C5×#924C2214yescomplemented
28C2×C5×Dic3⋊C4—21no—
29C22×C5×C3⋊C8C2211yescharacteristic
30C22×C5×C3⋊C8C2211yescharacteristic
31C5×#835C2214yescomplemented
32C5×#832C2214yescomplemented
33C5×#830C2214yescomplemented
34C2×#5239C511yesmaximal, characteristic, direct product factor, Hall
35C22×C5×#41D311yescharacteristic
36C22×C5×Q16—31no—
37C22×C5×SD16—31no—
38C2×C5×C22⋊Q8—31no—
39C5×#452—38no—
40C2×C5×#103—31no—
41C2×C5×#102—31no—
42C2×C5×C22⋊C8—31no—
43C24×C3×C5—21no—
44C24×C3×C5D411yescharacteristic
45C3×C5×#41—216no—
46C3×C5×#41—28no—
47C3×C5×#41—28no—
48C2×C3×C5×Q8—22no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8D414yes—
51C2×C3×C5×Q8C2312yes—
52C2×C3×C5×D4—28no—
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4D414yes—
57C2×C3×C5×D4C2312yes—
58C22×C3×C4×C5—28no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5D411yescharacteristic
64C22×C3×C4×C5D412yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C5×Dic3—21no—
68C22×C5×Dic3—21no—
69C2×C5×Dic6—22no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6C2312yes—
73C5×#217—24no—
74C5×#216—28no—
75C5×#214—28no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C5×Dic3⋊C4—24no—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8—22no—
81C2×C5×C3⋊C8C2312yes—
82C2×C5×C3⋊C8C2312yes—
83C22×C3×#41C2×C511yescharacteristic
84C22×#216C2×C511yescharacteristic, complemented
85C22×#214C2×C511yescharacteristic, complemented
86C2×#924C2×C511yescharacteristic, complemented
87#5239C2×C518yesdirect product factor
88C2×#835C2×C511yescharacteristic, complemented
89C2×#832C2×C511yescharacteristic, complemented
90C2×#830C2×C511yescharacteristic, complemented
91C2×C5×#41—24no—
92C2×C5×#41—24no—
93C2×C5×#41—22no—
94C2×C5×#41C2×D314yes—
95C22×C5×Q8—31no—
96C22×C5×Q8C2×D311yescharacteristic
97C22×C5×D4—21no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5—21no—
100C23×C4×C5C2×D311yescharacteristic
101C2×C5×Q16—34no—
102C2×C5×Q16—64no—
103C2×C5×SD16—34no—
104C2×C5×SD16—64no—
105C22×C5×C8—31no—
106C22×C5×C8—31no—
107C5×C22⋊Q8—34no—
108C5×C22⋊Q8—62no—
109C2×C5×C4⋊C4—31no—
110C2×C5×C4⋊C4—61no—
111C2×C5×C22⋊C4—61no—
112C5×#103—34no—
113C5×#102—34no—
114C5×C22⋊C8—34no—
115C2×#452—31noSylow
116C23×C3×C5—22no—
117C23×C3×C5—24no—
118C23×C3×C5—22no—
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—42no—
122C23×C3×C5—42no—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D411yescharacteristic
125C3×C5×Q8—24no—
126C3×C5×Q8—22no—
127C3×C5×Q8C2×D414yes—
128C3×C5×D4—216no—
129C3×C5×D4—24no—
130C3×C5×D4—22no—
131C3×C5×D4C2×D414yes—
132C2×C3×C4×C5—216no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—24no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—24no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—42no—
147C2×C5×Dic3—42no—
148C5×Dic6—22no—
149C5×Dic6—22no—
150C5×Dic6—42no—
151C5×C3⋊C8—22no—
152C5×C3⋊C8—22no—
153C2×C3×#41—24no—
154C2×C3×#41—24no—
155C2×C3×#41—22no—
156C2×C3×#41C22×C514yes—
157C22×C3×Q8C22×C511yescharacteristic
158C22×C3×D4—21no—
159C22×C3×D4C22×C511yescharacteristic
160C23×C3×C4—21no—
161C23×C3×C4C22×C511yescharacteristic
162C22×Dic6C22×C511yescharacteristic
163C2×#217—21no—
164C2×#216—24no—
165C2×#216C22×C514yescomplemented
166C2×#214—24no—
167C2×#214C22×C514yescomplemented
168C2×C4⋊Dic3C22×C511yescharacteristic
169#924—22no—
170#924C22×C514yescomplemented
171C2×Dic3⋊C4—21no—
172C22×C3⋊C8C22×C511yescharacteristic
173C22×C3⋊C8C22×C511yescharacteristic
174#835C22×C514yescomplemented
175#832C22×C514yescomplemented
176#830C22×C514yescomplemented
177C24×C5—21no—
178C24×C5#6711yescharacteristic
179C5×#41—216no—
180C5×#41—28no—
181C5×#41—28no—
182C2×C5×Q8—22no—
183C2×C5×Q8—21no—
184C2×C5×Q8—32no—
185C2×C5×Q8—61no—
186C2×C5×Q8—62no—
187C2×C5×Q8—62no—
188C2×C5×Q8#6714yes—
189C2×C5×Q8C22×D312yes—
190C2×C5×D4—28no—
191C2×C5×D4—24no—
192C2×C5×D4—21no—
193C2×C5×D4—22no—
194C2×C5×D4#6714yes—
195C2×C5×D4C22×D312yes—
196C22×C4×C5—28no—
197C22×C4×C5—21no—
198C22×C4×C5—24no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—61no—
202C22×C4×C5—61no—
203C22×C4×C5#6712yes—
204C22×C4×C5#6711yescharacteristic
205C22×C4×C5C22×D312yes—
206C22×C4×C5C22×D311yescharacteristic
207C5×Q16—68no—
208C5×SD16—68no—
209C2×C5×C8—32no—
210C2×C5×C8—32no—
211C2×C5×C8—62no—
212C2×C5×C8—62no—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—61no—
215C5×C4⋊C4—64no—
216C5×C22⋊C4—64no—
217C22×#41C5×D311yescharacteristic
218C22×Q16—31no—
219C22×SD16—31no—
220C2×C22⋊Q8—31no—
221#452—38no—
222C2×#103—31no—
223C2×#102—31no—
224C2×C22⋊C8—31no—
225C22×C3×C5—22no—
226C22×C3×C5—24no—
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—42no—
230C22×C3×C5—42no—
231C22×C3×C5—44no—
232C22×C3×C5—48no—
233C22×C3×C5#12012yes—
234C22×C3×C5#13512yes—
235C22×C3×C5#13712yes—
236C22×C3×C5C22×D411yescharacteristic
237C3×C4×C5—22no—
238C3×C4×C5—24no—
239C3×C4×C5#12012yes—
240C3×C4×C5C22×D411yescharacteristic
241C3×C4×C5C22×D411yescharacteristic
242C5×Dic3—42no—
243C5×Dic3—42no—
244C24×C3—21no—
245C24×C3C5×D411yescharacteristic
246C3×#41—216no—
247C3×#41—28no—
248C3×#41—28no—
249C2×C3×Q8—22no—
250C2×C3×Q8—21no—
251C2×C3×Q8C5×D414yes—
252C2×C3×Q8C23×C512yes—
253C2×C3×D4—28no—
254C2×C3×D4—24no—
255C2×C3×D4—21no—
256C2×C3×D4—22no—
257C2×C3×D4C5×D414yes—
258C2×C3×D4C23×C512yes—
259C22×C3×C4—28no—
260C22×C3×C4—21no—
261C22×C3×C4—24no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4C5×D411yescharacteristic
265C22×C3×C4C5×D412yes—
266C22×C3×C4C23×C512yes—
267C22×C3×C4C23×C511yescharacteristic
268C22×Dic3—21no—
269C22×Dic3—21no—
270C2×Dic6—22no—
271C2×Dic6—22no—
272C2×Dic6—21no—
273C2×Dic6C23×C512yes—
274#217—24no—
275#216—28no—
276#214—28no—
277C4⋊Dic3—21no—
278C4⋊Dic3C23×C512yes—
279Dic3⋊C4—24no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8C23×C512yes—
283C2×C3⋊C8C23×C512yes—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—24no—
288C23×C5—22no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5C2×#6712yes—
292C23×C5C2×#6711yescharacteristic
293C5×Q8—24no—
294C5×Q8—22no—
295C5×Q8—62no—
296C5×Q8—62no—
297C5×Q8—122no—
298C5×Q8C2×#6714yes—
299C5×D4—216no—
300C5×D4—24no—
301C5×D4—22no—
302C5×D4C2×#6714yes—
303C2×C4×C5—216no—
304C2×C4×C5—22no—
305C2×C4×C5—24no—
306C2×C4×C5—22no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—62no—
311C2×C4×C5—62no—
312C2×C4×C5—122no—
313C2×C4×C5—122no—
314C2×C4×C5C2×#6712yes—
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C2×#6712yes—
317C2×C4×C5C2×#6712yes—
318C2×C4×C5C23×D311yescharacteristic
319C5×C8—62no—
320C5×C8—62no—
321C2×#41—24no—
322C2×#41—24no—
323C2×#41—22no—
324C2×#41C2×C5×D314yes—
325C22×Q8—31no—
326C22×Q8C2×C5×D311yescharacteristic
327C22×D4—21no—
328C22×D4C2×C5×D311yescharacteristic
329C23×C4—21no—
330C23×C4C2×C5×D311yescharacteristic
331C2×Q16—34no—
332C2×Q16—64no—
333C2×SD16—34no—
334C2×SD16—64no—
335C22×C8—31no—
336C22×C8—31no—
337C22⋊Q8—34no—
338C22⋊Q8—62no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—61no—
341C2×C22⋊C4—61no—
342#103—34no—
343#102—34no—
344C22⋊C8—34no—
345C2×C3×C5—42no—
346C2×C3×C5—44no—
347C2×C3×C5#45214yescomplemented
348C2×C3×C5C2×#12011yescharacteristic
349C2×C3×C5C2×#13511yescharacteristic
350C2×C3×C5C2×#13711yescharacteristic
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3C2×C5×D412yes—
359C23×C3C2×C5×D411yescharacteristic
360C3×Q8—24no—
361C3×Q8—22no—
362C3×Q8C2×C5×D414yes—
363C3×D4—216no—
364C3×D4—24no—
365C3×D4—22no—
366C3×D4C2×C5×D414yes—
367C2×C3×C4—216no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4C2×C5×D412yes—
375C2×C3×C4C2×C5×D411yescharacteristic
376C2×C3×C4C2×C5×D412yes—
377C2×C3×C4C2×C5×D412yes—
378C2×C3×C4C24×C511yescharacteristic
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—42no—
382C2×Dic3—42no—
383Dic6—22no—
384Dic6—22no—
385Dic6—42no—
386C3⋊C8—22no—
387C3⋊C8—22no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—22no—
391C22×C5—24no—
392C22×C5—44no—
393C22×C5—48no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5#95012yes—
397C22×C5#95112yes—
398C22×C5#95312yes—
399C22×C5C22×#6711yescharacteristic
400C4×C5—22no—
401C4×C5—24no—
402C4×C5—122no—
403C4×C5—122no—
404C4×C5#95312yes—
405C4×C5C22×#6711yescharacteristic
406C4×C5C22×#6711yescharacteristic
407C24—21no—
408C24C5×#6711yescharacteristic
409#41—216no—
410#41—28no—
411#41—28no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—32no—
415C2×Q8—61no—
416C2×Q8—62no—
417C2×Q8—62no—
418C2×Q8C5×#6714yes—
419C2×Q8C22×C5×D312yes—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4C5×#6714yes—
425C2×D4C22×C5×D312yes—
426C22×C4—28no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4C5×#6711yescharacteristic
434C22×C4C5×#6712yes—
435C22×C4C22×C5×D312yes—
436C22×C4C22×C5×D311yescharacteristic
437Q16—68no—
438SD16—68no—
439C2×C8—32no—
440C2×C8—32no—
441C2×C8—62no—
442C2×C8—62no—
443C4⋊C4—32no—
444C4⋊C4—61no—
445C4⋊C4—64no—
446C22⋊C4—64no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—24no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—44no—
453C22×C3—48no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3C5×#12012yes—
457C22×C3C5×#13512yes—
458C22×C3C5×#13712yes—
459C22×C3C22×C5×D411yescharacteristic
460C3×C4—22no—
461C3×C4—24no—
462C3×C4C5×#12012yes—
463C3×C4C22×C5×D411yescharacteristic
464C3×C4C22×C5×D411yescharacteristic
465Dic3—42no—
466Dic3—42no—
467C2×C5—42no—
468C2×C5—44no—
469C2×C5#523914yesdirect product factor
470C2×C5C2×#95011yescharacteristic
471C2×C5C2×#95111yescharacteristic
472C2×C5C2×#95311yescharacteristic
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—42no—
479C23—42no—
480C23C2×C5×#6712yes—
481C23C2×C5×#6711yescharacteristic
482Q8—24no—
483Q8—22no—
484Q8—62no—
485Q8—62no—
486Q8—122no—
487Q8C2×C5×#6714yes—
488D4—216no—
489D4—24no—
490D4—22no—
491D4C2×C5×#6714yes—
492C2×C4—216no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—122no—
502C2×C4—122no—
503C2×C4C2×C5×#6712yes—
504C2×C4C2×C5×#6711yescharacteristic
505C2×C4C2×C5×#6712yes—
506C2×C4C2×C5×#6712yes—
507C2×C4C23×C5×D311yescharacteristic
508C8—62no—
509C8—62no—
510C2×C3—42no—
511C2×C3—44no—
512C2×C3C5×#45214yescomplemented
513C2×C3C2×C5×#12011yescharacteristic
514C2×C3C2×C5×#13511yescharacteristic
515C2×C3C2×C5×#13711yescharacteristic
516C5C2×#523911yescharacteristic, direct product factor, Sylow
517C22—22no—
518C22—22no—
519C22—22no—
520C22—24no—
521C22—44no—
522C22—48no—
523C22—42no—
524C22—42no—
525C22C5×#95012yes—
526C22C5×#95112yes—
527C22C5×#95312yes—
528C22C22×C5×#6711yescharacteristic
529C4—22no—
530C4—24no—
531C4—122no—
532C4—122no—
533C4C5×#95312yes—
534C4C22×C5×#6711yescharacteristic
535C4C22×C5×#6711yescharacteristic
536C3C2×C5×#45211yescharacteristic, complemented, Sylow
537C2—42no—
538C2—44no—
539C2C5×#523914yesdirect product factor
540C2C2×C5×#95011yescharacteristic
541C2C2×C5×#95111yescharacteristic
542C2C2×C5×#95311yescharacteristic
subgroupG/H
centerC23×C5C2×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC22×C3×C5×#41C2
socleC23×C3×C5C2×D4
hypercenterC22×C5×#41D3
hypocenterC3C2×C5×#452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ C22×C5×#41

Complements

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

NH ≅ G/Ntype
2. C22×C5×#216C2semidirect
3. C22×C5×#214C2semidirect
4. C2×C5×#924C2semidirect
5. C5×#5239C2direct (N × H)
6. C2×C5×#835C2semidirect
7. C2×C5×#832C2semidirect
8. C2×C5×#830C2semidirect
22. C2×C5×#216C22semidirect
24. C2×C5×#214C22semidirect
27. C5×#924C22semidirect
31. C5×#835C22semidirect
32. C5×#832C22semidirect
33. C5×#830C22semidirect
34. C2×#5239C5direct (N × H)
84. C22×#216C2×C5semidirect
85. C22×#214C2×C5semidirect
86. C2×#924C2×C5semidirect
87. #5239C2×C5direct (N × H)
88. C2×#835C2×C5semidirect
89. C2×#832C2×C5semidirect
90. C2×#830C2×C5semidirect
165. C2×#216C22×C5semidirect
167. C2×#214C22×C5semidirect
170. #924C22×C5semidirect
174. #835C22×C5semidirect
175. #832C22×C5semidirect
176. #830C22×C5semidirect
347. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
469. C2×C5#5239direct (N × H)
512. C2×C3C5×#452semidirect
516. C5C2×#5239direct (N × H)
536. C3C2×C5×#452semidirect
539. C2C5×#5239direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C22×C5×#2162
C22×C5×#2142
C2×C5×#9242
C5×#52392
C2×C5×#8352
C2×C5×#8322
C2×C5×#8302
C2×C5×#4523
C2×#52395