Finite Group Databasebeta

← D5×C3⋊#564 #14495584

Subgroups — D5×C3⋊#564 #14495584

Order 1920.

1792 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756445C211yesmaximal, characteristic, complemented
2C5×C3⋊#564C211yesmaximal, characteristic, complemented
3C3×D5×#125C211yesmaximal, characteristic
4D5×#890C214yesmaximal
5D5×#889C214yesmaximal
6D5×#889C214yesmaximal
7#11753395C214yesmaximal, complemented
8#11753393C214yesmaximal, complemented
9#11753333C214yesmaximal, complemented
10D5×#870C212yesmaximal
11#11752488C212yesmaximal, complemented
12D5×#564—31nomaximal, Hall
13C3×C5×#125C2211yescharacteristic
14#91779C2214yes—
15#91778C2214yes—
16#91778C2214yes—
17#91759C2212yes—
18C5×#890C2214yes—
19C5×#889C2214yes—
20C5×#889C2214yes—
21C5×#870C2212yes—
22C3×D5×C4⋊C4C2214yes—
23C3×D5×C4⋊C4C2212yes—
24C3×#4036C2212yes—
25C3×#4035C2214yes—
26C3×C42×D5C2211yescharacteristic
27C3×#4016C2211yescharacteristic
28D5×C4⋊Dic3C2212yes—
29D5×C4⋊Dic3C2214yes—
30D5×C4⋊Dic3C2212yes—
31D5×Dic3⋊C4C2214yes—
32D5×Dic3⋊C4C2214yes—
33D5×Dic3⋊C4C2214yes—
34D5×Dic3⋊C4C2214yes—
35C4×D5×Dic3C2214yes—
36#91388C2212yes—
37#91388C2212yes—
38#91384C2214yes—
39#91382C2214yes—
40#91382C2214yes—
41#91381C2214yes—
42#91379C2214yes—
43#91379C2214yes—
44#91378C2214yes—
45#91378C2214yes—
46#91346C2214yes—
47#91346C2214yes—
48#91343C2214yes—
49#91343C2214yes—
50#91339C2214yes—
51#91339C2214yes—
52#91336C2214yes—
53#91336C2214yes—
54#91335C2214yes—
55#91335C2214yes—
56#91334C2214yes—
57#91334C2214yes—
58C2×C3⋊#564—51nomaximal, Hall
59C5×#564—31no—
60D5×#125—34no—
61D5×#125—34no—
62D5×#125—34no—
63D5×#125—32no—
64D5×#125D311yescharacteristic
65C5⋊#564—34no—
66C5⋊#564—34no—
67C5⋊#564—34no—
68C5⋊#564—32no—
69C5⋊#564—31no—
70C2×C3×C4×D5C2311yescharacteristic
71C2×C3×C4×D5C2312yes—
72C2×C3×C4×D5C2314yes—
73C2×D5×Dic3C2314yes—
74C2×D5×Dic3C2314yes—
75C3×C5×C4⋊C4C2312yes—
76C3×C5×C4⋊C4C2314yes—
77C3×C42×C5C2311yescharacteristic
78C4⋊Dic15C2312yes—
79C4⋊Dic15C2312yes—
80C4⋊Dic15C2314yes—
81#6712C2314yes—
82#6712C2314yes—
83#6712C2314yes—
84#6712C2314yes—
85C4×Dic15C2314yes—
86C5×C4⋊Dic3C2312yes—
87C5×C4⋊Dic3C2312yes—
88C5×C4⋊Dic3C2314yes—
89C5×Dic3⋊C4C2314yes—
90C5×Dic3⋊C4C2314yes—
91C5×Dic3⋊C4C2314yes—
92C5×Dic3⋊C4C2314yes—
93C4×C5×Dic3C2314yes—
94C3×C4⋊Dic5C2312yes—
95C3×C4⋊Dic5C2314yes—
96C3×#683C2314yes—
97C3×#683C2314yes—
98C3×#683C2314yes—
99C3×C4×Dic5C2312yes—
100C3×C4×Dic5C2311yescharacteristic
101Dic3⋊Dic5C2314yes—
102Dic3⋊Dic5C2314yes—
103Dic3⋊Dic5C2314yes—
104Dic3⋊Dic5C2314yes—
105#6669C2314yes—
106#6669C2314yes—
107#6669C2314yes—
108#6669C2314yes—
109#6668C2314yes—
110#6668C2314yes—
111#6668C2314yes—
112#6668C2314yes—
113Dic3×Dic5C2314yes—
114Dic3×Dic5C2314yes—
115C2×C3×#125—51no—
116C3⋊#564—51no—
117C3⋊#564—54no—
118C3⋊#564—54no—
119C3⋊#564—54no—
120C3⋊#564—52no—
121C3⋊#564D511yescharacteristic, direct product factor
122C2×#890—54no—
123C2×#889—54no—
124C2×#889—54no—
125C2×#870—52no—
126C5×#125—34no—
127C5×#125—34no—
128C5×#125—34no—
129C5×#125—32no—
130C5×#125C2×D311yescharacteristic
131D5×C4⋊C4—34no—
132D5×C4⋊C4—34no—
133D5×C4⋊C4—34no—
134D5×C4⋊C4—34no—
135D5×C4⋊C4—34no—
136D5×C4⋊C4—32no—
137D5×C4⋊C4—32no—
138D5×C4⋊C4C2×D314yes—
139D5×C4⋊C4C2×D312yes—
140#4036—34no—
141#4036—34no—
142#4036—34no—
143#4036—34no—
144#4036—34no—
145#4036—34no—
146#4036—32no—
147#4036—32no—
148#4036C2×D312yes—
149#4035—34no—
150#4035—34no—
151#4035—34no—
152#4035—34no—
153#4035—34no—
154#4035—34no—
155#4035—34no—
156#4035—34no—
157#4035—34no—
158#4035—34no—
159#4035—34no—
160#4035—34no—
161#4035—34no—
162#4035—34no—
163#4035C2×D314yes—
164C42×D5—34no—
165C42×D5C2×D311yescharacteristic
166#4016—32no—
167#4016—34no—
168#4016—34no—
169#4016—34no—
170#4016C2×D311yescharacteristic
171C2×#564—151noSylow
172C22×C3×D5C2411yescharacteristic
173C2×C3×C4×C5C2412yes—
174C2×C3×C4×C5C2411yescharacteristic
175C2×C3×C4×C5C2414yes—
176C2×Dic15C2414yes—
177C2×Dic15C2414yes—
178C2×C5×Dic3C2414yes—
179C2×C5×Dic3C2414yes—
180C2×C3×Dic5C2414yes—
181C2×C3×Dic5C2412yes—
182C2×C3×Dic5C2411yescharacteristic
183C3×C4×D5—22no—
184C3×C4×D5—24no—
185C3×C4×D5—28no—
186D5×Dic3—28no—
187D5×Dic3—28no—
188C3×#125—54no—
189C3×#125—52no—
190C3×#125—51no—
191C3×#125C2×D511yescharacteristic
192C2×C3×C4⋊C4—52no—
193C2×C3×C4⋊C4—54no—
194C2×C3×C42—51no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—54no—
198C2×Dic3⋊C4—54no—
199C2×Dic3⋊C4—54no—
200C2×Dic3⋊C4—54no—
201C2×Dic3⋊C4—54no—
202C2×C4×Dic3—54no—
203#890—54no—
204#890—54no—
205#890—54no—
206#890—54no—
207#890—54no—
208#890—54no—
209#890—54no—
210#890C2×D514yes—
211#889—54no—
212#889—54no—
213#889—54no—
214#889—54no—
215#889—54no—
216#889—54no—
217#889—54no—
218#889—54no—
219#889—54no—
220#889—54no—
221#889—54no—
222#889—54no—
223#889—54no—
224#889—54no—
225#889C2×D514yes—
226#889C2×D514yes—
227#870—52no—
228#870—52no—
229#870—52no—
230#870—54no—
231#870—54no—
232#870C2×D512yes—
233C2×C4×D5—34no—
234C2×C4×D5—34no—
235C2×C4×D5C22×D314yes—
236C2×C4×D5C22×D311yescharacteristic
237C2×C4×D5C22×D312yes—
238C5×C4⋊C4—34no—
239C5×C4⋊C4—34no—
240C5×C4⋊C4—34no—
241C5×C4⋊C4—34no—
242C5×C4⋊C4—34no—
243C5×C4⋊C4—32no—
244C5×C4⋊C4—32no—
245C5×C4⋊C4C22×D312yes—
246C5×C4⋊C4C22×D314yes—
247C42×C5—34no—
248C42×C5C22×D311yescharacteristic
249C4⋊Dic5—34no—
250C4⋊Dic5—32no—
251C4⋊Dic5—32no—
252C4⋊Dic5—34no—
253C4⋊Dic5—34no—
254C4⋊Dic5—34no—
255C4⋊Dic5—34no—
256C4⋊Dic5C22×D314yes—
257C4⋊Dic5C22×D312yes—
258#683—34no—
259#683—34no—
260#683—34no—
261#683—34no—
262#683—34no—
263#683—34no—
264#683—34no—
265#683—34no—
266#683—34no—
267#683—34no—
268#683—34no—
269#683—34no—
270#683C22×D314yes—
271#683C22×D314yes—
272#683C22×D314yes—
273C4×Dic5—34no—
274C4×Dic5—34no—
275C4×Dic5—34no—
276C4×Dic5C22×D311yescharacteristic
277C4×Dic5C22×D312yes—
278#564—31no—
279#564—154no—
280#564—154no—
281#564—154no—
282#564—152no—
283#564—151no—
284C2×#125—51no—
285C2×#125—152no—
286C2×#125—154no—
287C2×#125—154no—
288C2×#125—154no—
289C22×C3×C5C2511yescharacteristic
290C2×C3×D52−1+412yes—
291C2×C3×D52−1+414yes—
292C3×C4×C5—21no—
293C3×C4×C5—22no—
294C3×C4×C5—24no—
295Dic15—24no—
296Dic15—24no—
297C3×Dic5—21no—
298C3×Dic5—24no—
299C3×Dic5—22no—
300C5×Dic3—24no—
301C5×Dic3—24no—
302C22×C3×C4—54no—
303C22×C3×C4—51no—
304C22×C3×C4—52no—
305C22×Dic3—54no—
306C22×Dic3—54no—
307C3×C4⋊C4—54no—
308C3×C4⋊C4—54no—
309C3×C4⋊C4—54no—
310C3×C4⋊C4—52no—
311C3×C4⋊C4—54no—
312C3×C4⋊C4C22×D512yes—
313C3×C4⋊C4C22×D514yes—
314C3×C42—52no—
315C3×C42—51no—
316C3×C42C22×D511yescharacteristic
317C4⋊Dic3—52no—
318C4⋊Dic3—52no—
319C4⋊Dic3—54no—
320C4⋊Dic3—54no—
321C4⋊Dic3—54no—
322C4⋊Dic3—54no—
323C4⋊Dic3—54no—
324C4⋊Dic3C22×D512yes—
325C4⋊Dic3C22×D512yes—
326C4⋊Dic3C22×D514yes—
327Dic3⋊C4—54no—
328Dic3⋊C4—54no—
329Dic3⋊C4—54no—
330Dic3⋊C4—54no—
331Dic3⋊C4—54no—
332Dic3⋊C4—54no—
333Dic3⋊C4—54no—
334Dic3⋊C4—54no—
335Dic3⋊C4—54no—
336Dic3⋊C4—54no—
337Dic3⋊C4—54no—
338Dic3⋊C4—54no—
339Dic3⋊C4C22×D514yes—
340Dic3⋊C4C22×D514yes—
341Dic3⋊C4C22×D514yes—
342Dic3⋊C4C22×D514yes—
343C4×Dic3—54no—
344C4×Dic3—54no—
345C4×Dic3—54no—
346C4×Dic3C22×D514yes—
347C22×D5C23×D311yescharacteristic
348C2×C4×C5—34no—
349C2×C4×C5—34no—
350C2×C4×C5C23×D314yes—
351C2×C4×C5C23×D311yescharacteristic
352C2×C4×C5C23×D312yes—
353C2×Dic5—34no—
354C2×Dic5—34no—
355C2×Dic5C23×D314yes—
356C2×Dic5C23×D312yes—
357C2×Dic5C23×D311yescharacteristic
358C4×D5—22no—
359C4×D5—28no—
360C4×D5—24no—
361C4×D5—68no—
362C4×D5—68no—
363#125—34no—
364#125—34no—
365#125—34no—
366#125—32no—
367#125—54no—
368#125—52no—
369#125—51no—
370#125—154no—
371#125—154no—
372#125—154no—
373#125—154no—
374#125—154no—
375#125—152no—
376#125—152no—
377#125—154no—
378#125—154no—
379#125—154no—
380#125—154no—
381#125—154no—
382#125—154no—
383#125—154no—
384#125—154no—
385#125—154no—
386#125—154no—
387#125—154no—
388#125—154no—
389#125—154no—
390#125—154no—
391#125—154no—
392#125—154no—
393#125—154no—
394#125—154no—
395#125—152no—
396#125D3×D511yescharacteristic
397C2×C4⋊C4—52no—
398C2×C4⋊C4—54no—
399C2×C4⋊C4—154no—
400C2×C4⋊C4—154no—
401C2×C4⋊C4—154no—
402C2×C4⋊C4—154no—
403C2×C4⋊C4—152no—
404C2×C4⋊C4—152no—
405C2×C4⋊C4—154no—
406C2×C42—51no—
407C2×C42—154no—
408C2×C3×C5C2×2−1+411yescharacteristic
409C2×C3×C5C2×2−1+412yes—
410C3×D5#56414yescomplemented
411C23×C3—51no—
412C2×C3×C4—54no—
413C2×C3×C4—51no—
414C2×C3×C4—52no—
415C2×C3×C4—102no—
416C2×C3×C4—108no—
417C2×C3×C4—104no—
418C2×C3×C4C23×D514yes—
419C2×C3×C4C23×D511yescharacteristic
420C2×C3×C4C23×D512yes—
421C2×Dic3—54no—
422C2×Dic3—54no—
423C2×Dic3—108no—
424C2×Dic3—108no—
425C2×Dic3C23×D514yes—
426C2×Dic3C23×D514yes—
427C22×C5C24×D311yescharacteristic
428C2×D5#100712yes—
429C2×D5#101014yes—
430C4×C5—21no—
431C4×C5—24no—
432C4×C5—22no—
433C4×C5—64no—
434C4×C5—64no—
435Dic5—21no—
436Dic5—24no—
437Dic5—22no—
438Dic5—64no—
439Dic5—64no—
440C22×C4—51no—
441C22×C4—52no—
442C22×C4—54no—
443C22×C4—154no—
444C22×C4—154no—
445C4⋊C4—34no—
446C4⋊C4—34no—
447C4⋊C4—34no—
448C4⋊C4—34no—
449C4⋊C4—34no—
450C4⋊C4—32no—
451C4⋊C4—32no—
452C4⋊C4—54no—
453C4⋊C4—54no—
454C4⋊C4—54no—
455C4⋊C4—54no—
456C4⋊C4—52no—
457C4⋊C4—154no—
458C4⋊C4—154no—
459C4⋊C4—154no—
460C4⋊C4—154no—
461C4⋊C4—154no—
462C4⋊C4—154no—
463C4⋊C4—154no—
464C4⋊C4—154no—
465C4⋊C4—154no—
466C4⋊C4—154no—
467C4⋊C4—154no—
468C4⋊C4—154no—
469C4⋊C4—154no—
470C4⋊C4—154no—
471C4⋊C4—154no—
472C4⋊C4—154no—
473C4⋊C4—154no—
474C4⋊C4—152no—
475C4⋊C4—152no—
476C4⋊C4C2×D3×D512yes—
477C4⋊C4C2×D3×D514yes—
478C42—34no—
479C42—52no—
480C42—51no—
481C42—154no—
482C42—154no—
483C42—154no—
484C42C2×D3×D511yescharacteristic
485C3×C5C2×#56411yescharacteristic, complemented, Hall
486C22×C3—52no—
487C22×C3—54no—
488C22×C3C24×D511yescharacteristic
489C3×C4—21no—
490C3×C4—24no—
491C3×C4—22no—
492C3×C4—101no—
493C3×C4—104no—
494C3×C4—102no—
495Dic3—24no—
496Dic3—24no—
497Dic3—104no—
498Dic3—104no—
499C2×C5C2×#100711yescharacteristic
500C2×C5C2×#101012yes—
501D5C3⋊#56414yesdirect product factor
502C23—51no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—51no—
506C2×C4—52no—
507C2×C4—54no—
508C2×C4—102no—
509C2×C4—104no—
510C2×C4—108no—
511C2×C4—154no—
512C2×C4—154no—
513C2×C4—308no—
514C2×C4—308no—
515C2×C4C22×D3×D514yes—
516C2×C4C22×D3×D511yescharacteristic
517C2×C4C22×D3×D512yes—
518C2×C3—54no—
519C2×C3D5×2−1+411yescharacteristic
520C2×C3D5×2−1+412yes—
521C5C2×C3⋊#56411yescharacteristic, complemented, Sylow
522C22—52no—
523C22—54no—
524C22C23×D3×D511yescharacteristic
525C4—21no—
526C4—24no—
527C4—22no—
528C4—64no—
529C4—64no—
530C4—101no—
531C4—102no—
532C4—104no—
533C4—304no—
534C4—304no—
535C3D5×#56411yescharacteristic, complemented, Sylow
536C2—54no—
537C2D5×#100711yescharacteristic
538C2D5×#101012yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#125C22
prime radicalC22×C3×D5C24
hypercenter#125D3×D5
hypocenterC3×C5C2×#564
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #11756445C2semidirect
2. C5×C3⋊#564C2semidirect
7. #11753395C2semidirect
8. #11753393C2semidirect
9. #11753333C2semidirect
11. #11752488C2semidirect
121. C3⋊#564D5direct (N × H)
410. C3×D5#564semidirect
485. C3×C5C2×#564semidirect
501. D5C3⋊#564direct (N × H)
521. C5C2×C3⋊#564semidirect
535. C3D5×#564semidirect

Maximal subgroups

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

subgroupindex
#117564452
C5×C3⋊#5642
C3×D5×#1252
D5×#8902
D5×#8892
#117533952
#117533932
#117533332
D5×#8702
#117524882
D5×#5643
C2×C3⋊#5645