Finite Group Databasebeta

← D5×#4986 #14332046

Subgroups — D5×#4986 #14332046

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic
3#11751087C211yesmaximal, characteristic, complemented
4C5×#4986C211yesmaximal, characteristic, complemented
5D5×C3⋊#95C212yesmaximal
6D5×C3⋊#95C212yesmaximal
7D5×C3⋊#95C211yesmaximal, characteristic
8#11748823C212yesmaximal, complemented
9#11748615C211yesmaximal, characteristic, complemented
10#11748614C211yesmaximal, characteristic, complemented
11#11748570C212yesmaximal, complemented
12D5×#400—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C22×D5×Dic3C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×C3×#683C2211yescharacteristic
23C2×C3×#683C2211yescharacteristic
24C3×D5×C4⋊C4—24no—
25C2×#6668C2212yes—
26D5×C4⋊Dic3—24no—
27#91115C2211yescharacteristic
28#91115C2212yes—
29#91115C2212yes—
30C5×C3⋊#95C2211yescharacteristic
31C5×C3⋊#95C2212yes—
32C5×C3⋊#95C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38C2×#4986—51nomaximal, Hall
39C2×D5×C4⋊C4—31no—
40C2×D5×C4⋊C4D311yescharacteristic
41C5×#400—31no—
42#65275—31no—
43#65271—31no—
44D5×#95—32no—
45D5×#95—32no—
46D5×#95—31no—
47#64949—32no—
48#64948—31no—
49#64947—32no—
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—24no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5D414yes—
67C2×C3×C4×D5Q814yes—
68C2×D5×Dic3—24no—
69C2×D5×Dic3—28no—
70C2×D5×Dic3—24no—
71C2×D5×Dic3—24no—
72C2×D5×Dic3—24no—
73C3×C5×C4⋊C4—22no—
74C4⋊Dic15—22no—
75C5×C4⋊Dic3—22no—
76C3×C4⋊Dic5—22no—
77C3×#683—22no—
78C3×#683—22no—
79#6668—24no—
80C22×C3×C4⋊C4—51no—
81C22×C4⋊Dic3—51no—
82C2×C3⋊#95—51no—
83C2×C3⋊#95—52no—
84C2×C3⋊#95—52no—
85#4986—51no—
86#4986—51no—
87#4986—51no—
88#4986—52no—
89#4986—52no—
90#4986D511yescharacteristic, direct product factor
91C22×C4×D5—32no—
92C22×C4×D5—32no—
93C22×C4×D5C2×D311yescharacteristic
94C22×C4×D5C2×D311yescharacteristic
95C22×C4×D5C2×D311yescharacteristic
96C2×C5×C4⋊C4—31no—
97C2×C5×C4⋊C4C2×D311yescharacteristic
98C2×C4⋊Dic5—31no—
99C2×C4⋊Dic5C2×D311yescharacteristic
100C2×#683—32no—
101C2×#683C2×D311yescharacteristic
102C2×#683C2×D311yescharacteristic
103D5×C4⋊C4—24no—
104D5×C4⋊C4—64no—
105C5×#95—32no—
106C5×#95—31no—
107C5×#95—32no—
108#3963—32no—
109#3963—32no—
110#3963—31no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963—32no—
115#3963—32no—
116C2×#400—151noSylow
117C23×C3×C5C2411yescharacteristic
118C22×C3×D5C2×D412yes—
119C22×C3×D5C2×Q812yes—
120C22×C3×D5#4112yes—
121C22×C3×D5#4114yes—
122C22×C3×D5#4114yes—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2×Q812yes—
130C2×Dic15—22no—
131C2×Dic15—24no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—24no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×Q812yes—
147C3×C4×D5—28no—
148C3×C4×D5—28no—
149C3×C4×D5—44no—
150D5×Dic3—48no—
151D5×Dic3—48no—
152C23×C3×C4—51no—
153C23×C3×C4—51no—
154C23×C3×C4—51no—
155C23×Dic3—52no—
156C23×Dic3—52no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4—51no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C4⋊C4—104no—
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C2×C4⋊Dic3—51no—
163C2×C4⋊Dic3—52no—
164C2×C4⋊Dic3—104no—
165C2×C4⋊Dic3C2×D511yescharacteristic
166C3⋊#95—51no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C3⋊#95—52no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95C2×D511yescharacteristic
175C3⋊#95C2×D512yes—
176C3⋊#95C2×D512yes—
177C23×D5C22×D311yescharacteristic
178C22×C4×C5—32no—
179C22×C4×C5—32no—
180C22×C4×C5C22×D311yescharacteristic
181C22×C4×C5C22×D311yescharacteristic
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—32no—
184C22×Dic5—32no—
185C22×Dic5C22×D311yescharacteristic
186C22×Dic5C22×D311yescharacteristic
187C22×Dic5C22×D311yescharacteristic
188C2×C4×D5—22no—
189C2×C4×D5—24no—
190C2×C4×D5—22no—
191C2×C4×D5—24no—
192C2×C4×D5—22no—
193C2×C4×D5—64no—
194C2×C4×D5—64no—
195C2×C4×D5—64no—
196C2×C4×D5—68no—
197C2×C4×D5—64no—
198C2×C4×D5Dic614yes—
199C2×C4×D5#6714yes—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—62no—
202C4⋊Dic5—22no—
203C4⋊Dic5—62no—
204#683—22no—
205#683—22no—
206#683—64no—
207C22×C4⋊C4—51no—
208C22×C4⋊C4—151no—
209#400—31no—
210#400—152no—
211#400—151no—
212#400—152no—
213#400—151no—
214#400—151no—
215C2×#95—151no—
216C2×#95—152no—
217C2×#95—152no—
218C22×C3×C5C22×D411yescharacteristic
219C22×C3×C5C22×Q811yescharacteristic
220C22×C3×C5C2×#4111yescharacteristic
221C22×C3×C5C2×#4112yes—
222C22×C3×C5C2×#4112yes—
223C2×C3×D5C22⋊Q814yes—
224C2×C3×D5#12314yes—
225C2×C3×D5#12414yes—
226C2×C3×D5#12518yes—
227C2×C3×D5#12618yes—
228C3×C4×C5—22no—
229C3×C4×C5—22no—
230C3×C4×C5—41no—
231Dic15—42no—
232Dic15—42no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C3×Dic5—41no—
236C5×Dic3—42no—
237C5×Dic3—42no—
238C24×C3—51no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—54no—
242C22×C3×C4—54no—
243C22×C3×C4—51no—
244C22×C3×C4—102no—
245C22×C3×C4—102no—
246C22×C3×C4—104no—
247C22×C3×C4—102no—
248C22×C3×C4—104no—
249C22×C3×C4C22×D511yescharacteristic
250C22×C3×C4C22×D511yescharacteristic
251C22×C3×C4C22×D511yescharacteristic
252C22×Dic3—52no—
253C22×Dic3—52no—
254C22×Dic3—104no—
255C22×Dic3—104no—
256C22×Dic3—108no—
257C22×Dic3—104no—
258C22×Dic3—104no—
259C22×Dic3C22×D512yes—
260C22×Dic3C22×D512yes—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—102no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4—102no—
265C4⋊Dic3—22no—
266C4⋊Dic3—104no—
267C4⋊Dic3—102no—
268C23×C5C23×D311yescharacteristic
269C22×D5C2×Dic612yes—
270C22×D5#23512yes—
271C22×D5#23714yes—
272C22×D5#23914yes—
273C22×D5C2×#6712yes—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—21no—
277C2×C4×C5—22no—
278C2×C4×C5—21no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—64no—
283C2×C4×C5—62no—
284C2×C4×C5C2×Dic612yes—
285C2×C4×C5C2×#6712yes—
286C2×Dic5—21no—
287C2×Dic5—22no—
288C2×Dic5—21no—
289C2×Dic5—22no—
290C2×Dic5—21no—
291C2×Dic5—62no—
292C2×Dic5—62no—
293C2×Dic5—62no—
294C2×Dic5—64no—
295C2×Dic5—62no—
296C2×Dic5C2×Dic612yes—
297C2×Dic5C2×#6712yes—
298C4×D5—28no—
299C4×D5—28no—
300C4×D5—44no—
301C4×D5—128no—
302C4×D5—128no—
303C23×C4—51no—
304C23×C4—51no—
305C23×C4—51no—
306C23×C4—152no—
307C23×C4—152no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—51no—
310C2×C4⋊C4—51no—
311C2×C4⋊C4—51no—
312C2×C4⋊C4—104no—
313C2×C4⋊C4—152no—
314C2×C4⋊C4—151no—
315C2×C4⋊C4—304no—
316C2×C4⋊C4D3×D511yescharacteristic
317#95—31no—
318#95—32no—
319#95—32no—
320#95—152no—
321#95—152no—
322#95—152no—
323#95—152no—
324#95—152no—
325#95—151no—
326#95—152no—
327#95—152no—
328C2×C3×C5C2×C22⋊Q811yescharacteristic
329C2×C3×C5C2×#12311yescharacteristic
330C2×C3×C5C2×#12411yescharacteristic
331C2×C3×C5C2×#12512yes—
332C2×C3×C5C2×#12612yes—
333C3×D5#40018yescomplemented
334C23×C3—52no—
335C23×C3—52no—
336C23×C3—54no—
337C23×C3—52no—
338C23×C3—54no—
339C23×C3C23×D511yescharacteristic
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—52no—
346C2×C3×C4—52no—
347C2×C3×C4—108no—
348C2×C3×C4—108no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—102no—
352C2×C3×C4—101no—
353C2×C3×C4—102no—
354C2×C3×C4—204no—
355C2×C3×C4D4×D512yes—
356C2×C3×C4Q8×D512yes—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—24no—
361C2×Dic3—22no—
362C2×Dic3—102no—
363C2×Dic3—102no—
364C2×Dic3—102no—
365C2×Dic3—104no—
366C2×Dic3—102no—
367C2×Dic3—208no—
368C2×Dic3—208no—
369C22×C5C22×Dic611yescharacteristic
370C22×C5C2×#23511yescharacteristic
371C22×C5C2×#23712yes—
372C22×C5C2×#23912yes—
373C22×C5C22×#6711yescharacteristic
374C2×D5#89018yes—
375C2×D5#89818yes—
376C2×D5#92414yes—
377C2×D5#93514yes—
378C2×D5#94714yes—
379C4×C5—22no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5—122no—
383C4×C5—122no—
384Dic5—22no—
385Dic5—22no—
386Dic5—41no—
387Dic5—122no—
388Dic5—122no—
389C24—51no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—51no—
393C22×C4—51no—
394C22×C4—54no—
395C22×C4—54no—
396C22×C4—51no—
397C22×C4—102no—
398C22×C4—102no—
399C22×C4—104no—
400C22×C4—102no—
401C22×C4—104no—
402C22×C4—152no—
403C22×C4—152no—
404C22×C4—304no—
405C22×C4—304no—
406C22×C4—304no—
407C22×C4—308no—
408C22×C4—304no—
409C22×C4C2×D3×D511yescharacteristic
410C22×C4C2×D3×D511yescharacteristic
411C22×C4C2×D3×D511yescharacteristic
412C4⋊C4—22no—
413C4⋊C4—62no—
414C4⋊C4—102no—
415C4⋊C4—102no—
416C4⋊C4—102no—
417C4⋊C4—304no—
418C4⋊C4—302no—
419C3×C5C2×#40011yescharacteristic, complemented, Hall
420C22×C3—54no—
421C22×C3—54no—
422C22×C3—54no—
423C22×C3—58no—
424C22×C3—58no—
425C22×C3C2×D4×D511yescharacteristic
426C22×C3C2×Q8×D511yescharacteristic
427C22×C3D5×#4111yescharacteristic
428C22×C3D5×#4112yes—
429C22×C3D5×#4112yes—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—102no—
434C3×C4—102no—
435C3×C4—201no—
436Dic3—42no—
437Dic3—42no—
438Dic3—202no—
439Dic3—202no—
440C2×C5C2×#89012yes—
441C2×C5C2×#89812yes—
442C2×C5C2×#92411yescharacteristic
443C2×C5C2×#93511yescharacteristic
444C2×C5C2×#94711yescharacteristic
445D5#498618yesdirect product factor
446C23—52no—
447C23—52no—
448C23—54no—
449C23—54no—
450C23—52no—
451C23C22×D3×D511yescharacteristic
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—52no—
458C2×C4—52no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—64no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—108no—
465C2×C4—108no—
466C2×C4—101no—
467C2×C4—102no—
468C2×C4—101no—
469C2×C4—102no—
470C2×C4—101no—
471C2×C4—204no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—304no—
475C2×C4—302no—
476C2×C4—302no—
477C2×C4—608no—
478C2×C4—608no—
479C2×C4D5×Dic612yes—
480C2×C4D5×#6712yes—
481C2×C3—58no—
482C2×C3D5×C22⋊Q811yescharacteristic
483C2×C3D5×#12311yescharacteristic
484C2×C3D5×#12411yescharacteristic
485C2×C3D5×#12512yes—
486C2×C3D5×#12612yes—
487C5C2×#498611yescharacteristic, complemented, Sylow
488C22—54no—
489C22—58no—
490C22—54no—
491C22—54no—
492C22—58no—
493C22C2×D5×Dic611yescharacteristic
494C22D5×#23511yescharacteristic
495C22D5×#23712yes—
496C22D5×#23912yes—
497C22C2×D5×#6711yescharacteristic
498C4—22no—
499C4—22no—
500C4—41no—
501C4—102no—
502C4—102no—
503C4—122no—
504C4—122no—
505C4—201no—
506C4—602no—
507C4—602no—
508C3D5×#40011yescharacteristic, complemented, Sylow
509C2—58no—
510C2D5×#89012yes—
511C2D5×#89812yes—
512C2D5×#92411yescharacteristic
513C2D5×#93511yescharacteristic
514C2D5×#94711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC2×C3×C5×C4⋊C4C22
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#400
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11751087C2semidirect
4. C5×#4986C2semidirect
8. #11748823C2semidirect
9. #11748615C2semidirect
10. #11748614C2semidirect
11. #11748570C2semidirect
90. #4986D5direct (N × H)
333. C3×D5#400semidirect
419. C3×C5C2×#400semidirect
445. D5#4986direct (N × H)
487. C5C2×#4986semidirect
508. C3D5×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×D5×C4⋊Dic32
#117510872
C5×#49862
D5×C3⋊#952
#117488232
#117486152
#117486142
#117485702
D5×#4003
C2×#49865