Finite Group Databasebeta

← D5×#4528 #14280783

Subgroups — D5×#4528 #14280783

Order 1920.

656 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2D5×#830C212yesmaximal
3#11746349C211yesmaximal, characteristic, complemented
4C5×#4528C211yesmaximal, characteristic, complemented
5#11745951C212yesmaximal, complemented
6D5×#324—31nomaximal, Hall
7C22×C3×C4×D5C411yescharacteristic
8C22×C3×C4×D5C411yescharacteristic
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C4⋊Dic5C411yescharacteristic
12C2×C3×#683C411yescharacteristic
13C2×C3×#683C2211yescharacteristic
14C3×D5×C4⋊C4—22no—
15C3×D5×C4⋊C4—22no—
16C2×D5×C3⋊C8—22no—
17#91114C2212yes—
18C5×#830C2212yes—
19#90955—22no—
20C2×#4528—51nomaximal, Hall
21C2×D5×C4⋊C4D311yescharacteristic
22D5×C22⋊C8—32no—
23C5×#324—31no—
24#64748—31no—
25#64689—32no—
26C23×C3×D5C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C22×C3×Dic5C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2×C411yescharacteristic
33C2×C3×C4×D5—21no—
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5—22no—
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—42no—
39C2×C3×C4×D5—42no—
40C2×C3×C4×D5C814yescomplemented
41C2×C3×C4×D5D412yes—
42C2×C3×C4×D5D412yes—
43C3×C5×C4⋊C4—22no—
44C2×C3⋊#168—22no—
45C2×C5×C3⋊C8—22no—
46C3×C4⋊Dic5—22no—
47C3×#683—22no—
48C3×#683—22no—
49D5×C3⋊C8—44no—
50C22×C3×C4⋊C4—51no—
51C2×#830—52no—
52#4528—51no—
53#4528—52no—
54#4528D511yescharacteristic, direct product factor
55C22×C4×D5Dic311yescharacteristic
56C22×C4×D5Dic311yescharacteristic
57C22×C4×D5C2×D311yescharacteristic
58C2×C5×C4⋊C4C2×D311yescharacteristic
59C2×C4⋊Dic5Dic311yescharacteristic
60C2×#683Dic311yescharacteristic
61C2×#683C2×D311yescharacteristic
62C2×C8×D5—62no—
63D5×C4⋊C4—22no—
64D5×C4⋊C4—22no—
65C5×C22⋊C8—32no—
66C22⋊#168—32no—
67#3952—62no—
68C2×#324—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×C3×D5—22no—
71C22×C3×D5—22no—
72C22×C3×D5C22⋊C411yescharacteristic
73C22×C3×D5C22⋊C411yescharacteristic
74C22×C3×D5C2×C812yes—
75C22×C3×D5M1612yes—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×C812yescomplemented
82C2×C3×C4×C5C2×D412yes—
83C2×C3×Dic5—21no—
84C2×C3×Dic5—21no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5—41no—
88C2×C3×Dic5C22⋊C412yes—
89C2×C3×Dic5C2×C812yescomplemented
90C3×C4×D5—24no—
91C3×C4×D5—24no—
92C3×C4×D5—24no—
93C3×C4×D5—42no—
94C3×C4×D5—42no—
95C3×C4×D5—42no—
96C3⋊#168—42no—
97C5×C3⋊C8—42no—
98C23×C3×C4—51no—
99C23×C3×C4—51no—
100C23×C3×C4—51no—
101C2×C3×C4⋊C4—51no—
102C2×C3×C4⋊C4—51no—
103C2×C3×C4⋊C4—51no—
104C2×C3×C4⋊C4—102no—
105C2×C3×C4⋊C4—102no—
106C2×C3×C4⋊C4C2×D511yescharacteristic
107C22×C3⋊C8—102no—
108#830—52no—
109#830—102no—
110#830C2×D512yes—
111C23×D5C2×Dic311yescharacteristic
112C22×C4×C5C2×Dic311yescharacteristic
113C22×C4×C5C2×Dic311yescharacteristic
114C22×C4×C5C22×D311yescharacteristic
115C22×Dic5C2×Dic311yescharacteristic
116C22×Dic5C2×Dic311yescharacteristic
117C22×Dic5C2×Dic311yescharacteristic
118C2×C4×D5—22no—
119C2×C4×D5—21no—
120C2×C4×D5—21no—
121C2×C4×D5—21no—
122C2×C4×D5—21no—
123C2×C4×D5—42no—
124C2×C4×D5—42no—
125C2×C4×D5C3⋊C814yescomplemented
126C2×C4×D5#6712yes—
127C2×C4×D5#6712yes—
128C2×C5×C8—62no—
129C5×C4⋊C4—22no—
130C4⋊Dic5—22no—
131#683—22no—
132#683—22no—
133C2×#168—62no—
134C8×D5—124no—
135C22×C4⋊C4—51no—
136C2×C22⋊C8—152no—
137#324—31no—
138#324—152no—
139#324—151no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5C2×C22⋊C411yescharacteristic
143C22×C3×C5C22×C811yescharacteristic
144C22×C3×C5C2×M1611yescharacteristic
145C2×C3×D5—21no—
146C2×C3×D5—21no—
147C2×C3×D5—24no—
148C2×C3×D5—24no—
149C2×C3×D5C22⋊C812yes—
150C2×C3×D5C22⋊C812yes—
151C2×C3×D5#9912yes—
152C2×C3×D5#10112yes—
153C3×C4×C5—22no—
154C3×C4×C5—22no—
155C3×C4×C5—41no—
156C3×Dic5—22no—
157C3×Dic5—22no—
158C3×Dic5—41no—
159C24×C3—51no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—54no—
163C22×C3×C4—52no—
164C22×C3×C4—52no—
165C22×C3×C4—51no—
166C22×C3×C4—101no—
167C22×C3×C4—101no—
168C22×C3×C4—102no—
169C22×C3×C4—101no—
170C22×C3×C4—101no—
171C22×C3×C4—202no—
172C22×C3×C4—202no—
173C22×C3×C4C4×D511yescharacteristic
174C22×C3×C4C4×D511yescharacteristic
175C22×C3×C4C22×D511yescharacteristic
176C3×C4⋊C4—22no—
177C3×C4⋊C4—102no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—102no—
180C2×C3⋊C8—22no—
181C2×C3⋊C8—102no—
182C2×C3⋊C8—204no—
183C23×C5C22×Dic311yescharacteristic
184C22×D5—22no—
185C22×D5—22no—
186C22×D5C2×C3⋊C812yes—
187C22×D5#20812yes—
188C22×D5#21711yescharacteristic
189C22×D5#21711yescharacteristic
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5C2×C3⋊C812yescomplemented
196C2×C4×C5C2×#6712yes—
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—41no—
201C2×Dic5—41no—
202C2×Dic5C2×C3⋊C812yescomplemented
203C2×Dic5#21712yes—
204C4×D5—24no—
205C4×D5—24no—
206C4×D5—24no—
207C4×D5—42no—
208C4×D5—42no—
209C4×D5—42no—
210C5×C8—122no—
211#168—122no—
212C23×C4—51no—
213C23×C4—51no—
214C23×C4—51no—
215C22×C8—302no—
216C2×C4⋊C4—51no—
217C2×C4⋊C4—51no—
218C2×C4⋊C4—51no—
219C2×C4⋊C4—102no—
220C2×C4⋊C4—102no—
221C2×C4⋊C4D3×D511yescharacteristic
222C22⋊C8—32no—
223C22⋊C8—152no—
224C22⋊C8—302no—
225C2×C3×C5—21no—
226C2×C3×C5—21no—
227C2×C3×C5C2×C22⋊C811yescharacteristic
228C2×C3×C5C2×#9911yescharacteristic
229C2×C3×C5C2×#10111yescharacteristic
230C3×D5—22no—
231C3×D5#32414yescomplemented
232C23×C3—51no—
233C23×C3—51no—
234C23×C3—52no—
235C23×C3—52no—
236C23×C3—102no—
237C23×C3—102no—
238C23×C3C2×C4×D511yescharacteristic
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—52no—
245C2×C3×C4—52no—
246C2×C3×C4—104no—
247C2×C3×C4—104no—
248C2×C3×C4—104no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4—202no—
253C2×C3×C4—202no—
254C2×C3×C4—202no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4C8×D512yescomplemented
258C2×C3×C4D4×D512yes—
259C3⋊C8—42no—
260C3⋊C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5C22×C3⋊C811yescharacteristic
264C22×C5C2×#20811yescharacteristic
265C22×C5C2×#21711yescharacteristic
266C2×D5—21no—
267C2×D5—21no—
268C2×D5—24no—
269C2×D5—24no—
270C2×D5#83012yes—
271C2×D5#83012yes—
272C2×D5#83412yes—
273C2×D5#83612yes—
274C4×C5—22no—
275C4×C5—22no—
276C4×C5—41no—
277Dic5—22no—
278Dic5—22no—
279Dic5—41no—
280C24—51no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—52no—
284C22×C4—54no—
285C22×C4—52no—
286C22×C4—51no—
287C22×C4—101no—
288C22×C4—101no—
289C22×C4—102no—
290C22×C4—101no—
291C22×C4—101no—
292C22×C4—202no—
293C22×C4—202no—
294C22×C4D5×Dic311yescharacteristic
295C22×C4D5×Dic311yescharacteristic
296C22×C4C2×D3×D511yescharacteristic
297C2×C8—62no—
298C2×C8—302no—
299C2×C8—604no—
300C4⋊C4—22no—
301C4⋊C4—102no—
302C4⋊C4—102no—
303C4⋊C4—102no—
304C3×C5C2×#32411yescharacteristic, complemented, Hall
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—52no—
308C22×C3—52no—
309C22×C3—52no—
310C22×C3—52no—
311C22×C3—104no—
312C22×C3—104no—
313C22×C3—101no—
314C22×C3—101no—
315C22×C3D5×C22⋊C411yescharacteristic
316C22×C3C2×C8×D511yescharacteristic
317C22×C3D5×M1611yescharacteristic
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—41no—
321C3×C4—102no—
322C3×C4—102no—
323C3×C4—201no—
324C2×C5—21no—
325C2×C5—21no—
326C2×C5C2×#83011yescharacteristic
327C2×C5C2×#83411yescharacteristic
328C2×C5C2×#83611yescharacteristic
329D5—22no—
330D5#452814yesdirect product factor
331C23—51no—
332C23—52no—
333C23—52no—
334C23—51no—
335C23—102no—
336C23—102no—
337C23C2×D5×Dic311yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—52no—
344C2×C4—52no—
345C2×C4—104no—
346C2×C4—104no—
347C2×C4—104no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—202no—
352C2×C4—202no—
353C2×C4—202no—
354C2×C4—201no—
355C2×C4—201no—
356C2×C4D5×C3⋊C812yescomplemented
357C2×C4D5×#6712yes—
358C8—122no—
359C8—602no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—54no—
363C2×C3—102no—
364C2×C3D5×C22⋊C811yescharacteristic
365C2×C3D5×#9911yescharacteristic
366C2×C3D5×#10111yescharacteristic
367C5C2×#452811yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—52no—
371C22—52no—
372C22—52no—
373C22—52no—
374C22—104no—
375C22—104no—
376C22—101no—
377C22—101no—
378C22C2×D5×C3⋊C811yescharacteristic
379C22D5×#20811yescharacteristic
380C22D5×#21711yescharacteristic
381C4—22no—
382C4—22no—
383C4—41no—
384C4—102no—
385C4—102no—
386C4—201no—
387C3D5×#32411yescharacteristic, complemented, Sylow
388C2—21no—
389C2—21no—
390C2—54no—
391C2—102no—
392C2D5×#83011yescharacteristic
393C2D5×#83411yescharacteristic
394C2D5×#83611yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#324
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11746349C2semidirect
4. C5×#4528C2semidirect
5. #11745951C2semidirect
40. C2×C3×C4×D5C8semidirect
54. #4528D5direct (N × H)
81. C2×C3×C4×C5C2×C8semidirect
89. C2×C3×Dic5C2×C8semidirect
125. C2×C4×D5C3⋊C8semidirect
195. C2×C4×C5C2×C3⋊C8semidirect
202. C2×Dic5C2×C3⋊C8semidirect
231. C3×D5#324semidirect
257. C2×C3×C4C8×D5semidirect
304. C3×C5C2×#324semidirect
330. D5#4528direct (N × H)
356. C2×C4D5×C3⋊C8semidirect
367. C5C2×#4528semidirect
387. C3D5×#324semidirect

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
D5×#8302
#117463492
C5×#45282
#117459512
D5×#3243
C2×#45285