Finite Group Databasebeta

← D5×#4677 #14332019

Subgroups — D5×#4677 #14332019

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×(C2×D3)⋊C4C213yesmaximal
2C2×D5×C4⋊Dic3C213yesmaximal, complemented
3#11750778C211yesmaximal, characteristic, complemented
4C5×#4677C211yesmaximal, characteristic, complemented
5C3×D5×#95C211yesmaximal, characteristic, complemented
6#11748835C213yesmaximal, complemented
7#11748762C213yesmaximal, complemented
8D5×#399—31nomaximal, Hall
9C23×D3×D5C2211yescharacteristic
10C22×C3×C4×D5C2213yes—
11C22×D5×Dic3C2213yes—
12C2×#6714C2213yes—
13C2×C4⋊Dic15C2213yescomplemented
14C2×C5×(C2×D3)⋊C4C2213yes—
15C2×C5×C4⋊Dic3C2213yescomplemented
16C2×#6668C2216yescomplemented
17C2×#6667C2213yes—
18C2×(C2×D3)⋊Dic5C2213yes—
19D5×(C2×D3)⋊C4—212no—
20D5×C4⋊Dic3—212no—
21C3×C5×#95C2211yescharacteristic, complemented
22C3×#3963C2213yescomplemented
23C2×#4677—51nomaximal, Hall
24C2×D5×C4⋊C4—33no—
25C2×D5×C22⋊C4—33no—
26C5×#399—31no—
27#65281—33no—
28#65238—33no—
29#64966—31no—
30D5×#95D311yescharacteristic, complemented
31C23×D15C2311yescharacteristic
32C23×C5×D3C2311yescharacteristic
33C23×C3×D5C2311yescharacteristic
34C22×D3×D5—26no—
35C22×D3×D5—26no—
36C22×D3×D5Q814yes—
37C22×C3×C4×C5C2313yes—
38C22×Dic15C2313yes—
39C22×C5×Dic3C2313yes—
40C22×C3×Dic5C2313yes—
41C2×C3×C4×D5—212no—
42C2×C3×C4×D5D4112yes—
43C2×D5×Dic3—212no—
44C2×D5×Dic3—26no—
45#6714—26no—
46C4⋊Dic15—26no—
47C5×(C2×D3)⋊C4—26no—
48C5×C4⋊Dic3—26no—
49#6668—212no—
50#6667—26no—
51(C2×D3)⋊Dic5—26no—
52C22×(C2×D3)⋊C4—53no—
53C22×C4⋊Dic3—53no—
54C2×C3×#95—51no—
55#4677—53no—
56#4677—53no—
57#4677—51no—
58#4677D511yescharacteristic, direct product factor
59C24×D5—31no—
60C22×C4×D5—33no—
61C22×C4×D5C2×D313yes—
62C2×C5×C4⋊C4—33no—
63C2×C5×C22⋊C4—33no—
64C2×C22⋊Dic5—33no—
65C2×#685—33no—
66C2×#685—33no—
67C2×C4⋊Dic5—33no—
68C2×#683—36no—
69D5×C4⋊C4—612no—
70D5×C22⋊C4—612no—
71C5×#95C2×D311yescharacteristic, complemented
72#3963C2×D313yescomplemented
73C2×#399—151noSylow
74C23×C3×C5C2411yescharacteristic
75C22×D15—23no—
76C22×D15—23no—
77C22×D15C2×Q812yes—
78C22×C5×D3—23no—
79C22×C5×D3—23no—
80C22×C5×D3C2×Q812yes—
81C22×C3×D5C2×D416yes—
82C22×C3×D5C2×Q812yes—
83C22×C3×D5#4116yes—
84C2×D3×D5—224no—
85C2×D3×D5—412no—
86C2×D3×D5—44no—
87C2×C3×C4×C5—26no—
88C2×C3×C4×C5C2×D416yes—
89C2×Dic15—23no—
90C2×Dic15—26no—
91C2×C5×Dic3—23no—
92C2×C5×Dic3—26no—
93C2×C3×Dic5—26no—
94C2×C3×Dic5C2×D416yes—
95C3×C4×D5—224no—
96D5×Dic3—412no—
97C24×D3—51no—
98C23×C3×C4—53no—
99C23×Dic3—53no—
100C2×(C2×D3)⋊C4—53no—
101C2×(C2×D3)⋊C4—53no—
102C2×(C2×D3)⋊C4—53no—
103C2×(C2×D3)⋊C4—1012no—
104C2×(C2×D3)⋊C4C2×D513yes—
105C2×C4⋊Dic3—53no—
106C2×C4⋊Dic3—56no—
107C2×C4⋊Dic3—1012no—
108C2×C4⋊Dic3C2×D513yescomplemented
109C3×#95—53no—
110C3×#95C2×D511yescharacteristic, complemented
111C24×C5—31no—
112C23×D5—31no—
113C23×D5—34no—
114C23×D5—66no—
115C23×D5—66no—
116C23×D5C22×D311yescharacteristic
117C22×C4×C5—33no—
118C22×C4×C5C22×D313yes—
119C22×Dic5—33no—
120C22×Dic5C22×D313yes—
121C2×C4×D5—212no—
122C2×C4×D5—66no—
123C2×C4×D5—612no—
124C2×C4×D5D12112yes—
125C5×C4⋊C4—66no—
126C5×C22⋊C4—66no—
127C22⋊Dic5—66no—
128#685—66no—
129#685—66no—
130C4⋊Dic5—66no—
131#683—612no—
132C22×C4⋊C4—153no—
133C22×C22⋊C4—153no—
134#399—31no—
135#399—153no—
136#399—153no—
137#399—151no—
138C2×#95—51no—
139C22×C3×C5C22×D413yes—
140C22×C3×C5C22×Q811yescharacteristic
141C22×C3×C5C2×#4113yes—
142C2×D15—26no—
143C2×D15—43no—
144C2×D15—41no—
145C2×C5×D3—26no—
146C2×C5×D3—43no—
147C2×C5×D3—41no—
148C2×C3×D5C22⋊Q8112yes—
149C2×C3×D5#123112yes—
150C2×C3×D5#12714yes—
151D3×D5—416no—
152C3×C4×C5—26no—
153Dic15—43no—
154C3×Dic5—26no—
155C5×Dic3—43no—
156C24×C3—51no—
157C23×D3—51no—
158C23×D3—54no—
159C23×D3—106no—
160C23×D3—106no—
161C23×D3C22×D511yescharacteristic
162C22×C3×C4—53no—
163C22×C3×C4—512no—
164C22×C3×C4—1012no—
165C22×C3×C4C22×D513yes—
166C22×Dic3—53no—
167C22×Dic3—1012no—
168C22×Dic3—106no—
169C22×Dic3C22×D513yes—
170(C2×D3)⋊C4—26no—
171(C2×D3)⋊C4—106no—
172(C2×D3)⋊C4—106no—
173(C2×D3)⋊C4—106no—
174C4⋊Dic3—26no—
175C4⋊Dic3—1012no—
176C4⋊Dic3—106no—
177C23×C5—32no—
178C23×C5—63no—
179C23×C5—63no—
180C23×C5C23×D311yescharacteristic
181C22×D5—32no—
182C22×D5—63no—
183C22×D5—63no—
184C22×D5—624no—
185C22×D5—124no—
186C22×D5—1212no—
187C22×D5C2×D1216yes—
188C22×D5#23716yes—
189C22×D5D3×Q812yes—
190C2×C4×C5—26no—
191C2×C4×C5—66no—
192C2×C4×C5—63no—
193C2×C4×C5C2×D1216yes—
194C2×Dic5—26no—
195C2×Dic5—66no—
196C2×Dic5—63no—
197C2×Dic5C2×D1216yes—
198C4×D5—224no—
199C4×D5—1212no—
200C25—151no—
201C23×C4—53no—
202C23×C4—153no—
203C2×C4⋊C4—33no—
204C2×C4⋊C4—156no—
205C2×C4⋊C4—153no—
206C2×C4⋊C4—3012no—
207C2×C22⋊C4—33no—
208C2×C22⋊C4—153no—
209C2×C22⋊C4—153no—
210C2×C22⋊C4—153no—
211C2×C22⋊C4—3012no—
212#95—53no—
213#95D3×D511yescharacteristic, complemented
214C2×C3×C5C2×C22⋊Q813yes—
215C2×C3×C5C2×#12313yes—
216C2×C3×C5C2×#12711yescharacteristic
217D15—42no—
218C3×D5#39918yescomplemented
219C5×D3—42no—
220C23×C3—56no—
221C23×C3—52no—
222C23×C3—56no—
223C23×C3C23×D511yescharacteristic
224C22×D3—23no—
225C22×D3—23no—
226C22×D3—52no—
227C22×D3—1024no—
228C22×D3—103no—
229C22×D3—103no—
230C22×D3—204no—
231C22×D3—2012no—
232C22×D3Q8×D512yes—
233C2×C3×C4—26no—
234C2×C3×C4—56no—
235C2×C3×C4—1024no—
236C2×C3×C4—106no—
237C2×C3×C4D4×D516yes—
238C2×Dic3—26no—
239C2×Dic3—23no—
240C2×Dic3—106no—
241C2×Dic3—103no—
242C2×Dic3—2012no—
243C22×C5—66no—
244C22×C5—121no—
245C22×C5—123no—
246C22×C5C22×D1213yes—
247C22×C5C2×#23713yes—
248C22×C5C2×D3×Q811yescharacteristic
249C2×D5—66no—
250C2×D5—121no—
251C2×D5—123no—
252C2×D5—1216no—
253C2×D5#87414yes—
254C2×D5#886112yes—
255C2×D5#897112yes—
256C4×C5—26no—
257C4×C5—123no—
258Dic5—26no—
259Dic5—123no—
260C24—31no—
261C24—51no—
262C24—154no—
263C24—151no—
264C24—306no—
265C24—306no—
266C22×C4—33no—
267C22×C4—53no—
268C22×C4—512no—
269C22×C4—1012no—
270C22×C4—153no—
271C22×C4—306no—
272C22×C4—3012no—
273C22×C4C2×D3×D513yes—
274C4⋊C4—66no—
275C4⋊C4—3012no—
276C4⋊C4—306no—
277C22⋊C4—66no—
278C22⋊C4—306no—
279C22⋊C4—306no—
280C22⋊C4—306no—
281C3×C5C2×#39911yescharacteristic, complemented, Hall
282C22×C3—54no—
283C22×C3—512no—
284C22×C3—512no—
285C22×C3C2×D4×D513yes—
286C22×C3C2×Q8×D511yescharacteristic
287C22×C3D5×#4113yes—
288C2×D3—26no—
289C2×D3—41no—
290C2×D3—43no—
291C2×D3—106no—
292C2×D3—2016no—
293C2×D3—201no—
294C2×D3—203no—
295C3×C4—26no—
296C3×C4—106no—
297Dic3—43no—
298Dic3—203no—
299C2×C5—122no—
300C2×C5C2×#87411yescharacteristic
301C2×C5C2×#88613yes—
302C2×C5C2×#89713yes—
303D5—122no—
304D5#467718yesdirect product factor
305C23—32no—
306C23—56no—
307C23—56no—
308C23—52no—
309C23—63no—
310C23—63no—
311C23—152no—
312C23—3024no—
313C23—303no—
314C23—303no—
315C23—604no—
316C23—6012no—
317C23C22×D3×D511yescharacteristic
318C2×C4—26no—
319C2×C4—56no—
320C2×C4—63no—
321C2×C4—66no—
322C2×C4—1024no—
323C2×C4—106no—
324C2×C4—303no—
325C2×C4—306no—
326C2×C4—6012no—
327C2×C4D5×D1216yes—
328C2×C3—58no—
329C2×C3D5×C22⋊Q813yes—
330C2×C3D5×#12313yes—
331C2×C3D5×#12711yescharacteristic
332D3—42no—
333D3—202no—
334C5C2×#467711yescharacteristic, complemented, Sylow
335C22—54no—
336C22—512no—
337C22—512no—
338C22—66no—
339C22—121no—
340C22—123no—
341C22—306no—
342C22—6016no—
343C22—601no—
344C22—603no—
345C22C2×D5×D1213yes—
346C22D5×#23713yes—
347C22D3×Q8×D511yescharacteristic
348C4—26no—
349C4—106no—
350C4—123no—
351C4—603no—
352C3D5×#39911yescharacteristic, complemented, Sylow
353C2—58no—
354C2—122no—
355C2—602no—
356C2D5×#87411yescharacteristic
357C2D5×#88613yes—
358C2D5×#89713yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC3×C5×#95C22
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5C2×#399
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×D5×C4⋊Dic3C2semidirect
3. #11750778C2semidirect
4. C5×#4677C2semidirect
5. C3×D5×#95C2semidirect
6. #11748835C2semidirect
7. #11748762C2semidirect
13. C2×C4⋊Dic15C22semidirect
15. C2×C5×C4⋊Dic3C22semidirect
16. C2×#6668C22semidirect
21. C3×C5×#95C22semidirect
22. C3×#3963C22semidirect
30. D5×#95D3semidirect
58. #4677D5direct (N × H)
71. C5×#95C2×D3semidirect
72. #3963C2×D3semidirect
108. C2×C4⋊Dic3C2×D5semidirect
110. C3×#95C2×D5semidirect
213. #95D3×D5semidirect
218. C3×D5#399semidirect
281. C3×C5C2×#399semidirect
304. D5#4677direct (N × H)
334. C5C2×#4677semidirect
352. C3D5×#399semidirect

Maximal subgroups

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

subgroupindex
C2×D5×(C2×D3)⋊C42
C2×D5×C4⋊Dic32
#117507782
C5×#46772
C3×D5×#952
#117488352
#117487622
D5×#3993
C2×#46775