Finite Group Databasebeta

← D5×#4676 #14331715

Subgroups — D5×#4676 #14331715

Order 1920.

1816 conjugacy classes of subgroups; only the 304 normal subgroups are shown.

normal subgroups only

This group has 1816 conjugacy classes of subgroups — too many to draw. Only its 304 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×(C2×D3)⋊C4C213yesmaximal
2C2×D5×Dic3⋊C4C213yesmaximal, complemented
3#11750777C211yesmaximal, characteristic, complemented
4C5×#4676C211yesmaximal, characteristic, complemented
5C3×D5×#95C211yesmaximal, characteristic, complemented
6#11748855C213yesmaximal, complemented
7#11748781C213yesmaximal, complemented
8D5×#396—31nomaximal, Hall
9C23×D3×D5C2211yescharacteristic
10C22×C3×C4×D5C2213yes—
11C22×D5×Dic3C2213yes—
12C2×#6714C2213yes—
13C2×#6712C2213yescomplemented
14C2×C5×(C2×D3)⋊C4C2213yes—
15C2×C5×Dic3⋊C4C2213yescomplemented
16C2×Dic3⋊Dic5C2213yescomplemented
17C2×#6669C2213yescomplemented
18C2×#6667C2213yes—
19C2×(C2×D3)⋊Dic5C2213yes—
20D5×(C2×D3)⋊C4—212no—
21D5×Dic3⋊C4—212no—
22C3×C5×#95C2211yescharacteristic, complemented
23C3×#3963C2213yescomplemented
24C2×#4676—51nomaximal, Hall
25C2×D5×C4⋊C4—33no—
26C2×D5×C22⋊C4—33no—
27C5×#396—31no—
28#65283—33no—
29#65237—33no—
30#64965—31no—
31D5×#95D311yescharacteristic, complemented
32C23×D15C2311yescharacteristic
33C23×C5×D3C2311yescharacteristic
34C23×C3×D5C2311yescharacteristic
35C22×D3×D5—26no—
36C22×D3×D5—26no—
37C22×D3×D5Q814yes—
38C22×C3×C4×C5C2313yes—
39C22×Dic15C2313yes—
40C22×C5×Dic3C2313yes—
41C22×C3×Dic5C2313yes—
42C2×C3×C4×D5—26no—
43C2×C3×C4×D5—26no—
44C2×C3×C4×D5—26no—
45C2×D5×Dic3—26no—
46C2×D5×Dic3—26no—
47C2×D5×Dic3D4112yes—
48#6714—26no—
49#6712—26no—
50C5×(C2×D3)⋊C4—26no—
51C5×Dic3⋊C4—26no—
52Dic3⋊Dic5—26no—
53#6669—26no—
54#6667—26no—
55(C2×D3)⋊Dic5—26no—
56C22×(C2×D3)⋊C4—53no—
57C22×Dic3⋊C4—53no—
58C2×C3×#95—51no—
59#4676—53no—
60#4676—53no—
61#4676—51no—
62#4676D511yescharacteristic, direct product factor
63C24×D5—31no—
64C22×C4×D5—33no—
65C22×C4×D5C2×D313yes—
66C2×C5×C4⋊C4—33no—
67C2×C5×C22⋊C4—33no—
68C2×C22⋊Dic5—33no—
69C2×#685—33no—
70C2×#685—33no—
71C2×C4⋊Dic5—33no—
72C2×#683—33no—
73C2×#683—33no—
74D5×C4⋊C4—612no—
75D5×C22⋊C4—612no—
76C5×#95C2×D311yescharacteristic, complemented
77#3963C2×D313yescomplemented
78C2×#396—151noSylow
79C23×C3×C5C2411yescharacteristic
80C22×D15—23no—
81C22×D15—23no—
82C22×D15C2×Q812yes—
83C22×C5×D3—23no—
84C22×C5×D3—23no—
85C22×C5×D3C2×Q812yes—
86C22×C3×D5C2×D416yes—
87C22×C3×D5C2×Q812yes—
88C22×C3×D5#4116yes—
89C2×D3×D5—224no—
90C2×D3×D5—412no—
91C2×D3×D5—44no—
92C2×C3×C4×C5—23no—
93C2×C3×C4×C5—23no—
94C2×C3×C4×C5—23no—
95C2×Dic15—23no—
96C2×Dic15—23no—
97C2×Dic15C2×D416yes—
98C2×C5×Dic3—23no—
99C2×C5×Dic3—23no—
100C2×C5×Dic3C2×D416yes—
101C2×C3×Dic5—23no—
102C2×C3×Dic5—23no—
103C2×C3×Dic5—23no—
104C3×C4×D5—412no—
105D5×Dic3—224no—
106C24×D3—51no—
107C23×C3×C4—53no—
108C23×Dic3—53no—
109C2×(C2×D3)⋊C4—53no—
110C2×(C2×D3)⋊C4—53no—
111C2×(C2×D3)⋊C4—53no—
112C2×(C2×D3)⋊C4—1012no—
113C2×(C2×D3)⋊C4C2×D513yes—
114C2×Dic3⋊C4—53no—
115C2×Dic3⋊C4—53no—
116C2×Dic3⋊C4—53no—
117C2×Dic3⋊C4—1012no—
118C2×Dic3⋊C4C2×D513yescomplemented
119C3×#95—53no—
120C3×#95C2×D511yescharacteristic, complemented
121C24×C5—31no—
122C23×D5—31no—
123C23×D5—34no—
124C23×D5—66no—
125C23×D5—66no—
126C23×D5C22×D311yescharacteristic
127C22×C4×C5—33no—
128C22×C4×C5C22×D313yes—
129C22×Dic5—33no—
130C22×Dic5C22×D313yes—
131C2×C4×D5—26no—
132C2×C4×D5—26no—
133C2×C4×D5—26no—
134C2×C4×D5—312no—
135C2×C4×D5—66no—
136C2×C4×D5—66no—
137C5×C4⋊C4—66no—
138C5×C22⋊C4—66no—
139C22⋊Dic5—66no—
140#685—66no—
141#685—66no—
142C4⋊Dic5—66no—
143#683—66no—
144#683—66no—
145C22×C4⋊C4—153no—
146C22×C22⋊C4—153no—
147#396—31no—
148#396—153no—
149#396—153no—
150#396—151no—
151C2×#95—51no—
152C22×C3×C5C22×D413yes—
153C22×C3×C5C22×Q811yescharacteristic
154C22×C3×C5C2×#4113yes—
155C2×D15—26no—
156C2×D15—43no—
157C2×D15—41no—
158C2×C5×D3—26no—
159C2×C5×D3—43no—
160C2×C5×D3—41no—
161C2×C3×D5#121112yes—
162C2×C3×D5C22⋊Q8112yes—
163C2×C3×D5#12614yes—
164D3×D5—416no—
165C3×C4×C5—43no—
166Dic15—26no—
167C3×Dic5—43no—
168C5×Dic3—26no—
169C24×C3—51no—
170C23×D3—51no—
171C23×D3—54no—
172C23×D3—106no—
173C23×D3—106no—
174C23×D3C22×D511yescharacteristic
175C22×C3×C4—53no—
176C22×C3×C4—106no—
177C22×C3×C4—106no—
178C22×C3×C4—106no—
179C22×C3×C4C22×D513yes—
180C22×Dic3—53no—
181C22×Dic3—512no—
182C22×Dic3—106no—
183C22×Dic3—106no—
184C22×Dic3C22×D513yes—
185(C2×D3)⋊C4—26no—
186(C2×D3)⋊C4—106no—
187(C2×D3)⋊C4—106no—
188(C2×D3)⋊C4—106no—
189Dic3⋊C4—26no—
190Dic3⋊C4—106no—
191Dic3⋊C4—106no—
192Dic3⋊C4—106no—
193C23×C5—32no—
194C23×C5—63no—
195C23×C5—63no—
196C23×C5C23×D311yescharacteristic
197C22×D5—32no—
198C22×D5—63no—
199C22×D5—63no—
200C22×D5—624no—
201C22×D5—124no—
202C22×D5—1212no—
203C22×D5#23516yes—
204C22×D5D3×D416yes—
205C22×D5D3×Q812yes—
206C2×C4×C5—23no—
207C2×C4×C5—23no—
208C2×C4×C5—23no—
209C2×C4×C5—36no—
210C2×C4×C5—63no—
211C2×C4×C5—63no—
212C2×Dic5—23no—
213C2×Dic5—23no—
214C2×Dic5—23no—
215C2×Dic5—36no—
216C2×Dic5—63no—
217C2×Dic5—63no—
218C4×D5—412no—
219C4×D5—624no—
220C25—151no—
221C23×C4—53no—
222C23×C4—153no—
223C2×C4⋊C4—33no—
224C2×C4⋊C4—153no—
225C2×C4⋊C4—153no—
226C2×C4⋊C4—153no—
227C2×C4⋊C4—3012no—
228C2×C22⋊C4—33no—
229C2×C22⋊C4—153no—
230C2×C22⋊C4—153no—
231C2×C22⋊C4—153no—
232C2×C22⋊C4—3012no—
233#95—53no—
234#95D3×D511yescharacteristic, complemented
235C2×C3×C5C2×#12113yes—
236C2×C3×C5C2×C22⋊Q813yes—
237C2×C3×C5C2×#12611yescharacteristic
238D15—42no—
239C3×D5#39618yescomplemented
240C5×D3—42no—
241C23×C3—56no—
242C23×C3—52no—
243C23×C3—56no—
244C23×C3C23×D511yescharacteristic
245C22×D3—23no—
246C22×D3—23no—
247C22×D3—52no—
248C22×D3—1024no—
249C22×D3—103no—
250C22×D3—103no—
251C22×D3—2012no—
252C22×D3—204no—
253C22×D3Q8×D512yes—
254C2×C3×C4—23no—
255C2×C3×C4—23no—
256C2×C3×C4—23no—
257C2×C3×C4—103no—
258C2×C3×C4—103no—
259C2×C3×C4—103no—
260C2×C3×C4—2012no—
261C2×Dic3—23no—
262C2×Dic3—23no—
263C2×Dic3—56no—
264C2×Dic3—1024no—
265C2×Dic3—103no—
266C2×Dic3—103no—
267C2×Dic3D4×D516yes—
268C22×C5—66no—
269C22×C5—121no—
270C22×C5—123no—
271C22×C5C2×#23513yes—
272C22×C5C2×D3×D413yes—
273C22×C5C2×D3×Q811yescharacteristic
274C2×D5—66no—
275C2×D5—121no—
276C2×D5—123no—
277C2×D5—1216no—
278C2×D5#87614yes—
279C2×D5#884112yes—
280C2×D5#896112yes—
281C4×C5—43no—
282C4×C5—66no—
283Dic5—43no—
284Dic5—66no—
285C24—31no—
286C24—51no—
287C24—154no—
288C24—151no—
289C24—306no—
290C24—306no—
291C22×C4—33no—
292C22×C4—53no—
293C22×C4—106no—
294C22×C4—106no—
295C22×C4—106no—
296C22×C4—1512no—
297C22×C4—153no—
298C22×C4—306no—
299C22×C4—306no—
300C22×C4C2×D3×D513yes—
301C4⋊C4—66no—
302C4⋊C4—306no—
303C4⋊C4—306no—
304C4⋊C4—306no—
305C22⋊C4—66no—
306C22⋊C4—306no—
307C22⋊C4—306no—
308C22⋊C4—306no—
309C3×C5C2×#39611yescharacteristic, complemented, Hall
310C22×C3—512no—
311C22×C3—512no—
312C22×C3—54no—
313C22×C3C2×D4×D513yes—
314C22×C3C2×Q8×D511yescharacteristic
315C22×C3D5×#4113yes—
316C2×D3—26no—
317C2×D3—43no—
318C2×D3—41no—
319C2×D3—106no—
320C2×D3—2016no—
321C2×D3—203no—
322C2×D3—201no—
323C3×C4—43no—
324C3×C4—203no—
325Dic3—26no—
326Dic3—106no—
327C2×C5—122no—
328C2×C5C2×#87611yescharacteristic
329C2×C5C2×#88413yes—
330C2×C5C2×#89613yes—
331D5—122no—
332D5#467618yesdirect product factor
333C23—32no—
334C23—56no—
335C23—56no—
336C23—52no—
337C23—63no—
338C23—63no—
339C23—152no—
340C23—3024no—
341C23—303no—
342C23—303no—
343C23—604no—
344C23—6012no—
345C23C22×D3×D511yescharacteristic
346C2×C4—23no—
347C2×C4—23no—
348C2×C4—23no—
349C2×C4—36no—
350C2×C4—63no—
351C2×C4—63no—
352C2×C4—103no—
353C2×C4—103no—
354C2×C4—103no—
355C2×C4—156no—
356C2×C4—2012no—
357C2×C4—3024no—
358C2×C4—303no—
359C2×C4—303no—
360C2×C3—58no—
361C2×C3D5×#12113yes—
362C2×C3D5×C22⋊Q813yes—
363C2×C3D5×#12611yescharacteristic
364D3—42no—
365D3—202no—
366C5C2×#467611yescharacteristic, complemented, Sylow
367C22—54no—
368C22—512no—
369C22—512no—
370C22—66no—
371C22—121no—
372C22—123no—
373C22—306no—
374C22—6016no—
375C22—601no—
376C22—603no—
377C22D5×#23513yes—
378C22D3×D4×D513yes—
379C22D3×Q8×D511yescharacteristic
380C4—43no—
381C4—66no—
382C4—203no—
383C4—306no—
384C3D5×#39611yescharacteristic, complemented, Sylow
385C2—58no—
386C2—122no—
387C2—602no—
388C2D5×#87611yescharacteristic
389C2D5×#88413yes—
390C2D5×#89613yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC3×C5×#95C22
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5C2×#396
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×Dic3⋊C4C2semidirect
3. #11750777C2semidirect
4. C5×#4676C2semidirect
5. C3×D5×#95C2semidirect
6. #11748855C2semidirect
7. #11748781C2semidirect
13. C2×#6712C22semidirect
15. C2×C5×Dic3⋊C4C22semidirect
16. C2×Dic3⋊Dic5C22semidirect
17. C2×#6669C22semidirect
22. C3×C5×#95C22semidirect
23. C3×#3963C22semidirect
31. D5×#95D3semidirect
62. #4676D5direct (N × H)
76. C5×#95C2×D3semidirect
77. #3963C2×D3semidirect
118. C2×Dic3⋊C4C2×D5semidirect
120. C3×#95C2×D5semidirect
234. #95D3×D5semidirect
239. C3×D5#396semidirect
309. C3×C5C2×#396semidirect
332. D5#4676direct (N × H)
366. C5C2×#4676semidirect
384. C3D5×#396semidirect

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×Dic3⋊C42
#117507772
C5×#46762
C3×D5×#952
#117488552
#117487812
D5×#3963
C2×#46765