Finite Group Databasebeta

← #14332020

Subgroups — #14332020

Order 1920.

1816 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 1816 conjugacy classes of subgroups — too many to draw. Only its 268 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×#91473C213yesmaximal
2C2×#91437C213yesmaximal, complemented
3D15×#95C211yesmaximal, characteristic, complemented
4C5×#4677C211yesmaximal, characteristic, complemented
5C3×#64966C211yesmaximal, characteristic, complemented
6#11748798C213yesmaximal, complemented
7#11748792C213yesmaximal, complemented
8D5×#399—31nomaximal, Hall
9C23×D3×D5C2211yescharacteristic
10C22×C4×D15C2213yes—
11C22×#1200C2213yes—
12C2×C5×(C2×D3)⋊C4C2213yes—
13C2×C5×C4⋊Dic3C2213yescomplemented
14C2×C3×#685C2213yes—
15C2×C3×C4⋊Dic5C2213yescomplemented
16C2×#6669C2216yescomplemented
17C2×(C2×D3)⋊Dic5C2213yes—
18C2×#6665C2213yes—
19#91473—212no—
20#91437—212no—
21C3×C5×#95C2211yescharacteristic, complemented
22#91115C2213yescomplemented
23D3×#399—51nomaximal, Hall
24C2×D5×C4⋊C4—33no—
25C2×D5×C22⋊C4—33no—
26C5×#399—31no—
27#65281—33no—
28#65238—33no—
29#64966D311yescharacteristic, complemented
30D5×#95—31no—
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—
39C2×C4×D15—212no—
40C2×C4×D15D4112yes—
41C22×C5×Dic3C2313yes—
42C22×C3×Dic5C2313yes—
43C2×#1200—212no—
44C2×#1200—26no—
45C5×(C2×D3)⋊C4—26no—
46C5×C4⋊Dic3—26no—
47C3×#685—26no—
48C3×C4⋊Dic5—26no—
49#6669—212no—
50(C2×D3)⋊Dic5—26no—
51#6665—26no—
52C2×D3×C4⋊C4—53no—
53C2×D3×C22⋊C4—53no—
54C3×#399—51no—
55#4993—53no—
56#4949—53no—
57#4677D511yescharacteristic, complemented
58D3×#95—51no—
59C24×D5—31no—
60C22×C4×D5—33no—
61C22×C4×D5—33no—
62C2×C5×C4⋊C4—33no—
63C2×C5×C22⋊C4—33no—
64C2×C22⋊Dic5—33no—
65C2×#685—33no—
66C2×#685C2×D313yes—
67C2×C4⋊Dic5C2×D313yescomplemented
68C2×#683—36no—
69D5×C4⋊C4—612no—
70D5×C22⋊C4—612no—
71C5×#95C2×D311yescharacteristic, complemented
72#3963—33no—
73C2×#399—151noSylow
74C23×C3×C5C2411yescharacteristic
75C22×D15C2×D416yes—
76C22×D15C2×Q812yes—
77C22×D15#4116yes—
78C22×C5×D3—23no—
79C22×C5×D3—23no—
80C22×C5×D3C2×Q812yes—
81C22×C3×D5—23no—
82C22×C3×D5—23no—
83C22×C3×D5C2×Q812yes—
84C2×D3×D5—224no—
85C2×D3×D5—412no—
86C2×D3×D5—44no—
87C2×C3×C4×C5—26no—
88C2×C3×C4×C5C2×D416yes—
89C2×Dic15—26no—
90C2×Dic15C2×D416yes—
91C4×D15—224no—
92C2×C5×Dic3—23no—
93C2×C5×Dic3—26no—
94C2×C3×Dic5—23no—
95C2×C3×Dic5—26no—
96#1200—412no—
97C24×D3—51no—
98C22×C4×D3—53no—
99C22×C4×D3—53no—
100C2×C3×C4⋊C4—53no—
101C2×C3×C22⋊C4—53no—
102C2×#217—53no—
103C2×(C2×D3)⋊C4—53no—
104C2×(C2×D3)⋊C4C2×D513yes—
105C2×C4⋊Dic3C2×D513yescomplemented
106C2×Dic3⋊C4—56no—
107D3×C4⋊C4—1012no—
108D3×C22⋊C4—1012no—
109C3×#95C2×D511yescharacteristic, complemented
110C3⋊#95—53no—
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—312no—
122C2×C4×D5—612no—
123C2×C4×D5—66no—
124C2×C4×D5—612no—
125C5×C4⋊C4—66no—
126C5×C22⋊C4—66no—
127C22⋊Dic5—66no—
128#685—26no—
129#685—66no—
130C4⋊Dic5—26no—
131#683—612no—
132C22×C4⋊C4—153no—
133C22×C22⋊C4—153no—
134#399—31no—
135#399—51no—
136#399—153no—
137#399—153no—
138C2×#95—151no—
139C22×C3×C5C22×D413yes—
140C22×C3×C5C22×Q811yescharacteristic
141C22×C3×C5C2×#4113yes—
142C2×D15C22⋊Q8112yes—
143C2×D15#123112yes—
144C2×D15#12714yes—
145C2×C5×D3—26no—
146C2×C5×D3—43no—
147C2×C5×D3—41no—
148C2×C3×D5—26no—
149C2×C3×D5—43no—
150C2×C3×D5—41no—
151D3×D5—416no—
152C3×C4×C5—26no—
153Dic15—26no—
154C3×Dic5—43no—
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×C4C22×D513yes—
164C22×Dic3—53no—
165C22×Dic3C22×D513yes—
166C2×C4×D3—512no—
167C2×C4×D3—1012no—
168C2×C4×D3—106no—
169C2×C4×D3—1012no—
170C3×C4⋊C4—106no—
171C3×C22⋊C4—106no—
172#217—106no—
173(C2×D3)⋊C4—26no—
174(C2×D3)⋊C4—106no—
175C4⋊Dic3—26no—
176Dic3⋊C4—1012no—
177C23×C5—32no—
178C23×C5—63no—
179C23×C5—63no—
180C23×C5C23×D311yescharacteristic
181C22×D5—23no—
182C22×D5—23no—
183C22×D5—36no—
184C22×D5—32no—
185C22×D5—36no—
186C22×D5—624no—
187C22×D5—1212no—
188C22×D5—124no—
189C22×D5D3×Q812yes—
190C2×C4×C5—26no—
191C2×C4×C5—66no—
192C2×C4×C5—63no—
193C2×C4×C5D3×D416yes—
194C2×Dic5—26no—
195C2×Dic5—23no—
196C2×Dic5—36no—
197C2×Dic5—66no—
198C4×D5—624no—
199C4×D5—1212no—
200C25—151no—
201C23×C4—153no—
202C23×C4—153no—
203C2×C4⋊C4—33no—
204C2×C4⋊C4—53no—
205C2×C4⋊C4—156no—
206C2×C4⋊C4—3012no—
207C2×C22⋊C4—33no—
208C2×C22⋊C4—53no—
209C2×C22⋊C4—153no—
210C2×C22⋊C4—153no—
211C2×C22⋊C4—3012no—
212#95—153no—
213#95D3×D511yescharacteristic, complemented
214C2×C3×C5C2×C22⋊Q813yes—
215C2×C3×C5C2×#12313yes—
216C2×C3×C5C2×#12711yescharacteristic
217D15#39918yescomplemented
218C3×D5—42no—
219C5×D3—42no—
220C23×C3—52no—
221C23×C3—103no—
222C23×C3—103no—
223C23×C3C23×D511yescharacteristic
224C22×D3—23no—
225C22×D3—23no—
226C22×D3—56no—
227C22×D3—52no—
228C22×D3—56no—
229C22×D3—1024no—
230C22×D3—204no—
231C22×D3—2012no—
232C22×D3Q8×D512yes—
233C2×C3×C4—26no—
234C2×C3×C4—106no—
235C2×C3×C4—103no—
236C2×C3×C4D4×D516yes—
237C2×Dic3—26no—
238C2×Dic3—23no—
239C2×Dic3—56no—
240C2×Dic3—106no—
241C4×D3—1024no—
242C4×D3—2012no—
243C22×C5—66no—
244C22×C5—123no—
245C22×C5—121no—
246C22×C5C2×D3×D413yes—
247C22×C5C2×D3×Q811yescharacteristic
248C22×C5D3×#4113yes—
249C2×D5—26no—
250C2×D5—312no—
251C2×D5—34no—
252C2×D5—312no—
253C2×D5—43no—
254C2×D5—41no—
255C2×D5—1216no—
256C4×C5—26no—
257C4×C5—123no—
258Dic5—43no—
259Dic5—66no—
260C24—31no—
261C24—51no—
262C24—154no—
263C24—151no—
264C24—306no—
265C24—306no—
266C22×C4—33no—
267C22×C4—53no—
268C22×C4—153no—
269C22×C4—1512no—
270C22×C4—3012no—
271C22×C4—306no—
272C22×C4—3012no—
273C22×C4C2×D3×D513yes—
274C4⋊C4—66no—
275C4⋊C4—106no—
276C4⋊C4—3012no—
277C22⋊C4—66no—
278C22⋊C4—106no—
279C22⋊C4—306no—
280C22⋊C4—306no—
281C3×C5C2×#39911yescharacteristic, complemented, Hall
282C22×C3—106no—
283C22×C3—201no—
284C22×C3—203no—
285C22×C3C2×D4×D513yes—
286C22×C3C2×Q8×D511yescharacteristic
287C22×C3D5×#4113yes—
288C2×D3—26no—
289C2×D3—41no—
290C2×D3—43no—
291C2×D3—54no—
292C2×D3—512no—
293C2×D3—512no—
294C2×D3—2016no—
295C3×C4—26no—
296C3×C4—203no—
297Dic3—43no—
298Dic3—106no—
299C2×C5—122no—
300C2×C5D3×C22⋊Q813yes—
301C2×C5D3×#12313yes—
302C2×C5D3×#12711yescharacteristic
303D5—38no—
304D5—42no—
305C23—32no—
306C23—52no—
307C23—63no—
308C23—63no—
309C23—103no—
310C23—103no—
311C23—156no—
312C23—156no—
313C23—152no—
314C23—3024no—
315C23—604no—
316C23—6012no—
317C23C22×D3×D511yescharacteristic
318C2×C4—26no—
319C2×C4—63no—
320C2×C4—66no—
321C2×C4—103no—
322C2×C4—106no—
323C2×C4—156no—
324C2×C4—3024no—
325C2×C4—306no—
326C2×C4—6012no—
327C2×C4#677716yes—
328C2×C3—202no—
329C2×C3D5×C22⋊Q813yes—
330C2×C3D5×#12313yes—
331C2×C3D5×#12711yescharacteristic
332D3—42no—
333D3—58no—
334C5D3×#39911yescharacteristic, complemented, Sylow
335C22—66no—
336C22—106no—
337C22—121no—
338C22—123no—
339C22—154no—
340C22—1512no—
341C22—1512no—
342C22—201no—
343C22—203no—
344C22—6016no—
345C22C2×#677713yes—
346C22#9202413yes—
347C22D3×Q8×D511yescharacteristic
348C4—26no—
349C4—123no—
350C4—203no—
351C4—306no—
352C3D5×#39911yescharacteristic, complemented, Sylow
353C2—122no—
354C2—158no—
355C2—202no—
356C2#1175275011yescharacteristic
357C2#1175327413yes—
358C2#1175388413yes—
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×#91437C2semidirect
3. D15×#95C2semidirect
4. C5×#4677C2semidirect
5. C3×#64966C2semidirect
6. #11748798C2semidirect
7. #11748792C2semidirect
13. C2×C5×C4⋊Dic3C22semidirect
15. C2×C3×C4⋊Dic5C22semidirect
16. C2×#6669C22semidirect
21. C3×C5×#95C22semidirect
22. #91115C22semidirect
29. #64966D3semidirect
57. #4677D5semidirect
67. C2×C4⋊Dic5C2×D3semidirect
71. C5×#95C2×D3semidirect
105. C2×C4⋊Dic3C2×D5semidirect
109. C3×#95C2×D5semidirect
213. #95D3×D5semidirect
217. D15#399semidirect
281. C3×C5C2×#399semidirect
334. C5D3×#399semidirect
352. C3D5×#399semidirect

Maximal subgroups

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

subgroupindex
C2×#914732
C2×#914372
D15×#952
C5×#46772
C3×#649662
#117487982
#117487922
D5×#3993
D3×#3995