Finite Group Databasebeta

← #14322332

Subgroups — #14322332

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91758C211yesmaximal, characteristic
2C2×#91333C212yesmaximal
3C5×#4935C211yesmaximal, characteristic
4C3×C42×Dic5C211yesmaximal, characteristic
5#11748841C214yesmaximal
6Dic5×C4⋊Dic3C214yesmaximal
7#11748587C212yesmaximal
8#10606051—31nomaximal, Hall
9C22×Dic30C2212yes—
10C2×C3×C42×C5C2211yescharacteristic
11C2×C4⋊Dic15C2214yes—
12#91758C418yescomplemented
13C2×C5×C4⋊Dic3C2214yes—
14C2×C5×C4⋊Dic3C2212yes—
15C2×C3×C4×Dic5C2212yes—
16C2×C3×C4×Dic5C2211yescharacteristic
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×C3×C4×Dic5C2212yes—
19C2×#6669C2214yes—
20C2×Dic3×Dic5C2214yes—
21#91333—28no—
22#90994C2218yes—
23C4×#869—51nomaximal, Hall
24C2×#4033—32no—
25C2×#4015—31no—
26C5×#384—31no—
27C4⋊C4×Dic5—34no—
28#65263—32no—
29#65262—34no—
30C42×Dic5D311yescharacteristic
31C22×C3×C4×C5C2311yescharacteristic
32C22×C3×C4×C5C2312yes—
33C22×Dic15C2314yes—
34C2×Dic30—24no—
35C2×Dic30—24no—
36C2×Dic30C2×C418yes—
37C22×C5×Dic3C2314yes—
38C22×C3×Dic5C2311yescharacteristic
39C22×C3×Dic5C2312yes—
40C22×C3×Dic5C2311yescharacteristic
41C3×C42×C5C2×C414yes—
42C4⋊Dic15C2×C4116yes—
43C5×C4⋊Dic3—24no—
44C5×C4⋊Dic3—28no—
45C3×C4×Dic5—22no—
46C3×C4×Dic5—24no—
47C3×C4×Dic5D414yes—
48C3×C4×Dic5Q818yescomplemented
49#6669—28no—
50Dic3×Dic5—28no—
51C2×#869—51no—
52C2×C4×Dic6—52no—
53C3×C43—51no—
54#4935D511yescharacteristic
55C4×C4⋊Dic3—54no—
56#4929—52no—
57#4928—54no—
58C22×Dic10—32no—
59C2×C5×C4⋊C4—32no—
60C2×C5×C4⋊C4—34no—
61C2×C42×C5C2×D311yescharacteristic
62C2×C4⋊Dic5—34no—
63C2×#683—34no—
64C2×C4×Dic5—34no—
65C2×C4×Dic5C2×D312yes—
66C2×C4×Dic5C2×D311yescharacteristic
67C2×C4×Dic5C2×D312yes—
68C2×C4×Dic5C2×D311yescharacteristic
69#4033—68no—
70#4015—38no—
71#3963—38no—
72C4×C4⋊Q8—151noSylow
73C23×C3×C5C2411yescharacteristic
74C2×C3×C4×C5C22×C412yes—
75C2×C3×C4×C5C22×C414yes—
76C2×C3×C4×C5C2×D412yes—
77C2×C3×C4×C5C2×Q814yes—
78C2×C3×C4×C5#4112yes—
79C2×C3×C4×C5#4114yes—
80C2×Dic15—24no—
81C2×Dic15—24no—
82C2×Dic15C22×C418yes—
83Dic30—216no—
84C2×C5×Dic3—24no—
85C2×C5×Dic3—28no—
86C2×C3×Dic5—22no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5C2×D412yes—
90C2×C3×Dic5C2×D412yes—
91C2×C3×Dic5C2×Q814yes—
92C2×C3×Dic5C2×Q814yes—
93C22×Dic6—52no—
94C2×C3×C42—52no—
95C2×C3×C42—51no—
96C2×C3×C42—52no—
97C2×C3×C42—51no—
98C2×C3×C42C2×D511yescharacteristic
99C2×C4⋊Dic3—54no—
100C2×C4⋊Dic3C2×D514yes—
101C2×C4⋊Dic3C2×D512yes—
102C2×Dic3⋊C4—54no—
103C2×C4×Dic3—54no—
104#869—58no—
105C4×Dic6—108no—
106C3⋊#95—58no—
107C22×C4×C5—34no—
108C22×C4×C5C22×D312yes—
109C22×C4×C5C22×D311yescharacteristic
110C22×Dic5—34no—
111C22×Dic5C22×D312yes—
112C22×Dic5C22×D311yescharacteristic
113C22×Dic5C22×D311yescharacteristic
114C2×Dic10—38no—
115C2×Dic10—64no—
116C2×Dic10—64no—
117C5×C4⋊C4—64no—
118C5×C4⋊C4—68no—
119C42×C5C4×D314yes—
120C4⋊Dic5—316no—
121#683—68no—
122C4×Dic5—24no—
123C4×Dic5—22no—
124C4×Dic5—68no—
125C4×Dic5Dic618yescomplemented
126C4×Dic5D1214yes—
127C2×C4⋊Q8—151no—
128C2×C4×Q8—152no—
129#391—152no—
130#389—154no—
131#384—31no—
132C4×C4⋊C4—154no—
133C43—51no—
134C22×C3×C5C23×C411yescharacteristic
135C22×C3×C5C22×D411yescharacteristic
136C22×C3×C5C22×Q812yes—
137C22×C3×C5C2×#4112yes—
138C22×C3×C5C2×#4111yescharacteristic
139C3×C4×C5C4×D414yes—
140C3×C4×C5C4×Q818yescomplemented
141Dic15—28no—
142C3×Dic5—22no—
143C3×Dic5—24no—
144C3×Dic5C4⋊Q814yescomplemented
145C5×Dic3—44no—
146C22×C3×C4—51no—
147C22×C3×C4—52no—
148C22×C3×C4—51no—
149C22×C3×C4C22×D511yescharacteristic
150C22×C3×C4C22×D512yes—
151C22×Dic3—54no—
152C22×Dic3C22×D514yes—
153C2×Dic6—58no—
154C2×Dic6—104no—
155C2×Dic6—104no—
156C3×C42—54no—
157C3×C42—58no—
158C3×C42—104no—
159C3×C42—102no—
160C3×C42C4×D514yes—
161C4⋊Dic3—24no—
162C4⋊Dic3—28no—
163C4⋊Dic3—516no—
164Dic3⋊C4—108no—
165C4×Dic3—108no—
166C23×C5C23×D311yescharacteristic
167C2×C4×C5—64no—
168C2×C4×C5—68no—
169C2×C4×C5C2×Dic614yes—
170C2×C4×C5C2×C4×D314yes—
171C2×C4×C5C2×C4×D312yes—
172C2×C4×C5C2×D1212yes—
173C2×C4×C5#23514yes—
174C2×C4×C5#23512yes—
175C2×Dic5—22no—
176C2×Dic5—22no—
177C2×Dic5—22no—
178C2×Dic5—38no—
179C2×Dic5—64no—
180C2×Dic5—64no—
181C2×Dic5C2×Dic614yes—
182C2×Dic5C2×Dic614yes—
183C2×Dic5C2×D1212yes—
184C2×Dic5C2×D1212yes—
185Dic10—616no—
186C22×Q8—152no—
187C4⋊Q8—158no—
188C4×Q8—308no—
189C2×C4⋊C4—32no—
190C2×C4⋊C4—34no—
191C2×C4⋊C4—154no—
192C2×C4⋊C4—154no—
193C2×C42—51no—
194C2×C42—52no—
195C2×C42—52no—
196C2×C42—51no—
197C2×C42—154no—
198C2×C42D3×D511yescharacteristic
199#95—158no—
200C2×C3×C5C2×C4×D411yescharacteristic
201C2×C3×C5C2×C4×Q812yes—
202C2×C3×C5C2×C4⋊Q811yescharacteristic
203C2×C3×C5#53211yescharacteristic
204C2×C3×C5#53312yes—
205C23×C3C23×D511yescharacteristic
206C2×C3×C4—52no—
207C2×C3×C4—54no—
208C2×C3×C4—52no—
209C2×C3×C4—54no—
210C2×C3×C4—102no—
211C2×C3×C4—102no—
212C2×C3×C4—102no—
213C2×C3×C4C2×C4×D514yes—
214C2×C3×C4C2×C4×D512yes—
215C2×C3×C4D4×D512yes—
216C2×C3×C4#71114yes—
217C2×C3×C4Q8×D514yes—
218C2×C3×C4#71312yes—
219C2×Dic3—24no—
220C2×Dic3—28no—
221C2×Dic3—58no—
222C2×Dic3—104no—
223C2×Dic3—104no—
224Dic6—1016no—
225C22×C5C22×Dic612yes—
226C22×C5C22×C4×D311yescharacteristic
227C22×C5C22×D1211yescharacteristic
228C22×C5C2×#23512yes—
229C22×C5C2×#23511yescharacteristic
230C4×C5—124no—
231C4×C5C4×Dic618yescomplemented
232C4×C5C4×D1214yes—
233Dic5—24no—
234Dic5—22no—
235Dic5—68no—
236Dic5#86914yescomplemented
237C2×Q8—158no—
238C2×Q8—304no—
239C2×Q8—304no—
240C22×C4—34no—
241C22×C4—51no—
242C22×C4—52no—
243C22×C4—51no—
244C22×C4—154no—
245C22×C4C2×D3×D512yes—
246C22×C4C2×D3×D511yescharacteristic
247C4⋊C4—68no—
248C4⋊C4—64no—
249C4⋊C4—1516no—
250C4⋊C4—308no—
251C42—58no—
252C42—54no—
253C42—104no—
254C42—102no—
255C42—308no—
256C42#120014yes—
257C3×C5C4×C4⋊Q811yescharacteristic, complemented, Hall
258C22×C3C22×C4×D511yescharacteristic
259C22×C3C2×D4×D511yescharacteristic
260C22×C3C2×#71112yes—
261C22×C3C2×Q8×D512yes—
262C22×C3C2×#71311yescharacteristic
263C3×C4—54no—
264C3×C4—102no—
265C3×C4—104no—
266C3×C4#403318yescomplemented
267C3×C4#403914yes—
268Dic3—44no—
269Dic3—108no—
270C2×C5C2×C4×Dic612yes—
271C2×C5C2×#86911yescharacteristic
272C2×C5#547012yes—
273C2×C5C2×C4×D1211yescharacteristic
274C2×C5#547711yescharacteristic
275C23C22×D3×D511yescharacteristic
276Q8—3016no—
277C2×C4—54no—
278C2×C4—52no—
279C2×C4—54no—
280C2×C4—52no—
281C2×C4—68no—
282C2×C4—64no—
283C2×C4—102no—
284C2×C4—102no—
285C2×C4—102no—
286C2×C4—158no—
287C2×C4—304no—
288C2×C4—304no—
289C2×C4D5×Dic614yes—
290C2×C4#677214yes—
291C2×C4#677312yes—
292C2×C4D5×D1212yes—
293C2×C4C2×#120012yes—
294C2×C4C2×#120014yes—
295C2×C3C2×#403312yes—
296C2×C3C2×#403911yescharacteristic
297C2×C3#6605011yescharacteristic
298C2×C3D5×C4⋊Q811yescharacteristic
299C2×C3#6606212yes—
300C5C4×#86911yescharacteristic, complemented, Sylow
301C22C2×D5×Dic612yes—
302C22C2×#677212yes—
303C22C2×#677311yescharacteristic
304C22C2×D5×D1211yescharacteristic
305C22C22×#120011yescharacteristic
306C4—54no—
307C4—104no—
308C4—102no—
309C4—124no—
310C4—308no—
311C4#9133318yescomplemented
312C4#9141814yes—
313C3#1060605111yescharacteristic, complemented, Sylow
314C2#1175250612yes—
315C2D5×#86911yescharacteristic
316C2#1175267211yescharacteristic
317C2C2×#9133312yes—
318C2C2×#9141811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×C4⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
12. #91758C4semidirect
48. C3×C4×Dic5Q8semidirect
125. C4×Dic5Dic6semidirect
140. C3×C4×C5C4×Q8semidirect
144. C3×Dic5C4⋊Q8semidirect
231. C4×C5C4×Dic6semidirect
236. Dic5#869semidirect
257. C3×C5C4×C4⋊Q8semidirect
266. C3×C4#4033semidirect
300. C5C4×#869semidirect
311. C4#91333semidirect
313. C3#10606051semidirect

Maximal subgroups

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

subgroupindex
C2×#917582
C2×#913332
C5×#49352
C3×C42×Dic52
#117488412
Dic5×C4⋊Dic32
#117485872
#106060513
C4×#8695