Finite Group Databasebeta

← #14322334

Subgroups — #14322334

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×#91340C212yesmaximal
3C42×C5×Dic3C211yesmaximal, characteristic
4C3×#65224C211yesmaximal, characteristic
5#11748858C214yesmaximal
6Dic3×C4⋊Dic5C214yesmaximal
7#11748599C212yesmaximal
8C4×#4015—31nomaximal, Hall
9C22×Dic30C2212yes—
10C2×C3×C42×C5C2211yescharacteristic
11C2×C4⋊Dic15C2214yes—
12#91758C418yescomplemented
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C4×C5×Dic3C2212yes—
15C2×C4×C5×Dic3C2211yescharacteristic
16C2×C4×C5×Dic3C2212yes—
17C2×C3×C4⋊Dic5C2214yes—
18C2×C3×C4⋊Dic5C2212yes—
19C2×#6669C2214yes—
20C2×Dic3×Dic5C2214yes—
21#91340—28no—
22#90994C2218yes—
23#74320—51nomaximal, Hall
24C2×#4015—31no—
25C2×C4×Dic10—32no—
26C43×C5—31no—
27#65224D311yescharacteristic
28C4×C4⋊Dic5—34no—
29#65218—32no—
30#65217—34no—
31C22×C3×C4×C5C2311yescharacteristic
32C22×C3×C4×C5C2312yes—
33C22×Dic15C2314yes—
34C2×Dic30—24no—
35C2×Dic30—24no—
36C2×Dic30C2×C418yes—
37C22×C5×Dic3C2311yescharacteristic
38C22×C5×Dic3C2312yes—
39C22×C5×Dic3C2311yescharacteristic
40C22×C3×Dic5C2314yes—
41C3×C42×C5C2×C414yes—
42C4⋊Dic15C2×C4116yes—
43C4×C5×Dic3—24no—
44C4×C5×Dic3—22no—
45C4×C5×Dic3D414yes—
46C4×C5×Dic3Q818yescomplemented
47C3×C4⋊Dic5—24no—
48C3×C4⋊Dic5—28no—
49#6669—28no—
50Dic3×Dic5—28no—
51C2×#887—52no—
52C2×#869—51no—
53C3×#384—51no—
54Dic3×C4⋊C4—54no—
55#4973—52no—
56#4972—54no—
57C42×Dic3D511yescharacteristic
58C22×Dic10—32no—
59C2×C42×C5—31no—
60C2×C42×C5—32no—
61C2×C42×C5—32no—
62C2×C42×C5—31no—
63C2×C42×C5C2×D311yescharacteristic
64C2×C4⋊Dic5—34no—
65C2×C4⋊Dic5C2×D312yes—
66C2×C4⋊Dic5C2×D314yes—
67C2×#683—34no—
68C2×C4×Dic5—34no—
69#4015—38no—
70C4×Dic10—68no—
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—22no—
85C2×C5×Dic3—22no—
86C2×C5×Dic3—22no—
87C2×C5×Dic3C2×D412yes—
88C2×C5×Dic3C2×D412yes—
89C2×C5×Dic3C2×Q814yes—
90C2×C5×Dic3C2×Q814yes—
91C2×C3×Dic5—24no—
92C2×C3×Dic5—28no—
93C22×Dic6—52no—
94C2×C3×C4⋊C4—54no—
95C2×C3×C4⋊C4—52no—
96C2×C3×C42C2×D511yescharacteristic
97C2×C4⋊Dic3—54no—
98C2×Dic3⋊C4—54no—
99C2×C4×Dic3—54no—
100C2×C4×Dic3C2×D512yes—
101C2×C4×Dic3C2×D511yescharacteristic
102C2×C4×Dic3C2×D512yes—
103C2×C4×Dic3C2×D511yescharacteristic
104#887—108no—
105#869—58no—
106C3⋊#95—58no—
107C22×C4×C5—31no—
108C22×C4×C5—32no—
109C22×C4×C5—31no—
110C22×C4×C5C22×D311yescharacteristic
111C22×C4×C5C22×D312yes—
112C22×Dic5—34no—
113C22×Dic5C22×D314yes—
114C2×Dic10—38no—
115C2×Dic10—64no—
116C2×Dic10—64no—
117C42×C5—34no—
118C42×C5—38no—
119C42×C5—64no—
120C42×C5—62no—
121C42×C5C4×D314yes—
122C4⋊Dic5—24no—
123C4⋊Dic5—28no—
124C4⋊Dic5—316no—
125#683—68no—
126C4×Dic5—68no—
127C2×C4⋊Q8—151no—
128C2×C4×Q8—152no—
129#391—152no—
130#389—154no—
131#384—51no—
132C4×C4⋊C4—154no—
133C43—31no—
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—44no—
143C5×Dic3—22no—
144C5×Dic3—24no—
145C5×Dic3C4⋊Q814yescomplemented
146C22×C3×C4—54no—
147C22×C3×C4C22×D512yes—
148C22×C3×C4C22×D511yescharacteristic
149C22×Dic3—54no—
150C22×Dic3C22×D512yes—
151C22×Dic3C22×D511yescharacteristic
152C22×Dic3C22×D511yescharacteristic
153C2×Dic6—58no—
154C2×Dic6—104no—
155C2×Dic6—104no—
156C3×C4⋊C4—104no—
157C3×C4⋊C4—108no—
158C3×C42C4×D514yes—
159C4⋊Dic3—516no—
160Dic3⋊C4—108no—
161C4×Dic3—24no—
162C4×Dic3—22no—
163C4×Dic3—108no—
164C4×Dic3Dic1018yescomplemented
165C4×Dic3D2014yes—
166C23×C5C23×D311yescharacteristic
167C2×C4×C5—32no—
168C2×C4×C5—34no—
169C2×C4×C5—32no—
170C2×C4×C5—34no—
171C2×C4×C5—62no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5C2×C4×D314yes—
175C2×C4×C5C2×C4×D312yes—
176C2×C4×C5D3×D412yes—
177C2×C4×C5#23714yes—
178C2×C4×C5D3×Q814yes—
179C2×C4×C5#23912yes—
180C2×Dic5—24no—
181C2×Dic5—28no—
182C2×Dic5—38no—
183C2×Dic5—64no—
184C2×Dic5—64no—
185Dic10—616no—
186C22×Q8—152no—
187C4⋊Q8—158no—
188C4×Q8—308no—
189C2×C4⋊C4—52no—
190C2×C4⋊C4—54no—
191C2×C4⋊C4—154no—
192C2×C4⋊C4—154no—
193C2×C42—31no—
194C2×C42—32no—
195C2×C42—32no—
196C2×C42—31no—
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—104no—
207C2×C3×C4—108no—
208C2×C3×C4C2×Dic1014yes—
209C2×C3×C4C2×C4×D514yes—
210C2×C3×C4C2×C4×D512yes—
211C2×C3×C4C2×D2012yes—
212C2×C3×C4#70914yes—
213C2×C3×C4#70912yes—
214C2×Dic3—22no—
215C2×Dic3—22no—
216C2×Dic3—22no—
217C2×Dic3—58no—
218C2×Dic3—104no—
219C2×Dic3—104no—
220C2×Dic3C2×Dic1014yes—
221C2×Dic3C2×Dic1014yes—
222C2×Dic3C2×D2012yes—
223C2×Dic3C2×D2012yes—
224Dic6—1016no—
225C22×C5C22×C4×D311yescharacteristic
226C22×C5C2×D3×D411yescharacteristic
227C22×C5C2×#23712yes—
228C22×C5C2×D3×Q812yes—
229C22×C5C2×#23911yescharacteristic
230C4×C5—34no—
231C4×C5—62no—
232C4×C5—64no—
233C4×C5#88718yescomplemented
234C4×C5#89314yes—
235Dic5—44no—
236Dic5—68no—
237C2×Q8—158no—
238C2×Q8—304no—
239C2×Q8—304no—
240C22×C4—31no—
241C22×C4—32no—
242C22×C4—31no—
243C22×C4—54no—
244C22×C4—154no—
245C22×C4C2×D3×D512yes—
246C22×C4C2×D3×D511yescharacteristic
247C4⋊C4—108no—
248C4⋊C4—104no—
249C4⋊C4—1516no—
250C4⋊C4—308no—
251C42—38no—
252C42—34no—
253C42—64no—
254C42—62no—
255C42—308no—
256C42#120014yes—
257C3×C5C4×C4⋊Q811yescharacteristic, complemented, Hall
258C22×C3C22×Dic1012yes—
259C22×C3C22×C4×D511yescharacteristic
260C22×C3C22×D2011yescharacteristic
261C22×C3C2×#70912yes—
262C22×C3C2×#70911yescharacteristic
263C3×C4—204no—
264C3×C4C4×Dic1018yescomplemented
265C3×C4C4×D2014yes—
266Dic3—24no—
267Dic3—22no—
268Dic3—108no—
269Dic3#401514yescomplemented
270C2×C5C2×#88712yes—
271C2×C5C2×#89311yescharacteristic
272C2×C5#571611yescharacteristic
273C2×C5D3×C4⋊Q811yescharacteristic
274C2×C5#572812yes—
275C23C22×D3×D511yescharacteristic
276Q8—3016no—
277C2×C4—34no—
278C2×C4—32no—
279C2×C4—34no—
280C2×C4—32no—
281C2×C4—62no—
282C2×C4—62no—
283C2×C4—62no—
284C2×C4—108no—
285C2×C4—104no—
286C2×C4—158no—
287C2×C4—304no—
288C2×C4—304no—
289C2×C4#676514yes—
290C2×C4D3×Dic1014yes—
291C2×C4#676912yes—
292C2×C4D3×D2012yes—
293C2×C4C2×#120012yes—
294C2×C4C2×#120014yes—
295C2×C3C2×C4×Dic1012yes—
296C2×C3C2×#401511yescharacteristic
297C2×C3#6580412yes—
298C2×C3C2×C4×D2011yescharacteristic
299C2×C3#6581111yescharacteristic
300C5#7432011yescharacteristic, complemented, Sylow
301C22C2×#676512yes—
302C22C2×D3×Dic1012yes—
303C22C2×#676911yescharacteristic
304C22C2×D3×D2011yescharacteristic
305C22C22×#120011yescharacteristic
306C4—34no—
307C4—64no—
308C4—62no—
309C4—204no—
310C4—308no—
311C4#9134018yescomplemented
312C4#9142814yes—
313C3C4×#401511yescharacteristic, complemented, Sylow
314C2#1175247812yes—
315C2#1175254211yescharacteristic
316C2D3×#401511yescharacteristic
317C2C2×#9134012yes—
318C2C2×#9142811yescharacteristic
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
46. C4×C5×Dic3Q8semidirect
140. C3×C4×C5C4×Q8semidirect
145. C5×Dic3C4⋊Q8semidirect
164. C4×Dic3Dic10semidirect
233. C4×C5#887semidirect
257. C3×C5C4×C4⋊Q8semidirect
264. C3×C4C4×Dic10semidirect
269. Dic3#4015semidirect
300. C5#74320semidirect
311. C4#91340semidirect
313. C3C4×#4015semidirect

Maximal subgroups

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

subgroupindex
C2×#917582
C2×#913402
C42×C5×Dic32
C3×#652242
#117488582
Dic3×C4⋊Dic52
#117485992
C4×#40153
#743205