Finite Group Databasebeta

← #14305112

Subgroups — #14305112

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×Dic15C211yesmaximal, characteristic
2C2×C5×#818C211yesmaximal, characteristic
3C2×C3×#3950C211yesmaximal, characteristic
4#11748868C212yesmaximal
5#11745979C212yesmaximal
6#10601405—31nomaximal, Hall
7C22×C3×C5×C8C2211yescharacteristic
8C2×C4×Dic15C2211yescharacteristic
9C22×C3⋊#168C2211yescharacteristic
10C2×C5×C4⋊Dic3C2212yes—
11C2×C3×C4⋊Dic5C2212yes—
12C2×Dic3⋊Dic5—22no—
13C8×Dic15—22no—
14C5×#818C414yescomplemented
15C3×#3950—22no—
16#90994—22no—
17#70611—51nomaximal, Hall
18C2×C5×#107—31no—
19C2×#3950D311yescharacteristic
20C2×C8×Dic5—31no—
21#65274—32no—
22#64749—32no—
23C22×C3×C4×C5C2311yescharacteristic
24C22×Dic15D411yescharacteristic
25C22×Dic15D411yescharacteristic
26C22×C5×Dic3—22no—
27C22×C3×Dic5—22no—
28C2×C3×C5×C8C2×C412yes—
29C2×C3×C5×C8D412yes—
30C2×C3×C5×C8Q812yes—
31C4×Dic15—21no—
32C4×Dic15—21no—
33C2×C3⋊#168—21no—
34C2×C3⋊#168—21no—
35C2×C3⋊#168Q812yes—
36C5×C4⋊Dic3—22no—
37C5×C4⋊Dic3C2×C414yes—
38C3×C4⋊Dic5—22no—
39C3×C4⋊Dic5—22no—
40Dic3⋊Dic5—44no—
41C2×C3×#107—51no—
42C2×#818D511yescharacteristic
43C2×C8×Dic3—51no—
44#4972—52no—
45#4529—52no—
46C22×C5×C8C2×D311yescharacteristic
47C2×C5×C4⋊C4—32no—
48C2×C4⋊Dic5—62no—
49C2×C4⋊Dic5C2×D312yes—
50C2×C4×Dic5—31no—
51C22×#168—31no—
52C5×#107—34no—
53#3963—62no—
54#3950—22no—
55C8×Dic5—62no—
56#1942—151noSylow
57C23×C3×C5C2×D411yescharacteristic
58C2×C3×C4×C5C22×C411yescharacteristic
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5C2×Q811yescharacteristic
61C2×C3×C4×C5C2×Q811yescharacteristic
62C2×C3×C4×C5#4111yescharacteristic
63C2×C3×C4×C5#4111yescharacteristic
64C2×Dic15—21no—
65C2×Dic15—21no—
66C2×Dic15—21no—
67C2×Dic15—21no—
68C2×Dic15D812yes—
69C2×Dic15Q1612yes—
70C2×C5×Dic3—24no—
71C2×C5×Dic3—42no—
72C2×C5×Dic3—42no—
73C2×C3×Dic5—42no—
74C2×C3×Dic5—42no—
75C2×C3×Dic5—42no—
76C3×C5×C8C4⋊C414yescomplemented
77C3⋊#168—22no—
78C22×C3×C8C2×D511yescharacteristic
79C2×C3×C4⋊C4—52no—
80C2×C4⋊Dic3C2×D512yes—
81C2×Dic3⋊C4—102no—
82C2×C4×Dic3—51no—
83C22×C3⋊C8—51no—
84C3×#107—102no—
85C3⋊#95—102no—
86#818Dic514yescomplemented
87C8×Dic3—102no—
88C22×C4×C5—62no—
89C22×C4×C5C22×D311yescharacteristic
90C22×Dic5—22no—
91C22×Dic5—31no—
92C22×Dic5—31no—
93C2×C5×C8Dic612yes—
94C2×C5×C8C4×D312yes—
95C2×C5×C8#6712yes—
96C5×C4⋊C4—34no—
97C5×C4⋊C4—62no—
98C4⋊Dic5—22no—
99C4⋊Dic5—22no—
100C4⋊Dic5—124no—
101C4×Dic5—61no—
102C4×Dic5—61no—
103C2×#168—32no—
104C2×#168—61no—
105C2×#168—61no—
106C2×#107—31no—
107C2×#107—51no—
108C2×C4×C8—151no—
109#389—152no—
110#340—152no—
111C22×C3×C5C4×D411yescharacteristic
112C22×C3×C5#12111yescharacteristic
113C22×C3×C5C4⋊Q811yescharacteristic
114C22×C3×C5C2×D811yescharacteristic
115C22×C3×C5C2×Q1611yescharacteristic
116C22×C3×C5#13511yescharacteristic
117C22×C3×C5#13511yescharacteristic
118C3×C4×C5C2×C4⋊C411yescharacteristic
119C3×C4×C5C4×Q811yescharacteristic
120C3×C4×C5C22⋊Q811yescharacteristic
121C3×C4×C5#12511yescharacteristic
122Dic15—22no—
123Dic15—22no—
124C3×Dic5—82no—
125C5×Dic3—44no—
126C22×C3×C4—102no—
127C22×C3×C4C22×D511yescharacteristic
128C22×Dic3—22no—
129C22×Dic3—51no—
130C22×Dic3—51no—
131C2×C3×C8Dic1012yes—
132C2×C3×C8D2012yes—
133C2×C3×C8C2×Dic512yes—
134C3×C4⋊C4—102no—
135C3×C4⋊C4—102no—
136C4⋊Dic3—22no—
137C4⋊Dic3C2×Dic514yes—
138Dic3⋊C4—204no—
139C4×Dic3—101no—
140C4×Dic3—101no—
141C2×C3⋊C8—52no—
142C2×C3⋊C8—101no—
143C2×C3⋊C8—101no—
144C23×C5D3×D411yescharacteristic
145C2×C4×C5—64no—
146C2×C4×C5—122no—
147C2×C4×C5—122no—
148C2×C4×C5C2×Dic611yescharacteristic
149C2×C4×C5C2×C4×D311yescharacteristic
150C2×C4×C5#23711yescharacteristic
151C2×C4×C5D3×Q811yescharacteristic
152C2×C4×C5#23911yescharacteristic
153C2×C4×C5C2×#6711yescharacteristic
154C2×Dic5—32no—
155C2×Dic5—32no—
156C2×Dic5—42no—
157C2×Dic5—42no—
158C2×Dic5—42no—
159C2×Dic5—61no—
160C2×Dic5—61no—
161C2×Dic5—61no—
162C2×Dic5—61no—
163C5×C8Dic3⋊C414yescomplemented
164#168—62no—
165C22×C8—151no—
166C22×C8D3×D511yescharacteristic
167C2×C4⋊C4—32no—
168C2×C4⋊C4—52no—
169C2×C4⋊C4—302no—
170C2×C42—151no—
171#107—34no—
172#107—102no—
173C4×C8—302no—
174#95—302no—
175C2×C3×C5#38911yescharacteristic
176C2×C3×C5C4×D811yescharacteristic
177C2×C3×C5C4×Q1611yescharacteristic
178C2×C3×C5#46611yescharacteristic
179C2×C3×C5#46711yescharacteristic
180C2×C3×C5#49911yescharacteristic
181C2×C3×C5#50011yescharacteristic
182C23×C3D4×D511yescharacteristic
183C2×C3×C4—202no—
184C2×C3×C4—202no—
185C2×C3×C4—202no—
186C2×C3×C4C2×Dic1011yescharacteristic
187C2×C3×C4C2×D2011yescharacteristic
188C2×C3×C4#71111yescharacteristic
189C2×C3×C4Q8×D511yescharacteristic
190C2×C3×C4#71311yescharacteristic
191C2×C3×C4C22×Dic511yescharacteristic
192C2×Dic3—24no—
193C2×Dic3—42no—
194C2×Dic3—42no—
195C2×Dic3—52no—
196C2×Dic3—52no—
197C2×Dic3—101no—
198C2×Dic3—101no—
199C2×Dic3—101no—
200C2×Dic3—101no—
201C3×C8C4⋊Dic514yescomplemented
202C3⋊C8—102no—
203C22×C5#88811yescharacteristic
204C22×C5#89311yescharacteristic
205C22×C5D3×D811yescharacteristic
206C22×C5#91211yescharacteristic
207C22×C5D3×Q1611yescharacteristic
208C22×C5#91911yescharacteristic
209C22×C5#93811yescharacteristic
210C4×C5—124no—
211C4×C5#88711yescharacteristic
212C4×C5#89011yescharacteristic
213C4×C5C2×Dic3⋊C411yescharacteristic
214C4×C5#94611yescharacteristic
215Dic5—62no—
216Dic5—62no—
217Dic5—82no—
218C22×C4—62no—
219C22×C4—102no—
220C22×C4—151no—
221C22×C4—151no—
222C22×C4C2×D3×D511yescharacteristic
223C2×C8—152no—
224C2×C8—301no—
225C2×C8—301no—
226C2×C8D3×Dic512yes—
227C2×C8#120212yes—
228C2×C8#120412yes—
229C4⋊C4—34no—
230C4⋊C4—62no—
231C4⋊C4—102no—
232C4⋊C4—102no—
233C4⋊C4—604no—
234C42—301no—
235C42—301no—
236C3×C5#194211yescharacteristic, complemented, Hall
237C22×C3#403411yescharacteristic
238C22×C3#404111yescharacteristic
239C22×C3D5×D811yescharacteristic
240C22×C3#405811yescharacteristic
241C22×C3D5×Q1611yescharacteristic
242C22×C3#406511yescharacteristic
243C22×C3D4×Dic511yescharacteristic
244C3×C4—402no—
245C3×C4#403611yescharacteristic
246C3×C4#404311yescharacteristic
247C3×C4C2×C4⋊Dic511yescharacteristic
248C3×C4Q8×Dic511yescharacteristic
249Dic3—44no—
250Dic3—102no—
251Dic3—102no—
252C2×C5#487211yescharacteristic
253C2×C5#487311yescharacteristic
254C2×C5#487411yescharacteristic
255C2×C5#487811yescharacteristic
256C2×C5#497211yescharacteristic
257C2×C5#515711yescharacteristic
258C2×C5#518811yescharacteristic
259C23#677711yescharacteristic
260C2×C4—64no—
261C2×C4—122no—
262C2×C4—122no—
263C2×C4—152no—
264C2×C4—152no—
265C2×C4—202no—
266C2×C4—202no—
267C2×C4—202no—
268C2×C4—301no—
269C2×C4—301no—
270C2×C4—301no—
271C2×C4—301no—
272C2×C4#676611yescharacteristic
273C2×C4#676811yescharacteristic
274C2×C4D15⋊Q811yescharacteristic
275C2×C4C2×D3×Dic511yescharacteristic
276C2×C4C2×#120211yescharacteristic
277C2×C4C2×#120411yescharacteristic
278C8—302no—
279C8Dic3⋊Dic514yescomplemented
280C2×C3#6516311yescharacteristic
281C2×C3#6516711yescharacteristic
282C2×C3#6517211yescharacteristic
283C2×C3#6517611yescharacteristic
284C2×C3#6527411yescharacteristic
285C2×C3D8×Dic511yescharacteristic
286C2×C3Q16×Dic511yescharacteristic
287C5#7061111yescharacteristic, complemented, Sylow
288C22#9125611yescharacteristic
289C22#9126411yescharacteristic
290C22#9127711yescharacteristic
291C22#9127911yescharacteristic
292C22#9143511yescharacteristic
293C22#9146511yescharacteristic
294C22#9147011yescharacteristic
295C4—124no—
296C4—302no—
297C4—302no—
298C4—402no—
299C4#9134411yescharacteristic
300C4#9138411yescharacteristic
301C4#9139011yescharacteristic
302C4C2×Dic3⋊Dic511yescharacteristic
303C3#1060140511yescharacteristic, complemented, Sylow
304C2#1174781011yescharacteristic
305C2#1174788611yescharacteristic
306C2#1174793211yescharacteristic
307C2#1174795811yescharacteristic
308C2#1174799211yescharacteristic
309C2#1174803711yescharacteristic
310C2#1174886811yescharacteristic
subgroupG/H
centerC23#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1942
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
14. C5×#818C4semidirect
76. C3×C5×C8C4⋊C4semidirect
86. #818Dic5semidirect
163. C5×C8Dic3⋊C4semidirect
201. C3×C8C4⋊Dic5semidirect
236. C3×C5#1942semidirect
279. C8Dic3⋊Dic5semidirect
287. C5#70611semidirect
303. C3#10601405semidirect

Maximal subgroups

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

subgroupindex
C2×C8×Dic152
C2×C5×#8182
C2×C3×#39502
#117488682
#117459792
#106014053
#706115