Finite Group Databasebeta

← #14291405

Subgroups — #14291405

Order 1920.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C3×C5×#493C211yesmaximal, characteristic, complemented
2#11751173C212yesmaximal, complemented
3C8×D60C211yesmaximal, characteristic, complemented
4#11746365C212yesmaximal, complemented
5#11746279C211yesmaximal, characteristic, complemented
6#10602075—31nomaximal, Hall
7C2×C3×C5×D8—21no—
8C2×C3×C5×D8—21no—
9C3×C5×#127C2212yes—
10C2×#6715—22no—
11C2×C8×D15—21no—
12C4×D60C2211yescharacteristic
13C3×C4×C5×C8C2211yescharacteristic
14#91116—22no—
15#91104—21no—
16C4⋊(C3⋊#168)C2212yes—
17C4⋊(C3⋊#168)C2211yescharacteristic
18#71282—51nomaximal, Hall
19C5×#493D311yescharacteristic, complemented
20#65361—32no—
21C8×D20—31no—
22#64764—32no—
23#64678—31no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4—22no—
27C2×D60D411yescharacteristic
28C2×C4×D15—21no—
29C3×C5×D8—42no—
30C3×C5×D8—42no—
31C2×C3×C5×C8D411yescharacteristic
32C2×C3×C5×C8D411yescharacteristic
33C3×C42×C5C2311yescharacteristic
34#6715—44no—
35#6714—21no—
36C4⋊Dic15D411yescharacteristic
37C2×C3⋊#168—21no—
38C2×C3⋊#168—22no—
39C8×D15—42no—
40C3×#493D511yescharacteristic, complemented
41#5072—52no—
42C8×D12—51no—
43#4544—52no—
44#4458—51no—
45C2×C5×D8—21no—
46C2×C5×D8—21no—
47C5×#127C2×D312yes—
48C2×#686—62no—
49C2×C8×D5—61no—
50C4×D20—31no—
51C4×C5×C8C2×D311yescharacteristic
52#3964—62no—
53#3952—61no—
54C4⋊#168—32no—
55C4⋊#168—31no—
56#1667—151noSylow
57C23×C3×C5—42no—
58C22×D15—21no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C3×C5×D4—42no—
63C3×C5×D4—82no—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5#4111yescharacteristic
67C2×Dic15—21no—
68D60—21no—
69D60D812yescomplemented
70C4×D15—41no—
71C4×D15—41no—
72C3×C5×C8—21no—
73C3×C5×C8D812yescomplemented
74C3⋊#168—41no—
75C3⋊#168—42no—
76C2×C3×D8—21no—
77C2×C3×D8—21no—
78C3×#127C2×D512yes—
79C2×#213—102no—
80C2×D3×C8—101no—
81C4×D12—51no—
82C3×C4×C8C2×D511yescharacteristic
83#832—102no—
84(C2×D3)⋊C8—101no—
85C4⋊(C3⋊C8)—51no—
86C4⋊(C3⋊C8)—52no—
87C2×C5×D4—22no—
88C2×C5×D4—22no—
89C2×C5×D4—22no—
90C2×D20—31no—
91C2×C4×D5—61no—
92C5×D8—42no—
93C5×D8—42no—
94C2×C5×C8#6711yescharacteristic
95C2×C5×C8#6711yescharacteristic
96C42×C5C22×D311yescharacteristic
97#686—124no—
98#685—61no—
99C4⋊Dic5—31no—
100C2×#168—62no—
101C2×#168—61no—
102C8×D5—122no—
103#493D1511yescharacteristic, complemented
104#459—152no—
105C8×D4—151no—
106#335—151no—
107#331—152no—
108C22×C3×C5—82no—
109C22×C3×C5—82no—
110C22×C3×C5—82no—
111C22×C3×C5#12111yescharacteristic
112C2×D15—22no—
113C2×D15—41no—
114C2×D15—41no—
115C3×C4×C5—21no—
116C3×C4×C5C2×D811yescharacteristic
117C3×C4×C5C2×D811yescharacteristic
118C3×C4×C5#13511yescharacteristic
119C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
120Dic15—41no—
121C2×C3×D4—22no—
122C2×C3×D4—22no—
123C2×C3×D4—22no—
124C2×D12—51no—
125C2×C4×D3—101no—
126C3×D8—42no—
127C3×D8—42no—
128C2×C3×C8C22⋊D511yescharacteristic
129C2×C3×C8C22⋊D511yescharacteristic
130C3×C42C22×D511yescharacteristic
131#213—204no—
132(C2×D3)⋊C4—101no—
133C4⋊Dic3—51no—
134C2×C3⋊C8—102no—
135C2×C3⋊C8—101no—
136D3×C8—202no—
137C23×C5—42no—
138C22×D5—61no—
139C5×D4—42no—
140C5×D4—42no—
141C5×D4—42no—
142C5×D4—42no—
143C5×D4—82no—
144C2×C4×C5D3×D411yescharacteristic
145C2×C4×C5#23711yescharacteristic
146C2×C4×C5C2×#6711yescharacteristic
147C2×Dic5—61no—
148D20—32no—
149D20—61no—
150C4×D5—121no—
151C4×D5—121no—
152C5×C8—21no—
153C5×C8#21312yescomplemented
154#168—122no—
155#168—121no—
156C2×D8—21no—
157C2×D8—21no—
158C2×D8—302no—
159C22×C8—301no—
160#127C2×D1512yes—
161C4×D4—151no—
162C4⋊C8—151no—
163C4⋊C8—152no—
164#102—302no—
165C22⋊C8—301no—
166C4×C8C2×D1511yescharacteristic
167C2×C3×C5—162no—
168C2×C3×C5#45911yescharacteristic
169C2×C3×C5#46611yescharacteristic
170C2×C3×C5#47211yescharacteristic
171D15—42no—
172C23×C3—42no—
173C22×D3—101no—
174C3×D4—42no—
175C3×D4—42no—
176C3×D4—42no—
177C3×D4—42no—
178C3×D4—82no—
179C2×C3×C4D4×D511yescharacteristic
180C2×C3×C4#71111yescharacteristic
181C2×C3×C4C2×C22⋊D511yescharacteristic
182C2×Dic3—101no—
183D12—52no—
184D12—101no—
185C4×D3—201no—
186C4×D3—201no—
187C3×C8—21no—
188C3×C8#68612yescomplemented
189C3⋊C8—202no—
190C3⋊C8—201no—
191C22×C5—82no—
192C22×C5—82no—
193C22×C5—82no—
194C22×C5#93811yescharacteristic
195C2×D5—62no—
196C2×D5—121no—
197C2×D5—121no—
198C4×C5—21no—
199C4×C5D3×D811yescharacteristic
200C4×C5#91211yescharacteristic
201C4×C5C2×#21311yescharacteristic
202C4×C5#93211yescharacteristic
203Dic5—121no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—151no—
208C22×C4—301no—
209D8—42no—
210D8—42no—
211D8—604no—
212C2×C8—302no—
213C2×C8—301no—
214C2×C8—602no—
215C2×C8#122011yescharacteristic
216C2×C8#122011yescharacteristic
217C4⋊C4—151no—
218C22⋊C4—301no—
219C42C22×D1511yescharacteristic
220C3×C5#166711yescharacteristic, complemented, Hall
221C22×C3—82no—
222C22×C3—82no—
223C22×C3—82no—
224C22×C3#408411yescharacteristic
225C2×D3—102no—
226C2×D3—201no—
227C2×D3—201no—
228C3×C4—21no—
229C3×C4D5×D811yescharacteristic
230C3×C4#405811yescharacteristic
231C3×C4C2×#68611yescharacteristic
232C3×C4#407811yescharacteristic
233Dic3—201no—
234C2×C5—162no—
235C2×C5#507211yescharacteristic
236C2×C5#515711yescharacteristic
237C2×C5#516011yescharacteristic
238D5—122no—
239C23—42no—
240C23—301no—
241D4—42no—
242D4—42no—
243D4—42no—
244D4—42no—
245D4—82no—
246D4—152no—
247D4—301no—
248C2×C4—301no—
249C2×C4—601no—
250C2×C4—601no—
251C2×C4D4×D1511yescharacteristic
252C2×C4#681911yescharacteristic
253C2×C4C2×#122011yescharacteristic
254C8—21no—
255C8—602no—
256C8—601no—
257C8#671512yescomplemented
258C2×C3—162no—
259C2×C3#6536111yescharacteristic
260C2×C3#6544611yescharacteristic
261C2×C3#6544911yescharacteristic
262D3—202no—
263C5#7128211yescharacteristic, complemented, Sylow
264C22—82no—
265C22—82no—
266C22—82no—
267C22—302no—
268C22—601no—
269C22—601no—
270C22#9182711yescharacteristic
271C4—21no—
272C4—601no—
273C4D8×D1511yescharacteristic
274C4#9180111yescharacteristic
275C4C2×#671511yescharacteristic
276C4#9182111yescharacteristic
277C3#1060207511yescharacteristic, complemented, Sylow
278C2—162no—
279C2—602no—
280C2#1175117311yescharacteristic
281C2#1175125811yescharacteristic
282C2#1175126111yescharacteristic
subgroupG/H
centerC22#91827
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#493C2
socleC22×C3×C5#121
hypercenter#493D15
hypocenterC3×C5#1667
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C3×C5×#493C2semidirect
2. #11751173C2semidirect
3. C8×D60C2semidirect
4. #11746365C2semidirect
5. #11746279C2semidirect
19. C5×#493D3semidirect
40. C3×#493D5semidirect
69. D60D8semidirect
73. C3×C5×C8D8semidirect
103. #493D15semidirect
153. C5×C8#213semidirect
188. C3×C8#686semidirect
220. C3×C5#1667semidirect
257. C8#6715semidirect
263. C5#71282semidirect
277. C3#10602075semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4932
#117511732
C8×D602
#117463652
#117462792
#106020753
#712825