Finite Group Databasebeta

← #14276976

Subgroups — #14276976

Order 1920.

312 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#11752413C211yesmaximal, characteristic
2C3×#65758C211yesmaximal, characteristic
3#11748580C211yesmaximal, characteristic
4#10598508—31nomaximal, Hall
5C2×C3×#704—21no—
6C2×C3×C4×Dic5C2211yescharacteristic
7C2×#6668—21no—
8#91241—21no—
9#91233—21no—
10C4×C3⋊#170C412yescomplemented
11C3×#4004C412yescomplemented
12C3×C4⋊#170—21no—
13#91115C411yescharacteristic
14C5×C3⋊#95C411yescharacteristic
15#90994—21no—
16#67713—51nomaximal, Hall
17#65758D311yescharacteristic
18#65754—31no—
19#64939—31no—
20C22×C3×C4×C5C2×C411yescharacteristic
21C22×Dic15—21no—
22C22×C5×Dic3—21no—
23C22×C3×Dic5D411yescharacteristic
24C22×C3×Dic5D411yescharacteristic
25C2×C3⋊#170—22no—
26C3×#704—41no—
27C3×#704—41no—
28C2×C3×#170—22no—
29C3×C4×Dic5C2×C411yescharacteristic
30C3×C4×Dic5C2×C411yescharacteristic
31C3×C4×Dic5D411yescharacteristic
32C3×C4×Dic5Q811yescharacteristic
33#6668—41no—
34#6668—41no—
35C3×#423—51no—
36#4936—51no—
37#4925—51no—
38C2×#704—21no—
39C2×#683—61no—
40C2×C4×Dic5C2×D311yescharacteristic
41C22⋊#170—61no—
42#4004—61no—
43#4004Dic312yescomplemented
44C4⋊#170—21no—
45C4×#170—32no—
46C5×#95—31no—
47#3963—31no—
48#3963—61no—
49#1286—151noSylow
50C23×C3×C5C22⋊C411yescharacteristic
51C2×C3×C4×C5—41no—
52C2×C3×C4×C5C4211yescharacteristic
53C2×C3×C4×C5C4⋊C411yescharacteristic
54C2×Dic15—41no—
55C2×Dic15—41no—
56C2×Dic15—41no—
57C2×C5×Dic3—41no—
58C2×C5×Dic3—41no—
59C2×C5×Dic3—41no—
60C2×C3×Dic5—41no—
61C2×C3×Dic5C22⋊C411yescharacteristic
62C2×C3×Dic5C22⋊C411yescharacteristic
63C2×C3×Dic5C4⋊C411yescharacteristic
64C2×C3×Dic5C4⋊C411yescharacteristic
65C2×C3×Dic5D811yescharacteristic
66C2×C3×Dic5SD1611yescharacteristic
67C2×C3×Dic5SD1611yescharacteristic
68C2×C3×Dic5Q1611yescharacteristic
69C3⋊#170—42no—
70C3×#170—42no—
71C2×C3×M16—101no—
72C2×C3×C42—51no—
73C2×C4⋊Dic3—101no—
74C3×C4⋊C8—52no—
75C3×C4⋊C8—101no—
76C3⋊#95—51no—
77C3⋊#95—101no—
78C3⋊#95AGL(1,𝔽5)11yescharacteristic
79#830—101no—
80C4⋊(C3⋊C8)—101no—
81C4×C3⋊C8—52no—
82C22×C4×C5—61no—
83C22×C4×C5C4×D311yescharacteristic
84C22×Dic5—61no—
85C22×Dic5D1211yescharacteristic
86C22×Dic5#6711yescharacteristic
87#704—41no—
88#704—41no—
89C2×#170—22no—
90C2×#170—62no—
91#683—121no—
92#683—121no—
93C4×Dic5Dic611yescharacteristic
94C4×Dic5C4×D311yescharacteristic
95C4×Dic5C2×Dic311yescharacteristic
96C4×Dic5#6711yescharacteristic
97#431—151no—
98#423—51no—
99#382—151no—
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5#9511yescharacteristic
103C22×C3×C5#10211yescharacteristic
104C22×C3×C5#10311yescharacteristic
105C3×C4×C5—21no—
106C3×C4×C5—21no—
107Dic15—81no—
108C3×Dic5—21no—
109C3×Dic5—21no—
110C3×Dic5#10211yescharacteristic
111C3×Dic5#10311yescharacteristic
112C3×Dic5#10611yescharacteristic
113C3×Dic5#10711yescharacteristic
114C5×Dic3—81no—
115C22×C3×C4—51no—
116C22×C3×C4—51no—
117C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
118C22×Dic3—21no—
119C22×Dic3—101no—
120C3×M16—201no—
121C3×M16—201no—
122C2×C3×C8—102no—
123C3×C42—51no—
124C3×C42—51no—
125C3×C42—51no—
126C3×C42—51no—
127C4⋊Dic3—201no—
128C4⋊Dic3—201no—
129C2×C3⋊C8—102no—
130C23×C5(C2×D3)⋊C411yescharacteristic
131C2×C4×C5—41no—
132C2×C4×C5—121no—
133C2×C4×C5—121no—
134C2×C4×C5—121no—
135C2×C4×C5C4×Dic311yescharacteristic
136C2×C4×C5Dic3⋊C411yescharacteristic
137C2×Dic5—41no—
138C2×Dic5—121no—
139C2×Dic5—121no—
140C2×Dic5—121no—
141C2×Dic5Dic3⋊C411yescharacteristic
142C2×Dic5C4⋊Dic311yescharacteristic
143C2×Dic5(C2×D3)⋊C411yescharacteristic
144C2×Dic5#21311yescharacteristic
145C2×Dic5#21411yescharacteristic
146C2×Dic5#21511yescharacteristic
147C2×Dic5#21611yescharacteristic
148C2×Dic5#21711yescharacteristic
149#170—42no—
150#170—122no—
151C2×M16—101no—
152C2×C4⋊C4—301no—
153C2×C42—51no—
154C4⋊C8—52no—
155C4⋊C8—101no—
156C4⋊C8—301no—
157C22⋊C8—301no—
158C4×C8—152no—
159#95—31no—
160#95—151no—
161#95—301no—
162C2×C3×C5—21no—
163C2×C3×C5—21no—
164C2×C3×C5H(3,ℤ/4)11yescharacteristic
165C2×C3×C5#34011yescharacteristic
166C2×C3×C5#34411yescharacteristic
167C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4—41no—
169C2×C3×C4—51no—
170C2×C3×C4—51no—
171C2×C3×C4—51no—
172C2×C3×C4—51no—
173C2×C3×C4—51no—
174C2×C3×C4—51no—
175C2×C3×C4—51no—
176C2×C3×C4—51no—
177C2×C3×C4—201no—
178C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
179C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—201no—
184C2×Dic3—201no—
185C2×Dic3—201no—
186C3×C8—202no—
187C3⋊C8—202no—
188C22×C5—21no—
189C22×C5—21no—
190C22×C5#80911yescharacteristic
191C22×C5#81011yescharacteristic
192C22×C5C3⋊#9511yescharacteristic
193C4×C5—21no—
194C4×C5—21no—
195C4×C5—241no—
196Dic5—21no—
197Dic5—21no—
198Dic5—241no—
199Dic5#80711yescharacteristic
200Dic5#80811yescharacteristic
201Dic5#83211yescharacteristic
202Dic5#83511yescharacteristic
203C22×C4—51no—
204C22×C4—51no—
205C22×C4—61no—
206C22×C4—301no—
207C22×C4D3×AGL(1,𝔽5)11yescharacteristic
208M16—201no—
209M16—201no—
210C2×C8—102no—
211C2×C8—302no—
212C4⋊C4—601no—
213C4⋊C4—601no—
214C42—51no—
215C42—51no—
216C42—51no—
217C42—51no—
218C3×C5#128611yescharacteristic, complemented, Hall
219C22×C3—21no—
220C22×C3—21no—
221C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
222C22×C3#400711yescharacteristic
223C22×C3#400911yescharacteristic
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—51no—
227C3×C4—51no—
228C3×C4—51no—
229C3×C4—51no—
230C3×C4—101no—
231C3×C4—101no—
232Dic3—81no—
233Dic3—401no—
234C2×C5—21no—
235C2×C5—21no—
236C2×C5#452911yescharacteristic
237C2×C5#455711yescharacteristic
238C2×C5#455911yescharacteristic
239C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
240C2×C4—41no—
241C2×C4—51no—
242C2×C4—51no—
243C2×C4—51no—
244C2×C4—51no—
245C2×C4—51no—
246C2×C4—51no—
247C2×C4—51no—
248C2×C4—51no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—201no—
253C2×C4—601no—
254C2×C4—601no—
255C2×C4—601no—
256C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
257C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
258C8—202no—
259C8—602no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3#6486311yescharacteristic
263C2×C3#6486711yescharacteristic
264C2×C3#6487411yescharacteristic
265C5#6771311yescharacteristic, complemented, Sylow
266C22—21no—
267C22—21no—
268C22#9115111yescharacteristic
269C22#9115311yescharacteristic
270C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
271C4—21no—
272C4—21no—
273C4—51no—
274C4—51no—
275C4—51no—
276C4—51no—
277C4—101no—
278C4—101no—
279C4—241no—
280C4—1201no—
281C3#1059850811yescharacteristic, complemented, Sylow
282C2—21no—
283C2—21no—
284C2#1174652011yescharacteristic
285C2#1174652811yescharacteristic
286C2#1174657611yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C4×Dic5C22
hypocenterC3×C5#1286
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. C4×C3⋊#170C4semidirect
11. C3×#4004C4semidirect
43. #4004Dic3semidirect
218. C3×C5#1286semidirect
265. C5#67713semidirect
281. C3#10598508semidirect

Maximal subgroups

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

subgroupindex
#117524132
C3×#657582
#117485802
#105985083
#677135