Finite Group Databasebeta

← #14511848

Subgroups — #14511848

Order 1920.

340 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C2×C5×#986C211yesmaximal, characteristic
2C2×#4094⋊C3C211yesmaximal, characteristic, complemented
3#11752145C211yesmaximal, characteristic, complemented
4#10602884—31nomaximal, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6C5×#986—21no—
7C5×#986C412yescomplemented
8C2×C5×GL(2,𝔽3)—21no—
9#4094⋊C3—21no—
10#91184—21no—
11#90967—41nomaximal
12#73128—51nomaximal, Hall
13C2×C5×AGL(1,ℤ/8)—31no—
14C2×#4094D311yescharacteristic, complemented
15#65521—31no—
16C2×#3965—31no—
17C2×#3964—31no—
18#64778—31no—
19#64774—31no—
20C2×C5×D12—41no—
21C5×#41⋊C3C2×C411yescharacteristic
22C5×#41⋊C3D411yescharacteristic
23C2×C5×SL(2,𝔽3)D411yescharacteristic
24C5×GL(2,𝔽3)—22no—
25C4⋊Dic15—41no—
26C2×C3×#168—41no—
27C2×#986D511yescharacteristic
28C2×#131⋊C3—51no—
29#5426—51no—
30C2×C5×#41C2×D311yescharacteristic
31C22×C5×D4—31no—
32C5×AGL(1,ℤ/8)—32no—
33C5×AGL(1,ℤ/8)—32no—
34C5×AGL(1,ℤ/8)—61no—
35C5×AGL(1,ℤ/8)—61no—
36C2×C5×SD16—61no—
37C2×C5×D8—61no—
38C2×C5×M16—31no—
39#4094—21no—
40#4094—61no—
41C2×C4⋊Dic5—31no—
42C2×#681—31no—
43C2×#681—31no—
44C22×#168—31no—
45#3967—61no—
46#3965—62no—
47#3964—61no—
48#3964—61no—
49#3964—61no—
50#1907—151noSylow
51C22×C5×D3—81no—
52C2×C3×C4×C5—41no—
53C2×Dic15—81no—
54C5×D12—42no—
55C5×D12—81no—
56C5×SL(2,𝔽3)C22⋊C411yescharacteristic
57C3×#168—81no—
58C2×#41⋊C3C2×D511yescharacteristic
59#986—21no—
60#986Dic512yescomplemented
61C2×GL(2,𝔽3)—21no—
62#131⋊C3—101no—
63#859—101no—
64#821—201no—
65C24×C5—61no—
66C5×#41—31no—
67C5×#41—31no—
68C5×#41C4×D311yescharacteristic
69C5×#41#6711yescharacteristic
70C2×C5×Q8D1211yescharacteristic
71C2×C5×D4—31no—
72C2×C5×D4—32no—
73C2×C5×D4—61no—
74C2×C5×D4—61no—
75C2×C5×D4—61no—
76C2×C5×D4—61no—
77C2×C5×D4—61no—
78C22×C4×C5—31no—
79C22×Dic5—61no—
80C5×SD16—62no—
81C5×SD16—62no—
82C5×D8—62no—
83C5×D8—62no—
84C5×M16—32no—
85C5×M16—61no—
86C2×C5×C8—61no—
87C4⋊Dic5—61no—
88C4⋊Dic5—61no—
89#681—32no—
90#681—61no—
91#681—61no—
92#681—61no—
93C2×#168—31no—
94C2×#168—61no—
95C2×#168—61no—
96C2×#168—61no—
97C2×#168S411yescharacteristic
98C2×AGL(1,ℤ/8)—31no—
99C2×#131—51no—
100#417—151no—
101C2×#102—151no—
102C2×#100—151no—
103#343—151no—
104#341—151no—
105C22×C3×C5—41no—
106C2×C5×D3—82no—
107C2×C5×D3—161no—
108C2×C5×D3—161no—
109C3×C4×C5—41no—
110C3×C4×C5—41no—
111Dic15—161no—
112C2×D12—41no—
113#41⋊C3C2×Dic511yescharacteristic
114#41⋊C3C22⋊D511yescharacteristic
115C2×SL(2,𝔽3)C22⋊D511yescharacteristic
116GL(2,𝔽3)—22no—
117C2×C3×C8—201no—
118C4⋊Dic3—201no—
119C23×C5—31no—
120C23×C5—62no—
121C23×C5—121no—
122C23×C5—121no—
123C23×C5—241no—
124C23×C5—241no—
125C5×Q8—31no—
126C5×Q8(C2×D3)⋊C411yescharacteristic
127C5×D4—31no—
128C5×D4—31no—
129C5×D4—61no—
130C5×D4—62no—
131C5×D4—62no—
132C5×D4—121no—
133C5×D4—121no—
134C2×C4×C5—31no—
135C2×C4×C5—31no—
136C2×C4×C5—31no—
137C2×C4×C5—31no—
138C2×C4×C5—31no—
139C2×C4×C5C2×S411yescharacteristic
140C2×Dic5—121no—
141C2×Dic5—241no—
142C5×C8—62no—
143#168—21no—
144#168—61no—
145#168—121no—
146C2×#41D3×D511yescharacteristic
147C22×D4—31no—
148AGL(1,ℤ/8)—32no—
149AGL(1,ℤ/8)—32no—
150AGL(1,ℤ/8)—61no—
151AGL(1,ℤ/8)—61no—
152C2×SD16—61no—
153C2×D8—61no—
154#131—101no—
155#131—301no—
156C2×M16—31no—
157C2×M16—151no—
158C2×M16—151no—
159C22×C8—151no—
160C2×C4⋊C4—151no—
161#103—301no—
162#102—301no—
163#102—301no—
164#102—301no—
165#100—302no—
166C2×C3×C5—41no—
167C2×C3×C5—41no—
168C2×C3×C5—41no—
169C5×D3—162no—
170C22×D3—81no—
171C2×C3×C4—41no—
172C2×Dic3—401no—
173D12—42no—
174D12—81no—
175SL(2,𝔽3)C22⋊Dic511yescharacteristic
176C3×C8—401no—
177C22×C5—31no—
178C22×C5—31no—
179C22×C5—61no—
180C22×C5—61no—
181C22×C5—122no—
182C22×C5—242no—
183C22×C5—242no—
184C22×C5—241no—
185C22×C5—241no—
186C22×C5C4⋊S411yescharacteristic
187C4×C5—31no—
188C4×C5—31no—
189C4×C5C4×S411yescharacteristic
190C4×C5GL(2,ℤ/4)11yescharacteristic
191Dic5—241no—
192C24—61no—
193#41—31no—
194#41—31no—
195#41D3×Dic511yescharacteristic
196#41#120111yescharacteristic
197C2×Q8#120311yescharacteristic
198C2×D4—31no—
199C2×D4—32no—
200C2×D4—61no—
201C2×D4—61no—
202C2×D4—61no—
203C2×D4—61no—
204C2×D4—61no—
205C22×C4—31no—
206C22×C4—301no—
207SD16—62no—
208SD16—62no—
209D8—62no—
210D8—62no—
211M16—32no—
212M16—61no—
213M16—152no—
214M16—301no—
215M16—301no—
216M16—301no—
217C2×C8—51no—
218C2×C8—61no—
219C2×C8—151no—
220C2×C8—301no—
221C2×C8—301no—
222C2×C8—301no—
223C4⋊C4—301no—
224C4⋊C4—301no—
225C3×C5—41noHall
226C22×C3—41no—
227C2×D3—82no—
228C2×D3—161no—
229C2×D3—161no—
230C3×C4—41no—
231C3×C4—41no—
232Dic3—801no—
233C2×C5—61no—
234C2×C5—61no—
235C2×C5—242no—
236C2×C5#540611yescharacteristic
237C2×C5#540711yescharacteristic
238C2×C5(C2×S4)⋊C411yescharacteristic
239C23—31no—
240C23—62no—
241C23—121no—
242C23—121no—
243C23—241no—
244C23—241no—
245Q8—31no—
246Q8(C2×D3)⋊Dic511yescharacteristic
247D4—31no—
248D4—31no—
249D4—61no—
250D4—62no—
251D4—62no—
252D4—121no—
253D4—121no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—31no—
259C2×C4—601no—
260C2×C4—1201no—
261C2×C4D5×S411yescharacteristic
262C8—62no—
263C8—101no—
264C8—301no—
265C8—601no—
266C2×C3—41no—
267C2×C3—41no—
268C2×C3—41no—
269D3—162no—
270C5#7312811yescharacteristic, complemented, Sylow
271C22—31no—
272C22—31no—
273C22—61no—
274C22—61no—
275C22—122no—
276C22—242no—
277C22—242no—
278C22—241no—
279C22—241no—
280C22#9190211yescharacteristic
281C4—31no—
282C4—31no—
283C4—1201no—
284C4Dic5×S411yescharacteristic
285C4#9190411yescharacteristic
286C3—41noSylow
287C2—61no—
288C2—61no—
289C2—242no—
290C2#1175161911yescharacteristic
291C2#1175162111yescharacteristic
292C2(C2×S4)⋊Dic511yescharacteristic
subgroupG/H
centerC22#91902
commutatorC5×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D5×S4
FittingC2×C5×#41C2×D3
socleC22×C5C4⋊S4
prime radicalC2×C5×#986C2
cosocleC2×C5×#41⋊C3C22
hypocenterC5×SL(2,𝔽3)C22⋊C4
LCSG ▷ C5×#41⋊C3 ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#4094⋊C3C2semidirect
3. #11752145C2semidirect
7. C5×#986C4semidirect
14. C2×#4094D3semidirect
60. #986Dic5semidirect
270. C5#73128semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9862
C2×#4094⋊C32
#117521452
#106028843
#909674
#731285