Finite Group Databasebeta

← #14513969

Subgroups — #14513969

Order 1920.

330 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 27 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
1C5×#5950C211yesmaximal, characteristic
2#10602939—31nomaximal, Hall
3C5×#997C411yescharacteristic, complemented
4#91185—42nomaximal
5A4⋊#168—41nomaximal
6#85567—51nomaximal, Hall
7C5×#585D311yescharacteristic
8#65529—31no—
9#65525—32no—
10#65523—31no—
11#65522—32no—
12C5×#41⋊C3—42no—
13C4×C5×A4—41no—
14C4×C5×A4—81no—
15#5950D511yescharacteristic
16C5×2−1+4—32no—
17C5×H(5,𝔽2)—31no—
18C5×H(5,𝔽2)—61no—
19C5×H(5,𝔽2)Dic311yescharacteristic
20C2×C5×#41—31no—
21C2×C5×#41—32no—
22C2×C5×#41—61no—
23#4072—32no—
24C2×#681—31no—
25C22×#168—31no—
26#3969—62no—
27#3969—62no—
28#3967—62no—
29#3966—61no—
30#3966—61no—
31#3964—62no—
32C22⋊#168—61no—
33C22⋊#168—61no—
34#1794—151noSylow
35C2×C5×A4—41no—
36C2×C5×A4—81no—
37C5×SL(2,𝔽3)—42no—
38C3⋊#168—161no—
39#997Dic511yescharacteristic, complemented
40GU(2,𝔽3)—202no—
41A4⋊C8—201no—
42C5×#41—32no—
43C5×#41—32no—
44C5×#41—32no—
45C5×#41—62no—
46C5×#41—62no—
47C5×#41—62no—
48C5×#41—62no—
49C5×#41—62no—
50C5×#41S412yes—
51C2×C5×Q8—31no—
52C2×C5×Q8—32no—
53C2×C5×Q8—61no—
54C2×C5×D4—32no—
55C2×C5×D4—31no—
56C2×C5×D4—31no—
57C2×C5×D4—31no—
58C2×C5×D4—61no—
59C2×C5×D4—62no—
60C2×C5×D4—61no—
61C2×C5×D4—61no—
62C22×C4×C5—21no—
63C22×C4×C5—31no—
64C22×C4×C5—31no—
65C22×C4×C5—61no—
66C22×C4×C5S411yescharacteristic
67C22⋊Dic5—62no—
68C4⋊Dic5—62no—
69C4×Dic5—62no—
70#681—62no—
71C2×#168—61no—
72C2×#168—61no—
73C2×#168—62no—
74#585D1511yescharacteristic
75#421—152no—
76#416—152no—
77#410—151no—
78#408—151no—
79C5×A4—41no—
80C5×A4—81no—
81C3×C4×C5—161no—
82#41⋊C3—42no—
83C4×A4—41no—
84C4×A4—81no—
85C23×C5—21no—
86C23×C5—31no—
87C23×C5—31no—
88C23×C5—61no—
89C23×C5SL(2,ℤ/4)11yescharacteristic
90C5×Q8—32no—
91C5×Q8—62no—
92C5×Q8SL(2,ℤ/4)12yes—
93C5×D4—32no—
94C5×D4—32no—
95C5×D4—62no—
96C5×D4—62no—
97C5×D4—62no—
98C5×D4—62no—
99C2×C4×C5—32no—
100C2×C4×C5—31no—
101C2×C4×C5—31no—
102C2×C4×C5—32no—
103C2×C4×C5—31no—
104C2×C4×C5—31no—
105C2×C4×C5—61no—
106C2×C4×C5—62no—
107C2×C4×C5—61no—
108C2×C4×C5—61no—
109C2×C4×C5—61no—
110C2×Dic5—122no—
111#168—121no—
112#168—121no—
1132−1+4—32no—
114H(5,𝔽2)—31no—
115H(5,𝔽2)—61no—
116H(5,𝔽2)Dic1511yescharacteristic
117C2×#41—31no—
118C2×#41—32no—
119C2×#41—61no—
120C2×M16—151no—
121C22×C8—151no—
122#117—152no—
123#104—302no—
124#104—302no—
125#103—302no—
126#102—302no—
127#99—301no—
128#99—301no—
129C22⋊C8—301no—
130C22⋊C8—301no—
131C2×C3×C5—161no—
132C2×A4—41no—
133C2×A4—81no—
134SL(2,𝔽3)—42no—
135C3⋊C8—801no—
136C22×C5—32no—
137C22×C5—31no—
138C22×C5—41no—
139C22×C5—61no—
140C22×C5—81no—
141C22×C5—121no—
142C22×C5—121no—
143C22×C5—241no—
144C4×C5—31no—
145C4×C5—32no—
146C4×C5—61no—
147C4×C5#102011yescharacteristic
148Dic5—242no—
149#41—32no—
150#41—32no—
151#41—32no—
152#41—62no—
153#41—62no—
154#41—62no—
155#41—62no—
156#41—62no—
157#41C5⋊S412yes—
158C2×Q8—31no—
159C2×Q8—32no—
160C2×Q8—61no—
161C2×D4—32no—
162C2×D4—31no—
163C2×D4—31no—
164C2×D4—31no—
165C2×D4—61no—
166C2×D4—62no—
167C2×D4—61no—
168C2×D4—61no—
169C22×C4—21no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—61no—
173C22×C4C5⋊S411yescharacteristic
174M16—302no—
175C2×C8—301no—
176C2×C8—301no—
177C2×C8—302no—
178C4⋊C4—302no—
179C22⋊C4—302no—
180C42—302no—
181C3×C5—161noHall
182A4—41no—
183A4—81no—
184C3×C4—161no—
185C2×C5—62no—
186C2×C5—61no—
187C2×C5—121no—
188C2×C5#593611yescharacteristic
189C23—21no—
190C23—31no—
191C23—31no—
192C23—61no—
193C23A4⋊Dic511yescharacteristic
194Q8—32no—
195Q8—62no—
196Q8A4⋊Dic512yes—
197D4—32no—
198D4—32no—
199D4—62no—
200D4—62no—
201D4—62no—
202D4—62no—
203C2×C4—32no—
204C2×C4—31no—
205C2×C4—32no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—61no—
210C2×C4—62no—
211C2×C4—61no—
212C2×C4—61no—
213C2×C4—61no—
214C2×C4—602no—
215C8—601no—
216C8—601no—
217C2×C3—161no—
218C5#8556711yescharacteristic, complemented, Sylow
219C22—31no—
220C22—32no—
221C22—41no—
222C22—61no—
223C22—81no—
224C22—121no—
225C22—121no—
226C22—241no—
227C4—31no—
228C4—32no—
229C4—61no—
230C4—1202no—
231C4C5⋊#102011yescharacteristic
232C3—161noSylow
233C2—62no—
234C2—61no—
235C2—121no—
236C2#1175692711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4C5⋊#1020
commutator, hypocenterC5×#997C4
FittingC5×#585D3
socleC2×C5#5936
prime radical, cosocleC5×#5950C2
LCSG ▷ C5×#997
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
3. C5×#997C4semidirect
39. #997Dic5semidirect
218. C5#85567semidirect

Maximal subgroups

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

subgroupindex
C5×#59502
#106029393
#911854
A4⋊#1684
#855675