Finite Group Databasebeta

← #14512460

Subgroups — #14512460

Order 1920.

254 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 42 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#11756716C212yesmaximal
2C8×D5×A4C211yesmaximal, characteristic
3#10604732—31nomaximal, Hall
4C4×D5×A4C2211yescharacteristic
5A4⋊#170—22no—
6C5×C8×A4C411yescharacteristic
7#91225—41nomaximal
8A4×#168C411yescharacteristic
9#73105—51nomaximal, Hall
10C22×C8×D5D311yescharacteristic
11#65756—32no—
12C2×#3996—31no—
13C2×#3996—31no—
14#64896—32no—
15C2×D5×A4Q811yescharacteristic
16C4×C5×A4C2×C411yescharacteristic
17#6758—42no—
18A4×Dic5D411yescharacteristic
19C3×C8×D5—41no—
20C2×C8×A4—51no—
21#5409—52no—
22C22×C4×D5C2×D311yescharacteristic
23C2×#700—32no—
24C2×#700—32no—
25C22×C5×C8Dic311yescharacteristic
26C22×#168Dic311yescharacteristic
27C2×C8×D5—31no—
28C2×C8×D5—31no—
29C2×C8×D5—31no—
30C2×C8×D5—31no—
31C22⋊#170—62no—
32#4003—62no—
33#3996—61no—
34#3996—61no—
35#3996—61no—
36#3996—61no—
37#1810—151noSylow
38C2×C5×A4C4⋊C411yescharacteristic
39D5×A4—21no—
40C3×C4×D5—41no—
41C3⋊#170—82no—
42C3×C5×C8—41no—
43C3×#168—41no—
44C2×C4×A4—51no—
45C8×A4—51no—
46C8×A4AGL(1,𝔽5)11yescharacteristic
47A4⋊C8—102no—
48#819—201no—
49C23×D5Dic611yescharacteristic
50C22×C4×C5C2×Dic311yescharacteristic
51C22×Dic5D1211yescharacteristic
52C2×C4×D5—31no—
53C2×C4×D5—31no—
54C2×C4×D5—31no—
55C2×C4×D5—31no—
56C2×#170—62no—
57C2×#170—62no—
58#700—62no—
59#700—62no—
60#700—62no—
61#700—62no—
62C2×C5×C8—31no—
63C2×C5×C8—31no—
64C2×#168—31no—
65C2×#168—31no—
66C8×D5—31no—
67C8×D5—31no—
68C8×D5—31no—
69C8×D5—61no—
70C8×D5S411yescharacteristic
71C23×C8—51no—
72C2×#108—151no—
73C2×#108—151no—
74#407—152no—
75#341—152no—
76C2×C3×D5—41no—
77C5×A4#10811yescharacteristic, complemented
78C3×C4×C5—41no—
79C3×Dic5—41no—
80C22×A4—51no—
81C4×A4—51no—
82C4×A4C2×AGL(1,𝔽5)11yescharacteristic
83C2×C3×C8—201no—
84#208—202no—
85C23×C5C4⋊Dic311yescharacteristic
86C22×D5—21no—
87C22×D5—31no—
88C22×D5—31no—
89C22×D5—61no—
90C2×C4×C5—31no—
91C2×C4×C5—31no—
92C2×Dic5—31no—
93C2×Dic5—31no—
94C4×D5—31no—
95C4×D5—31no—
96C4×D5—31no—
97C4×D5—61no—
98C4×D5C2×S411yescharacteristic
99#170—122no—
100#170—122no—
101C5×C8—31no—
102C5×C8SL(2,ℤ/4)11yescharacteristic
103#168—31no—
104#168SL(2,ℤ/4)11yescharacteristic
105C23×C4—51no—
106C2×M16—152no—
107C2×M16—152no—
108C22×C8—51no—
109C22×C8—151no—
110C22×C8—151no—
111C22×C8—151no—
112C22×C8—151no—
113C22×C8ΓL(1,𝔽16)11yescharacteristic
114#108—301no—
115#108—301no—
116#108—301no—
117#108—301no—
118C22⋊C8—302no—
119C22⋊C8—302no—
120C2×C3×C5—41no—
121C3×D5—81no—
122C2×A4—101no—
123C2×A4C4⋊AGL(1,𝔽5)11yescharacteristic
124C2×C3×C4—201no—
125C3×C8—41no—
126C3×C8—201no—
127C3⋊C8—402no—
128C22×C5—31no—
129C22×C5—31no—
130C22×C5#81911yescharacteristic, complemented
131C2×D5—32no—
132C2×D5—31no—
133C2×D5—61no—
134C2×D5—61no—
135C2×D5—61no—
136C2×D5A4⋊Q811yescharacteristic
137C4×C5—31no—
138C4×C5C2×SL(2,ℤ/4)11yescharacteristic
139Dic5—31no—
140Dic5C4⋊S411yescharacteristic
141C24—51no—
142C22×C4—51no—
143C22×C4—151no—
144C22×C4—151no—
145C22×C4—151no—
146C22×C4—151no—
147C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
148M16—302no—
149M16—302no—
150M16—302no—
151M16—302no—
152C2×C8—31no—
153C2×C8—31no—
154C2×C8—51no—
155C2×C8—151no—
156C2×C8—151no—
157C2×C8—151no—
158C2×C8—151no—
159C2×C8—151no—
160C2×C8—301no—
161C2×C8—302no—
162C2×C8—302no—
163C3×C5—41noHall
164C22×C3—201no—
165A4#399611yescharacteristic, complemented
166C3×C4—41no—
167C3×C4—201no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5C4⋊SL(2,ℤ/4)11yescharacteristic
171D5—21no—
172D5—61no—
173C23—101no—
174C23—151no—
175C23—151no—
176C23—301no—
177C23C4⋊ΓL(1,𝔽16)11yescharacteristic
178C2×C4—31no—
179C2×C4—31no—
180C2×C4—51no—
181C2×C4—151no—
182C2×C4—151no—
183C2×C4—151no—
184C2×C4—151no—
185C2×C4—151no—
186C2×C4—301no—
187C8—31no—
188C8—51no—
189C8—151no—
190C8—602no—
191C8—602no—
192C8A4⋊AGL(1,𝔽5)11yescharacteristic
193C2×C3—41no—
194C2×C3—401no—
195C5#7310511yescharacteristic, complemented, Sylow
196C22—31no—
197C22—31no—
198C22—51no—
199C22—152no—
200C22—151no—
201C22—301no—
202C22—301no—
203C22—301no—
204C22#9122511yescharacteristic, complemented
205C4—31no—
206C4—51no—
207C4—151no—
208C4C2×A4⋊AGL(1,𝔽5)11yescharacteristic
209C3—41noSylow
210C2—31no—
211C2—31no—
212C2—101no—
213C2—301no—
214C2C4⋊(A4⋊AGL(1,𝔽5))11yescharacteristic
subgroupG/H
centerC2C4⋊(A4⋊AGL(1,𝔽5))
commutatorC4×C5×A4C2×C4
FrattiniC4C2×A4⋊AGL(1,𝔽5)
FittingC22×C5×C8Dic3
socleC23×C5C4⋊Dic3
prime radicalC2×D5×A4Q8
cosocleC4×D5×A4C22
hypercenterC8A4⋊AGL(1,𝔽5)
hypocenterC5×A4#108
LCSG ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
77. C5×A4#108semidirect
130. C22×C5#819semidirect
165. A4#3996semidirect
195. C5#73105semidirect
204. C22#91225semidirect

Maximal subgroups

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

subgroupindex
#117567162
C8×D5×A42
#106047323
#912254
#731055