Finite Group Databasebeta

← #14511775

Subgroups — #14511775

Order 1920.

254 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 49 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×A4×#168C211yesmaximal, characteristic
2#11752128C211yesmaximal, characteristic
3C5×#5409C211yesmaximal, characteristic
4#10600775—31nomaximal, Hall
5C2×C4×C5×A4C2211yescharacteristic
6A4×#168C412yes—
7A4⋊#168—21no—
8C5×A4⋊C8—21no—
9#90991—41nomaximal
10#73105—51nomaximal, Hall
11C23×#168D311yescharacteristic
12C5×#407—31no—
13#65496—31no—
14C2×#3954—31no—
15C2×#3954—31no—
16#64778—31no—
17#64778—31no—
18C22×C5×A4Q811yescharacteristic
19C4×C5×A4C2×C411yescharacteristic
20C4×C5×A4D411yescharacteristic
21#6710—41no—
22C5×#208—41no—
23C2×C3×#168—41no—
24C2×C8×A4—51no—
25#5409—51no—
26#5409D511yescharacteristic
27C23×C4×C5C2×D311yescharacteristic
28C2×C5×M16—31no—
29C2×C5×M16—31no—
30C2×#681—31no—
31C2×#681—31no—
32C22×#168—31no—
33C22×#168—31no—
34C22×#168—32no—
35C22×#168Dic312yes—
36C5×C22⋊C8—61no—
37C5×C22⋊C8—61no—
38C22⋊#168—61no—
39C22⋊#168—61no—
40#3954—61no—
41#3954—62no—
42#3954—61no—
43#1810—151noSylow
44C2×C5×A4—21no—
45C2×C5×A4C4⋊C411yescharacteristic
46C2×C3×C4×C5—41no—
47C3⋊#168—81no—
48C3×#168—42no—
49C5×C3⋊C8—81no—
50C2×C4×A4C2×D511yescharacteristic
51C8×A4—52no—
52A4⋊C8—21no—
53A4⋊C8—101no—
54#819—201no—
55C24×C5Dic611yescharacteristic
56C22×C4×C5—31no—
57C22×C4×C5—31no—
58C22×C4×C5—31no—
59C22×C4×C5—31no—
60C22×C4×C5D1211yescharacteristic
61C22×C4×C5C2×Dic311yescharacteristic
62C5×M16—61no—
63C5×M16—61no—
64C5×M16—61no—
65C5×M16—61no—
66C2×C5×C8—61no—
67C2×C5×C8—61no—
68#681—61no—
69#681—61no—
70#681—61no—
71#681—61no—
72C2×#168—31no—
73C2×#168—32no—
74C2×#168—32no—
75C2×#168—32no—
76C2×#168—61no—
77C2×#168—61no—
78C2×#168—61no—
79C2×#168S411yescharacteristic
80C23×C8—51no—
81C2×#108—151no—
82C2×#108—151no—
83#407—31no—
84#407—151no—
85#341—151no—
86#341—151no—
87C22×C3×C5—41no—
88C5×A4#10811yescharacteristic, complemented
89C3×C4×C5—41no—
90C3×C4×C5—41no—
91C22×A4Dic1011yescharacteristic
92C4×A4C4×D511yescharacteristic
93C4×A4C22⋊D511yescharacteristic
94C2×C3×C8—201no—
95#208—41no—
96#208—201no—
97C23×C5—21no—
98C23×C5—31no—
99C23×C5—31no—
100C23×C5—61no—
101C23×C5C4⋊Dic311yescharacteristic
102C2×C4×C5—31no—
103C2×C4×C5—31no—
104C2×C4×C5—31no—
105C2×C4×C5—31no—
106C2×C4×C5—31no—
107C2×C4×C5—31no—
108C2×C4×C5—31no—
109C2×C4×C5—61no—
110C2×C4×C5C2×S411yescharacteristic
111C5×C8—121no—
112C5×C8—121no—
113#168—32no—
114#168—121no—
115#168—121no—
116#168SL(2,ℤ/4)12yes—
117C23×C4D3×D511yescharacteristic
118C2×M16—31no—
119C2×M16—31no—
120C2×M16—151no—
121C2×M16—151no—
122C22×C8—52no—
123C22×C8—151no—
124C22×C8—151no—
125C22×C8—152no—
126#108—301no—
127#108—302no—
128#108—301no—
129C22⋊C8—61no—
130C22⋊C8—61no—
131C22⋊C8—301no—
132C22⋊C8—301no—
133C2×C3×C5—41no—
134C2×C3×C5—81no—
135C2×A4—21no—
136C2×A4#68311yescharacteristic
137C2×C3×C4—41no—
138C3×C8—202no—
139C3⋊C8—81no—
140C3⋊C8—401no—
141C22×C5—31no—
142C22×C5—31no—
143C22×C5—32no—
144C22×C5—31no—
145C22×C5—61no—
146C22×C5—61no—
147C22×C5—61no—
148C22×C5#81911yescharacteristic, complemented
149C22×C5A4⋊Q811yescharacteristic
150C4×C5—31no—
151C4×C5—31no—
152C4×C5C4⋊S411yescharacteristic
153C4×C5C2×SL(2,ℤ/4)11yescharacteristic
154C24#120411yescharacteristic
155C22×C4—31no—
156C22×C4—31no—
157C22×C4—31no—
158C22×C4—31no—
159C22×C4D5×Dic311yescharacteristic
160C22×C4#120311yescharacteristic
161M16—61no—
162M16—61no—
163M16—61no—
164M16—61no—
165M16—301no—
166M16—301no—
167M16—301no—
168M16—301no—
169C2×C8—51no—
170C2×C8—61no—
171C2×C8—61no—
172C2×C8—152no—
173C2×C8—152no—
174C2×C8—151no—
175C2×C8—152no—
176C2×C8—301no—
177C2×C8—301no—
178C2×C8—301no—
179C3×C5—41noHall
180C22×C3—41no—
181A4#395411yescharacteristic, complemented
182C3×C4—41no—
183C3×C4—41no—
184C2×C5—21no—
185C2×C5—31no—
186C2×C5—31no—
187C2×C5—61no—
188C2×C5C4⋊SL(2,ℤ/4)11yescharacteristic
189C23—21no—
190C23—31no—
191C23—31no—
192C23—61no—
193C23#666811yescharacteristic
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—31no—
201C2×C4—61no—
202C2×C4D5×S411yescharacteristic
203C8—52no—
204C8—121no—
205C8—121no—
206C8—152no—
207C8—601no—
208C8—601no—
209C2×C3—41no—
210C2×C3—81no—
211C5#7310511yescharacteristic, complemented, Sylow
212C22—31no—
213C22—31no—
214C22—32no—
215C22—31no—
216C22—61no—
217C22—61no—
218C22—61no—
219C22#9099111yescharacteristic, complemented
220C22#9189911yescharacteristic
221C4—31no—
222C4—31no—
223C4#9190211yescharacteristic
224C4D5×SL(2,ℤ/4)11yescharacteristic
225C3—41noSylow
226C2—21no—
227C2—31no—
228C2—31no—
229C2—61no—
230C2#1175163611yescharacteristic
subgroupG/H
centerC4#91902
commutatorC4×C5×A4C2×C4
Frattini, hypercenterC2×C4D5×S4
FittingC23×C4×C5C2×D3
socleC23×C5C4⋊Dic3
prime radicalC22×C5×A4Q8
cosocleC2×C4×C5×A4C22
hypocenterC5×A4#108
LCSG ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
88. C5×A4#108semidirect
148. C22×C5#819semidirect
181. A4#3954semidirect
211. C5#73105semidirect
219. C22#90991semidirect

Maximal subgroups

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

subgroupindex
C2×A4×#1682
#117521282
C5×#54092
#106007753
#909914
#731055