Finite Group Databasebeta

← #14279103

Subgroups — #14279103

Order 1920.

316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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#11752420C212yesmaximal
2C3×#65418C211yesmaximal, characteristic
3#10598792—31nomaximal, Hall
4C2×C3×#709C2211yescharacteristic
5D5⋊#208—22no—
6C2×C3×C5×M16C411yescharacteristic
7C22×C3×#168C411yescharacteristic
8#91242C414yes—
9#91234—22no—
10C3×#3952—22no—
11#67693—51nomaximal, Hall
12#65761—32no—
13#65418D311yescharacteristic
14C22×C3×C4×C5C2×C411yescharacteristic
15C2×C3×C22⋊D5C2×C412yes—
16C3×#709—41no—
17C3×#709—41no—
18C2×C3×D20Q811yescharacteristic
19C2×C3×C4×D5D412yes—
20C2×C3×Dic10D411yescharacteristic
21#6762—24no—
22#6758—42no—
23D5⋊(C3⋊C8)—42no—
24C3×C5×M16—41no—
25C2×C3×C5×C8—21no—
26C2×C3×#168—21no—
27C2×C3×#168—41no—
28C3×#408—51no—
29#5237—52no—
30C2×#709C2×D311yescharacteristic
31D5⋊M16—62no—
32C2×C5×M16Dic311yescharacteristic
33C22×#168Dic311yescharacteristic
34#4013—34no—
35#4005—62no—
36#3952—22no—
37#1392—151noSylow
38C23×C3×C5C4211yescharacteristic
39C22×C3×D5C4⋊C412yes—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C2×C3×C4×C5C4⋊C411yescharacteristic
44C3×C22⋊D5—42no—
45C2×C3×Dic5C22⋊C412yes—
46C3×D20—41no—
47C3×C4×D5—22no—
48C3×C4×D5—22no—
49C3×Dic10—41no—
50C3⋊#170—44no—
51C3×C5×C8—41no—
52C3×#168—41no—
53C2×C3×#41—51no—
54C2×C3×M16AGL(1,𝔽5)11yescharacteristic
55C22×C3×C8—51no—
56C2×#208—102no—
57C3×C22⋊C8—102no—
58#836—102no—
59#833—54no—
60C22×C4×C5C2×Dic311yescharacteristic
61C2×C22⋊D5C4×D312yes—
62#709—41no—
63#709—41no—
64C2×D20Dic611yescharacteristic
65C2×C4×D5#6712yes—
66C2×Dic10D1211yescharacteristic
67#704—64no—
68#700—122no—
69D5⋊C8—122no—
70C5×M16—41no—
71C2×C5×C8—21no—
72C2×#168—21no—
73C2×#168—41no—
74#413—152no—
75#408—51no—
76C22×C3×C5—21no—
77C22×C3×C5—41no—
78C22×C3×C5#9511yescharacteristic
79C2×C3×D5—22no—
80C2×C3×D5—42no—
81C3×C4×C5—21no—
82C3×C4×C5#9911yescharacteristic
83C3×C4×C5#9911yescharacteristic
84C3×Dic5—22no—
85C3×#41—201no—
86C3×#41—201no—
87C2×C3×Q8—51no—
88C2×C3×D4—52no—
89C2×C3×D4—51no—
90C22×C3×C4—52no—
91C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
92C3×M16—41no—
93C2×C3×C8—21no—
94C2×C3×C8—101no—
95C2×C3×C8—201no—
96#208—104no—
97#208—202no—
98C2×C3⋊C8—202no—
99C23×C5C4×Dic311yescharacteristic
100C22×D5Dic3⋊C412yes—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5C4⋊Dic311yescharacteristic
104C2×C4×C5#21711yescharacteristic
105C22⋊D5—42no—
106C2×Dic5(C2×D3)⋊C412yes—
107D20—41no—
108C4×D5—22no—
109C4×D5—22no—
110Dic10—41no—
111#170—124no—
112C5×C8—41no—
113#168—41no—
114C2×#41—51no—
115C2×M16—302no—
116C2×M16ΓL(1,𝔽16)11yescharacteristic
117C22×C8—51no—
118#101—302no—
119#100—154no—
120C22⋊C8—102no—
121C2×C3×C5—21no—
122C2×C3×C5—41no—
123C2×C3×C5#34211yescharacteristic
124C3×D5—42no—
125C23×C3—52no—
126C23×C3C4×AGL(1,𝔽5)11yescharacteristic
127C3×Q8—201no—
128C3×D4—201no—
129C3×D4—202no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—52no—
133C2×C3×C4—102no—
134C2×C3×C4—102no—
135C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
136C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
137C3×C8—41no—
138C3×C8—201no—
139C3⋊C8—204no—
140C22×C5—21no—
141C22×C5—41no—
142C22×C5C3⋊#9511yescharacteristic
143C2×D5—22no—
144C2×D5—42no—
145C4×C5—21no—
146C4×C5#83411yescharacteristic
147C4×C5#83411yescharacteristic
148Dic5—22no—
149#41—201no—
150#41—201no—
151C2×Q8—51no—
152C2×D4—52no—
153C2×D4—51no—
154C22×C4—52no—
155C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
156M16—41no—
157M16—304no—
158M16—602no—
159C2×C8—21no—
160C2×C8—101no—
161C2×C8—201no—
162C2×C8—602no—
163C3×C5#139211yescharacteristic, complemented, Hall
164C22×C3—21no—
165C22×C3—41no—
166C22×C3—102no—
167C22×C3—202no—
168C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
169C3×C4—21no—
170C3×C4—102no—
171C3×C4#399911yescharacteristic
172C3×C4#401111yescharacteristic
173C2×C5—21no—
174C2×C5—41no—
175C2×C5#452611yescharacteristic
176D5—42no—
177C23—52no—
178C23C4×ΓL(1,𝔽16)11yescharacteristic
179Q8—201no—
180D4—201no—
181D4—202no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—52no—
185C2×C4—102no—
186C2×C4—102no—
187C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
188C2×C4#676311yescharacteristic
189C8—41no—
190C8—201no—
191C8—604no—
192C2×C3—21no—
193C2×C3—41no—
194C2×C3—202no—
195C2×C3#6491711yescharacteristic
196C5#6769311yescharacteristic, complemented, Sylow
197C22—21no—
198C22—41no—
199C22—102no—
200C22—202no—
201C22#9123511yescharacteristic
202C4—21no—
203C4—102no—
204C4#9122811yescharacteristic
205C4#9124011yescharacteristic
206C3#1059879211yescharacteristic, complemented, Sylow
207C2—21no—
208C2—41no—
209C2—202no—
210C2#1174678811yescharacteristic
subgroupG/H
centerC4#91228
commutatorC23×C3×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC2×C3×C5×M16C4
socleC2×C3×C5#342
prime radical, cosocleC2×C3×#709C22
hypercenterC2×M16ΓL(1,𝔽16)
hypocenterC3×C5#1392
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
163. C3×C5#1392semidirect
196. C5#67693semidirect
206. C3#10598792semidirect

Maximal subgroups

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

subgroupindex
#117524202
C3×#654182
#105987923
#676935