Finite Group Databasebeta

← #14278253

Subgroups — #14278253

Order 1920.

208 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 54 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#11747942C211yesmaximal, characteristic
2#11746767C211yesmaximal, characteristic
3C3×#64887C211yesmaximal, characteristic
4#10598814—31nomaximal, Hall
5C2×#6758—21no—
6C2×C5×Dic12C411yescharacteristic
7C2×C3×C8×D5C2211yescharacteristic
8#91359—21no—
9C2×C3×#674—21no—
10#91102C411yescharacteristic
11#90973—21no—
12#67529—51nomaximal, Hall
13#65477—31no—
14#64896—31no—
15#64887D311yescharacteristic
16C2×C5×Dic6—21no—
17C2×C3×C4×D5D411yescharacteristic
18C2×C3⋊#170—41no—
19#6758—22no—
20#6758—41no—
21C2×C3×C5×C8C2×C411yescharacteristic
22C4⋊Dic15—21no—
23C5×Dic12—41no—
24C2×C3×#168D411yescharacteristic
25C3×C8×D5—41no—
26#6669—41no—
27#6665—41no—
28C3×#674—41no—
29#5116—51no—
30C3×C22⋊C16—51no—
31#4552—51no—
32C2×#700—61no—
33C2×C5×Q16—31no—
34#4092—61no—
35C2×C8×D5C2×D311yescharacteristic
36C2×#674—21no—
37#3967—61no—
38#3950—31no—
39#1350—151noSylow
40C22×C3×D5SD1611yescharacteristic
41C2×C3×C4×C5C22⋊C411yescharacteristic
42C2×Dic15—41no—
43C2×C5×Dic3—41no—
44C5×Dic6—41no—
45C5×Dic6—41no—
46C2×C3×Dic5D811yescharacteristic
47C3×C4×D5—21no—
48C3×C4×D5—21no—
49C3⋊#170—42no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C22×C3×C8—51no—
53#924—101no—
54C2×#208—101no—
55C2×Dic12AGL(1,𝔽5)11yescharacteristic
56C2×C3×C16—101no—
57#818—51no—
58#816—101no—
59C2×C5×Q8—61no—
60C2×C4×D5D1211yescharacteristic
61C2×#170—121no—
62#700—62no—
63#700—121no—
64C5×Q16—121no—
65C2×C5×C8C4×D311yescharacteristic
66#685—121no—
67C4⋊Dic5—61no—
68#683—121no—
69C2×#168#6711yescharacteristic
70C8×D5—41no—
71#674—41no—
72#467—151no—
73C22⋊C16—51no—
74#341—151no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—21no—
78C2×C3×D5—21no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81Dic15—81no—
82C3×Dic5—21no—
83C5×Dic3—81no—
84C22×C3×C4—51no—
85C2×Dic6—21no—
86C2×C3×C8—51no—
87C2×C3×C8—201no—
88C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
89#217—201no—
90C4⋊Dic3—101no—
91Dic3⋊C4—201no—
92#208—102no—
93#208—201no—
94C2×C3⋊C8—201no—
95Dic12—41no—
96C3×C16—201no—
97C22×D5#20411yescharacteristic
98C5×Q8—121no—
99C5×Q8—121no—
100C2×C4×C5—121no—
101C2×C4×C5(C2×D3)⋊C411yescharacteristic
102C2×Dic5—121no—
103C2×Dic5D2411yescharacteristic
104C4×D5—21no—
105C4×D5—21no—
106#170—122no—
107C5×C8—21no—
108#168—21no—
109C2×Q16—31no—
110C2×M16—301no—
111C22×C8—51no—
112C22⋊Q8—301no—
113C2×C16—101no—
114#107—151no—
115#103—301no—
116C2×C3×C5#32711yescharacteristic
117C2×C3×C5#35911yescharacteristic
118C2×C3×C5#36211yescharacteristic
119C3×D5—41no—
120C23×C3—51no—
121C2×C3×C4—51no—
122C2×C3×C4—101no—
123C2×C3×C4—101no—
124C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
125C2×Dic3—41no—
126C2×Dic3—201no—
127Dic6—41no—
128Dic6—41no—
129C3×C8—21no—
130C3×C8—101no—
131C3⋊C8—202no—
132C22×C5#82111yescharacteristic
133C2×D5—21no—
134C2×D5—21no—
135C2×D5—21no—
136C4×C5—241no—
137C4×C5#80611yescharacteristic
138C4×C5#82511yescharacteristic
139Dic5—21no—
140Dic5—241no—
141C2×Q8—61no—
142C22×C4—51no—
143Q16—121no—
144M16—302no—
145M16—601no—
146C2×C8—51no—
147C2×C8—201no—
148C2×C8—601no—
149C2×C8D3×AGL(1,𝔽5)11yescharacteristic
150C4⋊C4—301no—
151C4⋊C4—601no—
152C22⋊C4—601no—
153C16—201no—
154C3×C5#135011yescharacteristic, complemented, Hall
155C22×C3—101no—
156C22×C3—101no—
157C22×C3—101no—
158C22×C3#400711yescharacteristic
159C3×C4—101no—
160C3×C4#400811yescharacteristic
161C3×C4#401111yescharacteristic
162Dic3—81no—
163Dic3—401no—
164C2×C5#447011yescharacteristic
165C2×C5#451011yescharacteristic
166C2×C5#451711yescharacteristic
167D5—41no—
168C23—51no—
169Q8—121no—
170Q8—121no—
171C2×C4—51no—
172C2×C4—101no—
173C2×C4—101no—
174C2×C4—121no—
175C2×C4—601no—
176C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
177C8—21no—
178C8—101no—
179C8—602no—
180C2×C3—201no—
181C2×C3#6490911yescharacteristic
182C2×C3#6491011yescharacteristic
183C2×C3#6492011yescharacteristic
184C5#6752911yescharacteristic, complemented, Sylow
185C22—101no—
186C22—101no—
187C22—101no—
188C22#9115211yescharacteristic
189C4—101no—
190C4—241no—
191C4—1201no—
192C4#9115511yescharacteristic
193C4#9117211yescharacteristic
194C3#1059881411yescharacteristic, complemented, Sylow
195C2—201no—
196C2#1174646311yescharacteristic
197C2#1174647111yescharacteristic
198C2#1174649811yescharacteristic
subgroupG/H
centerC22#91152
commutator, FittingC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×C8D3×AGL(1,𝔽5)
socleC22×C3×C5#102
prime radicalC22×C3×D5SD16
cosocleC2×C3×C8×D5C22
hypocenterC3×C5#1350
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
154. C3×C5#1350semidirect
184. C5#67529semidirect
194. C3#10598814semidirect

Maximal subgroups

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

subgroupindex
#117479422
#117467672
C3×#648872
#105988143
#675295