Finite Group Databasebeta

← #14278242

Subgroups — #14278242

Order 1920.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C3×#65477C211yesmaximal, characteristic
2#11746767C211yesmaximal, characteristic
3#11746758C211yesmaximal, characteristic
4#10598814—31nomaximal, Hall
5C2×#6758—21no—
6C2×C3×C5×Q16C411yescharacteristic
7C3×#4092—21no—
8C2×C3×C8×D5C2211yescharacteristic
9C2×C3⋊#674—21no—
10C3×#3967—21no—
11C3×#3950C411yescharacteristic
12#67777—51nomaximal, Hall
13#65477D311yescharacteristic
14#64896—31no—
15#64887—31no—
16C2×C3×C5×Q8—21no—
17C2×C3×C4×D5D411yescharacteristic
18C2×C3⋊#170—41no—
19#6758—22no—
20#6758—41no—
21C3×C5×Q16—41no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C3×#685—41no—
24C3×C4⋊Dic5—21no—
25C3×#683—41no—
26C2×C3×#168D411yescharacteristic
27C3×C8×D5—41no—
28C3⋊#674—41no—
29C3×#467—51no—
30#4552—51no—
31#4549—51no—
32C2×#700—61no—
33C2×C5×Q16Dic311yescharacteristic
34#4092—21no—
35C2×C8×D5C2×D311yescharacteristic
36C2×#674—61no—
37#3967—21no—
38#3950Dic311yescharacteristic
39#1350—151noSylow
40C22×C3×D5SD1611yescharacteristic
41C3×C5×Q8—41no—
42C3×C5×Q8—41no—
43C2×C3×C4×C5—41no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×Dic5—41no—
46C2×C3×Dic5D811yescharacteristic
47C3×C4×D5—21no—
48C3×C4×D5—21no—
49C3⋊#170—42no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C2×C3×Q16AGL(1,𝔽5)11yescharacteristic
53C22×C3×C8—51no—
54C3×C22⋊Q8—101no—
55C2×#208—101no—
56C3×#107—51no—
57C3×#103—101no—
58C2×C3⋊C16—101no—
59C2×C5×Q8—21no—
60C2×C4×D5#6711yescharacteristic
61C2×#170—121no—
62#700—62no—
63#700—121no—
64C5×Q16—41no—
65C2×C5×C8C2×Dic311yescharacteristic
66#685—41no—
67C4⋊Dic5—21no—
68#683—41no—
69C2×#168#6711yescharacteristic
70C8×D5—41no—
71#674—121no—
72#467—51no—
73C22⋊C16—151no—
74#341—151no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—21no—
78C2×C3×D5—21no—
79C3×C4×C5—81no—
80C3×C4×C5#9911yescharacteristic
81C3×C4×C5#10411yescharacteristic
82C3×Dic5—21no—
83C3×Dic5—81no—
84C2×C3×Q8—21no—
85C22×C3×C4—51no—
86C3×Q16—41no—
87C2×C3×C8—51no—
88C2×C3×C8—201no—
89C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
90C3×C4⋊C4—101no—
91C3×C4⋊C4—201no—
92C3×C22⋊C4—201no—
93#208—102no—
94#208—201no—
95C2×C3⋊C8—201no—
96C3⋊C16—201no—
97C22×D5#21411yescharacteristic
98C5×Q8—41no—
99C5×Q8—41no—
100C2×C4×C5—41no—
101C2×C4×C5#21711yescharacteristic
102C2×Dic5—41no—
103C2×Dic5#21311yescharacteristic
104C4×D5—21no—
105C4×D5—21no—
106#170—122no—
107C5×C8—21no—
108#168—21no—
109C2×Q16ΓL(1,𝔽16)11yescharacteristic
110C2×M16—301no—
111C22×C8—51no—
112C22⋊Q8—101no—
113C2×C16—301no—
114#107—51no—
115#103—101no—
116C2×C3×C5#32711yescharacteristic
117C2×C3×C5#35911yescharacteristic
118C2×C3×C5#36211yescharacteristic
119C3×D5—41no—
120C23×C3—51no—
121C3×Q8—41no—
122C3×Q8—41no—
123C2×C3×C4—41no—
124C2×C3×C4—51no—
125C2×C3×C4—101no—
126C2×C3×C4—101no—
127C2×C3×C4—201no—
128C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
129C3×C8—21no—
130C3×C8—101no—
131C3⋊C8—202no—
132C22×C5#83211yescharacteristic
133C2×D5—21no—
134C2×D5—21no—
135C2×D5—21no—
136C4×C5—81no—
137C4×C5#83411yescharacteristic
138C4×C5#83711yescharacteristic
139Dic5—21no—
140Dic5—81no—
141C2×Q8—21no—
142C22×C4—51no—
143Q16—41no—
144M16—302no—
145M16—601no—
146C2×C8—51no—
147C2×C8—201no—
148C2×C8—601no—
149C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
150C4⋊C4—101no—
151C4⋊C4—201no—
152C22⋊C4—201no—
153C16—601no—
154C3×C5#135011yescharacteristic, complemented, Hall
155C22×C3—101no—
156C22×C3—101no—
157C22×C3—101no—
158C22×C3#400711yescharacteristic
159C3×C4—81no—
160C3×C4—101no—
161C3×C4—401no—
162C3×C4#400811yescharacteristic
163C3×C4#401111yescharacteristic
164C2×C5#453711yescharacteristic
165C2×C5#456511yescharacteristic
166C2×C5#456711yescharacteristic
167D5—41no—
168C23—51no—
169Q8—41no—
170Q8—41no—
171C2×C4—41no—
172C2×C4—51no—
173C2×C4—101no—
174C2×C4—101no—
175C2×C4—201no—
176C2×C4#676311yescharacteristic
177C8—21no—
178C8—101no—
179C8—602no—
180C2×C3—201no—
181C2×C3#6490911yescharacteristic
182C2×C3#6491011yescharacteristic
183C2×C3#6492011yescharacteristic
184C5#6777711yescharacteristic, complemented, Sylow
185C22—101no—
186C22—101no—
187C22—101no—
188C22#9123611yescharacteristic
189C4—81no—
190C4—101no—
191C4—401no—
192C4#9123711yescharacteristic
193C4#9124011yescharacteristic
194C3#1059881411yescharacteristic, complemented, Sylow
195C2—201no—
196C2#1174678011yescharacteristic
197C2#1174678111yescharacteristic
198C2#1174679111yescharacteristic
subgroupG/H
centerC22#91236
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×C8C2×ΓL(1,𝔽16)
FittingC2×C3×C5×Q16C4
socleC22×C3×C5#102
prime radicalC22×C3×D5SD16
cosocleC2×C3×C8×D5C22
hypercenterC2×Q16ΓL(1,𝔽16)
hypocenterC3×C5#1350
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
154. C3×C5#1350semidirect
184. C5#67777semidirect
194. C3#10598814semidirect

Maximal subgroups

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

subgroupindex
C3×#654772
#117467672
#117467582
#105988143
#677775