Finite Group Databasebeta

← #14277998

Subgroups — #14277998

Order 1920.

228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 46 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#11747905C211yesmaximal, characteristic
2#11746762C211yesmaximal, characteristic, complemented
3C3×#64895C211yesmaximal, characteristic, complemented
4#10598803—31nomaximal, Hall
5C3×#4130—21no—
6C2×C5×D24C411yescharacteristic, complemented
7C2×C3×#676C2211yescharacteristic
8#91449—21no—
9#91227—21no—
10#91101C411yescharacteristic, complemented
11#90967—21no—
12#67481—51nomaximal, Hall
13#65448—31no—
14#64895D311yescharacteristic, complemented
15#64891—31no—
16C2×C5×D12—21no—
17C2×C3×C4×D5D411yescharacteristic
18C2×#1201—41no—
19C3×C22⋊AGL(1,𝔽5)—41no—
20C3×C4⋊AGL(1,𝔽5)—41no—
21C3×C4×AGL(1,𝔽5)—22no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C4⋊Dic15—21no—
24C5×D24—41no—
25C2×C3×#168D411yescharacteristic
26C3×#676—41no—
27(C2×D3)⋊Dic5—41no—
28C3⋊#674—41no—
29#5135—51no—
30C3×H(3,ℤ/4)—51no—
31#4553—51no—
32#4130—21no—
33C2×C5×D8—31no—
34#4084—61no—
35C2×#676C2×D311yescharacteristic
36#3998—61no—
37#3964—61no—
38#3949—31no—
39#1339—151noSylow
40C22×C5×D3—41no—
41C22×C3×D5D811yescharacteristic
42C2×C3×AGL(1,𝔽5)—42no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×Dic15—41no—
45C5×D12—41no—
46C5×D12—41no—
47C2×C3×Dic5SD1611yescharacteristic
48C3×C4×D5—21no—
49C3×C4×D5—21no—
50#1201—82no—
51C3×C5×C8—21no—
52C3×#168—21no—
53C2×C3×M16—51no—
54C3×#117—101no—
55#930—101no—
56C2×D24AGL(1,𝔽5)11yescharacteristic, complemented
57#821—101no—
58#817—51no—
59#812—101no—
60C2×C5×D4—61no—
61C2×C22⋊D5—121no—
62C2×C4×D5#6711yescharacteristic
63C22⋊AGL(1,𝔽5)—41no—
64C4⋊AGL(1,𝔽5)—41no—
65C4×AGL(1,𝔽5)—22no—
66C5×D8—121no—
67C2×C5×C8C4×D311yescharacteristic
68C22⋊Dic5—121no—
69C4⋊Dic5—61no—
70C2×#168D1211yescharacteristic
71#676—41no—
72#674—121no—
73#469—151no—
74#349—151no—
75H(3,ℤ/4)—51no—
76C22×C3×C5#10211yescharacteristic
77C2×C5×D3—81no—
78C2×C5×D3—81no—
79C2×C5×D3—81no—
80C2×C3×D5—21no—
81C2×C3×D5—41no—
82C3×AGL(1,𝔽5)—82no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#10411yescharacteristic
85Dic15—81no—
86C3×Dic5—21no—
87C22×C3×C4—51no—
88C2×#67—201no—
89C2×D12—21no—
90C3×M16—201no—
91C2×C3×C8—51no—
92C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
93C3×C4⋊C4—201no—
94C3×C22⋊C4—201no—
95C3×C42—102no—
96(C2×D3)⋊C4—201no—
97C4⋊Dic3—101no—
98D24—41no—
99C3⋊C16—201no—
100C23×C5—121no—
101C22×D5#21311yescharacteristic
102C2×AGL(1,𝔽5)—42no—
103C5×D4—121no—
104C5×D4—121no—
105C2×C4×C5(C2×D3)⋊C411yescharacteristic
106C22⋊D5—242no—
107C2×Dic5—121no—
108C2×Dic5#21511yescharacteristic
109C4×D5—21no—
110C4×D5—21no—
111C5×C8—21no—
112#168—21no—
113C2×D8—31no—
114C2×M16—51no—
115#121—301no—
116#117—101no—
117M32—301no—
118#106—151no—
119#102—301no—
120C2×C3×C5—21no—
121C2×C3×C5#32711yescharacteristic
122C3×D5—41no—
123C5×D3—161no—
124C23×C3—51no—
125C22×D3—41no—
126C2×C3×C4—51no—
127C2×C3×C4—101no—
128C2×C3×C4—101no—
129C2×C3×C4—202no—
130C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
131#67—402no—
132C2×Dic3—201no—
133D12—41no—
134D12—41no—
135C3×C8—21no—
136C3×C8—101no—
137C22×C5—241no—
138C22×C5—241no—
139C22×C5—241no—
140C22×C5#80911yescharacteristic
141C2×D5—21no—
142C2×D5—41no—
143AGL(1,𝔽5)—82no—
144C4×C5#80511yescharacteristic
145C4×C5#80611yescharacteristic
146Dic5—21no—
147Dic5—241no—
148C2×D4—61no—
149C2×D4—601no—
150C22×C4—51no—
151D8—121no—
152M16—201no—
153C2×C8—51no—
154C2×C8D3×AGL(1,𝔽5)11yescharacteristic
155C4⋊C4—201no—
156C4⋊C4—301no—
157C22⋊C4—201no—
158C22⋊C4—601no—
159C42—102no—
160C16—601no—
161C3×C5#133911yescharacteristic, complemented, Hall
162C22×C3—101no—
163C22×C3—201no—
164C22×C3#400711yescharacteristic
165C2×D3—81no—
166C2×D3—81no—
167C2×D3—81no—
168C3×C4—101no—
169C3×C4—402no—
170C3×C4#400811yescharacteristic
171C3×C4#401111yescharacteristic
172Dic3—401no—
173C2×C5—21no—
174C2×C5—481no—
175C2×C5#445111yescharacteristic
176D5—41no—
177C23—51no—
178C23—121no—
179D4—121no—
180D4—121no—
181D4—1202no—
182C2×C4—51no—
183C2×C4—101no—
184C2×C4—101no—
185C2×C4—202no—
186C2×C4—601no—
187C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
188C8—21no—
189C8—101no—
190C2×C3—21no—
191C2×C3—201no—
192C2×C3#6492011yescharacteristic
193D3—161no—
194C5#6748111yescharacteristic, complemented, Sylow
195C22—101no—
196C22—201no—
197C22—241no—
198C22—241no—
199C22—241no—
200C22#9115111yescharacteristic
201C4—101no—
202C4—402no—
203C4—1201no—
204C4#9115611yescharacteristic
205C4#9117211yescharacteristic
206C3#1059880311yescharacteristic, complemented, Sylow
207C2—21no—
208C2—201no—
209C2—481no—
210C2#1174649611yescharacteristic
subgroupG/H
centerC2#11746496
commutator, FittingC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×C8D3×AGL(1,𝔽5)
socleC2×C3×C5#327
prime radical#11747905C2
cosocleC2×C3×#676C22
hypocenterC3×C5#1339
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #11746762C2semidirect
3. C3×#64895C2semidirect
6. C2×C5×D24C4semidirect
10. #91101C4semidirect
14. #64895D3semidirect
56. C2×D24AGL(1,𝔽5)semidirect
161. C3×C5#1339semidirect
194. C5#67481semidirect
206. C3#10598803semidirect

Maximal subgroups

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

subgroupindex
#117479052
#117467622
C3×#648952
#105988033
#674815