Finite Group Databasebeta

← #14278017

Subgroups — #14278017

Order 1920.

208 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C5×#5137C211yesmaximal, characteristic
2#11746374C211yesmaximal, characteristic
3C3×#64777C211yesmaximal, characteristic
4#10598271—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6C5×#924—21no—
7C2×C5×Dic12C411yescharacteristic, complemented
8C3×#4072—21no—
9#91096—21no—
10C5×#817C411yescharacteristic, complemented
11C5×#816—21no—
12#67482—51nomaximal, Hall
13C5×#470—31no—
14#64777D311yescharacteristic
15#64773—31no—
16C22×C3×C4×C5D411yescharacteristic
17C2×C5×Dic6—21no—
18C3×C5×M16—41no—
19C2×C3×C5×C8C2×C411yescharacteristic
20C2×C3×C5×C8D411yescharacteristic
21C5×#217—41no—
22C5×C4⋊Dic3—21no—
23C5×Dic3⋊C4—41no—
24C5×Dic12—41no—
25C3×C22⋊Dic5—41no—
26C3×C4⋊Dic5—41no—
27C3×C4×Dic5—22no—
28C3⋊#672—41no—
29#5137D511yescharacteristic
30C3×H(3,ℤ/4)—51no—
31#4553—51no—
32C2×C5×Q16—31no—
33C2×C5×M16C2×D311yescharacteristic
34C5×C22⋊Q8—61no—
35#4072—21no—
36C5×#106—31no—
37C5×#103—61no—
38#3944—61no—
39#1340—151noSylow
40C23×C3×C5D811yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×C4×C5SD1611yescharacteristic
45C2×C5×Dic3—41no—
46C2×C5×Dic3—41no—
47C5×Dic6—41no—
48C5×Dic6—41no—
49C2×C3×Dic5—42no—
50C3×C5×C8—21no—
51C3×C5×C8—21no—
52C2×C3×M16C2×D511yescharacteristic
53C3×#117—101no—
54#924—21no—
55C2×Dic12Dic511yescharacteristic, complemented
56#817Dic511yescharacteristic, complemented
57#816—21no—
58#812—101no—
59C2×C5×Q8—61no—
60C22×C4×C5#6711yescharacteristic
61C5×Q16—121no—
62C5×M16—41no—
63C2×C5×C8C4×D311yescharacteristic
64C2×C5×C8D1211yescharacteristic
65C5×C4⋊C4—61no—
66C5×C4⋊C4—121no—
67C5×C22⋊C4—121no—
68C22⋊Dic5—41no—
69C4⋊Dic5—41no—
70C4×Dic5—22no—
71#672—121no—
72#470—31no—
73#349—151no—
74H(3,ℤ/4)—51no—
75C22×C3×C5—21no—
76C22×C3×C5—41no—
77C22×C3×C5#10211yescharacteristic
78C3×C4×C5—21no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81C3×Dic5—82no—
82C5×Dic3—81no—
83C5×Dic3—81no—
84C22×C3×C4C22⋊D511yescharacteristic
85C2×Dic6—21no—
86C3×M16—41no—
87C2×C3×C8C2×Dic511yescharacteristic
88C2×C3×C8C22⋊D511yescharacteristic
89C3×C4⋊C4—201no—
90C3×C22⋊C4—201no—
91C3×C42—102no—
92#217—41no—
93C4⋊Dic3—21no—
94Dic3⋊C4—41no—
95Dic12—41no—
96C3⋊C16—201no—
97C23×C5#21311yescharacteristic
98C5×Q8—121no—
99C5×Q8—121no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—121no—
103C2×C4×C5—121no—
104C2×C4×C5(C2×D3)⋊C411yescharacteristic
105C2×C4×C5#21511yescharacteristic
106C2×Dic5—42no—
107C5×C8—21no—
108C5×C8—21no—
109C2×Q16—31no—
110C2×M16D3×D511yescharacteristic
111C22⋊Q8—61no—
112#117—101no—
113M32—301no—
114#106—31no—
115#103—61no—
116C2×C3×C5—21no—
117C2×C3×C5—41no—
118C2×C3×C5#32711yescharacteristic
119C23×C3#68611yescharacteristic
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—202no—
123C2×C3×C4#68711yescharacteristic
124C2×C3×C4C22⋊Dic511yescharacteristic
125C2×Dic3—41no—
126C2×Dic3—41no—
127Dic6—41no—
128Dic6—41no—
129C3×C8—21no—
130C3×C8—21no—
131C22×C5—21no—
132C22×C5—41no—
133C22×C5#80911yescharacteristic
134C4×C5—21no—
135C4×C5—241no—
136C4×C5—241no—
137C4×C5#80511yescharacteristic
138C4×C5#80611yescharacteristic
139Dic5—82no—
140C2×Q8—61no—
141C22×C4#120111yescharacteristic
142Q16—121no—
143M16—41no—
144C2×C8D3×Dic511yescharacteristic
145C2×C8#120311yescharacteristic
146C4⋊C4—61no—
147C4⋊C4—121no—
148C4⋊C4—201no—
149C22⋊C4—121no—
150C22⋊C4—201no—
151C42—102no—
152C16—601no—
153C3×C5#134011yescharacteristic, complemented, Hall
154C22×C3—21no—
155C22×C3—41no—
156C22×C3#396411yescharacteristic
157C3×C4—21no—
158C3×C4—402no—
159C3×C4#396611yescharacteristic
160C3×C4#396911yescharacteristic
161Dic3—81no—
162Dic3—81no—
163C2×C5—21no—
164C2×C5—41no—
165C2×C5#445111yescharacteristic
166C23#665211yescharacteristic
167Q8—121no—
168Q8—121no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—121no—
172C2×C4—121no—
173C2×C4—202no—
174C2×C4#665611yescharacteristic
175C2×C4(C2×D3)⋊Dic511yescharacteristic
176C8—21no—
177C8—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3#6475711yescharacteristic
181C5#6748211yescharacteristic, complemented, Sylow
182C22—21no—
183C22—41no—
184C22#9096611yescharacteristic
185C4—21no—
186C4—241no—
187C4—241no—
188C4—402no—
189C4#9097911yescharacteristic
190C4#9099611yescharacteristic
191C3#1059827111yescharacteristic, complemented, Sylow
192C2—21no—
193C2—41no—
194C2#1174595611yescharacteristic
subgroupG/H
centerC2#11745956
commutatorC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×M16D3×D5
Fitting, cosocleC2×C3×C5×M16C22
socleC2×C3×C5#327
prime radicalC23×C3×C5D8
hypocenterC3×C5#1340
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
7. C2×C5×Dic12C4semidirect
10. C5×#817C4semidirect
55. C2×Dic12Dic5semidirect
56. #817Dic5semidirect
153. C3×C5#1340semidirect
181. C5#67482semidirect
191. C3#10598271semidirect

Maximal subgroups

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

subgroupindex
C5×#51372
#117463742
C3×#647772
#105982713
#674825