Finite Group Databasebeta

← #14278037

Subgroups — #14278037

Order 1920.

220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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×#65154C211yesmaximal, characteristic
2#11746768C211yesmaximal, characteristic, complemented
3#11746762C211yesmaximal, characteristic, complemented
4#10598601—31nomaximal, Hall
5D5⋊#208—21no—
6C2×C3×D40C411yescharacteristic
7C2×C3×#676C2211yescharacteristic
8C3×#4041—21no—
9#91227—21no—
10C3×C5×#106C411yescharacteristic
11C3×#3941—21no—
12#67779—51nomaximal, Hall
13#65154D311yescharacteristic
14#64897—31no—
15#64891—31no—
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×C4×D5D411yescharacteristic
19#6762—41no—
20#6758—41no—
21D5⋊(C3⋊C8)—22no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C3×C5×C4⋊C4—21no—
24C3×#685—41no—
25C2×C3×#168D411yescharacteristic
26C3×D40—41no—
27C3×#676—41no—
28C3⋊#674—41no—
29C3×#469—51no—
30C3⋊#338—51no—
31#4553—51no—
32D5⋊M16—61no—
33C2×D40Dic311yescharacteristic
34C2×#676C2×D311yescharacteristic
35#4041—21no—
36#3998—61no—
37C5×#106Dic311yescharacteristic
38#3941—21no—
39#1341—151noSylow
40C22×C3×D5—41no—
41C22×C3×D5SD1611yescharacteristic
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×Dic5D811yescharacteristic
45C3×D20—41no—
46C3×D20—41no—
47C3×D20—82no—
48C3×C4×D5—21no—
49C3×C4×D5—21no—
50C3⋊#170—42no—
51C3×C5×C8—21no—
52C3×#168—21no—
53C2×C3×D8—51no—
54C2×C3×M16—51no—
55C3×#121—101no—
56C2×#208—101no—
57C3×#106AGL(1,𝔽5)11yescharacteristic
58C3×#102—101no—
59#812—101no—
60C2×D20—21no—
61C2×D20—41no—
62C2×C4×D5#6711yescharacteristic
63#704—121no—
64#700—121no—
65D5⋊C8—62no—
66C2×C5×C8C2×Dic311yescharacteristic
67C5×C4⋊C4—21no—
68#685—41no—
69C2×#168#6711yescharacteristic
70D40—41no—
71#676—41no—
72#674—121no—
73#469—51no—
74#349—151no—
75#338—151no—
76C22×C3×C5#10211yescharacteristic
77C2×C3×D5—21no—
78C2×C3×D5—41no—
79C2×C3×D5—81no—
80C2×C3×D5—81no—
81C2×C3×D5—81no—
82C3×C4×C5—81no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#10411yescharacteristic
85C3×Dic5—21no—
86C2×C3×D4—101no—
87C2×C3×D4—201no—
88C22×C3×C4—51no—
89C3×D8—201no—
90C3×M16—201no—
91C2×C3×C8—51no—
92C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
93C3×C4⋊C4—21no—
94C3×C22⋊C4—201no—
95#208—201no—
96#208—201no—
97C2×C3⋊C8—102no—
98C3⋊C16—201no—
99C22×D5—41no—
100C22×D5#21411yescharacteristic
101C2×C4×C5—41no—
102C2×C4×C5#21711yescharacteristic
103C2×Dic5#21311yescharacteristic
104D20—41no—
105D20—41no—
106D20—82no—
107C4×D5—21no—
108C4×D5—21no—
109#170—122no—
110C5×C8—21no—
111#168—21no—
112C2×D8—51no—
113C2×M16—51no—
114C2×M16—301no—
115#121—101no—
116M32—301no—
117#106ΓL(1,𝔽16)11yescharacteristic
118#102—101no—
119C2×C3×C5—21no—
120C2×C3×C5#32711yescharacteristic
121C3×D5—41no—
122C3×D5—161no—
123C23×C3—51no—
124C23×C3—201no—
125C3×D4—201no—
126C3×D4—201no—
127C3×D4—402no—
128C2×C3×C4—41no—
129C2×C3×C4—51no—
130C2×C3×C4—101no—
131C2×C3×C4—101no—
132C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
133C3×C8—21no—
134C3×C8—101no—
135C3⋊C8—202no—
136C22×C5#83211yescharacteristic
137C2×D5—21no—
138C2×D5—41no—
139C2×D5—81no—
140C2×D5—81no—
141C2×D5—81no—
142C4×C5—81no—
143C4×C5#83411yescharacteristic
144C4×C5#83711yescharacteristic
145Dic5—21no—
146C2×D4—101no—
147C2×D4—201no—
148C22×C4—51no—
149D8—201no—
150M16—201no—
151M16—601no—
152M16—601no—
153C2×C8—51no—
154C2×C8—302no—
155C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
156C4⋊C4—21no—
157C22⋊C4—201no—
158C16—601no—
159C3×C5#134111yescharacteristic, complemented, Hall
160C22×C3—101no—
161C22×C3—201no—
162C22×C3—401no—
163C22×C3—401no—
164C22×C3—401no—
165C22×C3#400711yescharacteristic
166C3×C4—81no—
167C3×C4—101no—
168C3×C4#399911yescharacteristic
169C3×C4#401011yescharacteristic
170C2×C5—21no—
171C2×C5#453711yescharacteristic
172D5—41no—
173D5—161no—
174C23—51no—
175C23—201no—
176D4—201no—
177D4—201no—
178D4—402no—
179C2×C4—41no—
180C2×C4—51no—
181C2×C4—101no—
182C2×C4—101no—
183C2×C4#676311yescharacteristic
184C8—21no—
185C8—101no—
186C8—602no—
187C2×C3—21no—
188C2×C3—201no—
189C2×C3—801no—
190C2×C3#6486811yescharacteristic
191C5#6777911yescharacteristic, complemented, Sylow
192C22—101no—
193C22—201no—
194C22—401no—
195C22—401no—
196C22—401no—
197C22#9123611yescharacteristic
198C4—81no—
199C4—101no—
200C4#9122811yescharacteristic
201C4#9123911yescharacteristic
202C3#1059860111yescharacteristic, complemented, Sylow
203C2—21no—
204C2—201no—
205C2—801no—
206C2#1174673911yescharacteristic
subgroupG/H
centerC2#11746739
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×C8C2×ΓL(1,𝔽16)
FittingC3×C5×#106C4
socleC2×C3×C5#327
prime radicalC3×#65154C2
cosocleC2×C3×#676C22
hypercenter#106ΓL(1,𝔽16)
hypocenterC3×C5#1341
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11746768C2semidirect
3. #11746762C2semidirect
159. C3×C5#1341semidirect
191. C5#67779semidirect
202. C3#10598601semidirect

Maximal subgroups

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

subgroupindex
C3×#651542
#117467682
#117467622
#105986013
#677795