Finite Group Databasebeta

← #14279398

Subgroups — #14279398

Order 1920.

216 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 37 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×#65001C211yesmaximal, characteristic
2#11746727C211yesmaximal, characteristic, complemented
3#11746725C211yesmaximal, characteristic, complemented
4#10598540—31nomaximal, Hall
5C2×C3×D40—21no—
6C2×C3×#677—21no—
7C3×#4021C2211yescharacteristic
8C3×#4020C411yescharacteristic, complemented
9#91234—21no—
10#91228—21no—
11C3×C5×#97C411yescharacteristic, complemented
12#67797—51nomaximal, Hall
13#65001D311yescharacteristic
14#64856—31no—
15#64854—31no—
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×D20D411yescharacteristic
19C2×C3×Dic10D411yescharacteristic
20#6763—41no—
21#6762—41no—
22C2×C3×C5×C8—21no—
23C3×C42×C5C2×C411yescharacteristic
24C3×#685—41no—
25C3×D40—42no—
26C3×#677—42no—
27C3×#496—51no—
28#4542—51no—
29#4541—51no—
30C2×D40—21no—
31C2×#677—21no—
32#4021C2×D311yescharacteristic
33#4020Dic311yescharacteristic, complemented
34#4005—61no—
35#3999—61no—
36C5×#97Dic311yescharacteristic, complemented
37#1406—151noSylow
38C22×C3×D5—21no—
39C22×C3×D5—41no—
40C2×ΓL(1,𝔽16)—81no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C2×C3×Dic5—21no—
44C3×D20—41no—
45C3×D20—41no—
46C3×D20—41no—
47C3×D20—82no—
48C3×Dic10—41no—
49C3⋊#170—81no—
50C3×C5×C8—22no—
51C2×C3×SD16—101no—
52C2×C3×D8—101no—
53C3×#127—51no—
54C3×#124—51no—
55C3×#97AGL(1,𝔽5)11yescharacteristic, complemented
56#836—101no—
57#834—101no—
58C2×D20—21no—
59C2×D20—41no—
60C2×D20#6711yescharacteristic
61C2×Dic10#6711yescharacteristic
62C22⋊AGL(1,𝔽5)—121no—
63#704—121no—
64C2×C5×C8—21no—
65C42×C5C2×Dic311yescharacteristic
66#685—41no—
67D40—42no—
68#677—42no—
69#496—51no—
70#355—151no—
71#354—151no—
72C22×C3×C5#9911yescharacteristic
73C2×C3×D5—41no—
74C2×C3×D5—81no—
75C2×C3×D5—82no—
76C2×C3×D5—81no—
77ΓL(1,𝔽16)—161no—
78C3×C4×C5—21no—
79C3×C4×C5—41no—
80C3×Dic5—41no—
81C2×C3×Q8—51no—
82C2×C3×D4—51no—
83C2×C3×D4—101no—
84C2×C3×D4—201no—
85C3×SD16—202no—
86C3×D8—202no—
87C2×C3×C8—21no—
88C3×C22⋊C4—201no—
89C3×C42C2×AGL(1,𝔽5)11yescharacteristic
90#217—201no—
91#208—201no—
92C22×D5—21no—
93C22×D5—41no—
94C2×AGL(1,𝔽5)—241no—
95C2×C4×C5—21no—
96C2×C4×C5#21711yescharacteristic
97C2×Dic5—21no—
98D20—41no—
99D20—41no—
100D20—41no—
101D20—82no—
102Dic10—41no—
103#170—241no—
104C5×C8—22no—
105C2×SD16—101no—
106C2×D8—101no—
107#127—51no—
108#124—51no—
109#101—301no—
110#99—301no—
111#97ΓL(1,𝔽16)11yescharacteristic, complemented
112C2×C3×C5—21no—
113C2×C3×C5#35311yescharacteristic
114C3×D5—81no—
115C3×D5—161no—
116C23×C3—101no—
117C23×C3—201no—
118C3×Q8—201no—
119C3×D4—201no—
120C3×D4—201no—
121C3×D4—201no—
122C3×D4—402no—
123C2×C3×C4—21no—
124C2×C3×C4—101no—
125C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
126C2×Dic3—401no—
127C3×C8—22no—
128C3⋊C8—401no—
129C22×C5#83411yescharacteristic
130C2×D5—41no—
131C2×D5—81no—
132C2×D5—82no—
133C2×D5—81no—
134AGL(1,𝔽5)—481no—
135C4×C5—21no—
136C4×C5—41no—
137Dic5—41no—
138C2×Q8—51no—
139C2×D4—51no—
140C2×D4—101no—
141C2×D4—201no—
142SD16—202no—
143D8—202no—
144M16—601no—
145C2×C8—21no—
146C22⋊C4—201no—
147C22⋊C4—601no—
148C42C2×ΓL(1,𝔽16)11yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—201no—
151C22×C3—401no—
152C22×C3—402no—
153C22×C3—401no—
154C22×C3#399911yescharacteristic
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—201no—
158Dic3—801no—
159C2×C5—21no—
160C2×C5#454511yescharacteristic
161D5—81no—
162D5—161no—
163C23—101no—
164C23—201no—
165Q8—201no—
166D4—201no—
167D4—201no—
168D4—201no—
169D4—402no—
170C2×C4—21no—
171C2×C4—101no—
172C2×C4—1201no—
173C2×C4#676311yescharacteristic
174C8—22no—
175C8—1201no—
176C2×C3—21no—
177C2×C3—401no—
178C2×C3—801no—
179C2×C3#6485311yescharacteristic
180C5#6779711yescharacteristic, complemented, Sylow
181C22—201no—
182C22—401no—
183C22—402no—
184C22—401no—
185C22#9122811yescharacteristic
186C4—21no—
187C4—41no—
188C4—201no—
189C4—2401no—
190C3#1059854011yescharacteristic, complemented, Sylow
191C2—21no—
192C2—401no—
193C2—801no—
194C2#1174672411yescharacteristic
subgroupG/H
centerC2#11746724
commutatorC3×C42×C5C2×C4
FrattiniC42C2×ΓL(1,𝔽16)
FittingC3×C5×#97C4
socleC2×C3×C5#353
prime radicalC3×#65001C2
cosocleC3×#4021C22
hypercenter#97ΓL(1,𝔽16)
hypocenterC3×C5#1406
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11746727C2semidirect
3. #11746725C2semidirect
8. C3×#4020C4semidirect
11. C3×C5×#97C4semidirect
33. #4020Dic3semidirect
36. C5×#97Dic3semidirect
55. C3×#97AGL(1,𝔽5)semidirect
111. #97ΓL(1,𝔽16)semidirect
149. C3×C5#1406semidirect
180. C5#67797semidirect
190. C3#10598540semidirect

Maximal subgroups

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

subgroupindex
C3×#650012
#117467272
#117467252
#105985403
#677975