Finite Group Databasebeta

← #14319208

Subgroups — #14319208

Order 1920.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#11751020C211yesmaximal, characteristic, complemented
2#11751013C211yesmaximal, characteristic, complemented
3C3×C5×SD64C211yesmaximal, characteristic, complemented
4#11746343C211yesmaximal, characteristic, complemented
5#11746340C211yesmaximal, characteristic, complemented
6#11746270C211yesmaximal, characteristic, complemented
7D15×C32C211yesmaximal, characteristic, complemented
8#10600172—31nomaximal, Hall
9#91808—21no—
10#91801—21no—
11C3×C5×Q32C2211yescharacteristic
12C3×C5×D16C2211yescharacteristic
13#91112—21no—
14#91111—21no—
15Dic120C2211yescharacteristic
16D240C2211yescharacteristic
17C16×D15C2211yescharacteristic
18C3×C5×C32C2211yescharacteristic
19C3⋊#3926C2211yescharacteristic
20#69379—51nomaximal, Hall
21#65208—31no—
22#65201—31no—
23C5×SD64D311yescharacteristic, complemented
24#64742—31no—
25#64739—31no—
26#64669—31no—
27D5×C32—31no—
28#6821—41no—
29#6819—41no—
30C3×C5×Q16—21no—
31C3×C5×D8—21no—
32#6717—41no—
33#6716—41no—
34Dic60—21no—
35D120—21no—
36C8×D15D411yescharacteristic
37C3×C5×C16C2311yescharacteristic
38C3⋊#672D411yescharacteristic
39#4919—51no—
40#4912—51no—
41C3×SD64D511yescharacteristic, complemented
42#4522—51no—
43#4519—51no—
44#4449—51no—
45D3×C32—51no—
46#4065—61no—
47#4058—61no—
48C5×Q32C2×D311yescharacteristic
49C5×D16C2×D311yescharacteristic
50#3960—61no—
51#3959—61no—
52Dic40—31no—
53D80—31no—
54D5×C16—31no—
55C5×C32C2×D311yescharacteristic
56#3926—31no—
57#2262—151noSylow
58C3×C5×Q8—41no—
59C3×C5×D4—41no—
60#1220—81no—
61C2×Dic15—81no—
62D60—41no—
63D60—81no—
64C4×D15—81no—
65C4×D15D811yescharacteristic
66Dic30—41no—
67C3×C5×C8C2×D411yescharacteristic
68C3⋊#168D811yescharacteristic
69#919—101no—
70#912—101no—
71C3×Q32C2×D511yescharacteristic
72C3×D16C2×D511yescharacteristic
73#828—101no—
74#827—101no—
75Dic24—51no—
76D48—51no—
77D3×C16—51no—
78C3×C32C2×D511yescharacteristic
79C3⋊C32—51no—
80#713—121no—
81#711—121no—
82C5×Q16—21no—
83C5×D8—21no—
84#688—121no—
85#687—121no—
86Dic20—61no—
87D40—61no—
88C8×D5—31no—
89C5×C16C22×D311yescharacteristic
90#672—31no—
91#508—151no—
92#508—151no—
93Q64—151no—
94SD64—151no—
95SD64D1511yescharacteristic, complemented
96D32—151no—
97C2×C32—151no—
98C22×C3×C5—81no—
99C2×D15—81no—
100C2×D15D1611yescharacteristic
101C3×C4×C5—81no—
102C3×C4×C5C2×D811yescharacteristic
103Dic15—81no—
104Dic15D1611yescharacteristic
105#239—201no—
106#237—201no—
107C3×Q16—21no—
108C3×D8—21no—
109#215—201no—
110#214—201no—
111Dic12—101no—
112D24—101no—
113D3×C8—51no—
114C3×C16C22×D511yescharacteristic
115C3⋊C16—51no—
116C5×Q8—41no—
117C5×D4—41no—
118C22⋊D5—241no—
119C2×Dic5—241no—
120D20—121no—
121D20—241no—
122C4×D5—31no—
123C4×D5—241no—
124Dic10—121no—
125C5×C8D3×D411yescharacteristic
126#168—31no—
127#135—301no—
128#135—301no—
129Q32—151no—
130Q32C2×D1511yescharacteristic
131SD32—301no—
132SD32—301no—
133D16—151no—
134D16C2×D1511yescharacteristic
135C2×C16—151no—
136C32—151no—
137C32C2×D1511yescharacteristic
138C2×C3×C5—161no—
139C2×C3×C5C2×D1611yescharacteristic
140D15—21no—
141D15—161no—
142C3×Q8—41no—
143C3×D4—41no—
144#67—401no—
145C2×Dic3—401no—
146D12—201no—
147D12—401no—
148C4×D3—51no—
149C4×D3—401no—
150Dic6—201no—
151C3×C8D4×D511yescharacteristic
152C3⋊C8—51no—
153C22×C5—81no—
154C2×D5—31no—
155C2×D5—241no—
156C4×C5—81no—
157C4×C5D3×D811yescharacteristic
158Dic5—31no—
159Dic5—241no—
160#41—601no—
161#41—601no—
162Q16—21no—
163Q16—301no—
164SD16—601no—
165SD16—601no—
166D8—21no—
167D8—301no—
168C2×C8—151no—
169C16—151no—
170C16C22×D1511yescharacteristic
171C3×C5#226211yescharacteristic, complemented, Hall
172C22×C3—81no—
173C2×D3—51no—
174C2×D3—401no—
175C3×C4—81no—
176C3×C4D5×D811yescharacteristic
177Dic3—51no—
178Dic3—401no—
179C2×C5—161no—
180C2×C5D3×D1611yescharacteristic
181D5—61no—
182D5—481no—
183Q8—41no—
184Q8—601no—
185D4—41no—
186D4—601no—
187D4—1201no—
188D4—1201no—
189C2×C4—151no—
190C2×C4—1201no—
191C2×C4—1201no—
192C8—151no—
193C8D4×D1511yescharacteristic
194C2×C3—161no—
195C2×C3D5×D1611yescharacteristic
196D3—101no—
197D3—801no—
198C5#6937911yescharacteristic, complemented, Sylow
199C22—81no—
200C22—151no—
201C22—1201no—
202C4—81no—
203C4—151no—
204C4—1201no—
205C4D8×D1511yescharacteristic
206C3#1060017211yescharacteristic, complemented, Sylow
207C2—161no—
208C2—301no—
209C2—2401no—
210C2D15×D1611yescharacteristic
subgroupG/H
centerC2D15×D16
commutator, cosocleC3×C5×C16C23
FrattiniC16C22×D15
FittingC3×C5×SD64C2
socleC2×C3×C5C2×D16
hypercenterSD64D15
hypocenterC3×C5#2262
LCSG ▷ C3×C5×C16 ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
1. #11751020C2semidirect
2. #11751013C2semidirect
3. C3×C5×SD64C2semidirect
4. #11746343C2semidirect
5. #11746340C2semidirect
6. #11746270C2semidirect
7. D15×C32C2semidirect
23. C5×SD64D3semidirect
41. C3×SD64D5semidirect
95. SD64D15semidirect
171. C3×C5#2262semidirect
198. C5#69379semidirect
206. C3#10600172semidirect

Maximal subgroups

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

subgroupindex
#117510202
#117510132
C3×C5×SD642
#117463432
#117463402
#117462702
D15×C322
#106001723
#693795