Finite Group Databasebeta

← #14319289

Subgroups — #14319289

Order 1920.

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

normal subgroups only

This group has 208 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
2D15×Q32C211yesmaximal, characteristic, complemented
3C3×C5×Q64C211yesmaximal, characteristic, complemented
4#11746343C211yesmaximal, characteristic, complemented
5#11746342C211yesmaximal, characteristic, complemented
6#11746270C211yesmaximal, characteristic, complemented
7#11746268C211yesmaximal, characteristic, complemented
8#10600177—31nomaximal, Hall
9#91808—21no—
10Q16×D15—21no—
11C3×C5×Q32C2211yescharacteristic
12C3×C5×Q32C2211yescharacteristic
13#91113—21no—
14#91112—21no—
15Dic120C2211yescharacteristic
16D240C2211yescharacteristic
17C16×D15C2211yescharacteristic
18C3×C5×C32C2211yescharacteristic
19C3⋊#3926C2211yescharacteristic
20#69384—51nomaximal, Hall
21#65208—31no—
22D5×Q32—31no—
23C5×Q64D311yescharacteristic, complemented
24#64742—31no—
25#64741—31no—
26#64669—31no—
27#64667—31no—
28#6821—41no—
29Q8×D15—41no—
30C3×C5×Q16—21no—
31C3×C5×Q16—21no—
32#6718—41no—
33#6717—41no—
34Dic60—21no—
35D120—21no—
36C8×D15D411yescharacteristic
37C3×C5×C16C2311yescharacteristic
38C3⋊#672D411yescharacteristic
39#4919—51no—
40D3×Q32—51no—
41C3×Q64D511yescharacteristic, complemented
42#4522—51no—
43#4521—51no—
44#4449—51no—
45#4447—51no—
46#4065—61no—
47D5×Q16—61no—
48C5×Q32C2×D311yescharacteristic
49C5×Q32C2×D311yescharacteristic
50#3961—61no—
51#3960—61no—
52Dic40—31no—
53D80—31no—
54D5×C16—31no—
55C5×C32C2×D311yescharacteristic
56#3926—31no—
57#2264—151noSylow
58C3×C5×Q8—41no—
59C3×C5×Q8—41no—
60D60—41no—
61D60—81no—
62C4×D15—81no—
63C4×D15—81no—
64C4×D15D811yescharacteristic
65Dic30—41no—
66Dic30—81no—
67C3×C5×C8C2×D411yescharacteristic
68C3⋊#168D811yescharacteristic
69#919—101no—
70D3×Q16—101no—
71C3×Q32C2×D511yescharacteristic
72C3×Q32C2×D511yescharacteristic
73#829—101no—
74#828—101no—
75Dic24—51no—
76D48—51no—
77D3×C16—51no—
78C3×C32C2×D511yescharacteristic
79C3⋊C32—51no—
80#713—121no—
81Q8×D5—121no—
82C5×Q16—21no—
83C5×Q16—21no—
84#689—121no—
85#688—121no—
86Dic20—61no—
87D40—61no—
88C8×D5—31no—
89C5×C16C22×D311yescharacteristic
90#672—31no—
91#508—151no—
92C2×Q32—151no—
93Q64—151no—
94Q64D1511yescharacteristic, complemented
95SD64—151no—
96SD64—151no—
97M64—151no—
98C2×D15—81no—
99C2×D15D1611yescharacteristic
100C3×C4×C5—81no—
101C3×C4×C5—81no—
102C3×C4×C5C2×D811yescharacteristic
103Dic15—81no—
104Dic15D1611yescharacteristic
105#239—201no—
106D3×Q8—201no—
107C3×Q16—21no—
108C3×Q16—21no—
109#216—201no—
110#215—201no—
111Dic12—101no—
112D24—101no—
113D3×C8—51no—
114C3×C16C22×D511yescharacteristic
115C3⋊C16—51no—
116C5×Q8—41no—
117C5×Q8—41no—
118D20—121no—
119D20—241no—
120C4×D5—31no—
121C4×D5—241no—
122C4×D5—241no—
123Dic10—121no—
124Dic10—241no—
125C5×C8D3×D411yescharacteristic
126#168—31no—
127#135—301no—
128C2×Q16—301no—
129Q32—151no—
130Q32—301no—
131Q32C2×D1511yescharacteristic
132Q32C2×D1511yescharacteristic
133SD32—301no—
134D16—151no—
135C2×C16—151no—
136C32—151no—
137C32C2×D1511yescharacteristic
138C2×C3×C5C2×D1611yescharacteristic
139D15—21no—
140D15—161no—
141C3×Q8—41no—
142C3×Q8—41no—
143D12—201no—
144D12—401no—
145C4×D3—51no—
146C4×D3—401no—
147C4×D3—401no—
148Dic6—201no—
149Dic6—401no—
150C3×C8D4×D511yescharacteristic
151C3⋊C8—51no—
152C2×D5—31no—
153C2×D5—241no—
154C4×C5—81no—
155C4×C5—81no—
156C4×C5D3×D811yescharacteristic
157Dic5—31no—
158Dic5—241no—
159#41—601no—
160C2×Q8—601no—
161Q16—21no—
162Q16—21no—
163Q16—301no—
164Q16—601no—
165SD16—601no—
166D8—301no—
167C2×C8—151no—
168C16—151no—
169C16C22×D1511yescharacteristic
170C3×C5#226411yescharacteristic, complemented, Hall
171C2×D3—51no—
172C2×D3—401no—
173C3×C4—81no—
174C3×C4—81no—
175C3×C4D5×D811yescharacteristic
176Dic3—51no—
177Dic3—401no—
178C2×C5D3×D1611yescharacteristic
179D5—61no—
180D5—481no—
181Q8—41no—
182Q8—41no—
183Q8—601no—
184Q8—1201no—
185D4—601no—
186D4—1201no—
187C2×C4—151no—
188C2×C4—1201no—
189C2×C4—1201no—
190C8—151no—
191C8D4×D1511yescharacteristic
192C2×C3D5×D1611yescharacteristic
193D3—101no—
194D3—801no—
195C5#6938411yescharacteristic, complemented, Sylow
196C22—151no—
197C22—1201no—
198C4—81no—
199C4—81no—
200C4—151no—
201C4—1201no—
202C4D8×D1511yescharacteristic
203C3#1060017711yescharacteristic, complemented, Sylow
204C2—301no—
205C2—2401no—
206C2D15×D1611yescharacteristic
subgroupG/H
centerC2D15×D16
commutator, cosocleC3×C5×C16C23
FrattiniC16C22×D15
FittingC3×C5×Q64C2
socleC2×C3×C5C2×D16
prime radical#11751020C2
hypercenterQ64D15
hypocenterC3×C5#2264
LCSG ▷ C3×C5×C16 ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

Complements

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

NH ≅ G/Ntype
2. D15×Q32C2semidirect
3. C3×C5×Q64C2semidirect
4. #11746343C2semidirect
5. #11746342C2semidirect
6. #11746270C2semidirect
7. #11746268C2semidirect
23. C5×Q64D3semidirect
41. C3×Q64D5semidirect
94. Q64D15semidirect
170. C3×C5#2264semidirect
195. C5#69384semidirect
203. C3#10600177semidirect

Maximal subgroups

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

subgroupindex
#117510202
D15×Q322
C3×C5×Q642
#117463432
#117463422
#117462702
#117462682
#106001773
#693845