Finite Group Databasebeta

← #14319280

Subgroups — #14319280

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
1D15×Q32C211yesmaximal, characteristic, complemented
2#11751013C211yesmaximal, characteristic
3C3×C5×SD64C211yesmaximal, characteristic, complemented
4#11746343C211yesmaximal, characteristic, complemented
5#11746341C211yesmaximal, characteristic, complemented
6Dic240C211yesmaximal, characteristic, complemented
7#11746268C211yesmaximal, characteristic, complemented
8#10600174—31nomaximal, Hall
9Q16×D15—21no—
10#91801—21no—
11C3×C5×Q32C2211yescharacteristic
12C3×C5×D16C2211yescharacteristic
13#91113—21no—
14#91111—21no—
15Dic120C2211yescharacteristic
16Dic120C2211yescharacteristic
17C16×D15C2211yescharacteristic
18C3×C5×C32C2211yescharacteristic
19C3⋊#3926C2211yescharacteristic
20#69381—51nomaximal, Hall
21D5×Q32—31no—
22#65201—31no—
23C5×SD64D311yescharacteristic, complemented
24#64742—31no—
25#64740—31no—
26Dic80—31no—
27#64667—31no—
28Q8×D15—41no—
29#6819—41no—
30C3×C5×Q16—21no—
31C3×C5×D8—21no—
32#6718—41no—
33#6716—41no—
34Dic60—21no—
35Dic60—21no—
36C8×D15D411yescharacteristic
37C3×C5×C16C2311yescharacteristic
38C3⋊#672D411yescharacteristic
39D3×Q32—51no—
40#4912—51no—
41C3×SD64D511yescharacteristic, complemented
42#4522—51no—
43#4520—51no—
44Dic48—51no—
45#4447—51no—
46D5×Q16—61no—
47#4058—61no—
48C5×Q32C2×D311yescharacteristic
49C5×D16C2×D311yescharacteristic
50#3961—61no—
51#3959—61no—
52Dic40—31no—
53Dic40—31no—
54D5×C16—31no—
55C5×C32C2×D311yescharacteristic
56#3926—31no—
57#2264—151noSylow
58C3×C5×Q8—41no—
59C3×C5×D4—41no—
60#1220—81no—
61C2×Dic15—81no—
62C4×D15—81no—
63C4×D15D811yescharacteristic
64Dic30—41no—
65Dic30—41no—
66Dic30—81no—
67C3×C5×C8C2×D411yescharacteristic
68C3⋊#168D811yescharacteristic
69D3×Q16—101no—
70#912—101no—
71C3×Q32C2×D511yescharacteristic
72C3×D16C2×D511yescharacteristic
73#829—101no—
74#827—101no—
75Dic24—51no—
76Dic24—51no—
77D3×C16—51no—
78C3×C32C2×D511yescharacteristic
79C3⋊C32—51no—
80Q8×D5—121no—
81#711—121no—
82C5×Q16—21no—
83C5×D8—21no—
84#689—121no—
85#687—121no—
86Dic20—61no—
87Dic20—61no—
88C8×D5—31no—
89C5×C16C22×D311yescharacteristic
90#672—31no—
91#508—151no—
92C2×Q32—151no—
93Q64—151no—
94Q64—151no—
95SD64—151no—
96SD64D1511yescharacteristic, complemented
97M64—151no—
98C22×C3×C5—81no—
99C2×D15D1611yescharacteristic
100C3×C4×C5—81no—
101C3×C4×C5C2×D811yescharacteristic
102Dic15—81no—
103Dic15—81no—
104Dic15D1611yescharacteristic
105D3×Q8—201no—
106#237—201no—
107C3×Q16—21no—
108C3×D8—21no—
109#216—201no—
110#214—201no—
111Dic12—101no—
112Dic12—101no—
113D3×C8—51no—
114C3×C16C22×D511yescharacteristic
115C3⋊C16—51no—
116C5×Q8—41no—
117C5×D4—41no—
118C22⋊D5—241no—
119C2×Dic5—241no—
120C4×D5—31no—
121C4×D5—241no—
122Dic10—121no—
123Dic10—121no—
124Dic10—241no—
125C5×C8D3×D411yescharacteristic
126#168—31no—
127#135—301no—
128C2×Q16—301no—
129Q32—151no—
130Q32—151no—
131Q32—301no—
132Q32C2×D1511yescharacteristic
133SD32—301no—
134D16C2×D1511yescharacteristic
135C2×C16—151no—
136C32—151no—
137C32C2×D1511yescharacteristic
138C2×C3×C5—161no—
139C2×C3×C5C2×D1611yescharacteristic
140D15—21no—
141C3×Q8—41no—
142C3×D4—41no—
143#67—401no—
144C2×Dic3—401no—
145C4×D3—51no—
146C4×D3—401no—
147Dic6—201no—
148Dic6—201no—
149Dic6—401no—
150C3×C8D4×D511yescharacteristic
151C3⋊C8—51no—
152C22×C5—81no—
153C2×D5—31no—
154C4×C5—81no—
155C4×C5D3×D811yescharacteristic
156Dic5—31no—
157Dic5—241no—
158Dic5—241no—
159#41—601no—
160C2×Q8—601no—
161Q16—21no—
162Q16—301no—
163Q16—301no—
164Q16—601no—
165SD16—601no—
166D8—21no—
167C2×C8—151no—
168C16—151no—
169C16C22×D1511yescharacteristic
170C3×C5#226411yescharacteristic, complemented, Hall
171C22×C3—81no—
172C2×D3—51no—
173C3×C4—81no—
174C3×C4D5×D811yescharacteristic
175Dic3—51no—
176Dic3—401no—
177Dic3—401no—
178C2×C5—161no—
179C2×C5D3×D1611yescharacteristic
180D5—61no—
181Q8—41no—
182Q8—601no—
183Q8—601no—
184Q8—1201no—
185D4—41no—
186D4—1201no—
187C2×C4—151no—
188C2×C4—1201no—
189C2×C4—1201no—
190C8—151no—
191C8D4×D1511yescharacteristic
192C2×C3—161no—
193C2×C3D5×D1611yescharacteristic
194D3—101no—
195C5#6938111yescharacteristic, complemented, Sylow
196C22—81no—
197C22—151no—
198C4—81no—
199C4—151no—
200C4—1201no—
201C4—1201no—
202C4D8×D1511yescharacteristic
203C3#1060017411yescharacteristic, complemented, Sylow
204C2—161no—
205C2—301no—
206C2D15×D1611yescharacteristic
subgroupG/H
centerC2D15×D16
commutator, cosocleC3×C5×C16C23
FrattiniC16C22×D15
FittingC3×C5×SD64C2
socleC2×C3×C5C2×D16
prime radical#11751013C2
hypercenterSD64D15
hypocenterC3×C5#2264
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. D15×Q32C2semidirect
3. C3×C5×SD64C2semidirect
4. #11746343C2semidirect
5. #11746341C2semidirect
6. Dic240C2semidirect
7. #11746268C2semidirect
23. C5×SD64D3semidirect
41. C3×SD64D5semidirect
96. SD64D15semidirect
170. C3×C5#2264semidirect
195. C5#69381semidirect
203. C3#10600174semidirect

Maximal subgroups

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

subgroupindex
D15×Q322
#117510132
C3×C5×SD642
#117463432
#117463412
Dic2402
#117462682
#106001743
#693815