Finite Group Databasebeta

← #14318561

Subgroups — #14318561

Order 1920.

248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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×C5×#430C211yesmaximal, characteristic
2#11751238C211yesmaximal, characteristic
3#11746374C211yesmaximal, characteristic
4#11746317C212yesmaximal, complemented
5#11746315C212yesmaximal, complemented
6#10601517—31nomaximal, Hall
7C2×C3×C5×M16—21no—
8C2×C3×C5×M16C2211yescharacteristic
9#91813—21no—
10C2×Dic60C2211yescharacteristic
11C3×C5×#108—21no—
12C3×C5×#108C2212yes—
13#91101C2211yescharacteristic
14#91100—21no—
15#91096C2212yes—
16#70724—51nomaximal, Hall
17C5×#430D311yescharacteristic
18#65426—31no—
19#64773—31no—
20#64716—32no—
21#64714—32no—
22C22×C3×C4×C5D411yescharacteristic
23C2×Dic30—21no—
24C3×C5×M16—22no—
25C3×C5×M16—22no—
26C3×C5×M16—41no—
27C2×C3×C5×C8—41no—
28C2×C3×C5×C8D411yescharacteristic
29C2×C3×C5×C8C2311yescharacteristic
30#6719—41no—
31C4⋊Dic15—21no—
32#6712—41no—
33Dic60—22no—
34C3⋊#672—22no—
35C3×#430D511yescharacteristic
36#5137—51no—
37#4553—51no—
38#4496—52no—
39#4494—52no—
40C2×C5×M16—21no—
41C2×C5×M16C2×D311yescharacteristic
42#4070—61no—
43C2×Dic20—31no—
44C5×#108—21no—
45C5×#108C2×D312yes—
46#3949—31no—
47#3948—61no—
48#3944—32no—
49#2239—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5SD1611yescharacteristic
54C2×C3×C4×C5C2×D411yescharacteristic
55C2×Dic15—41no—
56C2×Dic15—41no—
57Dic30—41no—
58Dic30—41no—
59C3×C5×C8—21no—
60C3×C5×C8—42no—
61C3×C5×C8#4112yes—
62C2×C3×M16—21no—
63C2×C3×M16C2×D511yescharacteristic
64#924—101no—
65C2×Dic12—51no—
66C3×#108—21no—
67C3×#108C2×D512yes—
68#817—51no—
69#816—101no—
70#812—52no—
71C22×C4×C5#6711yescharacteristic
72C2×Dic10—61no—
73C5×M16—22no—
74C5×M16—22no—
75C5×M16—41no—
76C2×C5×C8—41no—
77C2×C5×C8#6711yescharacteristic
78C2×C5×C8C22×D311yescharacteristic
79C22⋊Dic5—121no—
80C4⋊Dic5—61no—
81#683—121no—
82Dic20—62no—
83#672—62no—
84#470—151no—
85#430D1511yescharacteristic
86#365—152no—
87#362—152no—
88#349—151no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5C2×SD1611yescharacteristic
92C3×C4×C5—21no—
93C3×C4×C5#12311yescharacteristic
94C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
95Dic15—81no—
96Dic15—81no—
97C22×C3×C4C22⋊D511yescharacteristic
98C2×Dic6—101no—
99C3×M16—22no—
100C3×M16—22no—
101C3×M16—41no—
102C2×C3×C8—41no—
103C2×C3×C8C22⋊D511yescharacteristic
104C2×C3×C8C22×D511yescharacteristic
105#217—201no—
106C4⋊Dic3—101no—
107Dic3⋊C4—201no—
108Dic12—102no—
109C3⋊C16—102no—
110C23×C5#21511yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5#21511yescharacteristic
114C2×C4×C5C2×#6711yescharacteristic
115C2×Dic5—121no—
116C2×Dic5—121no—
117Dic10—121no—
118Dic10—121no—
119C5×C8—21no—
120C5×C8—42no—
121C5×C8#23512yes—
122C2×Q16—151no—
123C2×M16—21no—
124C2×M16C2×D1511yescharacteristic
125C22⋊Q8—301no—
126M32—152no—
127#108—21no—
128#108C2×D1512yes—
129#106—151no—
130#103—301no—
131C2×C3×C5—21no—
132C2×C3×C5—41no—
133C2×C3×C5#48111yescharacteristic
134C23×C3#68811yescharacteristic
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4#68811yescharacteristic
138C2×C3×C4C2×C22⋊D511yescharacteristic
139C2×Dic3—201no—
140C2×Dic3—201no—
141Dic6—201no—
142Dic6—201no—
143C3×C8—21no—
144C3×C8—42no—
145C3×C8#70912yes—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5C2×#21511yescharacteristic
149C4×C5—21no—
150C4×C5#92911yescharacteristic
151C4×C5#93211yescharacteristic
152Dic5—241no—
153Dic5—241no—
154C2×Q8—301no—
155C22×C4#122011yescharacteristic
156Q16—302no—
157M16—22no—
158M16—22no—
159M16—41no—
160C2×C8—41no—
161C2×C8#122011yescharacteristic
162C2×C8C22×D1511yescharacteristic
163C4⋊C4—301no—
164C4⋊C4—601no—
165C22⋊C4—601no—
166C16—302no—
167C3×C5#223911yescharacteristic, complemented, Hall
168C22×C3—21no—
169C22×C3—41no—
170C22×C3C2×#68811yescharacteristic
171C3×C4—21no—
172C3×C4#407511yescharacteristic
173C3×C4#407811yescharacteristic
174Dic3—401no—
175Dic3—401no—
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#496811yescharacteristic
179C23#671711yescharacteristic
180Q8—601no—
181Q8—601no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—601no—
185C2×C4—601no—
186C2×C4#671711yescharacteristic
187C2×C4C2×#122011yescharacteristic
188C8—21no—
189C8—42no—
190C8#681712yes—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3#6525711yescharacteristic
194C5#7072411yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22C2×#671711yescharacteristic
198C4—21no—
199C4—1201no—
200C4—1201no—
201C4#9181811yescharacteristic
202C4#9182111yescharacteristic
203C3#1060151711yescharacteristic, complemented, Sylow
204C2—21no—
205C2—41no—
206C2#1175106911yescharacteristic
subgroupG/H
centerC2#11751069
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#430C2
socleC2×C3×C5#481
prime radicalC23×C3×C5SD16
hypercenter#430D15
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #430

Complements

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

NH ≅ G/Ntype
4. #11746317C2semidirect
5. #11746315C2semidirect
167. C3×C5#2239semidirect
194. C5#70724semidirect
203. C3#10601517semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4302
#117512382
#117463742
#117463172
#117463152
#106015173
#707245