Finite Group Databasebeta

← #14279391

Subgroups — #14279391

Order 1920.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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×#496C211yesmaximal, characteristic
2#11746363C211yesmaximal, characteristic, complemented
3#11746362C211yesmaximal, characteristic, complemented
4#10598288—31nomaximal, Hall
5C2×C3×C5×SD16—21no—
6C2×C3×C5×D8—21no—
7C3×C5×#127C411yescharacteristic, complemented
8C3×C5×#124C2211yescharacteristic
9C3×C5×#97C411yescharacteristic, complemented
10#91120—21no—
11#91118—21no—
12#67797—51nomaximal, Hall
13C5×#496D311yescharacteristic
14#64762—31no—
15#64761—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4—21no—
18C2×C3×C5×D4—41no—
19C2×C3×C5×D4D411yescharacteristic
20C3×C5×SD16—42no—
21C3×C5×D8—42no—
22C2×C3×C5×C8—21no—
23C3×C5×C22⋊C4—41no—
24C3×C42×C5C2×C411yescharacteristic
25#6719—41no—
26#6710—41no—
27C3×#496D511yescharacteristic
28#4542—51no—
29#4541—51no—
30C2×C5×SD16—21no—
31C2×C5×D8—21no—
32C5×#127Dic311yescharacteristic, complemented
33C5×#124C2×D311yescharacteristic
34C5×#97Dic311yescharacteristic, complemented
35#3968—61no—
36#3966—61no—
37#1406—151noSylow
38C23×C3×C5—21no—
39C23×C3×C5—41no—
40C3×C5×Q8—41no—
41C3×C5×D4—41no—
42C3×C5×D4—41no—
43C3×C5×D4—41no—
44C3×C5×D4—82no—
45C2×C3×C4×C5—21no—
46C2×C3×C4×C5—21no—
47C2×C3×C4×C5C22⋊C411yescharacteristic
48C2×Dic15—81no—
49C3×C5×C8—22no—
50C3⋊#168—81no—
51C2×C3×SD16—21no—
52C2×C3×D8—21no—
53C3×#127Dic511yescharacteristic, complemented
54C3×#124C2×D511yescharacteristic
55C3×#97Dic511yescharacteristic, complemented
56#836—101no—
57#834—101no—
58C2×C5×Q8#6711yescharacteristic
59C2×C5×D4—21no—
60C2×C5×D4—41no—
61C2×C5×D4#6711yescharacteristic
62C5×SD16—42no—
63C5×D8—42no—
64C2×C5×C8—21no—
65C5×C22⋊C4—41no—
66C42×C5C2×Dic311yescharacteristic
67C22⋊Dic5—121no—
68#681—121no—
69#496D1511yescharacteristic
70#355—151no—
71#354—151no—
72C22×C3×C5—41no—
73C22×C3×C5—81no—
74C22×C3×C5—82no—
75C22×C3×C5—81no—
76C22×C3×C5#9911yescharacteristic
77C3×C4×C5—21no—
78C3×C4×C5—41no—
79C3×C4×C5—41no—
80Dic15—161no—
81C2×C3×Q8C22⋊D511yescharacteristic
82C2×C3×D4—21no—
83C2×C3×D4—41no—
84C2×C3×D4C22⋊D511yescharacteristic
85C3×SD16—42no—
86C3×D8—42no—
87C2×C3×C8—21no—
88C3×C22⋊C4—41no—
89C3×C42C2×Dic511yescharacteristic
90#217—201no—
91#208—201no—
92C23×C5—21no—
93C23×C5—41no—
94C5×Q8—41no—
95C5×D4—41no—
96C5×D4—41no—
97C5×D4—41no—
98C5×D4—82no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5#21711yescharacteristic
102C2×Dic5—241no—
103C5×C8—22no—
104#168—241no—
105C2×SD16—21no—
106C2×D8—21no—
107#127Dic1511yescharacteristic, complemented
108#124C2×D1511yescharacteristic
109#101—301no—
110#99—301no—
111#97Dic1511yescharacteristic, complemented
112C2×C3×C5—21no—
113C2×C3×C5—81no—
114C2×C3×C5—161no—
115C2×C3×C5#35311yescharacteristic
116C23×C3—21no—
117C23×C3—41no—
118C3×Q8—41no—
119C3×D4—41no—
120C3×D4—41no—
121C3×D4—41no—
122C3×D4—82no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4C22⋊Dic511yescharacteristic
126C2×Dic3—401no—
127C3×C8—22no—
128C3⋊C8—401no—
129C22×C5—41no—
130C22×C5—81no—
131C22×C5—82no—
132C22×C5—81no—
133C22×C5#83411yescharacteristic
134C4×C5—21no—
135C4×C5—41no—
136C4×C5—41no—
137Dic5—481no—
138C2×Q8#122011yescharacteristic
139C2×D4—21no—
140C2×D4—41no—
141C2×D4#122011yescharacteristic
142SD16—42no—
143D8—42no—
144M16—601no—
145C2×C8—21no—
146C22⋊C4—41no—
147C22⋊C4—601no—
148C42C2×Dic1511yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—81no—
152C22×C3—82no—
153C22×C3—81no—
154C22×C3#396611yescharacteristic
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—41no—
158Dic3—801no—
159C2×C5—21no—
160C2×C5—81no—
161C2×C5—161no—
162C2×C5#454511yescharacteristic
163C23—21no—
164C23—41no—
165Q8—41no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—82no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—1201no—
173C2×C4#671911yescharacteristic
174C8—22no—
175C8—1201no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3—161no—
179C2×C3#6476511yescharacteristic
180C5#6779711yescharacteristic, complemented, Sylow
181C22—41no—
182C22—81no—
183C22—82no—
184C22—81no—
185C22#9111811yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—2401no—
190C3#1059828811yescharacteristic, complemented, Sylow
191C2—21no—
192C2—81no—
193C2—161no—
194C2#1174636611yescharacteristic
subgroupG/H
centerC2#11746366
commutatorC3×C42×C5C2×C4
Frattini#124C2×D15
Fitting, prime radicalC3×C5×#496C2
socleC2×C3×C5#353
cosocleC3×C5×#124C22
hypercenter#496D15
hypocenterC3×C5#1406
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #496

Complements

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

NH ≅ G/Ntype
2. #11746363C2semidirect
3. #11746362C2semidirect
7. C3×C5×#127C4semidirect
9. C3×C5×#97C4semidirect
32. C5×#127Dic3semidirect
34. C5×#97Dic3semidirect
53. C3×#127Dic5semidirect
55. C3×#97Dic5semidirect
107. #127Dic15semidirect
111. #97Dic15semidirect
149. C3×C5#1406semidirect
180. C5#67797semidirect
190. C3#10598288semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4962
#117463632
#117463622
#105982883
#677975