Finite Group Databasebeta

← #14277686

Subgroups — #14277686

Order 1920.

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

normal subgroups only

This group has 268 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×#384C211yesmaximal, characteristic
2#11746349C212yesmaximal
3#10598126—31nomaximal, Hall
4C2×C3×C5×C4⋊C4—22no—
5C2×C3×C5×C4⋊C4C411yescharacteristic
6C2×C3×C5×C4⋊C4C2211yescharacteristic
7C2×C3×C42×C5C411yescharacteristic
8#91114—22no—
9#67635—51nomaximal, Hall
10C5×#384D311yescharacteristic
11#64748—32no—
12C22×C3×C4×C5—21no—
13C22×C3×C4×C5—21no—
14C22×C3×C4×C5C2×C411yescharacteristic
15C22×C3×C4×C5D412yes—
16C3×C5×C4⋊C4—41no—
17C3×C5×C4⋊C4—44no—
18C3×C5×C4⋊C4—41no—
19C3×C42×C5—21no—
20C3×C42×C5C812yescomplemented
21C2×C3⋊#168—42no—
22C3×#384D511yescharacteristic
23#4528—52no—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4Dic311yescharacteristic
26C2×C5×C4⋊C4C2×D311yescharacteristic
27C2×C42×C5Dic311yescharacteristic
28C22⋊#168—62no—
29#1325—151noSylow
30C23×C3×C5C22⋊C411yescharacteristic
31C2×C3×C4×C5—22no—
32C2×C3×C4×C5—22no—
33C2×C3×C4×C5—22no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5—21no—
36C2×C3×C4×C5—22no—
37C2×C3×C4×C5—42no—
38C2×C3×C4×C5—42no—
39C2×C3×C4×C5—41no—
40C2×C3×C4×C5C2×C811yescharacteristic
41C2×C3×C4×C5M1611yescharacteristic
42C3⋊#168—82no—
43C2×C3×C4⋊C4—22no—
44C2×C3×C4⋊C4Dic511yescharacteristic
45C2×C3×C4⋊C4C2×D511yescharacteristic
46C2×C3×C42Dic511yescharacteristic
47#830—102no—
48C22×C4×C5—21no—
49C22×C4×C5—21no—
50C22×C4×C5C2×Dic311yescharacteristic
51C22×C4×C5#6712yes—
52C5×C4⋊C4—41no—
53C5×C4⋊C4—41no—
54C5×C4⋊C4—44no—
55C42×C5—21no—
56C42×C5C3⋊C812yescomplemented
57C2×#168—122no—
58#384D1511yescharacteristic
59#324—152no—
60C22×C3×C5—21no—
61C22×C3×C5—21no—
62C22×C3×C5C22⋊C811yescharacteristic
63C22×C3×C5#9911yescharacteristic
64C22×C3×C5#10111yescharacteristic
65C3×C4×C5—24no—
66C3×C4×C5—21no—
67C3×C4×C5—21no—
68C3×C4×C5—42no—
69C3×C4×C5—81no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4C2×Dic511yescharacteristic
73C22×C3×C4C22⋊D512yes—
74C3×C4⋊C4—41no—
75C3×C4⋊C4—41no—
76C3×C4⋊C4—44no—
77C3×C42—21no—
78C3×C42#16812yescomplemented
79C2×C3⋊C8—202no—
80C23×C5#21711yescharacteristic
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—21no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5—42no—
88C2×C4×C5—42no—
89C2×C4×C5—41no—
90C2×C4×C5C2×C3⋊C811yescharacteristic
91C2×C4×C5#20811yescharacteristic
92#168—242no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4Dic1511yescharacteristic
95C2×C4⋊C4C2×D1511yescharacteristic
96C2×C42Dic1511yescharacteristic
97C22⋊C8—302no—
98C2×C3×C5—21no—
99C2×C3×C5—21no—
100C2×C3×C5#32411yescharacteristic
101C2×C3×C5#35311yescharacteristic
102C2×C3×C5#35611yescharacteristic
103C23×C3C22⋊Dic511yescharacteristic
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×C3×C4—22no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—22no—
110C2×C3×C4—42no—
111C2×C3×C4—42no—
112C2×C3×C4—41no—
113C2×C3×C4C2×#16811yescharacteristic
114C2×C3×C4#68111yescharacteristic
115C3⋊C8—402no—
116C22×C5—21no—
117C22×C5—21no—
118C22×C5#83011yescharacteristic
119C22×C5#83411yescharacteristic
120C22×C5#83611yescharacteristic
121C4×C5—24no—
122C4×C5—21no—
123C4×C5—21no—
124C4×C5—42no—
125C4×C5—81no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4C2×Dic1511yescharacteristic
129C22×C4#122012yes—
130C2×C8—602no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—44no—
134C42—21no—
135C42C3⋊#16812yescomplemented
136C3×C5#132511yescharacteristic, complemented, Hall
137C22×C3—21no—
138C22×C3—21no—
139C22×C3C22⋊#16811yescharacteristic
140C22×C3#396611yescharacteristic
141C22×C3#396811yescharacteristic
142C3×C4—24no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—42no—
146C3×C4—81no—
147C2×C5—21no—
148C2×C5—21no—
149C2×C5#452811yescharacteristic
150C2×C5#454511yescharacteristic
151C2×C5#454811yescharacteristic
152C23#671911yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4C2×C3⋊#16811yescharacteristic
163C2×C4#671011yescharacteristic
164C8—1202no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3#6474811yescharacteristic
168C2×C3#6476511yescharacteristic
169C2×C3#6476811yescharacteristic
170C5#6763511yescharacteristic, complemented, Sylow
171C22—21no—
172C22—21no—
173C22#9111411yescharacteristic
174C22#9111811yescharacteristic
175C22#9112011yescharacteristic
176C4—24no—
177C4—21no—
178C4—21no—
179C4—42no—
180C4—81no—
181C3#1059812611yescharacteristic, complemented, Sylow
182C2—21no—
183C2—21no—
184C2#1174634911yescharacteristic
185C2#1174636611yescharacteristic
186C2#1174636911yescharacteristic
subgroupG/H
centerC22#91118
commutatorC2×C3×C4×C5C2×C8
FrattiniC2×C4⋊C4C2×D15
FittingC3×C5×#384C2
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C5×C4⋊C4C22
hypercenter#384D15
hypocenterC3×C5#1325
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
20. C3×C42×C5C8semidirect
56. C42×C5C3⋊C8semidirect
78. C3×C42#168semidirect
135. C42C3⋊#168semidirect
136. C3×C5#1325semidirect
170. C5#67635semidirect
181. C3#10598126semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#3842
#117463492
#105981263
#676355