Finite Group Databasebeta

← #14312748

Subgroups — #14312748

Order 1920.

320 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 123 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×M32C212yesmaximal
2#11750809C211yesmaximal, characteristic
3C3×C5×#347C211yesmaximal, characteristic, complemented
4#11746333C212yesmaximal, complemented
5#11746287C211yesmaximal, characteristic, complemented
6#10599880—31nomaximal, Hall
7C2×#6705C411yescharacteristic
8C2×C8×D15C2211yescharacteristic
9#91761C411yescharacteristic
10C3×C5×M32C2212yes—
11C3×C5×#97C2211yescharacteristic
12#91099C2211yescharacteristic
13C8×Dic15C411yescharacteristic
14#91096C2212yes—
15C4×C3⋊#168C411yescharacteristic
16#91082C414yescomplemented
17C16×D15C414yescomplemented
18#69087—51nomaximal, Hall
19D5×M32—32no—
20#64997—31no—
21C5×#347D311yescharacteristic, complemented
22#64732—32no—
23#64686—31no—
24C2×C4×D15C2×C411yescharacteristic
25C2×C3×C5×C8C2×C411yescharacteristic
26C2×C3×C5×C8C2311yescharacteristic
27C3×C42×C5C2×C411yescharacteristic
28#6714—21no—
29#6712—21no—
30C4×Dic15C2×C411yescharacteristic
31C2×C3⋊#168C2×C411yescharacteristic
32C2×C3⋊#168C2×C411yescharacteristic
33#6705—22no—
34C8×D15C2×C412yes—
35C8×D15C2×C412yes—
36C3×C5×C16C2×C414yes—
37C3⋊#672C2×C414yes—
38D3×M32—52no—
39#4708—51no—
40C3×#347D511yescharacteristic, complemented
41#4512—52no—
42#4466—51no—
43C2×#676—31no—
44C2×C8×D5—31no—
45#4018—31no—
46C5×M32C2×D312yes—
47C5×#97C2×D311yescharacteristic
48#3947—31no—
49C8×Dic5—31no—
50#3944—32no—
51C4×#168—31no—
52#3930—34no—
53D5×C16—34no—
54#2110—151noSylow
55C22×D15M1611yescharacteristic
56C2×C3×C4×C5—21no—
57C2×C3×C4×C5C22×C411yescharacteristic
58C2×Dic15—21no—
59C2×Dic15M1611yescharacteristic
60C4×D15C4212yes—
61C4×D15M1612yes—
62C3×C5×C8—21no—
63C3×C5×C8C22×C412yes—
64C3⋊#168—21no—
65C3⋊#168C4211yescharacteristic
66C3⋊#168C4211yescharacteristic
67C2×ΓL(1,𝔽25)—51no—
68C2×D3×C8—51no—
69#872—51no—
70C3×M32C2×D512yes—
71C3×#97C2×D511yescharacteristic
72#815—51no—
73C8×Dic3—51no—
74#812—52no—
75C4×C3⋊C8—51no—
76#798—54no—
77D3×C16—54no—
78C2×C4×D5—31no—
79C2×C5×C8C4×D311yescharacteristic
80C2×C5×C8C22×D311yescharacteristic
81C42×C5C4×D311yescharacteristic
82#685—61no—
83#683—61no—
84C4×Dic5—31no—
85C2×#168—31no—
86C2×#168—31no—
87#676—62no—
88C8×D5—32no—
89C8×D5—32no—
90C5×C16C4×D314yes—
91#672—34no—
92C2×M32—152no—
93#405—151no—
94#347—152no—
95#347—151no—
96#347D1511yescharacteristic, complemented
97C22×C3×C5C2×M1611yescharacteristic
98C2×D15—41no—
99C2×D15#9712yes—
100C3×C4×C5—41no—
101C3×C4×C5C2×C4211yescharacteristic
102C3×C4×C5C2×M1611yescharacteristic
103Dic15—41no—
104Dic15#9712yes—
105C2×C4×D3—51no—
106C2×C3×C8C4×D511yescharacteristic
107C2×C3×C8C22×D511yescharacteristic
108C3×C42C4×D511yescharacteristic
109(C2×D3)⋊C4—101no—
110Dic3⋊C4—101no—
111C4×Dic3—51no—
112C2×C3⋊C8—51no—
113C2×C3⋊C8—51no—
114ΓL(1,𝔽25)—102no—
115D3×C8—52no—
116D3×C8—52no—
117C3×C16C4×D514yes—
118C3⋊C16—54no—
119C22×D5—31no—
120C2×C4×C5—21no—
121C2×C4×C5C2×C4×D311yescharacteristic
122C2×Dic5—31no—
123C2×Dic5—61no—
124C4×D5—32no—
125C4×D5—32no—
126C5×C8—21no—
127C5×C8C2×C4×D312yes—
128#168—31no—
129#168—31no—
130#168—61no—
131C2×M16—151no—
132C22×C8—151no—
133#117—151no—
134M32—152no—
135M32—154no—
136M32C2×D1512yes—
137C2×C16—154no—
138#97—151no—
139#97C2×D1511yescharacteristic
140C4×C8—151no—
141C4×C8—151no—
142C2×C3×C5—21no—
143C2×C3×C5C2×#9711yescharacteristic
144D15—22no—
145C22×D3—51no—
146C2×C3×C4—21no—
147C2×C3×C4C2×C4×D511yescharacteristic
148C2×Dic3—51no—
149C2×Dic3—101no—
150C4×D3—52no—
151C4×D3—52no—
152C3×C8—21no—
153C3×C8C2×C4×D512yes—
154C3⋊C8—51no—
155C3⋊C8—51no—
156C3⋊C8—101no—
157C22×C5D3×M1611yescharacteristic
158C2×D5—32no—
159C2×D5—121no—
160C4×C5—41no—
161C4×C5C42×D311yescharacteristic
162C4×C5D3×M1611yescharacteristic
163Dic5—32no—
164Dic5—121no—
165C22×C4—151no—
166M16—302no—
167C2×C8—151no—
168C2×C8—152no—
169C2×C8—152no—
170C2×C8—151no—
171C2×C8C4×D1511yescharacteristic
172C2×C8C22×D1511yescharacteristic
173C4⋊C4—301no—
174C22⋊C4—301no—
175C42—151no—
176C42C4×D1511yescharacteristic
177C16—154no—
178C16C4×D1514yes—
179C3×C5#211011yescharacteristic, complemented, Hall
180C22×C3D5×M1611yescharacteristic
181C2×D3—52no—
182C2×D3—201no—
183C3×C4—41no—
184C3×C4C42×D511yescharacteristic
185C3×C4D5×M1611yescharacteristic
186Dic3—52no—
187Dic3—201no—
188C2×C5—21no—
189C2×C5D3×#9711yescharacteristic
190D5—62no—
191C23—151no—
192C2×C4—21no—
193C2×C4—151no—
194C2×C4—152no—
195C2×C4—152no—
196C2×C4—301no—
197C2×C4C2×C4×D1511yescharacteristic
198C8—21no—
199C8—151no—
200C8—151no—
201C8—301no—
202C8C2×C4×D1512yes—
203C2×C3—21no—
204C2×C3D5×#9711yescharacteristic
205D3—102no—
206C5#6908711yescharacteristic, complemented, Sylow
207C22—152no—
208C22—601no—
209C22M16×D1511yescharacteristic
210C4—41no—
211C4—152no—
212C4—601no—
213C4C42×D1511yescharacteristic
214C4M16×D1511yescharacteristic
215C3#1059988011yescharacteristic, complemented, Sylow
216C2—21no—
217C2—302no—
218C2D15×#9711yescharacteristic
subgroupG/H
centerC4C42×D15
commutatorC3×C4×C5C2×C42
FrattiniC2×C8C22×D15
FittingC3×C5×#347C2
socleC2×C3×C5C2×#97
prime radicalC22×D15M16
cosocleC2×C3×C5×C8C23
hypercenter#347D15
hypocenterC3×C5#2110
LCSG ▷ C3×C4×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ #347

Complements

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

NH ≅ G/Ntype
3. C3×C5×#347C2semidirect
4. #11746333C2semidirect
5. #11746287C2semidirect
16. #91082C4semidirect
17. C16×D15C4semidirect
21. C5×#347D3semidirect
40. C3×#347D5semidirect
96. #347D15semidirect
179. C3×C5#2110semidirect
206. C5#69087semidirect
215. C3#10599880semidirect

Maximal subgroups

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

subgroupindex
D15×M322
#117508092
C3×C5×#3472
#117463332
#117462872
#105998803
#690875