Finite Group Databasebeta

← #14312421

Subgroups — #14312421

Order 1920.

316 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 111 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×#423C211yesmaximal, characteristic
2#11751226C211yesmaximal, characteristic
3#11746380C212yesmaximal
4#11746378C211yesmaximal, characteristic
5#11746344C212yesmaximal
6#10601319—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8C2×C3×C5×M16C2211yescharacteristic
9C2×C3×C42×C5C2211yescharacteristic
10#91815C2212yes—
11C2×#6710C2212yes—
12C3×C5×C4⋊C8—22no—
13#91103—22no—
14#70526—51nomaximal, Hall
15C5×#423D311yescharacteristic
16#65414—31no—
17#64779—32no—
18#64777—31no—
19#64743—32no—
20C22×C3×C4×C5—21no—
21C22×C3×C4×C5C2311yescharacteristic
22C3×C5×M16—22no—
23C3×C5×M16—22no—
24C2×C3×C5×C8—21no—
25C2×C3×C5×C8D412yes—
26C3×C42×C5—21no—
27C3×C42×C5Q811yescharacteristic
28C3×C42×C5Q811yescharacteristic
29#6719—22no—
30C4⋊Dic15—22no—
31C4×Dic15—22no—
32#6710—22no—
33#6710—22no—
34C2×C3⋊#168—22no—
35C3×#423D511yescharacteristic
36#5125—51no—
37#4559—52no—
38#4557—51no—
39#4523—52no—
40C2×C5×M16C2×D311yescharacteristic
41C2×C5×M16C2×D311yescharacteristic
42C2×C42×C5C2×D311yescharacteristic
43#4072—32no—
44C2×#681—32no—
45C5×C4⋊C8—22no—
46#3951—62no—
47#2102—151noSylow
48C23×C3×C5#4111yescharacteristic
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—42no—
52C2×C3×C4×C5C2×D411yescharacteristic
53C2×C3×C4×C5C2×Q811yescharacteristic
54C2×C3×C4×C5#4112yes—
55C2×C3×C4×C5#4112yes—
56C2×Dic15—42no—
57C3×C5×C8—22no—
58C3×C5×C8—41no—
59C3⋊#168—42no—
60C2×C3×M16C2×D511yescharacteristic
61C2×C3×M16C2×D511yescharacteristic
62C2×C3×C42C2×D511yescharacteristic
63#926—52no—
64C2×#208—52no—
65C3×C4⋊C8—22no—
66#819—102no—
67C22×C4×C5—21no—
68C22×C4×C5C22×D311yescharacteristic
69C5×M16—22no—
70C5×M16—22no—
71C2×C5×C8—21no—
72C2×C5×C8#6712yes—
73C42×C5—21no—
74C42×C5Dic611yescharacteristic
75C42×C5Dic611yescharacteristic
76C22⋊Dic5—62no—
77C4⋊Dic5—62no—
78C4×Dic5—62no—
79#681—62no—
80#681—62no—
81C2×#168—62no—
82#430—151no—
83#423D1511yescharacteristic
84#344—152no—
85#339—152no—
86H(3,ℤ/4)—151no—
87C22×C3×C5—41no—
88C22×C3×C5C22⋊Q811yescharacteristic
89C22×C3×C5#12612yes—
90C3×C4×C5—22no—
91C3×C4×C5—41no—
92C3×C4×C5#12311yescharacteristic
93C3×C4×C5#12411yescharacteristic
94C3×C4×C5#12512yes—
95Dic15—82no—
96C22×C3×C4—21no—
97C22×C3×C4C22×D511yescharacteristic
98C3×M16—22no—
99C3×M16—22no—
100C2×C3×C8—21no—
101C2×C3×C8C22⋊D512yes—
102C3×C42—21no—
103C3×C42Dic1011yescharacteristic
104C3×C42Dic1011yescharacteristic
105#217—102no—
106C4⋊Dic3—102no—
107C4×Dic3—102no—
108#208—102no—
109#208—102no—
110C2×C3⋊C8—102no—
111C23×C5#23511yescharacteristic
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—42no—
115C2×C4×C5C2×Dic611yescharacteristic
116C2×C4×C5#23712yes—
117C2×C4×C5#23912yes—
118C2×C4×C5C2×#6711yescharacteristic
119C2×Dic5—122no—
120C5×C8—22no—
121C5×C8—41no—
122#168—122no—
123C2×M16—152no—
124C2×M16C2×D1511yescharacteristic
125C2×M16C2×D1511yescharacteristic
126#117—152no—
127C2×C42C2×D1511yescharacteristic
128#108—302no—
129C4⋊C8—22no—
130C2×C3×C5—22no—
131C2×C3×C5—21no—
132C2×C3×C5#40011yescharacteristic
133C23×C3#70911yescharacteristic
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—42no—
137C2×C3×C4C2×Dic1011yescharacteristic
138C2×C3×C4#71112yes—
139C2×C3×C4#71312yes—
140C2×C3×C4C2×C22⋊D511yescharacteristic
141C2×Dic3—202no—
142C3×C8—22no—
143C3×C8—41no—
144C3⋊C8—202no—
145C22×C5—41no—
146C22×C5#89812yes—
147C22×C5#92411yescharacteristic
148C4×C5—22no—
149C4×C5—41no—
150C4×C5#89012yes—
151C4×C5#93511yescharacteristic
152C4×C5#94711yescharacteristic
153Dic5—242no—
154C22×C4—21no—
155C22×C4C22×D1511yescharacteristic
156M16—22no—
157M16—22no—
158M16—302no—
159M16—302no—
160C2×C8—21no—
161C2×C8—302no—
162C2×C8#122012yes—
163C4⋊C4—302no—
164C22⋊C4—302no—
165C42—21no—
166C42—302no—
167C42Dic3011yescharacteristic
168C42Dic3011yescharacteristic
169C3×C5#210211yescharacteristic, complemented, Hall
170C22×C3—41no—
171C22×C3#404412yes—
172C22×C3#407011yescharacteristic
173C3×C4—22no—
174C3×C4—41no—
175C3×C4#403612yes—
176C3×C4#408111yescharacteristic
177C3×C4#409311yescharacteristic
178Dic3—402no—
179C2×C5—22no—
180C2×C5—21no—
181C2×C5#498611yescharacteristic
182C23#681711yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—602no—
187C2×C4C2×Dic3011yescharacteristic
188C2×C4#681912yes—
189C2×C4#682112yes—
190C2×C4C2×#122011yescharacteristic
191C8—22no—
192C8—41no—
193C8—602no—
194C2×C3—22no—
195C2×C3—21no—
196C2×C3#6527511yescharacteristic
197C5#7052611yescharacteristic, complemented, Sylow
198C22—41no—
199C22#9178712yes—
200C22#9181311yescharacteristic
201C4—22no—
202C4—41no—
203C4—1202no—
204C4#9177912yes—
205C4#9182411yescharacteristic
206C4#9183611yescharacteristic
207C3#1060131911yescharacteristic, complemented, Sylow
208C2—21no—
209C2—22no—
210C2#1175108711yescharacteristic
subgroupG/H
centerC4#91836
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#423C2
socleC2×C3×C5#400
prime radicalC23×C3×C5#41
hypercenter#423D15
hypocenterC3×C5#2102
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
169. C3×C5#2102semidirect
197. C5#70526semidirect
207. C3#10601319semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4232
#117512262
#117463802
#117463782
#117463442
#106013193
#705265