Finite Group Databasebeta

← #14318537

Subgroups — #14318537

Order 1920.

268 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 76 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
1#11751236C211yesmaximal, characteristic
2C3×#65414C211yesmaximal, characteristic, complemented
3C5×#4553C211yesmaximal, characteristic, complemented
4#11745938C212yesmaximal, complemented
5#11745919C212yesmaximal, complemented
6#10599909—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8#91819—21no—
9C2×D120C2211yescharacteristic
10C2×C3×#681—21no—
11#91105—21no—
12#91101C2211yescharacteristic
13C5×#812C2212yes—
14C3×#3951—21no—
15C3×#3951C2212yes—
16#70723—51nomaximal, Hall
17#65424—31no—
18#65414D311yescharacteristic, complemented
19C5×#349—31no—
20#64736—32no—
21#64733—32no—
22C22×C3×C4×C5D411yescharacteristic
23C2×#1220—41no—
24C2×D60—21no—
25C3×C5×M16—22no—
26C2×C3×C5×C8D411yescharacteristic
27C2×C3×C5×C8C2311yescharacteristic
28#6714—41no—
29C4⋊Dic15—21no—
30D120—22no—
31C3×#681—22no—
32C3×#681—41no—
33C2×C3×#168—41no—
34C5×C3⋊C16—22no—
35C3×#430—51no—
36#5135—51no—
37#4553D511yescharacteristic, complemented
38#4495—52no—
39#4494—52no—
40C2×C5×M16C2×D311yescharacteristic
41#4076—61no—
42C2×#681—21no—
43C2×D40—31no—
44C5×M32—32no—
45#3953—61no—
46#3951—21no—
47#3951C2×D312yes—
48#3949—31no—
49#2238—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C22×D15—41no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5—21no—
54C2×C3×C4×C5SD1611yescharacteristic
55C2×C3×C4×C5C2×D411yescharacteristic
56#1220—82no—
57C2×Dic15—41no—
58D60—41no—
59D60—41no—
60C3×C5×C8—21no—
61C3×C5×C8#4112yes—
62C3×#168—42no—
63C2×C3×M16—101no—
64C2×C3×M16C2×D511yescharacteristic
65#930—101no—
66C2×D24—51no—
67C3×#108—52no—
68C3×#108—101no—
69#821—101no—
70#817—51no—
71#812C2×D512yes—
72C22×C4×C5#6711yescharacteristic
73C2×C22⋊D5—121no—
74C2×D20—61no—
75C5×M16—22no—
76C2×C5×C8#6711yescharacteristic
77C2×C5×C8C22×D311yescharacteristic
78#685—121no—
79C4⋊Dic5—61no—
80#681—22no—
81#681—41no—
82C2×#168—41no—
83D40—62no—
84C5×C16—62no—
85#469—151no—
86#430—51no—
87#365—152no—
88#361—152no—
89#349—31no—
90C22×C3×C5—21no—
91C22×C3×C5—41no—
92C22×C3×C5C2×SD1611yescharacteristic
93C2×D15—81no—
94C2×D15—81no—
95C2×D15—81no—
96C3×C4×C5—21no—
97C3×C4×C5#12311yescharacteristic
98C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
99Dic15—81no—
100C22×C3×C4D2011yescharacteristic
101C2×#67—201no—
102C2×D12—101no—
103C3×M16—22no—
104C3×M16—102no—
105C3×M16—201no—
106C2×C3×C8—201no—
107C2×C3×C8D2011yescharacteristic
108C2×C3×C8C22×D511yescharacteristic
109(C2×D3)⋊C4—201no—
110C4⋊Dic3—101no—
111D24—102no—
112C3⋊C16—22no—
113C23×C5#21511yescharacteristic
114C22×D5—121no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5#21511yescharacteristic
118C2×C4×C5C2×#6711yescharacteristic
119C22⋊D5—242no—
120C2×Dic5—121no—
121D20—121no—
122D20—121no—
123C5×C8—21no—
124C5×C8#23512yes—
125#168—42no—
126C2×D8—151no—
127C2×M16—101no—
128C2×M16D3×D511yescharacteristic
129#121—301no—
130M32—32no—
131#108—52no—
132#108—101no—
133#106—151no—
134#102—301no—
135C2×C3×C5—21no—
136C2×C3×C5—41no—
137C2×C3×C5#48111yescharacteristic
138D15—161no—
139C23×C3#67711yescharacteristic
140C22×D3—201no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4#67711yescharacteristic
144C2×C3×C4C2×D2011yescharacteristic
145#67—402no—
146C2×Dic3—201no—
147D12—201no—
148D12—201no—
149C3×C8—21no—
150C3×C8—202no—
151C3×C8#71112yes—
152C22×C5—21no—
153C22×C5—41no—
154C22×C5C2×#21511yescharacteristic
155C2×D5—241no—
156C2×D5—241no—
157C2×D5—241no—
158C4×C5—21no—
159C4×C5#92911yescharacteristic
160C4×C5#93211yescharacteristic
161Dic5—241no—
162C2×D4—301no—
163C2×D4—601no—
164C22×C4#120211yescharacteristic
165D8—302no—
166M16—22no—
167M16—102no—
168M16—201no—
169C2×C8—201no—
170C2×C8#120211yescharacteristic
171C2×C8C2×D3×D511yescharacteristic
172C4⋊C4—301no—
173C22⋊C4—601no—
174C16—62no—
175C3×C5#223811yescharacteristic, complemented, Hall
176C22×C3—21no—
177C22×C3—41no—
178C22×C3C2×#67711yescharacteristic
179C2×D3—401no—
180C2×D3—401no—
181C2×D3—401no—
182C3×C4—21no—
183C3×C4#403211yescharacteristic
184C3×C4#405411yescharacteristic
185Dic3—401no—
186C2×C5—21no—
187C2×C5—41no—
188C2×C5#496811yescharacteristic
189D5—481no—
190C23—601no—
191C23#665811yescharacteristic
192D4—601no—
193D4—601no—
194D4—1202no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—601no—
198C2×C4#665811yescharacteristic
199C2×C4C2×#120211yescharacteristic
200C8—21no—
201C8—202no—
202C8#678212yes—
203C2×C3—21no—
204C2×C3—41no—
205C2×C3#6502411yescharacteristic
206D3—801no—
207C5#7072311yescharacteristic, complemented, Sylow
208C22—21no—
209C22—41no—
210C22—1201no—
211C22—1201no—
212C22—1201no—
213C22C2×#665811yescharacteristic
214C4—21no—
215C4—1201no—
216C4#9131211yescharacteristic
217C4#9154611yescharacteristic
218C3#1059990911yescharacteristic, complemented, Sylow
219C2—21no—
220C2—41no—
221C2—2401no—
222C2#1174845411yescharacteristic
subgroupG/H
centerC2#11748454
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#481
prime radical#11751236C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#65414C2semidirect
3. C5×#4553C2semidirect
4. #11745938C2semidirect
5. #11745919C2semidirect
18. #65414D3semidirect
37. #4553D5semidirect
175. C3×C5#2238semidirect
207. C5#70723semidirect
218. C3#10599909semidirect

Maximal subgroups

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

subgroupindex
#117512362
C3×#654142
C5×#45532
#117459382
#117459192
#105999093
#707235