Finite Group Databasebeta

← #14318536

Subgroups — #14318536

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#11751226C211yesmaximal, characteristic, complemented
2C3×#65424C211yesmaximal, characteristic
3C5×#4553C211yesmaximal, characteristic, complemented
4#11745937C212yesmaximal, complemented
5#11745916C212yesmaximal, complemented
6#10599909—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8C2×#6710—21no—
9C3×#4076—21no—
10C2×C3×D40C2211yescharacteristic
11#91103—21no—
12#91103C2212yes—
13C5×#812C2212yes—
14C3×#3953—21no—
15C3×#3949C2211yescharacteristic
16#71088—51nomaximal, Hall
17#65424D311yescharacteristic
18#65414—31no—
19C5×#349—31no—
20#64736—32no—
21#64733—32no—
22C22×C3×C4×C5D411yescharacteristic
23C2×C3×C22⋊D5—41no—
24C2×C3×D20—21no—
25C3×C5×M16—22no—
26C2×C3×C5×C8D411yescharacteristic
27C2×C3×C5×C8C2311yescharacteristic
28#6710—22no—
29#6710—41no—
30C2×C3⋊#168—41no—
31C3×#685—41no—
32C3×C4⋊Dic5—21no—
33C3×D40—22no—
34C5×C3⋊C16—22no—
35C3×#469—51no—
36#5125—51no—
37#4563—52no—
38#4553D511yescharacteristic, complemented
39#4487—52no—
40C2×C5×M16C2×D311yescharacteristic
41#4076—21no—
42C2×#681—61no—
43C2×D40C2×D311yescharacteristic
44C5×M32—32no—
45#3953—21no—
46#3951—32no—
47#3951—61no—
48#3949C2×D311yescharacteristic
49#2238—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C22×C3×D5—41no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5—21no—
54C2×C3×C4×C5SD1611yescharacteristic
55C2×C3×C4×C5C2×D411yescharacteristic
56C3×C22⋊D5—82no—
57C2×C3×Dic5—41no—
58C3×D20—41no—
59C3×D20—41no—
60C3×C5×C8—21no—
61C3×C5×C8#4112yes—
62C3⋊#168—42no—
63C2×C3×D8—51no—
64C2×C3×M16C2×D511yescharacteristic
65C3×#121—101no—
66C2×#208—101no—
67C3×#106—51no—
68C3×#102—101no—
69#819—52no—
70#819—101no—
71#812C2×D512yes—
72C22×C4×C5#6711yescharacteristic
73C2×C22⋊D5—41no—
74C2×D20—21no—
75C5×M16—22no—
76C2×C5×C8#6711yescharacteristic
77C2×C5×C8C22×D311yescharacteristic
78#685—41no—
79C4⋊Dic5—21no—
80#681—62no—
81#681—121no—
82C2×#168—121no—
83D40—22no—
84C5×C16—62no—
85#469—51no—
86#430—151no—
87#365—152no—
88#361—152no—
89#349—31no—
90C22×C3×C5—21no—
91C22×C3×C5—41no—
92C22×C3×C5C2×SD1611yescharacteristic
93C2×C3×D5—81no—
94C2×C3×D5—81no—
95C2×C3×D5—81no—
96C3×C4×C5—21no—
97C3×C4×C5#12311yescharacteristic
98C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
99C3×Dic5—81no—
100C2×C3×D4—101no—
101C2×C3×D4—201no—
102C22×C3×C4D2011yescharacteristic
103C3×D8—102no—
104C3×M16—22no—
105C2×C3×C8D2011yescharacteristic
106C2×C3×C8C22×D511yescharacteristic
107C3×C4⋊C4—101no—
108C3×C22⋊C4—201no—
109#208—102no—
110#208—201no—
111C2×C3⋊C8—201no—
112C3⋊C16—22no—
113C23×C5#21411yescharacteristic
114C22×D5—41no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5#21411yescharacteristic
118C2×C4×C5C2×#6711yescharacteristic
119C22⋊D5—82no—
120C2×Dic5—41no—
121D20—41no—
122D20—41no—
123C5×C8—21no—
124C5×C8#23712yes—
125#168—122no—
126C2×D8—51no—
127C2×M16—301no—
128C2×M16D3×D511yescharacteristic
129#121—101no—
130M32—32no—
131#108—152no—
132#108—301no—
133#106—51no—
134#102—101no—
135C2×C3×C5—21no—
136C2×C3×C5—41no—
137C2×C3×C5#48111yescharacteristic
138C3×D5—161no—
139C23×C3—201no—
140C23×C3#67711yescharacteristic
141C3×D4—201no—
142C3×D4—201no—
143C3×D4—402no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—201no—
147C2×C3×C4#67711yescharacteristic
148C2×C3×C4C2×D2011yescharacteristic
149C3×C8—21no—
150C3×C8#71112yes—
151C3⋊C8—202no—
152C22×C5—21no—
153C22×C5—41no—
154C22×C5C2×#21411yescharacteristic
155C2×D5—81no—
156C2×D5—81no—
157C2×D5—81no—
158C4×C5—21no—
159C4×C5#93511yescharacteristic
160C4×C5#94911yescharacteristic
161Dic5—81no—
162C2×D4—101no—
163C2×D4—201no—
164C22×C4#120211yescharacteristic
165D8—102no—
166M16—22no—
167M16—302no—
168M16—601no—
169C2×C8—601no—
170C2×C8#120211yescharacteristic
171C2×C8C2×D3×D511yescharacteristic
172C4⋊C4—101no—
173C22⋊C4—201no—
174C16—62no—
175C3×C5#223811yescharacteristic, complemented, Hall
176C22×C3—21no—
177C22×C3—41no—
178C22×C3—401no—
179C22×C3—401no—
180C22×C3—401no—
181C22×C3C2×#67711yescharacteristic
182C3×C4—21no—
183C3×C4—401no—
184C3×C4#403211yescharacteristic
185C3×C4#405411yescharacteristic
186C2×C5—21no—
187C2×C5—41no—
188C2×C5#503411yescharacteristic
189D5—161no—
190C23—201no—
191C23#665711yescharacteristic
192D4—201no—
193D4—201no—
194D4—402no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—201no—
198C2×C4#665711yescharacteristic
199C2×C4C2×#120211yescharacteristic
200C8—21no—
201C8—602no—
202C8#678012yes—
203C2×C3—21no—
204C2×C3—41no—
205C2×C3—801no—
206C2×C3#6502411yescharacteristic
207C5#7108811yescharacteristic, complemented, Sylow
208C22—21no—
209C22—41no—
210C22—401no—
211C22—401no—
212C22—401no—
213C22C2×#665711yescharacteristic
214C4—21no—
215C4—401no—
216C4#9130111yescharacteristic
217C4#9153711yescharacteristic
218C3#1059990911yescharacteristic, complemented, Sylow
219C2—21no—
220C2—41no—
221C2—801no—
222C2#1174837511yescharacteristic
subgroupG/H
centerC2#11748375
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#481
prime radicalC3×#65424C2
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
1. #11751226C2semidirect
3. C5×#4553C2semidirect
4. #11745937C2semidirect
5. #11745916C2semidirect
38. #4553D5semidirect
175. C3×C5#2238semidirect
207. C5#71088semidirect
218. C3#10599909semidirect

Maximal subgroups

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

subgroupindex
#117512262
C3×#654242
C5×#45532
#117459372
#117459162
#105999093
#710885