Finite Group Databasebeta

← #14318572

Subgroups — #14318572

Order 1920.

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

normal subgroups only

This group has 248 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
2C5×#5137C211yesmaximal, characteristic
3C3×#64773C211yesmaximal, characteristic
4#11745933C212yesmaximal, complemented
5#11745924C212yesmaximal, complemented
6#10601883—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8C2×#6710—21no—
9C5×#924—21no—
10C2×C5×Dic12C2211yescharacteristic
11#91103—21no—
12#91103C2212yes—
13C5×#817C2211yescharacteristic
14C5×#816—21no—
15C3×#3944C2212yes—
16#69117—51nomaximal, Hall
17C5×#470—31no—
18#65414—31no—
19#64785—32no—
20#64773D311yescharacteristic
21#64707—32no—
22C22×C3×C4×C5D411yescharacteristic
23C2×C5×Dic6—21no—
24C3×C5×M16—22no—
25C2×C3×C5×C8D411yescharacteristic
26C2×C3×C5×C8C2311yescharacteristic
27#6710—22no—
28#6710—41no—
29C2×C3⋊#168—41no—
30C5×#217—41no—
31C5×C4⋊Dic3—21no—
32C5×Dic3⋊C4—41no—
33C5×Dic12—22no—
34C3×#672—22no—
35#5137D511yescharacteristic
36#5125—51no—
37C3×#349—51no—
38#4517—52no—
39#4513—52no—
40C2×C5×Q16—31no—
41C2×C5×M16C2×D311yescharacteristic
42C5×C22⋊Q8—61no—
43C2×#681—61no—
44C5×#106—31no—
45C5×#103—61no—
46#3951—32no—
47#3951—61no—
48#3944C2×D312yes—
49#2239—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5SD1611yescharacteristic
54C2×C3×C4×C5C2×D411yescharacteristic
55C2×C5×Dic3—41no—
56C2×C5×Dic3—41no—
57C5×Dic6—41no—
58C5×Dic6—41no—
59C3×C5×C8—21no—
60C3×C5×C8#4112yes—
61C3⋊#168—42no—
62C2×C3×M16C2×D511yescharacteristic
63#924—21no—
64C2×#208—101no—
65C2×Dic12C2×D511yescharacteristic
66C3×M32—52no—
67#819—52no—
68#819—101no—
69#817C2×D511yescharacteristic
70#816—21no—
71C2×C5×Q8—61no—
72C22×C4×C5D1211yescharacteristic
73C5×Q16—62no—
74C5×M16—22no—
75C2×C5×C8D1211yescharacteristic
76C2×C5×C8C22×D311yescharacteristic
77C5×C4⋊C4—61no—
78C5×C4⋊C4—121no—
79C5×C22⋊C4—121no—
80#681—62no—
81#681—121no—
82C2×#168—121no—
83#672—22no—
84#470—31no—
85#430—151no—
86#365—152no—
87#362—152no—
88#349—51no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5C2×SD1611yescharacteristic
92C3×C4×C5—21no—
93C3×C4×C5#12311yescharacteristic
94C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
95C5×Dic3—81no—
96C5×Dic3—81no—
97C22×C3×C4C22⋊D511yescharacteristic
98C2×Dic6—21no—
99C3×M16—22no—
100C2×C3×C8C22⋊D511yescharacteristic
101C2×C3×C8C22×D511yescharacteristic
102#217—41no—
103C4⋊Dic3—21no—
104Dic3⋊C4—41no—
105#208—102no—
106#208—201no—
107C2×C3⋊C8—201no—
108Dic12—22no—
109C3×C16—102no—
110C23×C5#20411yescharacteristic
111C5×Q8—121no—
112C5×Q8—121no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—121no—
116C2×C4×C5—121no—
117C2×C4×C5#20411yescharacteristic
118C2×C4×C5C2×D1211yescharacteristic
119C5×C8—21no—
120C5×C8#23712yes—
121#168—122no—
122C2×Q16—31no—
123C2×M16—301no—
124C2×M16D3×D511yescharacteristic
125C22⋊Q8—61no—
126M32—52no—
127#108—152no—
128#108—301no—
129#106—31no—
130#103—61no—
131C2×C3×C5—21no—
132C2×C3×C5—41no—
133C2×C3×C5#48111yescharacteristic
134C23×C3#68711yescharacteristic
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4#68711yescharacteristic
138C2×C3×C4C2×C22⋊D511yescharacteristic
139C2×Dic3—41no—
140C2×Dic3—41no—
141Dic6—41no—
142Dic6—41no—
143C3×C8—21no—
144C3×C8#71112yes—
145C3⋊C8—202no—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5C2×#20411yescharacteristic
149C4×C5—21no—
150C4×C5—241no—
151C4×C5—241no—
152C4×C5#88611yescharacteristic
153C4×C5#90811yescharacteristic
154C2×Q8—61no—
155C22×C4#120311yescharacteristic
156Q16—62no—
157M16—22no—
158M16—302no—
159M16—601no—
160C2×C8—601no—
161C2×C8#120311yescharacteristic
162C2×C8C2×D3×D511yescharacteristic
163C4⋊C4—61no—
164C4⋊C4—121no—
165C22⋊C4—121no—
166C16—102no—
167C3×C5#223911yescharacteristic, complemented, Hall
168C22×C3—21no—
169C22×C3—41no—
170C22×C3C2×#68711yescharacteristic
171C3×C4—21no—
172C3×C4#408111yescharacteristic
173C3×C4#409511yescharacteristic
174Dic3—81no—
175Dic3—81no—
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#473511yescharacteristic
179C23#665911yescharacteristic
180Q8—121no—
181Q8—121no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—121no—
185C2×C4—121no—
186C2×C4#665911yescharacteristic
187C2×C4C2×#120311yescharacteristic
188C8—21no—
189C8—602no—
190C8#678012yes—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3#6532311yescharacteristic
194C5#6911711yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22C2×#665911yescharacteristic
198C4—21no—
199C4—241no—
200C4—241no—
201C4#9130511yescharacteristic
202C4#9154311yescharacteristic
203C3#1060188311yescharacteristic, complemented, Sylow
204C2—21no—
205C2—41no—
206C2#1174837911yescharacteristic
subgroupG/H
centerC2#11748379
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#481
prime radicalC23×C3×C5SD16
hypercenterC2×M16D3×D5
hypocenterC3×C5#2239
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
4. #11745933C2semidirect
5. #11745924C2semidirect
167. C3×C5#2239semidirect
194. C5#69117semidirect
203. C3#10601883semidirect

Maximal subgroups

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

subgroupindex
#117512262
C5×#51372
C3×#647732
#117459332
#117459242
#106018833
#691175