Finite Group Databasebeta

← #14279373

Subgroups — #14279373

Order 1920.

212 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 37 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×#65535C211yesmaximal, characteristic
2#11746802C211yesmaximal, characteristic, complemented
3#11746800C211yesmaximal, characteristic, complemented
4#10598836—31nomaximal, Hall
5C3×C5×2−1+4C411yescharacteristic
6C3×#4097—21no—
7C3×#4090C2211yescharacteristic
8#91234—21no—
9#91233—21no—
10C3×#3969—21no—
11C3×#3968C411yescharacteristic
12#67773—51nomaximal, Hall
13#65535D311yescharacteristic
14#64931—31no—
15#64929—31no—
16C3×C5×#41—21no—
17C3×C5×#41—41no—
18C3×C5×#41—41no—
19C2×C3×C5×Q8—41no—
20C2×C3×C5×Q8C2×C411yescharacteristic
21C2×C3×Dic10D411yescharacteristic
22#6762—41no—
23C2×C3⋊#170—41no—
24C3×#689—41no—
25C3×#687—41no—
26C3×#683—41no—
27C3×C4×Dic5D411yescharacteristic
28C3×#681—21no—
29C3×#456—51no—
30#4548—51no—
31#4546—51no—
32C5×2−1+4Dic311yescharacteristic
33#4097—21no—
34#4090C2×D311yescharacteristic
35#4005—61no—
36#4004—61no—
37#3969—21no—
38#3968Dic311yescharacteristic
39#1405—151noSylow
40C3×C5×Q8—21no—
41C3×C5×Q8—41no—
42C3×C5×Q8—41no—
43C3×C5×D4—21no—
44C3×C5×D4—41no—
45C3×C5×D4—41no—
46C2×C3×C4×C5—21no—
47C2×C3×C4×C5—41no—
48C2×C3×C4×C5—42no—
49C2×C3×C4×C5C22⋊C411yescharacteristic
50C2×C3×Dic5—21no—
51C2×C3×Dic5—21no—
52C3×Dic10—41no—
53C3⋊#170—81no—
54C3⋊#170—81no—
55C3×#168—41no—
56C3×2−1+4AGL(1,𝔽5)11yescharacteristic
57C3×#137—101no—
58C3×C4⋊Q8—51no—
59C3×#104—101no—
60C3×#101—51no—
61#836—101no—
62C4⋊(C3⋊C8)—101no—
63C5×#41—21no—
64C5×#41—41no—
65C5×#41—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8C2×Dic311yescharacteristic
68C2×Dic10#6711yescharacteristic
69#704—121no—
70C2×#170—121no—
71#689—41no—
72#687—41no—
73#683—41no—
74C4×Dic5#6711yescharacteristic
75#681—21no—
76#456—51no—
77#356—151no—
78#333—151no—
79C22×C3×C5—41no—
80C22×C3×C5#9911yescharacteristic
81C3×C4×C5—21no—
82C3×C4×C5—41no—
83C3×C4×C5—41no—
84C3×Dic5—21no—
85C3×Dic5—21no—
86C3×Dic5—41no—
87C3×#41—21no—
88C3×#41—41no—
89C3×#41—41no—
90C2×C3×Q8—41no—
91C2×C3×Q8—51no—
92C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
93C3×Q16—201no—
94C3×SD16—201no—
95C3×M16—101no—
96C3×C4⋊C4—201no—
97C3×C42—51no—
98#208—201no—
99C2×C3⋊C8—201no—
100C5×Q8—21no—
101C5×Q8—41no—
102C5×Q8—41no—
103C5×D4—21no—
104C5×D4—41no—
105C5×D4—41no—
106C2×C4×C5—21no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5#21711yescharacteristic
110C2×Dic5—21no—
111C2×Dic5—21no—
112Dic10—41no—
113#170—241no—
114#170—241no—
115#168—41no—
1162−1+4ΓL(1,𝔽16)11yescharacteristic
117#137—101no—
118C4⋊Q8—51no—
119C4⋊C8—301no—
120#104—101no—
121#101—51no—
122#101—301no—
123C2×C3×C5—21no—
124C2×C3×C5—81no—
125C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
126C3×Q8—21no—
127C3×Q8—41no—
128C3×Q8—41no—
129C3×Q8—201no—
130C3×D4—21no—
131C3×D4—41no—
132C3×D4—41no—
133C2×C3×C4—21no—
134C2×C3×C4—41no—
135C2×C3×C4—42no—
136C2×C3×C4—101no—
137C2×C3×C4—101no—
138C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
139C3×C8—201no—
140C3⋊C8—401no—
141C3⋊C8—401no—
142C22×C5—41no—
143C22×C5#83411yescharacteristic
144C4×C5—21no—
145C4×C5—41no—
146C4×C5—41no—
147Dic5—21no—
148Dic5—21no—
149Dic5—41no—
150#41—21no—
151#41—41no—
152#41—41no—
153C2×Q8—41no—
154C2×Q8—51no—
155C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
156Q16—201no—
157SD16—201no—
158M16—101no—
159M16—601no—
160C2×C8—601no—
161C4⋊C4—201no—
162C42—51no—
163C3×C5#140511yescharacteristic, complemented, Hall
164C22×C3—41no—
165C22×C3#401111yescharacteristic
166C3×C4—21no—
167C3×C4—41no—
168C3×C4—41no—
169C3×C4—101no—
170C3×C4—101no—
171C3×C4—201no—
172C2×C5—21no—
173C2×C5—81no—
174C2×C5#453611yescharacteristic
175Q8—21no—
176Q8—41no—
177Q8—41no—
178Q8—201no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—101no—
186C2×C4—101no—
187C2×C4#676311yescharacteristic
188C8—201no—
189C8—1201no—
190C8—1201no—
191C2×C3—21no—
192C2×C3—81no—
193C2×C3#6493411yescharacteristic
194C5#6777311yescharacteristic, complemented, Sylow
195C22—41no—
196C22#9124011yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—101no—
201C4—101no—
202C4—201no—
203C3#1059883611yescharacteristic, complemented, Sylow
204C2—21no—
205C2—81no—
206C2#1174680511yescharacteristic
subgroupG/H
centerC2#11746805
commutatorC2×C3×C5×Q8C2×C4
FrattiniC2×Q8C2×ΓL(1,𝔽16)
Fitting, prime radicalC3×C5×2−1+4C4
socleC2×C3×C5AΣL(1,𝔽16)
cosocleC3×#4090C22
hypercenter2−1+4ΓL(1,𝔽16)
hypocenterC3×C5#1405
LCSG ▷ C2×C3×C5×Q8 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
2. #11746802C2semidirect
3. #11746800C2semidirect
163. C3×C5#1405semidirect
194. C5#67773semidirect
203. C3#10598836semidirect

Maximal subgroups

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

subgroupindex
C3×#655352
#117468022
#117468002
#105988363
#677735