Finite Group Databasebeta

← #14315733

Subgroups — #14315733

Order 1920.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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#11751683C212yesmaximal, complemented
2#11746834C211yesmaximal, characteristic
3#11746723C211yesmaximal, characteristic, complemented
4C3×#64844C211yesmaximal, characteristic, complemented
5#11746463C212yesmaximal, complemented
6#10604137—31nomaximal, Hall
7#91914—22no—
8#91271C2212yes—
9#91225C2212yes—
10C3×C8×AGL(1,𝔽5)C2211yescharacteristic
11C3×D5⋊C16C2211yescharacteristic
12#91158—22no—
13D240C411yescharacteristic, complemented
14C5×Dic24C411yescharacteristic, complemented
15C3×D5×C16C2211yescharacteristic
16#90945C412yescomplemented
17#69085—51nomaximal, Hall
18#65740—32no—
19#65208—31no—
20#64909—32no—
21#64852—31no—
22#64844D311yescharacteristic, complemented
23#6773—22no—
24#6758—22no—
25C3×C4×AGL(1,𝔽5)D411yescharacteristic
26C3×D5⋊C8D411yescharacteristic
27#6740—42no—
28#6738—42no—
29D120C2×C412yes—
30C5×Dic12C2×C412yes—
31C3×C8×D5C2311yescharacteristic
32#6660—22no—
33C3×#674—21no—
34C3×C5×C16C2×C411yescharacteristic
35C3×#672C2×C411yescharacteristic
36#4904—51no—
37#4700—52no—
38C3×#346—51no—
39#4510—52no—
40#4506—51no—
41#4133—62no—
42#4065—32no—
43#4010—62no—
44#3996—32no—
45C8×AGL(1,𝔽5)C2×D311yescharacteristic
46D5⋊C16C2×D311yescharacteristic
47C5×Q32—31no—
48#3960—32no—
49D80—31no—
50D5×C16C2×D311yescharacteristic
51#2179—151noSylow
52C2×C3×AGL(1,𝔽5)—21no—
53D60—22no—
54C5×Dic6—22no—
55C3×C4×D5C2×D411yescharacteristic
56#1202—42no—
57#1200—42no—
58C3⋊#170—42no—
59C3×#170D812yes—
60C3×C5×C8C22×C411yescharacteristic
61C3×#168#4111yescharacteristic
62#904—52no—
63#901—102no—
64C2×C3×C16—51no—
65C2×C3×C16—51no—
66C3×C4×C8—51no—
67#819—52no—
68#805—102no—
69Dic24AGL(1,𝔽5)11yescharacteristic, complemented
70#800—52no—
71D48—51no—
72#713—62no—
73C4×AGL(1,𝔽5)D1211yescharacteristic
74#700—62no—
75#700—122no—
76D5⋊C8—122no—
77D5⋊C8D1211yescharacteristic
78C5×Q16—32no—
79#688—62no—
80D40—32no—
81C8×D5C22×D311yescharacteristic
82#674—21no—
83C5×C16C4×D311yescharacteristic
84#672C4×D311yescharacteristic
85#508—151no—
86#443—152no—
87#368—151no—
88#359—152no—
89#346—51no—
90C2×D15—42no—
91C2×C3×D5#13511yescharacteristic
92C3×AGL(1,𝔽5)—41no—
93C3×C4×C5C4×D411yescharacteristic
94C3×Dic5C2×D811yescharacteristic
95C5×Dic3—42no—
96#235—102no—
97C2×C3×C8—51no—
98C2×C3×C8—51no—
99C3×C42—51no—
100#208—102no—
101Dic12C2×AGL(1,𝔽5)12yes—
102D24—52no—
103#204—102no—
104ΓL(1,𝔽25)—202no—
105D3×C8—202no—
106C3×C16—51no—
107C3×C16—101no—
108C3×C16C2×AGL(1,𝔽5)11yescharacteristic
109C2×AGL(1,𝔽5)—21no—
110C5×Q8—62no—
111D20—62no—
112D20—122no—
113C4×D5—122no—
114C4×D5C2×D1211yescharacteristic
115#170—122no—
116#170D2412yes—
117C5×C8C2×C4×D311yescharacteristic
118#168#23511yescharacteristic
119#135—152no—
120#131—302no—
121Q32—31no—
122SD32—152no—
123D16—151no—
124C2×C16—51no—
125C2×C16—51no—
126#108—152no—
127#104—302no—
128C4×C8—51no—
129C2×C3×C5C4×D811yescharacteristic
130D15—82no—
131C3×D5—21no—
132C2×C3×C4—51no—
133C2×C3×C4—101no—
134#67—202no—
135D12—102no—
136C4×D3—202no—
137Dic6—22no—
138C3×C8—52no—
139C3×C8—51no—
140C3×C8C22×AGL(1,𝔽5)11yescharacteristic
141C3⋊C8—202no—
142C2×D5—122no—
143C2×D5#90411yescharacteristic
144AGL(1,𝔽5)—41no—
145C4×C5—122no—
146C4×C5C4×D1211yescharacteristic
147Dic5C2×D2411yescharacteristic
148#41—302no—
149Q16—32no—
150SD16—302no—
151D8—152no—
152M16—302no—
153M16—602no—
154C2×C8—51no—
155C2×C8—51no—
156C2×C8—602no—
157C42—51no—
158C16—51no—
159C16—101no—
160C16D3×AGL(1,𝔽5)11yescharacteristic
161C3×C5#217911yescharacteristic, complemented, Hall
162C22×C3—51no—
163C2×D3—202no—
164C3×C4—51no—
165C3×C4—201no—
166C3×C4D4×AGL(1,𝔽5)11yescharacteristic
167Dic3—42no—
168C2×C5C4×D2411yescharacteristic
169D5—21no—
170D5—242no—
171Q8—62no—
172D4—302no—
173D4—602no—
174C2×C4—51no—
175C2×C4—101no—
176C2×C4—602no—
177C8—52no—
178C8—51no—
179C8—602no—
180C8C2×D3×AGL(1,𝔽5)11yescharacteristic
181C2×C3—101no—
182C2×C3D8×AGL(1,𝔽5)11yescharacteristic
183D3—402no—
184C5#6908511yescharacteristic, complemented, Sylow
185C22—51no—
186C22—602no—
187C4—51no—
188C4—122no—
189C4—201no—
190C4AGL(1,𝔽5)×D1211yescharacteristic
191C3#1060413711yescharacteristic, complemented, Sylow
192C2—101no—
193C2—1202no—
194C2AGL(1,𝔽5)×D2411yescharacteristic
subgroupG/H
centerC2AGL(1,𝔽5)×D24
commutatorC3×C5×C8C22×C4
FrattiniC8C2×D3×AGL(1,𝔽5)
FittingC3×C5×C16C2×C4
socleC2×C3×C5C4×D8
prime radical#11746834C2
cosocleC3×C8×D5C23
hypercenterC16D3×AGL(1,𝔽5)
hypocenterC3×C5#2179
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
1. #11751683C2semidirect
3. #11746723C2semidirect
4. C3×#64844C2semidirect
5. #11746463C2semidirect
13. D240C4semidirect
14. C5×Dic24C4semidirect
16. #90945C4semidirect
22. #64844D3semidirect
69. Dic24AGL(1,𝔽5)semidirect
161. C3×C5#2179semidirect
184. C5#69085semidirect
191. C3#10604137semidirect

Maximal subgroups

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

subgroupindex
#117516832
#117468342
#117467232
C3×#648442
#117464632
#106041373
#690855