Finite Group Databasebeta

← #14314965

Subgroups — #14314965

Order 1920.

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

normal subgroups only

This group has 244 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#11747657C211yesmaximal, characteristic
2#11746760C211yesmaximal, characteristic, complemented
3C3×#64889C211yesmaximal, characteristic, complemented
4#11746549C212yesmaximal
5#11746544C212yesmaximal, complemented
6#10603835—31nomaximal, Hall
7C2×C8×D15C411yescharacteristic
8#91386C411yescharacteristic
9C2×#6651C2211yescharacteristic
10#91227C2212yes—
11C3×#3998C2212yes—
12C5×C8×Dic3C411yescharacteristic
13C3×C8×Dic5C2211yescharacteristic
14#90953C2211yescharacteristic
15#90952C411yescharacteristic
16#69299—51nomaximal, Hall
17#64978—31no—
18#64891—32no—
19#64889—31no—
20#64889D311yescharacteristic, complemented
21#64860—32no—
22C2×C4×D15C2×C411yescharacteristic
23C2×C3×C5×C8C2×C411yescharacteristic
24C2×C3⋊#168C2×C411yescharacteristic
25C8×D15—22no—
26C4×C5×Dic3C2×C411yescharacteristic
27C2×C5×C3⋊C8C2×C411yescharacteristic
28C3×C4×Dic5C2×C411yescharacteristic
29C2×C3×#168C2311yescharacteristic
30#6669—21no—
31#6667—21no—
32#6651—21no—
33#6651—21no—
34C3⋊#674—22no—
35C3×#674—22no—
36#4689—51no—
37C3×#364—51no—
38#4514—52no—
39#4512—52no—
40#4463—51no—
41C2×#676—31no—
42C2×C8×D5—31no—
43#4018—31no—
44#3998—32no—
45#3998C2×D312yes—
46C4×C5×C8—31no—
47#3947—31no—
48C8×Dic5C2×D311yescharacteristic
49#3935—31no—
50#2166—151noSylow
51C22×D15M1611yescharacteristic
52C2×C3×C4×C5C22×C411yescharacteristic
53C2×Dic15M1611yescharacteristic
54C4×D15—21no—
55C4×D15—21no—
56C2×C5×Dic3—21no—
57C2×C3×Dic5—21no—
58C3×C5×C8M1612yes—
59C3⋊#168—21no—
60C3×#168#4111yescharacteristic
61C3×#168#4111yescharacteristic
62C5×C3⋊C8—21no—
63C2×ΓL(1,𝔽25)—51no—
64C2×D3×C8—51no—
65#872—51no—
66C3×M32—52no—
67C3×C4×C8—51no—
68#815—51no—
69C8×Dic3AGL(1,𝔽5)11yescharacteristic
70#812—52no—
71#803—51no—
72C2×C4×D5—31no—
73C2×C5×C8—31no—
74C2×C5×C8C4×D311yescharacteristic
75C42×C5—31no—
76#685—61no—
77#683—61no—
78C4×Dic5C4×D311yescharacteristic
79C2×#168—31no—
80C2×#168C22×D311yescharacteristic
81#676—61no—
82#676—61no—
83C8×D5—62no—
84#674—22no—
85#674—62no—
86#405—151no—
87#364—51no—
88#364—151no—
89#349—152no—
90#347—152no—
91C22×C3×C5C2×M1611yescharacteristic
92C2×D15—21no—
93C2×D15—41no—
94C3×C4×C5#11711yescharacteristic
95C3×C4×C5C2×M1611yescharacteristic
96Dic15—21no—
97C3×Dic5—41no—
98C5×Dic3—41no—
99C2×C4×D3—51no—
100C2×C3×C8—51no—
101C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
102C3×C42—51no—
103(C2×D3)⋊C4—101no—
104Dic3⋊C4—101no—
105C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
106C2×C3⋊C8—51no—
107C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
108ΓL(1,𝔽25)—101no—
109ΓL(1,𝔽25)—101no—
110D3×C8—102no—
111C3×C16—102no—
112C3⋊C16—102no—
113C22×D5—31no—
114C2×C4×C5—61no—
115C2×C4×C5C2×C4×D311yescharacteristic
116C2×Dic5—21no—
117C2×Dic5—31no—
118C4×D5—61no—
119C4×D5—61no—
120C5×C8—61no—
121C5×C8ΓL(1,𝔽25)12yes—
122#168—61no—
123#168#23711yescharacteristic
124#168#23911yescharacteristic
125C2×M16—151no—
126C22×C8—151no—
127#117—151no—
128M32—52no—
129M32—152no—
130#97—151no—
131#97—151no—
132C4×C8—31no—
133C4×C8—51no—
134C2×C3×C5—21no—
135C2×C3×C5#43211yescharacteristic
136D15—41no—
137C22×D3—51no—
138C2×C3×C4—101no—
139C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
140C2×Dic3—21no—
141C2×Dic3—51no—
142C4×D3—101no—
143C4×D3—101no—
144C3×C8—51no—
145C3×C8—51no—
146C3×C8#70012yes—
147C3⋊C8—21no—
148C3⋊C8—101no—
149C22×C5D3×M1611yescharacteristic
150C2×D5—61no—
151C2×D5—121no—
152C4×C5—121no—
153C4×C5#89211yescharacteristic
154C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
155Dic5—41no—
156Dic5—61no—
157C22×C4—151no—
158M16—301no—
159M16—301no—
160C2×C8—31no—
161C2×C8—51no—
162C2×C8—151no—
163C2×C8—302no—
164C2×C8D3×AGL(1,𝔽5)11yescharacteristic
165C4⋊C4—301no—
166C22⋊C4—301no—
167C42—31no—
168C42—51no—
169C16—102no—
170C16—302no—
171C3×C5#216611yescharacteristic, complemented, Hall
172C22×C3D5⋊M1611yescharacteristic
173C2×D3—101no—
174C2×D3—201no—
175C3×C4—201no—
176C3×C4C2×#70011yescharacteristic
177C3×C4#413011yescharacteristic
178Dic3—41no—
179Dic3—101no—
180C2×C5—21no—
181C2×C5#483511yescharacteristic
182D5—121no—
183C23—151no—
184C2×C4—61no—
185C2×C4—101no—
186C2×C4—151no—
187C2×C4—301no—
188C2×C4—301no—
189C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
190C8—51no—
191C8—51no—
192C8—61no—
193C8—301no—
194C8#674012yes—
195C2×C3—21no—
196C2×C3#6568311yescharacteristic
197D3—201no—
198C5#6929911yescharacteristic, complemented, Sylow
199C22—301no—
200C22—601no—
201C22#9191511yescharacteristic
202C4—121no—
203C4—201no—
204C4—301no—
205C4#9190711yescharacteristic
206C4C2×#674011yescharacteristic
207C3#1060383511yescharacteristic, complemented, Sylow
208C2—21no—
209C2—601no—
210C2#1175179111yescharacteristic
subgroupG/H
centerC4#91907
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC2×C3×C5#432
prime radicalC22×D15M16
cosocleC2×C3×#168C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#2166
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #11746760C2semidirect
3. C3×#64889C2semidirect
5. #11746544C2semidirect
20. #64889D3semidirect
171. C3×C5#2166semidirect
198. C5#69299semidirect
207. C3#10603835semidirect

Maximal subgroups

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

subgroupindex
#117476572
#117467602
C3×#648892
#117465492
#117465442
#106038353
#692995