Finite Group Databasebeta

← #14278252

Subgroups — #14278252

Order 1920.

208 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 54 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#11747943C211yesmaximal, characteristic
2#11746758C211yesmaximal, characteristic
3C3×#64896C211yesmaximal, characteristic
4#10598614—31nomaximal, Hall
5C2×C3×#700—21no—
6C2×Dic60C411yescharacteristic
7C2×C3×C8×D5C2211yescharacteristic
8#91360—21no—
9C2×C3⋊#674—21no—
10C5×#818C411yescharacteristic
11#90975—21no—
12#67488—51nomaximal, Hall
13#65176—31no—
14#64896D311yescharacteristic
15#64887—31no—
16C2×Dic30—21no—
17C2×C3×C4×D5D411yescharacteristic
18C2×C3×#170—41no—
19C3×#700—22no—
20C3×#700—41no—
21C2×C3×C5×C8C2×C411yescharacteristic
22Dic60—41no—
23C5×C4⋊Dic3—21no—
24C2×C3×#168D411yescharacteristic
25C3×C8×D5—41no—
26Dic3⋊Dic5—41no—
27#6665—41no—
28C3⋊#674—41no—
29#5116—51no—
30C3×#341—51no—
31#4549—51no—
32C2×#700—21no—
33C2×Dic20—31no—
34C2×C8×D5C2×D311yescharacteristic
35#4043—61no—
36C2×#674—61no—
37C5×#107—31no—
38#3942—61no—
39#1350—151noSylow
40C22×C3×D5SD1611yescharacteristic
41C2×C3×C4×C5C22⋊C411yescharacteristic
42C2×Dic15—41no—
43Dic30—41no—
44Dic30—41no—
45C2×C5×Dic3—41no—
46C2×C3×Dic5D811yescharacteristic
47C3×C4×D5—21no—
48C3×C4×D5—21no—
49C3×#170—42no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C2×C3×M16—101no—
53C22×C3×C8—51no—
54#924—101no—
55C2×Dic12—51no—
56#818AGL(1,𝔽5)11yescharacteristic
57#816—101no—
58C2×C3⋊C16—101no—
59C2×C4×D5#6711yescharacteristic
60C2×Dic10—61no—
61C2×#170—41no—
62#700—22no—
63#700—41no—
64C2×C5×C8C4×D311yescharacteristic
65C5×C4⋊C4—61no—
66#685—121no—
67C4⋊Dic5—121no—
68C2×#168D1211yescharacteristic
69Dic20—121no—
70C8×D5—41no—
71#674—121no—
72#467—151no—
73C22⋊C16—151no—
74#341—51no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—21no—
78C2×C3×D5—21no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81Dic15—81no—
82C3×Dic5—21no—
83C5×Dic3—81no—
84C22×C3×C4—51no—
85C2×Dic6—101no—
86C3×M16—102no—
87C3×M16—201no—
88C2×C3×C8—51no—
89C2×C3×C8—201no—
90C2×C3×C8—201no—
91C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
92#217—201no—
93C4⋊Dic3—21no—
94Dic3⋊C4—201no—
95Dic12—201no—
96C3⋊C16—201no—
97C22×D5#21511yescharacteristic
98C2×C4×C5—121no—
99C2×C4×C5(C2×D3)⋊C411yescharacteristic
100C2×Dic5—121no—
101C2×Dic5#21311yescharacteristic
102C4×D5—21no—
103C4×D5—21no—
104Dic10—121no—
105Dic10—121no—
106#170—42no—
107C5×C8—21no—
108#168—21no—
109C2×Q16—151no—
110C2×M16—101no—
111C22×C8—51no—
112C22⋊Q8—301no—
113C2×C16—301no—
114#107—31no—
115#103—301no—
116C2×C3×C5#32711yescharacteristic
117C2×C3×C5#35911yescharacteristic
118C2×C3×C5#36211yescharacteristic
119C3×D5—41no—
120C23×C3—51no—
121C2×C3×C4—51no—
122C2×C3×C4—101no—
123C2×C3×C4—101no—
124C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
125C2×Dic3—41no—
126C2×Dic3—201no—
127Dic6—201no—
128Dic6—201no—
129C3×C8—21no—
130C3×C8—101no—
131C3×C8—202no—
132C22×C5#80911yescharacteristic
133C2×D5—21no—
134C2×D5—21no—
135C2×D5—21no—
136C4×C5—241no—
137C4×C5#80511yescharacteristic
138C4×C5#80611yescharacteristic
139Dic5—21no—
140Dic5—241no—
141C2×Q8—301no—
142C22×C4—51no—
143Q16—601no—
144M16—102no—
145M16—201no—
146C2×C8—51no—
147C2×C8—201no—
148C2×C8—201no—
149C2×C8D3×AGL(1,𝔽5)11yescharacteristic
150C4⋊C4—61no—
151C4⋊C4—601no—
152C22⋊C4—601no—
153C16—601no—
154C3×C5#135011yescharacteristic, complemented, Hall
155C22×C3—101no—
156C22×C3—101no—
157C22×C3—101no—
158C22×C3#400711yescharacteristic
159C3×C4—101no—
160C3×C4#399911yescharacteristic
161C3×C4#401011yescharacteristic
162Dic3—81no—
163Dic3—401no—
164C2×C5#445111yescharacteristic
165C2×C5#449611yescharacteristic
166C2×C5#449711yescharacteristic
167D5—41no—
168C23—51no—
169Q8—601no—
170Q8—601no—
171C2×C4—51no—
172C2×C4—101no—
173C2×C4—101no—
174C2×C4—121no—
175C2×C4—601no—
176C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
177C8—21no—
178C8—101no—
179C8—202no—
180C2×C3—201no—
181C2×C3#6486811yescharacteristic
182C2×C3#6490511yescharacteristic
183C2×C3#6491011yescharacteristic
184C5#6748811yescharacteristic, complemented, Sylow
185C22—101no—
186C22—101no—
187C22—101no—
188C22#9115111yescharacteristic
189C4—101no—
190C4—241no—
191C4—1201no—
192C4#9115811yescharacteristic
193C4#9117311yescharacteristic
194C3#1059861411yescharacteristic, complemented, Sylow
195C2—201no—
196C2#1174646011yescharacteristic
197C2#1174647011yescharacteristic
198C2#1174649711yescharacteristic
subgroupG/H
centerC22#91151
commutator, FittingC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×C8D3×AGL(1,𝔽5)
socleC22×C3×C5#102
prime radicalC22×C3×D5SD16
cosocleC2×C3×C8×D5C22
hypocenterC3×C5#1350
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
154. C3×C5#1350semidirect
184. C5#67488semidirect
194. C3#10598614semidirect

Maximal subgroups

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

subgroupindex
#117479432
#117467582
C3×#648962
#105986143
#674885