Finite Group Databasebeta

← #14278058

Subgroups — #14278058

Order 1920.

200 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 49 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×#65478C211yesmaximal, characteristic
2#11746768C211yesmaximal, characteristic
3#11746762C211yesmaximal, characteristic
4#10598812—31nomaximal, Hall
5D5⋊#208—21no—
6C2×C3×C5×Q16C411yescharacteristic
7C3×#4092—21no—
8C2×C3×#676C2211yescharacteristic
9#91227—21no—
10C3×#3967—21no—
11C3×#3949C411yescharacteristic
12#67781—51nomaximal, Hall
13#65478D311yescharacteristic
14#64897—31no—
15#64891—31no—
16C2×C3×C5×Q8—21no—
17C2×C3×C4×D5D411yescharacteristic
18#6762—41no—
19#6758—41no—
20D5⋊(C3⋊C8)—22no—
21C3×C5×Q16—41no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C3×#685—41no—
24C3×C4⋊Dic5—21no—
25C3×#683—41no—
26C2×C3×#168D411yescharacteristic
27C3×#676—41no—
28C3⋊#674—41no—
29C3×#470—51no—
30C3⋊#338—51no—
31#4553—51no—
32D5⋊M16—61no—
33C2×C5×Q16Dic311yescharacteristic
34#4092—21no—
35C2×#676C2×D311yescharacteristic
36#3998—61no—
37#3967—21no—
38#3949Dic311yescharacteristic
39#1342—151noSylow
40C22×C3×D5SD1611yescharacteristic
41C3×C5×Q8—41no—
42C3×C5×Q8—41no—
43C2×C3×C4×C5—41no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×Dic5—41no—
46C2×C3×Dic5D811yescharacteristic
47C3×C4×D5—21no—
48C3×C4×D5—21no—
49C3⋊#170—42no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C2×C3×Q16AGL(1,𝔽5)11yescharacteristic
53C2×C3×M16—51no—
54C3×C22⋊Q8—101no—
55C2×#208—101no—
56C3×#106—51no—
57C3×#103—101no—
58#812—101no—
59C2×C5×Q8—21no—
60C2×C4×D5#6711yescharacteristic
61#704—121no—
62#700—121no—
63D5⋊C8—62no—
64C5×Q16—41no—
65C2×C5×C8C2×Dic311yescharacteristic
66#685—41no—
67C4⋊Dic5—21no—
68#683—41no—
69C2×#168#6711yescharacteristic
70#676—41no—
71#674—121no—
72#470—51no—
73#349—151no—
74#338—151no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—41no—
78C3×C4×C5—81no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81C3×Dic5—21no—
82C3×Dic5—81no—
83C2×C3×Q8—21no—
84C22×C3×C4—51no—
85C3×Q16—41no—
86C3×M16—201no—
87C2×C3×C8—51no—
88C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
89C3×C4⋊C4—101no—
90C3×C4⋊C4—201no—
91C3×C22⋊C4—201no—
92#208—201no—
93#208—201no—
94C2×C3⋊C8—102no—
95C3⋊C16—201no—
96C22×D5#21411yescharacteristic
97C5×Q8—41no—
98C5×Q8—41no—
99C2×C4×C5—41no—
100C2×C4×C5#21711yescharacteristic
101C2×Dic5—41no—
102C2×Dic5#21311yescharacteristic
103C4×D5—21no—
104C4×D5—21no—
105#170—122no—
106C5×C8—21no—
107#168—21no—
108C2×Q16ΓL(1,𝔽16)11yescharacteristic
109C2×M16—51no—
110C2×M16—301no—
111C22⋊Q8—101no—
112M32—301no—
113#106—51no—
114#103—101no—
115C2×C3×C5—21no—
116C2×C3×C5#32711yescharacteristic
117C3×D5—41no—
118C23×C3—51no—
119C3×Q8—41no—
120C3×Q8—41no—
121C2×C3×C4—41no—
122C2×C3×C4—51no—
123C2×C3×C4—101no—
124C2×C3×C4—101no—
125C2×C3×C4—201no—
126C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
127C3×C8—21no—
128C3×C8—101no—
129C3⋊C8—202no—
130C22×C5#83211yescharacteristic
131C2×D5—21no—
132C2×D5—41no—
133C4×C5—81no—
134C4×C5#83411yescharacteristic
135C4×C5#83711yescharacteristic
136Dic5—21no—
137Dic5—81no—
138C2×Q8—21no—
139C22×C4—51no—
140Q16—41no—
141M16—201no—
142M16—601no—
143M16—601no—
144C2×C8—51no—
145C2×C8—302no—
146C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
147C4⋊C4—101no—
148C4⋊C4—201no—
149C22⋊C4—201no—
150C16—601no—
151C3×C5#134211yescharacteristic, complemented, Hall
152C22×C3—101no—
153C22×C3—201no—
154C22×C3#400711yescharacteristic
155C3×C4—81no—
156C3×C4—101no—
157C3×C4—401no—
158C3×C4#400811yescharacteristic
159C3×C4#401111yescharacteristic
160C2×C5—21no—
161C2×C5#453711yescharacteristic
162D5—41no—
163C23—51no—
164Q8—41no—
165Q8—41no—
166C2×C4—41no—
167C2×C4—51no—
168C2×C4—101no—
169C2×C4—101no—
170C2×C4—201no—
171C2×C4#676311yescharacteristic
172C8—21no—
173C8—101no—
174C8—602no—
175C2×C3—21no—
176C2×C3—201no—
177C2×C3#6492011yescharacteristic
178C5#6778111yescharacteristic, complemented, Sylow
179C22—101no—
180C22—201no—
181C22#9123611yescharacteristic
182C4—81no—
183C4—101no—
184C4—401no—
185C4#9123711yescharacteristic
186C4#9124011yescharacteristic
187C3#1059881211yescharacteristic, complemented, Sylow
188C2—21no—
189C2—201no—
190C2#1174679111yescharacteristic
subgroupG/H
centerC2#11746791
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×C8C2×ΓL(1,𝔽16)
FittingC2×C3×C5×Q16C4
socleC2×C3×C5#327
prime radicalC22×C3×D5SD16
cosocleC2×C3×#676C22
hypercenterC2×Q16ΓL(1,𝔽16)
hypocenterC3×C5#1342
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
151. C3×C5#1342semidirect
178. C5#67781semidirect
187. C3#10598812semidirect

Maximal subgroups

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

subgroupindex
C3×#654782
#117467682
#117467622
#105988123
#677815