Finite Group Databasebeta

← #14277081

Subgroups — #14277081

Order 1920.

276 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 77 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#11752416C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic
3C3×#65008C211yesmaximal, characteristic
4#10598558—31nomaximal, Hall
5C2×#6762—21no—
6C2×C3×C4×Dic5C2211yescharacteristic
7#91241—21no—
8#91233C412yes—
9#91231—21no—
10#91231—21no—
11C4×C3⋊#170C412yes—
12C3×C5×C22⋊C8C411yescharacteristic
13C3×C22⋊#168C411yescharacteristic
14C3×#3947—21no—
15C3×#3946—21no—
16#67754—51nomaximal, Hall
17#65757—31no—
18C4×#704—31no—
19#65008D311yescharacteristic
20C22×C3×C4×C5C2×C411yescharacteristic
21C22×C3×Dic5D411yescharacteristic
22C22×C3×Dic5Q811yescharacteristic
23#6762—24no—
24C2×C3⋊#170—22no—
25C2×C3⋊#170—22no—
26C2×C3×C5×C8—21no—
27C3×C4×Dic5C2×C411yescharacteristic
28C3×C4×Dic5C2×C411yescharacteristic
29C3×C4×Dic5D411yescharacteristic
30C3×C4×Dic5D411yescharacteristic
31C2×C3×#168—21no—
32C3×#432—51no—
33#4926—51no—
34C4×#208—51no—
35C2×#704—61no—
36C2×C4×Dic5C2×D311yescharacteristic
37C22⋊#170—61no—
38#4004—32no—
39#4002—61no—
40#4002—61no—
41C4×#170—32no—
42C5×C22⋊C8Dic311yescharacteristic
43C22⋊#168Dic311yescharacteristic
44#3947—21no—
45#3946—21no—
46#1291—151noSylow
47C23×C3×C5C4⋊C411yescharacteristic
48C2×C3×C4×C5—41no—
49C2×C3×C4×C5C4211yescharacteristic
50C2×C3×C4×C5C22⋊C411yescharacteristic
51C2×C3×Dic5—22no—
52C2×C3×Dic5—41no—
53C2×C3×Dic5C22⋊C411yescharacteristic
54C2×C3×Dic5C22⋊C411yescharacteristic
55C2×C3×Dic5C4⋊C411yescharacteristic
56C2×C3×Dic5C4⋊C411yescharacteristic
57C3⋊#170—24no—
58C3⋊#170—42no—
59C3×C5×C8—41no—
60C3×#168—41no—
61C2×C3×C42—51no—
62C2×#208—101no—
63C3×C4⋊C8—101no—
64C3×C22⋊C8—51no—
65C3×C22⋊C8AGL(1,𝔽5)11yescharacteristic
66C3×#97—101no—
67#830—101no—
68C4⋊(C3⋊C8)—52no—
69#803—101no—
70#803—101no—
71C4×C3⋊C8—52no—
72C22×C4×C5C2×Dic311yescharacteristic
73C22×Dic5Dic611yescharacteristic
74C22×Dic5D1211yescharacteristic
75#704—64no—
76C2×#170—62no—
77C2×#170—62no—
78C2×C5×C8—21no—
79C4×Dic5C4×D311yescharacteristic
80C4×Dic5C4×D311yescharacteristic
81C4×Dic5#6711yescharacteristic
82C4×Dic5#6711yescharacteristic
83C2×#168—21no—
84#432—51no—
85#432—151no—
86C4×M16—151no—
87C22×C3×C5—21no—
88C22×C3×C5—21no—
89C22×C3×C5—21no—
90C22×C3×C5#9511yescharacteristic
91C3×C4×C5—21no—
92C3×C4×C5—21no—
93C3×Dic5—21no—
94C3×Dic5—21no—
95C3×Dic5—21no—
96C3×Dic5#10412yes—
97C22×C3×C4—51no—
98C22×C3×C4—51no—
99C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
100C2×C3×C8—21no—
101C2×C3×C8—101no—
102C3×C42—51no—
103C3×C42—51no—
104C3×C42—51no—
105C3×C42—51no—
106#208—104no—
107C2×C3⋊C8—102no—
108C2×C3⋊C8—102no—
109C23×C5C4⋊Dic311yescharacteristic
110C2×C4×C5—41no—
111C2×C4×C5C4×Dic311yescharacteristic
112C2×C4×C5#21711yescharacteristic
113C2×Dic5—22no—
114C2×Dic5—41no—
115C2×Dic5Dic3⋊C411yescharacteristic
116C2×Dic5Dic3⋊C411yescharacteristic
117C2×Dic5(C2×D3)⋊C411yescharacteristic
118C2×Dic5(C2×D3)⋊C411yescharacteristic
119#170—64no—
120#170—122no—
121C5×C8—41no—
122#168—41no—
123C2×M16—301no—
124C2×C42—51no—
125C4⋊C8—101no—
126C4⋊C8—152no—
127C22⋊C8—51no—
128C22⋊C8—301no—
129C22⋊C8ΓL(1,𝔽16)11yescharacteristic
130#97—101no—
131#97—301no—
132#97—301no—
133C4×C8—152no—
134C2×C3×C5—41no—
135C2×C3×C5#33811yescharacteristic
136C2×C3×C5#33911yescharacteristic
137C2×C3×C5#34411yescharacteristic
138C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
139C2×C3×C4—41no—
140C2×C3×C4—51no—
141C2×C3×C4—51no—
142C2×C3×C4—51no—
143C2×C3×C4—51no—
144C2×C3×C4—102no—
145C2×C3×C4—201no—
146C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
147C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
148C3×C8—41no—
149C3×C8—201no—
150C3⋊C8—104no—
151C3⋊C8—202no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5C3⋊#9511yescharacteristic
156C4×C5—21no—
157C4×C5—21no—
158Dic5—21no—
159Dic5—21no—
160Dic5—21no—
161Dic5#82512yes—
162C22×C4—51no—
163C22×C4—51no—
164C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
165M16—304no—
166C2×C8—21no—
167C2×C8—101no—
168C2×C8—302no—
169C2×C8—302no—
170C42—51no—
171C42—51no—
172C42—51no—
173C42—51no—
174C3×C5#129111yescharacteristic, complemented, Hall
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—52no—
182C3×C4—101no—
183C3×C4—101no—
184C3×C4—101no—
185C2×C5—41no—
186C2×C5#453311yescharacteristic
187C2×C5#455511yescharacteristic
188C2×C5C3⋊#33811yescharacteristic
189C23C4⋊ΓL(1,𝔽16)11yescharacteristic
190C2×C4—41no—
191C2×C4—51no—
192C2×C4—51no—
193C2×C4—51no—
194C2×C4—51no—
195C2×C4—102no—
196C2×C4—201no—
197C2×C4C4×ΓL(1,𝔽16)11yescharacteristic
198C2×C4#676311yescharacteristic
199C8—41no—
200C8—201no—
201C8—304no—
202C8—602no—
203C2×C3—41no—
204C2×C3#6486711yescharacteristic
205C2×C3#6489711yescharacteristic
206C2×C3#6490011yescharacteristic
207C5#6775411yescharacteristic, complemented, Sylow
208C22—21no—
209C22—21no—
210C22—21no—
211C22#9123511yescharacteristic
212C4—21no—
213C4—21no—
214C4—52no—
215C4—101no—
216C4—101no—
217C4—101no—
218C3#1059855811yescharacteristic, complemented, Sylow
219C2—41no—
220C2#1174673811yescharacteristic
221C2#1174676811yescharacteristic
222C2#1174677111yescharacteristic
subgroupG/H
centerC22#91235
commutatorC2×C3×C4×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5#95
prime radicalC23×C3×C5C4⋊C4
cosocleC2×C3×C4×Dic5C22
hypercenterC22⋊C8ΓL(1,𝔽16)
hypocenterC3×C5#1291
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
174. C3×C5#1291semidirect
207. C5#67754semidirect
218. C3#10598558semidirect

Maximal subgroups

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

subgroupindex
#117524162
C4×#67622
C3×#650082
#105985583
#677545