Finite Group Databasebeta

← #14277079

Subgroups — #14277079

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#11752343C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic
3C3×C4×#676C211yesmaximal, characteristic
4#10598533—31nomaximal, Hall
5C2×C3×#676—21no—
6C3×C42×D5C2211yescharacteristic
7#91233—21no—
8#91233C412yes—
9#91232—21no—
10#91232C412yes—
11#91231—21no—
12#91231—21no—
13C3×C4×C5×C8C411yescharacteristic
14C3×#3947—21no—
15C3×C4×#168C411yescharacteristic
16#67670—51nomaximal, Hall
17#65684—31no—
18#65684—31no—
19C4×#676D311yescharacteristic
20C2×C3×C4×D5C2×C411yescharacteristic
21C2×C3×C4×D5D411yescharacteristic
22C2×C3×C4×D5Q811yescharacteristic
23C2×C3⋊#170—22no—
24C2×C3⋊#170—22no—
25C2×C3×C5×C8—21no—
26C3×C42×C5C2×C411yescharacteristic
27C3×C4×Dic5C2×C411yescharacteristic
28C3×C4×Dic5D411yescharacteristic
29C3×C4×Dic5D411yescharacteristic
30C2×C3×#168—21no—
31C3×#676—24no—
32C3×C4×M16—51no—
33#4926—51no—
34#4926—51no—
35C2×#676—21no—
36C42×D5C2×D311yescharacteristic
37#4004—32no—
38#4004—61no—
39#4003—32no—
40#4003—61no—
41#4002—61no—
42#4002—61no—
43C4×C5×C8Dic311yescharacteristic
44#3947—21no—
45C4×#168Dic311yescharacteristic
46#1291—151noSylow
47C22×C3×D5C4⋊C411yescharacteristic
48C2×C3×C4×C5C4211yescharacteristic
49C2×C3×C4×C5C22⋊C411yescharacteristic
50C2×C3×C4×C5C4⋊C411yescharacteristic
51C2×C3×Dic5C22⋊C411yescharacteristic
52C2×C3×Dic5C22⋊C411yescharacteristic
53C2×C3×Dic5C4⋊C411yescharacteristic
54C3×C4×D5—22no—
55C3×C4×D5—41no—
56C3×C4×D5—41no—
57C3⋊#170—42no—
58C3⋊#170—42no—
59C3×C5×C8—22no—
60C3×#168—22no—
61C2×C3×M16—101no—
62C2×C3×C42—51no—
63C3×#97—101no—
64C3×C4×C8—51no—
65C3×C4×C8AGL(1,𝔽5)11yescharacteristic
66#830—52no—
67#830—101no—
68C4⋊(C3⋊C8)—52no—
69C4⋊(C3⋊C8)—101no—
70#803—101no—
71#803—101no—
72C2×C4×D5Dic611yescharacteristic
73C2×C4×D5C4×D311yescharacteristic
74C2×C4×D5#6711yescharacteristic
75C2×#170—62no—
76C2×#170—62no—
77C2×C5×C8—21no—
78C42×C5C2×Dic311yescharacteristic
79C4×Dic5C4×D311yescharacteristic
80C4×Dic5D1211yescharacteristic
81C4×Dic5#6711yescharacteristic
82C2×#168—21no—
83#676—24no—
84#432—151no—
85#432—151no—
86C4×M16—51no—
87C22×C3×C5#9511yescharacteristic
88C2×C3×D5—21no—
89C2×C3×D5—21no—
90C2×C3×D5—21no—
91C3×C4×C5—21no—
92C3×C4×C5—21no—
93C3×C4×C5—21no—
94C3×Dic5—21no—
95C3×Dic5—21no—
96C3×Dic5#10412yes—
97C22×C3×C4—51no—
98C22×C3×C4—51no—
99C22×C3×C4—51no—
100C3×M16—104no—
101C2×C3×C8—21no—
102C2×C3×C8—101no—
103C3×C42—51no—
104C3×C42—51no—
105C3×C42—51no—
106C3×C42C2×AGL(1,𝔽5)11yescharacteristic
107C2×C3⋊C8—102no—
108C2×C3⋊C8—102no—
109C22×D5Dic3⋊C411yescharacteristic
110C2×C4×C5C4×Dic311yescharacteristic
111C2×C4×C5C4⋊Dic311yescharacteristic
112C2×C4×C5#21711yescharacteristic
113C2×Dic5Dic3⋊C411yescharacteristic
114C2×Dic5(C2×D3)⋊C411yescharacteristic
115C2×Dic5(C2×D3)⋊C411yescharacteristic
116C4×D5—22no—
117C4×D5—41no—
118C4×D5—41no—
119#170—122no—
120#170—122no—
121C5×C8—22no—
122#168—22no—
123C2×M16—101no—
124C2×C42—51no—
125C4⋊C8—152no—
126C4⋊C8—301no—
127C22⋊C8—152no—
128C22⋊C8—301no—
129#97—101no—
130#97—301no—
131#97—301no—
132C4×C8—51no—
133C4×C8ΓL(1,𝔽16)11yescharacteristic
134C2×C3×C5#33811yescharacteristic
135C2×C3×C5#33911yescharacteristic
136C2×C3×C5#34411yescharacteristic
137C3×D5—41no—
138C23×C3—51no—
139C2×C3×C4—51no—
140C2×C3×C4—51no—
141C2×C3×C4—51no—
142C2×C3×C4—102no—
143C2×C3×C4—201no—
144C2×C3×C4—201no—
145C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
146C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
147C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
148C3×C8—22no—
149C3×C8—102no—
150C3⋊C8—202no—
151C3⋊C8—202no—
152C22×C5C3⋊#9511yescharacteristic
153C2×D5—21no—
154C2×D5—21no—
155C2×D5—21no—
156C4×C5—21no—
157C4×C5—21no—
158C4×C5—21no—
159Dic5—21no—
160Dic5—21no—
161Dic5#80512yes—
162C22×C4—51no—
163C22×C4—51no—
164C22×C4—51no—
165M16—104no—
166C2×C8—21no—
167C2×C8—101no—
168C2×C8—302no—
169C2×C8—302no—
170C42—51no—
171C42—51no—
172C42—51no—
173C42C2×ΓL(1,𝔽16)11yescharacteristic
174C3×C5#129111yescharacteristic, complemented, Hall
175C22×C3—101no—
176C22×C3—101no—
177C22×C3—101no—
178C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—52no—
183C3×C4—101no—
184C3×C4—101no—
185C2×C5#452311yescharacteristic
186C2×C5#455611yescharacteristic
187C2×C5C3⋊#33811yescharacteristic
188D5—41no—
189C23—51no—
190C2×C4—51no—
191C2×C4—51no—
192C2×C4—51no—
193C2×C4—102no—
194C2×C4—201no—
195C2×C4—201no—
196C2×C4C4×ΓL(1,𝔽16)11yescharacteristic
197C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
198C2×C4#676311yescharacteristic
199C8—22no—
200C8—102no—
201C8—602no—
202C8—602no—
203C2×C3—201no—
204C2×C3#6486211yescharacteristic
205C2×C3#6489411yescharacteristic
206C2×C3#6489711yescharacteristic
207C5#6767011yescharacteristic, complemented, Sylow
208C22—101no—
209C22—101no—
210C22—101no—
211C22#9123511yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—52no—
216C4—101no—
217C4—101no—
218C3#1059853311yescharacteristic, complemented, Sylow
219C2—201no—
220C2#1174673311yescharacteristic
221C2#1174676511yescharacteristic
222C2#1174676811yescharacteristic
subgroupG/H
centerC22#91235
commutatorC2×C3×C4×C5C42
FrattiniC42C2×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C4⋊C4
cosocleC3×C42×D5C22
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5#1291
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
174. C3×C5#1291semidirect
207. C5#67670semidirect
218. C3#10598533semidirect

Maximal subgroups

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

subgroupindex
#117523432
C3×C4×#6762
#105985333
#676705