Finite Group Databasebeta

← #14278145

Subgroups — #14278145

Order 1920.

248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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×C5×#398C211yesmaximal, characteristic
2#11746351C211yesmaximal, characteristic
3#11746349C211yesmaximal, characteristic
4#10598141—31nomaximal, Hall
5C2×C3×C5×C4⋊C4—21no—
6C2×C3×C5×C4⋊C4C411yescharacteristic
7C2×C3×C5×C4⋊C4C2211yescharacteristic
8C2×#6710—21no—
9C3×C5×#95—21no—
10C3×C5×#95C411yescharacteristic
11#91114—21no—
12#67650—51nomaximal, Hall
13C5×#398D311yescharacteristic
14#64750—31no—
15#64748—31no—
16C22×C3×C4×C5—21no—
17C22×C3×C4×C5—21no—
18C22×C3×C4×C5C2×C411yescharacteristic
19C22×C3×C4×C5D411yescharacteristic
20C22×C3×C4×C5D411yescharacteristic
21C3×C5×C4⋊C4—41no—
22C3×C5×C4⋊C4—41no—
23C3×C5×C4⋊C4—41no—
24C3×C5×C4⋊C4—41no—
25#6710—22no—
26#6710—41no—
27C2×C3⋊#168—41no—
28C2×C3⋊#168—41no—
29C3×#398D511yescharacteristic
30#4530—51no—
31#4528—51no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4Dic311yescharacteristic
34C2×C5×C4⋊C4C2×D311yescharacteristic
35C2×#681—61no—
36C5×#95—21no—
37C5×#95Dic311yescharacteristic
38C22⋊#168—61no—
39#1346—151noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—22no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—21no—
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5—41no—
48C2×C3×C4×C5—41no—
49C2×C3×C4×C5—41no—
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5—41no—
52C2×C3×C4×C5—41no—
53C2×C3×C4×C5D811yescharacteristic
54C2×C3×C4×C5SD1611yescharacteristic
55C3⋊#168—42no—
56C3⋊#168—81no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4Dic511yescharacteristic
59C2×C3×C4⋊C4C2×D511yescharacteristic
60C2×#208—101no—
61C3×#95—21no—
62C3×#95Dic511yescharacteristic
63#830—101no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5C2×Dic311yescharacteristic
67C22×C4×C5#6711yescharacteristic
68C22×C4×C5#6711yescharacteristic
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73#681—62no—
74#681—121no—
75C2×#168—121no—
76C2×#168—121no—
77#398D1511yescharacteristic
78#343—151no—
79#324—151no—
80C22×C3×C5—21no—
81C22×C3×C5—21no—
82C22×C3×C5#9911yescharacteristic
83C22×C3×C5#10211yescharacteristic
84C22×C3×C5#10411yescharacteristic
85C3×C4×C5—21no—
86C3×C4×C5—21no—
87C3×C4×C5—42no—
88C3×C4×C5—41no—
89C3×C4×C5—41no—
90C3×C4×C5—81no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4C2×Dic511yescharacteristic
94C22×C3×C4C22⋊D511yescharacteristic
95C22×C3×C4C22⋊D511yescharacteristic
96C3×C4⋊C4—41no—
97C3×C4⋊C4—41no—
98C3×C4⋊C4—41no—
99C3×C4⋊C4—41no—
100#208—102no—
101#208—201no—
102C2×C3⋊C8—201no—
103C2×C3⋊C8—201no—
104C23×C5#21711yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—22no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—41no—
111C2×C4×C5—41no—
112C2×C4×C5—41no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5#21311yescharacteristic
118C2×C4×C5#21411yescharacteristic
119#168—122no—
120#168—241no—
121C2×M16—301no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4Dic1511yescharacteristic
124C2×C4⋊C4C2×D1511yescharacteristic
125C22⋊C8—301no—
126#95—21no—
127#95Dic1511yescharacteristic
128C2×C3×C5—21no—
129C2×C3×C5—21no—
130C2×C3×C5#32711yescharacteristic
131C2×C3×C5#35211yescharacteristic
132C2×C3×C5#35611yescharacteristic
133C23×C3C22⋊Dic511yescharacteristic
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—41no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—41no—
146C2×C3×C4#68611yescharacteristic
147C2×C3×C4#68711yescharacteristic
148C3⋊C8—202no—
149C3⋊C8—401no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5#83211yescharacteristic
153C22×C5#83411yescharacteristic
154C22×C5#83711yescharacteristic
155C4×C5—21no—
156C4×C5—21no—
157C4×C5—42no—
158C4×C5—41no—
159C4×C5—41no—
160C4×C5—81no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4C2×Dic1511yescharacteristic
164C22×C4#122011yescharacteristic
165C22×C4#122011yescharacteristic
166M16—302no—
167M16—601no—
168C2×C8—601no—
169C2×C8—601no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C3×C5#134611yescharacteristic, complemented, Hall
175C22×C3—21no—
176C22×C3—21no—
177C22×C3#396411yescharacteristic
178C22×C3#396611yescharacteristic
179C22×C3#396911yescharacteristic
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—42no—
183C3×C4—41no—
184C3×C4—41no—
185C3×C4—81no—
186C2×C5—21no—
187C2×C5—21no—
188C2×C5#453711yescharacteristic
189C2×C5#453911yescharacteristic
190C2×C5#454811yescharacteristic
191C23#671911yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4#671511yescharacteristic
205C2×C4#671611yescharacteristic
206C8—602no—
207C8—1201no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3#6475711yescharacteristic
211C2×C3#6475911yescharacteristic
212C2×C3#6476811yescharacteristic
213C5#6765011yescharacteristic, complemented, Sylow
214C22—21no—
215C22—21no—
216C22#9111611yescharacteristic
217C22#9111811yescharacteristic
218C22#9112111yescharacteristic
219C4—21no—
220C4—21no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—81no—
225C3#1059814111yescharacteristic, complemented, Sylow
226C2—21no—
227C2—21no—
228C2#1174635811yescharacteristic
229C2#1174636011yescharacteristic
230C2#1174636911yescharacteristic
subgroupG/H
centerC22#91118
commutatorC22×C3×C4×C5C2×C4
FrattiniC2×C4⋊C4C2×D15
FittingC3×C5×#398C2
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C5×C4⋊C4C22
hypercenter#398D15
hypocenterC3×C5#1346
LCSG ▷ C22×C3×C4×C5 ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
174. C3×C5#1346semidirect
213. C5#67650semidirect
225. C3#10598141semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#3982
#117463512
#117463492
#105981413
#676505