Finite Group Databasebeta

← C5×#67681 #14277609

Subgroups — C5×#67681 #14277609

Order 1920.

256 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 74 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×#407C211yesmaximal, characteristic
2C5×#4553C212yesmaximal, complemented
3C5×#1320—31nomaximal, Hall
4C23×C3×C4×C5C411yescharacteristic
5C2×C3×C5×M16C411yescharacteristic
6C2×C3×C5×M16C2211yescharacteristic
7C3×C5×C22⋊C8—22no—
8C5×#812—22no—
9#67681C511yesmaximal, characteristic, direct product factor, Hall
10C5×#407D311yescharacteristic
11C5×#349—32no—
12C24×C3×C5C811yescharacteristic
13C22×C3×C4×C5—21no—
14C22×C3×C4×C5—21no—
15C22×C3×C4×C5—41no—
16C22×C3×C4×C5—41no—
17C22×C3×C4×C5C811yescharacteristic
18C22×C3×C4×C5C2×C411yescharacteristic
19C3×C5×M16—41no—
20C3×C5×M16—41no—
21C2×C3×C5×C8—21no—
22C2×C3×C5×C8D412yes—
23C5×C3⋊C16—42no—
24C3×#407C2×C511yescharacteristic
25#4553C2×C512yescomplemented
26C23×C4×C5Dic311yescharacteristic
27C2×C5×M16Dic311yescharacteristic
28C2×C5×M16C2×D311yescharacteristic
29C5×M32—62no—
30C5×C22⋊C8—22no—
31#1320—31noSylow
32C23×C3×C5—21no—
33C23×C3×C5—41no—
34C23×C3×C5—42no—
35C23×C3×C5C2×C811yescharacteristic
36C2×C3×C4×C5—21no—
37C2×C3×C4×C5—21no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5—42no—
40C2×C3×C4×C5—41no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×C4×C5M1611yescharacteristic
45C3×C5×C8—22no—
46C3×C5×C8—41no—
47C23×C3×C4C4×C511yescharacteristic
48C2×C3×M16C4×C511yescharacteristic
49C2×C3×M16C22×C511yescharacteristic
50C3×C22⋊C8—22no—
51#812—22no—
52C24×C5C3⋊C811yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—41no—
56C22×C4×C5—41no—
57C22×C4×C5C3⋊C811yescharacteristic
58C22×C4×C5C2×Dic311yescharacteristic
59C5×M16—41no—
60C5×M16—41no—
61C2×C5×C8—21no—
62C2×C5×C8#6712yes—
63C5×C16—122no—
64#407C5×D311yescharacteristic
65#349—32no—
66C22×C3×C5—22no—
67C22×C3×C5—21no—
68C22×C3×C5—41no—
69C22×C3×C5—41no—
70C22×C3×C5—42no—
71C22×C3×C5—42no—
72C22×C3×C5—41no—
73C22×C3×C5C22⋊C811yescharacteristic
74C3×C4×C5—21no—
75C3×C4×C5—41no—
76C3×C4×C5#9911yescharacteristic
77C3×C4×C5#10011yescharacteristic
78C24×C3C5×C811yescharacteristic
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×C3×C4—41no—
82C22×C3×C4—41no—
83C22×C3×C4C5×C811yescharacteristic
84C22×C3×C4C2×C4×C511yescharacteristic
85C3×M16—41no—
86C3×M16—41no—
87C2×C3×C8—21no—
88C2×C3×C8C5×D412yes—
89C3⋊C16—42no—
90C23×C5—21no—
91C23×C5—41no—
92C23×C5—42no—
93C23×C5C2×C3⋊C811yescharacteristic
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—42no—
98C2×C4×C5—41no—
99C2×C4×C5—41no—
100C2×C4×C5—41no—
101C2×C4×C5#20811yescharacteristic
102C2×C4×C5#21711yescharacteristic
103C5×C8—22no—
104C5×C8—41no—
105C23×C4C5×Dic311yescharacteristic
106C2×M16C5×Dic311yescharacteristic
107C2×M16C2×C5×D311yescharacteristic
108M32—62no—
109C22⋊C8—22no—
110C2×C3×C5—21no—
111C2×C3×C5—42no—
112C2×C3×C5—41no—
113C2×C3×C5#32311yescharacteristic
114C23×C3—21no—
115C23×C3—41no—
116C23×C3—42no—
117C23×C3C2×C5×C811yescharacteristic
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—42no—
122C2×C3×C4—41no—
123C2×C3×C4—41no—
124C2×C3×C4—41no—
125C2×C3×C4C5×C22⋊C411yescharacteristic
126C2×C3×C4C5×M1611yescharacteristic
127C3×C8—22no—
128C3×C8—41no—
129C22×C5—22no—
130C22×C5—21no—
131C22×C5—41no—
132C22×C5—41no—
133C22×C5—42no—
134C22×C5—42no—
135C22×C5—41no—
136C22×C5#83011yescharacteristic
137C4×C5—21no—
138C4×C5—41no—
139C4×C5#83311yescharacteristic
140C4×C5#83411yescharacteristic
141C24C5×C3⋊C811yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4C5×C3⋊C811yescharacteristic
147C22×C4C2×C5×Dic311yescharacteristic
148M16—41no—
149M16—41no—
150C2×C8—21no—
151C2×C8C5×#6712yes—
152C16—122no—
153C3×C5#132011yescharacteristic, complemented, Hall
154C22×C3—22no—
155C22×C3—21no—
156C22×C3—41no—
157C22×C3—41no—
158C22×C3—42no—
159C22×C3—42no—
160C22×C3—41no—
161C22×C3C5×C22⋊C811yescharacteristic
162C3×C4—21no—
163C3×C4—41no—
164C3×C4C5×#9911yescharacteristic
165C3×C4C5×#10011yescharacteristic
166C2×C5—21no—
167C2×C5—42no—
168C2×C5—41no—
169C2×C5#452511yescharacteristic
170C23—21no—
171C23—41no—
172C23—42no—
173C23C2×C5×C3⋊C811yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4C5×#20811yescharacteristic
182C2×C4C5×#21711yescharacteristic
183C8—22no—
184C8—41no—
185C2×C3—21no—
186C2×C3—42no—
187C2×C3—41no—
188C2×C3C5×#32311yescharacteristic
189C5#6768111yescharacteristic, direct product factor, Sylow
190C22—22no—
191C22—21no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—41no—
197C22C5×#83011yescharacteristic
198C4—21no—
199C4—41no—
200C4C5×#83311yescharacteristic
201C4C5×#83411yescharacteristic
202C3C5×#132011yescharacteristic, complemented, Sylow
203C2—21no—
204C2—42no—
205C2—41no—
206C2C5×#452511yescharacteristic
subgroupG/H
centerC4×C5#834
commutatorC23×C3C2×C5×C8
FrattiniC2×M16C2×C5×D3
FittingC3×C5×#407C2
socleC2×C3×C5#323
prime radicalC24×C3×C5C8
cosocleC2×C3×M16C22×C5
hypercenterC5×#407D3
hypocenterC3C5×#1320
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×M16 ◁ C5×#407

Complements

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

NH ≅ G/Ntype
2. C5×#4553C2semidirect
9. #67681C5direct (N × H)
25. #4553C2×C5semidirect
153. C3×C5#1320semidirect
189. C5#67681direct (N × H)
202. C3C5×#1320semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4072
C5×#45532
C5×#13203
#676815