Finite Group Databasebeta

← C5×#1779⋊C3 #14510683

Subgroups — C5×#1779⋊C3 #14510683

Order 1920.

344 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C4×C5×C22⋊A4C211yesmaximal, characteristic
2C5×#1779C311yesmaximal, characteristic, complemented, Hall
3C2×C5×C22⋊A4C411yescharacteristic
4C5×C8×A4—41nomaximal
5#1779⋊C3C511yesmaximal, characteristic, direct product factor, Hall
6C24×C4×C5C2×C311yescharacteristic
7C2×C5×C22⋊C8—31no—
8C2×C5×C22⋊C8—31no—
9C5×C22⋊A4C811yescharacteristic, complemented
10C4×C5×A4—41no—
11C4×C5×A4—82no—
12C4×C22⋊A4C2×C511yescharacteristic
13C25×C5C3×C411yescharacteristic
14C23×C4×C5—31no—
15C23×C4×C5—31no—
16C23×C4×C5—62no—
17C23×C4×C5—62no—
18C22×C5×C8—31no—
19C22×C5×C8A411yescharacteristic, complemented
20C5×C22⋊C8—62no—
21C5×C22⋊C8—62no—
22#1779C3×C511yescharacteristic, complemented, Sylow
23C2×C5×A4—41no—
24C2×C5×A4—82no—
25C3×C5×C8—161no—
26C2×C22⋊A4C4×C511yescharacteristic
27C8×A4—41no—
28C24×C5—31no—
29C24×C5—31no—
30C24×C5—62no—
31C24×C5—62no—
32C24×C5C3×C811yescharacteristic, complemented
33C22×C4×C5—22no—
34C22×C4×C5—32no—
35C22×C4×C5—32no—
36C22×C4×C5—31no—
37C22×C4×C5—62no—
38C22×C4×C5—62no—
39C22×C4×C5—64no—
40C22×C4×C5—62no—
41C22×C4×C5—62no—
42C22×C4×C5—64no—
43C22×C4×C5—62no—
44C22×C4×C5—62no—
45C22×C4×C5C2×A411yescharacteristic
46C2×C5×C8—61no—
47C2×C5×C8—61no—
48C2×C5×C8—62no—
49C24×C4C2×C3×C511yescharacteristic
50C2×C22⋊C8—31no—
51C2×C22⋊C8—31no—
52C5×A4—41no—
53C5×A4—82no—
54C3×C4×C5—161no—
55C22⋊A4C5×C811yescharacteristic, complemented
56C4×A4—41no—
57C4×A4—82no—
58C23×C5—22no—
59C23×C5—32no—
60C23×C5—32no—
61C23×C5—31no—
62C23×C5—31no—
63C23×C5—62no—
64C23×C5—62no—
65C23×C5—62no—
66C23×C5—62no—
67C23×C5—62no—
68C23×C5—64no—
69C23×C5—62no—
70C23×C5—62no—
71C23×C5—64no—
72C23×C5C4×A411yescharacteristic
73C2×C4×C5—31no—
74C2×C4×C5—31no—
75C2×C4×C5—32no—
76C2×C4×C5—62no—
77C2×C4×C5—64no—
78C2×C4×C5—62no—
79C2×C4×C5—64no—
80C2×C4×C5—62no—
81C2×C4×C5—62no—
82C2×C4×C5—62no—
83C5×C8—41no—
84C5×C8—121no—
85C25C3×C4×C511yescharacteristic
86C23×C4—31no—
87C23×C4—31no—
88C23×C4—62no—
89C23×C4—62no—
90C22×C8—31no—
91C22×C8C5×A411yescharacteristic, complemented
92C22⋊C8—62no—
93C22⋊C8—62no—
94C2×C3×C5—161no—
95C2×A4—41no—
96C2×A4—82no—
97C3×C8—161no—
98C22×C5—22no—
99C22×C5—31no—
100C22×C5—31no—
101C22×C5—32no—
102C22×C5—32no—
103C22×C5—62no—
104C22×C5—62no—
105C22×C5—62no—
106C22×C5—64no—
107C22×C5—62no—
108C22×C5—62no—
109C22×C5—62no—
110C22×C5—64no—
111C22×C5—62no—
112C22×C5C8×A411yescharacteristic
113C4×C5—31no—
114C4×C5—62no—
115C4×C5#120⋊C311yescharacteristic
116C24—31no—
117C24—31no—
118C24—62no—
119C24—62no—
120C24C3×C5×C811yescharacteristic, complemented
121C22×C4—22no—
122C22×C4—32no—
123C22×C4—32no—
124C22×C4—31no—
125C22×C4—62no—
126C22×C4—62no—
127C22×C4—64no—
128C22×C4—62no—
129C22×C4—62no—
130C22×C4—64no—
131C22×C4—62no—
132C22×C4—62no—
133C22×C4C2×C5×A411yescharacteristic
134C2×C8—61no—
135C2×C8—61no—
136C2×C8—62no—
137C3×C5—161noHall
138A4—41no—
139A4—82no—
140C3×C4—161no—
141C2×C5—31no—
142C2×C5—31no—
143C2×C5—62no—
144C2×C5—62no—
145C2×C5#379⋊C311yescharacteristic
146C23—22no—
147C23—32no—
148C23—32no—
149C23—31no—
150C23—31no—
151C23—62no—
152C23—62no—
153C23—62no—
154C23—62no—
155C23—62no—
156C23—64no—
157C23—62no—
158C23—62no—
159C23—64no—
160C23C4×C5×A411yescharacteristic
161C2×C4—31no—
162C2×C4—31no—
163C2×C4—32no—
164C2×C4—62no—
165C2×C4—64no—
166C2×C4—62no—
167C2×C4—64no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C8—41no—
172C8—121no—
173C2×C3—161no—
174C5#1779⋊C311yescharacteristic, direct product factor, Sylow
175C22—22no—
176C22—31no—
177C22—31no—
178C22—32no—
179C22—32no—
180C22—62no—
181C22—62no—
182C22—62no—
183C22—64no—
184C22—62no—
185C22—62no—
186C22—62no—
187C22—64no—
188C22—62no—
189C22C5×C8×A411yescharacteristic
190C4—31no—
191C4—62no—
192C4C5×#120⋊C311yescharacteristic
193C3—161noSylow
194C2—31no—
195C2—31no—
196C2—62no—
197C2—62no—
198C2C5×#379⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4×C5#120⋊C3
commutator, hypocenterC24C3×C5×C8
FrattiniC22×C4C2×C5×A4
FittingC5×#1779C3
socleC23×C5C4×A4
prime radicalC2×C5×C22⋊A4C4
cosocleC24×C4C2×C3×C5
LCSG ▷ C24
UCSC1 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
2. C5×#1779C3semidirect
5. #1779⋊C3C5direct (N × H)
9. C5×C22⋊A4C8semidirect
19. C22×C5×C8A4semidirect
22. #1779C3×C5semidirect
32. C24×C5C3×C8semidirect
55. C22⋊A4C5×C8semidirect
91. C22×C8C5×A4semidirect
120. C24C3×C5×C8semidirect
174. C5#1779⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊A42
C5×#17793
C5×C8×A44
#1779⋊C35