Finite Group Databasebeta

← C5×#85550 #14511288

Subgroups — C5×#85550 #14511288

Order 1920.

220 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 24 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
1C5×#543⋊C3C211yesmaximal, characteristic
2C5×#1614—31nomaximal, Hall
3C2×C5×SL(2,ℤ/4)—41nomaximal
4C5×#859—42nomaximal
5#85550C511yesmaximal, characteristic, direct product factor, Hall
6C5×#543D311yescharacteristic
7C5×#484—32no—
8C5×#399—31no—
9C5×#328—32no—
10C5×#323—31no—
11C22×C5×A4—41no—
12C2×C5×SL(2,𝔽3)—42no—
13C2×C5×SL(2,𝔽3)—81no—
14C5×SL(2,ℤ/4)—42no—
15#543⋊C3C2×C511yescharacteristic
16C5×C22⋊Q8—32no—
17C5×C22⋊Q8—61no—
18C2×C5×C4⋊C4—31no—
19C2×C5×C4⋊C4—61no—
20C2×C5×C22⋊C4—31no—
21C2×C5×C22⋊C4—61no—
22C5×#107—62no—
23C5×#103—62no—
24C5×C22⋊C8—32no—
25C5×#95—31no—
26#1614—31noSylow
27C2×C5×A4—41no—
28C2×C5×A4—41no—
29C2×C5×A4—41no—
30C2×C5×Dic3—161no—
31C5×SL(2,𝔽3)—42no—
32C5×SL(2,𝔽3)—81no—
33C2×SL(2,ℤ/4)—41no—
34#859—42no—
35C24×C5S411yescharacteristic
36C2×C5×Q8—21no—
37C2×C5×Q8S412yes—
38C22×C4×C5—31no—
39C22×C4×C5—31no—
40C22×C4×C5—61no—
41C22×C4×C5—61no—
42C2×C5×C8—62no—
43C5×C4⋊C4—32no—
44C5×C4⋊C4—61no—
45C5×C4⋊C4—62no—
46C5×C4⋊C4—122no—
47C5×C22⋊C4—62no—
48C5×C22⋊C4—122no—
49#543C5×D311yescharacteristic
50#484—32no—
51#399—31no—
52#328—32no—
53#323—31no—
54C22×C3×C5—161no—
55C5×A4—41no—
56C5×Dic3—162no—
57C22×A4—41no—
58C2×SL(2,𝔽3)—42no—
59C2×SL(2,𝔽3)—81no—
60SL(2,ℤ/4)—42no—
61C23×C5—31no—
62C23×C5—31no—
63C23×C5—41no—
64C23×C5—41no—
65C23×C5#22611yescharacteristic
66C5×Q8—42no—
67C5×Q8—81no—
68C2×C4×C5—32no—
69C2×C4×C5—62no—
70C2×C4×C5—61no—
71C2×C4×C5—121no—
72C2×C4×C5—121no—
73C2×C4×C5—121no—
74C2×C4×C5—121no—
75C2×C4×C5—121no—
76C2×C4×C5—121no—
77C2×C4×C5—121no—
78C5×C8—122no—
79C22⋊Q8—32no—
80C22⋊Q8—61no—
81C2×C4⋊C4—31no—
82C2×C4⋊C4—61no—
83C2×C22⋊C4—31no—
84C2×C22⋊C4—61no—
85#107—62no—
86#103—62no—
87C22⋊C8—32no—
88#95—31no—
89C2×C3×C5—161no—
90C2×C3×C5—161no—
91C2×C3×C5—161no—
92C2×A4—41no—
93C2×A4—41no—
94C2×A4—41no—
95C2×Dic3—161no—
96SL(2,𝔽3)—42no—
97SL(2,𝔽3)—81no—
98C22×C5—31no—
99C22×C5—31no—
100C22×C5—41no—
101C22×C5—61no—
102C22×C5—61no—
103C22×C5—121no—
104C22×C5#102011yescharacteristic
105C4×C5—62no—
106C4×C5—122no—
107C4×C5—121no—
108C4×C5—241no—
109C24C5×S411yescharacteristic
110C2×Q8—21no—
111C2×Q8C5×S412yes—
112C22×C4—31no—
113C22×C4—31no—
114C22×C4—61no—
115C22×C4—61no—
116C2×C8—62no—
117C4⋊C4—32no—
118C4⋊C4—61no—
119C4⋊C4—62no—
120C4⋊C4—122no—
121C22⋊C4—62no—
122C22⋊C4—122no—
123C3×C5—161noHall
124C22×C3—161no—
125A4—41no—
126Dic3—162no—
127C2×C5—61no—
128C2×C5—61no—
129C2×C5#593011yescharacteristic
130C2×C5#593211yescharacteristic
131C2×C5#593511yescharacteristic
132C23—31no—
133C23—31no—
134C23—41no—
135C23—41no—
136C23C5×#22611yescharacteristic
137Q8—42no—
138Q8—81no—
139C2×C4—32no—
140C2×C4—62no—
141C2×C4—61no—
142C2×C4—121no—
143C2×C4—121no—
144C2×C4—121no—
145C2×C4—121no—
146C2×C4—121no—
147C2×C4—121no—
148C2×C4—121no—
149C8—122no—
150C2×C3—161no—
151C2×C3—161no—
152C2×C3—161no—
153C5#8555011yescharacteristic, direct product factor, Sylow
154C22—31no—
155C22—31no—
156C22—41no—
157C22—61no—
158C22—61no—
159C22—121no—
160C22C5×#102011yescharacteristic
161C4—62no—
162C4—122no—
163C4—121no—
164C4—241no—
165C3—161noSylow
166C2—61no—
167C2—61no—
168C2C5×#593011yescharacteristic
169C2C5×#593211yescharacteristic
170C2C5×#593511yescharacteristic
subgroupG/H
center, socle, hypercenterC22×C5#1020
commutator, cosocle, hypocenter#543⋊C3C2×C5
FrattiniC22C5×#1020
FittingC5×#543D3
prime radicalC5×#543⋊C3C2
LCSG ▷ #543⋊C3
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
5. #85550C5direct (N × H)
153. C5#85550direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#543⋊C32
C5×#16143
C2×C5×SL(2,ℤ/4)4
C5×#8594
#855505