Finite Group Databasebeta

← C53×#1895 #20270832

Subgroups — C53×#1895 #20270832

Order 6784.

412 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C22×M16×C53C211yesmaximal, characteristic, complemented
2C2×#121×C53C211yesmaximal, characteristic
3C2×#102×C53C212yesmaximal, complemented
4C53×#380C211yesmaximal, characteristic, complemented
5C53×#340C212yesmaximal, complemented
6C22×D4×C53—21no—
7C22×D4×C53C2211yescharacteristic
8C23×C4×C53C2211yescharacteristic
9C2×M16×C53—24no—
10C2×M16×C53—22no—
11C22×C8×C53C2212yes—
12#121×C53—22no—
13#121×C53C414yescomplemented
14C2×C4⋊C4×C53C2212yes—
15C2×C4⋊C4×C53C2211yescharacteristic
16C2×C22⋊C4×C53—21no—
17C2×C22⋊C4×C53—21no—
18#102×C53—24no—
19#95×C53—21no—
20C24×C53—21no—
21C24×C53D411yescharacteristic
22C2×D4×C53—24no—
23C2×D4×C53—22no—
24C2×D4×C53—21no—
25C2×D4×C53—22no—
26C2×D4×C53—44no—
27C2×D4×C53C2×C412yes—
28C22×C4×C53—22no—
29C22×C4×C53—22no—
30C22×C4×C53—21no—
31C22×C4×C53—22no—
32C22×C4×C53C2×C412yes—
33C22×C4×C53D411yescharacteristic
34C22×C4×C53D412yes—
35C22×C4×C53C2311yescharacteristic
36M16×C53—28no—
37C2×C8×C53—22no—
38C2×C8×C53—22no—
39C2×C8×C53D414yescomplemented
40C4⋊C4×C53—21no—
41C4⋊C4×C53—22no—
42C4⋊C4×C53—22no—
43C4⋊C4×C53C2×C412yes—
44C22⋊C4×C53—24no—
45C22⋊C4×C53—42no—
46C23×C53—22no—
47C23×C53—22no—
48C23×C53—21no—
49C23×C53—21no—
50C23×C53—22no—
51C23×C53—42no—
52C23×C53—42no—
53C23×C53—41no—
54C23×C53—41no—
55C23×C53C22⋊C412yes—
56C23×C53C2×D411yescharacteristic
57D4×C53—24no—
58D4×C53—48no—
59D4×C53—41no—
60D4×C53—41no—
61C2×C4×C53—22no—
62C2×C4×C53—24no—
63C2×C4×C53—22no—
64C2×C4×C53—22no—
65C2×C4×C53—22no—
66C2×C4×C53—42no—
67C2×C4×C53—42no—
68C2×C4×C53—42no—
69C2×C4×C53—42no—
70C2×C4×C53C22⋊C412yes—
71C2×C4×C53C22×C411yescharacteristic
72C2×C4×C53C2×D412yes—
73C2×C4×C53C2×D411yescharacteristic
74C2×C4×C53#4112yes—
75C8×C53—24no—
76C22×C53—22no—
77C22×C53—22no—
78C22×C53—22no—
79C22×C53—42no—
80C22×C53—42no—
81C22×C53—42no—
82C22×C53—42no—
83C22×C53—42no—
84C22×C53—82no—
85C22×C53—82no—
86C22×C53C2×C22⋊C411yescharacteristic
87C22×C53#12112yes—
88C22×C53AGL(1,ℤ/8)11yescharacteristic
89C22×C53AGL(1,ℤ/8)12yes—
90C22×C53#13711yescharacteristic
91C4×C53—22no—
92C4×C53—42no—
93C4×C53—82no—
94C4×C53C4×D412yes—
95C4×C53#12011yescharacteristic
96C4×C53#12311yescharacteristic
97#1895C5311yesmaximal, characteristic, direct product factor, Sylow
98C2×C53—42no—
99C2×C53—82no—
100C2×C53#38611yescharacteristic
101C2×C53#41711yescharacteristic
102C2×C53#41811yescharacteristic
103C2×C53#46812yes—
104C2×C53#46912yes—
105C22×M16C2×C5311yescharacteristic, complemented
106C2×#121C2×C5311yescharacteristic
107C2×#102C2×C5312yescomplemented
108#380C2×C5311yescharacteristic, complemented
109#340C2×C5312yescomplemented
110C53#189511yescharacteristic, direct product factor, Sylow
111C22×D4—21no—
112C22×D4C22×C5311yescharacteristic
113C23×C4C22×C5311yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C22×C5312yes—
117#121—22no—
118#121C4×C5314yescomplemented
119C2×C4⋊C4C22×C5312yes—
120C2×C4⋊C4C22×C5311yescharacteristic
121C2×C22⋊C4—21no—
122C2×C22⋊C4—21no—
123#102—24no—
124#95—21no—
125C24—21no—
126C24D4×C5311yescharacteristic
127C2×D4—24no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—22no—
131C2×D4—44no—
132C2×D4C2×C4×C5312yes—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—22no—
137C22×C4C2×C4×C5312yes—
138C22×C4D4×C5312yes—
139C22×C4D4×C5311yescharacteristic
140C22×C4C23×C5311yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8D4×C5314yescomplemented
145C4⋊C4—21no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4C2×C4×C5312yes—
149C22⋊C4—24no—
150C22⋊C4—42no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—22no—
156C23—42no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23C22⋊C4×C5312yes—
161C23C2×D4×C5311yescharacteristic
162D4—24no—
163D4—48no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4C22⋊C4×C5312yes—
176C2×C4C22×C4×C5311yescharacteristic
177C2×C4C2×D4×C5312yes—
178C2×C4C2×D4×C5311yescharacteristic
179C2×C4#41×C5312yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22C2×C22⋊C4×C5311yescharacteristic
192C22#121×C5312yes—
193C22AGL(1,ℤ/8)×C5311yescharacteristic
194C22AGL(1,ℤ/8)×C5312yes—
195C22#137×C5311yescharacteristic
196C4—22no—
197C4—42no—
198C4—82no—
199C4C4×D4×C5312yes—
200C4#120×C5311yescharacteristic
201C4#123×C5311yescharacteristic
202C2—42no—
203C2—82no—
204C2C53×#38611yescharacteristic
205C2C53×#41711yescharacteristic
206C2C53×#41811yescharacteristic
207C2C53×#46812yes—
208C2C53×#46912yes—
subgroupG/H
center, socleC23×C53C2×D4
commutatorC2×C4C22×C4×C53
Frattini, cosocleC22×C4C23×C53
prime radicalC2×#121×C53C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×M16×C53C2semidirect
3. C2×#102×C53C2semidirect
4. C53×#380C2semidirect
5. C53×#340C2semidirect
13. #121×C53C4semidirect
39. C2×C8×C53D4semidirect
97. #1895C53direct (N × H)
105. C22×M16C2×C53semidirect
107. C2×#102C2×C53semidirect
108. #380C2×C53semidirect
109. #340C2×C53semidirect
110. C53#1895direct (N × H)
118. #121C4×C53semidirect
144. C2×C8D4×C53semidirect

Maximal subgroups

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

subgroupindex
C22×M16×C532
C2×#121×C532
C2×#102×C532
C53×#3802
C53×#3402
#189553