Finite Group Databasebeta

← C53×#7427 #27214939

Subgroups — C53×#7427 #27214939

Order 13568.

214 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C53×#2030C211yesmaximal, characteristic
2C53×#1317C211yesmaximal, characteristic
3C53×#1306C211yesmaximal, characteristic
4C53×#543C411yescharacteristic
5C53×#407—21no—
6C53×#381—21no—
7C53×#381C2211yescharacteristic
8C53×#342—21no—
9C53×#342C411yescharacteristic
10C53×#323—21no—
11C23×C4×C53D411yescharacteristic
12C2×M16×C53—41no—
13C22⋊Q8×C53—42no—
14C22⋊Q8×C53—41no—
15C2×C22⋊C4×C53—21no—
16C2×C22⋊C4×C53—21no—
17C2×C22⋊C4×C53C2×C411yescharacteristic
18C2×C22⋊C4×C53D411yescharacteristic
19C22⋊C8×C53—22no—
20C22⋊C8×C53—41no—
21C22⋊C8×C53—41no—
22#95×C53—41no—
23#95×C53—42no—
24C24×C53C22⋊C411yescharacteristic
25C2×Q8×C53—41no—
26C22×C4×C53—21no—
27C22×C4×C53—21no—
28C22×C4×C53—22no—
29C22×C4×C53—21no—
30C22×C4×C53—21no—
31C22×C4×C53—41no—
32C22×C4×C53—41no—
33C22×C4×C53—41no—
34C22×C4×C53SD1611yescharacteristic
35C22×C4×C53Q1611yescharacteristic
36M16×C53—81no—
37M16×C53—81no—
38C2×C8×C53—42no—
39C2×C8×C53—81no—
40C4⋊C4×C53—41no—
41C4⋊C4×C53—42no—
42C22⋊C4×C53—41no—
43C22⋊C4×C53—41no—
44C22⋊C4×C53—41no—
45C22⋊C4×C53—41no—
46C22⋊C4×C53—41no—
47C22⋊C4×C53—41no—
48C23×C53—21no—
49C23×C53—21no—
50C23×C53—81no—
51C23×C53#9911yescharacteristic
52C23×C53#10311yescharacteristic
53C23×C53#10411yescharacteristic
54Q8×C53—161no—
55C2×C4×C53—21no—
56C2×C4×C53—21no—
57C2×C4×C53—41no—
58C2×C4×C53—41no—
59C2×C4×C53—41no—
60C2×C4×C53—41no—
61C2×C4×C53—42no—
62C2×C4×C53—41no—
63C2×C4×C53—41no—
64C2×C4×C53—81no—
65C2×C4×C53—81no—
66C2×C4×C53—81no—
67C2×C4×C53—82no—
68C2×C4×C53—81no—
69C2×C4×C53—82no—
70C8×C53—82no—
71C8×C53—161no—
72#7427C5311yesmaximal, characteristic, direct product factor, Sylow
73C22×C53—21no—
74C22×C53—21no—
75C22×C53—41no—
76C22×C53—41no—
77C22×C53—41no—
78C22×C53—42no—
79C22×C53—81no—
80C22×C53#32811yescharacteristic
81C22×C53AΣL(1,𝔽16)11yescharacteristic
82C22×C53#35411yescharacteristic
83C4×C53—41no—
84C4×C53—41no—
85C4×C53—81no—
86C4×C53—82no—
87C4×C53—81no—
88C4×C53—161no—
89#2030C2×C5311yescharacteristic
90#1317C2×C5311yescharacteristic
91#1306C2×C5311yescharacteristic
92C2×C53—21no—
93C2×C53—21no—
94C2×C53—21no—
95C2×C53—41no—
96C2×C53—41no—
97C2×C53#135111yescharacteristic
98#543C4×C5311yescharacteristic
99#407—21no—
100#381—21no—
101#381C22×C5311yescharacteristic
102#342—21no—
103#342C4×C5311yescharacteristic
104#323—21no—
105C53#742711yescharacteristic, direct product factor, Sylow
106C23×C4D4×C5311yescharacteristic
107C2×M16—41no—
108C22⋊Q8—42no—
109C22⋊Q8—41no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C22⋊C4C2×C4×C5311yescharacteristic
113C2×C22⋊C4D4×C5311yescharacteristic
114C22⋊C8—22no—
115C22⋊C8—41no—
116C22⋊C8—41no—
117#95—41no—
118#95—42no—
119C24C22⋊C4×C5311yescharacteristic
120C2×Q8—41no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4SD16×C5311yescharacteristic
130C22×C4Q16×C5311yescharacteristic
131M16—81no—
132M16—81no—
133C2×C8—42no—
134C2×C8—81no—
135C4⋊C4—42no—
136C4⋊C4—41no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C22⋊C4—41no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#99×C5311yescharacteristic
147C23#103×C5311yescharacteristic
148C23#104×C5311yescharacteristic
149Q8—161no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—82no—
165C8—82no—
166C8—161no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22C53×#32811yescharacteristic
175C22C53×AΣL(1,𝔽16)11yescharacteristic
176C22C53×#35411yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—82no—
181C4—81no—
182C4—161no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2C53×#135111yescharacteristic
subgroupG/H
center, socleC2×C53#1351
commutatorC2×C22⋊C4C2×C4×C53
Frattini, cosocle#381C22×C53
prime radicalC24×C53C22⋊C4
LCSG ▷ C2×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C53 ◁ C23×C53 ◁ C24×C53 ◁ C53×#381 ◁ G

Complements

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

NH ≅ G/Ntype
72. #7427C53direct (N × H)
105. C53#7427direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#20302
C53×#13172
C53×#13062
#742753