Finite Group Databasebeta

← C53×#10428 #27217940

Subgroups — C53×#10428 #27217940

Order 13568.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2822C211yesmaximal, characteristic
2C53×#1992C212yesmaximal
3C53×#1836C211yesmaximal, characteristic
4C2×C53×#330C212yesmaximal
5C53×#1295C211yesmaximal, characteristic
6C2×#125×C53C2212yes—
7C2×#97×C53C2212yes—
8C2×#97×C53C2211yescharacteristic
9C53×#400—22no—
10C53×#398—22no—
11C53×#398—22no—
12C53×#384C2211yescharacteristic
13C53×#382C2211yescharacteristic
14C53×#340—22no—
15C53×#340—22no—
16C53×#340—22no—
17C53×#330—24no—
18C22×C8×C53—22no—
19C22×C8×C53—21no—
20#125×C53—22no—
21#125×C53—22no—
22#125×C53—22no—
23#125×C53—22no—
24C2×C4⋊C4×C53—22no—
25C2×C4⋊C4×C53—22no—
26C2×C4⋊C4×C53—22no—
27C2×C4⋊C4×C53—22no—
28C2×C4⋊C4×C53—21no—
29C2×C4⋊C4×C53D412yes—
30C2×C4⋊C4×C53D412yes—
31C2×C4⋊C4×C53D412yes—
32C2×C42×C53C2311yescharacteristic
33#97×C53—22no—
34#97×C53—21no—
35#97×C53—22no—
36#97×C53D412yes—
37#95×C53—24no—
38#95×C53—22no—
39#95×C53—22no—
40C22×C4×C53—22no—
41C22×C4×C53—22no—
42C22×C4×C53—22no—
43C22×C4×C53—41no—
44C22×C4×C53C2×D412yes—
45C22×C4×C53C2×D411yescharacteristic
46C2×C8×C53—24no—
47C2×C8×C53—22no—
48C2×C8×C53—42no—
49C2×C8×C53—41no—
50C2×C8×C53—41no—
51C2×C8×C53—42no—
52C4⋊C4×C53—22no—
53C4⋊C4×C53—22no—
54C4⋊C4×C53—22no—
55C4⋊C4×C53—22no—
56C4⋊C4×C53—42no—
57C4⋊C4×C53—44no—
58C4⋊C4×C53—42no—
59C4⋊C4×C53—42no—
60C4⋊C4×C53—42no—
61C4⋊C4×C53—42no—
62C4⋊C4×C53—42no—
63C4⋊C4×C53—82no—
64C42×C53C2×D411yescharacteristic
65C42×C53#4111yescharacteristic
66C42×C53#4112yes—
67C23×C53#12011yescharacteristic
68C2×C4×C53—22no—
69C2×C4×C53—21no—
70C2×C4×C53—21no—
71C2×C4×C53—22no—
72C2×C4×C53—42no—
73C2×C4×C53—42no—
74C2×C4×C53—42no—
75C2×C4×C53—42no—
76C2×C4×C53—42no—
77C2×C4×C53—42no—
78C2×C4×C53—42no—
79C2×C4×C53—42no—
80C2×C4×C53—42no—
81C2×C4×C53—81no—
82C2×C4×C53—82no—
83C2×C4×C53#12112yes—
84C2×C4×C53#12111yescharacteristic
85C2×C4×C53#12312yes—
86C2×C4×C53#12411yescharacteristic
87C8×C53—44no—
88C8×C53—42no—
89#10428C5311yesmaximal, characteristic, direct product factor, Sylow
90C22×C53#39411yescharacteristic
91C22×C53#45411yescharacteristic
92C22×C53#45412yes—
93C22×C53#45511yescharacteristic
94C22×C53#45612yes—
95C4×C53—22no—
96C4×C53—22no—
97C4×C53—21no—
98C4×C53—21no—
99C4×C53—82no—
100C4×C53—82no—
101C4×C53—82no—
102C4×C53—161no—
103#2822C2×C5311yescharacteristic
104#1992C2×C5312yes—
105#1836C2×C5311yescharacteristic
106C2×#330C2×C5312yes—
107#1295C2×C5311yescharacteristic
108C2×C53#165811yescharacteristic
109C2×C53#166311yescharacteristic
110C2×C53#166412yes—
111C2×C53#203812yes—
112C2×C53#204011yescharacteristic
113C2×#125C22×C5312yes—
114C2×#97C22×C5312yes—
115C2×#97C22×C5311yescharacteristic
116#400—22no—
117#398—22no—
118#398—22no—
119#384C22×C5311yescharacteristic
120#382C22×C5311yescharacteristic
121#340—22no—
122#340—22no—
123#340—22no—
124#330—24no—
125C53#1042811yescharacteristic, direct product factor, Sylow
126C22×C8—22no—
127C22×C8—21no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4D4×C5312yes—
138C2×C4⋊C4D4×C5312yes—
139C2×C4⋊C4D4×C5312yes—
140C2×C42C23×C5311yescharacteristic
141#97—22no—
142#97—21no—
143#97—22no—
144#97D4×C5312yes—
145#95—24no—
146#95—22no—
147#95—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C2×D4×C5312yes—
153C22×C4C2×D4×C5311yescharacteristic
154C2×C8—24no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—82no—
172C42C2×D4×C5311yescharacteristic
173C42#41×C5311yescharacteristic
174C42#41×C5312yes—
175C23#120×C5311yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—81no—
190C2×C4—82no—
191C2×C4#121×C5312yes—
192C2×C4#121×C5311yescharacteristic
193C2×C4#123×C5312yes—
194C2×C4#124×C5311yescharacteristic
195C8—44no—
196C8—42no—
197C22C53×#39411yescharacteristic
198C22C53×#45411yescharacteristic
199C22C53×#45412yes—
200C22C53×#45511yescharacteristic
201C22C53×#45612yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C53×#165811yescharacteristic
211C2C53×#166311yescharacteristic
212C2C53×#166412yes—
213C2C53×#203812yes—
214C2C53×#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C53#120
commutator, Frattini, cosocleC2×C42C23×C53
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
89. #10428C53direct (N × H)
125. C53#10428direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#28222
C53×#19922
C53×#18362
C2×C53×#3302
C53×#12952
#1042853