Finite Group Databasebeta

← C53×#10429 #27217941

Subgroups — C53×#10429 #27217941

Order 13568.

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

normal subgroups only

This group has 402 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×#1847C211yesmaximal, characteristic
4C2×C53×#330C212yesmaximal
5C53×#1295C211yesmaximal, characteristic
6C2×#125×C53C2212yes—
7C2×#107×C53—21no—
8C2×#106×C53—21no—
9C2×#97×C53C2212yes—
10C2×#97×C53C2211yescharacteristic
11C53×#400—22no—
12C53×#398—21no—
13C53×#398—21no—
14C53×#398—22no—
15C53×#384C2211yescharacteristic
16C53×#382C2211yescharacteristic
17C53×#340—22no—
18C53×#340—22no—
19C53×#330—24no—
20C22×C8×C53—21no—
21C22×C8×C53—22no—
22#125×C53—22no—
23#125×C53—22no—
24#125×C53—22no—
25#125×C53—22no—
26C2×C4⋊C4×C53—21no—
27C2×C4⋊C4×C53—21no—
28C2×C4⋊C4×C53—22no—
29C2×C4⋊C4×C53—22no—
30C2×C4⋊C4×C53—22no—
31C2×C4⋊C4×C53—21no—
32C2×C4⋊C4×C53D412yes—
33C2×C4⋊C4×C53D412yes—
34C2×C4⋊C4×C53D411yescharacteristic
35C2×C4⋊C4×C53D411yescharacteristic
36C2×C42×C53C2311yescharacteristic
37#107×C53—42no—
38#106×C53—42no—
39#97×C53—22no—
40#97×C53—21no—
41#97×C53—22no—
42#97×C53D412yes—
43#95×C53—22no—
44#95×C53—22no—
45#95×C53—21no—
46#95×C53—21no—
47#95×C53—22no—
48C22×C4×C53—21no—
49C22×C4×C53—21no—
50C22×C4×C53—22no—
51C22×C4×C53—22no—
52C22×C4×C53—41no—
53C22×C4×C53C2×D412yes—
54C22×C4×C53C2×D411yescharacteristic
55C2×C8×C53—22no—
56C2×C8×C53—22no—
57C2×C8×C53—22no—
58C2×C8×C53—24no—
59C2×C8×C53—42no—
60C2×C8×C53—42no—
61C4⋊C4×C53—22no—
62C4⋊C4×C53—22no—
63C4⋊C4×C53—22no—
64C4⋊C4×C53—22no—
65C4⋊C4×C53—41no—
66C4⋊C4×C53—41no—
67C4⋊C4×C53—41no—
68C4⋊C4×C53—41no—
69C4⋊C4×C53—44no—
70C4⋊C4×C53—42no—
71C4⋊C4×C53—42no—
72C4⋊C4×C53—42no—
73C4⋊C4×C53—42no—
74C4⋊C4×C53—81no—
75C4⋊C4×C53—81no—
76C42×C53C2×D411yescharacteristic
77C42×C53#4111yescharacteristic
78C42×C53#4112yes—
79C23×C53#12011yescharacteristic
80C2×C4×C53—21no—
81C2×C4×C53—22no—
82C2×C4×C53—22no—
83C2×C4×C53—21no—
84C2×C4×C53—42no—
85C2×C4×C53—42no—
86C2×C4×C53—41no—
87C2×C4×C53—41no—
88C2×C4×C53—42no—
89C2×C4×C53—42no—
90C2×C4×C53—42no—
91C2×C4×C53—42no—
92C2×C4×C53—42no—
93C2×C4×C53—42no—
94C2×C4×C53—81no—
95C2×C4×C53—82no—
96C2×C4×C53#12112yes—
97C2×C4×C53#12111yescharacteristic
98C2×C4×C53#12312yes—
99C2×C4×C53#12411yescharacteristic
100C8×C53—24no—
101C8×C53—44no—
102#10429C5311yesmaximal, characteristic, direct product factor, Sylow
103C22×C53#39411yescharacteristic
104C22×C53#45311yescharacteristic
105C22×C53#45412yes—
106C22×C53#45612yes—
107C22×C53#45611yescharacteristic
108C4×C53—22no—
109C4×C53—22no—
110C4×C53—21no—
111C4×C53—21no—
112C4×C53—81no—
113C4×C53—81no—
114C4×C53—82no—
115C4×C53—82no—
116C4×C53—161no—
117#2822C2×C5311yescharacteristic
118#1992C2×C5312yes—
119#1847C2×C5311yescharacteristic
120C2×#330C2×C5312yes—
121#1295C2×C5311yescharacteristic
122C2×C53#165711yescharacteristic
123C2×C53#166011yescharacteristic
124C2×C53#166312yes—
125C2×C53#203812yes—
126C2×C53#203911yescharacteristic
127C2×#125C22×C5312yes—
128C2×#107—21no—
129C2×#106—21no—
130C2×#97C22×C5312yes—
131C2×#97C22×C5311yescharacteristic
132#400—22no—
133#398—21no—
134#398—21no—
135#398—22no—
136#384C22×C5311yescharacteristic
137#382C22×C5311yescharacteristic
138#340—22no—
139#340—22no—
140#330—24no—
141C53#1042911yescharacteristic, direct product factor, Sylow
142C22×C8—21no—
143C22×C8—22no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4D4×C5312yes—
155C2×C4⋊C4D4×C5312yes—
156C2×C4⋊C4D4×C5311yescharacteristic
157C2×C4⋊C4D4×C5311yescharacteristic
158C2×C42C23×C5311yescharacteristic
159#107—42no—
160#106—42no—
161#97—22no—
162#97—21no—
163#97—22no—
164#97D4×C5312yes—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—21no—
169#95—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4C2×D4×C5312yes—
176C22×C4C2×D4×C5311yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—24no—
181C2×C8—42no—
182C2×C8—42no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—44no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C42C2×D4×C5311yescharacteristic
199C42#41×C5311yescharacteristic
200C42#41×C5312yes—
201C23#120×C5311yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—81no—
217C2×C4—82no—
218C2×C4#121×C5312yes—
219C2×C4#121×C5311yescharacteristic
220C2×C4#123×C5312yes—
221C2×C4#124×C5311yescharacteristic
222C8—24no—
223C8—44no—
224C22C53×#39411yescharacteristic
225C22C53×#45311yescharacteristic
226C22C53×#45412yes—
227C22C53×#45612yes—
228C22C53×#45611yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—161no—
238C2C53×#165711yescharacteristic
239C2C53×#166011yescharacteristic
240C2C53×#166312yes—
241C2C53×#203812yes—
242C2C53×#203911yescharacteristic
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
102. #10429C53direct (N × H)
141. C53#10429direct (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×#18472
C2×C53×#3302
C53×#12952
#1042953