Finite Group Databasebeta

← C13×#13436 #15699775

Subgroups — C13×#13436 #15699775

Order 3328.

438 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C13×#3199C211yesmaximal, characteristic
2C13×#2122C212yesmaximal, complemented
3C13×#1910C212yesmaximal, complemented
4C13×#1858C211yesmaximal, characteristic, complemented
5C13×#1391C211yesmaximal, characteristic, complemented
6C13×#568C2211yescharacteristic
7C13×#535C2212yes—
8C13×#482—22no—
9C13×#469—21no—
10C13×#466—21no—
11C13×#447—22no—
12C13×#430—21no—
13C13×#418—22no—
14C13×#413C2211yescharacteristic
15C13×#410C2212yes—
16C13×#408C2211yescharacteristic
17C13×AΣL(1,𝔽16)—24no—
18C13×#341—21no—
19C13×H(3,ℤ/4)—22no—
20C2×C13×#41C2311yescharacteristic
21C22×D4×C13D412yes—
22C2×C13×D8—21no—
23C2×C13×D8—21no—
24C13×#131—42no—
25C2×C13×M16—22no—
26C2×C13×M16—21no—
27C2×C13×M16—21no—
28C2×C13×M16D411yescharacteristic
29C22×C8×C13D411yescharacteristic
30C13×#127—22no—
31C13×#124—22no—
32C13×#121—22no—
33C13×#121—22no—
34C13×#120—22no—
35C13×#120—22no—
36C13×#117—22no—
37C13×#117D412yes—
38C13×#108—42no—
39C13×#107—21no—
40C13×#106—21no—
41C13×#102—22no—
42C13×#102—22no—
43C13×#102—44no—
44C13×#101—21no—
45C13×#100D412yes—
46C13×#99—22no—
47C13×#99—22no—
48C13×C22⋊C8—22no—
49#13436C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13—22no—
51C13×#41—41no—
52C13×#41—41no—
53C2×Q8×C13#4111yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13C2×D411yescharacteristic
61C2×D4×C13#4112yes—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D412yes—
64C13×D8—81no—
65C13×D8—81no—
66C13×M16—22no—
67C13×M16—22no—
68C13×M16—41no—
69C13×M16—42no—
70C13×M16—41no—
71C13×M16—41no—
72C2×C8×C13—24no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C42×C13—22no—
85C42×C13—42no—
86#3199C2×C1311yescharacteristic
87#2122C2×C1312yescomplemented
88#1910C2×C1312yescomplemented
89#1858C2×C1311yescharacteristic, complemented
90#1391C2×C1311yescharacteristic, complemented
91C23×C13—42no—
92C23×C13—82no—
93C23×C13—162no—
94C23×C13#12112yes—
95C23×C13#12411yescharacteristic
96Q8×C13—41no—
97D4×C13—41no—
98D4×C13—42no—
99D4×C13—44no—
100D4×C13—42no—
101D4×C13—42no—
102D4×C13—162no—
103D4×C13—162no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—82no—
110C2×C4×C13#12011yescharacteristic
111C2×C4×C13#12111yescharacteristic
112C2×C4×C13#12312yes—
113C8×C13—42no—
114C8×C13—42no—
115C8×C13—41no—
116C8×C13—41no—
117#568C22×C1311yescharacteristic
118#535C22×C1312yes—
119#482—22no—
120#469—21no—
121#466—21no—
122#447—22no—
123#430—21no—
124#418—22no—
125#413C22×C1311yescharacteristic
126#410C22×C1312yes—
127#408C22×C1311yescharacteristic
128AΣL(1,𝔽16)—24no—
129#341—21no—
130H(3,ℤ/4)—22no—
131C22×C13—22no—
132C22×C13—21no—
133C22×C13—41no—
134C22×C13—42no—
135C22×C13—82no—
136C22×C13—82no—
137C22×C13—82no—
138C22×C13—164no—
139C22×C13#39411yescharacteristic
140C4×C13—21no—
141C4×C13—22no—
142C4×C13—82no—
143C4×C13—162no—
144C4×C13B(4,𝔽2)11yescharacteristic
145C4×C13#45811yescharacteristic
146C2×#41C23×C1311yescharacteristic
147C22×D4D4×C1312yes—
148C2×D8—21no—
149C2×D8—21no—
150#131—42no—
151C2×M16—22no—
152C2×M16—21no—
153C2×M16—21no—
154C2×M16D4×C1311yescharacteristic
155C22×C8D4×C1311yescharacteristic
156#127—22no—
157#124—22no—
158#121—22no—
159#121—22no—
160#120—22no—
161#120—22no—
162#117—22no—
163#117D4×C1312yes—
164#108—42no—
165#107—21no—
166#106—21no—
167#102—22no—
168#102—22no—
169#102—44no—
170#101—21no—
171#100D4×C1312yes—
172#99—22no—
173#99—22no—
174C22⋊C8—22no—
175C2×C13—21no—
176C2×C13—42no—
177C2×C13—41no—
178C2×C13—162no—
179C2×C13#204411yescharacteristic
180C24—22no—
181#41—41no—
182#41—41no—
183C2×Q8C13×#4111yescharacteristic
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4C2×D4×C1311yescharacteristic
191C2×D4C13×#4112yes—
192C22×C4C2×D4×C1311yescharacteristic
193C22×C4C2×D4×C1312yes—
194D8—81no—
195D8—81no—
196M16—22no—
197M16—22no—
198M16—42no—
199M16—41no—
200M16—41no—
201M16—41no—
202C2×C8—24no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C4⋊C4—22no—
209C4⋊C4—42no—
210C22⋊C4—22no—
211C22⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C42—22no—
215C42—42no—
216C13#1343611yescharacteristic, direct product factor, Sylow
217C23—42no—
218C23—82no—
219C23—162no—
220C23C13×#12112yes—
221C23C13×#12411yescharacteristic
222Q8—41no—
223D4—41no—
224D4—42no—
225D4—44no—
226D4—42no—
227D4—42no—
228D4—162no—
229D4—162no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4C13×#12011yescharacteristic
237C2×C4C13×#12111yescharacteristic
238C2×C4C13×#12312yes—
239C8—42no—
240C8—42no—
241C8—41no—
242C8—41no—
243C22—22no—
244C22—21no—
245C22—41no—
246C22—42no—
247C22—82no—
248C22—82no—
249C22—82no—
250C22—164no—
251C22C13×#39411yescharacteristic
252C4—21no—
253C4—22no—
254C4—82no—
255C4—162no—
256C4C13×B(4,𝔽2)11yescharacteristic
257C4C13×#45811yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—162no—
262C2C13×#204411yescharacteristic
subgroupG/H
center, socleC2×C13#2044
commutator, Frattini, cosocleC2×#41C23×C13
prime radicalC13×#3199C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2122C2semidirect
3. C13×#1910C2semidirect
4. C13×#1858C2semidirect
5. C13×#1391C2semidirect
49. #13436C13direct (N × H)
87. #2122C2×C13semidirect
88. #1910C2×C13semidirect
89. #1858C2×C13semidirect
90. #1391C2×C13semidirect
216. C13#13436direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31992
C13×#21222
C13×#19102
C13×#18582
C13×#13912
#1343613