Finite Group Databasebeta

← C13×#10213 #15696552

Subgroups — C13×#10213 #15696552

Order 3328.

498 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3253C211yesmaximal, characteristic
2C13×#3216C212yesmaximal, complemented
3C13×#1995C211yesmaximal, characteristic, complemented
4C13×#1505C212yesmaximal, complemented
5C13×#1307C211yesmaximal, characteristic, complemented
6C13×#533C2211yescharacteristic
7C13×#532C2212yes—
8C13×#497—22no—
9C13×#489—22no—
10C13×#476—22no—
11C13×#469—22no—
12C13×#462—22no—
13C13×#460—22no—
14C13×#459—22no—
15C13×#452—24no—
16C13×#432C2212yes—
17C13×#423C2211yescharacteristic
18C13×#376C2211yescharacteristic
19C13×#339—22no—
20C13×#327—24no—
21C2×C13×#41—22no—
22C2×C13×Q16—24no—
23C2×C13×SD16—24no—
24C2×C13×D8—22no—
25C2×C13×M16D412yes—
26C13×C4⋊Q8D412yes—
27C13×C4⋊Q8D412yes—
28C13×#127D412yes—
29C13×#125—21no—
30C13×#124—22no—
31C13×C22⋊Q8—22no—
32C13×#121—22no—
33C13×#121—22no—
34C4×Q8×C13—22no—
35C4×D4×C13—22no—
36C4×D4×C13—22no—
37C13×#117—21no—
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40C13×#106—22no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×#103—24no—
44C13×#102—24no—
45C13×#102—24no—
46C13×C22⋊C8D414yes—
47C13×#97—22no—
48C13×#95—22no—
49#10213C1311yesmaximal, characteristic, direct product factor, Sylow
50C13×#41—84no—
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—42no—
57C22×C4×C13—41no—
58C22×C4×C13—42no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D412yes—
61C13×Q16—84no—
62C13×SD16—84no—
63C13×D8—82no—
64C13×M16—42no—
65C2×C8×C13—24no—
66C2×C8×C13—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—42no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C42×C13—22no—
76C42×C13—41no—
77C42×C13—41no—
78C42×C13C2×D411yescharacteristic
79C42×C13C2×D412yes—
80C42×C13#4111yescharacteristic
81#3253C2×C1311yescharacteristic
82#3216C2×C1312yescomplemented
83#1995C2×C1311yescharacteristic, complemented
84#1505C2×C1312yescomplemented
85#1307C2×C1311yescharacteristic, complemented
86C23×C13—42no—
87C23×C13#12711yescharacteristic
88Q8×C13—42no—
89Q8×C13—42no—
90Q8×C13—44no—
91D4×C13—44no—
92D4×C13—42no—
93D4×C13—42no—
94D4×C13—82no—
95D4×C13—84no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—84no—
103C2×C4×C13—82no—
104C2×C4×C13#12012yes—
105C2×C4×C13#12011yescharacteristic
106C2×C4×C13#12111yescharacteristic
107C2×C4×C13#12112yes—
108C8×C13—44no—
109C8×C13—42no—
110#533C22×C1311yescharacteristic
111#532C22×C1312yes—
112#497—22no—
113#489—22no—
114#476—22no—
115#469—22no—
116#462—22no—
117#460—22no—
118#459—22no—
119#452—24no—
120#432C22×C1312yes—
121#423C22×C1311yescharacteristic
122#376C22×C1311yescharacteristic
123#339—22no—
124#327—24no—
125C22×C13—21no—
126C22×C13—22no—
127C22×C13—82no—
128C22×C13—82no—
129C22×C13—82no—
130C22×C13#39211yescharacteristic
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—82no—
135C4×C13—82no—
136C4×C13—82no—
137C4×C13#45511yescharacteristic
138C4×C13#45611yescharacteristic
139C2×#41—22no—
140C2×Q16—24no—
141C2×SD16—24no—
142C2×D8—22no—
143C2×M16D4×C1312yes—
144C4⋊Q8D4×C1312yes—
145C4⋊Q8D4×C1312yes—
146#127D4×C1312yes—
147#125—21no—
148#124—22no—
149C22⋊Q8—22no—
150#121—22no—
151#121—22no—
152C4×Q8—22no—
153C4×D4—22no—
154C4×D4—22no—
155#117—21no—
156C2×C42—21no—
157C2×C42C23×C1311yescharacteristic
158#106—22no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161#103—24no—
162#102—24no—
163#102—24no—
164C22⋊C8D4×C1314yes—
165#97—22no—
166#95—22no—
167C2×C13—41no—
168C2×C13—162no—
169C2×C13#200711yescharacteristic
170C2×C13#200812yes—
171#41—84no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—42no—
178C22×C4—41no—
179C22×C4—42no—
180C22×C4C2×D4×C1311yescharacteristic
181C22×C4C2×D4×C1312yes—
182Q16—84no—
183SD16—84no—
184D8—82no—
185M16—42no—
186C2×C8—24no—
187C2×C8—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C22⋊C4—41no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C42—22no—
197C42—41no—
198C42—41no—
199C42C2×D4×C1311yescharacteristic
200C42C2×D4×C1312yes—
201C42C13×#4111yescharacteristic
202C13#1021311yescharacteristic, direct product factor, Sylow
203C23—42no—
204C23C13×#12711yescharacteristic
205Q8—42no—
206Q8—42no—
207Q8—44no—
208D4—44no—
209D4—42no—
210D4—42no—
211D4—82no—
212D4—84no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—84no—
220C2×C4—82no—
221C2×C4C13×#12012yes—
222C2×C4C13×#12011yescharacteristic
223C2×C4C13×#12111yescharacteristic
224C2×C4C13×#12112yes—
225C8—44no—
226C8—42no—
227C22—21no—
228C22—22no—
229C22—82no—
230C22—82no—
231C22—82no—
232C22C13×#39211yescharacteristic
233C4—21no—
234C4—22no—
235C4—22no—
236C4—82no—
237C4—82no—
238C4—82no—
239C4C13×#45511yescharacteristic
240C4C13×#45611yescharacteristic
241C2—41no—
242C2—162no—
243C2C13×#200711yescharacteristic
244C2C13×#200812yes—
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3253C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3216C2semidirect
3. C13×#1995C2semidirect
4. C13×#1505C2semidirect
5. C13×#1307C2semidirect
49. #10213C13direct (N × H)
82. #3216C2×C13semidirect
83. #1995C2×C13semidirect
84. #1505C2×C13semidirect
85. #1307C2×C13semidirect
202. C13#10213direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32532
C13×#32162
C13×#19952
C13×#15052
C13×#13072
#1021313