Finite Group Databasebeta

← C13×#10014 #15696353

Subgroups — C13×#10014 #15696353

Order 3328.

566 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3103C212yesmaximal
2C13×#2399C211yesmaximal, characteristic, complemented
3C13×#1963C211yesmaximal, characteristic
4C13×#1487C212yesmaximal, complemented
5C13×#1274C211yesmaximal, characteristic, complemented
6C13×#532C2211yescharacteristic
7C2×C4×Q8×C13C2212yes—
8C13×#481—22no—
9C13×#475—22no—
10C13×#460—22no—
11C13×#448—22no—
12C4×C13×SD16—24no—
13C13×#431C2212yes—
14C13×#423C2211yescharacteristic
15C2×C13×#104—22no—
16C13×#398—22no—
17C13×#395—22no—
18C4×C13×C4⋊C4—22no—
19C13×#376C2211yescharacteristic
20C13×Q8⋊C8—24no—
21C2×C13×#41—21no—
22C22×Q8×C13D412yes—
23C2×C13×SD16—24no—
24C2×C13×M16—21no—
25C13×C4⋊Q8D411yescharacteristic
26C13×#127D411yescharacteristic
27C13×#124—21no—
28C13×#121—22no—
29C4×Q8×C13—22no—
30C4×Q8×C13—22no—
31C4×Q8×C13—22no—
32C4×Q8×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4—24no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4D412yes—
37C2×C42×C13—22no—
38C2×C42×C13D412yes—
39C2×C42×C13C2311yescharacteristic
40C13×#106—24no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×#104—44no—
44C13×#103—24no—
45C13×#102—24no—
46C13×C22⋊C8—22no—
47C4×C8×C13D414yes—
48C13×#95—22no—
49C13×#95—22no—
50C13×#95—22no—
51#10014C1311yesmaximal, characteristic, direct product factor, Sylow
52C13×#41—42no—
53C13×#41—42no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13—21no—
57C2×Q8×C13—44no—
58C2×D4×C13—22no—
59C2×D4×C13—21no—
60C2×D4×C13—41no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—41no—
65C22×C4×C13C2×D412yes—
66C22×C4×C13C2×D411yescharacteristic
67C13×SD16—48no—
68C13×M16—42no—
69C2×C8×C13—24no—
70C2×C8×C13—41no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—48no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C22⋊C4—42no—
78C42×C13—22no—
79C42×C13—42no—
80C42×C13—42no—
81C42×C13SD1614yescomplemented
82C42×C13C2×D411yescharacteristic
83C42×C13C2×D412yes—
84C42×C13#4111yescharacteristic
85#3103C2×C1312yes—
86#2399C2×C1311yescharacteristic, complemented
87#1963C2×C1311yescharacteristic
88#1487C2×C1312yescomplemented
89#1274C2×C1311yescharacteristic, complemented
90C23×C13—41no—
91C23×C13#12011yescharacteristic
92Q8×C13—24no—
93Q8×C13—24no—
94Q8×C13—42no—
95Q8×C13—42no—
96Q8×C13—42no—
97D4×C13—44no—
98D4×C13—42no—
99D4×C13—82no—
100C2×C4×C13—24no—
101C2×C4×C13—24no—
102C2×C4×C13—42no—
103C2×C4×C13—44no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—44no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—81no—
110C2×C4×C13—81no—
111C2×C4×C13#12012yes—
112C2×C4×C13#12112yes—
113C2×C4×C13#12111yescharacteristic
114C2×C4×C13#12711yescharacteristic
115C2×C4×C13C2×SD1612yes—
116C2×C4×C13#13712yes—
117C8×C13—44no—
118C8×C13—81no—
119#532C22×C1311yescharacteristic
120C2×C4×Q8C22×C1312yes—
121#481—22no—
122#475—22no—
123#460—22no—
124#448—22no—
125C4×SD16—24no—
126#431C22×C1312yes—
127#423C22×C1311yescharacteristic
128C2×#104—22no—
129#398—22no—
130#395—22no—
131C4×C4⋊C4—22no—
132#376C22×C1311yescharacteristic
133Q8⋊C8—24no—
134C22×C13—22no—
135C22×C13—82no—
136C22×C13—81no—
137C22×C13#39211yescharacteristic
138C22×C13#44812yes—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—44no—
142C4×C13—44no—
143C4×C13—82no—
144C4×C13—81no—
145C4×C13#46112yes—
146C4×C13#49211yescharacteristic
147C4×C13#49711yescharacteristic
148C2×#41—21no—
149C22×Q8D4×C1312yes—
150C2×SD16—24no—
151C2×M16—21no—
152C4⋊Q8D4×C1311yescharacteristic
153#127D4×C1311yescharacteristic
154#124—21no—
155#121—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×D4—22no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4D4×C1312yes—
164C2×C42—22no—
165C2×C42D4×C1312yes—
166C2×C42C23×C1311yescharacteristic
167#106—24no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170#104—44no—
171#103—24no—
172#102—24no—
173C22⋊C8—22no—
174C4×C8D4×C1314yes—
175#95—22no—
176#95—22no—
177#95—22no—
178C2×C13—22no—
179C2×C13—161no—
180C2×C13#201012yes—
181C2×C13#201311yescharacteristic
182#41—42no—
183#41—42no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—21no—
187C2×Q8—44no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—41no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—41no—
195C22×C4C2×D4×C1312yes—
196C22×C4C2×D4×C1311yescharacteristic
197SD16—48no—
198M16—42no—
199C2×C8—24no—
200C2×C8—41no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—48no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C22⋊C4—42no—
208C42—22no—
209C42—42no—
210C42—42no—
211C42C13×SD1614yescomplemented
212C42C2×D4×C1311yescharacteristic
213C42C2×D4×C1312yes—
214C42C13×#4111yescharacteristic
215C13#1001411yescharacteristic, direct product factor, Sylow
216C23—41no—
217C23C13×#12011yescharacteristic
218Q8—24no—
219Q8—24no—
220Q8—42no—
221Q8—42no—
222Q8—42no—
223D4—44no—
224D4—42no—
225D4—82no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4C13×#12012yes—
238C2×C4C13×#12112yes—
239C2×C4C13×#12111yescharacteristic
240C2×C4C13×#12711yescharacteristic
241C2×C4C2×C13×SD1612yes—
242C2×C4C13×#13712yes—
243C8—44no—
244C8—81no—
245C22—22no—
246C22—82no—
247C22—81no—
248C22C13×#39211yescharacteristic
249C22C13×#44812yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—44no—
254C4—82no—
255C4—81no—
256C4C13×#46112yes—
257C4C13×#49211yescharacteristic
258C4C13×#49711yescharacteristic
259C2—22no—
260C2—161no—
261C2C13×#201012yes—
262C2C13×#201311yescharacteristic
subgroupG/H
centerC2×C4×C13#127
commutator, Frattini, cosocleC2×C42C23×C13
socleC22×C13#392
prime radicalC13×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2399C2semidirect
4. C13×#1487C2semidirect
5. C13×#1274C2semidirect
51. #10014C13direct (N × H)
81. C42×C13SD16semidirect
86. #2399C2×C13semidirect
88. #1487C2×C13semidirect
89. #1274C2×C13semidirect
211. C42C13×SD16semidirect
215. C13#10014direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31032
C13×#23992
C13×#19632
C13×#14872
C13×#12742
#1001413