Finite Group Databasebeta

← C13×#9487 #15695826

Subgroups — C13×#9487 #15695826

Order 3328.

518 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2975C211yesmaximal, characteristic
2C13×#2580C211yesmaximal, characteristic
3C13×#1800C211yesmaximal, characteristic
4C13×#1487C212yesmaximal, complemented
5C13×#1286C212yesmaximal, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#436—24no—
9C13×#431C2212yes—
10C13×#423C2212yes—
11C2×C13×#100—21no—
12C13×#407—22no—
13C13×#399C412yes—
14C13×#393C412yes—
15C13×#390—21no—
16C13×#389—21no—
17C13×#385—22no—
18C13×#382C2211yescharacteristic
19C13×#343—21no—
20C13×Q8⋊C8—24no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×D4×C13D411yescharacteristic
23C23×C4×C13D412yes—
24C2×C13×M16—24no—
25C2×C13×M16—22no—
26C4×Q8×C13—22no—
27C4×Q8×C13—22no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C412yes—
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40C13×C4⋊C8—22no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×#100—42no—
44C13×C22⋊C8—24no—
45C13×C22⋊C8—22no—
46C4×C8×C13D414yes—
47C13×#95—22no—
48C13×#95—21no—
49C13×#95C2×C412yes—
50#9487C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C22⋊C412yes—
52C2×Q8×C13—22no—
53C2×Q8×C13—42no—
54C2×D4×C13—22no—
55C2×D4×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—82no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C13×M16—42no—
69C13×M16—42no—
70C13×M16—84no—
71C2×C8×C13—24no—
72C2×C8×C13—42no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—82no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—44no—
82C13×C22⋊C4—82no—
83C42×C13—42no—
84C42×C13C2×D412yes—
85C42×C13#4112yes—
86#2975C2×C1311yescharacteristic
87#2580C2×C1311yescharacteristic
88#1800C2×C1311yescharacteristic
89#1487C2×C1312yescomplemented
90#1286C2×C1312yescomplemented
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13C2×C22⋊C411yescharacteristic
97Q8×C13—24no—
98Q8×C13—42no—
99D4×C13—42no—
100D4×C13—42no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—44no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—82no—
116C2×C4×C13C4×D412yes—
117C2×C4×C13#12011yescharacteristic
118C2×C4×C13#12112yes—
119C2×C4×C13#12311yescharacteristic
120C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C13#13712yes—
122C2×C4×C13#13711yescharacteristic
123C8×C13—44no—
124C8×C13—82no—
125C2×C4×Q8C22×C1311yescharacteristic
126C2×C4×D4C22×C1311yescharacteristic
127#436—24no—
128#431C22×C1312yes—
129#423C22×C1312yes—
130C2×#100—21no—
131#407—22no—
132#399C4×C1312yes—
133#393C4×C1312yes—
134#390—21no—
135#389—21no—
136#385—22no—
137#382C22×C1311yescharacteristic
138#343—21no—
139Q8⋊C8—24no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—44no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—82no—
147C22×C13#38611yescharacteristic
148C22×C13#41711yescharacteristic
149C22×C13#41911yescharacteristic
150C4×C13—22no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—42no—
154C4×C13—42no—
155C4×C13—82no—
156C4×C13—81no—
157C4×C13#46812yes—
158C4×C13#47012yes—
159C22×Q8C2×C4×C1311yescharacteristic
160C22×D4D4×C1311yescharacteristic
161C23×C4D4×C1312yes—
162C2×M16—24no—
163C2×M16—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×D4—22no—
167C4×D4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×C4×C1311yescharacteristic
172C2×C4⋊C4D4×C1311yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4C2×C4×C1312yes—
176C2×C42—21no—
177C2×C42C23×C1311yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181#100—42no—
182C22⋊C8—24no—
183C22⋊C8—22no—
184C4×C8D4×C1314yes—
185#95—22no—
186#95—21no—
187#95C2×C4×C1312yes—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—82no—
191C2×C13#189111yescharacteristic
192C2×C13#189411yescharacteristic
193C2×C13#191111yescharacteristic
194C24C13×C22⋊C412yes—
195C2×Q8—22no—
196C2×Q8—42no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—82no—
207C22×C4C13×C22⋊C412yes—
208C22×C4C22×C4×C1311yescharacteristic
209C22×C4C2×D4×C1311yescharacteristic
210C22×C4C2×D4×C1311yescharacteristic
211M16—42no—
212M16—42no—
213M16—84no—
214C2×C8—24no—
215C2×C8—42no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—82no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—82no—
226C42—42no—
227C42C2×D4×C1312yes—
228C42C13×#4112yes—
229C13#948711yescharacteristic, direct product factor, Sylow
230C23—22no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—42no—
235C23C2×C13×C22⋊C411yescharacteristic
236Q8—24no—
237Q8—42no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—44no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—82no—
255C2×C4C4×D4×C1312yes—
256C2×C4C13×#12011yescharacteristic
257C2×C4C13×#12112yes—
258C2×C4C13×#12311yescharacteristic
259C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
260C2×C4C13×#13712yes—
261C2×C4C13×#13711yescharacteristic
262C8—44no—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22C13×#38611yescharacteristic
272C22C13×#41711yescharacteristic
273C22C13×#41911yescharacteristic
274C4—22no—
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—82no—
280C4—81no—
281C4C13×#46812yes—
282C4C13×#47012yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2C13×#189111yescharacteristic
287C2C13×#189411yescharacteristic
288C2C13×#191111yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1487C2semidirect
5. C13×#1286C2semidirect
50. #9487C13direct (N × H)
89. #1487C2×C13semidirect
90. #1286C2×C13semidirect
229. C13#9487direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29752
C13×#25802
C13×#18002
C13×#14872
C13×#12862
#948713