Finite Group Databasebeta

← C13×#9483 #15695822

Subgroups — C13×#9483 #15695822

Order 3328.

542 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 150 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×#2972C211yesmaximal, characteristic
2C13×#2580C211yesmaximal, characteristic
3C13×#1800C211yesmaximal, characteristic
4C13×#1487C212yesmaximal, complemented
5C13×#1286C212yesmaximal, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C8×D4×C13—24no—
9C13×#431C2212yes—
10C13×#423C2212yes—
11C2×C13×#100—21no—
12C2×C13×C22⋊C8—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—22no—
25C22×C8×C13—24no—
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#9483C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C22⋊C412yes—
52C2×Q8×C13—22no—
53C2×Q8×C13—42no—
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13SD1612yes—
57C2×D4×C13Q1612yes—
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—
70C2×C8×C13—24no—
71C2×C8×C13—42no—
72C2×C8×C13—84no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—82no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—82no—
82C42×C13—42no—
83C42×C13C2×D412yes—
84C42×C13#4112yes—
85#2972C2×C1311yescharacteristic
86#2580C2×C1311yescharacteristic
87#1800C2×C1311yescharacteristic
88#1487C2×C1312yescomplemented
89#1286C2×C1312yescomplemented
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13#10314yes—
95C23×C13C2×C22⋊C411yescharacteristic
96Q8×C13—24no—
97Q8×C13—42no—
98D4×C13—24no—
99D4×C13—24no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—44no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—82no—
115C2×C4×C13C4×D412yes—
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12112yes—
118C2×C4×C13#12311yescharacteristic
119C2×C4×C13C2×SD1611yescharacteristic
120C2×C4×C13C2×Q1611yescharacteristic
121C2×C4×C13#13512yes—
122C8×C13—44no—
123C8×C13—82no—
124C2×C4×Q8C22×C1311yescharacteristic
125C2×C4×D4C22×C1311yescharacteristic
126C8×D4—24no—
127#431C22×C1312yes—
128#423C22×C1312yes—
129C2×#100—21no—
130C2×C22⋊C8—22no—
131#399C4×C1312yes—
132#393C4×C1312yes—
133#390—21no—
134#389—21no—
135#385—22no—
136#382C22×C1311yescharacteristic
137#343—21no—
138Q8⋊C8—24no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—24no—
142C22×C13—44no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—82no—
146C22×C13#38611yescharacteristic
147C22×C13C2×#10311yescharacteristic
148C22×C13#41611yescharacteristic
149C4×C13—22no—
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—42no—
153C4×C13—42no—
154C4×C13—82no—
155C4×C13—81no—
156C4×C13#46512yes—
157C4×C13#46712yes—
158C22×Q8C2×C4×C1311yescharacteristic
159C22×D4D4×C1311yescharacteristic
160C23×C4D4×C1312yes—
161C2×M16—22no—
162C22×C8—24no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—22no—
166C4×D4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C2×C4×C1311yescharacteristic
171C2×C4⋊C4D4×C1311yescharacteristic
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4C2×C4×C1312yes—
175C2×C42—21no—
176C2×C42C23×C1311yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180#100—42no—
181C22⋊C8—24no—
182C22⋊C8—22no—
183C4×C8D4×C1314yes—
184#95—22no—
185#95—21no—
186#95C2×C4×C1312yes—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13—44no—
190C2×C13#189111yescharacteristic
191C2×C13#189211yescharacteristic
192C2×C13#191111yescharacteristic
193C24C13×C22⋊C412yes—
194C2×Q8—22no—
195C2×Q8—42no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4C13×SD1612yes—
199C2×D4C13×Q1612yes—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—82no—
206C22×C4C13×C22⋊C412yes—
207C22×C4C22×C4×C1311yescharacteristic
208C22×C4C2×D4×C1311yescharacteristic
209C22×C4C2×D4×C1311yescharacteristic
210M16—42no—
211M16—42no—
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—84no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—82no—
221C22⋊C4—24no—
222C22⋊C4—44no—
223C22⋊C4—82no—
224C42—42no—
225C42C2×D4×C1312yes—
226C42C13×#4112yes—
227C13#948311yescharacteristic, direct product factor, Sylow
228C23—22no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23C13×#10314yes—
233C23C2×C13×C22⋊C411yescharacteristic
234Q8—24no—
235Q8—42no—
236D4—24no—
237D4—24no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—44no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4C4×D4×C1312yes—
254C2×C4C13×#12011yescharacteristic
255C2×C4C13×#12112yes—
256C2×C4C13×#12311yescharacteristic
257C2×C4C2×C13×SD1611yescharacteristic
258C2×C4C2×C13×Q1611yescharacteristic
259C2×C4C13×#13512yes—
260C8—44no—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22C13×#38611yescharacteristic
270C22C2×C13×#10311yescharacteristic
271C22C13×#41611yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—42no—
277C4—82no—
278C4—81no—
279C4C13×#46512yes—
280C4C13×#46712yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2C13×#189111yescharacteristic
285C2C13×#189211yescharacteristic
286C2C13×#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. #9483C13direct (N × H)
88. #1487C2×C13semidirect
89. #1286C2×C13semidirect
227. C13#9483direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29722
C13×#25802
C13×#18002
C13×#14872
C13×#12862
#948313