Finite Group Databasebeta

← C13×#13461 #15699800

Subgroups — C13×#13461 #15699800

Order 3328.

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

normal subgroups only

This group has 540 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×#2683C211yesmaximal, characteristic
2C13×#1867C212yesmaximal
3C13×#1856C211yesmaximal, characteristic
4C13×#1393C211yesmaximal, characteristic
5C13×#1390C212yesmaximal
6C2×C13×C22⋊Q8—22no—
7C13×#518C2211yescharacteristic
8C13×#428—21no—
9C2×C13×#100C2211yescharacteristic
10C2×C13×#99C2212yes—
11C13×#396—22no—
12C13×#395—21no—
13C13×#390C2211yescharacteristic
14C13×#389—21no—
15C13×#386C2212yes—
16C13×#385—22no—
17C13×#342—22no—
18C13×#339—21no—
19C22×Q8×C13—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13D412yes—
22C2×C13×M16—21no—
23C13×C22⋊Q8—48no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C13×#117—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—42no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4D412yes—
38C2×C42×C13D411yescharacteristic
39C13×#107—41no—
40C13×#106—41no—
41C13×#100—21no—
42C13×#100Q812yescomplemented
43C13×#99—22no—
44C13×#99Q814yescomplemented
45C13×#95—21no—
46C13×#95—22no—
47C13×#95—42no—
48#13461C1311yesmaximal, characteristic, direct product factor, Sylow
49C24×C13C2×D412yes—
50C2×Q8×C13—44no—
51C2×Q8×C13—81no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C2×Q811yescharacteristic
55C2×D4×C13C2×Q812yes—
56C2×D4×C13#4111yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—44no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C2×D411yescharacteristic
67C13×M16—22no—
68C13×M16—41no—
69C2×C8×C13—41no—
70C13×C4⋊C4—24no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—44no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—81no—
77C13×C4⋊C4—84no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—44no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C42×C13—41no—
86C42×C13—41no—
87#2683C2×C1311yescharacteristic
88#1867C2×C1312yes—
89#1856C2×C1311yescharacteristic
90#1393C2×C1311yescharacteristic
91#1390C2×C1312yes—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13#12011yescharacteristic
97C23×C13C22⋊Q812yes—
98C23×C13C4⋊Q812yes—
99Q8×C13—84no—
100D4×C13—41no—
101D4×C13—42no—
102D4×C13—41no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—24no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—44no—
112C2×C4×C13—44no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—82no—
121C2×C4×C13—82no—
122C2×C4×C13—82no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13C22⋊Q811yescharacteristic
126C2×C4×C13C4⋊Q811yescharacteristic
127C8×C13—42no—
128C2×C22⋊Q8—22no—
129#518C22×C1311yescharacteristic
130#428—21no—
131C2×#100C22×C1311yescharacteristic
132C2×#99C22×C1312yes—
133#396—22no—
134#395—21no—
135#390C22×C1311yescharacteristic
136#389—21no—
137#386C22×C1312yes—
138#385—22no—
139#342—22no—
140#339—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—82no—
150C22×C13#39511yescharacteristic
151C22×C13B(4,𝔽2)11yescharacteristic
152C22×C13#45811yescharacteristic
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—42no—
156C4×C13—44no—
157C4×C13—82no—
158C4×C13—84no—
159C4×C13—81no—
160C4×C13—81no—
161C4×C13—81no—
162C22×Q8—21no—
163C22×D4C23×C1311yescharacteristic
164C23×C4D4×C1312yes—
165C2×M16—21no—
166C22⋊Q8—48no—
167C4×D4—41no—
168C4×D4—41no—
169#117—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4D4×C1311yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4D4×C1312yes—
181C2×C42D4×C1311yescharacteristic
182#107—41no—
183#106—41no—
184#100—21no—
185#100Q8×C1312yescomplemented
186#99—22no—
187#99Q8×C1314yescomplemented
188#95—21no—
189#95—22no—
190#95—42no—
191C2×C13—21no—
192C2×C13—21no—
193C2×C13—42no—
194C2×C13—42no—
195C2×C13#206211yescharacteristic
196C2×C13#219611yescharacteristic
197C2×C13#220111yescharacteristic
198C24C2×D4×C1312yes—
199C2×Q8—44no—
200C2×Q8—81no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4C2×Q8×C1311yescharacteristic
204C2×D4C2×Q8×C1312yes—
205C2×D4C13×#4111yescharacteristic
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—44no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4C2×D4×C1311yescharacteristic
216M16—22no—
217M16—41no—
218C2×C8—41no—
219C4⋊C4—24no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—44no—
224C4⋊C4—44no—
225C4⋊C4—81no—
226C4⋊C4—84no—
227C22⋊C4—24no—
228C22⋊C4—44no—
229C22⋊C4—44no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C42—41no—
235C42—41no—
236C13#1346111yescharacteristic, direct product factor, Sylow
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23C13×#12011yescharacteristic
242C23C13×C22⋊Q812yes—
243C23C13×C4⋊Q812yes—
244Q8—84no—
245D4—41no—
246D4—42no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4C13×C22⋊Q811yescharacteristic
271C2×C4C13×C4⋊Q811yescharacteristic
272C8—42no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22C13×#39511yescharacteristic
283C22C13×B(4,𝔽2)11yescharacteristic
284C22C13×#45811yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—44no—
289C4—82no—
290C4—84no—
291C4—81no—
292C4—81no—
293C4—81no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2C13×#206211yescharacteristic
299C2C13×#219611yescharacteristic
300C2C13×#220111yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
42. C13×#100Q8semidirect
44. C13×#99Q8semidirect
48. #13461C13direct (N × H)
185. #100Q8×C13semidirect
187. #99Q8×C13semidirect
236. C13#13461direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26832
C13×#18672
C13×#18562
C13×#13932
C13×#13902
#1346113