Finite Group Databasebeta

← C13×#9206 #15695545

Subgroups — C13×#9206 #15695545

Order 3328.

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

normal subgroups only

This group has 578 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×#2618C211yesmaximal, characteristic
2C13×#2313C211yesmaximal, characteristic, complemented
3C13×#1519C212yesmaximal
4C2×C13×#324C211yesmaximal, characteristic, complemented
5C13×#1289C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10C13×#398C412yescomplemented
11C13×#396—22no—
12C13×#394C412yescomplemented
13C13×#387—24no—
14C13×#386—21no—
15C13×#381—21no—
16C13×#380C2211yescharacteristic
17C13×#380C2212yes—
18C4×C13×C22⋊C4—21no—
19C13×#327—24no—
20C13×#324—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C22×C8×C13—22no—
27C13×#123—44no—
28C13×#121—22no—
29C13×#121—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C412yes—
37C2×C13×C4⋊C4D412yes—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—22no—
43C2×C42×C13—22no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46C13×#95—22no—
47C13×#95—24no—
48C13×#95—22no—
49C13×#95C2×C412yes—
50C13×#95D414yes—
51#9206C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C24×C13C2×D411yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—81no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—24no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4112yes—
77C2×C8×C13—42no—
78C2×C8×C13—82no—
79C13×C4⋊C4—24no—
80C13×C4⋊C4—24no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—44no—
83C13×C4⋊C4—82no—
84C13×C4⋊C4—81no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—82no—
91C42×C13—82no—
92#2618C2×C1311yescharacteristic
93#2313C2×C1311yescharacteristic, complemented
94#1519C2×C1312yes—
95C2×#324C2×C1311yescharacteristic, complemented
96#1289C2×C1312yescomplemented
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13#12011yescharacteristic
106C23×C13#12311yescharacteristic
107C23×C13#13512yes—
108C23×C13AGL(1,ℤ/8)12yes—
109D4×C13—82no—
110D4×C13—82no—
111D4×C13—82no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—44no—
125C2×C4×C13—42no—
126C2×C4×C13—44no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—44no—
133C2×C4×C13—81no—
134C2×C4×C13C4×D412yes—
135C2×C4×C13#12112yes—
136C8×C13—82no—
137C2×#123—21no—
138C2×#121C22×C1311yescharacteristic
139C22×C4⋊C4C22×C1311yescharacteristic
140C2×C22⋊C8C22×C1312yes—
141#398C4×C1312yescomplemented
142#396—22no—
143#394C4×C1312yescomplemented
144#387—24no—
145#386—21no—
146#381—21no—
147#380C22×C1311yescharacteristic
148#380C22×C1312yes—
149C4×C22⋊C4—21no—
150#327—24no—
151#324—22no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—82no—
161C22×C13—82no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13#38611yescharacteristic
166C22×C13#41611yescharacteristic
167C22×C13#41811yescharacteristic
168C22×C13#44912yes—
169C22×C13#48212yes—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—42no—
173C4×C13—42no—
174C4×C13—82no—
175C4×C13—84no—
176C4×C13—81no—
177C22×D4—21no—
178C22×D4C2×C4×C1311yescharacteristic
179C23×C4D4×C1311yescharacteristic
180C23×C4D4×C1311yescharacteristic
181C23×C4C23×C1311yescharacteristic
182C22×C8—22no—
183#123—44no—
184#121—22no—
185#121—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×C4×C1311yescharacteristic
192C2×C4⋊C4C2×C4×C1312yes—
193C2×C4⋊C4D4×C1312yes—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—22no—
199C2×C42—22no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202#95—22no—
203#95—24no—
204#95—22no—
205#95C2×C4×C1312yes—
206#95D4×C1314yes—
207C2×C13—21no—
208C2×C13—22no—
209C2×C13—21no—
210C2×C13—22no—
211C2×C13—161no—
212C2×C13#187511yescharacteristic
213C2×C13#191211yescharacteristic
214C2×C13#191311yescharacteristic
215C24—21no—
216C24C2×D4×C1311yescharacteristic
217C2×D4—22no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—81no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4C13×C22⋊C412yes—
235C22×C4C13×C22⋊C412yes—
236C22×C4C22×C4×C1311yescharacteristic
237C22×C4C2×D4×C1312yes—
238C22×C4C2×D4×C1311yescharacteristic
239C22×C4C13×#4112yes—
240C2×C8—42no—
241C2×C8—82no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—22no—
245C4⋊C4—44no—
246C4⋊C4—82no—
247C4⋊C4—81no—
248C22⋊C4—44no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—82no—
254C42—82no—
255C13#920611yescharacteristic, direct product factor, Sylow
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×C13×C22⋊C411yescharacteristic
264C23C13×#12011yescharacteristic
265C23C13×#12311yescharacteristic
266C23C13×#13512yes—
267C23C13×AGL(1,ℤ/8)12yes—
268D4—82no—
269D4—82no—
270D4—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—81no—
293C2×C4C4×D4×C1312yes—
294C2×C4C13×#12112yes—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22C13×#38611yescharacteristic
310C22C13×#41611yescharacteristic
311C22C13×#41811yescharacteristic
312C22C13×#44912yes—
313C22C13×#48212yes—
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—82no—
319C4—84no—
320C4—81no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—161no—
326C2C13×#187511yescharacteristic
327C2C13×#191211yescharacteristic
328C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2313C2semidirect
4. C2×C13×#324C2semidirect
5. C13×#1289C2semidirect
10. C13×#398C4semidirect
12. C13×#394C4semidirect
51. #9206C13direct (N × H)
93. #2313C2×C13semidirect
95. C2×#324C2×C13semidirect
96. #1289C2×C13semidirect
141. #398C4×C13semidirect
143. #394C4×C13semidirect
255. C13#9206direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26182
C13×#23132
C13×#15192
C2×C13×#3242
C13×#12892
#920613