Finite Group Databasebeta

← C13×#11846 #15698185

Subgroups — C13×#11846 #15698185

Order 3328.

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

normal subgroups only

This group has 382 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×#2611C211yesmaximal, characteristic
2C13×#1820C211yesmaximal, characteristic
3C13×#1458C211yesmaximal, characteristic
4C13×#1352C212yesmaximal
5C13×#1344C212yesmaximal
6C2×C13×#125C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C13×#431—21no—
9C13×#400C411yescharacteristic, complemented
10C13×#399C2211yescharacteristic
11C13×#398C411yescharacteristic, complemented
12C13×#397C2211yescharacteristic
13C13×#389—21no—
14C13×#388—21no—
15C13×#387—21no—
16C13×#385—21no—
17C13×#381—21no—
18C13×#376C411yescharacteristic, complemented
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#324—21no—
22C13×#323C2212yes—
23C23×C4×C13D411yescharacteristic
24C13×#125—41no—
25C13×#125—41no—
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4C2311yescharacteristic
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C4×C8×C13—41no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—41no—
53C13×#95—41no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56#11846C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—42no—
94#2611C2×C1311yescharacteristic
95#1820C2×C1311yescharacteristic
96#1458C2×C1311yescharacteristic
97#1352C2×C1312yes—
98#1344C2×C1312yes—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#13512yes—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—82no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137C8×C13—82no—
138C2×#125C4×C1311yescharacteristic, complemented
139C2×#117C22×C1311yescharacteristic
140#431—21no—
141#400C4×C1311yescharacteristic, complemented
142#399C22×C1311yescharacteristic
143#398C4×C1311yescharacteristic, complemented
144#397C22×C1311yescharacteristic
145#389—21no—
146#388—21no—
147#387—21no—
148#385—21no—
149#381—21no—
150#376C4×C1311yescharacteristic, complemented
151#342—21no—
152#342C22×C1312yes—
153#324—21no—
154#323C22×C1312yes—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—22no—
158C22×C13—42no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—81no—
162C22×C13C2×#9911yescharacteristic
163C22×C13#41611yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—42no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—81no—
174C4×C13—81no—
175C4×C13—81no—
176C4×C13—162no—
177C23×C4D4×C1311yescharacteristic
178#125—41no—
179#125—41no—
180#117—41no—
181#117—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×C4×C1311yescharacteristic
187C2×C4⋊C4C2×C4×C1311yescharacteristic
188C2×C4⋊C4C2×C4×C1311yescharacteristic
189C2×C4⋊C4D4×C1311yescharacteristic
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4D4×C1311yescharacteristic
194C2×C22⋊C4C23×C1311yescharacteristic
195C2×C42—21no—
196C2×C42C2×C4×C1311yescharacteristic
197C2×C42D4×C1311yescharacteristic
198C4⋊C8—41no—
199C22⋊C8—22no—
200C4×C8—41no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—41no—
207#95—41no—
208#95C2×C4×C1311yescharacteristic
209#95C2×C4×C1311yescharacteristic
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—42no—
213C2×C13#151611yescharacteristic
214C2×C13#212311yescharacteristic
215C2×C13#212611yescharacteristic
216C24C2×D4×C1311yescharacteristic
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4C13×C22⋊C411yescharacteristic
227C22×C4C13×C22⋊C411yescharacteristic
228C22×C4C13×C22⋊C411yescharacteristic
229C22×C4C13×C22⋊C411yescharacteristic
230C22×C4C22×C4×C1311yescharacteristic
231C22×C4C2×D4×C1311yescharacteristic
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—42no—
253C13#1184611yescharacteristic, direct product factor, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C13×C22⋊C411yescharacteristic
259C23C13×#13512yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C13×#9911yescharacteristic
291C2×C4C13×#9911yescharacteristic
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×C13×#9911yescharacteristic
301C22C13×#41611yescharacteristic
302C22C13×#42111yescharacteristic
303C4—21no—
304C4—21no—
305C4—42no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—162no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2C13×#151611yescharacteristic
319C2C13×#212311yescharacteristic
320C2C13×#212611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
9. C13×#400C4semidirect
11. C13×#398C4semidirect
18. C13×#376C4semidirect
56. #11846C13direct (N × H)
138. C2×#125C4×C13semidirect
141. #400C4×C13semidirect
143. #398C4×C13semidirect
150. #376C4×C13semidirect
253. C13#11846direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26112
C13×#18202
C13×#14582
C13×#13522
C13×#13442
#1184613