Finite Group Databasebeta

← C13×#11800 #15698139

Subgroups — C13×#11800 #15698139

Order 3328.

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

normal subgroups only

This group has 502 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×#2619C211yesmaximal, characteristic
2C13×#1820C211yesmaximal, characteristic, complemented
3C13×#1464C211yesmaximal, characteristic, complemented
4C13×#1343C214yesmaximal, complemented
5C2×C13×#127C411yescharacteristic, complemented
6C2×C13×#121—21no—
7C2×C13×#117C2211yescharacteristic
8C13×#432—21no—
9C13×#394—21no—
10C13×#394C412yescomplemented
11C13×#392—21no—
12C13×#392C2212yes—
13C13×#390—21no—
14C13×#382C411yescharacteristic, complemented
15C13×#381—21no—
16C13×#342—21no—
17C13×#342C2212yes—
18C13×#324—21no—
19C13×#323C2212yes—
20C22×D4×C13—22no—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C23×C4×C13D411yescharacteristic
25C13×#127—41no—
26C13×#127—41no—
27C13×#121—44no—
28C13×#117—41no—
29C13×#117—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
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⋊C4D411yescharacteristic
38C2×C13×C22⋊C4C2311yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C13×#97—41no—
44C13×#95—21no—
45C13×#95—41no—
46C13×#95—41no—
47C13×#95C2×C412yes—
48#11800C1311yesmaximal, characteristic, direct product factor, Sylow
49C24×C13—22no—
50C24×C13C2×D411yescharacteristic
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C2×D4×C13—42no—
55C2×D4×C13—44no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—82no—
59C2×D4×C13—82no—
60C2×D4×C13—82no—
61C2×D4×C13—82no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13—42no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—82no—
84C13×C22⋊C4—82no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89#2619C2×C1311yescharacteristic
90#1820C2×C1311yescharacteristic, complemented
91#1464C2×C1311yescharacteristic, complemented
92#1343C2×C1314yescomplemented
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13AGL(1,ℤ/8)12yes—
106D4×C13—82no—
107D4×C13—82no—
108D4×C13—84no—
109D4×C13—84no—
110D4×C13—88no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13—82no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C8×C13—82no—
135C2×#127C4×C1311yescharacteristic, complemented
136C2×#121—21no—
137C2×#117C22×C1311yescharacteristic
138#432—21no—
139#394—21no—
140#394C4×C1312yescomplemented
141#392—21no—
142#392C22×C1312yes—
143#390—21no—
144#382C4×C1311yescharacteristic, complemented
145#381—21no—
146#342—21no—
147#342C22×C1312yes—
148#324—21no—
149#323C22×C1312yes—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—81no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13—82no—
160C22×C13—82no—
161C22×C13—82no—
162C22×C13—82no—
163C22×C13—82no—
164C22×C13C2×#9911yescharacteristic
165C22×C13#41811yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—82no—
175C4×C13—162no—
176C22×D4—22no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4C2×C4×C1312yes—
180C23×C4D4×C1311yescharacteristic
181#127—41no—
182#127—41no—
183#121—44no—
184#117—41no—
185#117—41no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×C4×C1311yescharacteristic
188C2×C4⋊C4D4×C1311yescharacteristic
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4D4×C1311yescharacteristic
194C2×C22⋊C4C23×C1311yescharacteristic
195C2×C42C2×C4×C1311yescharacteristic
196C2×C42D4×C1311yescharacteristic
197C4⋊C8—41no—
198C22⋊C8—22no—
199#97—41no—
200#95—21no—
201#95—41no—
202#95—41no—
203#95C2×C4×C1312yes—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—42no—
207C2×C13—162no—
208C2×C13#151011yescharacteristic
209C2×C13#212211yescharacteristic
210C2×C13#212811yescharacteristic
211C24—22no—
212C24C2×D4×C1311yescharacteristic
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—44no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—82no—
221C2×D4—82no—
222C2×D4—82no—
223C2×D4—82no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4C13×C22⋊C411yescharacteristic
231C22×C4C13×C22⋊C411yescharacteristic
232C22×C4C13×C22⋊C411yescharacteristic
233C22×C4C13×C22⋊C411yescharacteristic
234C22×C4C22×C4×C1311yescharacteristic
235C22×C4C2×D4×C1311yescharacteristic
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—82no—
246C22⋊C4—82no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C13#1180011yescharacteristic, direct product factor, Sylow
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23C2×C13×C22⋊C411yescharacteristic
264C23C13×AGL(1,ℤ/8)12yes—
265D4—82no—
266D4—82no—
267D4—84no—
268D4—84no—
269D4—88no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4C13×#9911yescharacteristic
292C2×C4C13×#9911yescharacteristic
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—81no—
301C22—82no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22—82no—
306C22—82no—
307C22—82no—
308C22C2×C13×#9911yescharacteristic
309C22C13×#41811yescharacteristic
310C22C13×#42111yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—82no—
319C4—162no—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—162no—
324C2C13×#151011yescharacteristic
325C2C13×#212211yescharacteristic
326C2C13×#212811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2619C2
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
2. C13×#1820C2semidirect
3. C13×#1464C2semidirect
4. C13×#1343C2semidirect
5. C2×C13×#127C4semidirect
10. C13×#394C4semidirect
14. C13×#382C4semidirect
48. #11800C13direct (N × H)
90. #1820C2×C13semidirect
91. #1464C2×C13semidirect
92. #1343C2×C13semidirect
135. C2×#127C4×C13semidirect
140. #394C4×C13semidirect
144. #382C4×C13semidirect
251. C13#11800direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26192
C13×#18202
C13×#14642
C13×#13432
#1180013