Finite Group Databasebeta

← C13×#13143 #15699482

Subgroups — C13×#13143 #15699482

Order 3328.

338 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#365C211yesmaximal, characteristic, complemented
2C2×C13×#360C211yesmaximal, characteristic
3C13×#2139C211yesmaximal, characteristic
4C13×#1975C211yesmaximal, characteristic
5C13×#1776C211yesmaximal, characteristic, complemented
6C13×#1387C211yesmaximal, characteristic, complemented
7C13×#1375C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C2×C13×M32C2211yescharacteristic
10C2×C13×M32C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×C13×#106C2211yescharacteristic
14C2×C13×#104—21no—
15C13×#408—21no—
16C2×C13×#97C2211yescharacteristic
17C4×C13×C4⋊C4—21no—
18C13×#365—22no—
19C13×#360—22no—
20C13×#358C412yescomplemented
21C13×#357C412yescomplemented
22C13×#340—21no—
23C2×C13×#41—21no—
24C13×#135—21no—
25C13×#135—21no—
26C13×#135—21no—
27C13×#135—21no—
28C2×C13×Q16C2×C411yescharacteristic
29C2×C13×SD16—21no—
30C2×C13×D8C2×C411yescharacteristic
31C2×C13×M16—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13C2311yescharacteristic
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13—41no—
37C2×C42×C13D411yescharacteristic
38C13×M32—21no—
39C13×M32—21no—
40C13×M32—21no—
41C13×M32—21no—
42C2×C13×C16—21no—
43C2×C13×C16C2×C412yes—
44C13×#108—21no—
45C13×#108—21no—
46C13×#107—21no—
47C13×#107C2×C412yes—
48C13×#106—21no—
49C13×#106D412yes—
50C13×#104—42no—
51C13×C22⋊C8—42no—
52C13×#97—21no—
53C13×#97—21no—
54C13×#95—41no—
55#13143C1311yesmaximal, characteristic, direct product factor, Sylow
56C13×#41—41no—
57C13×#41—41no—
58C13×#41—41no—
59C13×#41—41no—
60C2×Q8×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C22×C4×C13—21no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C2×D411yescharacteristic
68C13×Q16—21no—
69C13×Q16—21no—
70C13×SD16—41no—
71C13×SD16—41no—
72C13×D8—21no—
73C13×D8—21no—
74C13×M16—41no—
75C13×M16—41no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13—41no—
80C2×C8×C13C22×C411yescharacteristic
81C2×C8×C13C2×D411yescharacteristic
82C2×C8×C13#4111yescharacteristic
83C2×C8×C13#4111yescharacteristic
84C2×C8×C13#4111yescharacteristic
85C2×C8×C13#4111yescharacteristic
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C42×C13—21no—
91C42×C13—82no—
92C42×C13SD1612yes—
93C13×C16—22no—
94C13×C16—41no—
95C2×#365C2×C1311yescharacteristic, complemented
96C2×#360C2×C1311yescharacteristic
97#2139C2×C1311yescharacteristic
98#1975C2×C1311yescharacteristic
99#1776C2×C1311yescharacteristic, complemented
100#1387C2×C1311yescharacteristic, complemented
101#1375C2×C1311yescharacteristic, complemented
102C23×C13—41no—
103C23×C13AGL(1,ℤ/8)11yescharacteristic
104Q8×C13—41no—
105Q8×C13—41no—
106D4×C13—41no—
107D4×C13—41no—
108D4×C13—81no—
109D4×C13—81no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13C4×D411yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13C2×SD1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
128C8×C13—41no—
129C8×C13—81no—
130C8×C13#11711yescharacteristic
131C8×C13C4×D411yescharacteristic
132C8×C13#12411yescharacteristic
133C8×C13#12611yescharacteristic
134C2×#135C22×C1311yescharacteristic
135C2×M32C22×C1311yescharacteristic
136C2×M32C22×C1311yescharacteristic
137C2×#108C22×C1311yescharacteristic
138C2×#107C22×C1311yescharacteristic
139C2×#106C22×C1311yescharacteristic
140C2×#104—21no—
141#408—21no—
142C2×#97C22×C1311yescharacteristic
143C4×C4⋊C4—21no—
144#365—22no—
145#360—22no—
146#358C4×C1312yescomplemented
147#357C4×C1312yescomplemented
148#340—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—81no—
152C22×C13—81no—
153C22×C13—81no—
154C22×C13#44211yescharacteristic
155C22×C13#46311yescharacteristic
156C22×C13#48111yescharacteristic
157C4×C13—42no—
158C4×C13—82no—
159C4×C13—82no—
160C4×C13—81no—
161C4×C13#38811yescharacteristic
162C4×C13C4×SD1611yescharacteristic
163C4×C13#46011yescharacteristic
164C4×C13#48211yescharacteristic
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170C2×Q16C2×C4×C1311yescharacteristic
171C2×SD16—21no—
172C2×D8C2×C4×C1311yescharacteristic
173C2×M16—21no—
174C22×C8D4×C1311yescharacteristic
175C22×C8C23×C1311yescharacteristic
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C42—41no—
179C2×C42D4×C1311yescharacteristic
180M32—21no—
181M32—21no—
182M32—21no—
183M32—21no—
184C2×C16—21no—
185C2×C16C2×C4×C1312yes—
186#108—21no—
187#108—21no—
188#107—21no—
189#107C2×C4×C1312yes—
190#106—21no—
191#106D4×C1312yes—
192#104—42no—
193C22⋊C8—42no—
194#97—21no—
195#97—21no—
196#95—41no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—161no—
200C2×C13#192611yescharacteristic
201C2×C13#218011yescharacteristic
202C2×C13AGL(1,ℤ/16)11yescharacteristic
203#41—41no—
204#41—41no—
205#41—41no—
206#41—41no—
207C2×Q8—21no—
208C2×D4—21no—
209C2×D4—41no—
210C22×C4—21no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C2×D4×C1311yescharacteristic
215Q16—21no—
216Q16—21no—
217SD16—41no—
218SD16—41no—
219D8—21no—
220D8—21no—
221M16—41no—
222M16—41no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8C22×C4×C1311yescharacteristic
228C2×C8C2×D4×C1311yescharacteristic
229C2×C8C13×#4111yescharacteristic
230C2×C8C13×#4111yescharacteristic
231C2×C8C13×#4111yescharacteristic
232C2×C8C13×#4111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C42—21no—
238C42—82no—
239C42C13×SD1612yes—
240C16—22no—
241C16—41no—
242C13#1314311yescharacteristic, direct product factor, Sylow
243C23—41no—
244C23C13×AGL(1,ℤ/8)11yescharacteristic
245Q8—41no—
246Q8—41no—
247D4—41no—
248D4—41no—
249D4—81no—
250D4—81no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C4×D4×C1311yescharacteristic
264C2×C4C13×#12111yescharacteristic
265C2×C4C13×#12311yescharacteristic
266C2×C4C2×C13×SD1611yescharacteristic
267C2×C4C13×#13511yescharacteristic
268C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
269C8—41no—
270C8—81no—
271C8C13×#11711yescharacteristic
272C8C4×D4×C1311yescharacteristic
273C8C13×#12411yescharacteristic
274C8C13×#12611yescharacteristic
275C22—21no—
276C22—21no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22C13×#44211yescharacteristic
281C22C13×#46311yescharacteristic
282C22C13×#48111yescharacteristic
283C4—42no—
284C4—82no—
285C4—82no—
286C4—81no—
287C4C13×#38811yescharacteristic
288C4C4×C13×SD1611yescharacteristic
289C4C13×#46011yescharacteristic
290C4C13×#48211yescharacteristic
291C2—21no—
292C2—21no—
293C2—161no—
294C2C13×#192611yescharacteristic
295C2C13×#218011yescharacteristic
296C2C13×AGL(1,ℤ/16)11yescharacteristic
subgroupG/H
center, socleC22×C13#442
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#365C2semidirect
5. C13×#1776C2semidirect
6. C13×#1387C2semidirect
7. C13×#1375C2semidirect
20. C13×#358C4semidirect
21. C13×#357C4semidirect
55. #13143C13direct (N × H)
95. C2×#365C2×C13semidirect
99. #1776C2×C13semidirect
100. #1387C2×C13semidirect
101. #1375C2×C13semidirect
146. #358C4×C13semidirect
147. #357C4×C13semidirect
242. C13#13143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3652
C2×C13×#3602
C13×#21392
C13×#19752
C13×#17762
C13×#13872
C13×#13752
#1314313