Finite Group Databasebeta

← C13×#13140 #15699479

Subgroups — C13×#13140 #15699479

Order 3328.

314 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2155C211yesmaximal, characteristic, complemented
2C13×#2148C211yesmaximal, characteristic
3C13×#2145C211yesmaximal, characteristic
4C13×#1975C211yesmaximal, characteristic
5C13×#1773C211yesmaximal, characteristic, complemented
6C13×#1385C211yesmaximal, characteristic, complemented
7C13×#1377C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C2×C13×M32C2211yescharacteristic
10C2×C13×M32C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C2×C13×#108C2211yescharacteristic
13C13×#427C2211yescharacteristic
14C2×C13×#104—21no—
15C13×#408—21no—
16C13×#405—21no—
17C2×C13×#97C2211yescharacteristic
18C13×#365—22no—
19C13×#362C412yescomplemented
20C13×#361C412yescomplemented
21C13×#360—22no—
22C13×#339—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—
32C2×C13×M16—21no—
33C22×C8×C13D411yescharacteristic
34C22×C8×C13C2311yescharacteristic
35C13×#117—21no—
36C2×C42×C13D411yescharacteristic
37C13×M32—21no—
38C13×M32—21no—
39C13×M32—21no—
40C13×M32C2×C412yes—
41C2×C13×C16—21no—
42C2×C13×C16—21no—
43C13×#108—21no—
44C13×#108—21no—
45C13×#108—21no—
46C13×#108C2×C412yes—
47C13×#107—21no—
48C13×#106D412yes—
49C13×#104—42no—
50C13×C22⋊C8—42no—
51C13×#97—21no—
52C13×#97—21no—
53C13×#97—41no—
54C4×C8×C13—41no—
55#13140C1311yesmaximal, 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×C13C2×D411yescharacteristic
66C13×Q16—21no—
67C13×Q16—21no—
68C13×SD16—41no—
69C13×SD16—41no—
70C13×D8—21no—
71C13×D8—21no—
72C13×M16—22no—
73C13×M16—41no—
74C13×M16—41no—
75C13×M16—41no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13SD1612yes—
81C2×C8×C13C22×C411yescharacteristic
82C2×C8×C13C2×D411yescharacteristic
83C2×C8×C13#4111yescharacteristic
84C2×C8×C13#4111yescharacteristic
85C2×C8×C13#4111yescharacteristic
86C2×C8×C13#4111yescharacteristic
87C13×C4⋊C4—22no—
88C13×C22⋊C4—41no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—41no—
92C13×C16—22no—
93C13×C16—41no—
94#2155C2×C1311yescharacteristic, complemented
95#2148C2×C1311yescharacteristic
96#2145C2×C1311yescharacteristic
97#1975C2×C1311yescharacteristic
98#1773C2×C1311yescharacteristic, complemented
99#1385C2×C1311yescharacteristic, complemented
100#1377C2×C1311yescharacteristic, complemented
101C23×C13—41no—
102C23×C13#13511yescharacteristic
103Q8×C13—41no—
104Q8×C13—41no—
105D4×C13—41no—
106D4×C13—41no—
107D4×C13—81no—
108D4×C13—81no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—81no—
113C2×C4×C13—81no—
114C2×C4×C13—81no—
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13#12111yescharacteristic
117C2×C4×C13#12311yescharacteristic
118C2×C4×C13C2×SD1611yescharacteristic
119C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
121C8×C13—22no—
122C8×C13—42no—
123C8×C13—81no—
124C8×C13#11711yescharacteristic
125C8×C13C4×D411yescharacteristic
126C8×C13#12411yescharacteristic
127C8×C13#12611yescharacteristic
128C2×#135C22×C1311yescharacteristic
129C2×M32C22×C1311yescharacteristic
130C2×M32C22×C1311yescharacteristic
131C2×#108C22×C1311yescharacteristic
132C2×#108C22×C1311yescharacteristic
133#427C22×C1311yescharacteristic
134C2×#104—21no—
135#408—21no—
136#405—21no—
137C2×#97C22×C1311yescharacteristic
138#365—22no—
139#362C4×C1312yescomplemented
140#361C4×C1312yescomplemented
141#360—22no—
142#339—21no—
143C22×C13—41no—
144C22×C13—82no—
145C22×C13—81no—
146C22×C13C4×SD1611yescharacteristic
147C22×C13#46311yescharacteristic
148C22×C13#48211yescharacteristic
149C4×C13—82no—
150C4×C13—81no—
151C4×C13—81no—
152C4×C13#38811yescharacteristic
153C4×C13#44211yescharacteristic
154C4×C13#46011yescharacteristic
155C4×C13#48111yescharacteristic
156C2×#41—21no—
157#135—21no—
158#135—21no—
159#135—21no—
160#135—21no—
161C2×Q16C2×C4×C1311yescharacteristic
162C2×SD16—21no—
163C2×D8C2×C4×C1311yescharacteristic
164C2×M16—21no—
165C2×M16—21no—
166C22×C8D4×C1311yescharacteristic
167C22×C8C23×C1311yescharacteristic
168#117—21no—
169C2×C42D4×C1311yescharacteristic
170M32—21no—
171M32—21no—
172M32—21no—
173M32C2×C4×C1312yes—
174C2×C16—21no—
175C2×C16—21no—
176#108—21no—
177#108—21no—
178#108—21no—
179#108C2×C4×C1312yes—
180#107—21no—
181#106D4×C1312yes—
182#104—42no—
183C22⋊C8—42no—
184#97—21no—
185#97—21no—
186#97—41no—
187C4×C8—41no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13—161no—
192C2×C13#192611yescharacteristic
193#41—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197C2×Q8—21no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—21no—
201C22×C4—41no—
202C22×C4C2×D4×C1311yescharacteristic
203Q16—21no—
204Q16—21no—
205SD16—41no—
206SD16—41no—
207D8—21no—
208D8—21no—
209M16—22no—
210M16—41no—
211M16—41no—
212M16—41no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C13×SD1612yes—
218C2×C8C22×C4×C1311yescharacteristic
219C2×C8C2×D4×C1311yescharacteristic
220C2×C8C13×#4111yescharacteristic
221C2×C8C13×#4111yescharacteristic
222C2×C8C13×#4111yescharacteristic
223C2×C8C13×#4111yescharacteristic
224C4⋊C4—22no—
225C22⋊C4—41no—
226C42—21no—
227C42—21no—
228C42—41no—
229C16—22no—
230C16—41no—
231C13#1314011yescharacteristic, direct product factor, Sylow
232C23—41no—
233C23C13×#13511yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—81no—
239D4—81no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C4×D4×C1311yescharacteristic
247C2×C4C13×#12111yescharacteristic
248C2×C4C13×#12311yescharacteristic
249C2×C4C2×C13×SD1611yescharacteristic
250C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
251C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
252C8—22no—
253C8—42no—
254C8—81no—
255C8C13×#11711yescharacteristic
256C8C4×D4×C1311yescharacteristic
257C8C13×#12411yescharacteristic
258C8C13×#12611yescharacteristic
259C22—41no—
260C22—82no—
261C22—81no—
262C22C4×C13×SD1611yescharacteristic
263C22C13×#46311yescharacteristic
264C22C13×#48211yescharacteristic
265C4—82no—
266C4—81no—
267C4—81no—
268C4C13×#38811yescharacteristic
269C4C13×#44211yescharacteristic
270C4C13×#46011yescharacteristic
271C4C13×#48111yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—161no—
276C2C13×#192611yescharacteristic
subgroupG/H
centerC4×C13#481
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
socleC2×C13#1926
prime radicalC2×C13×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2155C2semidirect
5. C13×#1773C2semidirect
6. C13×#1385C2semidirect
7. C13×#1377C2semidirect
19. C13×#362C4semidirect
20. C13×#361C4semidirect
55. #13140C13direct (N × H)
94. #2155C2×C13semidirect
98. #1773C2×C13semidirect
99. #1385C2×C13semidirect
100. #1377C2×C13semidirect
139. #362C4×C13semidirect
140. #361C4×C13semidirect
231. C13#13140direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#21552
C13×#21482
C13×#21452
C13×#19752
C13×#17732
C13×#13852
C13×#13772
#1314013