Finite Group Databasebeta

← C13×#13134 #15699473

Subgroups — C13×#13134 #15699473

Order 3328.

324 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#368C211yesmaximal, characteristic, complemented
2C2×C13×#359C211yesmaximal, characteristic
3C13×#2138C211yesmaximal, characteristic
4C13×#1974C211yesmaximal, characteristic
5C13×#1772C211yesmaximal, characteristic, complemented
6C13×#1382C211yesmaximal, characteristic, complemented
7C13×#1374C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×C16C2211yescharacteristic
10C22×C13×C16C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C2×C13×#108C2211yescharacteristic
13C13×#427C2211yescharacteristic
14C2×C13×#104—21no—
15C13×#408—21no—
16C13×#405—21no—
17C2×C4×C8×C13C2211yescharacteristic
18C13×#368—22no—
19C13×#359—22no—
20C13×#358C411yescharacteristic, complemented
21C13×#358C411yescharacteristic, complemented
22C13×#357C411yescharacteristic, complemented
23C13×#357C411yescharacteristic, complemented
24C13×#339—21no—
25C2×C13×#41—21no—
26C13×#135—21no—
27C13×#135—21no—
28C13×#135—21no—
29C13×#135—21no—
30C2×C13×Q16C2×C411yescharacteristic
31C2×C13×SD16—21no—
32C2×C13×D8C2×C411yescharacteristic
33C2×C13×M16—21no—
34C2×C13×M16—21no—
35C22×C8×C13D411yescharacteristic
36C22×C8×C13C2311yescharacteristic
37C13×#117—21no—
38C2×C42×C13D411yescharacteristic
39C2×C13×C16—21no—
40C2×C13×C16—21no—
41C2×C13×C16—21no—
42C2×C13×C16—21no—
43C2×C13×C16—21no—
44C2×C13×C16C2×C411yescharacteristic
45C2×C13×C16C2×C411yescharacteristic
46C13×#108—21no—
47C13×#108—21no—
48C13×#108—21no—
49C13×#108D412yes—
50C13×#107C2×C411yescharacteristic
51C13×#107C2×C411yescharacteristic
52C13×#106—21no—
53C13×#104—42no—
54C13×C22⋊C8—41no—
55C13×C22⋊C8—41no—
56C13×#97—41no—
57C4×C8×C13—21no—
58C4×C8×C13—21no—
59C4×C8×C13—41no—
60#13134C1311yesmaximal, characteristic, direct product factor, Sylow
61C13×#41—41no—
62C13×#41—41no—
63C13×#41—41no—
64C13×#41—41no—
65C2×Q8×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—41no—
70C22×C4×C13C2×D411yescharacteristic
71C13×Q16—21no—
72C13×Q16—21no—
73C13×SD16—41no—
74C13×SD16—41no—
75C13×D8—21no—
76C13×D8—21no—
77C13×M16—22no—
78C13×M16—41no—
79C13×M16—41no—
80C13×M16—41no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13D811yescharacteristic
86C2×C8×C13D811yescharacteristic
87C2×C8×C13C22×C411yescharacteristic
88C2×C8×C13C2×D411yescharacteristic
89C2×C8×C13#4111yescharacteristic
90C2×C8×C13#4111yescharacteristic
91C2×C8×C13#4111yescharacteristic
92C2×C8×C13#4111yescharacteristic
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C22⋊C4—41no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—41no—
99C13×C16—21no—
100C13×C16—21no—
101C13×C16—41no—
102C2×#368C2×C1311yescharacteristic, complemented
103C2×#359C2×C1311yescharacteristic
104#2138C2×C1311yescharacteristic
105#1974C2×C1311yescharacteristic
106#1772C2×C1311yescharacteristic, complemented
107#1382C2×C1311yescharacteristic, complemented
108#1374C2×C1311yescharacteristic, complemented
109C23×C13—41no—
110C23×C13#13511yescharacteristic
111Q8×C13—41no—
112Q8×C13—41no—
113D4×C13—41no—
114D4×C13—41no—
115D4×C13—81no—
116D4×C13—81no—
117C2×C4×C13—22no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13#12311yescharacteristic
128C2×C4×C13C2×D811yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C8×C13—21no—
132C8×C13—21no—
133C8×C13—42no—
134C8×C13—81no—
135C8×C13#11711yescharacteristic
136C8×C13C4×D411yescharacteristic
137C8×C13#12411yescharacteristic
138C8×C13#12611yescharacteristic
139C2×#135C22×C1311yescharacteristic
140C22×C16C22×C1311yescharacteristic
141C22×C16C22×C1311yescharacteristic
142C2×#108C22×C1311yescharacteristic
143C2×#108C22×C1311yescharacteristic
144#427C22×C1311yescharacteristic
145C2×#104—21no—
146#408—21no—
147#405—21no—
148C2×C4×C8C22×C1311yescharacteristic
149#368—22no—
150#359—22no—
151#358C4×C1311yescharacteristic, complemented
152#358C4×C1311yescharacteristic, complemented
153#357C4×C1311yescharacteristic, complemented
154#357C4×C1311yescharacteristic, complemented
155#339—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13C4×D811yescharacteristic
162C22×C13#46411yescharacteristic
163C22×C13#48211yescharacteristic
164C4×C13—42no—
165C4×C13—81no—
166C4×C13—81no—
167C4×C13—81no—
168C4×C13#38811yescharacteristic
169C4×C13#44011yescharacteristic
170C4×C13#45911yescharacteristic
171C4×C13#48011yescharacteristic
172C2×#41—21no—
173#135—21no—
174#135—21no—
175#135—21no—
176#135—21no—
177C2×Q16C2×C4×C1311yescharacteristic
178C2×SD16—21no—
179C2×D8C2×C4×C1311yescharacteristic
180C2×M16—21no—
181C2×M16—21no—
182C22×C8D4×C1311yescharacteristic
183C22×C8C23×C1311yescharacteristic
184#117—21no—
185C2×C42D4×C1311yescharacteristic
186C2×C16—21no—
187C2×C16—21no—
188C2×C16—21no—
189C2×C16—21no—
190C2×C16—21no—
191C2×C16C2×C4×C1311yescharacteristic
192C2×C16C2×C4×C1311yescharacteristic
193#108—21no—
194#108—21no—
195#108—21no—
196#108D4×C1312yes—
197#107C2×C4×C1311yescharacteristic
198#107C2×C4×C1311yescharacteristic
199#106—21no—
200#104—42no—
201C22⋊C8—41no—
202C22⋊C8—41no—
203#97—41no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—41no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—161no—
210C2×C13#192511yescharacteristic
211C2×C13#217811yescharacteristic
212C2×C13#217911yescharacteristic
213#41—41no—
214#41—41no—
215#41—41no—
216#41—41no—
217C2×Q8—21no—
218C2×D4—21no—
219C2×D4—41no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4C2×D4×C1311yescharacteristic
223Q16—21no—
224Q16—21no—
225SD16—41no—
226SD16—41no—
227D8—21no—
228D8—21no—
229M16—22no—
230M16—41no—
231M16—41no—
232M16—41no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8C13×D811yescharacteristic
238C2×C8C13×D811yescharacteristic
239C2×C8C22×C4×C1311yescharacteristic
240C2×C8C2×D4×C1311yescharacteristic
241C2×C8C13×#4111yescharacteristic
242C2×C8C13×#4111yescharacteristic
243C2×C8C13×#4111yescharacteristic
244C2×C8C13×#4111yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—21no—
247C22⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—41no—
251C16—21no—
252C16—21no—
253C16—41no—
254C13#1313411yescharacteristic, direct product factor, Sylow
255C23—41no—
256C23C13×#13511yescharacteristic
257Q8—41no—
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—81no—
262D4—81no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4C4×D4×C1311yescharacteristic
272C2×C4C13×#12111yescharacteristic
273C2×C4C13×#12311yescharacteristic
274C2×C4C2×C13×D811yescharacteristic
275C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
276C2×C4C13×#13711yescharacteristic
277C8—21no—
278C8—21no—
279C8—42no—
280C8—81no—
281C8C13×#11711yescharacteristic
282C8C4×D4×C1311yescharacteristic
283C8C13×#12411yescharacteristic
284C8C13×#12611yescharacteristic
285C22—21no—
286C22—21no—
287C22—81no—
288C22—81no—
289C22—81no—
290C22C4×C13×D811yescharacteristic
291C22C13×#46411yescharacteristic
292C22C13×#48211yescharacteristic
293C4—42no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4C13×#38811yescharacteristic
298C4C13×#44011yescharacteristic
299C4C13×#45911yescharacteristic
300C4C13×#48011yescharacteristic
301C2—21no—
302C2—21no—
303C2—161no—
304C2C13×#192511yescharacteristic
305C2C13×#217811yescharacteristic
306C2C13×#217911yescharacteristic
subgroupG/H
centerC2×C4×C13C2×D8
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
socleC22×C13C4×D8
prime radicalC2×C13×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#368C2semidirect
5. C13×#1772C2semidirect
6. C13×#1382C2semidirect
7. C13×#1374C2semidirect
20. C13×#358C4semidirect
21. C13×#358C4semidirect
22. C13×#357C4semidirect
23. C13×#357C4semidirect
60. #13134C13direct (N × H)
102. C2×#368C2×C13semidirect
106. #1772C2×C13semidirect
107. #1382C2×C13semidirect
108. #1374C2×C13semidirect
151. #358C4×C13semidirect
152. #358C4×C13semidirect
153. #357C4×C13semidirect
154. #357C4×C13semidirect
254. C13#13134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3682
C2×C13×#3592
C13×#21382
C13×#19742
C13×#17722
C13×#13822
C13×#13742
#1313413