Finite Group Databasebeta

← C13×#13395 #15699734

Subgroups — C13×#13395 #15699734

Order 3328.

422 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3050C211yesmaximal, characteristic
2C13×#2155C211yesmaximal, characteristic, complemented
3C13×#2148C211yesmaximal, characteristic, complemented
4C13×#2143C211yesmaximal, characteristic, complemented
5C13×#2112C211yesmaximal, characteristic, complemented
6C13×#1810C211yesmaximal, characteristic, complemented
7C13×#1389C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C13×#525—21no—
11C2×C13×M32C2211yescharacteristic
12C2×C13×M32C2211yescharacteristic
13C13×#467—21no—
14C13×#466—21no—
15C13×#465—22no—
16C2×C13×#108C2211yescharacteristic
17C2×C13×#108C2211yescharacteristic
18C13×#427C2211yescharacteristic
19C13×#416—21no—
20C13×#407—21no—
21C13×#365—22no—
22C13×#362—21no—
23C13×#361—21no—
24C13×#359—22no—
25C13×C22⋊C16—22no—
26C13×#341—21no—
27C2×C13×#41—21no—
28C23×C4×C13D411yescharacteristic
29C13×#135—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135—21no—
33C2×C13×Q16D411yescharacteristic
34C2×C13×SD16—21no—
35C2×C13×D8D411yescharacteristic
36C2×C13×M16—21no—
37C2×C13×M16—21no—
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13—21no—
44C22×C8×C13D411yescharacteristic
45C22×C8×C13C2311yescharacteristic
46C13×#123—41no—
47C13×C22⋊Q8—22no—
48C13×#121—22no—
49C13×#120—41no—
50C4×D4×C13—42no—
51C13×#117—21no—
52C13×M32—21no—
53C13×M32—21no—
54C13×M32—21no—
55C13×M32—21no—
56C2×C13×C16—21no—
57C2×C13×C16D412yescomplemented
58C13×#108—21no—
59C13×#108—21no—
60C13×#108—21no—
61C13×#108—21no—
62C13×#107—21no—
63C13×#106D412yes—
64C13×#103—22no—
65C13×#102—22no—
66C13×C22⋊C8—42no—
67#13395C1311yesmaximal, characteristic, direct product factor, Sylow
68C24×C13SD1611yescharacteristic
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C13×#41—41no—
73C2×Q8×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—42no—
76C2×D4×C13—41no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13SD1611yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×Q16—21no—
87C13×Q16—21no—
88C13×SD16—41no—
89C13×SD16—41no—
90C13×D8—21no—
91C13×D8—21no—
92C13×M16—41no—
93C13×M16—41no—
94C13×M16—41no—
95C13×M16—41no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13#4111yescharacteristic
109C2×C8×C13#4111yescharacteristic
110C2×C8×C13#4111yescharacteristic
111C13×C4⋊C4—22no—
112C13×C4⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117C13×C16—22no—
118C13×C16—41no—
119#3050C2×C1311yescharacteristic
120#2155C2×C1311yescharacteristic, complemented
121#2148C2×C1311yescharacteristic, complemented
122#2143C2×C1311yescharacteristic, complemented
123#2112C2×C1311yescharacteristic, complemented
124#1810C2×C1311yescharacteristic, complemented
125#1389C2×C1311yescharacteristic, complemented
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—42no—
130C23×C13—41no—
131C23×C13C2×SD1611yescharacteristic
132Q8×C13—41no—
133Q8×C13—41no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—84no—
137D4×C13—81no—
138D4×C13—81no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C8×C13—41no—
157C8×C13—81no—
158C8×C13—81no—
159C8×C13#12111yescharacteristic
160C8×C13#12111yescharacteristic
161C8×C13#12311yescharacteristic
162C8×C13#12411yescharacteristic
163C2×#135C22×C1311yescharacteristic
164C23×C8C22×C1311yescharacteristic
165#525—21no—
166C2×M32C22×C1311yescharacteristic
167C2×M32C22×C1311yescharacteristic
168#467—21no—
169#466—21no—
170#465—22no—
171C2×#108C22×C1311yescharacteristic
172C2×#108C22×C1311yescharacteristic
173#427C22×C1311yescharacteristic
174#416—21no—
175#407—21no—
176#365—22no—
177#362—21no—
178#361—21no—
179#359—22no—
180C22⋊C16—22no—
181#341—21no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—82no—
191C22×C13—81no—
192C22×C13#45011yescharacteristic
193C22×C13#46511yescharacteristic
194C22×C13#48111yescharacteristic
195C4×C13—41no—
196C4×C13—82no—
197C4×C13—81no—
198C4×C13#39411yescharacteristic
199C4×C13#44911yescharacteristic
200C4×C13#46911yescharacteristic
201C4×C13#48211yescharacteristic
202C2×#41—21no—
203C23×C4D4×C1311yescharacteristic
204#135—21no—
205#135—21no—
206#135—21no—
207#135—21no—
208C2×Q16D4×C1311yescharacteristic
209C2×SD16—21no—
210C2×D8D4×C1311yescharacteristic
211C2×M16—21no—
212C2×M16—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8D4×C1311yescharacteristic
220C22×C8C23×C1311yescharacteristic
221#123—41no—
222C22⋊Q8—22no—
223#121—22no—
224#120—41no—
225C4×D4—42no—
226#117—21no—
227M32—21no—
228M32—21no—
229M32—21no—
230M32—21no—
231C2×C16—21no—
232C2×C16D4×C1312yescomplemented
233#108—21no—
234#108—21no—
235#108—21no—
236#108—21no—
237#107—21no—
238#106D4×C1312yes—
239#103—22no—
240#102—22no—
241C22⋊C8—42no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—21no—
245C2×C13—42no—
246C2×C13—161no—
247C2×C13#203411yescharacteristic
248C24C13×SD1611yescharacteristic
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—42no—
256C2×D4—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4C13×SD1611yescharacteristic
265C22×C4C2×D4×C1311yescharacteristic
266Q16—21no—
267Q16—21no—
268SD16—41no—
269SD16—41no—
270D8—21no—
271D8—21no—
272M16—41no—
273M16—41no—
274M16—41no—
275M16—41no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8C2×D4×C1311yescharacteristic
286C2×C8C2×D4×C1311yescharacteristic
287C2×C8C2×D4×C1311yescharacteristic
288C2×C8C13×#4111yescharacteristic
289C2×C8C13×#4111yescharacteristic
290C2×C8C13×#4111yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C42—41no—
297C16—22no—
298C16—41no—
299C13#1339511yescharacteristic, direct product factor, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—42no—
304C23—41no—
305C23C2×C13×SD1611yescharacteristic
306Q8—41no—
307Q8—41no—
308D4—41no—
309D4—41no—
310D4—84no—
311D4—81no—
312D4—81no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C13×#12011yescharacteristic
325C2×C4C13×#12111yescharacteristic
326C2×C4C13×#12311yescharacteristic
327C2×C4C13×#13511yescharacteristic
328C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
329C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
330C8—41no—
331C8—81no—
332C8—81no—
333C8C13×#12111yescharacteristic
334C8C13×#12111yescharacteristic
335C8C13×#12311yescharacteristic
336C8C13×#12411yescharacteristic
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—82no—
346C22—81no—
347C22C13×#45011yescharacteristic
348C22C13×#46511yescharacteristic
349C22C13×#48111yescharacteristic
350C4—41no—
351C4—82no—
352C4—81no—
353C4C13×#39411yescharacteristic
354C4C13×#44911yescharacteristic
355C4C13×#46911yescharacteristic
356C4C13×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—161no—
362C2C13×#203411yescharacteristic
subgroupG/H
centerC4×C13#469
commutator, Frattini, cosocleC22×C8C23×C13
socleC2×C13#2034
prime radicalC13×#3050C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C23×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2155C2semidirect
3. C13×#2148C2semidirect
4. C13×#2143C2semidirect
5. C13×#2112C2semidirect
6. C13×#1810C2semidirect
7. C13×#1389C2semidirect
57. C2×C13×C16D4semidirect
67. #13395C13direct (N × H)
120. #2155C2×C13semidirect
121. #2148C2×C13semidirect
122. #2143C2×C13semidirect
123. #2112C2×C13semidirect
124. #1810C2×C13semidirect
125. #1389C2×C13semidirect
232. C2×C16D4×C13semidirect
299. C13#13395direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30502
C13×#21552
C13×#21482
C13×#21432
C13×#21122
C13×#18102
C13×#13892
#1339513