Finite Group Databasebeta

← C13×#13400 #15699739

Subgroups — C13×#13400 #15699739

Order 3328.

402 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3060C211yesmaximal, characteristic
2C2×C13×#365C211yesmaximal, characteristic, complemented
3C13×#2148C211yesmaximal, characteristic, complemented
4C13×#2145C211yesmaximal, characteristic, complemented
5C13×#2117C211yesmaximal, characteristic, complemented
6C13×#1814C211yesmaximal, characteristic, complemented
7C13×#1386C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C2×C13×#131C2211yescharacteristic
10C13×#537—21no—
11C2×C13×M32C2211yescharacteristic
12C2×C13×M32C2211yescharacteristic
13C13×#470—21no—
14C13×#469—21no—
15C13×#465—22no—
16C2×C13×#108C2211yescharacteristic
17C13×#427C2211yescharacteristic
18C2×C13×#106C2211yescharacteristic
19C13×#421—21no—
20C13×#417—21no—
21C13×#365—22no—
22C13×#362—21no—
23C13×#361—21no—
24C13×#360—22no—
25C13×#350—22no—
26C13×#344—21no—
27C2×C13×#41—21no—
28C2×C13×#41D411yescharacteristic
29C13×#135—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135—21no—
33C2×C13×Q16D411yescharacteristic
34C2×C13×SD16—21no—
35C2×C13×D8D411yescharacteristic
36C13×#131—21no—
37C13×#131—21no—
38C13×#131—21no—
39C13×#131—21no—
40C2×C13×M16—21no—
41C2×C13×M16—21no—
42C2×C13×M16D411yescharacteristic
43C22×C8×C13—21no—
44C22×C8×C13C2311yescharacteristic
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8—41no—
47C13×#121—22no—
48C13×#121—42no—
49C13×#121—41no—
50C13×#117—21no—
51C2×C13×C4⋊C4—21no—
52C13×M32—21no—
53C13×M32—21no—
54C13×M32—21no—
55C13×M32D412yescomplemented
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C13×#108—21no—
59C13×#108—21no—
60C13×#107—21no—
61C13×#106—21no—
62C13×#106—21no—
63C13×#106D412yes—
64C13×#104—42no—
65C13×#103—22no—
66C13×#102—22no—
67#13400C1311yesmaximal, characteristic, direct product factor, Sylow
68C13×#41—21no—
69C13×#41—21no—
70C13×#41—21no—
71C13×#41—21no—
72C13×#41—41no—
73C13×#41—41no—
74C13×#41—41no—
75C13×#41—41no—
76C2×Q8×C13—21no—
77C2×Q8×C13SD1611yescharacteristic
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13—41no—
81C2×D4×C13—42no—
82C2×D4×C13SD1611yescharacteristic
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C13×Q16—21no—
88C13×Q16—21no—
89C13×SD16—41no—
90C13×SD16—41no—
91C13×D8—21no—
92C13×D8—21no—
93C13×M16—21no—
94C13×M16—21no—
95C13×M16—41no—
96C13×M16—41no—
97C13×M16—41no—
98C13×M16—41no—
99C2×C8×C13—21no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13C2×D411yescharacteristic
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13#4111yescharacteristic
107C2×C8×C13#4111yescharacteristic
108C2×C8×C13#4111yescharacteristic
109C13×C4⋊C4—22no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117C13×C16—22no—
118C13×C16—41no—
119#3060C2×C1311yescharacteristic
120C2×#365C2×C1311yescharacteristic, complemented
121#2148C2×C1311yescharacteristic, complemented
122#2145C2×C1311yescharacteristic, complemented
123#2117C2×C1311yescharacteristic, complemented
124#1814C2×C1311yescharacteristic, complemented
125#1386C2×C1311yescharacteristic, complemented
126C23×C13—21no—
127C23×C13—41no—
128C23×C13AGL(1,ℤ/8)11yescharacteristic
129Q8×C13—21no—
130Q8×C13—21no—
131Q8×C13—41no—
132Q8×C13—41no—
133D4×C13—21no—
134D4×C13—21no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—41no—
138D4×C13—41no—
139D4×C13—81no—
140D4×C13—81no—
141D4×C13—162no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—161no—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12311yescharacteristic
154C2×C4×C13C2×SD1611yescharacteristic
155C2×C4×C13#13511yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C8×C13—41no—
158C8×C13—81no—
159C8×C13#12111yescharacteristic
160C8×C13#12111yescharacteristic
161C8×C13#12311yescharacteristic
162C8×C13#12411yescharacteristic
163C2×#135C22×C1311yescharacteristic
164C2×#131C22×C1311yescharacteristic
165#537—21no—
166C2×M32C22×C1311yescharacteristic
167C2×M32C22×C1311yescharacteristic
168#470—21no—
169#469—21no—
170#465—22no—
171C2×#108C22×C1311yescharacteristic
172#427C22×C1311yescharacteristic
173C2×#106C22×C1311yescharacteristic
174#421—21no—
175#417—21no—
176#365—22no—
177#362—21no—
178#361—21no—
179#360—22no—
180#350—22no—
181#344—21no—
182C22×C13—41no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#45011yescharacteristic
189C22×C13#46911yescharacteristic
190C22×C13#48211yescharacteristic
191C4×C13—41no—
192C4×C13—82no—
193C4×C13—81no—
194C4×C13—161no—
195C4×C13#39411yescharacteristic
196C4×C13#44911yescharacteristic
197C4×C13#46511yescharacteristic
198C4×C13#48111yescharacteristic
199C2×#41—21no—
200C2×#41D4×C1311yescharacteristic
201#135—21no—
202#135—21no—
203#135—21no—
204#135—21no—
205C2×Q16D4×C1311yescharacteristic
206C2×SD16—21no—
207C2×D8D4×C1311yescharacteristic
208#131—21no—
209#131—21no—
210#131—21no—
211#131—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16D4×C1311yescharacteristic
215C22×C8—21no—
216C22×C8C23×C1311yescharacteristic
217C22⋊Q8—22no—
218C22⋊Q8—41no—
219#121—22no—
220#121—42no—
221#121—41no—
222#117—21no—
223C2×C4⋊C4—21no—
224M32—21no—
225M32—21no—
226M32—21no—
227M32D4×C1312yescomplemented
228C2×C16—21no—
229C2×C16—21no—
230#108—21no—
231#108—21no—
232#107—21no—
233#106—21no—
234#106—21no—
235#106D4×C1312yes—
236#104—42no—
237#103—22no—
238#102—22no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—81no—
243C2×C13—161no—
244C2×C13#203411yescharacteristic
245#41—21no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8C13×SD1611yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4C13×SD1611yescharacteristic
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4C2×D4×C1311yescharacteristic
264Q16—21no—
265Q16—21no—
266SD16—41no—
267SD16—41no—
268D8—21no—
269D8—21no—
270M16—21no—
271M16—21no—
272M16—41no—
273M16—41no—
274M16—41no—
275M16—41no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8C2×D4×C1311yescharacteristic
281C2×C8C2×D4×C1311yescharacteristic
282C2×C8C2×D4×C1311yescharacteristic
283C2×C8C13×#4111yescharacteristic
284C2×C8C13×#4111yescharacteristic
285C2×C8C13×#4111yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C42—41no—
294C16—22no—
295C16—41no—
296C13#1340011yescharacteristic, direct product factor, Sylow
297C23—21no—
298C23—41no—
299C23C13×AGL(1,ℤ/8)11yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311D4—81no—
312D4—162no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4C13×#12011yescharacteristic
323C2×C4C13×#12111yescharacteristic
324C2×C4C13×#12311yescharacteristic
325C2×C4C2×C13×SD1611yescharacteristic
326C2×C4C13×#13511yescharacteristic
327C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
328C8—41no—
329C8—81no—
330C8C13×#12111yescharacteristic
331C8C13×#12111yescharacteristic
332C8C13×#12311yescharacteristic
333C8C13×#12411yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C13×#45011yescharacteristic
341C22C13×#46911yescharacteristic
342C22C13×#48211yescharacteristic
343C4—41no—
344C4—82no—
345C4—81no—
346C4—161no—
347C4C13×#39411yescharacteristic
348C4C13×#44911yescharacteristic
349C4C13×#46511yescharacteristic
350C4C13×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—81no—
355C2—161no—
356C2C13×#203411yescharacteristic
subgroupG/H
center, socleC2×C13#2034
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3060C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#365C2semidirect
3. C13×#2148C2semidirect
4. C13×#2145C2semidirect
5. C13×#2117C2semidirect
6. C13×#1814C2semidirect
7. C13×#1386C2semidirect
55. C13×M32D4semidirect
67. #13400C13direct (N × H)
120. C2×#365C2×C13semidirect
121. #2148C2×C13semidirect
122. #2145C2×C13semidirect
123. #2117C2×C13semidirect
124. #1814C2×C13semidirect
125. #1386C2×C13semidirect
227. M32D4×C13semidirect
296. C13#13400direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30602
C2×C13×#3652
C13×#21482
C13×#21452
C13×#21172
C13×#18142
C13×#13862
#1340013