Finite Group Databasebeta

← C13×#13401 #15699740

Subgroups — C13×#13401 #15699740

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3067C211yesmaximal, characteristic
2C13×#2155C211yesmaximal, characteristic, complemented
3C13×#2145C211yesmaximal, characteristic, complemented
4C13×#2138C211yesmaximal, characteristic, complemented
5C2×C13×#350C211yesmaximal, characteristic, complemented
6C13×#1812C211yesmaximal, characteristic, complemented
7C13×#1382C211yesmaximal, characteristic, complemented
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C2×C13×M32C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C13×#473—21no—
14C13×#472—21no—
15C13×#471—22no—
16C2×C13×#108C2211yescharacteristic
17C13×#427C2211yescharacteristic
18C13×#427C2211yescharacteristic
19C13×#413—21no—
20C13×#410—21no—
21C13×#365—22no—
22C13×#360—22no—
23C13×#358—21no—
24C13×#357—21no—
25C13×#350—22no—
26C13×H(3,ℤ/4)—21no—
27C2×C13×#41—21no—
28C2×C13×#41D411yescharacteristic
29C13×#137—22no—
30C13×#137—41no—
31C13×AGL(1,ℤ/8)—22no—
32C13×AGL(1,ℤ/8)—41no—
33C13×#135—21no—
34C13×#135—21no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135—42no—
38C2×C13×Q16D411yescharacteristic
39C2×C13×SD16—21no—
40C2×C13×D8D411yescharacteristic
41C13×#131—21no—
42C13×#131—21no—
43C13×#131—21no—
44C13×#131—21no—
45C2×C13×M16—21no—
46C2×C13×M16—21no—
47C2×C13×M16D411yescharacteristic
48C22×C8×C13—21no—
49C22×C8×C13C2311yescharacteristic
50C13×#117—21no—
51C13×#117—21no—
52C13×M32—21no—
53C13×M32D412yes—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C13×#108—21no—
59C13×#108D412yes—
60C13×#107—21no—
61C13×#107—21no—
62C13×#106—21no—
63C13×#106—21no—
64C13×#101—22no—
65C13×#100—22no—
66C13×#99—42no—
67#13401C1311yesmaximal, 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×C13SD1611yescharacteristic
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13C2×D411yescharacteristic
85C13×Q16—21no—
86C13×Q16—21no—
87C13×Q16—42no—
88C13×SD16—42no—
89C13×SD16—42no—
90C13×SD16—41no—
91C13×SD16—41no—
92C13×D8—21no—
93C13×D8—21no—
94C13×D8—42no—
95C13×M16—21no—
96C13×M16—22no—
97C13×M16—21no—
98C13×M16—41no—
99C13×M16—41no—
100C13×M16—41no—
101C2×C8×C13—21no—
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—41no—
112C13×C4⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C42×C13—41no—
116C42×C13—41no—
117C13×C16—22no—
118C13×C16—41no—
119#3067C2×C1311yescharacteristic
120#2155C2×C1311yescharacteristic, complemented
121#2145C2×C1311yescharacteristic, complemented
122#2138C2×C1311yescharacteristic, complemented
123C2×#350C2×C1311yescharacteristic, complemented
124#1812C2×C1311yescharacteristic, complemented
125#1382C2×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—
141C2×C4×C13—21no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13#12011yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12311yescharacteristic
152C2×C4×C13C2×SD1611yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C8×C13—41no—
156C8×C13—42no—
157C8×C13#12111yescharacteristic
158C8×C13#12111yescharacteristic
159C8×C13#12311yescharacteristic
160C8×C13#12411yescharacteristic
161#575—21no—
162C2×#135C22×C1311yescharacteristic
163C2×#131C22×C1311yescharacteristic
164C2×M32C22×C1311yescharacteristic
165C22×C16C22×C1311yescharacteristic
166#473—21no—
167#472—21no—
168#471—22no—
169C2×#108C22×C1311yescharacteristic
170#427C22×C1311yescharacteristic
171#427C22×C1311yescharacteristic
172#413—21no—
173#410—21no—
174#365—22no—
175#360—22no—
176#358—21no—
177#357—21no—
178#350—22no—
179H(3,ℤ/4)—21no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—161no—
185C22×C13#44911yescharacteristic
186C22×C13#46911yescharacteristic
187C22×C13#48111yescharacteristic
188C4×C13—41no—
189C4×C13—81no—
190C4×C13—161no—
191C4×C13—161no—
192C4×C13#39411yescharacteristic
193C4×C13#45011yescharacteristic
194C4×C13#46511yescharacteristic
195C4×C13#48211yescharacteristic
196C2×#41—21no—
197C2×#41D4×C1311yescharacteristic
198#137—22no—
199#137—41no—
200AGL(1,ℤ/8)—22no—
201AGL(1,ℤ/8)—41no—
202#135—21no—
203#135—21no—
204#135—21no—
205#135—21no—
206#135—42no—
207C2×Q16D4×C1311yescharacteristic
208C2×SD16—21no—
209C2×D8D4×C1311yescharacteristic
210#131—21no—
211#131—21no—
212#131—21no—
213#131—21no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16D4×C1311yescharacteristic
217C22×C8—21no—
218C22×C8C23×C1311yescharacteristic
219#117—21no—
220#117—21no—
221M32—21no—
222M32D4×C1312yes—
223C2×C16—21no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227#108—21no—
228#108D4×C1312yes—
229#107—21no—
230#107—21no—
231#106—21no—
232#106—21no—
233#101—22no—
234#100—22no—
235#99—42no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—81no—
240C2×C13—161no—
241C2×C13#203411yescharacteristic
242#41—21no—
243#41—21no—
244#41—21no—
245#41—21no—
246#41—41no—
247#41—41no—
248#41—41no—
249#41—41no—
250C2×Q8—21no—
251C2×Q8C13×SD1611yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C13×SD1611yescharacteristic
256C22×C4—21no—
257C22×C4—41no—
258C22×C4C2×D4×C1311yescharacteristic
259Q16—21no—
260Q16—21no—
261Q16—42no—
262SD16—42no—
263SD16—42no—
264SD16—41no—
265SD16—41no—
266D8—21no—
267D8—21no—
268D8—42no—
269M16—21no—
270M16—22no—
271M16—21no—
272M16—41no—
273M16—41no—
274M16—41no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8C2×D4×C1311yescharacteristic
280C2×C8C2×D4×C1311yescharacteristic
281C2×C8C2×D4×C1311yescharacteristic
282C2×C8C13×#4111yescharacteristic
283C2×C8C13×#4111yescharacteristic
284C2×C8C13×#4111yescharacteristic
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C42—41no—
290C42—41no—
291C16—22no—
292C16—41no—
293C13#1340111yescharacteristic, direct product factor, Sylow
294C23—21no—
295C23—41no—
296C23C13×AGL(1,ℤ/8)11yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—41no—
300Q8—41no—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4C13×#12011yescharacteristic
318C2×C4C13×#12111yescharacteristic
319C2×C4C13×#12311yescharacteristic
320C2×C4C2×C13×SD1611yescharacteristic
321C2×C4C13×#13511yescharacteristic
322C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
323C8—41no—
324C8—42no—
325C8C13×#12111yescharacteristic
326C8C13×#12111yescharacteristic
327C8C13×#12311yescharacteristic
328C8C13×#12411yescharacteristic
329C22—41no—
330C22—41no—
331C22—81no—
332C22—81no—
333C22—161no—
334C22C13×#44911yescharacteristic
335C22C13×#46911yescharacteristic
336C22C13×#48111yescharacteristic
337C4—41no—
338C4—81no—
339C4—161no—
340C4—161no—
341C4C13×#39411yescharacteristic
342C4C13×#45011yescharacteristic
343C4C13×#46511yescharacteristic
344C4C13×#48211yescharacteristic
345C2—21no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—161no—
350C2C13×#203411yescharacteristic
subgroupG/H
centerC4×C13#482
commutator, Frattini, cosocleC22×C8C23×C13
socleC2×C13#2034
prime radicalC13×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2155C2semidirect
3. C13×#2145C2semidirect
4. C13×#2138C2semidirect
5. C2×C13×#350C2semidirect
6. C13×#1812C2semidirect
7. C13×#1382C2semidirect
67. #13401C13direct (N × H)
120. #2155C2×C13semidirect
121. #2145C2×C13semidirect
122. #2138C2×C13semidirect
123. C2×#350C2×C13semidirect
124. #1812C2×C13semidirect
125. #1382C2×C13semidirect
293. C13#13401direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30672
C13×#21552
C13×#21452
C13×#21382
C2×C13×#3502
C13×#18122
C13×#13822
#1340113