Finite Group Databasebeta

← C13×#13391 #15699730

Subgroups — C13×#13391 #15699730

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3067C211yesmaximal, characteristic
2C13×#2161C211yesmaximal, characteristic, complemented
3C13×#2148C211yesmaximal, characteristic, complemented
4C2×C13×#360C211yesmaximal, characteristic, complemented
5C13×#2115C211yesmaximal, characteristic, complemented
6C13×#1815C211yesmaximal, characteristic, complemented
7C13×#1383C211yesmaximal, characteristic, complemented
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C2×C13×M32C2211yescharacteristic
12C2×C13×M32C2211yescharacteristic
13C13×#473—21no—
14C13×#472—21no—
15C13×#471—22no—
16C2×C13×#108C2211yescharacteristic
17C2×C13×#108C2211yescharacteristic
18C2×C13×#106C2211yescharacteristic
19C13×#417—21no—
20C13×#413—21no—
21C13×#368—22no—
22C13×#362—21no—
23C13×#361—21no—
24C13×#360—22no—
25C13×#349—22no—
26C13×#343—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×M16—21no—
48C2×C13×M16D411yescharacteristic
49C22×C8×C13—21no—
50C22×C8×C13C2311yescharacteristic
51C2×C13×C4⋊C4—21no—
52C13×M32—21no—
53C13×M32—21no—
54C13×M32—21no—
55C13×M32D412yes—
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C13×#108—21no—
59C13×#108—21no—
60C13×#108—21no—
61C13×#108D412yes—
62C13×#106—21no—
63C13×#106—21no—
64C13×#103—41no—
65C13×#102—41no—
66C13×#101—22no—
67C13×#100—22no—
68#13391C1311yesmaximal, characteristic, direct product factor, Sylow
69C13×#41—21no—
70C13×#41—21no—
71C13×#41—21no—
72C13×#41—21no—
73C13×#41—41no—
74C13×#41—41no—
75C13×#41—41no—
76C13×#41—41no—
77C2×Q8×C13—21no—
78C2×Q8×C13D811yescharacteristic
79C2×D4×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—41no—
82C2×D4×C13D811yescharacteristic
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C13×Q16—21no—
88C13×Q16—21no—
89C13×Q16—42no—
90C13×SD16—42no—
91C13×SD16—42no—
92C13×SD16—41no—
93C13×SD16—41no—
94C13×D8—21no—
95C13×D8—21no—
96C13×D8—42no—
97C13×M16—21no—
98C13×M16—22no—
99C13×M16—21no—
100C13×M16—41no—
101C13×M16—41no—
102C13×M16—41no—
103C13×M16—41no—
104C13×M16—41no—
105C2×C8×C13—21no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×D411yescharacteristic
113C2×C8×C13#4111yescharacteristic
114C2×C8×C13#4111yescharacteristic
115C2×C8×C13#4111yescharacteristic
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C16—22no—
119C13×C16—41no—
120#3067C2×C1311yescharacteristic
121#2161C2×C1311yescharacteristic, complemented
122#2148C2×C1311yescharacteristic, complemented
123C2×#360C2×C1311yescharacteristic, complemented
124#2115C2×C1311yescharacteristic, complemented
125#1815C2×C1311yescharacteristic, complemented
126#1383C2×C1311yescharacteristic, complemented
127C23×C13—21no—
128C23×C13—41no—
129C23×C13#13511yescharacteristic
130Q8×C13—21no—
131Q8×C13—21no—
132Q8×C13—41no—
133Q8×C13—41no—
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—41no—
137D4×C13—41no—
138D4×C13—41no—
139D4×C13—41no—
140D4×C13—81no—
141D4×C13—81no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—161no—
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13#13711yescharacteristic
156C8×C13—41no—
157C8×C13—42no—
158C8×C13—81no—
159C8×C13#12111yescharacteristic
160C8×C13#12111yescharacteristic
161C8×C13#12311yescharacteristic
162C8×C13#12411yescharacteristic
163#575—21no—
164C2×#135C22×C1311yescharacteristic
165C2×#131C22×C1311yescharacteristic
166C2×M32C22×C1311yescharacteristic
167C2×M32C22×C1311yescharacteristic
168#473—21no—
169#472—21no—
170#471—22no—
171C2×#108C22×C1311yescharacteristic
172C2×#108C22×C1311yescharacteristic
173C2×#106C22×C1311yescharacteristic
174#417—21no—
175#413—21no—
176#368—22no—
177#362—21no—
178#361—21no—
179#360—22no—
180#349—22no—
181#343—21no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—161no—
187C22×C13#45211yescharacteristic
188C22×C13#46611yescharacteristic
189C22×C13#48211yescharacteristic
190C4×C13—41no—
191C4×C13—81no—
192C4×C13—161no—
193C4×C13#39411yescharacteristic
194C4×C13#44711yescharacteristic
195C4×C13#46811yescharacteristic
196C4×C13#48011yescharacteristic
197C2×#41—21no—
198C2×#41D4×C1311yescharacteristic
199#137—22no—
200#137—41no—
201AGL(1,ℤ/8)—22no—
202AGL(1,ℤ/8)—41no—
203#135—21no—
204#135—21no—
205#135—21no—
206#135—21no—
207#135—42no—
208C2×Q16D4×C1311yescharacteristic
209C2×SD16—21no—
210C2×D8D4×C1311yescharacteristic
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16D4×C1311yescharacteristic
219C22×C8—21no—
220C22×C8C23×C1311yescharacteristic
221C2×C4⋊C4—21no—
222M32—21no—
223M32—21no—
224M32—21no—
225M32D4×C1312yes—
226C2×C16—21no—
227C2×C16—21no—
228#108—21no—
229#108—21no—
230#108—21no—
231#108D4×C1312yes—
232#106—21no—
233#106—21no—
234#103—41no—
235#102—41no—
236#101—22no—
237#100—22no—
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—81no—
242C2×C13—161no—
243C2×C13#203311yescharacteristic
244#41—21no—
245#41—21no—
246#41—21no—
247#41—21no—
248#41—41no—
249#41—41no—
250#41—41no—
251#41—41no—
252C2×Q8—21no—
253C2×Q8C13×D811yescharacteristic
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4C13×D811yescharacteristic
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C2×D4×C1311yescharacteristic
262Q16—21no—
263Q16—21no—
264Q16—42no—
265SD16—42no—
266SD16—42no—
267SD16—41no—
268SD16—41no—
269D8—21no—
270D8—21no—
271D8—42no—
272M16—21no—
273M16—22no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—21no—
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—41no—
292C4⋊C4—41no—
293C16—22no—
294C16—41no—
295C13#1339111yescharacteristic, direct product factor, Sylow
296C23—21no—
297C23—41no—
298C23C13×#13511yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—41no—
303D4—21no—
304D4—21no—
305D4—41no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—161no—
319C2×C4C13×#12011yescharacteristic
320C2×C4C13×#12111yescharacteristic
321C2×C4C13×#12311yescharacteristic
322C2×C4C2×C13×D811yescharacteristic
323C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
324C2×C4C13×#13711yescharacteristic
325C8—41no—
326C8—42no—
327C8—81no—
328C8C13×#12111yescharacteristic
329C8C13×#12111yescharacteristic
330C8C13×#12311yescharacteristic
331C8C13×#12411yescharacteristic
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22—161no—
337C22C13×#45211yescharacteristic
338C22C13×#46611yescharacteristic
339C22C13×#48211yescharacteristic
340C4—41no—
341C4—81no—
342C4—161no—
343C4C13×#39411yescharacteristic
344C4C13×#44711yescharacteristic
345C4C13×#46811yescharacteristic
346C4C13×#48011yescharacteristic
347C2—21no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2C13×#203311yescharacteristic
subgroupG/H
center, socleC2×C13#2033
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3067C2
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. C13×#2161C2semidirect
3. C13×#2148C2semidirect
4. C2×C13×#360C2semidirect
5. C13×#2115C2semidirect
6. C13×#1815C2semidirect
7. C13×#1383C2semidirect
68. #13391C13direct (N × H)
121. #2161C2×C13semidirect
122. #2148C2×C13semidirect
123. C2×#360C2×C13semidirect
124. #2115C2×C13semidirect
125. #1815C2×C13semidirect
126. #1383C2×C13semidirect
295. C13#13391direct (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×#21612
C13×#21482
C2×C13×#3602
C13×#21152
C13×#18152
C13×#13832
#1339113