Finite Group Databasebeta

← C13×#13411 #15699750

Subgroups — C13×#13411 #15699750

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3155C211yesmaximal, characteristic
2C2×C13×#361C211yesmaximal, characteristic, complemented
3C2×C13×#359C211yesmaximal, characteristic, complemented
4C13×#2139C211yesmaximal, characteristic, complemented
5C2×C13×#357C211yesmaximal, characteristic, complemented
6C13×#1952C211yesmaximal, characteristic, complemented
7C13×#1379C211yesmaximal, characteristic, complemented
8C2×C13×AGL(1,ℤ/8)—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×D8C2211yescharacteristic
11C13×#535—21no—
12C2×C13×M32C2211yescharacteristic
13C22×C13×C16C2211yescharacteristic
14C13×#496—22no—
15C13×#495—21no—
16C13×#493—21no—
17C2×C13×#108C2211yescharacteristic
18C13×#428—21no—
19C2×C13×#107C2211yescharacteristic
20C13×#405C2211yescharacteristic
21C13×#361—22no—
22C13×#359—22no—
23C13×#358—21no—
24C13×#357—22no—
25C13×#357—21no—
26C13×#343—21no—
27C2×C13×#41—21no—
28C22×D4×C13—21no—
29C13×AGL(1,ℤ/8)—42no—
30C13×AGL(1,ℤ/8)—42no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135—21no—
34C13×#135—21no—
35C2×C13×Q16D411yescharacteristic
36C2×C13×SD16—22no—
37C2×C13×SD16—21no—
38C2×C13×D8—22no—
39C2×C13×D8—21no—
40C2×C13×D8—21no—
41C2×C13×D8—21no—
42C2×C13×D8—21no—
43C2×C13×D8—21no—
44C2×C13×D8D411yescharacteristic
45C2×C13×D8D412yes—
46C2×C13×M16—21no—
47C2×C13×M16D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C13×#127—22no—
50C13×#124—22no—
51C13×#121—41no—
52C13×#121—41no—
53C13×#120—42no—
54C13×#117D411yescharacteristic
55C2×C13×C4⋊C4—21no—
56C13×M32—21no—
57C13×M32—21no—
58C2×C13×C16—21no—
59C2×C13×C16—21no—
60C2×C13×C16—21no—
61C2×C13×C16—21no—
62C13×#108—21no—
63C13×#108D412yescomplemented
64C13×#107—21no—
65C13×#107—21no—
66C13×#107—41no—
67C13×#106—41no—
68C13×#97—21no—
69C4×C8×C13—21no—
70#13411C1311yesmaximal, characteristic, direct product factor, Sylow
71C24×C13—41no—
72C13×#41—41no—
73C13×#41—41no—
74C13×#41—41no—
75C13×#41—41no—
76C2×Q8×C13—21no—
77C2×D4×C13—22no—
78C2×D4×C13—21no—
79C2×D4×C13—42no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C13×Q16—21no—
91C13×Q16—21no—
92C13×SD16—44no—
93C13×SD16—41no—
94C13×SD16—41no—
95C13×D8—22no—
96C13×D8—21no—
97C13×D8—22no—
98C13×D8—21no—
99C13×D8—44no—
100C13×D8—41no—
101C13×D8—41no—
102C13×M16—21no—
103C13×M16—22no—
104C13×M16—41no—
105C13×M16SD1612yes—
106C2×C8×C13—21no—
107C2×C8×C13—41no—
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13#4111yescharacteristic
112C2×C8×C13#4111yescharacteristic
113C2×C8×C13#4111yescharacteristic
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4D811yescharacteristic
117C13×C4⋊C4D811yescharacteristic
118C13×C22⋊C4—21no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—42no—
121C42×C13—21no—
122C13×C16—41no—
123C13×C16—41no—
124#3155C2×C1311yescharacteristic
125C2×#361C2×C1311yescharacteristic, complemented
126C2×#359C2×C1311yescharacteristic, complemented
127#2139C2×C1311yescharacteristic, complemented
128C2×#357C2×C1311yescharacteristic, complemented
129#1952C2×C1311yescharacteristic, complemented
130#1379C2×C1311yescharacteristic, complemented
131C23×C13—42no—
132C23×C13—41no—
133C23×C13—81no—
134C23×C13—81no—
135C23×C13—161no—
136C23×C13—161no—
137C23×C13AGL(1,ℤ/8)11yescharacteristic
138Q8×C13—41no—
139Q8×C13—41no—
140D4×C13—42no—
141D4×C13—41no—
142D4×C13—41no—
143D4×C13—42no—
144D4×C13—81no—
145D4×C13—81no—
146D4×C13—81no—
147D4×C13—81no—
148D4×C13—162no—
149D4×C13—162no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×C4×C13—161no—
157C2×C4×C13#12011yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12411yescharacteristic
160C2×C4×C13C2×D811yescharacteristic
161C2×C4×C13C2×SD1611yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C8×C13—22no—
164C8×C13—42no—
165C8×C13#12111yescharacteristic
166C8×C13#12111yescharacteristic
167C8×C13#12311yescharacteristic
168C8×C13#12311yescharacteristic
169C2×AGL(1,ℤ/8)—21no—
170C2×#135C22×C1311yescharacteristic
171C22×D8C22×C1311yescharacteristic
172#535—21no—
173C2×M32C22×C1311yescharacteristic
174C22×C16C22×C1311yescharacteristic
175#496—22no—
176#495—21no—
177#493—21no—
178C2×#108C22×C1311yescharacteristic
179#428—21no—
180C2×#107C22×C1311yescharacteristic
181#405C22×C1311yescharacteristic
182#361—22no—
183#359—22no—
184#358—21no—
185#357—22no—
186#357—21no—
187#343—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—81no—
191C22×C13—82no—
192C22×C13—81no—
193C22×C13—82no—
194C22×C13—81no—
195C22×C13—82no—
196C22×C13—162no—
197C22×C13—162no—
198C22×C13#44711yescharacteristic
199C22×C13#46011yescharacteristic
200C22×C13#49011yescharacteristic
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—81no—
204C4×C13—161no—
205C4×C13#39411yescharacteristic
206C4×C13#45011yescharacteristic
207C4×C13#45911yescharacteristic
208C4×C13#48611yescharacteristic
209C2×#41—21no—
210C22×D4—21no—
211AGL(1,ℤ/8)—42no—
212AGL(1,ℤ/8)—42no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217C2×Q16D4×C1311yescharacteristic
218C2×SD16—22no—
219C2×SD16—21no—
220C2×D8—22no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8D4×C1312yes—
227C2×D8D4×C1311yescharacteristic
228C2×M16—21no—
229C2×M16D4×C1311yescharacteristic
230C22×C8C23×C1311yescharacteristic
231#127—22no—
232#124—22no—
233#121—41no—
234#121—41no—
235#120—42no—
236#117D4×C1311yescharacteristic
237C2×C4⋊C4—21no—
238M32—21no—
239M32—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244#108—21no—
245#108D4×C1312yescomplemented
246#107—21no—
247#107—21no—
248#107—41no—
249#106—41no—
250#97—21no—
251C4×C8—21no—
252C2×C13—21no—
253C2×C13—21no—
254C2×C13—161no—
255C2×C13—162no—
256C2×C13#204111yescharacteristic
257C2×C13#219211yescharacteristic
258C2×C13#219411yescharacteristic
259C24—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×D4—22no—
266C2×D4—21no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4C2×D4×C1311yescharacteristic
278Q16—21no—
279Q16—21no—
280SD16—44no—
281SD16—41no—
282SD16—41no—
283D8—22no—
284D8—21no—
285D8—22no—
286D8—21no—
287D8—44no—
288D8—41no—
289D8—41no—
290M16—21no—
291M16—22no—
292M16—41no—
293M16C13×SD1612yes—
294C2×C8—21no—
295C2×C8—41no—
296C2×C8C2×D4×C1311yescharacteristic
297C2×C8C2×D4×C1311yescharacteristic
298C2×C8C2×D4×C1311yescharacteristic
299C2×C8C13×#4111yescharacteristic
300C2×C8C13×#4111yescharacteristic
301C2×C8C13×#4111yescharacteristic
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C13×D811yescharacteristic
305C4⋊C4C13×D811yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C42—21no—
310C16—41no—
311C16—41no—
312C13#1341111yescharacteristic, direct product factor, Sylow
313C23—42no—
314C23—41no—
315C23—81no—
316C23—81no—
317C23—161no—
318C23—161no—
319C23C13×AGL(1,ℤ/8)11yescharacteristic
320Q8—41no—
321Q8—41no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—162no—
331D4—162no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—161no—
339C2×C4C13×#12011yescharacteristic
340C2×C4C13×#12111yescharacteristic
341C2×C4C13×#12411yescharacteristic
342C2×C4C2×C13×D811yescharacteristic
343C2×C4C2×C13×SD1611yescharacteristic
344C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
345C8—22no—
346C8—42no—
347C8C13×#12111yescharacteristic
348C8C13×#12111yescharacteristic
349C8C13×#12311yescharacteristic
350C8C13×#12311yescharacteristic
351C22—21no—
352C22—21no—
353C22—81no—
354C22—82no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—162no—
360C22—162no—
361C22C13×#44711yescharacteristic
362C22C13×#46011yescharacteristic
363C22C13×#49011yescharacteristic
364C4—41no—
365C4—41no—
366C4—81no—
367C4—161no—
368C4C13×#39411yescharacteristic
369C4C13×#45011yescharacteristic
370C4C13×#45911yescharacteristic
371C4C13×#48611yescharacteristic
372C2—21no—
373C2—21no—
374C2—162no—
375C2—161no—
376C2C13×#204111yescharacteristic
377C2C13×#219211yescharacteristic
378C2C13×#219411yescharacteristic
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3155C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#361C2semidirect
3. C2×C13×#359C2semidirect
4. C13×#2139C2semidirect
5. C2×C13×#357C2semidirect
6. C13×#1952C2semidirect
7. C13×#1379C2semidirect
63. C13×#108D4semidirect
70. #13411C13direct (N × H)
125. C2×#361C2×C13semidirect
126. C2×#359C2×C13semidirect
127. #2139C2×C13semidirect
128. C2×#357C2×C13semidirect
129. #1952C2×C13semidirect
130. #1379C2×C13semidirect
245. #108D4×C13semidirect
312. C13#13411direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31552
C2×C13×#3612
C2×C13×#3592
C13×#21392
C2×C13×#3572
C13×#19522
C13×#13792
#1341113