Finite Group Databasebeta

← C13×#13387 #15699726

Subgroups — C13×#13387 #15699726

Order 3328.

428 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3058C211yesmaximal, characteristic
2C13×#2159C211yesmaximal, characteristic, complemented
3C2×C13×#361C211yesmaximal, characteristic, complemented
4C2×C13×#357C211yesmaximal, characteristic, complemented
5C2×C13×#350C211yesmaximal, characteristic, complemented
6C13×#1816C211yesmaximal, characteristic, complemented
7C13×#1382C211yesmaximal, characteristic, complemented
8C22×C13×D8C2211yescharacteristic
9C2×C13×#131C2211yescharacteristic
10C13×#535—21no—
11C2×C13×M32C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C13×#469—22no—
14C13×#466—21no—
15C13×#466—21no—
16C2×C13×#108C2211yescharacteristic
17C13×#427C2211yescharacteristic
18C2×C13×#107C2211yescharacteristic
19C13×#418—21no—
20C13×#417—21no—
21C13×#367—21no—
22C13×#366—21no—
23C13×#361—22no—
24C13×#357—22no—
25C13×#350—22no—
26C13×#343—21no—
27C2×C13×#41D411yescharacteristic
28C22×D4×C13—21no—
29C2×C13×D8—21no—
30C2×C13×D8—21no—
31C2×C13×D8—21no—
32C2×C13×D8—21no—
33C2×C13×D8—21no—
34C2×C13×D8D412yes—
35C13×#131—21no—
36C13×#131—21no—
37C13×#131—21no—
38C13×#131—21no—
39C2×C13×M16—21no—
40C2×C13×M16—21no—
41C2×C13×M16D411yescharacteristic
42C22×C8×C13—21no—
43C22×C8×C13C2311yescharacteristic
44C13×#127—41no—
45C13×#124—41no—
46C13×#121—22no—
47C13×#121—22no—
48C13×#120—42no—
49C13×#117—21no—
50C2×C13×C4⋊C4—21no—
51C13×M32—21no—
52C13×M32D412yescomplemented
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C13×#108—21no—
58C13×#108—21no—
59C13×#107—21no—
60C13×#107—21no—
61C13×#107D411yescharacteristic
62C13×#107D411yescharacteristic
63C13×#106—21no—
64C13×#103—41no—
65C13×#102—22no—
66C13×#102—22no—
67C13×#102—41no—
68#13387C1311yesmaximal, characteristic, direct product factor, Sylow
69C24×C13—41no—
70C13×#41—21no—
71C13×#41—21no—
72C13×#41—21no—
73C13×#41—21no—
74C2×Q8×C13D811yescharacteristic
75C2×D4×C13—21no—
76C2×D4×C13—22no—
77C2×D4×C13—42no—
78C2×D4×C13—42no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13D811yescharacteristic
85C22×C4×C13—21no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C13×D8—22no—
89C13×D8—22no—
90C13×D8—41no—
91C13×D8—41no—
92C13×M16—21no—
93C13×M16—21no—
94C13×M16—41no—
95C13×M16—41no—
96C13×M16—41no—
97C13×M16—41no—
98C2×C8×C13—21no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D411yescharacteristic
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13#4111yescharacteristic
106C2×C8×C13#4111yescharacteristic
107C2×C8×C13#4111yescharacteristic
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—41no—
115C42×C13—41no—
116C13×C16—22no—
117C13×C16—41no—
118#3058C2×C1311yescharacteristic
119#2159C2×C1311yescharacteristic, complemented
120C2×#361C2×C1311yescharacteristic, complemented
121C2×#357C2×C1311yescharacteristic, complemented
122C2×#350C2×C1311yescharacteristic, complemented
123#1816C2×C1311yescharacteristic, complemented
124#1382C2×C1311yescharacteristic, complemented
125C23×C13—21no—
126C23×C13—42no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—161no—
130C23×C13—161no—
131C23×C13AGL(1,ℤ/8)11yescharacteristic
132Q8×C13—21no—
133Q8×C13—21no—
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—41no—
137D4×C13—41no—
138D4×C13—42no—
139D4×C13—42no—
140D4×C13—81no—
141D4×C13—81no—
142D4×C13—162no—
143D4×C13—162no—
144C2×C4×C13—21no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—81no—
150C2×C4×C13—161no—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12311yescharacteristic
154C2×C4×C13C2×D811yescharacteristic
155C2×C4×C13#13511yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C8×C13—41no—
158C8×C13—81no—
159C8×C13#12111yescharacteristic
160C8×C13#12111yescharacteristic
161C8×C13#12311yescharacteristic
162C8×C13#12411yescharacteristic
163C22×D8C22×C1311yescharacteristic
164C2×#131C22×C1311yescharacteristic
165#535—21no—
166C2×M32C22×C1311yescharacteristic
167C22×C16C22×C1311yescharacteristic
168#469—22no—
169#466—21no—
170#466—21no—
171C2×#108C22×C1311yescharacteristic
172#427C22×C1311yescharacteristic
173C2×#107C22×C1311yescharacteristic
174#418—21no—
175#417—21no—
176#367—21no—
177#366—21no—
178#361—22no—
179#357—22no—
180#350—22no—
181#343—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—82no—
188C22×C13—82no—
189C22×C13—82no—
190C22×C13—162no—
191C22×C13—162no—
192C22×C13#44711yescharacteristic
193C22×C13#46811yescharacteristic
194C22×C13#48211yescharacteristic
195C4×C13—41no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—161no—
199C4×C13#39411yescharacteristic
200C4×C13#45211yescharacteristic
201C4×C13#46611yescharacteristic
202C4×C13#48011yescharacteristic
203C2×#41D4×C1311yescharacteristic
204C22×D4—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8D4×C1312yes—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16D4×C1311yescharacteristic
218C22×C8—21no—
219C22×C8C23×C1311yescharacteristic
220#127—41no—
221#124—41no—
222#121—22no—
223#121—22no—
224#120—42no—
225#117—21no—
226C2×C4⋊C4—21no—
227M32—21no—
228M32D4×C1312yescomplemented
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233#108—21no—
234#108—21no—
235#107—21no—
236#107—21no—
237#107D4×C1311yescharacteristic
238#107D4×C1311yescharacteristic
239#106—21no—
240#103—41no—
241#102—22no—
242#102—22no—
243#102—41no—
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—81no—
247C2×C13—162no—
248C2×C13#203311yescharacteristic
249C2×C13#219211yescharacteristic
250C2×C13#219411yescharacteristic
251C24—41no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256C2×Q8C13×D811yescharacteristic
257C2×D4—21no—
258C2×D4—22no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4C13×D811yescharacteristic
267C22×C4—21no—
268C22×C4—41no—
269C22×C4C2×D4×C1311yescharacteristic
270D8—22no—
271D8—22no—
272D8—41no—
273D8—41no—
274M16—21no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8C2×D4×C1311yescharacteristic
285C2×C8C2×D4×C1311yescharacteristic
286C2×C8C2×D4×C1311yescharacteristic
287C2×C8C13×#4111yescharacteristic
288C2×C8C13×#4111yescharacteristic
289C2×C8C13×#4111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C42—41no—
298C16—22no—
299C16—41no—
300C13#1338711yescharacteristic, direct product factor, Sylow
301C23—21no—
302C23—42no—
303C23—81no—
304C23—81no—
305C23—161no—
306C23—161no—
307C23C13×AGL(1,ℤ/8)11yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—81no—
317D4—81no—
318D4—162no—
319D4—162no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—161no—
327C2×C4C13×#12011yescharacteristic
328C2×C4C13×#12111yescharacteristic
329C2×C4C13×#12311yescharacteristic
330C2×C4C2×C13×D811yescharacteristic
331C2×C4C13×#13511yescharacteristic
332C2×C4C13×#13711yescharacteristic
333C8—41no—
334C8—81no—
335C8C13×#12111yescharacteristic
336C8C13×#12111yescharacteristic
337C8C13×#12311yescharacteristic
338C8C13×#12411yescharacteristic
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—82no—
345C22—82no—
346C22—82no—
347C22—162no—
348C22—162no—
349C22C13×#44711yescharacteristic
350C22C13×#46811yescharacteristic
351C22C13×#48211yescharacteristic
352C4—41no—
353C4—81no—
354C4—81no—
355C4—161no—
356C4C13×#39411yescharacteristic
357C4C13×#45211yescharacteristic
358C4C13×#46611yescharacteristic
359C4C13×#48011yescharacteristic
360C2—21no—
361C2—21no—
362C2—81no—
363C2—162no—
364C2C13×#203311yescharacteristic
365C2C13×#219211yescharacteristic
366C2C13×#219411yescharacteristic
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3058C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2159C2semidirect
3. C2×C13×#361C2semidirect
4. C2×C13×#357C2semidirect
5. C2×C13×#350C2semidirect
6. C13×#1816C2semidirect
7. C13×#1382C2semidirect
52. C13×M32D4semidirect
68. #13387C13direct (N × H)
119. #2159C2×C13semidirect
120. C2×#361C2×C13semidirect
121. C2×#357C2×C13semidirect
122. C2×#350C2×C13semidirect
123. #1816C2×C13semidirect
124. #1382C2×C13semidirect
228. M32D4×C13semidirect
300. C13#13387direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30582
C13×#21592
C2×C13×#3612
C2×C13×#3572
C2×C13×#3502
C13×#18162
C13×#13822
#1338713