Finite Group Databasebeta

← C13×#33618 #15719957

Subgroups — C13×#33618 #15719957

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic, complemented
2C13×#3407C211yesmaximal, characteristic, complemented
3C13×#3067C211yesmaximal, characteristic, complemented
4C2×C13×#472C211yesmaximal, characteristic, complemented
5C13×#2223C214yesmaximal, complemented
6C13×#2221C214yesmaximal, complemented
7C13×#2161C211yesmaximal, characteristic, complemented
8C13×#2148C211yesmaximal, characteristic, complemented
9C2×C13×#361C211yesmaximal, characteristic, complemented
10C13×#575—21no—
11C2×C13×AGL(1,ℤ/8)—21no—
12C2×C13×#135C2211yescharacteristic
13C22×C13×D8C2211yescharacteristic
14C2×C13×#131C2211yescharacteristic
15C13×#509—22no—
16C13×#509—22no—
17C2×C13×SD32C2212yescomplemented
18C2×C13×D16C2212yescomplemented
19C13×#504—22no—
20C13×#504C2214yescomplemented
21C2×C13×M32—22no—
22C2×C13×M32C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C13×#473C2212yescomplemented
25C13×#472—22no—
26C13×#472C2214yes—
27C13×#472C2212yescomplemented
28C13×#471—22no—
29C2×C13×#108C2211yescharacteristic
30C2×C13×#108C2211yescharacteristic
31C13×#413—21no—
32C2×C13×#100—21no—
33C13×#368C2214yescomplemented
34C13×#362C2212yescomplemented
35C13×#361C2214yescomplemented
36C13×#361C2212yescomplemented
37C2×C13×#41—21no—
38C2×C13×#41D411yescharacteristic
39C22×D4×C13—21no—
40C13×#137—22no—
41C13×#137—41no—
42C13×AGL(1,ℤ/8)—22no—
43C13×AGL(1,ℤ/8)—24no—
44C13×AGL(1,ℤ/8)—42no—
45C13×AGL(1,ℤ/8)—41no—
46C13×#135—21no—
47C13×#135—21no—
48C13×#135—21no—
49C13×#135—21no—
50C13×#135—42no—
51C2×C13×Q16C2311yescharacteristic
52C2×C13×SD16—21no—
53C2×C13×SD16—41no—
54C2×C13×D8—21no—
55C2×C13×D8—21no—
56C2×C13×D8—21no—
57C2×C13×D8—21no—
58C2×C13×D8—21no—
59C2×C13×D8—41no—
60C2×C13×D8C2312yes—
61C2×C13×D8C2311yescharacteristic
62C13×#131—21no—
63C13×#131—21no—
64C13×#131D412yes—
65C13×#131C2312yes—
66C2×C13×M16—21no—
67C2×C13×M16—21no—
68C2×C13×M16—21no—
69C2×C13×M16D411yescharacteristic
70C22×C8×C13—21no—
71C22×C8×C13C2311yescharacteristic
72C13×SD32—24no—
73C13×D16—24no—
74C13×M32—21no—
75C13×M32—24no—
76C13×M32D412yes—
77C13×M32D412yes—
78C13×M32C2312yes—
79C2×C13×C16—21no—
80C2×C13×C16—24no—
81C2×C13×C16C2312yes—
82C13×#108—21no—
83C13×#108—21no—
84C13×#108C2312yes—
85C13×#108C2312yes—
86C13×#101—22no—
87C13×#100—24no—
88C13×#100—22no—
89#33618C1311yesmaximal, characteristic, direct product factor, Sylow
90C24×C13—41no—
91C13×#41—21no—
92C13×#41—21no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—41no—
97C13×#41D812yes—
98C13×#41C2×D412yes—
99C2×Q8×C13—21no—
100C2×Q8×C13D811yescharacteristic
101C2×D4×C13—21no—
102C2×D4×C13—22no—
103C2×D4×C13—21no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—41no—
110C2×D4×C13D811yescharacteristic
111C22×C4×C13—21no—
112C22×C4×C13—41no—
113C22×C4×C13C2×D411yescharacteristic
114C13×Q16—21no—
115C13×Q16—21no—
116C13×Q16—42no—
117C13×SD16—44no—
118C13×SD16—42no—
119C13×SD16—42no—
120C13×SD16—41no—
121C13×SD16—41no—
122C13×D8—21no—
123C13×D8—22no—
124C13×D8—22no—
125C13×D8—21no—
126C13×D8—44no—
127C13×D8—42no—
128C13×D8—41no—
129C13×D8—41no—
130C13×M16—21no—
131C13×M16—22no—
132C13×M16—22no—
133C13×M16—22no—
134C13×M16—22no—
135C13×M16—41no—
136C13×M16—41no—
137C13×M16C2×D412yes—
138C2×C8×C13—21no—
139C2×C8×C13—22no—
140C2×C8×C13—22no—
141C2×C8×C13—41no—
142C2×C8×C13—41no—
143C2×C8×C13C2×D411yescharacteristic
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13#4111yescharacteristic
147C2×C8×C13#4111yescharacteristic
148C2×C8×C13C2411yescharacteristic
149C13×C16—22no—
150C13×C16C2×D414yes—
151C2×#509C2×C1311yescharacteristic, complemented
152#3407C2×C1311yescharacteristic, complemented
153#3067C2×C1311yescharacteristic, complemented
154C2×#472C2×C1311yescharacteristic, complemented
155#2223C2×C1314yescomplemented
156#2221C2×C1314yescomplemented
157#2161C2×C1311yescharacteristic, complemented
158#2148C2×C1311yescharacteristic, complemented
159C2×#361C2×C1311yescharacteristic, complemented
160C23×C13—21no—
161C23×C13—41no—
162C23×C13—42no—
163C23×C13—81no—
164C23×C13—81no—
165C23×C13—162no—
166C23×C13#13511yescharacteristic
167Q8×C13—21no—
168Q8×C13—41no—
169Q8×C13—41no—
170Q8×C13C2×D812yes—
171D4×C13—22no—
172D4×C13—22no—
173D4×C13—21no—
174D4×C13—42no—
175D4×C13—41no—
176D4×C13—42no—
177D4×C13—41no—
178D4×C13—81no—
179D4×C13—81no—
180D4×C13—81no—
181D4×C13—81no—
182D4×C13C2×D812yes—
183C2×C4×C13—21no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—41no—
187C2×C4×C13—81no—
188C2×C4×C13—81no—
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×C4×C13C2×D811yescharacteristic
192C2×C4×C13C2×D811yescharacteristic
193C2×C4×C13#13511yescharacteristic
194C2×C4×C13C22×D411yescharacteristic
195C8×C13—22no—
196C8×C13—42no—
197C8×C13—42no—
198C8×C13#12111yescharacteristic
199C8×C13#12111yescharacteristic
200C8×C13C22×D411yescharacteristic
201C8×C13C2×#4111yescharacteristic
202#575—21no—
203C2×AGL(1,ℤ/8)—21no—
204C2×#135C22×C1311yescharacteristic
205C22×D8C22×C1311yescharacteristic
206C2×#131C22×C1311yescharacteristic
207#509—22no—
208#509—22no—
209C2×SD32C22×C1312yescomplemented
210C2×D16C22×C1312yescomplemented
211#504—22no—
212#504C22×C1314yescomplemented
213C2×M32—22no—
214C2×M32C22×C1311yescharacteristic
215C2×M32C22×C1311yescharacteristic
216#473C22×C1312yescomplemented
217#472—22no—
218#472C22×C1314yes—
219#472C22×C1312yescomplemented
220#471—22no—
221C2×#108C22×C1311yescharacteristic
222C2×#108C22×C1311yescharacteristic
223#413—21no—
224C2×#100—21no—
225#368C22×C1314yescomplemented
226#362C22×C1312yescomplemented
227#361C22×C1314yescomplemented
228#361C22×C1312yescomplemented
229C22×C13—22no—
230C22×C13—41no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—82no—
234C22×C13—161no—
235C22×C13—162no—
236C22×C13—162no—
237C22×C13—162no—
238C22×C13#46611yescharacteristic
239C22×C13#46611yescharacteristic
240C22×C13C2×#13511yescharacteristic
241C4×C13—22no—
242C4×C13—81no—
243C4×C13#46611yescharacteristic
244C4×C13#46611yescharacteristic
245C4×C13C2×#12111yescharacteristic
246C4×C13C22×D811yescharacteristic
247C2×#41—21no—
248C2×#41D4×C1311yescharacteristic
249C22×D4—21no—
250#137—22no—
251#137—41no—
252AGL(1,ℤ/8)—24no—
253AGL(1,ℤ/8)—22no—
254AGL(1,ℤ/8)—42no—
255AGL(1,ℤ/8)—41no—
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260#135—42no—
261C2×Q16C23×C1311yescharacteristic
262C2×SD16—21no—
263C2×SD16—41no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—41no—
270C2×D8C23×C1312yes—
271C2×D8C23×C1311yescharacteristic
272#131—21no—
273#131—21no—
274#131D4×C1312yes—
275#131C23×C1312yes—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—21no—
279C2×M16D4×C1311yescharacteristic
280C22×C8—21no—
281C22×C8C23×C1311yescharacteristic
282SD32—24no—
283D16—24no—
284M32—21no—
285M32—24no—
286M32D4×C1312yes—
287M32D4×C1312yes—
288M32C23×C1312yes—
289C2×C16—21no—
290C2×C16—24no—
291C2×C16C23×C1312yes—
292#108—21no—
293#108—21no—
294#108C23×C1312yes—
295#108C23×C1312yes—
296#101—22no—
297#100—24no—
298#100—22no—
299C2×C13—21no—
300C2×C13—21no—
301C2×C13—21no—
302C2×C13—42no—
303C2×C13—161no—
304C2×C13—162no—
305C2×C13C2×#46611yescharacteristic
306C24—41no—
307#41—21no—
308#41—21no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—41no—
313#41C13×D812yes—
314#41C2×D4×C1312yes—
315C2×Q8—21no—
316C2×Q8C13×D811yescharacteristic
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4C13×D811yescharacteristic
327C22×C4—21no—
328C22×C4—41no—
329C22×C4C2×D4×C1311yescharacteristic
330Q16—21no—
331Q16—21no—
332Q16—42no—
333SD16—44no—
334SD16—42no—
335SD16—42no—
336SD16—41no—
337SD16—41no—
338D8—21no—
339D8—22no—
340D8—22no—
341D8—21no—
342D8—44no—
343D8—42no—
344D8—41no—
345D8—41no—
346M16—21no—
347M16—22no—
348M16—22no—
349M16—22no—
350M16—22no—
351M16—41no—
352M16—41no—
353M16C2×D4×C1312yes—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8C2×D4×C1311yescharacteristic
360C2×C8C2×D4×C1311yescharacteristic
361C2×C8C2×D4×C1311yescharacteristic
362C2×C8C13×#4111yescharacteristic
363C2×C8C13×#4111yescharacteristic
364C2×C8C24×C1311yescharacteristic
365C16—22no—
366C16C2×D4×C1314yes—
367C13#3361811yescharacteristic, direct product factor, Sylow
368C23—21no—
369C23—41no—
370C23—42no—
371C23—81no—
372C23—81no—
373C23—162no—
374C23C13×#13511yescharacteristic
375Q8—21no—
376Q8—41no—
377Q8—41no—
378Q8C2×C13×D812yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—42no—
383D4—41no—
384D4—42no—
385D4—41no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4C2×C13×D812yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C13×#12111yescharacteristic
398C2×C4C13×#12111yescharacteristic
399C2×C4C2×C13×D811yescharacteristic
400C2×C4C2×C13×D811yescharacteristic
401C2×C4C13×#13511yescharacteristic
402C2×C4C22×D4×C1311yescharacteristic
403C8—22no—
404C8—42no—
405C8—42no—
406C8C13×#12111yescharacteristic
407C8C13×#12111yescharacteristic
408C8C22×D4×C1311yescharacteristic
409C8C2×C13×#4111yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—81no—
414C22—82no—
415C22—161no—
416C22—162no—
417C22—162no—
418C22—162no—
419C22C13×#46611yescharacteristic
420C22C13×#46611yescharacteristic
421C22C2×C13×#13511yescharacteristic
422C4—22no—
423C4—81no—
424C4C13×#46611yescharacteristic
425C4C13×#46611yescharacteristic
426C4C2×C13×#12111yescharacteristic
427C4C22×C13×D811yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—162no—
433C2—161no—
434C2C2×C13×#46611yescharacteristic
subgroupG/H
center, socleC2×C13C2×#466
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×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
1. C2×C13×#509C2semidirect
2. C13×#3407C2semidirect
3. C13×#3067C2semidirect
4. C2×C13×#472C2semidirect
5. C13×#2223C2semidirect
6. C13×#2221C2semidirect
7. C13×#2161C2semidirect
8. C13×#2148C2semidirect
9. C2×C13×#361C2semidirect
17. C2×C13×SD32C22semidirect
18. C2×C13×D16C22semidirect
20. C13×#504C22semidirect
24. C13×#473C22semidirect
27. C13×#472C22semidirect
33. C13×#368C22semidirect
34. C13×#362C22semidirect
35. C13×#361C22semidirect
36. C13×#361C22semidirect
89. #33618C13direct (N × H)
151. C2×#509C2×C13semidirect
152. #3407C2×C13semidirect
153. #3067C2×C13semidirect
154. C2×#472C2×C13semidirect
155. #2223C2×C13semidirect
156. #2221C2×C13semidirect
157. #2161C2×C13semidirect
158. #2148C2×C13semidirect
159. C2×#361C2×C13semidirect
209. C2×SD32C22×C13semidirect
210. C2×D16C22×C13semidirect
212. #504C22×C13semidirect
216. #473C22×C13semidirect
219. #472C22×C13semidirect
225. #368C22×C13semidirect
226. #362C22×C13semidirect
227. #361C22×C13semidirect
228. #361C22×C13semidirect
367. C13#33618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5092
C13×#34072
C13×#30672
C2×C13×#4722
C13×#22232
C13×#22212
C13×#21612
C13×#21482
C2×C13×#3612
#3361813