Finite Group Databasebeta

← C13×#33671 #15720010

Subgroups — C13×#33671 #15720010

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3168C211yesmaximal, characteristic, complemented
2C4×C13×#135C211yesmaximal, characteristic, complemented
3C13×#2237C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic, complemented
5C13×#2229C211yesmaximal, characteristic, complemented
6C13×#2228C211yesmaximal, characteristic, complemented
7C13×#2211C211yesmaximal, characteristic, complemented
8C13×#2210C211yesmaximal, characteristic, complemented
9C13×#2189C211yesmaximal, characteristic, complemented
10C13×#2186C211yesmaximal, characteristic
11C13×#2177C211yesmaximal, characteristic, complemented
12C13×#2176C211yesmaximal, characteristic, complemented
13C13×#2175C211yesmaximal, characteristic, complemented
14C13×#2175C211yesmaximal, characteristic, complemented
15C13×#2163C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C13×#529—21no—
18C4×C13×#41—21no—
19C2×C13×Q32C2211yescharacteristic
20C2×C13×SD32C2211yescharacteristic
21C2×C13×SD32C2211yescharacteristic
22C2×C13×D16C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#495C2211yescharacteristic
25C13×#488—21no—
26C13×#467C2211yescharacteristic
27C13×#466C2211yescharacteristic
28C13×#465—21no—
29C4×C13×Q16C2211yescharacteristic
30C4×C13×Q16C2211yescharacteristic
31C4×C13×Q16C2211yescharacteristic
32C4×C13×SD16—21no—
33C4×C13×SD16—21no—
34C4×C13×SD16—21no—
35C4×C13×D8C2211yescharacteristic
36C4×C13×D8C2211yescharacteristic
37C4×C13×D8C2211yescharacteristic
38C13×#427C2211yescharacteristic
39C13×#416—21no—
40C2×C4×C8×C13C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×#41—21no—
60C13×#135—22no—
61C13×#135—22no—
62C2×C13×Q16C2311yescharacteristic
63C2×C13×Q16C2311yescharacteristic
64C2×C13×SD16—21no—
65C2×C13×SD16—21no—
66C2×C13×D8C2311yescharacteristic
67C2×C13×D8C2311yescharacteristic
68C22×C8×C13D411yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×#126—41no—
71C13×#125—21no—
72C13×#124—21no—
73C13×#123—41no—
74C13×C22⋊Q8—21no—
75C13×#121—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C4×Q8×C13—21no—
79C4×D4×C13—21no—
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13—41no—
83C4×D4×C13—41no—
84C4×D4×C13—41no—
85C13×#117—21no—
86C13×#117—41no—
87C13×#117—41no—
88C2×C42×C13—41no—
89C2×C42×C13D411yescharacteristic
90C13×Q32—22no—
91C13×SD32—22no—
92C13×SD32—22no—
93C13×D16—22no—
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C2×C13×C16C2311yescharacteristic
97C2×C13×C16C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#107C2311yescharacteristic
100C13×#107C2311yescharacteristic
101C13×#107C2311yescharacteristic
102C13×#106—21no—
103C13×#106—21no—
104C13×#103—21no—
105C13×#103—21no—
106C13×#103—21no—
107C13×#103—21no—
108C13×#102—21no—
109C13×#102—21no—
110C13×#102—21no—
111C13×#102—21no—
112C4×C8×C13D411yescharacteristic
113C4×C8×C13D411yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#33671C1311yesmaximal, characteristic, direct product factor, Sylow
117C13×#41—24no—
118C13×#41—42no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13D811yescharacteristic
130C22×C4×C13D811yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C13×Q16—21no—
133C13×Q16—21no—
134C13×Q16—21no—
135C13×Q16#4112yes—
136C13×SD16—24no—
137C13×SD16—42no—
138C13×D8—21no—
139C13×D8—21no—
140C13×D8—21no—
141C13×D8#4112yes—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—41no—
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13C2×D411yescharacteristic
148C2×C8×C13C2411yescharacteristic
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—41no—
158C13×C4⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C42×C13—41no—
168C42×C13—41no—
169C42×C13—41no—
170C42×C13—41no—
171C42×C13D811yescharacteristic
172C42×C13D811yescharacteristic
173C42×C13C2×D411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C13×C16—21no—
176C13×C16—21no—
177C13×C16—21no—
178C13×C16—21no—
179#3168C2×C1311yescharacteristic, complemented
180C4×#135C2×C1311yescharacteristic, complemented
181#2237C2×C1311yescharacteristic, complemented
182#2234C2×C1311yescharacteristic, complemented
183#2229C2×C1311yescharacteristic, complemented
184#2228C2×C1311yescharacteristic, complemented
185#2211C2×C1311yescharacteristic, complemented
186#2210C2×C1311yescharacteristic, complemented
187#2189C2×C1311yescharacteristic, complemented
188#2186C2×C1311yescharacteristic
189#2177C2×C1311yescharacteristic, complemented
190#2176C2×C1311yescharacteristic, complemented
191#2175C2×C1311yescharacteristic, complemented
192#2175C2×C1311yescharacteristic, complemented
193#2163C2×C1311yescharacteristic, complemented
194C23×C13—41no—
195C23×C13—41no—
196C23×C13C2×D811yescharacteristic
197Q8×C13—22no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13—41no—
201D4×C13—22no—
202D4×C13—44no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—82no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—44no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—82no—
219C2×C4×C13—82no—
220C2×C4×C13—82no—
221C2×C4×C13C2×D811yescharacteristic
222C2×C4×C13C2×D811yescharacteristic
223C2×C4×C13C2×D811yescharacteristic
224C2×C4×C13C2×D811yescharacteristic
225C2×C4×C13C2×D811yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C8×C13—21no—
228C8×C13—21no—
229C8×C13—21no—
230C8×C13C2×#4111yescharacteristic
231C8×C13C2×#4111yescharacteristic
232C2×#135C22×C1311yescharacteristic
233#529—21no—
234C4×#41—21no—
235C2×Q32C22×C1311yescharacteristic
236C2×SD32C22×C1311yescharacteristic
237C2×SD32C22×C1311yescharacteristic
238C2×D16C22×C1311yescharacteristic
239#499C22×C1311yescharacteristic
240#495C22×C1311yescharacteristic
241#488—21no—
242#467C22×C1311yescharacteristic
243#466C22×C1311yescharacteristic
244#465—21no—
245C4×Q16C22×C1311yescharacteristic
246C4×Q16C22×C1311yescharacteristic
247C4×Q16C22×C1311yescharacteristic
248C4×SD16—21no—
249C4×SD16—21no—
250C4×SD16—21no—
251C4×D8C22×C1311yescharacteristic
252C4×D8C22×C1311yescharacteristic
253C4×D8C22×C1311yescharacteristic
254#427C22×C1311yescharacteristic
255#416—21no—
256C2×C4×C8C22×C1311yescharacteristic
257#367C22×C1311yescharacteristic
258#367C22×C1311yescharacteristic
259#366C22×C1311yescharacteristic
260#366C22×C1311yescharacteristic
261C4⋊C16C22×C1311yescharacteristic
262C4⋊C16C22×C1311yescharacteristic
263#358C22×C1311yescharacteristic
264#358C22×C1311yescharacteristic
265#358C22×C1311yescharacteristic
266#358C22×C1311yescharacteristic
267#357C22×C1311yescharacteristic
268#357C22×C1311yescharacteristic
269#357C22×C1311yescharacteristic
270#357C22×C1311yescharacteristic
271C22⋊C16C22×C1311yescharacteristic
272C22⋊C16C22×C1311yescharacteristic
273#346C22×C1311yescharacteristic
274#346C22×C1311yescharacteristic
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—42no—
279C22×C13—81no—
280C22×C13—81no—
281C22×C13—81no—
282C22×C13—81no—
283C22×C13—81no—
284C22×C13C22×D811yescharacteristic
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—42no—
291C4×C13—81no—
292C4×C13—81no—
293C4×C13—81no—
294C4×C13—81no—
295C4×C13—81no—
296C4×C13#52511yescharacteristic
297C4×C13#57511yescharacteristic
298C2×#41—21no—
299#135—22no—
300#135—22no—
301C2×Q16C23×C1311yescharacteristic
302C2×Q16C23×C1311yescharacteristic
303C2×SD16—21no—
304C2×SD16—21no—
305C2×D8C23×C1311yescharacteristic
306C2×D8C23×C1311yescharacteristic
307C22×C8D4×C1311yescharacteristic
308C22×C8C23×C1311yescharacteristic
309#126—41no—
310#125—21no—
311#124—21no—
312#123—41no—
313C22⋊Q8—21no—
314#121—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—41no—
322C4×D4—41no—
323C4×D4—41no—
324#117—21no—
325#117—41no—
326#117—41no—
327C2×C42—41no—
328C2×C42D4×C1311yescharacteristic
329Q32—22no—
330SD32—22no—
331SD32—22no—
332D16—22no—
333C2×C16C23×C1311yescharacteristic
334C2×C16C23×C1311yescharacteristic
335C2×C16C23×C1311yescharacteristic
336C2×C16C23×C1311yescharacteristic
337#107C23×C1311yescharacteristic
338#107C23×C1311yescharacteristic
339#107C23×C1311yescharacteristic
340#107C23×C1311yescharacteristic
341#106—21no—
342#106—21no—
343#103—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349#102—21no—
350#102—21no—
351C4×C8D4×C1311yescharacteristic
352C4×C8D4×C1311yescharacteristic
353C4×C8C23×C1311yescharacteristic
354C4×C8C23×C1311yescharacteristic
355C2×C13—41no—
356C2×C13—82no—
357C2×C13—161no—
358C2×C13#310011yescharacteristic
359C2×C13#341411yescharacteristic
360C2×C13#341411yescharacteristic
361#41—24no—
362#41—42no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4C13×D811yescharacteristic
374C22×C4C13×D811yescharacteristic
375C22×C4C2×D4×C1311yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—21no—
379Q16C13×#4112yes—
380SD16—24no—
381SD16—42no—
382D8—21no—
383D8—21no—
384D8—21no—
385D8C13×#4112yes—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—41no—
389C2×C8C2×D4×C1311yescharacteristic
390C2×C8C2×D4×C1311yescharacteristic
391C2×C8C2×D4×C1311yescharacteristic
392C2×C8C24×C1311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42—41no—
412C42—41no—
413C42—41no—
414C42—41no—
415C42C13×D811yescharacteristic
416C42C13×D811yescharacteristic
417C42C2×D4×C1311yescharacteristic
418C42C2×D4×C1311yescharacteristic
419C16—21no—
420C16—21no—
421C16—21no—
422C16—21no—
423C13#3367111yescharacteristic, direct product factor, Sylow
424C23—41no—
425C23—41no—
426C23C2×C13×D811yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4C2×C13×D811yescharacteristic
452C2×C4C2×C13×D811yescharacteristic
453C2×C4C2×C13×D811yescharacteristic
454C2×C4C2×C13×D811yescharacteristic
455C2×C4C2×C13×D811yescharacteristic
456C2×C4C22×D4×C1311yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×C13×#4111yescharacteristic
461C8C2×C13×#4111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×C13×D811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4C13×#52511yescharacteristic
484C4C13×#57511yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2C13×#310011yescharacteristic
489C2C13×#341411yescharacteristic
490C2C13×#341411yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3168C2semidirect
2. C4×C13×#135C2semidirect
3. C13×#2237C2semidirect
4. C13×#2234C2semidirect
5. C13×#2229C2semidirect
6. C13×#2228C2semidirect
7. C13×#2211C2semidirect
8. C13×#2210C2semidirect
9. C13×#2189C2semidirect
11. C13×#2177C2semidirect
12. C13×#2176C2semidirect
13. C13×#2175C2semidirect
14. C13×#2175C2semidirect
15. C13×#2163C2semidirect
116. #33671C13direct (N × H)
179. #3168C2×C13semidirect
180. C4×#135C2×C13semidirect
181. #2237C2×C13semidirect
182. #2234C2×C13semidirect
183. #2229C2×C13semidirect
184. #2228C2×C13semidirect
185. #2211C2×C13semidirect
186. #2210C2×C13semidirect
187. #2189C2×C13semidirect
189. #2177C2×C13semidirect
190. #2176C2×C13semidirect
191. #2175C2×C13semidirect
192. #2175C2×C13semidirect
193. #2163C2×C13semidirect
423. C13#33671direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31682
C4×C13×#1352
C13×#22372
C13×#22342
C13×#22292
C13×#22282
C13×#22112
C13×#22102
C13×#21892
C13×#21862
C13×#21772
C13×#21762
C13×#21752
C13×#21632
#3367113