Finite Group Databasebeta

← C13×#36684 #15723023

Subgroups — C13×#36684 #15723023

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#529C212yesmaximal, complemented
2C13×#2823C214yesmaximal, complemented
3C13×#2822C211yesmaximal, characteristic, complemented
4C13×#2820C212yesmaximal, complemented
5C13×#2819C211yesmaximal, characteristic, complemented
6C13×#2814C214yesmaximal, complemented
7C13×#2813C214yesmaximal, complemented
8C13×#2396C214yesmaximal, complemented
9C13×#2392C214yesmaximal, complemented
10C13×#2392C214yesmaximal, complemented
11C13×#2285C211yesmaximal, characteristic, complemented
12C13×#529—216no—
13C2×C13×#126C2214yes—
14C2×C13×#125C2212yes—
15C2×C13×#124C2212yes—
16C2×C13×#123C2214yes—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121C2212yes—
19C2×C4×Q8×C13C2212yes—
20C2×C4×D4×C13C2214yes—
21C2×C4×D4×C13C2212yes—
22C2×C4×D4×C13C2214yes—
23C2×C13×#117C2214yes—
24C2×C13×#117C2212yes—
25C22×C42×C13C2211yescharacteristic
26C13×#400C2214yes—
27C13×#399C2214yes—
28C13×#398C2214yes—
29C13×#398C2218yes—
30C13×#398C2214yes—
31C13×#397C2214yes—
32C13×#397C2214yes—
33C13×#396C2218yes—
34C13×#396C2218yes—
35C13×#396C2218yes—
36C13×#395C2214yes—
37C13×#394C2218yes—
38C13×#394C2214yes—
39C13×#394C2218yes—
40C13×#394C2214yes—
41C13×#393C2214yes—
42C13×#392C2214yes—
43C13×#392C2214yes—
44C13×#384C2212yes—
45C13×#382C2211yescharacteristic
46C13×#382C2211yescharacteristic
47C13×#380C2214yes—
48C4×C13×C4⋊C4C2214yes—
49C4×C13×C4⋊C4C2214yes—
50C4×C13×C22⋊C4C2218yes—
51C22×Q8×C13C2312yes—
52C22×D4×C13C2314yes—
53C22×D4×C13C2312yes—
54C22×D4×C13C2314yes—
55C23×C4×C13C2314yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2312yes—
58C13×#126—216no—
59C13×#125—28no—
60C13×#124—28no—
61C13×#123—216no—
62C13×C22⋊Q8—28no—
63C13×#121—28no—
64C4×Q8×C13—28no—
65C4×D4×C13—216no—
66C4×D4×C13—28no—
67C4×D4×C13—48no—
68C13×#117—216no—
69C13×#117—44no—
70C2×C13×C4⋊C4C2314yes—
71C2×C13×C4⋊C4C2314yes—
72C2×C13×C4⋊C4C2314yes—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C4⋊C4C2312yes—
75C2×C13×C4⋊C4C2312yes—
76C2×C13×C4⋊C4C2318yes—
77C2×C13×C4⋊C4C2318yes—
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C4⋊C4C2312yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C22⋊C4C2314yes—
82C2×C13×C22⋊C4C2314yes—
83C2×C13×C22⋊C4C2314yes—
84C2×C13×C22⋊C4C2314yes—
85C2×C13×C22⋊C4C2314yes—
86C2×C13×C22⋊C4C2318yes—
87C2×C13×C22⋊C4C2318yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C13×C22⋊C4C2318yes—
90C2×C42×C13D418yescomplemented
91C2×C42×C13C2314yes—
92C2×C42×C13C2314yes—
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2312yes—
96C13×#95C2318yes—
97C13×#95C2318yes—
98C13×#95C2314yes—
99C13×#95C2314yes—
100C13×#95C2314yes—
101C13×#95C2314yes—
102#36684C1311yesmaximal, characteristic, direct product factor, Sylow
103C24×C13C2414yes—
104C24×C13C2411yescharacteristic
105C2×Q8×C13—24no—
106C2×Q8×C13—44no—
107C2×D4×C13—28no—
108C2×D4×C13—24no—
109C2×D4×C13—44no—
110C2×D4×C13—44no—
111C2×D4×C13—48no—
112C2×D4×C13—48no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—28no—
116C22×C4×C13—28no—
117C22×C4×C13—28no—
118C22×C4×C13—44no—
119C22×C4×C13C2×D414yes—
120C22×C4×C13C2×D418yes—
121C22×C4×C13C2414yes—
122C22×C4×C13C2414yes—
123C22×C4×C13C2414yes—
124C22×C4×C13C2414yes—
125C22×C4×C13C2414yes—
126C22×C4×C13C2412yes—
127C22×C4×C13C2411yescharacteristic
128C22×C4×C13C2412yes—
129C22×C4×C13C2411yescharacteristic
130C13×C4⋊C4—28no—
131C13×C4⋊C4—28no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4—28no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4—28no—
136C13×C4⋊C4—48no—
137C13×C4⋊C4—48no—
138C13×C4⋊C4—42no—
139C13×C4⋊C4—42no—
140C13×C4⋊C4—44no—
141C13×C22⋊C4—28no—
142C13×C22⋊C4—28no—
143C13×C22⋊C4—28no—
144C13×C22⋊C4—28no—
145C13×C22⋊C4—28no—
146C13×C22⋊C4—48no—
147C13×C22⋊C4—48no—
148C13×C22⋊C4—44no—
149C13×C22⋊C4—48no—
150C42×C13—28no—
151C42×C13—28no—
152C42×C13C2×D418yes—
153C42×C13C2×D414yes—
154C42×C13C2×D414yes—
155C2×#529C2×C1312yescomplemented
156#2823C2×C1314yescomplemented
157#2822C2×C1311yescharacteristic, complemented
158#2820C2×C1312yescomplemented
159#2819C2×C1311yescharacteristic, complemented
160#2814C2×C1314yescomplemented
161#2813C2×C1314yescomplemented
162#2396C2×C1314yescomplemented
163#2392C2×C1314yescomplemented
164#2392C2×C1314yescomplemented
165#2285C2×C1311yescharacteristic, complemented
166C23×C13—21no—
167C23×C13—21no—
168C23×C13—24no—
169C23×C13—24no—
170C23×C13—24no—
171C23×C13—24no—
172C23×C13—28no—
173C23×C13—28no—
174C23×C13C22×D412yes—
175C23×C13C2511yescharacteristic
176Q8×C13—48no—
177D4×C13—48no—
178D4×C13—416no—
179D4×C13—416no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—24no—
183C2×C4×C13—24no—
184C2×C4×C13—28no—
185C2×C4×C13—24no—
186C2×C4×C13—24no—
187C2×C4×C13—24no—
188C2×C4×C13—24no—
189C2×C4×C13—24no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—28no—
193C2×C4×C13—28no—
194C2×C4×C13—28no—
195C2×C4×C13—28no—
196C2×C4×C13—48no—
197C2×C4×C13—416no—
198C2×C4×C13C22×D412yes—
199C2×C4×C13C22×D414yes—
200C2×C4×C13C22×D414yes—
201C2×C4×C13C22×D412yes—
202C2×C4×C13H(5,𝔽2)12yes—
203C2×C4×C132−1+412yes—
204#529—216no—
205C2×#126C22×C1314yes—
206C2×#125C22×C1312yes—
207C2×#124C22×C1312yes—
208C2×#123C22×C1314yes—
209C2×C22⋊Q8C22×C1312yes—
210C2×#121C22×C1312yes—
211C2×C4×Q8C22×C1312yes—
212C2×C4×D4C22×C1314yes—
213C2×C4×D4C22×C1312yes—
214C2×C4×D4C22×C1314yes—
215C2×#117C22×C1314yes—
216C2×#117C22×C1312yes—
217C22×C42C22×C1311yescharacteristic
218#400C22×C1314yes—
219#399C22×C1314yes—
220#398C22×C1314yes—
221#398C22×C1314yes—
222#398C22×C1318yes—
223#397C22×C1314yes—
224#397C22×C1314yes—
225#396C22×C1318yes—
226#396C22×C1318yes—
227#396C22×C1318yes—
228#395C22×C1314yes—
229#394C22×C1314yes—
230#394C22×C1314yes—
231#394C22×C1318yes—
232#394C22×C1318yes—
233#393C22×C1314yes—
234#392C22×C1314yes—
235#392C22×C1314yes—
236#384C22×C1312yes—
237#382C22×C1311yescharacteristic
238#382C22×C1311yescharacteristic
239#380C22×C1314yes—
240C4×C4⋊C4C22×C1314yes—
241C4×C4⋊C4C22×C1314yes—
242C4×C22⋊C4C22×C1318yes—
243C22×C13—22no—
244C22×C13—24no—
245C22×C13—42no—
246C22×C13—42no—
247C22×C13—44no—
248C22×C13—44no—
249C22×C13—44no—
250C22×C13—48no—
251C22×C13—48no—
252C22×C13C23×D411yescharacteristic
253C22×C13C2×H(5,𝔽2)11yescharacteristic
254C22×C13C2×2−1+411yescharacteristic
255C22×C13#58514yes—
256C4×C13—22no—
257C4×C13—24no—
258C4×C13—24no—
259C4×C13—44no—
260C4×C13—44no—
261C4×C13—44no—
262C4×C13—44no—
263C4×C13—44no—
264C4×C13#53714yes—
265C22×Q8C23×C1312yes—
266C22×D4C23×C1314yes—
267C22×D4C23×C1312yes—
268C22×D4C23×C1314yes—
269C23×C4C23×C1314yes—
270C23×C4C23×C1311yescharacteristic
271C23×C4C23×C1312yes—
272#126—216no—
273#125—28no—
274#124—28no—
275#123—216no—
276C22⋊Q8—28no—
277#121—28no—
278C4×Q8—28no—
279C4×D4—216no—
280C4×D4—28no—
281C4×D4—48no—
282#117—216no—
283#117—44no—
284C2×C4⋊C4C23×C1314yes—
285C2×C4⋊C4C23×C1314yes—
286C2×C4⋊C4C23×C1312yes—
287C2×C4⋊C4C23×C1314yes—
288C2×C4⋊C4C23×C1312yes—
289C2×C4⋊C4C23×C1314yes—
290C2×C4⋊C4C23×C1312yes—
291C2×C4⋊C4C23×C1312yes—
292C2×C4⋊C4C23×C1314yes—
293C2×C4⋊C4C23×C1318yes—
294C2×C4⋊C4C23×C1318yes—
295C2×C22⋊C4C23×C1314yes—
296C2×C22⋊C4C23×C1314yes—
297C2×C22⋊C4C23×C1314yes—
298C2×C22⋊C4C23×C1314yes—
299C2×C22⋊C4C23×C1314yes—
300C2×C22⋊C4C23×C1314yes—
301C2×C22⋊C4C23×C1318yes—
302C2×C22⋊C4C23×C1318yes—
303C2×C22⋊C4C23×C1318yes—
304C2×C42D4×C1318yescomplemented
305C2×C42C23×C1314yes—
306C2×C42C23×C1314yes—
307C2×C42C23×C1312yes—
308C2×C42C23×C1311yescharacteristic
309C2×C42C23×C1311yescharacteristic
310#95C23×C1318yes—
311#95C23×C1318yes—
312#95C23×C1314yes—
313#95C23×C1314yes—
314#95C23×C1314yes—
315#95C23×C1314yes—
316C2×C13—42no—
317C2×C13—84no—
318C2×C13C2×#53711yescharacteristic
319C2×C13#344912yes—
320C2×C13#352912yes—
321C2×C13#353112yes—
322C24C24×C1314yes—
323C24C24×C1311yescharacteristic
324C2×Q8—24no—
325C2×Q8—44no—
326C2×D4—28no—
327C2×D4—24no—
328C2×D4—44no—
329C2×D4—44no—
330C2×D4—48no—
331C2×D4—48no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—28no—
335C22×C4—28no—
336C22×C4—28no—
337C22×C4—44no—
338C22×C4C2×D4×C1314yes—
339C22×C4C2×D4×C1318yes—
340C22×C4C24×C1314yes—
341C22×C4C24×C1314yes—
342C22×C4C24×C1314yes—
343C22×C4C24×C1314yes—
344C22×C4C24×C1314yes—
345C22×C4C24×C1312yes—
346C22×C4C24×C1311yescharacteristic
347C22×C4C24×C1312yes—
348C22×C4C24×C1311yescharacteristic
349C4⋊C4—28no—
350C4⋊C4—28no—
351C4⋊C4—24no—
352C4⋊C4—28no—
353C4⋊C4—24no—
354C4⋊C4—28no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—44no—
358C4⋊C4—48no—
359C4⋊C4—48no—
360C22⋊C4—28no—
361C22⋊C4—28no—
362C22⋊C4—28no—
363C22⋊C4—28no—
364C22⋊C4—28no—
365C22⋊C4—44no—
366C22⋊C4—48no—
367C22⋊C4—48no—
368C22⋊C4—48no—
369C42—28no—
370C42—28no—
371C42C2×D4×C1318yes—
372C42C2×D4×C1314yes—
373C42C2×D4×C1314yes—
374C13#3668411yescharacteristic, direct product factor, Sylow
375C23—21no—
376C23—21no—
377C23—24no—
378C23—24no—
379C23—24no—
380C23—24no—
381C23—28no—
382C23—28no—
383C23C22×D4×C1312yes—
384C23C25×C1311yescharacteristic
385Q8—48no—
386D4—48no—
387D4—416no—
388D4—416no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—28no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—28no—
403C2×C4—28no—
404C2×C4—28no—
405C2×C4—48no—
406C2×C4—416no—
407C2×C4C22×D4×C1312yes—
408C2×C4C22×D4×C1314yes—
409C2×C4C22×D4×C1314yes—
410C2×C4C22×D4×C1312yes—
411C2×C4C13×H(5,𝔽2)12yes—
412C2×C4C13×2−1+412yes—
413C22—22no—
414C22—24no—
415C22—42no—
416C22—42no—
417C22—48no—
418C22—48no—
419C22—44no—
420C22—44no—
421C22—44no—
422C22C23×D4×C1311yescharacteristic
423C22C2×C13×H(5,𝔽2)11yescharacteristic
424C22C2×C13×2−1+411yescharacteristic
425C22C13×#58514yes—
426C4—22no—
427C4—24no—
428C4—24no—
429C4—44no—
430C4—44no—
431C4—44no—
432C4—44no—
433C4—44no—
434C4C13×#53714yes—
435C2—42no—
436C2—84no—
437C2C2×C13×#53711yescharacteristic
438C2C13×#344912yes—
439C2C13×#352912yes—
440C2C13×#353112yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#529C2semidirect
2. C13×#2823C2semidirect
3. C13×#2822C2semidirect
4. C13×#2820C2semidirect
5. C13×#2819C2semidirect
6. C13×#2814C2semidirect
7. C13×#2813C2semidirect
8. C13×#2396C2semidirect
9. C13×#2392C2semidirect
10. C13×#2392C2semidirect
11. C13×#2285C2semidirect
90. C2×C42×C13D4semidirect
102. #36684C13direct (N × H)
155. C2×#529C2×C13semidirect
156. #2823C2×C13semidirect
157. #2822C2×C13semidirect
158. #2820C2×C13semidirect
159. #2819C2×C13semidirect
160. #2814C2×C13semidirect
161. #2813C2×C13semidirect
162. #2396C2×C13semidirect
163. #2392C2×C13semidirect
164. #2392C2×C13semidirect
165. #2285C2×C13semidirect
304. C2×C42D4×C13semidirect
374. C13#36684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5292
C13×#28232
C13×#28222
C13×#28202
C13×#28192
C13×#28142
C13×#28132
C13×#23962
C13×#23922
C13×#22852
#3668413