Finite Group Databasebeta

← C13×#33646 #15719985

Subgroups — C13×#33646 #15719985

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3050C211yesmaximal, characteristic
2C22×C13×#107C211yesmaximal, characteristic, complemented
3C13×#2236C212yesmaximal, complemented
4C13×#2235C212yesmaximal, complemented
5C13×#2233C212yesmaximal, complemented
6C13×#2232C212yesmaximal, complemented
7C13×#2159C212yesmaximal, complemented
8C13×#2139C212yesmaximal, complemented
9C13×#2112C211yesmaximal, characteristic, complemented
10C2×C13×#135C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C13×#525—21no—
13C22×C13×C4⋊C4—21no—
14C2×C13×M32C2212yes—
15C13×#467C2211yescharacteristic
16C13×#467C2211yescharacteristic
17C13×#466C2211yescharacteristic
18C13×#466C2211yescharacteristic
19C13×#465—21no—
20C13×#465—21no—
21C13×#427C2211yescharacteristic
22C2×C13×#107—21no—
23C2×C13×#107—21no—
24C2×C13×#107—21no—
25C2×C13×#107C2212yes—
26C2×C13×#107C2212yes—
27C2×C13×#107C2212yes—
28C13×#416—21no—
29C13×#367C2214yescomplemented
30C13×#366C2214yescomplemented
31C13×#358C2214yescomplemented
32C13×#357C2214yescomplemented
33C13×C22⋊C16C2212yes—
34C13×C22⋊C16C2212yes—
35C2×C13×#41—21no—
36C23×C4×C13—41no—
37C23×C4×C13D411yescharacteristic
38C13×#135—24no—
39C2×C13×Q16C2311yescharacteristic
40C2×C13×SD16—21no—
41C2×C13×D8C2311yescharacteristic
42C22×C8×C13—24no—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13D411yescharacteristic
45C22×C8×C13D411yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C13×#123—41no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×#121—21no—
53C13×#121—21no—
54C13×#120—41no—
55C4×D4×C13—41no—
56C4×D4×C13—41no—
57C13×#117—21no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—41no—
62C2×C13×C4⋊C4—41no—
63C2×C13×C4⋊C4—41no—
64C13×M32—24no—
65C2×C13×C16C2314yes—
66C13×#107—22no—
67C13×#107—22no—
68C13×#107—22no—
69C13×#107C2314yes—
70C13×#107C2311yescharacteristic
71C13×#107C2311yescharacteristic
72C13×#106—21no—
73C13×#103—21no—
74C13×#103—21no—
75C13×#102—21no—
76C13×#102—21no—
77#33646C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13D811yescharacteristic
79C13×#41—42no—
80C13×#41—42no—
81C2×Q8×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—42no—
91C22×C4×C13—41no—
92C22×C4×C13—84no—
93C22×C4×C13D811yescharacteristic
94C22×C4×C13D811yescharacteristic
95C22×C4×C13D811yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C13×Q16—22no—
100C13×SD16—42no—
101C13×D8—22no—
102C2×C8×C13—22no—
103C2×C8×C13—22no—
104C2×C8×C13—22no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13#4114yes—
111C2×C8×C13C2411yescharacteristic
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—42no—
116C13×C4⋊C4—42no—
117C13×C4⋊C4—42no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C42×C13—41no—
126C13×C16—24no—
127#3050C2×C1311yescharacteristic
128C22×#107C2×C1311yescharacteristic, complemented
129#2236C2×C1312yescomplemented
130#2235C2×C1312yescomplemented
131#2233C2×C1312yescomplemented
132#2232C2×C1312yescomplemented
133#2159C2×C1312yescomplemented
134#2139C2×C1312yescomplemented
135#2112C2×C1311yescharacteristic, complemented
136C23×C13—22no—
137C23×C13—22no—
138C23×C13—22no—
139C23×C13—41no—
140C23×C13C2×D811yescharacteristic
141C23×C13C2×D811yescharacteristic
142C23×C13C2×D811yescharacteristic
143Q8×C13—41no—
144Q8×C13—41no—
145D4×C13—41no—
146D4×C13—41no—
147D4×C13—82no—
148D4×C13—82no—
149D4×C13—82no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—44no—
161C2×C4×C13—84no—
162C2×C4×C13—84no—
163C2×C4×C13—84no—
164C2×C4×C13—82no—
165C2×C4×C13#12312yes—
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13#13712yes—
170C2×C4×C13C22×D411yescharacteristic
171C8×C13—21no—
172C8×C13—21no—
173C8×C13#12312yes—
174C8×C13C2×#4112yes—
175C2×#135C22×C1311yescharacteristic
176C23×C8C22×C1311yescharacteristic
177#525—21no—
178C22×C4⋊C4—21no—
179C2×M32C22×C1312yes—
180#467C22×C1311yescharacteristic
181#467C22×C1311yescharacteristic
182#466C22×C1311yescharacteristic
183#466C22×C1311yescharacteristic
184#465—21no—
185#465—21no—
186#427C22×C1311yescharacteristic
187C2×#107—21no—
188C2×#107—21no—
189C2×#107—21no—
190C2×#107C22×C1312yes—
191C2×#107C22×C1312yes—
192C2×#107C22×C1312yes—
193#416—21no—
194#367C22×C1314yescomplemented
195#366C22×C1314yescomplemented
196#358C22×C1314yescomplemented
197#357C22×C1314yescomplemented
198C22⋊C16C22×C1312yes—
199C22⋊C16C22×C1312yes—
200C22×C13—28no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13#48012yes—
211C22×C13#50912yes—
212C22×C13#51012yes—
213C22×C13C22×D811yescharacteristic
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—81no—
217C4×C13—84no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13#48012yes—
221C4×C13C2×#12311yescharacteristic
222C4×C13C2×#13711yescharacteristic
223C2×#41—21no—
224C23×C4—41no—
225C23×C4D4×C1311yescharacteristic
226#135—24no—
227C2×Q16C23×C1311yescharacteristic
228C2×SD16—21no—
229C2×D8C23×C1311yescharacteristic
230C22×C8—24no—
231C22×C8D4×C1311yescharacteristic
232C22×C8D4×C1311yescharacteristic
233C22×C8D4×C1311yescharacteristic
234C22×C8C23×C1311yescharacteristic
235C22×C8C23×C1311yescharacteristic
236C22×C8C23×C1311yescharacteristic
237#123—41no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240#121—21no—
241#121—21no—
242#120—41no—
243C4×D4—41no—
244C4×D4—41no—
245#117—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4—41no—
251C2×C4⋊C4—41no—
252M32—24no—
253C2×C16C23×C1314yes—
254#107—22no—
255#107—22no—
256#107—22no—
257#107C23×C1314yes—
258#107C23×C1311yescharacteristic
259#107C23×C1311yescharacteristic
260#106—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264#102—21no—
265C2×C13—22no—
266C2×C13—22no—
267C2×C13—22no—
268C2×C13—161no—
269C2×C13C2×#48011yescharacteristic
270C2×C13C2×#50911yescharacteristic
271C2×C13C2×#51011yescharacteristic
272C24C13×D811yescharacteristic
273#41—42no—
274#41—42no—
275C2×Q8—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—84no—
287C22×C4C13×D811yescharacteristic
288C22×C4C13×D811yescharacteristic
289C22×C4C13×D811yescharacteristic
290C22×C4C2×D4×C1311yescharacteristic
291C22×C4C2×D4×C1311yescharacteristic
292C22×C4C2×D4×C1311yescharacteristic
293Q16—22no—
294SD16—42no—
295D8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8C2×D4×C1311yescharacteristic
302C2×C8C2×D4×C1311yescharacteristic
303C2×C8C2×D4×C1311yescharacteristic
304C2×C8C13×#4114yes—
305C2×C8C24×C1311yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—24no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42—41no—
320C16—24no—
321C13#3364611yescharacteristic, direct product factor, Sylow
322C23—22no—
323C23—22no—
324C23—22no—
325C23—41no—
326C23C2×C13×D811yescharacteristic
327C23C2×C13×D811yescharacteristic
328C23C2×C13×D811yescharacteristic
329Q8—41no—
330Q8—41no—
331D4—41no—
332D4—41no—
333D4—82no—
334D4—82no—
335D4—82no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—44no—
347C2×C4—84no—
348C2×C4—84no—
349C2×C4—84no—
350C2×C4—82no—
351C2×C4C13×#12312yes—
352C2×C4C2×C13×D811yescharacteristic
353C2×C4C2×C13×D811yescharacteristic
354C2×C4C2×C13×D811yescharacteristic
355C2×C4C13×#13712yes—
356C2×C4C22×D4×C1311yescharacteristic
357C8—21no—
358C8—21no—
359C8C13×#12312yes—
360C8C2×C13×#4112yes—
361C22—28no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C13×#48012yes—
372C22C13×#50912yes—
373C22C13×#51012yes—
374C22C22×C13×D811yescharacteristic
375C4—21no—
376C4—21no—
377C4—81no—
378C4—84no—
379C4—81no—
380C4—81no—
381C4C13×#48012yes—
382C4C2×C13×#12311yescharacteristic
383C4C2×C13×#13711yescharacteristic
384C2—22no—
385C2—22no—
386C2—22no—
387C2—161no—
388C2C2×C13×#48011yescharacteristic
389C2C2×C13×#50911yescharacteristic
390C2C2×C13×#51011yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C13×#107C2semidirect
3. C13×#2236C2semidirect
4. C13×#2235C2semidirect
5. C13×#2233C2semidirect
6. C13×#2232C2semidirect
7. C13×#2159C2semidirect
8. C13×#2139C2semidirect
9. C13×#2112C2semidirect
29. C13×#367C22semidirect
30. C13×#366C22semidirect
31. C13×#358C22semidirect
32. C13×#357C22semidirect
77. #33646C13direct (N × H)
128. C22×#107C2×C13semidirect
129. #2236C2×C13semidirect
130. #2235C2×C13semidirect
131. #2233C2×C13semidirect
132. #2232C2×C13semidirect
133. #2159C2×C13semidirect
134. #2139C2×C13semidirect
135. #2112C2×C13semidirect
194. #367C22×C13semidirect
195. #366C22×C13semidirect
196. #358C22×C13semidirect
197. #357C22×C13semidirect
321. C13#33646direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30502
C22×C13×#1072
C13×#22362
C13×#22352
C13×#22332
C13×#22322
C13×#21592
C13×#21392
C13×#21122
#3364613