Finite Group Databasebeta

← C2×C13×#2204 #15719904

Subgroups — C2×C13×#2204 #15719904

Order 3328.

1200 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#555C211yesmaximal, characteristic, complemented
2C2×C13×#456C211yesmaximal, characteristic, complemented
3C2×C13×#454C212yesmaximal, complemented
4C13×#2204C218yesmaximal, direct product factor
5C2×C13×#356C211yesmaximal, characteristic, complemented
6C2×C13×#355C212yesmaximal, complemented
7C2×C13×2−1+4C2211yescharacteristic
8C2×C13×#137—21no—
9C2×C13×AGL(1,ℤ/8)—22no—
10C13×#555—22no—
11C13×#555—24no—
12C13×#555C2214yescomplemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C13×#124—21no—
15C2×C13×#124C2212yes—
16C2×C13×#121—22no—
17C2×C4×D4×C13—21no—
18C2×C13×#117—22no—
19C13×#456—22no—
20C13×#456C2214yescomplemented
21C13×#454—24no—
22C13×#454C2218yescomplemented
23C2×C13×#104—22no—
24C2×C13×#104—21no—
25C2×C13×#101C2212yes—
26C2×C13×#101C2211yescharacteristic
27C13×#356C2214yescomplemented
28C13×#355C2218yescomplemented
29C13×2−1+4—22no—
30C13×2−1+4—21no—
31C13×2−1+4—42no—
32C13×2−1+4C2312yes—
33C2×C13×#41—22no—
34C2×C13×#41—21no—
35C2×C13×#41—41no—
36C22×Q8×C13—41no—
37C22×Q8×C13D411yescharacteristic
38C22×Q8×C13C2311yescharacteristic
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13D412yes—
42C23×C4×C13—22no—
43C13×#137—24no—
44C13×#137—42no—
45C13×AGL(1,ℤ/8)—28no—
46C13×AGL(1,ℤ/8)—44no—
47C2×C13×Q16—41no—
48C2×C13×SD16—41no—
49C2×C13×SD16—42no—
50C2×C13×D8—42no—
51C2×C13×M16—22no—
52C2×C13×M16—21no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8D412yes—
55C13×C4⋊Q8C2312yes—
56C13×#124—24no—
57C13×#124—24no—
58C13×#124—22no—
59C13×#124—22no—
60C13×#124D414yes—
61C13×#124C2314yes—
62C13×#121—28no—
63C13×#121—28no—
64C4×D4×C13—24no—
65C4×D4×C13—24no—
66C13×#117—28no—
67C13×#117—28no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C42×C13—21no—
74C2×C42×C13D412yes—
75C2×C42×C13D411yescharacteristic
76C13×#104—28no—
77C13×#104—24no—
78C13×#101—22no—
79C13×#101—21no—
80C13×#101C2312yes—
81C13×#101C2314yes—
82C2×#2204C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—22no—
84C13×#41—24no—
85C13×#41—22no—
86C13×#41—24no—
87C13×#41—22no—
88C13×#41—42no—
89C13×#41—41no—
90C13×#41—42no—
91C13×#41—44no—
92C13×#41—42no—
93C13×#41—41no—
94C13×#41—42no—
95C2×Q8×C13—21no—
96C2×Q8×C13—22no—
97C2×Q8×C13—21no—
98C2×Q8×C13—41no—
99C2×Q8×C13—41no—
100C2×Q8×C13—41no—
101C2×Q8×C13—41no—
102C2×Q8×C13—42no—
103C2×Q8×C13—44no—
104C2×Q8×C13—42no—
105C2×Q8×C13C2×D412yes—
106C2×Q8×C13C2×D411yescharacteristic
107C2×Q8×C13C2×D412yes—
108C2×Q8×C13C2411yescharacteristic
109C2×D4×C13—22no—
110C2×D4×C13—21no—
111C2×D4×C13—24no—
112C2×D4×C13—24no—
113C2×D4×C13—22no—
114C2×D4×C13—44no—
115C2×D4×C13—42no—
116C2×D4×C13—42no—
117C2×D4×C13—41no—
118C2×D4×C13—81no—
119C2×D4×C13—81no—
120C2×D4×C13C2×D414yes—
121C22×C4×C13—21no—
122C22×C4×C13—28no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—48no—
126C22×C4×C13—42no—
127C22×C4×C13—41no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D412yes—
130C13×Q16—44no—
131C13×SD16—44no—
132C13×SD16—48no—
133C13×D8—48no—
134C13×M16—24no—
135C13×M16—22no—
136C13×M16—42no—
137C13×M16—41no—
138C2×C8×C13—42no—
139C2×C8×C13—41no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—24no—
142C13×C4⋊C4—24no—
143C13×C22⋊C4—28no—
144C13×C22⋊C4—24no—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—24no—
147C13×C22⋊C4—24no—
148C42×C13—24no—
149C42×C13—22no—
150C42×C13—21no—
151C42×C13C2×D414yes—
152C42×C13C2×D412yes—
153C2×#555C2×C1311yescharacteristic, complemented
154C2×#456C2×C1311yescharacteristic, complemented
155C2×#454C2×C1312yescomplemented
156#2204C2×C1318yesdirect product factor
157C2×#356C2×C1311yescharacteristic, complemented
158C2×#355C2×C1312yescomplemented
159C23×C13—24no—
160C23×C13—44no—
161C23×C13—44no—
162C23×C13—42no—
163C23×C13—41no—
164C23×C13—42no—
165C23×C13#12011yescharacteristic
166Q8×C13—24no—
167Q8×C13—22no—
168Q8×C13—42no—
169Q8×C13—41no—
170Q8×C13—41no—
171Q8×C13—42no—
172Q8×C13—41no—
173Q8×C13—42no—
174Q8×C13—81no—
175D4×C13—24no—
176D4×C13—22no—
177D4×C13—48no—
178D4×C13—42no—
179D4×C13—41no—
180D4×C13—44no—
181D4×C13—42no—
182D4×C13—42no—
183D4×C13—82no—
184D4×C13—84no—
185C2×C4×C13—24no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—21no—
189C2×C4×C13—22no—
190C2×C4×C13—21no—
191C2×C4×C13—24no—
192C2×C4×C13—22no—
193C2×C4×C13—416no—
194C2×C4×C13—44no—
195C2×C4×C13—42no—
196C2×C4×C13—44no—
197C2×C4×C13—42no—
198C2×C4×C13—44no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13#12011yescharacteristic
203C2×C4×C13#12012yes—
204C2×C4×C13C22×D411yescharacteristic
205C2×C4×C13C22×D412yes—
206C8×C13—44no—
207C8×C13—42no—
208C2×2−1+4C22×C1311yescharacteristic
209C2×#137—21no—
210C2×AGL(1,ℤ/8)—22no—
211#555—22no—
212#555—24no—
213#555C22×C1314yescomplemented
214C2×C4⋊Q8C22×C1311yescharacteristic
215C2×#124—21no—
216C2×#124C22×C1312yes—
217C2×#121—22no—
218C2×C4×D4—21no—
219C2×#117—22no—
220#456—22no—
221#456C22×C1314yescomplemented
222#454—24no—
223#454C22×C1318yescomplemented
224C2×#104—22no—
225C2×#104—21no—
226C2×#101C22×C1311yescharacteristic
227C2×#101C22×C1312yes—
228#356C22×C1314yescomplemented
229#355C22×C1318yescomplemented
230C22×C13—22no—
231C22×C13—44no—
232C22×C13—44no—
233C22×C13—42no—
234C22×C13—44no—
235C22×C13—84no—
236C22×C13—82no—
237C22×C13—84no—
238C22×C13B(4,𝔽2)11yescharacteristic
239C22×C13B(4,𝔽2)11yescharacteristic
240C22×C13C2×#12011yescharacteristic
241C4×C13—24no—
242C4×C13—22no—
243C4×C13—21no—
244C4×C13—22no—
245C4×C13—21no—
246C4×C13—44no—
247C4×C13—42no—
248C4×C13—42no—
2492−1+4—22no—
2502−1+4—21no—
2512−1+4—42no—
2522−1+4C23×C1312yes—
253C2×#41—22no—
254C2×#41—21no—
255C2×#41—41no—
256C22×Q8—41no—
257C22×Q8D4×C1311yescharacteristic
258C22×Q8C23×C1311yescharacteristic
259C22×D4—21no—
260C22×D4—21no—
261C22×D4D4×C1312yes—
262C23×C4—22no—
263#137—24no—
264#137—42no—
265AGL(1,ℤ/8)—28no—
266AGL(1,ℤ/8)—44no—
267C2×Q16—41no—
268C2×SD16—41no—
269C2×SD16—42no—
270C2×D8—42no—
271C2×M16—22no—
272C2×M16—21no—
273C4⋊Q8—22no—
274C4⋊Q8D4×C1312yes—
275C4⋊Q8C23×C1312yes—
276#124—24no—
277#124—24no—
278#124—22no—
279#124—22no—
280#124D4×C1314yes—
281#124C23×C1314yes—
282#121—28no—
283#121—28no—
284C4×D4—24no—
285C4×D4—24no—
286#117—28no—
287#117—28no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C42—21no—
294C2×C42D4×C1312yes—
295C2×C42D4×C1311yescharacteristic
296#104—28no—
297#104—24no—
298#101—22no—
299#101—21no—
300#101C23×C1312yes—
301#101C23×C1314yes—
302C2×C13—21no—
303C2×C13—21no—
304C2×C13—84no—
305C2×C13—82no—
306C2×C13#220412yesdirect product factor
307C2×C13C2×B(4,𝔽2)11yescharacteristic
308C24—22no—
309#41—24no—
310#41—22no—
311#41—24no—
312#41—22no—
313#41—42no—
314#41—41no—
315#41—42no—
316#41—44no—
317#41—42no—
318#41—41no—
319#41—42no—
320C2×Q8—21no—
321C2×Q8—22no—
322C2×Q8—21no—
323C2×Q8—41no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—42no—
328C2×Q8—44no—
329C2×Q8—42no—
330C2×Q8C2×D4×C1312yes—
331C2×Q8C2×D4×C1311yescharacteristic
332C2×Q8C2×D4×C1312yes—
333C2×Q8C24×C1311yescharacteristic
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—22no—
339C2×D4—44no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—41no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4C2×D4×C1314yes—
346C22×C4—21no—
347C22×C4—28no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—48no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4C2×D4×C1311yescharacteristic
354C22×C4C2×D4×C1312yes—
355Q16—44no—
356SD16—44no—
357SD16—48no—
358D8—48no—
359M16—24no—
360M16—22no—
361M16—42no—
362M16—41no—
363C2×C8—42no—
364C2×C8—41no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C22⋊C4—28no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C42—24no—
374C42—22no—
375C42—21no—
376C42C2×D4×C1314yes—
377C42C2×D4×C1312yes—
378C13C2×#220411yescharacteristic, direct product factor, Sylow
379C23—24no—
380C23—44no—
381C23—44no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23C13×#12011yescharacteristic
386Q8—24no—
387Q8—22no—
388Q8—42no—
389Q8—41no—
390Q8—41no—
391Q8—42no—
392Q8—42no—
393Q8—41no—
394Q8—81no—
395D4—24no—
396D4—22no—
397D4—44no—
398D4—48no—
399D4—42no—
400D4—41no—
401D4—42no—
402D4—42no—
403D4—82no—
404D4—84no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—416no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4C13×#12011yescharacteristic
423C2×C4C13×#12012yes—
424C2×C4C22×D4×C1311yescharacteristic
425C2×C4C22×D4×C1312yes—
426C8—44no—
427C8—42no—
428C22—22no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—44no—
433C22—84no—
434C22—82no—
435C22—84no—
436C22C13×B(4,𝔽2)11yescharacteristic
437C22C13×B(4,𝔽2)11yescharacteristic
438C22C2×C13×#12011yescharacteristic
439C4—24no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—44no—
445C4—42no—
446C4—42no—
447C2—21no—
448C2—21no—
449C2—84no—
450C2—82no—
451C2C13×#220412yesdirect product factor
452C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C13
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#555C2semidirect
2. C2×C13×#456C2semidirect
3. C2×C13×#454C2semidirect
4. C13×#2204C2direct (N × H)
5. C2×C13×#356C2semidirect
6. C2×C13×#355C2semidirect
12. C13×#555C22semidirect
20. C13×#456C22semidirect
22. C13×#454C22semidirect
27. C13×#356C22semidirect
28. C13×#355C22semidirect
82. C2×#2204C13direct (N × H)
153. C2×#555C2×C13semidirect
154. C2×#456C2×C13semidirect
155. C2×#454C2×C13semidirect
156. #2204C2×C13direct (N × H)
157. C2×#356C2×C13semidirect
158. C2×#355C2×C13semidirect
213. #555C22×C13semidirect
221. #456C22×C13semidirect
223. #454C22×C13semidirect
228. #356C22×C13semidirect
229. #355C22×C13semidirect
306. C2×C13#2204direct (N × H)
378. C13C2×#2204direct (N × H)
451. C2C13×#2204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5552
C2×C13×#4562
C2×C13×#4542
C13×#22042
C2×C13×#3562
C2×C13×#3552
C2×#220413