Finite Group Databasebeta

← C13×#32898 #15719237

Subgroups — C13×#32898 #15719237

Order 3328.

4360 conjugacy classes of subgroups; only the 370 normal subgroups are shown.

normal subgroups only

This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 370 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
1C22×C13×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×C13×B(4,𝔽2)C214yesmaximal, complemented
3C13×#2403C213yesmaximal, complemented
4C13×#1790C214yesmaximal, complemented
5C13×#1781C213yesmaximal, complemented
6C2×C13×H(5,𝔽2)—216no—
7C2×C13×H(5,𝔽2)—26no—
8C2×C13×H(5,𝔽2)C2214yes—
9C22×C13×#41—23no—
10C23×D4×C13—23no—
11C23×D4×C13C2213yes—
12C23×D4×C13C2211yescharacteristic, complemented
13C2×C13×#120—23no—
14C2×C13×#120C2216yescomplemented
15C13×B(4,𝔽2)—216no—
16C2×C13×#99C22112yescomplemented
17C13×#392—26no—
18C13×#386—23no—
19C13×#386C2216yescomplemented
20C13×#379C2213yescomplemented
21C25×C13—21no—
22C25×C13D413yescomplemented
23C25×C13C2311yescharacteristic
24C25×C13C2311yescharacteristic, complemented
25C13×H(5,𝔽2)—248no—
26C13×H(5,𝔽2)—248no—
27C13×H(5,𝔽2)—224no—
28C13×H(5,𝔽2)D4116yescomplemented
29C2×C13×#41—212no—
30C2×C13×#41—248no—
31C2×C13×#41—212no—
32C22×Q8×C13—21no—
33C22×D4×C13—23no—
34C22×D4×C13—248no—
35C22×D4×C13—212no—
36C22×D4×C13—26no—
37C22×D4×C13—212no—
38C22×D4×C13—26no—
39C22×D4×C13—224no—
40C22×D4×C13—23no—
41C22×D4×C13—23no—
42C22×D4×C13—26no—
43C22×D4×C13—44no—
44C22×D4×C13D416yescomplemented
45C22×D4×C13C2316yes—
46C23×C4×C13—23no—
47C23×C4×C13D413yescomplemented
48C23×C4×C13C2311yescharacteristic, complemented
49C13×#120—224no—
50C13×#120—412no—
51C2×C13×C22⋊C4—23no—
52C2×C13×C22⋊C4—26no—
53C2×C13×C22⋊C4—26no—
54C2×C13×C22⋊C4—23no—
55C2×C13×C22⋊C4C2316yescomplemented
56C13×#99—224no—
57C13×#95—26no—
58#32898C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13—28no—
60C24×C13—24no—
61C24×C13—23no—
62C24×C13—23no—
63C24×C13—212no—
64C24×C13—24no—
65C24×C13—23no—
66C24×C13—24no—
67C24×C13—42no—
68C24×C13—42no—
69C24×C13—46no—
70C24×C13—81no—
71C24×C13—81no—
72C24×C13—83no—
73C24×C13—82no—
74C24×C13—82no—
75C24×C13C2×D413yes—
76C24×C13C2×D413yes—
77C24×C13C2×D416yes—
78C24×C13C2411yescharacteristic
79C13×#41—296no—
80C13×#41—248no—
81C13×#41—248no—
82C2×Q8×C13—28no—
83C2×Q8×C13—24no—
84C2×D4×C13—224no—
85C2×D4×C13—248no—
86C2×D4×C13—212no—
87C2×D4×C13—296no—
88C2×D4×C13—248no—
89C2×D4×C13—248no—
90C2×D4×C13—212no—
91C2×D4×C13—248no—
92C2×D4×C13—212no—
93C2×D4×C13—212no—
94C2×D4×C13—212no—
95C2×D4×C13—212no—
96C2×D4×C13—212no—
97C2×D4×C13—46no—
98C2×D4×C13—46no—
99C2×D4×C13—46no—
100C2×D4×C13—43no—
101C2×D4×C13—41no—
102C2×D4×C13—412no—
103C2×D4×C13—412no—
104C2×D4×C13—86no—
105C2×D4×C13C2×D4124yes—
106C22×C4×C13—224no—
107C22×C4×C13—212no—
108C22×C4×C13—23no—
109C22×C4×C13—23no—
110C22×C4×C13—212no—
111C22×C4×C13—23no—
112C22×C4×C13—26no—
113C22×C4×C13—42no—
114C22×C4×C13C2×D416yes—
115C13×C22⋊C4—212no—
116C13×C22⋊C4—412no—
117C13×C22⋊C4—46no—
118C13×C22⋊C4—412no—
119C13×C22⋊C4—83no—
120C22×H(5,𝔽2)C2×C1311yescharacteristic, complemented
121C2×B(4,𝔽2)C2×C1314yescomplemented
122#2403C2×C1313yescomplemented
123#1790C2×C1314yescomplemented
124#1781C2×C1313yescomplemented
125C23×C13—212no—
126C23×C13—212no—
127C23×C13—216no—
128C23×C13—26no—
129C23×C13—26no—
130C23×C13—26no—
131C23×C13—26no—
132C23×C13—26no—
133C23×C13—26no—
134C23×C13—41no—
135C23×C13—43no—
136C23×C13—41no—
137C23×C13—43no—
138C23×C13—43no—
139C23×C13—46no—
140C23×C13—46no—
141C23×C13—46no—
142C23×C13—43no—
143C23×C13—46no—
144C23×C13—46no—
145C23×C13—46no—
146C23×C13—41no—
147C23×C13—83no—
148C23×C13—83no—
149C23×C13—88no—
150C23×C13—88no—
151C23×C13—824no—
152C23×C13—816no—
153C23×C13—84no—
154C23×C13—84no—
155C23×C13#12013yes—
156C23×C13#12011yescharacteristic
157C23×C13#120112yescomplemented
158C23×C13C22×D413yes—
159C23×C13C22×D414yes—
160Q8×C13—216no—
161D4×C13—248no—
162D4×C13—248no—
163D4×C13—248no—
164D4×C13—412no—
165D4×C13—44no—
166D4×C13—824no—
167C2×C4×C13—212no—
168C2×C4×C13—212no—
169C2×C4×C13—248no—
170C2×C4×C13—26no—
171C2×C4×C13—26no—
172C2×C4×C13—26no—
173C2×C4×C13—43no—
174C2×C4×C13—41no—
175C2×C4×C13—46no—
176C2×C4×C13—46no—
177C2×C4×C13—46no—
178C2×C4×C13#120112yescomplemented
179C2×H(5,𝔽2)—216no—
180C2×H(5,𝔽2)—26no—
181C2×H(5,𝔽2)C22×C1314yes—
182C22×#41—23no—
183C23×D4—23no—
184C23×D4C22×C1313yes—
185C23×D4C22×C1311yescharacteristic, complemented
186C2×#120—23no—
187C2×#120C22×C1316yescomplemented
188B(4,𝔽2)—216no—
189C2×#99C22×C13112yescomplemented
190#392—26no—
191#386—23no—
192#386C22×C1316yescomplemented
193#379C22×C1313yescomplemented
194C22×C13—21no—
195C22×C13—23no—
196C22×C13—23no—
197C22×C13—21no—
198C22×C13—23no—
199C22×C13—212no—
200C22×C13—23no—
201C22×C13—23no—
202C22×C13—44no—
203C22×C13—412no—
204C22×C13—412no—
205C22×C13—424no—
206C22×C13—412no—
207C22×C13—46no—
208C22×C13—46no—
209C22×C13—42no—
210C22×C13—86no—
211C22×C13—86no—
212C22×C13—86no—
213C22×C13—812no—
214C22×C13—816no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13B(4,𝔽2)12yescomplemented
218C22×C13C2×#12016yes—
219C22×C13C2×#12011yescharacteristic
220C4×C13—212no—
221C4×C13—42no—
222C4×C13—86no—
223C25—21no—
224C25D4×C1313yescomplemented
225C25C23×C1311yescharacteristic
226C25C23×C1311yescharacteristic, complemented
227H(5,𝔽2)—248no—
228H(5,𝔽2)—248no—
229H(5,𝔽2)—224no—
230H(5,𝔽2)D4×C13116yescomplemented
231C2×#41—212no—
232C2×#41—248no—
233C2×#41—212no—
234C22×Q8—21no—
235C22×D4—23no—
236C22×D4—248no—
237C22×D4—212no—
238C22×D4—26no—
239C22×D4—212no—
240C22×D4—26no—
241C22×D4—224no—
242C22×D4—23no—
243C22×D4—23no—
244C22×D4—26no—
245C22×D4—44no—
246C22×D4D4×C1316yescomplemented
247C22×D4C23×C1316yes—
248C23×C4—23no—
249C23×C4D4×C1313yescomplemented
250C23×C4C23×C1311yescharacteristic, complemented
251#120—224no—
252#120—412no—
253C2×C22⋊C4—23no—
254C2×C22⋊C4—26no—
255C2×C22⋊C4—26no—
256C2×C22⋊C4—23no—
257C2×C22⋊C4C23×C1316yescomplemented
258#99—224no—
259#95—26no—
260C2×C13—26no—
261C2×C13—22no—
262C2×C13—43no—
263C2×C13—412no—
264C2×C13—82no—
265C2×C13#284611yescharacteristic
266C2×C13C2×B(4,𝔽2)11yescharacteristic
267C2×C13#302611yescharacteristic
268C24—28no—
269C24—24no—
270C24—23no—
271C24—23no—
272C24—212no—
273C24—24no—
274C24—23no—
275C24—24no—
276C24—42no—
277C24—42no—
278C24—46no—
279C24—81no—
280C24—81no—
281C24—83no—
282C24—82no—
283C24—82no—
284C24C2×D4×C1313yes—
285C24C2×D4×C1313yes—
286C24C2×D4×C1316yes—
287C24C24×C1311yescharacteristic
288#41—296no—
289#41—248no—
290#41—248no—
291C2×Q8—28no—
292C2×Q8—24no—
293C2×D4—224no—
294C2×D4—248no—
295C2×D4—212no—
296C2×D4—296no—
297C2×D4—248no—
298C2×D4—248no—
299C2×D4—212no—
300C2×D4—248no—
301C2×D4—212no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—212no—
305C2×D4—212no—
306C2×D4—46no—
307C2×D4—46no—
308C2×D4—46no—
309C2×D4—43no—
310C2×D4—41no—
311C2×D4—412no—
312C2×D4—412no—
313C2×D4—86no—
314C2×D4C2×D4×C13124yes—
315C22×C4—224no—
316C22×C4—212no—
317C22×C4—23no—
318C22×C4—23no—
319C22×C4—212no—
320C22×C4—23no—
321C22×C4—26no—
322C22×C4—42no—
323C22×C4C2×D4×C1316yes—
324C22⋊C4—212no—
325C22⋊C4—412no—
326C22⋊C4—46no—
327C22⋊C4—412no—
328C22⋊C4—83no—
329C13#3289811yescharacteristic, direct product factor, Sylow
330C23—212no—
331C23—212no—
332C23—216no—
333C23—26no—
334C23—26no—
335C23—26no—
336C23—26no—
337C23—26no—
338C23—26no—
339C23—41no—
340C23—43no—
341C23—41no—
342C23—43no—
343C23—43no—
344C23—46no—
345C23—46no—
346C23—46no—
347C23—43no—
348C23—46no—
349C23—46no—
350C23—46no—
351C23—41no—
352C23—83no—
353C23—83no—
354C23—88no—
355C23—88no—
356C23—824no—
357C23—816no—
358C23—84no—
359C23—84no—
360C23C13×#12013yes—
361C23C13×#12011yescharacteristic
362C23C13×#120112yescomplemented
363C23C22×D4×C1313yes—
364C23C22×D4×C1314yes—
365Q8—216no—
366D4—248no—
367D4—248no—
368D4—248no—
369D4—412no—
370D4—44no—
371D4—824no—
372C2×C4—212no—
373C2×C4—212no—
374C2×C4—248no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—43no—
379C2×C4—41no—
380C2×C4—46no—
381C2×C4—46no—
382C2×C4—46no—
383C2×C4C13×#120112yescomplemented
384C22—23no—
385C22—23no—
386C22—21no—
387C22—21no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—212no—
392C22—44no—
393C22—412no—
394C22—412no—
395C22—424no—
396C22—412no—
397C22—46no—
398C22—46no—
399C22—42no—
400C22—86no—
401C22—86no—
402C22—86no—
403C22—812no—
404C22—816no—
405C22—81no—
406C22—81no—
407C22C13×B(4,𝔽2)12yescomplemented
408C22C2×C13×#12016yes—
409C22C2×C13×#12011yescharacteristic
410C4—212no—
411C4—42no—
412C4—86no—
413C2—26no—
414C2—22no—
415C2—43no—
416C2—412no—
417C2—82no—
418C2C13×#284611yescharacteristic
419C2C2×C13×B(4,𝔽2)11yescharacteristic
420C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×H(5,𝔽2)C2semidirect
2. C2×C13×B(4,𝔽2)C2semidirect
3. C13×#2403C2semidirect
4. C13×#1790C2semidirect
5. C13×#1781C2semidirect
12. C23×D4×C13C22semidirect
14. C2×C13×#120C22semidirect
16. C2×C13×#99C22semidirect
19. C13×#386C22semidirect
20. C13×#379C22semidirect
22. C25×C13D4semidirect
24. C25×C13C23semidirect
28. C13×H(5,𝔽2)D4semidirect
44. C22×D4×C13D4semidirect
47. C23×C4×C13D4semidirect
48. C23×C4×C13C23semidirect
55. C2×C13×C22⋊C4C23semidirect
58. #32898C13direct (N × H)
120. C22×H(5,𝔽2)C2×C13semidirect
121. C2×B(4,𝔽2)C2×C13semidirect
122. #2403C2×C13semidirect
123. #1790C2×C13semidirect
124. #1781C2×C13semidirect
157. C23×C13#120semidirect
178. C2×C4×C13#120semidirect
185. C23×D4C22×C13semidirect
187. C2×#120C22×C13semidirect
189. C2×#99C22×C13semidirect
192. #386C22×C13semidirect
193. #379C22×C13semidirect
217. C22×C13B(4,𝔽2)semidirect
224. C25D4×C13semidirect
226. C25C23×C13semidirect
230. H(5,𝔽2)D4×C13semidirect
246. C22×D4D4×C13semidirect
249. C23×C4D4×C13semidirect
250. C23×C4C23×C13semidirect
257. C2×C22⋊C4C23×C13semidirect
329. C13#32898direct (N × H)
362. C23C13×#120semidirect
383. C2×C4C13×#120semidirect
407. C22C13×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C22×C13×H(5,𝔽2)2
C2×C13×B(4,𝔽2)2
C13×#24032
C13×#17902
C13×#17812
#3289813