Finite Group Databasebeta

← C13×#32926 #15719265

Subgroups — C13×#32926 #15719265

Order 3328.

1922 conjugacy classes of subgroups; only the 298 normal subgroups are shown.

normal subgroups only

This group has 1922 conjugacy classes of subgroups — too many to draw. Only its 298 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
1C4×C13×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×C13×B(4,𝔽2)C212yesmaximal, complemented
3C13×#2408C213yesmaximal, complemented
4C13×#1889C216yesmaximal, complemented
5C13×#1799C213yesmaximal, complemented
6C2×C13×H(5,𝔽2)C2211yescharacteristic
7C23×D4×C13C2211yescharacteristic, complemented
8C2×C13×#121—23no—
9C2×C13×#120C2216yes—
10C13×#520—23no—
11C13×#518—23no—
12C13×#518C2213yes—
13C4×C13×#41—23no—
14C2×C4×D4×C13—23no—
15C2×C4×D4×C13C2213yes—
16C13×B(4,𝔽2)—28no—
17C2×C13×#99C2216yes—
18C13×#394—23no—
19C13×#392—23no—
20C13×#390—23no—
21C13×#380C2213yescomplemented
22C13×#379C2216yescomplemented
23C13×#342C2216yescomplemented
24C25×C13C2312yes—
25C13×H(5,𝔽2)—26no—
26C13×H(5,𝔽2)D414yescomplemented
27C2×C13×#41—23no—
28C22×D4×C13—23no—
29C22×D4×C13—26no—
30C22×D4×C13—23no—
31C22×D4×C13—23no—
32C22×D4×C13—44no—
33C22×D4×C13C2313yes—
34C23×C4×C13—21no—
35C23×C4×C13D413yescomplemented
36C23×C4×C13C2311yescharacteristic
37C13×#121—412no—
38C13×#120—212no—
39C13×#120—212no—
40C4×Q8×C13—21no—
41C4×Q8×C13—23no—
42C4×D4×C13—23no—
43C4×D4×C13—26no—
44C4×D4×C13—23no—
45C4×D4×C13—26no—
46C4×D4×C13—26no—
47C4×D4×C13—26no—
48C4×D4×C13—26no—
49C13×#117—26no—
50C13×#117—23no—
51C2×C13×C4⋊C4—23no—
52C2×C13×C4⋊C4—23no—
53C2×C13×C4⋊C4D413yescomplemented
54C2×C13×C22⋊C4—23no—
55C2×C13×C22⋊C4—23no—
56C2×C13×C22⋊C4—26no—
57C2×C13×C22⋊C4—26no—
58C2×C13×C22⋊C4—26no—
59C2×C13×C22⋊C4D413yescomplemented
60C2×C13×C22⋊C4C2316yes—
61C2×C13×C22⋊C4C2313yes—
62C2×C42×C13—23no—
63C2×C42×C13D413yescomplemented
64C13×#99—212no—
65C13×#95—23no—
66#32926C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13—21no—
68C24×C13—26no—
69C24×C13—22no—
70C24×C13—26no—
71C24×C13—44no—
72C24×C13—82no—
73C24×C13C2×D413yes—
74C24×C13C2411yescharacteristic
75C13×#41—212no—
76C13×#41—212no—
77C2×Q8×C13—21no—
78C2×D4×C13—23no—
79C2×D4×C13—212no—
80C2×D4×C13—212no—
81C2×D4×C13—26no—
82C2×D4×C13—26no—
83C2×D4×C13—212no—
84C2×D4×C13—46no—
85C2×D4×C13—412no—
86C2×D4×C13—412no—
87C2×D4×C13—412no—
88C2×D4×C13—43no—
89C2×D4×C13—41no—
90C2×D4×C13—86no—
91C2×D4×C13C2×D416yes—
92C2×D4×C13#4116yes—
93C22×C4×C13—23no—
94C22×C4×C13—23no—
95C22×C4×C13—23no—
96C22×C4×C13—23no—
97C22×C4×C13—23no—
98C22×C4×C13—26no—
99C22×C4×C13—42no—
100C22×C4×C13—46no—
101C22×C4×C13—82no—
102C22×C4×C13C2×D413yes—
103C22×C4×C13C2×D413yes—
104C22×C4×C13C2×D413yes—
105C22×C4×C13C2×D413yes—
106C22×C4×C13C2×D413yes—
107C13×C4⋊C4—23no—
108C13×C4⋊C4—23no—
109C13×C4⋊C4—26no—
110C13×C4⋊C4—46no—
111C13×C22⋊C4—26no—
112C13×C22⋊C4—26no—
113C13×C22⋊C4—26no—
114C13×C22⋊C4—26no—
115C13×C22⋊C4—26no—
116C13×C22⋊C4—412no—
117C13×C22⋊C4—412no—
118C13×C22⋊C4—86no—
119C42×C13—26no—
120C42×C13—23no—
121C42×C13—23no—
122C4×H(5,𝔽2)C2×C1311yescharacteristic, complemented
123C2×B(4,𝔽2)C2×C1312yescomplemented
124#2408C2×C1313yescomplemented
125#1889C2×C1316yescomplemented
126#1799C2×C1313yescomplemented
127C23×C13—24no—
128C23×C13—23no—
129C23×C13—23no—
130C23×C13—212no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—43no—
134C23×C13—43no—
135C23×C13—46no—
136C23×C13—46no—
137C23×C13—46no—
138C23×C13—42no—
139C23×C13—46no—
140C23×C13—46no—
141C23×C13—84no—
142C23×C13—812no—
143C23×C13—81no—
144C23×C13—81no—
145C23×C13#12116yescomplemented
146C23×C13C22×D413yes—
147C23×C13C22×D411yescharacteristic
148C23×C13C2×#4113yes—
149Q8×C13—24no—
150D4×C13—212no—
151D4×C13—212no—
152D4×C13—212no—
153D4×C13—412no—
154D4×C13—44no—
155D4×C13—824no—
156C2×C4×C13—212no—
157C2×C4×C13—23no—
158C2×C4×C13—23no—
159C2×C4×C13—26no—
160C2×C4×C13—23no—
161C2×C4×C13—23no—
162C2×C4×C13—43no—
163C2×C4×C13—46no—
164C2×C4×C13—43no—
165C2×C4×C13—43no—
166C2×C4×C13—46no—
167C2×C4×C13—46no—
168C2×C4×C13—46no—
169C2×C4×C13—83no—
170C2×C4×C13—83no—
171C2×C4×C13—83no—
172C2×C4×C13#12013yes—
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12116yescomplemented
175C2×H(5,𝔽2)C22×C1311yescharacteristic
176C23×D4C22×C1311yescharacteristic, complemented
177C2×#121—23no—
178C2×#120C22×C1316yes—
179#520—23no—
180#518—23no—
181#518C22×C1313yes—
182C4×#41—23no—
183C2×C4×D4—23no—
184C2×C4×D4C22×C1313yes—
185B(4,𝔽2)—28no—
186C2×#99C22×C1316yes—
187#394—23no—
188#392—23no—
189#390—23no—
190#380C22×C1313yescomplemented
191#379C22×C1316yescomplemented
192#342C22×C1316yescomplemented
193C22×C13—23no—
194C22×C13—23no—
195C22×C13—26no—
196C22×C13—41no—
197C22×C13—43no—
198C22×C13—46no—
199C22×C13—412no—
200C22×C13—412no—
201C22×C13—43no—
202C22×C13—43no—
203C22×C13—44no—
204C22×C13—83no—
205C22×C13—86no—
206C22×C13—86no—
207C22×C13—84no—
208C22×C13—82no—
209C22×C13—82no—
210C22×C13C2×#12011yescharacteristic
211C22×C13C2×#12113yes—
212C22×C13#52513yes—
213C4×C13—26no—
214C4×C13—23no—
215C4×C13—43no—
216C4×C13—43no—
217C4×C13—86no—
218C4×C13B(4,𝔽2)12yescomplemented
219C25C23×C1312yes—
220H(5,𝔽2)—26no—
221H(5,𝔽2)D4×C1314yescomplemented
222C2×#41—23no—
223C22×D4—23no—
224C22×D4—26no—
225C22×D4—23no—
226C22×D4—23no—
227C22×D4—44no—
228C22×D4C23×C1313yes—
229C23×C4—21no—
230C23×C4D4×C1313yescomplemented
231C23×C4C23×C1311yescharacteristic
232#121—412no—
233#120—212no—
234#120—212no—
235C4×Q8—21no—
236C4×Q8—23no—
237C4×D4—23no—
238C4×D4—26no—
239C4×D4—23no—
240C4×D4—26no—
241C4×D4—26no—
242C4×D4—26no—
243C4×D4—26no—
244#117—26no—
245#117—23no—
246C2×C4⋊C4—23no—
247C2×C4⋊C4—23no—
248C2×C4⋊C4D4×C1313yescomplemented
249C2×C22⋊C4—23no—
250C2×C22⋊C4—23no—
251C2×C22⋊C4—26no—
252C2×C22⋊C4—26no—
253C2×C22⋊C4—26no—
254C2×C22⋊C4D4×C1313yescomplemented
255C2×C22⋊C4C23×C1316yes—
256C2×C22⋊C4C23×C1313yes—
257C2×C42—23no—
258C2×C42D4×C1313yescomplemented
259#99—212no—
260#95—23no—
261C2×C13—23no—
262C2×C13—23no—
263C2×C13—46no—
264C2×C13—84no—
265C2×C13#284711yescharacteristic
266C2×C13C2×B(4,𝔽2)11yescharacteristic
267C2×C13#302711yescharacteristic
268C24—21no—
269C24—26no—
270C24—22no—
271C24—26no—
272C24—44no—
273C24—82no—
274C24C2×D4×C1313yes—
275C24C24×C1311yescharacteristic
276#41—212no—
277#41—212no—
278C2×Q8—21no—
279C2×D4—23no—
280C2×D4—212no—
281C2×D4—212no—
282C2×D4—26no—
283C2×D4—26no—
284C2×D4—212no—
285C2×D4—46no—
286C2×D4—412no—
287C2×D4—412no—
288C2×D4—412no—
289C2×D4—43no—
290C2×D4—41no—
291C2×D4—86no—
292C2×D4C2×D4×C1316yes—
293C2×D4C13×#4116yes—
294C22×C4—23no—
295C22×C4—23no—
296C22×C4—23no—
297C22×C4—23no—
298C22×C4—23no—
299C22×C4—26no—
300C22×C4—42no—
301C22×C4—46no—
302C22×C4—82no—
303C22×C4C2×D4×C1313yes—
304C22×C4C2×D4×C1313yes—
305C22×C4C2×D4×C1313yes—
306C22×C4C2×D4×C1313yes—
307C22×C4C2×D4×C1313yes—
308C4⋊C4—23no—
309C4⋊C4—23no—
310C4⋊C4—26no—
311C4⋊C4—46no—
312C22⋊C4—26no—
313C22⋊C4—26no—
314C22⋊C4—26no—
315C22⋊C4—26no—
316C22⋊C4—26no—
317C22⋊C4—412no—
318C22⋊C4—412no—
319C22⋊C4—86no—
320C42—26no—
321C42—23no—
322C42—23no—
323C13#3292611yescharacteristic, direct product factor, Sylow
324C23—24no—
325C23—23no—
326C23—23no—
327C23—212no—
328C23—41no—
329C23—41no—
330C23—43no—
331C23—43no—
332C23—46no—
333C23—46no—
334C23—46no—
335C23—42no—
336C23—46no—
337C23—46no—
338C23—84no—
339C23—812no—
340C23—81no—
341C23—81no—
342C23C13×#12116yescomplemented
343C23C22×D4×C1313yes—
344C23C22×D4×C1311yescharacteristic
345C23C2×C13×#4113yes—
346Q8—24no—
347D4—212no—
348D4—212no—
349D4—212no—
350D4—412no—
351D4—44no—
352D4—824no—
353C2×C4—212no—
354C2×C4—23no—
355C2×C4—23no—
356C2×C4—26no—
357C2×C4—23no—
358C2×C4—23no—
359C2×C4—43no—
360C2×C4—46no—
361C2×C4—43no—
362C2×C4—43no—
363C2×C4—46no—
364C2×C4—46no—
365C2×C4—46no—
366C2×C4—83no—
367C2×C4—83no—
368C2×C4—83no—
369C2×C4C13×#12013yes—
370C2×C4C13×#12011yescharacteristic
371C2×C4C13×#12116yescomplemented
372C22—23no—
373C22—23no—
374C22—26no—
375C22—41no—
376C22—43no—
377C22—46no—
378C22—412no—
379C22—412no—
380C22—43no—
381C22—43no—
382C22—44no—
383C22—83no—
384C22—86no—
385C22—86no—
386C22—84no—
387C22—82no—
388C22—82no—
389C22C2×C13×#12011yescharacteristic
390C22C2×C13×#12113yes—
391C22C13×#52513yes—
392C4—23no—
393C4—26no—
394C4—43no—
395C4—43no—
396C4—86no—
397C4C13×B(4,𝔽2)12yescomplemented
398C2—23no—
399C2—23no—
400C2—46no—
401C2—84no—
402C2C13×#284711yescharacteristic
403C2C2×C13×B(4,𝔽2)11yescharacteristic
404C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C13×H(5,𝔽2)C2semidirect
2. C2×C13×B(4,𝔽2)C2semidirect
3. C13×#2408C2semidirect
4. C13×#1889C2semidirect
5. C13×#1799C2semidirect
7. C23×D4×C13C22semidirect
21. C13×#380C22semidirect
22. C13×#379C22semidirect
23. C13×#342C22semidirect
26. C13×H(5,𝔽2)D4semidirect
35. C23×C4×C13D4semidirect
53. C2×C13×C4⋊C4D4semidirect
59. C2×C13×C22⋊C4D4semidirect
63. C2×C42×C13D4semidirect
66. #32926C13direct (N × H)
122. C4×H(5,𝔽2)C2×C13semidirect
123. C2×B(4,𝔽2)C2×C13semidirect
124. #2408C2×C13semidirect
125. #1889C2×C13semidirect
126. #1799C2×C13semidirect
145. C23×C13#121semidirect
174. C2×C4×C13#121semidirect
176. C23×D4C22×C13semidirect
190. #380C22×C13semidirect
191. #379C22×C13semidirect
192. #342C22×C13semidirect
218. C4×C13B(4,𝔽2)semidirect
221. H(5,𝔽2)D4×C13semidirect
230. C23×C4D4×C13semidirect
248. C2×C4⋊C4D4×C13semidirect
254. C2×C22⋊C4D4×C13semidirect
258. C2×C42D4×C13semidirect
323. C13#32926direct (N × H)
342. C23C13×#121semidirect
371. C2×C4C13×#121semidirect
397. C4C13×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C4×C13×H(5,𝔽2)2
C2×C13×B(4,𝔽2)2
C13×#24082
C13×#18892
C13×#17992
#3292613