Finite Group Databasebeta

← C13×#12154 #15698493

Subgroups — C13×#12154 #15698493

Order 3328.

458 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C13×#2609C211yesmaximal, characteristic, complemented
2C13×#2040C211yesmaximal, characteristic, complemented
3C13×#1610C211yesmaximal, characteristic, complemented
4C13×#1598C211yesmaximal, characteristic
5C13×#1346C211yesmaximal, characteristic, complemented
6C13×#1345C211yesmaximal, characteristic, complemented
7C13×#1324C211yesmaximal, characteristic, complemented
8C13×#537C2211yescharacteristic
9C2×C13×#117—21no—
10C13×#480—21no—
11C13×#447—21no—
12C2×C13×#104—21no—
13C13×#417—21no—
14C13×#398C2211yescharacteristic
15C13×#396—21no—
16C13×#394C2211yescharacteristic
17C13×#388—21no—
18C13×#387—21no—
19C13×#386—21no—
20C13×#385—21no—
21C13×#382C2211yescharacteristic
22C13×#343C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#324C2211yescharacteristic
26C13×#324C2211yescharacteristic
27C2×C13×#41—21no—
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C2×C13×D8—41no—
31C2×C13×M16—21no—
32C13×C22⋊Q8—41no—
33C13×#121—21no—
34C13×#121—21no—
35C13×#121—41no—
36C13×#117—42no—
37C13×#117—42no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C4⋊C4C2311yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C42×C13—21no—
50C2×C42×C13D411yescharacteristic
51C13×#107—41no—
52C13×#104—42no—
53C13×#103—41no—
54C13×#102—41no—
55C13×#102—41no—
56C13×#102—41no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65#12154C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—21no—
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C2×Q8×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—41no—
76C2×D4×C13—42no—
77C2×D4×C13—41no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—41no—
86C22×C4×C13—42no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C13×D8—82no—
91C13×M16—41no—
92C13×M16—41no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—42no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—81no—
113C42×C13—21no—
114C42×C13—42no—
115C42×C13D812yescomplemented
116#2609C2×C1311yescharacteristic, complemented
117#2040C2×C1311yescharacteristic, complemented
118#1610C2×C1311yescharacteristic, complemented
119#1598C2×C1311yescharacteristic
120#1346C2×C1311yescharacteristic, complemented
121#1345C2×C1311yescharacteristic, complemented
122#1324C2×C1311yescharacteristic, complemented
123C23×C13—22no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13#12011yescharacteristic
132Q8×C13—41no—
133Q8×C13—41no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—42no—
137D4×C13—81no—
138D4×C13—81no—
139D4×C13—81no—
140D4×C13—81no—
141D4×C13—81no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—48no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C8×C13—81no—
170C8×C13—81no—
171C8×C13—81no—
172#537C22×C1311yescharacteristic
173C2×#117—21no—
174#480—21no—
175#447—21no—
176C2×#104—21no—
177#417—21no—
178#398C22×C1311yescharacteristic
179#396—21no—
180#394C22×C1311yescharacteristic
181#388—21no—
182#387—21no—
183#386—21no—
184#385—21no—
185#382C22×C1311yescharacteristic
186#343C22×C1311yescharacteristic
187#327—21no—
188#327—21no—
189#324C22×C1311yescharacteristic
190#324C22×C1311yescharacteristic
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13#44711yescharacteristic
204C22×C13#45411yescharacteristic
205C22×C13B(4,𝔽2)11yescharacteristic
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—42no—
209C4×C13—42no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216C2×#41—21no—
217C22×D4D4×C1311yescharacteristic
218C23×C4—21no—
219C2×D8—41no—
220C2×M16—21no—
221C22⋊Q8—41no—
222#121—21no—
223#121—21no—
224#121—41no—
225#117—42no—
226#117—42no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C1311yescharacteristic
231C2×C4⋊C4D4×C1311yescharacteristic
232C2×C4⋊C4C23×C1311yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C42—21no—
239C2×C42D4×C1311yescharacteristic
240#107—41no—
241#104—42no—
242#103—41no—
243#102—41no—
244#102—41no—
245#102—41no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95D4×C1311yescharacteristic
253#95D4×C1311yescharacteristic
254C2×C13—21no—
255C2×C13—21no—
256C2×C13—82no—
257C2×C13—161no—
258C2×C13#159811yescharacteristic
259C2×C13#219711yescharacteristic
260C2×C13#220411yescharacteristic
261C24—21no—
262#41—41no—
263#41—41no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—41no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4C2×D4×C1311yescharacteristic
283C22×C4C2×D4×C1311yescharacteristic
284C22×C4C2×D4×C1311yescharacteristic
285D8—82no—
286M16—41no—
287M16—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C42—21no—
309C42—42no—
310C42C13×D812yescomplemented
311C13#1215411yescharacteristic, direct product factor, Sylow
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23C13×#12011yescharacteristic
321Q8—41no—
322Q8—41no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—48no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4C2×C13×D811yescharacteristic
357C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
358C8—81no—
359C8—81no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22C13×#44711yescharacteristic
374C22C13×#45411yescharacteristic
375C22C13×B(4,𝔽2)11yescharacteristic
376C4—21no—
377C4—21no—
378C4—42no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C2—21no—
387C2—21no—
388C2—82no—
389C2—161no—
390C2C13×#159811yescharacteristic
391C2C13×#219711yescharacteristic
392C2C13×#220411yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC13×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2609C2semidirect
2. C13×#2040C2semidirect
3. C13×#1610C2semidirect
5. C13×#1346C2semidirect
6. C13×#1345C2semidirect
7. C13×#1324C2semidirect
65. #12154C13direct (N × H)
115. C42×C13D8semidirect
116. #2609C2×C13semidirect
117. #2040C2×C13semidirect
118. #1610C2×C13semidirect
120. #1346C2×C13semidirect
121. #1345C2×C13semidirect
122. #1324C2×C13semidirect
310. C42C13×D8semidirect
311. C13#12154direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26092
C13×#20402
C13×#16102
C13×#15982
C13×#13462
C13×#13452
C13×#13242
#1215413