Finite Group Databasebeta

← C13×#12268 #15698607

Subgroups — C13×#12268 #15698607

Order 3328.

458 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2735C211yesmaximal, characteristic
2C13×#2029C211yesmaximal, characteristic
3C13×#1614C211yesmaximal, characteristic, complemented
4C13×#1608C211yesmaximal, characteristic, complemented
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1344C211yesmaximal, characteristic, complemented
7C13×#1316C211yesmaximal, characteristic
8C13×#543C2211yescharacteristic
9C13×#484—21no—
10C13×#483—21no—
11C13×#399C2211yescharacteristic
12C13×#397—21no—
13C13×#397C2211yescharacteristic
14C13×#396—21no—
15C13×#388—21no—
16C13×#388—21no—
17C13×#388—21no—
18C13×#379—21no—
19C13×#379—21no—
20C13×#379C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C25×C13D411yescharacteristic
28C13×C22⋊Q8—21no—
29C13×C22⋊Q8—21no—
30C13×C22⋊Q8—41no—
31C13×C22⋊Q8—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—41no—
47C2×C13×C22⋊C4—41no—
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4C2311yescharacteristic
50C2×C42×C13—21no—
51C13×#107—41no—
52C13×#106—41no—
53C13×#103—41no—
54C13×#103—41no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12268C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—41no—
67C24×C13—41no—
68C24×C13—42no—
69C24×C13—81no—
70C24×C13C2×D411yescharacteristic
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C13×C22⋊C4—81no—
105C13×C22⋊C4—81no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C13×C22⋊C4—82no—
109C13×C22⋊C4—82no—
110C42×C13—81no—
111#2735C2×C1311yescharacteristic
112#2029C2×C1311yescharacteristic
113#1614C2×C1311yescharacteristic, complemented
114#1608C2×C1311yescharacteristic, complemented
115#1352C2×C1311yescharacteristic, complemented
116#1344C2×C1311yescharacteristic, complemented
117#1316C2×C1311yescharacteristic
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—22no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—81no—
133C23×C13—82no—
134C23×C13—81no—
135C23×C13—84no—
136C23×C13—82no—
137C23×C13—81no—
138C23×C13#12011yescharacteristic
139C23×C13#13511yescharacteristic
140C23×C13#13711yescharacteristic
141Q8×C13—81no—
142Q8×C13—81no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
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—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C8×C13—81no—
170C8×C13—81no—
171#543C22×C1311yescharacteristic
172#484—21no—
173#483—21no—
174#399C22×C1311yescharacteristic
175#397—21no—
176#397C22×C1311yescharacteristic
177#396—21no—
178#388—21no—
179#388—21no—
180#388—21no—
181#379—21no—
182#379—21no—
183#379C22×C1311yescharacteristic
184#342—21no—
185#342C22×C1311yescharacteristic
186#328—21no—
187#328—21no—
188#323C22×C1311yescharacteristic
189#323C22×C1311yescharacteristic
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—44no—
201C22×C13—42no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—82no—
206C22×C13—82no—
207C22×C13—82no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13#45211yescharacteristic
211C22×C13#45511yescharacteristic
212C22×C13B(4,𝔽2)11yescharacteristic
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13—161no—
223C25D4×C1311yescharacteristic
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—41no—
227C22⋊Q8—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C1311yescharacteristic
231C2×C4⋊C4D4×C1311yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4—41no—
244C2×C22⋊C4D4×C1311yescharacteristic
245C2×C22⋊C4C23×C1311yescharacteristic
246C2×C42—21no—
247#107—41no—
248#106—41no—
249#103—41no—
250#103—41no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95D4×C1311yescharacteristic
257#95D4×C1311yescharacteristic
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—41no—
261C2×C13—41no—
262C2×C13—82no—
263C2×C13#160611yescharacteristic
264C2×C13#219711yescharacteristic
265C2×C13#220011yescharacteristic
266C24—21no—
267C24—21no—
268C24—21no—
269C24—41no—
270C24—41no—
271C24—42no—
272C24—81no—
273C24C2×D4×C1311yescharacteristic
274C2×Q8—21no—
275C2×Q8—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4C2×D4×C1311yescharacteristic
285C22×C4C2×D4×C1311yescharacteristic
286C2×C8—41no—
287C2×C8—41no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—82no—
312C22⋊C4—82no—
313C42—81no—
314C13#1226811yescharacteristic, direct product factor, Sylow
315C23—21no—
316C23—21no—
317C23—22no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—81no—
330C23—82no—
331C23—81no—
332C23—82no—
333C23—84no—
334C23—81no—
335C23C13×#12011yescharacteristic
336C23C13×#13511yescharacteristic
337C23C13×#13711yescharacteristic
338Q8—81no—
339Q8—81no—
340C2×C4—21no—
341C2×C4—21no—
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—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C8—81no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—44no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22C13×#45211yescharacteristic
389C22C13×#45511yescharacteristic
390C22C13×B(4,𝔽2)11yescharacteristic
391C4—41no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—81no—
400C4—161no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—82no—
406C2C13×#160611yescharacteristic
407C2C13×#219711yescharacteristic
408C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1614C2semidirect
4. C13×#1608C2semidirect
5. C13×#1352C2semidirect
6. C13×#1344C2semidirect
62. #12268C13direct (N × H)
113. #1614C2×C13semidirect
114. #1608C2×C13semidirect
115. #1352C2×C13semidirect
116. #1344C2×C13semidirect
314. C13#12268direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27352
C13×#20292
C13×#16142
C13×#16082
C13×#13522
C13×#13442
C13×#13162
#1226813