Finite Group Databasebeta

← C13×#9413 #15695752

Subgroups — C13×#9413 #15695752

Order 3328.

720 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2539C211yesmaximal, characteristic
2C13×#2312C211yesmaximal, characteristic, complemented
3C13×#1507C212yesmaximal, complemented
4C13×#1462C211yesmaximal, characteristic, complemented
5C13×#1297C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C2×C13×#120—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C13×#407C2212yes—
11C13×#399C412yescomplemented
12C13×#392C412yescomplemented
13C13×#390—22no—
14C13×#388—24no—
15C13×#380—21no—
16C13×#379—21no—
17C4×C13×C22⋊C4C2211yescharacteristic
18C4×C13×C22⋊C4C2212yes—
19C13×#327—24no—
20C13×#323—22no—
21C25×C13D411yescharacteristic
22C22×D4×C13—21no—
23C22×D4×C13—22no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C2×C13×M16—22no—
28C13×#123—44no—
29C13×#121—22no—
30C13×#121—22no—
31C13×#120—44no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4C2×C412yes—
45C2×C13×C22⋊C4D412yes—
46C2×C42×C13—22no—
47C2×C42×C13—21no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C13×#95—22no—
51C13×#95C2×C412yes—
52C13×#95D414yescomplemented
53#9413C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—21no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—42no—
58C24×C13—42no—
59C24×C13—81no—
60C24×C13C22⋊C412yes—
61C24×C13C2×D411yescharacteristic
62C2×D4×C13—22no—
63C2×D4×C13—44no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—44no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C2×D4×C13—82no—
70C2×D4×C13—81no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—24no—
76C22×C4×C13—42no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C412yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4112yes—
83C13×M16—82no—
84C2×C8×C13—42no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—44no—
87C13×C4⋊C4—82no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—24no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—44no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—82no—
96C13×C22⋊C4—82no—
97C42×C13—81no—
98C42×C13—82no—
99#2539C2×C1311yescharacteristic
100#2312C2×C1311yescharacteristic, complemented
101#1507C2×C1312yescomplemented
102#1462C2×C1311yescharacteristic, complemented
103#1297C2×C1312yescomplemented
104C23×C13—22no—
105C23×C13—22no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—41no—
110C23×C13—42no—
111C23×C13—42no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—42no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—42no—
121C23×C13—81no—
122C23×C13—81no—
123C23×C13—88no—
124C23×C13C2×C22⋊C411yescharacteristic
125C23×C13#12011yescharacteristic
126C23×C13#12311yescharacteristic
127D4×C13—82no—
128D4×C13—88no—
129D4×C13—82no—
130D4×C13—82no—
131C2×C4×C13—24no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—44no—
142C2×C4×C13—41no—
143C2×C4×C13—44no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—44no—
147C2×C4×C13—81no—
148C2×C4×C13C4×D412yes—
149C2×C4×C13#12112yes—
150C8×C13—82no—
151C2×#123—21no—
152C2×#121C22×C1311yescharacteristic
153C2×#120—21no—
154C22×C22⋊C4C22×C1311yescharacteristic
155#407C22×C1312yes—
156#399C4×C1312yescomplemented
157#392C4×C1312yescomplemented
158#390—22no—
159#388—24no—
160#380—21no—
161#379—21no—
162C4×C22⋊C4C22×C1311yescharacteristic
163C4×C22⋊C4C22×C1312yes—
164#327—24no—
165#323—22no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—44no—
174C22×C13—44no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—42no—
178C22×C13—82no—
179C22×C13—84no—
180C22×C13—82no—
181C22×C13—82no—
182C22×C13—84no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#38611yescharacteristic
187C22×C13#42112yes—
188C22×C13#45312yes—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—44no—
192C4×C13—42no—
193C4×C13—84no—
194C4×C13—81no—
195C25D4×C1311yescharacteristic
196C22×D4—21no—
197C22×D4—22no—
198C22×D4C2×C4×C1311yescharacteristic
199C23×C4D4×C1311yescharacteristic
200C23×C4C23×C1311yescharacteristic
201C2×M16—22no—
202#123—44no—
203#121—22no—
204#121—22no—
205#120—44no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4C2×C4×C1311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4C2×C4×C1312yes—
219C2×C22⋊C4D4×C1312yes—
220C2×C42—22no—
221C2×C42—21no—
222C22⋊C8—22no—
223C22⋊C8—22no—
224#95—22no—
225#95C2×C4×C1312yes—
226#95D4×C1314yescomplemented
227C2×C13—22no—
228C2×C13—22no—
229C2×C13—41no—
230C2×C13—82no—
231C2×C13—161no—
232C2×C13#188711yescharacteristic
233C2×C13#189711yescharacteristic
234C2×C13#191311yescharacteristic
235C24—21no—
236C24—21no—
237C24—21no—
238C24—42no—
239C24—42no—
240C24—81no—
241C24C13×C22⋊C412yes—
242C24C2×D4×C1311yescharacteristic
243C2×D4—22no—
244C2×D4—44no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—44no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—82no—
251C2×D4—81no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—81no—
259C22×C4C13×C22⋊C412yes—
260C22×C4C22×C4×C1311yescharacteristic
261C22×C4C2×D4×C1312yes—
262C22×C4C2×D4×C1311yescharacteristic
263C22×C4C13×#4112yes—
264M16—82no—
265C2×C8—42no—
266C4⋊C4—22no—
267C4⋊C4—44no—
268C4⋊C4—82no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—44no—
273C22⋊C4—44no—
274C22⋊C4—44no—
275C22⋊C4—42no—
276C22⋊C4—82no—
277C22⋊C4—82no—
278C42—81no—
279C42—82no—
280C13#941311yescharacteristic, direct product factor, Sylow
281C23—22no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—41no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—41no—
293C23—41no—
294C23—42no—
295C23—42no—
296C23—41no—
297C23—42no—
298C23—81no—
299C23—81no—
300C23—88no—
301C23C2×C13×C22⋊C411yescharacteristic
302C23C13×#12011yescharacteristic
303C23C13×#12311yescharacteristic
304D4—82no—
305D4—88no—
306D4—82no—
307D4—82no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—44no—
324C2×C4—81no—
325C2×C4C4×D4×C1312yes—
326C2×C4C13×#12112yes—
327C8—82no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—44no—
336C22—44no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—84no—
342C22—82no—
343C22—82no—
344C22—84no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C13×#38611yescharacteristic
349C22C13×#42112yes—
350C22C13×#45312yes—
351C4—22no—
352C4—22no—
353C4—44no—
354C4—42no—
355C4—84no—
356C4—81no—
357C2—22no—
358C2—22no—
359C2—41no—
360C2—82no—
361C2—161no—
362C2C13×#188711yescharacteristic
363C2C13×#189711yescharacteristic
364C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2539C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2312C2semidirect
3. C13×#1507C2semidirect
4. C13×#1462C2semidirect
5. C13×#1297C2semidirect
11. C13×#399C4semidirect
12. C13×#392C4semidirect
52. C13×#95D4semidirect
53. #9413C13direct (N × H)
100. #2312C2×C13semidirect
101. #1507C2×C13semidirect
102. #1462C2×C13semidirect
103. #1297C2×C13semidirect
156. #399C4×C13semidirect
157. #392C4×C13semidirect
226. #95D4×C13semidirect
280. C13#9413direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25392
C13×#23122
C13×#15072
C13×#14622
C13×#12972
#941313