Finite Group Databasebeta

← C13×#11549 #15697888

Subgroups — C13×#11549 #15697888

Order 3328.

496 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2501C211yesmaximal, characteristic
2C13×#1463C211yesmaximal, characteristic, complemented
3C2×C13×#324C211yesmaximal, characteristic, complemented
4C13×#1325C212yesmaximal, complemented
5C13×#1318C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#123—21no—
8C2×C13×#121C411yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C13×#407—21no—
11C2×C13×C22⋊C8—21no—
12C13×#399—21no—
13C13×#399—21no—
14C13×#390C411yescharacteristic
15C13×#390C2211yescharacteristic
16C13×#384C411yescharacteristic
17C13×#384C2211yescharacteristic
18C4×C13×C22⋊C4C411yescharacteristic
19C13×#324—21no—
20C13×#324—21no—
21C13×#324C2212yes—
22C13×#324C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C2×C13×M16—41no—
29C22×C8×C13—41no—
30C13×#123—44no—
31C13×#123—44no—
32C13×#121—41no—
33C13×#121—41no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—41no—
39C2×C13×C4⋊C4—41no—
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4C2311yescharacteristic
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C42×C13C2×C411yescharacteristic
52C2×C42×C13C2×C411yescharacteristic
53C13×C22⋊C8—22no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8—41no—
56C13×C22⋊C8—41no—
57C13×#95—21no—
58#11549C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13—21no—
60C24×C13C22⋊C411yescharacteristic
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—41no—
67C2×D4×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C13×M16—82no—
88C2×C8×C13—42no—
89C2×C8×C13—42no—
90C2×C8×C13—82no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—42no—
99C13×C4⋊C4—42no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C42×C13—22no—
107C42×C13—41no—
108#2501C2×C1311yescharacteristic
109#1463C2×C1311yescharacteristic, complemented
110C2×#324C2×C1311yescharacteristic, complemented
111#1325C2×C1312yescomplemented
112#1318C2×C1312yescomplemented
113C23×C13—22no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13#9911yescharacteristic
125C23×C13#9911yescharacteristic
126C23×C13C2×C22⋊C411yescharacteristic
127D4×C13—82no—
128D4×C13—82no—
129D4×C13—82no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
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—81no—
157C2×C4×C13—81no—
158C2×C4×C13#13112yes—
159C8×C13—82no—
160C8×C13—82no—
161C2×#123—21no—
162C2×#123—21no—
163C2×#121C4×C1311yescharacteristic
164C22×C4⋊C4C22×C1311yescharacteristic
165#407—21no—
166C2×C22⋊C8—21no—
167#399—21no—
168#399—21no—
169#390C4×C1311yescharacteristic
170#390C22×C1311yescharacteristic
171#384C4×C1311yescharacteristic
172#384C22×C1311yescharacteristic
173C4×C22⋊C4C4×C1311yescharacteristic
174#324—21no—
175#324—21no—
176#324C22×C1312yes—
177#324C22×C1312yes—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13#35312yes—
195C22×C13#40811yescharacteristic
196C22×C13C2×#9911yescharacteristic
197C22×C13#41311yescharacteristic
198C4×C13—22no—
199C4×C13—42no—
200C4×C13—42no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—81no—
207C22×D4—21no—
208C22×D4C2×C4×C1311yescharacteristic
209C23×C4C2×C4×C1311yescharacteristic
210C23×C4D4×C1311yescharacteristic
211C23×C4D4×C1311yescharacteristic
212C2×M16—41no—
213C22×C8—41no—
214#123—44no—
215#123—44no—
216#121—41no—
217#121—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4C2×C4×C1311yescharacteristic
225C2×C4⋊C4C2×C4×C1311yescharacteristic
226C2×C4⋊C4D4×C1311yescharacteristic
227C2×C4⋊C4D4×C1311yescharacteristic
228C2×C4⋊C4C23×C1311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C42C2×C4×C1311yescharacteristic
236C2×C42C2×C4×C1311yescharacteristic
237C22⋊C8—22no—
238C22⋊C8—22no—
239C22⋊C8—41no—
240C22⋊C8—41no—
241#95—21no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—22no—
245C2×C13—41no—
246C2×C13—161no—
247C2×C13#146811yescharacteristic
248C2×C13C2×#35311yescharacteristic
249C2×C13#213311yescharacteristic
250C24—21no—
251C24C13×C22⋊C411yescharacteristic
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C13×C22⋊C411yescharacteristic
273C22×C4C13×C22⋊C411yescharacteristic
274C22×C4C13×C22⋊C411yescharacteristic
275C22×C4C22×C4×C1311yescharacteristic
276C22×C4C2×D4×C1311yescharacteristic
277C22×C4C2×D4×C1311yescharacteristic
278M16—82no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—82no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—24no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C42—22no—
298C42—41no—
299C13#1154911yescharacteristic, direct product factor, Sylow
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C13×#9911yescharacteristic
312C23C13×#9911yescharacteristic
313C23C2×C13×C22⋊C411yescharacteristic
314D4—82no—
315D4—82no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4C13×#13112yes—
346C8—82no—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22C13×#35312yes—
365C22C13×#40811yescharacteristic
366C22C2×C13×#9911yescharacteristic
367C22C13×#41311yescharacteristic
368C4—22no—
369C4—42no—
370C4—42no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—81no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2C13×#146811yescharacteristic
383C2C2×C13×#35311yescharacteristic
384C2C13×#213311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC2×C13×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1463C2semidirect
3. C2×C13×#324C2semidirect
4. C13×#1325C2semidirect
5. C13×#1318C2semidirect
58. #11549C13direct (N × H)
109. #1463C2×C13semidirect
110. C2×#324C2×C13semidirect
111. #1325C2×C13semidirect
112. #1318C2×C13semidirect
299. C13#11549direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25012
C13×#14632
C2×C13×#3242
C13×#13252
C13×#13182
#1154913