Finite Group Databasebeta

← C13×#12202 #15698541

Subgroups — C13×#12202 #15698541

Order 3328.

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

normal subgroups only

This group has 976 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×#2403C211yesmaximal, characteristic
2C13×#2029C211yesmaximal, characteristic, complemented
3C13×#1596C212yesmaximal, complemented
4C13×#1343C212yesmaximal, complemented
5C13×#1316C211yesmaximal, characteristic, complemented
6C23×D4×C13—21no—
7C13×#543C2211yescharacteristic, complemented
8C2×C13×#120—22no—
9C13×#450—22no—
10C13×#392—21no—
11C13×#392C2212yes—
12C13×#386—22no—
13C13×#379—21no—
14C13×#379C2211yescharacteristic
15C13×#342—21no—
16C13×#342C2211yescharacteristic, complemented
17C13×#328—22no—
18C13×#323C2212yescomplemented
19C25×C13—21no—
20C25×C13D411yescharacteristic
21C22×D4×C13—22no—
22C22×D4×C13—22no—
23C22×D4×C13—21no—
24C22×D4×C13—48no—
25C22×D4×C13—42no—
26C22×D4×C13—42no—
27C22×D4×C13D412yes—
28C23×C4×C13—21no—
29C2×C13×SD16—42no—
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—42no—
32C13×#120—48no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—42no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4C2311yescharacteristic
41C13×#102—42no—
42C13×C22⋊C8—22no—
43C13×#95—21no—
44C13×#95D412yes—
45#12202C1311yesmaximal, characteristic, direct product factor, Sylow
46C24×C13—21no—
47C24×C13—22no—
48C24×C13—21no—
49C24×C13—41no—
50C24×C13—44no—
51C24×C13—42no—
52C24×C13—44no—
53C24×C13—41no—
54C24×C13—44no—
55C24×C13—81no—
56C24×C13—81no—
57C24×C13SD1612yescomplemented
58C24×C13C2×D411yescharacteristic
59C2×Q8×C13—22no—
60C2×D4×C13—28no—
61C2×D4×C13—44no—
62C2×D4×C13—42no—
63C2×D4×C13—44no—
64C2×D4×C13—44no—
65C2×D4×C13—44no—
66C2×D4×C13—416no—
67C2×D4×C13—416no—
68C2×D4×C13—42no—
69C2×D4×C13—42no—
70C2×D4×C13—44no—
71C2×D4×C13—44no—
72C2×D4×C13—81no—
73C22×C4×C13—22no—
74C22×C4×C13—21no—
75C22×C4×C13—22no—
76C22×C4×C13—44no—
77C22×C4×C13—42no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D412yes—
80C13×SD16—84no—
81C2×C8×C13—42no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—44no—
87C13×C22⋊C4—44no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—84no—
94#2403C2×C1311yescharacteristic
95#2029C2×C1311yescharacteristic, complemented
96#1596C2×C1312yescomplemented
97#1343C2×C1312yescomplemented
98#1316C2×C1311yescharacteristic, complemented
99C23×C13—24no—
100C23×C13—22no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—24no—
104C23×C13—42no—
105C23×C13—44no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13—44no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—44no—
115C23×C13—48no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—81no—
120C23×C13—84no—
121C23×C13—84no—
122C23×C13—82no—
123C23×C13—88no—
124C23×C13—88no—
125C23×C13—84no—
126C23×C13#12011yescharacteristic
127C23×C13C2×SD1611yescharacteristic
128C23×C13AGL(1,ℤ/8)11yescharacteristic
129Q8×C13—82no—
130D4×C13—416no—
131D4×C13—48no—
132D4×C13—48no—
133D4×C13—44no—
134D4×C13—82no—
135D4×C13—84no—
136C2×C4×C13—24no—
137C2×C4×C13—22no—
138C2×C4×C13—42no—
139C2×C4×C13—48no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13—82no—
146C2×C4×C13—81no—
147C2×C4×C13—82no—
148C8×C13—82no—
149C23×D4—21no—
150#543C22×C1311yescharacteristic, complemented
151C2×#120—22no—
152#450—22no—
153#392—21no—
154#392C22×C1312yes—
155#386—22no—
156#379—21no—
157#379C22×C1311yescharacteristic
158#342—21no—
159#342C22×C1311yescharacteristic, complemented
160#328—22no—
161#323C22×C1312yescomplemented
162C22×C13—22no—
163C22×C13—24no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—42no—
169C22×C13—44no—
170C22×C13—44no—
171C22×C13—44no—
172C22×C13—44no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—44no—
176C22×C13—44no—
177C22×C13—81no—
178C22×C13—82no—
179C22×C13—82no—
180C22×C13—84no—
181C22×C13—82no—
182C22×C13—816no—
183C22×C13—82no—
184C22×C13—82no—
185C22×C13#45011yescharacteristic
186C22×C13#45511yescharacteristic
187C22×C13B(4,𝔽2)11yescharacteristic
188C4×C13—44no—
189C4×C13—42no—
190C4×C13—81no—
191C4×C13—82no—
192C4×C13—161no—
193C25—21no—
194C25D4×C1311yescharacteristic
195C22×D4—22no—
196C22×D4—22no—
197C22×D4—21no—
198C22×D4—48no—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4D4×C1312yes—
202C23×C4—21no—
203C2×SD16—42no—
204C22⋊Q8—22no—
205C22⋊Q8—42no—
206#120—48no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—42no—
213C2×C22⋊C4D4×C1311yescharacteristic
214C2×C22⋊C4C23×C1311yescharacteristic
215#102—42no—
216C22⋊C8—22no—
217#95—21no—
218#95D4×C1312yes—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13—41no—
222C2×C13—41no—
223C2×C13—44no—
224C2×C13—84no—
225C2×C13#160111yescharacteristic
226C2×C13#219612yes—
227C24—21no—
228C24—22no—
229C24—21no—
230C24—41no—
231C24—44no—
232C24—42no—
233C24—44no—
234C24—41no—
235C24—44no—
236C24—81no—
237C24—81no—
238C24C13×SD1612yescomplemented
239C24C2×D4×C1311yescharacteristic
240C2×Q8—22no—
241C2×D4—28no—
242C2×D4—44no—
243C2×D4—42no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—416no—
248C2×D4—416no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—44no—
252C2×D4—44no—
253C2×D4—81no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—44no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4C2×D4×C1312yes—
261SD16—84no—
262C2×C8—42no—
263C4⋊C4—22no—
264C4⋊C4—42no—
265C22⋊C4—41no—
266C22⋊C4—44no—
267C22⋊C4—44no—
268C22⋊C4—44no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—84no—
275C13#1220211yescharacteristic, direct product factor, Sylow
276C23—24no—
277C23—22no—
278C23—21no—
279C23—21no—
280C23—24no—
281C23—42no—
282C23—44no—
283C23—42no—
284C23—42no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—44no—
289C23—41no—
290C23—41no—
291C23—44no—
292C23—48no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—81no—
297C23—84no—
298C23—84no—
299C23—82no—
300C23—88no—
301C23—88no—
302C23—84no—
303C23C13×#12011yescharacteristic
304C23C2×C13×SD1611yescharacteristic
305C23C13×AGL(1,ℤ/8)11yescharacteristic
306Q8—82no—
307D4—416no—
308D4—44no—
309D4—48no—
310D4—48no—
311D4—82no—
312D4—84no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—48no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—81no—
324C2×C4—82no—
325C8—82no—
326C22—22no—
327C22—24no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—42no—
333C22—44no—
334C22—44no—
335C22—44no—
336C22—44no—
337C22—42no—
338C22—42no—
339C22—44no—
340C22—44no—
341C22—81no—
342C22—82no—
343C22—82no—
344C22—84no—
345C22—82no—
346C22—816no—
347C22—82no—
348C22—82no—
349C22C13×#45011yescharacteristic
350C22C13×#45511yescharacteristic
351C22C13×B(4,𝔽2)11yescharacteristic
352C4—44no—
353C4—42no—
354C4—81no—
355C4—82no—
356C4—161no—
357C2—21no—
358C2—21no—
359C2—41no—
360C2—44no—
361C2—41no—
362C2—84no—
363C2C13×#160111yescharacteristic
364C2C13×#219612yes—
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2403C2
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
2. C13×#2029C2semidirect
3. C13×#1596C2semidirect
4. C13×#1343C2semidirect
5. C13×#1316C2semidirect
7. C13×#543C22semidirect
16. C13×#342C22semidirect
18. C13×#323C22semidirect
45. #12202C13direct (N × H)
57. C24×C13SD16semidirect
95. #2029C2×C13semidirect
96. #1596C2×C13semidirect
97. #1343C2×C13semidirect
98. #1316C2×C13semidirect
150. #543C22×C13semidirect
159. #342C22×C13semidirect
161. #323C22×C13semidirect
238. C24C13×SD16semidirect
275. C13#12202direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24032
C13×#20292
C13×#15962
C13×#13432
C13×#13162
#1220213