Finite Group Databasebeta

← C13×#19065 #15705404

Subgroups — C13×#19065 #15705404

Order 3328.

920 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 920 conjugacy classes of subgroups — too many to draw. Only its 222 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×#3548C211yesmaximal, characteristic
2C13×#3216C212yesmaximal, complemented
3C13×#3162C211yesmaximal, characteristic, complemented
4C13×#1661C218yesmaximal, complemented
5C13×#1537C211yesmaximal, characteristic, complemented
6C13×#1530C212yesmaximal, complemented
7C13×#562C2214yes—
8C13×#554—22no—
9C13×#550—22no—
10C13×#547—22no—
11C13×#540—22no—
12C13×#537—24no—
13C13×#533C2211yescharacteristic
14C13×#533C2211yescharacteristic
15C13×#532C2212yes—
16C13×#501—22no—
17C13×#501C2214yes—
18C13×#497C2214yes—
19C13×#489C2214yes—
20C13×#462—22no—
21C13×#460—22no—
22C13×#452—24no—
23C13×#432C2212yes—
24C13×#427—22no—
25C2×C13×#97C2211yescharacteristic
26C13×#330C2214yes—
27C13×#329C2218yes—
28C2×C13×#41—24no—
29C2×C13×#41D414yes—
30C2×C13×Q16—24no—
31C2×C13×SD16—24no—
32C22×C8×C13—21no—
33C13×C4⋊Q8D412yes—
34C13×C4⋊Q8D412yes—
35C13×C4⋊Q8C2312yes—
36C13×#127—22no—
37C13×#127D412yes—
38C13×#125—22no—
39C13×#125—21no—
40C13×#125C2312yes—
41C13×#124C2314yes—
42C13×#123—28no—
43C13×C22⋊Q8—24no—
44C13×C22⋊Q8—28no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8—22no—
47C13×#121—28no—
48C13×#121—24no—
49C13×#121—28no—
50C13×#121—22no—
51C13×#121—22no—
52C4×Q8×C13—22no—
53C4×Q8×C13—22no—
54C4×D4×C13—24no—
55C4×D4×C13—22no—
56C4×D4×C13—22no—
57C13×#117—21no—
58C13×#117D412yes—
59C2×C13×C4⋊C4—24no—
60C2×C42×C13C2311yescharacteristic
61C13×#107—24no—
62C13×#106—24no—
63C13×C4⋊C8—22no—
64C13×#103—24no—
65C13×#102—24no—
66C13×C22⋊C8—22no—
67C13×#97—21no—
68C13×#97C2312yes—
69C13×#97C2314yes—
70#19065C1311yesmaximal, characteristic, direct product factor, Sylow
71C13×#41—84no—
72C13×#41—88no—
73C2×Q8×C13—22no—
74C2×Q8×C13—22no—
75C2×Q8×C13C2×D414yes—
76C2×D4×C13—28no—
77C2×D4×C13—24no—
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C2×D4×C13C2×D414yes—
81C22×C4×C13—28no—
82C22×C4×C13—24no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D412yes—
85C13×Q16—84no—
86C13×SD16—84no—
87C2×C8×C13—24no—
88C2×C8×C13—22no—
89C2×C8×C13—24no—
90C13×C4⋊C4—28no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—24no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4C2×D414yes—
99C13×C22⋊C4—28no—
100C13×C22⋊C4—22no—
101C13×C22⋊C4—24no—
102C13×C22⋊C4—24no—
103C13×C22⋊C4—41no—
104C42×C13—22no—
105C42×C13—41no—
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D412yes—
108C42×C13C2411yescharacteristic
109#3548C2×C1311yescharacteristic
110#3216C2×C1312yescomplemented
111#3162C2×C1311yescharacteristic, complemented
112#1661C2×C1318yescomplemented
113#1537C2×C1311yescharacteristic, complemented
114#1530C2×C1312yescomplemented
115C23×C13—24no—
116C23×C13#12011yescharacteristic
117Q8×C13—44no—
118Q8×C13—44no—
119Q8×C13—42no—
120Q8×C13—42no—
121D4×C13—44no—
122D4×C13—44no—
123D4×C13—44no—
124D4×C13—84no—
125D4×C13—88no—
126C2×C4×C13—22no—
127C2×C4×C13—24no—
128C2×C4×C13—24no—
129C2×C4×C13—42no—
130C2×C4×C13—48no—
131C2×C4×C13—42no—
132C2×C4×C13—88no—
133C2×C4×C13#12012yes—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13C22×D411yescharacteristic
136C2×C4×C13C22×D412yes—
137C8×C13—24no—
138C8×C13—44no—
139#562C22×C1314yes—
140#554—22no—
141#550—22no—
142#547—22no—
143#540—22no—
144#537—24no—
145#533C22×C1311yescharacteristic
146#533C22×C1311yescharacteristic
147#532C22×C1312yes—
148#501—22no—
149#501C22×C1314yes—
150#497C22×C1314yes—
151#489C22×C1314yes—
152#462—22no—
153#460—22no—
154#452—24no—
155#432C22×C1312yes—
156#427—22no—
157C2×#97C22×C1311yescharacteristic
158#330C22×C1314yes—
159#329C22×C1318yes—
160C22×C13—21no—
161C22×C13—22no—
162C22×C13—44no—
163C22×C13—44no—
164C22×C13—44no—
165C22×C13C2×#12011yescharacteristic
166C4×C13—21no—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—44no—
170C4×C13—44no—
171C4×C13—82no—
172C4×C13#45612yes—
173C2×#41—24no—
174C2×#41D4×C1314yes—
175C2×Q16—24no—
176C2×SD16—24no—
177C22×C8—21no—
178C4⋊Q8D4×C1312yes—
179C4⋊Q8D4×C1312yes—
180C4⋊Q8C23×C1312yes—
181#127—22no—
182#127D4×C1312yes—
183#125—22no—
184#125—21no—
185#125C23×C1312yes—
186#124C23×C1314yes—
187#123—28no—
188C22⋊Q8—24no—
189C22⋊Q8—28no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192#121—28no—
193#121—24no—
194#121—28no—
195#121—22no—
196#121—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×D4—24no—
200C4×D4—22no—
201C4×D4—22no—
202#117—21no—
203#117D4×C1312yes—
204C2×C4⋊C4—24no—
205C2×C42C23×C1311yescharacteristic
206#107—24no—
207#106—24no—
208C4⋊C8—22no—
209#103—24no—
210#102—24no—
211C22⋊C8—22no—
212#97—21no—
213#97C23×C1312yes—
214#97C23×C1314yes—
215C2×C13—41no—
216C2×C13—84no—
217C2×C13C2×#45611yescharacteristic
218C2×C13#301912yes—
219#41—84no—
220#41—88no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8C2×D4×C1314yes—
224C2×D4—28no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4C2×D4×C1314yes—
229C22×C4—28no—
230C22×C4—24no—
231C22×C4C2×D4×C1311yescharacteristic
232C22×C4C2×D4×C1312yes—
233Q16—84no—
234SD16—84no—
235C2×C8—24no—
236C2×C8—22no—
237C2×C8—24no—
238C4⋊C4—28no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—42no—
246C4⋊C4C2×D4×C1314yes—
247C22⋊C4—28no—
248C22⋊C4—22no—
249C22⋊C4—24no—
250C22⋊C4—24no—
251C22⋊C4—41no—
252C42—22no—
253C42—41no—
254C42C2×D4×C1311yescharacteristic
255C42C2×D4×C1312yes—
256C42C24×C1311yescharacteristic
257C13#1906511yescharacteristic, direct product factor, Sylow
258C23—24no—
259C23C13×#12011yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—42no—
263Q8—42no—
264D4—44no—
265D4—44no—
266D4—44no—
267D4—84no—
268D4—88no—
269C2×C4—22no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—42no—
273C2×C4—48no—
274C2×C4—42no—
275C2×C4—88no—
276C2×C4C13×#12012yes—
277C2×C4C13×#12011yescharacteristic
278C2×C4C22×D4×C1311yescharacteristic
279C2×C4C22×D4×C1312yes—
280C8—24no—
281C8—44no—
282C22—21no—
283C22—22no—
284C22—44no—
285C22—44no—
286C22—44no—
287C22C2×C13×#12011yescharacteristic
288C4—21no—
289C4—22no—
290C4—22no—
291C4—44no—
292C4—44no—
293C4—82no—
294C4C13×#45612yes—
295C2—41no—
296C2—84no—
297C2C2×C13×#45611yescharacteristic
298C2C13×#301912yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3548C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3216C2semidirect
3. C13×#3162C2semidirect
4. C13×#1661C2semidirect
5. C13×#1537C2semidirect
6. C13×#1530C2semidirect
70. #19065C13direct (N × H)
110. #3216C2×C13semidirect
111. #3162C2×C13semidirect
112. #1661C2×C13semidirect
113. #1537C2×C13semidirect
114. #1530C2×C13semidirect
257. C13#19065direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35482
C13×#32162
C13×#31622
C13×#16612
C13×#15372
C13×#15302
#1906513