Finite Group Databasebeta

← C13×#9390 #15695729

Subgroups — C13×#9390 #15695729

Order 3328.

446 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic
2C13×#2611C211yesmaximal, characteristic
3C13×#1528C212yesmaximal, complemented
4C13×#1464C211yesmaximal, characteristic
5C13×#1300C212yesmaximal, complemented
6C2×C13×#125C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#433—24no—
9C13×#432C2212yes—
10C13×#423—21no—
11C13×#407—21no—
12C4×C13×M16C2212yes—
13C13×#400C411yescharacteristic
14C13×#399C411yescharacteristic
15C13×#398C411yescharacteristic
16C13×#397C411yescharacteristic
17C13×#389—21no—
18C13×#388—21no—
19C13×#387—21no—
20C13×#385—21no—
21C13×#376C2211yescharacteristic
22C13×#330—24no—
23C13×#324—21no—
24C13×#323—21no—
25C23×C4×C13D411yescharacteristic
26C2×C13×M16—22no—
27C13×#125—22no—
28C13×#125—22no—
29C13×#117—22no—
30C13×#117—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13—21no—
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C13×C4⋊C8—24no—
47C13×C4⋊C8—22no—
48C13×C22⋊C8—24no—
49C13×C22⋊C8—22no—
50C13×#97—22no—
51C13×#97D414yes—
52C4×C8×C13—22no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95C2×C411yescharacteristic
59C13×#95C2×C411yescharacteristic
60#9390C1311yesmaximal, characteristic, direct product factor, Sylow
61C24×C13C22⋊C411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×M16—42no—
77C13×M16—42no—
78C2×C8×C13—24no—
79C2×C8×C13—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—42no—
96C42×C13C2×D412yes—
97C42×C13#4112yes—
98#2921C2×C1311yescharacteristic
99#2611C2×C1311yescharacteristic
100#1528C2×C1312yescomplemented
101#1464C2×C1311yescharacteristic
102#1300C2×C1312yescomplemented
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13C4×D412yes—
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12112yes—
137C2×C4×C13#12311yescharacteristic
138C8×C13—44no—
139C8×C13—82no—
140C2×#125C22×C1311yescharacteristic
141C2×#117C22×C1311yescharacteristic
142#433—24no—
143#432C22×C1312yes—
144#423—21no—
145#407—21no—
146C4×M16C22×C1312yes—
147#400C4×C1311yescharacteristic
148#399C4×C1311yescharacteristic
149#398C4×C1311yescharacteristic
150#397C4×C1311yescharacteristic
151#389—21no—
152#388—21no—
153#387—21no—
154#385—21no—
155#376C22×C1311yescharacteristic
156#330—24no—
157#324—21no—
158#323—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—42no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—81no—
166C22×C13#38611yescharacteristic
167C22×C13#42111yescharacteristic
168C22×C13#42111yescharacteristic
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—42no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180C23×C4D4×C1311yescharacteristic
181C2×M16—22no—
182#125—22no—
183#125—22no—
184#117—22no—
185#117—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C1311yescharacteristic
191C2×C4⋊C4C2×C4×C1311yescharacteristic
192C2×C4⋊C4C2×C4×C1311yescharacteristic
193C2×C4⋊C4D4×C1311yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4C2×C4×C1311yescharacteristic
197C2×C22⋊C4D4×C1311yescharacteristic
198C2×C42—21no—
199C2×C42D4×C1311yescharacteristic
200C2×C42C23×C1311yescharacteristic
201C4⋊C8—24no—
202C4⋊C8—22no—
203C22⋊C8—24no—
204C22⋊C8—22no—
205#97—22no—
206#97D4×C1314yes—
207C4×C8—22no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95C2×C4×C1311yescharacteristic
214#95C2×C4×C1311yescharacteristic
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—81no—
218C2×C13#188411yescharacteristic
219C2×C13#189711yescharacteristic
220C2×C13#191511yescharacteristic
221C24C13×C22⋊C411yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C13×C22⋊C411yescharacteristic
231C22×C4C13×C22⋊C411yescharacteristic
232C22×C4C13×C22⋊C411yescharacteristic
233C22×C4C22×C4×C1311yescharacteristic
234C22×C4C2×D4×C1311yescharacteristic
235C22×C4C2×D4×C1311yescharacteristic
236M16—42no—
237M16—42no—
238C2×C8—24no—
239C2×C8—42no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—21no—
254C42—21no—
255C42—42no—
256C42C2×D4×C1312yes—
257C42C13×#4112yes—
258C13#939011yescharacteristic, direct product factor, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×C13×C22⋊C411yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4C4×D4×C1312yes—
291C2×C4C13×#12011yescharacteristic
292C2×C4C13×#12112yes—
293C2×C4C13×#12311yescharacteristic
294C8—44no—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C13×#38611yescharacteristic
304C22C13×#42111yescharacteristic
305C22C13×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—81no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2C13×#188411yescharacteristic
321C2C13×#189711yescharacteristic
322C2C13×#191511yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1528C2semidirect
5. C13×#1300C2semidirect
60. #9390C13direct (N × H)
100. #1528C2×C13semidirect
102. #1300C2×C13semidirect
258. C13#9390direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29212
C13×#26112
C13×#15282
C13×#14642
C13×#13002
#939013