Finite Group Databasebeta

← C13×#9028 #15695367

Subgroups — C13×#9028 #15695367

Order 3328.

696 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C13×#397C211yesmaximal, characteristic
2C13×#2312C211yesmaximal, characteristic
3C13×#1823C212yesmaximal, complemented
4C2×C13×#323C211yesmaximal, characteristic
5C13×#1294C212yesmaximal, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10C13×#397—22no—
11C13×#397C414yescomplemented
12C13×#388—24no—
13C13×#380C2212yes—
14C13×#379—21no—
15C4×C13×C22⋊C4—21no—
16C2×C13×#95—21no—
17C2×C13×#95C2211yescharacteristic
18C13×#340—24no—
19C13×#323—22no—
20C25×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C8×C13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D414yes—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—44no—
38C2×C13×C22⋊C4C2×C412yes—
39C2×C13×C22⋊C4D412yes—
40C2×C42×C13—22no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8—22no—
43C13×#95—22no—
44C13×#95—24no—
45C13×#95—22no—
46C13×#95—21no—
47C13×#95C2×C412yes—
48#9028C1311yesmaximal, characteristic, direct product factor, Sylow
49C24×C13—21no—
50C24×C13—22no—
51C24×C13—21no—
52C24×C13—22no—
53C24×C13—42no—
54C24×C13—42no—
55C24×C13C22⋊C412yes—
56C24×C13C2×D411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—24no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4112yes—
76C2×C8×C13—44no—
77C2×C8×C13—42no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—44no—
80C13×C4⋊C4—42no—
81C13×C22⋊C4—24no—
82C13×C22⋊C4—24no—
83C13×C22⋊C4—48no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—82no—
87C13×C22⋊C4—82no—
88C42×C13—82no—
89C2×#397C2×C1311yescharacteristic
90#2312C2×C1311yescharacteristic
91#1823C2×C1312yescomplemented
92C2×#323C2×C1311yescharacteristic
93#1294C2×C1312yescomplemented
94C23×C13—22no—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—48no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—81no—
107C23×C13—81no—
108C23×C13—84no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13#12011yescharacteristic
111C23×C13#12311yescharacteristic
112C23×C13#13512yes—
113C23×C13AGL(1,ℤ/8)12yes—
114C2×C4×C13—24no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13—81no—
131C2×C4×C13—84no—
132C2×C4×C13—82no—
133C2×C4×C13—82no—
134C2×C4×C13C4×D412yes—
135C2×C4×C13#12112yes—
136C8×C13—82no—
137C22×C4⋊C4C22×C1311yescharacteristic
138C22×C22⋊C4—21no—
139C22×C22⋊C4C22×C1311yescharacteristic
140C2×C22⋊C8C22×C1312yes—
141#397—22no—
142#397C4×C1314yescomplemented
143#388—24no—
144#380C22×C1312yes—
145#379—21no—
146C4×C22⋊C4—21no—
147C2×#95—21no—
148C2×#95C22×C1311yescharacteristic
149#340—24no—
150#323—22no—
151C22×C13—24no—
152C22×C13—24no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—82no—
162C22×C13—84no—
163C22×C13—84no—
164C22×C13#38611yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13#41811yescharacteristic
167C22×C13#44912yes—
168C22×C13#45512yes—
169C22×C13#45812yes—
170C22×C13#48212yes—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—42no—
174C4×C13—82no—
175C4×C13—84no—
176C4×C13—82no—
177C25D4×C1311yescharacteristic
178C23×C4—21no—
179C23×C4—21no—
180C23×C4D4×C1311yescharacteristic
181C23×C4C23×C1311yescharacteristic
182C22×C8—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×C4×C1312yes—
187C2×C4⋊C4D4×C1314yes—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—44no—
195C2×C22⋊C4C2×C4×C1312yes—
196C2×C22⋊C4D4×C1312yes—
197C2×C42—22no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200#95—22no—
201#95—24no—
202#95—21no—
203#95—22no—
204#95C2×C4×C1312yes—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13—22no—
208C2×C13—82no—
209C2×C13#161214yes—
210C2×C13#187511yescharacteristic
211C2×C13#188511yescharacteristic
212C2×C13#189011yescharacteristic
213C24—21no—
214C24—22no—
215C24—21no—
216C24—22no—
217C24—42no—
218C24—42no—
219C24C13×C22⋊C412yes—
220C24C2×D4×C1311yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C13×C22⋊C412yes—
236C22×C4C22×C4×C1311yescharacteristic
237C22×C4C2×D4×C1312yes—
238C22×C4C2×D4×C1311yescharacteristic
239C22×C4C13×#4112yes—
240C2×C8—44no—
241C2×C8—42no—
242C4⋊C4—24no—
243C4⋊C4—44no—
244C4⋊C4—42no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—48no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—82no—
251C22⋊C4—82no—
252C42—82no—
253C13#902811yescharacteristic, direct product factor, Sylow
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23—48no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—81no—
267C23—81no—
268C23—84no—
269C23C2×C13×C22⋊C411yescharacteristic
270C23C13×#12011yescharacteristic
271C23C13×#12311yescharacteristic
272C23C13×#13512yes—
273C23C13×AGL(1,ℤ/8)12yes—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—81no—
291C2×C4—84no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4C4×D4×C1312yes—
295C2×C4C13×#12112yes—
296C8—82no—
297C22—24no—
298C22—24no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—44no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—82no—
308C22—84no—
309C22—84no—
310C22C13×#38611yescharacteristic
311C22C13×#41611yescharacteristic
312C22C13×#41811yescharacteristic
313C22C13×#44912yes—
314C22C13×#45512yes—
315C22C13×#45812yes—
316C22C13×#48212yes—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—82no—
321C4—84no—
322C4—82no—
323C2—21no—
324C2—21no—
325C2—22no—
326C2—82no—
327C2C13×#161214yes—
328C2C13×#187511yescharacteristic
329C2C13×#188511yescharacteristic
330C2C13×#189011yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1823C2semidirect
5. C13×#1294C2semidirect
11. C13×#397C4semidirect
48. #9028C13direct (N × H)
91. #1823C2×C13semidirect
93. #1294C2×C13semidirect
142. #397C4×C13semidirect
253. C13#9028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C13×#23122
C13×#18232
C2×C13×#3232
C13×#12942
#902813