Finite Group Databasebeta

← C13×#9489 #15695828

Subgroups — C13×#9489 #15695828

Order 3328.

602 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2975C211yesmaximal, characteristic, complemented
2C13×#2535C211yesmaximal, characteristic
3C13×#1800C211yesmaximal, characteristic, complemented
4C13×#1486C212yesmaximal, complemented
5C13×#1286C212yesmaximal, complemented
6C2×C13×#121—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#436—24no—
10C13×#431C2212yes—
11C13×#423C2212yes—
12C2×C13×#100—21no—
13C13×#407—22no—
14C13×#397C412yes—
15C13×#392C412yes—
16C13×#386—22no—
17C13×#382C2211yescharacteristic
18C13×#380—21no—
19C13×#343—21no—
20C13×D4⋊C8—24no—
21C22×D4×C13—22no—
22C22×D4×C13C2×C411yescharacteristic
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13D412yes—
26C2×C13×M16—24no—
27C2×C13×M16—22no—
28C13×#121—44no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4C2×C412yes—
40C2×C42×C13C2311yescharacteristic
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×C4⋊C8—22no—
44C13×#100—42no—
45C13×C22⋊C8—24no—
46C13×C22⋊C8—22no—
47C4×C8×C13D414yescomplemented
48C13×#95—22no—
49C13×#95—21no—
50C13×#95C2×C412yes—
51#9489C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C24×C13C22⋊C412yes—
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—21no—
57C2×D4×C13—22no—
58C2×D4×C13—21no—
59C2×D4×C13—42no—
60C2×D4×C13—44no—
61C2×D4×C13—44no—
62C2×D4×C13—82no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—82no—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×M16—42no—
77C13×M16—42no—
78C13×M16—84no—
79C2×C8×C13—24no—
80C2×C8×C13—42no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—24no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—82no—
89C42×C13C2×D412yes—
90C42×C13#4112yes—
91#2975C2×C1311yescharacteristic, complemented
92#2535C2×C1311yescharacteristic
93#1800C2×C1311yescharacteristic, complemented
94#1486C2×C1312yescomplemented
95#1286C2×C1312yescomplemented
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109D4×C13—24no—
110D4×C13—42no—
111D4×C13—42no—
112D4×C13—42no—
113D4×C13—88no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—82no—
126C2×C4×C13—82no—
127C2×C4×C13—82no—
128C2×C4×C13C4×D412yes—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12112yes—
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)12yes—
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C8×C13—44no—
136C8×C13—82no—
137C2×#121—21no—
138C2×C4×D4C22×C1311yescharacteristic
139C2×C4×D4C22×C1311yescharacteristic
140#436—24no—
141#431C22×C1312yes—
142#423C22×C1312yes—
143C2×#100—21no—
144#407—22no—
145#397C4×C1312yes—
146#392C4×C1312yes—
147#386—22no—
148#382C22×C1311yescharacteristic
149#380—21no—
150#343—21no—
151D4⋊C8—24no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—42no—
155C22×C13—44no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—82no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13#38611yescharacteristic
167C22×C13#41711yescharacteristic
168C22×C13#41811yescharacteristic
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—42no—
173C4×C13—82no—
174C4×C13—81no—
175C4×C13#46812yes—
176C4×C13#46912yes—
177C22×D4—22no—
178C22×D4C2×C4×C1311yescharacteristic
179C22×D4D4×C1311yescharacteristic
180C23×C4—21no—
181C23×C4D4×C1312yes—
182C2×M16—24no—
183C2×M16—22no—
184#121—44no—
185C4×D4—22no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C1311yescharacteristic
191C2×C4⋊C4D4×C1311yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4C2×C4×C1312yes—
196C2×C42C23×C1311yescharacteristic
197C4⋊C8—22no—
198C4⋊C8—22no—
199C4⋊C8—22no—
200#100—42no—
201C22⋊C8—24no—
202C22⋊C8—22no—
203C4×C8D4×C1314yescomplemented
204#95—22no—
205#95—21no—
206#95C2×C4×C1312yes—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—82no—
210C2×C13—82no—
211C2×C13#189111yescharacteristic
212C2×C13#189511yescharacteristic
213C2×C13#191111yescharacteristic
214C24—21no—
215C24C13×C22⋊C412yes—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—21no—
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—42no—
222C2×D4—44no—
223C2×D4—44no—
224C2×D4—82no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—82no—
234C22×C4C13×C22⋊C412yes—
235C22×C4C22×C4×C1311yescharacteristic
236C22×C4C2×D4×C1311yescharacteristic
237C22×C4C2×D4×C1311yescharacteristic
238M16—42no—
239M16—42no—
240M16—84no—
241C2×C8—24no—
242C2×C8—42no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—42no—
246C22⋊C4—24no—
247C22⋊C4—44no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—82no—
251C42C2×D4×C1312yes—
252C42C13×#4112yes—
253C13#948911yescharacteristic, direct product factor, Sylow
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23C2×C13×C22⋊C411yescharacteristic
267D4—24no—
268D4—42no—
269D4—42no—
270D4—42no—
271D4—88no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4C4×D4×C1312yes—
287C2×C4C13×#12011yescharacteristic
288C2×C4C13×#12112yes—
289C2×C4C13×#12311yescharacteristic
290C2×C4C13×AGL(1,ℤ/8)12yes—
291C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
292C2×C4C13×#13711yescharacteristic
293C8—44no—
294C8—82no—
295C22—21no—
296C22—21no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22C13×#38611yescharacteristic
310C22C13×#41711yescharacteristic
311C22C13×#41811yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4C13×#46812yes—
319C4C13×#46912yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—82no—
324C2C13×#189111yescharacteristic
325C2C13×#189511yescharacteristic
326C2C13×#191111yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#2535C2
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
1. C13×#2975C2semidirect
3. C13×#1800C2semidirect
4. C13×#1486C2semidirect
5. C13×#1286C2semidirect
47. C4×C8×C13D4semidirect
51. #9489C13direct (N × H)
91. #2975C2×C13semidirect
93. #1800C2×C13semidirect
94. #1486C2×C13semidirect
95. #1286C2×C13semidirect
203. C4×C8D4×C13semidirect
253. C13#9489direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29752
C13×#25352
C13×#18002
C13×#14862
C13×#12862
#948913