Finite Group Databasebeta

← C13×#13220 #15699559

Subgroups — C13×#13220 #15699559

Order 3328.

540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2486C211yesmaximal, characteristic
2C2×C13×#352C214yesmaximal
3C13×#1800C211yesmaximal, characteristic
4C4×C13×#99C211yesmaximal, characteristic
5C2×C13×#123C2212yes—
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C13×#423—21no—
9C2×C13×#100C2212yes—
10C2×C13×#99C2212yes—
11C13×#398—21no—
12C13×#397—21no—
13C13×#389—21no—
14C13×#381C412yescomplemented
15C13×#380—21no—
16C13×#380C411yescharacteristic, complemented
17C4×C13×C22⋊C4—21no—
18C13×#352—28no—
19C13×#343—21no—
20C13×#342—21no—
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13C2×C412yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C2×C13×M16—22no—
26C13×#123—24no—
27C13×#123—24no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4C2×C412yes—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13—41no—
43C2×C42×C13D411yescharacteristic
44C13×C4⋊C8—41no—
45C13×C4⋊C8—41no—
46C13×#100—24no—
47C13×#99—22no—
48C13×#99D414yes—
49C13×#95—22no—
50C13×#95—21no—
51C13×#95—22no—
52C13×#95—41no—
53#13220C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13C22×C411yescharacteristic
55C24×C13C2×D411yescharacteristic
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13C2×D412yes—
59C2×D4×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—24no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×M16—42no—
78C13×M16—42no—
79C2×C8×C13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C22⋊C4—24no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—44no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—82no—
96#2486C2×C1311yescharacteristic
97C2×#352C2×C1314yes—
98#1800C2×C1311yescharacteristic
99C4×#99C2×C1311yescharacteristic
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13C4×D412yes—
110C23×C13#12112yes—
111D4×C13—42no—
112D4×C13—42no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—44no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—81no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13—84no—
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13#9911yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13#12711yescharacteristic
140C8×C13—82no—
141C2×#123C22×C1312yes—
142C2×C4×D4C22×C1311yescharacteristic
143C22×C4⋊C4C4×C1311yescharacteristic, complemented
144#423—21no—
145C2×#100C22×C1312yes—
146C2×#99C22×C1312yes—
147#398—21no—
148#397—21no—
149#389—21no—
150#381C4×C1312yescomplemented
151#380—21no—
152#380C4×C1311yescharacteristic, complemented
153C4×C22⋊C4—21no—
154#352—28no—
155#343—21no—
156#342—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—81no—
169C22×C13#39011yescharacteristic
170C22×C13C2×#9911yescharacteristic
171C22×C13#41011yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—82no—
179C4×C13—84no—
180C4×C13—82no—
181C4×C13#35212yescomplemented
182C22×D4C23×C1311yescharacteristic
183C23×C4C2×C4×C1312yes—
184C23×C4C2×C4×C1311yescharacteristic
185C23×C4D4×C1311yescharacteristic
186C2×M16—22no—
187#123—24no—
188#123—24no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4D4×C1311yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4C2×C4×C1312yes—
201C2×C22⋊C4C2×C4×C1311yescharacteristic
202C2×C22⋊C4D4×C1311yescharacteristic
203C2×C42—41no—
204C2×C42D4×C1311yescharacteristic
205C4⋊C8—41no—
206C4⋊C8—41no—
207#100—24no—
208#99—22no—
209#99D4×C1314yes—
210#95—22no—
211#95—21no—
212#95—22no—
213#95—41no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13—42no—
217C2×C13—42no—
218C2×C13#196411yescharacteristic
219C2×C13C2×#35211yescharacteristic
220C2×C13#212311yescharacteristic
221C24C22×C4×C1311yescharacteristic
222C24C2×D4×C1311yescharacteristic
223C2×D4—41no—
224C2×D4—41no—
225C2×D4C2×D4×C1312yes—
226C2×D4C13×#4112yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4C13×C22⋊C411yescharacteristic
240C22×C4C13×C22⋊C411yescharacteristic
241C22×C4C13×C22⋊C411yescharacteristic
242C22×C4C13×C22⋊C411yescharacteristic
243C22×C4C2×D4×C1311yescharacteristic
244M16—42no—
245M16—42no—
246C2×C8—42no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C22⋊C4—24no—
255C22⋊C4—24no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—42no—
259C22⋊C4—44no—
260C42—21no—
261C42—21no—
262C42—82no—
263C13#1322011yescharacteristic, direct product factor, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23C2×C13×C22⋊C411yescharacteristic
273C23C4×D4×C1312yes—
274C23C13×#12112yes—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—84no—
300C2×C4C13×#9911yescharacteristic
301C2×C4C13×#9911yescharacteristic
302C2×C4C13×#12411yescharacteristic
303C2×C4C13×#12711yescharacteristic
304C8—82no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22C13×#39011yescharacteristic
318C22C2×C13×#9911yescharacteristic
319C22C13×#41011yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—82no—
327C4—84no—
328C4—82no—
329C4C13×#35212yescomplemented
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2C13×#196411yescharacteristic
335C2C2×C13×#35211yescharacteristic
336C2C13×#212311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
7. C22×C13×C4⋊C4C4semidirect
14. C13×#381C4semidirect
16. C13×#380C4semidirect
53. #13220C13direct (N × H)
143. C22×C4⋊C4C4×C13semidirect
150. #381C4×C13semidirect
152. #380C4×C13semidirect
181. C4×C13#352semidirect
263. C13#13220direct (N × H)
329. C4C13×#352semidirect

Maximal subgroups

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

subgroupindex
C13×#24862
C2×C13×#3522
C13×#18002
C4×C13×#992
#1322013