Finite Group Databasebeta

← C13×#9201 #15695540

Subgroups — C13×#9201 #15695540

Order 3328.

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

normal subgroups only

This group has 612 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×#2626C211yesmaximal, characteristic
2C13×#2312C211yesmaximal, characteristic
3C13×#1520C212yesmaximal, complemented
4C2×C13×#323C211yesmaximal, characteristic
5C13×#1289C212yesmaximal, complemented
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9C13×#399C412yescomplemented
10C13×#396—22no—
11C13×#393C412yescomplemented
12C13×#388—24no—
13C13×#385—21no—
14C13×#380C2211yescharacteristic
15C13×#380C2212yes—
16C13×#379—21no—
17C13×#379—21no—
18C4×C13×C22⋊C4—21no—
19C13×#328—24no—
20C13×#323—22no—
21C25×C13D411yescharacteristic
22C22×Q8×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C8×C13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4C2×C412yes—
43C2×C13×C22⋊C4D412yes—
44C2×C42×C13—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95C2×C412yes—
50C13×#95D414yes—
51#9201C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C24×C13—21no—
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—81no—
57C24×C13—81no—
58C24×C13C22⋊C412yes—
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—22no—
61C2×Q8×C13—81no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—24no—
68C22×C4×C13—81no—
69C22×C4×C13—81no—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C2×C8×C13—42no—
76C2×C8×C13—82no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—82no—
80C13×C4⋊C4—81no—
81C13×C4⋊C4—82no—
82C13×C22⋊C4—24no—
83C13×C22⋊C4—24no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—82no—
90C13×C22⋊C4—82no—
91C13×C22⋊C4—82no—
92C13×C22⋊C4—82no—
93C42×C13—82no—
94#2626C2×C1311yescharacteristic
95#2312C2×C1311yescharacteristic
96#1520C2×C1312yescomplemented
97C2×#323C2×C1311yescharacteristic
98#1289C2×C1312yescomplemented
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—22no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—81no—
111C23×C13—81no—
112C23×C13—84no—
113C23×C13—84no—
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13#12011yescharacteristic
116C23×C13#12311yescharacteristic
117C23×C13#13512yes—
118C23×C13#13712yes—
119Q8×C13—82no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—44no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—44no—
137C2×C4×C13—81no—
138C2×C4×C13C4×D412yes—
139C2×C4×C13#12112yes—
140C8×C13—82no—
141C2×C22⋊Q8C22×C1311yescharacteristic
142C22×C22⋊C4C22×C1311yescharacteristic
143C2×C22⋊C8C22×C1312yes—
144#399C4×C1312yescomplemented
145#396—22no—
146#393C4×C1312yescomplemented
147#388—24no—
148#385—21no—
149#380C22×C1311yescharacteristic
150#380C22×C1312yes—
151#379—21no—
152#379—21no—
153C4×C22⋊C4—21no—
154#328—24no—
155#323—22no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—44no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—82no—
169C22×C13—84no—
170C22×C13—84no—
171C22×C13#38611yescharacteristic
172C22×C13#41611yescharacteristic
173C22×C13#41911yescharacteristic
174C22×C13#45212yes—
175C22×C13#48512yes—
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—42no—
179C4×C13—82no—
180C4×C13—84no—
181C4×C13—81no—
182C4×C13—81no—
183C25D4×C1311yescharacteristic
184C22×Q8C2×C4×C1311yescharacteristic
185C23×C4D4×C1311yescharacteristic
186C23×C4C23×C1311yescharacteristic
187C22×C8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C1311yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4C2×C4×C1312yes—
205C2×C22⋊C4D4×C1312yes—
206C2×C42—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209#95—22no—
210#95—22no—
211#95C2×C4×C1312yes—
212#95D4×C1314yes—
213C2×C13—21no—
214C2×C13—22no—
215C2×C13—21no—
216C2×C13—22no—
217C2×C13—82no—
218C2×C13#187311yescharacteristic
219C2×C13#191111yescharacteristic
220C2×C13#191311yescharacteristic
221C24—21no—
222C24—21no—
223C24—22no—
224C24—22no—
225C24—81no—
226C24—81no—
227C24C13×C22⋊C412yes—
228C24C2×D4×C1311yescharacteristic
229C2×Q8—22no—
230C2×Q8—81no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—24no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4C13×C22⋊C412yes—
240C22×C4C22×C4×C1311yescharacteristic
241C22×C4C2×D4×C1312yes—
242C22×C4C2×D4×C1311yescharacteristic
243C22×C4C13×#4112yes—
244C2×C8—42no—
245C2×C8—82no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—82no—
249C4⋊C4—81no—
250C4⋊C4—82no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—82no—
259C22⋊C4—82no—
260C22⋊C4—82no—
261C22⋊C4—82no—
262C42—82no—
263C13#920111yescharacteristic, direct product factor, Sylow
264C23—22no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—84no—
278C23—84no—
279C23C2×C13×C22⋊C411yescharacteristic
280C23C13×#12011yescharacteristic
281C23C13×#12311yescharacteristic
282C23C13×#13512yes—
283C23C13×#13712yes—
284Q8—82no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—81no—
303C2×C4C4×D4×C1312yes—
304C2×C4C13×#12112yes—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22—84no—
320C22—84no—
321C22C13×#38611yescharacteristic
322C22C13×#41611yescharacteristic
323C22C13×#41911yescharacteristic
324C22C13×#45212yes—
325C22C13×#48512yes—
326C4—22no—
327C4—22no—
328C4—42no—
329C4—82no—
330C4—84no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—22no—
335C2—21no—
336C2—22no—
337C2—82no—
338C2C13×#187311yescharacteristic
339C2C13×#191111yescharacteristic
340C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1520C2semidirect
5. C13×#1289C2semidirect
9. C13×#399C4semidirect
11. C13×#393C4semidirect
51. #9201C13direct (N × H)
96. #1520C2×C13semidirect
98. #1289C2×C13semidirect
144. #399C4×C13semidirect
146. #393C4×C13semidirect
263. C13#9201direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26262
C13×#23122
C13×#15202
C2×C13×#3232
C13×#12892
#920113