Finite Group Databasebeta

← C13×#9297 #15695636

Subgroups — C13×#9297 #15695636

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3209C211yesmaximal, characteristic
2C13×#2331C211yesmaximal, characteristic
3C13×#1995C211yesmaximal, characteristic
4C13×#1548C211yesmaximal, characteristic
5C13×#1518C211yesmaximal, characteristic
6C13×#1286C211yesmaximal, characteristic
7C13×#1274C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C13×#494C412yescomplemented
11C13×#487C412yescomplemented
12C13×#462—22no—
13C13×#451—22no—
14C13×#431C2211yescharacteristic
15C13×#431C2211yescharacteristic
16C13×#423C2211yescharacteristic
17C13×#391—22no—
18C13×#389—21no—
19C13×#387—22no—
20C13×#382C2211yescharacteristic
21C4×C13×C4⋊C4—21no—
22C13×#376C2211yescharacteristic
23C13×#339—21no—
24C13×#339—21no—
25C13×#333—22no—
26C13×#328—22no—
27C22×Q8×C13D412yes—
28C2×C13×Q16—24no—
29C2×C13×M16—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8C2×C411yescharacteristic
33C13×C4⋊Q8C2×C411yescharacteristic
34C13×C4⋊Q8C2×C412yes—
35C13×C4⋊Q8D412yes—
36C13×#125—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C13×#117—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—22no—
46C2×C42×C13—22no—
47C2×C42×C13D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13C2311yescharacteristic
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×#103—24no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C4×C8×C13—21no—
58C4×C8×C13C2×C412yes—
59C13×#95—22no—
60C13×#95—22no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95D412yes—
65#9297C1311yesmaximal, characteristic, direct product factor, Sylow
66C2×Q8×C13—22no—
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C2×Q8×C13—82no—
70C2×Q8×C13C22⋊C414yes—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×Q16—84no—
79C13×M16—41no—
80C13×M16—41no—
81C2×C8×C13—22no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—82no—
97C13×C22⋊C4—41no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—41no—
102C42×C13—82no—
103C42×C13Q1612yescomplemented
104C42×C13C22×C411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108#3209C2×C1311yescharacteristic
109#2331C2×C1311yescharacteristic
110#1995C2×C1311yescharacteristic
111#1548C2×C1311yescharacteristic
112#1518C2×C1311yescharacteristic
113#1286C2×C1311yescharacteristic
114#1274C2×C1311yescharacteristic
115C23×C13#12011yescharacteristic
116Q8×C13—44no—
117Q8×C13—42no—
118Q8×C13—82no—
119Q8×C13—81no—
120C2×C4×C13—24no—
121C2×C4×C13—22no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13C2×C22⋊C411yescharacteristic
137C2×C4×C13C4×D411yescharacteristic
138C2×C4×C13C4×D411yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13C2×Q1611yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×C4×C13#13711yescharacteristic
145C2×C4×C13#13711yescharacteristic
146C8×C13—42no—
147C8×C13—81no—
148C8×C13—81no—
149#533C22×C1311yescharacteristic
150C2×C4⋊Q8C22×C1311yescharacteristic
151#494C4×C1312yescomplemented
152#487C4×C1312yescomplemented
153#462—22no—
154#451—22no—
155#431C22×C1311yescharacteristic
156#431C22×C1311yescharacteristic
157#423C22×C1311yescharacteristic
158#391—22no—
159#389—21no—
160#387—22no—
161#382C22×C1311yescharacteristic
162C4×C4⋊C4—21no—
163#376C22×C1311yescharacteristic
164#339—21no—
165#339—21no—
166#333—22no—
167#328—22no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13#38611yescharacteristic
171C22×C13#45111yescharacteristic
172C22×C13#45211yescharacteristic
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—42no—
178C4×C13—44no—
179C4×C13—82no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13C4×Q1611yescharacteristic
184C4×C13#44111yescharacteristic
185C4×C13#46211yescharacteristic
186C4×C13#46411yescharacteristic
187C22×Q8D4×C1312yes—
188C2×Q16—24no—
189C2×M16—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8C2×C4×C1311yescharacteristic
193C4⋊Q8C2×C4×C1311yescharacteristic
194C4⋊Q8C2×C4×C1312yes—
195C4⋊Q8D4×C1312yes—
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C42—22no—
207C2×C42D4×C1311yescharacteristic
208C2×C42D4×C1311yescharacteristic
209C2×C42C23×C1311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214#103—24no—
215C22⋊C8—21no—
216C22⋊C8—21no—
217C4×C8—21no—
218C4×C8C2×C4×C1312yes—
219#95—22no—
220#95—22no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95D4×C1312yes—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13#187811yescharacteristic
228C2×C13#190511yescharacteristic
229C2×C13#191111yescharacteristic
230C2×Q8—22no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—82no—
234C2×Q8C13×C22⋊C414yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4C2×D4×C1311yescharacteristic
240C22×C4C2×D4×C1311yescharacteristic
241C22×C4C2×D4×C1311yescharacteristic
242Q16—84no—
243M16—41no—
244M16—41no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—82no—
261C22⋊C4—41no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—41no—
266C42—82no—
267C42C13×Q1612yescomplemented
268C42C22×C4×C1311yescharacteristic
269C42C2×D4×C1311yescharacteristic
270C42C13×#4111yescharacteristic
271C42C13×#4111yescharacteristic
272C13#929711yescharacteristic, direct product factor, Sylow
273C23C13×#12011yescharacteristic
274Q8—44no—
275Q8—42no—
276Q8—82no—
277Q8—81no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4C2×C13×C22⋊C411yescharacteristic
295C2×C4C4×D4×C1311yescharacteristic
296C2×C4C4×D4×C1311yescharacteristic
297C2×C4C13×#12111yescharacteristic
298C2×C4C13×#12111yescharacteristic
299C2×C4C13×#12311yescharacteristic
300C2×C4C2×C13×Q1611yescharacteristic
301C2×C4C13×#13511yescharacteristic
302C2×C4C13×#13711yescharacteristic
303C2×C4C13×#13711yescharacteristic
304C8—42no—
305C8—81no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22C13×#38611yescharacteristic
310C22C13×#45111yescharacteristic
311C22C13×#45211yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—44no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4C4×C13×Q1611yescharacteristic
323C4C13×#44111yescharacteristic
324C4C13×#46211yescharacteristic
325C4C13×#46411yescharacteristic
326C2—21no—
327C2—21no—
328C2C13×#187811yescharacteristic
329C2C13×#190511yescharacteristic
330C2C13×#191111yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
10. C13×#494C4semidirect
11. C13×#487C4semidirect
65. #9297C13direct (N × H)
103. C42×C13Q16semidirect
151. #494C4×C13semidirect
152. #487C4×C13semidirect
267. C42C13×Q16semidirect
272. C13#9297direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32092
C13×#23312
C13×#19952
C13×#15482
C13×#15182
C13×#12862
C13×#12742
#929713