Finite Group Databasebeta

← C13×#10201 #15696540

Subgroups — C13×#10201 #15696540

Order 3328.

528 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3246C211yesmaximal, characteristic
2C13×#3227C211yesmaximal, characteristic
3C13×#3165C211yesmaximal, characteristic, complemented
4C13×#1981C211yesmaximal, characteristic, complemented
5C13×#1980C211yesmaximal, characteristic
6C13×#1503C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#501—22no—
12C13×#500—21no—
13C13×#498—21no—
14C13×#498—21no—
15C13×#486—21no—
16C13×#481—22no—
17C13×#476—22no—
18C13×#476—21no—
19C13×#475—21no—
20C13×#465—22no—
21C13×#461—21no—
22C13×#460—21no—
23C13×#431C2211yescharacteristic
24C13×#428—22no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×#104—22no—
27C2×C13×#103—22no—
28C4×C13×M16C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C13×#328—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C2×C13×SD16—22no—
34C2×C13×M16D412yes—
35C22×C8×C13D412yes—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D411yescharacteristic
40C13×C4⋊Q8D411yescharacteristic
41C13×C4⋊Q8D411yescharacteristic
42C13×C4⋊Q8D412yes—
43C13×#127D411yescharacteristic
44C13×#125—21no—
45C13×#124—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C13×#121—21no—
49C13×#121—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C13×#117—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C42×C13—21no—
59C2×C42×C13C2311yescharacteristic
60C13×#107—24no—
61C13×#106—24no—
62C13×#106—22no—
63C13×#106—24no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×#104—44no—
68C13×#103—22no—
69C13×#103—44no—
70C13×#102—22no—
71C13×#102—24no—
72C13×C22⋊C8D412yes—
73C13×#97—21no—
74C4×C8×C13—21no—
75C4×C8×C13—21no—
76C13×#95—21no—
77#10201C1311yesmaximal, characteristic, direct product factor, Sylow
78C13×#41—42no—
79C13×#41—42no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—22no—
83C2×Q8×C13—21no—
84C2×Q8×C13—42no—
85C2×Q8×C13—42no—
86C2×Q8×C13—41no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C13×SD16—82no—
98C13×M16—22no—
99C13×M16SD1614yescomplemented
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—22no—
103C2×C8×C13—42no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C42×C13—41no—
122C42×C13—42no—
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13#4111yescharacteristic
127#3246C2×C1311yescharacteristic
128#3227C2×C1311yescharacteristic
129#3165C2×C1311yescharacteristic, complemented
130#1981C2×C1311yescharacteristic, complemented
131#1980C2×C1311yescharacteristic
132#1503C2×C1311yescharacteristic, complemented
133#1283C2×C1311yescharacteristic, complemented
134C23×C13—41no—
135C23×C13#12711yescharacteristic
136Q8×C13—44no—
137Q8×C13—41no—
138Q8×C13—41no—
139Q8×C13—42no—
140Q8×C13—81no—
141Q8×C13—81no—
142Q8×C13—81no—
143D4×C13—42no—
144D4×C13—41no—
145D4×C13—41no—
146D4×C13—42no—
147D4×C13—81no—
148D4×C13—81no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—81no—
158C2×C4×C13—82no—
159C2×C4×C13—81no—
160C2×C4×C13—82no—
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12011yescharacteristic
163C2×C4×C13#12011yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13#12111yescharacteristic
167C2×C4×C13C2×SD1612yes—
168C2×C4×C13#13712yes—
169C8×C13—24no—
170C8×C13—42no—
171C8×C13—42no—
172#533C22×C1311yescharacteristic
173#532C22×C1311yescharacteristic
174C2×C4⋊Q8C22×C1311yescharacteristic
175#501—22no—
176#500—21no—
177#498—21no—
178#498—21no—
179#486—21no—
180#481—22no—
181#476—22no—
182#476—21no—
183#475—21no—
184#465—22no—
185#461—21no—
186#460—21no—
187#431C22×C1311yescharacteristic
188#428—22no—
189C2×C4⋊C8C22×C1311yescharacteristic
190C2×#104—22no—
191C2×#103—22no—
192C4×M16C22×C1311yescharacteristic
193C4×C4⋊C4C22×C1311yescharacteristic
194#328—22no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13#39211yescharacteristic
201C22×C13#49211yescharacteristic
202C22×C13#49711yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—82no—
207C4×C13—82no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13#44812yes—
212C4×C13#45311yescharacteristic
213C4×C13#45411yescharacteristic
214C4×C13#46112yes—
215C2×#41—21no—
216C22×Q8—21no—
217C2×SD16—22no—
218C2×M16D4×C1312yes—
219C22×C8D4×C1312yes—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8D4×C1312yes—
224C4⋊Q8D4×C1311yescharacteristic
225C4⋊Q8D4×C1311yescharacteristic
226C4⋊Q8D4×C1311yescharacteristic
227#127D4×C1311yescharacteristic
228#125—21no—
229#124—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—21no—
233#121—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C42—21no—
243C2×C42C23×C1311yescharacteristic
244#107—24no—
245#106—24no—
246#106—22no—
247#106—24no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251#104—44no—
252#103—22no—
253#103—44no—
254#102—22no—
255#102—24no—
256C22⋊C8D4×C1312yes—
257#97—21no—
258C4×C8—21no—
259C4×C8—21no—
260#95—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—161no—
264C2×C13#200611yescharacteristic
265C2×C13#200911yescharacteristic
266C2×C13#201311yescharacteristic
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—41no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C2×D4×C1311yescharacteristic
284C22×C4C2×D4×C1311yescharacteristic
285C22×C4C2×D4×C1311yescharacteristic
286SD16—82no—
287M16—22no—
288M16C13×SD1614yescomplemented
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—41no—
311C42—42no—
312C42C2×D4×C1311yescharacteristic
313C42C2×D4×C1311yescharacteristic
314C42C2×D4×C1311yescharacteristic
315C42C13×#4111yescharacteristic
316C13#1020111yescharacteristic, direct product factor, Sylow
317C23—41no—
318C23C13×#12711yescharacteristic
319Q8—44no—
320Q8—41no—
321Q8—41no—
322Q8—42no—
323Q8—81no—
324Q8—81no—
325Q8—81no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—42no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4C13×#12011yescharacteristic
345C2×C4C13×#12011yescharacteristic
346C2×C4C13×#12011yescharacteristic
347C2×C4C13×#12111yescharacteristic
348C2×C4C13×#12111yescharacteristic
349C2×C4C13×#12111yescharacteristic
350C2×C4C2×C13×SD1612yes—
351C2×C4C13×#13712yes—
352C8—24no—
353C8—42no—
354C8—42no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C13×#39211yescharacteristic
361C22C13×#49211yescharacteristic
362C22C13×#49711yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4C13×#44812yes—
372C4C13×#45311yescharacteristic
373C4C13×#45411yescharacteristic
374C4C13×#46112yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2C13×#200611yescharacteristic
379C2C13×#200911yescharacteristic
380C2C13×#201311yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#3165C2semidirect
4. C13×#1981C2semidirect
6. C13×#1503C2semidirect
7. C13×#1283C2semidirect
77. #10201C13direct (N × H)
99. C13×M16SD16semidirect
129. #3165C2×C13semidirect
130. #1981C2×C13semidirect
132. #1503C2×C13semidirect
133. #1283C2×C13semidirect
288. M16C13×SD16semidirect
316. C13#10201direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32462
C13×#32272
C13×#31652
C13×#19812
C13×#19802
C13×#15032
C13×#12832
#1020113