Finite Group Databasebeta

← C13×#10198 #15696537

Subgroups — C13×#10198 #15696537

Order 3328.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3246C211yesmaximal, characteristic
2C13×#3209C211yesmaximal, characteristic, complemented
3C13×#3141C211yesmaximal, characteristic
4C13×#1987C211yesmaximal, characteristic, complemented
5C13×#1986C211yesmaximal, characteristic, complemented
6C13×#1502C211yesmaximal, characteristic
7C13×#1283C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C13×#494—21no—
12C13×#489—22no—
13C13×#487—21no—
14C13×#487—21no—
15C13×#486—21no—
16C13×#476—21no—
17C13×#475—21no—
18C13×#465—22no—
19C13×#462—22no—
20C13×#461—21no—
21C13×#460—21no—
22C13×#451—22no—
23C13×#431C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C13×#417—22no—
26C4×C13×M16C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#340—22no—
29C13×#339—22no—
30C13×#327—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C2×C13×Q16—24no—
34C2×C13×SD16—22no—
35C2×C13×M16D412yes—
36C22×C8×C13D412yes—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8D411yescharacteristic
41C13×C4⋊Q8D412yes—
42C13×C4⋊Q8D411yescharacteristic
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#125—21no—
46C13×#124—21no—
47C13×C22⋊Q8—21no—
48C13×C22⋊Q8—21no—
49C13×#121—21no—
50C13×#121—21no—
51C4×Q8×C13—21no—
52C4×Q8×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C13×#117—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C42×C13—21no—
60C2×C42×C13C2311yescharacteristic
61C13×#106—22no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#103—24no—
66C13×#103—24no—
67C13×#103—22no—
68C13×#102—24no—
69C13×#102—22no—
70C13×C22⋊C8D412yes—
71C13×#97—21no—
72C4×C8×C13—21no—
73C4×C8×C13—21no—
74C13×#95—21no—
75#10198C1311yesmaximal, characteristic, direct product factor, Sylow
76C13×#41—42no—
77C13×#41—42no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—22no—
81C2×Q8×C13—21no—
82C2×Q8×C13—41no—
83C2×Q8×C13—82no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C13×Q16—84no—
95C13×SD16—82no—
96C13×M16—22no—
97C13×M16—22no—
98C2×C8×C13—22no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13—42no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C42×C13—41no—
120C42×C13—42no—
121C42×C13C2×D411yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D411yescharacteristic
124C42×C13#4111yescharacteristic
125#3246C2×C1311yescharacteristic
126#3209C2×C1311yescharacteristic, complemented
127#3141C2×C1311yescharacteristic
128#1987C2×C1311yescharacteristic, complemented
129#1986C2×C1311yescharacteristic, complemented
130#1502C2×C1311yescharacteristic
131#1283C2×C1311yescharacteristic, complemented
132C23×C13—41no—
133C23×C13#12711yescharacteristic
134Q8×C13—42no—
135Q8×C13—44no—
136Q8×C13—42no—
137Q8×C13—41no—
138Q8×C13—41no—
139Q8×C13—82no—
140D4×C13—42no—
141D4×C13—41no—
142D4×C13—41no—
143D4×C13—81no—
144D4×C13—81no—
145D4×C13—81no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—81no—
155C2×C4×C13—82no—
156C2×C4×C13—81no—
157C2×C4×C13—82no—
158C2×C4×C13#12011yescharacteristic
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#13512yes—
165C2×C4×C13#13712yes—
166C8×C13—42no—
167C8×C13—42no—
168C8×C13—42no—
169#533C22×C1311yescharacteristic
170#532C22×C1311yescharacteristic
171C2×C4⋊Q8C22×C1311yescharacteristic
172#494—21no—
173#489—22no—
174#487—21no—
175#487—21no—
176#486—21no—
177#476—21no—
178#475—21no—
179#465—22no—
180#462—22no—
181#461—21no—
182#460—21no—
183#451—22no—
184#431C22×C1311yescharacteristic
185C2×C4⋊C8C22×C1311yescharacteristic
186#417—22no—
187C4×M16C22×C1311yescharacteristic
188C4×C4⋊C4C22×C1311yescharacteristic
189#340—22no—
190#339—22no—
191#327—22no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13#39211yescharacteristic
198C22×C13#49511yescharacteristic
199C22×C13#49711yescharacteristic
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—82no—
204C4×C13—81no—
205C4×C13—82no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13#45212yes—
209C4×C13#45511yescharacteristic
210C4×C13#45611yescharacteristic
211C4×C13#46412yes—
212C2×#41—21no—
213C22×Q8—21no—
214C2×Q16—24no—
215C2×SD16—22no—
216C2×M16D4×C1312yes—
217C22×C8D4×C1312yes—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8D4×C1312yes—
222C4⋊Q8D4×C1311yescharacteristic
223C4⋊Q8D4×C1311yescharacteristic
224C4⋊Q8D4×C1311yescharacteristic
225#127D4×C1311yescharacteristic
226#125—21no—
227#124—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230#121—21no—
231#121—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C1311yescharacteristic
242#106—22no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246#103—24no—
247#103—24no—
248#103—22no—
249#102—24no—
250#102—22no—
251C22⋊C8D4×C1312yes—
252#97—21no—
253C4×C8—21no—
254C4×C8—21no—
255#95—21no—
256C2×C13—21no—
257C2×C13—21no—
258C2×C13—161no—
259C2×C13#200711yescharacteristic
260C2×C13#200811yescharacteristic
261C2×C13#201511yescharacteristic
262#41—42no—
263#41—42no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—82no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4C2×D4×C1311yescharacteristic
278C22×C4C2×D4×C1311yescharacteristic
279C22×C4C2×D4×C1311yescharacteristic
280Q16—84no—
281SD16—82no—
282M16—22no—
283M16—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—42no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—41no—
306C42—42no—
307C42C2×D4×C1311yescharacteristic
308C42C2×D4×C1311yescharacteristic
309C42C2×D4×C1311yescharacteristic
310C42C13×#4111yescharacteristic
311C13#1019811yescharacteristic, direct product factor, Sylow
312C23—41no—
313C23C13×#12711yescharacteristic
314Q8—42no—
315Q8—44no—
316Q8—42no—
317Q8—41no—
318Q8—41no—
319Q8—82no—
320D4—42no—
321D4—41no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4C13×#12011yescharacteristic
339C2×C4C13×#12011yescharacteristic
340C2×C4C13×#12011yescharacteristic
341C2×C4C13×#12111yescharacteristic
342C2×C4C13×#12111yescharacteristic
343C2×C4C13×#12111yescharacteristic
344C2×C4C13×#13512yes—
345C2×C4C13×#13712yes—
346C8—42no—
347C8—42no—
348C8—42no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22C13×#39211yescharacteristic
355C22C13×#49511yescharacteristic
356C22C13×#49711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4C13×#45212yes—
366C4C13×#45511yescharacteristic
367C4C13×#45611yescharacteristic
368C4C13×#46412yes—
369C2—21no—
370C2—21no—
371C2—161no—
372C2C13×#200711yescharacteristic
373C2C13×#200811yescharacteristic
374C2C13×#201511yescharacteristic
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
2. C13×#3209C2semidirect
4. C13×#1987C2semidirect
5. C13×#1986C2semidirect
7. C13×#1283C2semidirect
75. #10198C13direct (N × H)
126. #3209C2×C13semidirect
128. #1987C2×C13semidirect
129. #1986C2×C13semidirect
131. #1283C2×C13semidirect
311. C13#10198direct (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×#32092
C13×#31412
C13×#19872
C13×#19862
C13×#15022
C13×#12832
#1019813