Finite Group Databasebeta

← C13×#10035 #15696374

Subgroups — C13×#10035 #15696374

Order 3328.

498 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3135C211yesmaximal, characteristic
2C13×#3104C211yesmaximal, characteristic, complemented
3C13×#3103C211yesmaximal, characteristic
4C13×#1985C211yesmaximal, characteristic, complemented
5C13×#1481C211yesmaximal, characteristic, complemented
6C13×#1480C211yesmaximal, characteristic
7C13×#1275C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C13×#491—21no—
12C13×#490—21no—
13C13×#489—21no—
14C13×#489—21no—
15C13×#484—21no—
16C13×#481—21no—
17C13×#477—21no—
18C13×#475—21no—
19C13×#462—21no—
20C13×#460—21no—
21C13×#451—21no—
22C13×#448—21no—
23C4×C13×Q16—22no—
24C4×C13×SD16—22no—
25C13×#431C2211yescharacteristic
26C13×#431C2211yescharacteristic
27C2×C13×C4⋊C8C2211yescharacteristic
28C13×#416—22no—
29C2×C13×#97C2211yescharacteristic
30C13×#336—22no—
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C2×C13×#41—21no—
34C22×Q8×C13D411yescharacteristic
35C2×C13×Q16—22no—
36C2×C13×SD16—22no—
37C22×C8×C13—21no—
38C22×C8×C13D412yes—
39C13×C4⋊Q8D411yescharacteristic
40C13×C4⋊Q8D411yescharacteristic
41C13×C4⋊Q8D411yescharacteristic
42C13×#127D411yescharacteristic
43C13×#125—21no—
44C13×#124—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×#121—21no—
48C13×#121—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×Q8×C13—21no—
53C4×Q8×C13—21no—
54C4×Q8×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C13×#117—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C13×#107—22no—
63C13×#106—22no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×#103—22no—
69C13×#103—22no—
70C13×#103—22no—
71C13×#103—22no—
72C13×#103—22no—
73C13×#102—22no—
74C13×#102—22no—
75C13×#102—22no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×#97—21no—
79C13×#97—21no—
80C4×C8×C13D412yes—
81C4×C8×C13D412yes—
82#10035C1311yesmaximal, characteristic, direct product factor, Sylow
83C13×#41—42no—
84C13×#41—42no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—42no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—41no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—41no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13#4111yescharacteristic
101C13×Q16—44no—
102C13×SD16—44no—
103C2×C8×C13—22no—
104C2×C8×C13—22no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—41no—
109C2×C8×C13—42no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C42×C13—41no—
126C42×C13—41no—
127C42×C13—41no—
128C42×C13C2×D411yescharacteristic
129C42×C13C2×D411yescharacteristic
130C42×C13C2×D411yescharacteristic
131C42×C13C2×D411yescharacteristic
132#3135C2×C1311yescharacteristic
133#3104C2×C1311yescharacteristic, complemented
134#3103C2×C1311yescharacteristic
135#1985C2×C1311yescharacteristic, complemented
136#1481C2×C1311yescharacteristic, complemented
137#1480C2×C1311yescharacteristic
138#1275C2×C1311yescharacteristic, complemented
139C23×C13—41no—
140C23×C13#12111yescharacteristic
141Q8×C13—22no—
142Q8×C13—22no—
143Q8×C13—41no—
144Q8×C13—41no—
145Q8×C13—42no—
146Q8×C13—42no—
147Q8×C13—42no—
148D4×C13—42no—
149D4×C13—42no—
150D4×C13—42no—
151D4×C13—82no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13#12011yescharacteristic
165C2×C4×C13#12011yescharacteristic
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12711yescharacteristic
170C2×C4×C13#13512yes—
171C2×C4×C13#13712yes—
172C8×C13—42no—
173C8×C13—42no—
174C8×C13—42no—
175C8×C13—81no—
176#533C22×C1311yescharacteristic
177#532C22×C1311yescharacteristic
178C2×C4×Q8C22×C1311yescharacteristic
179#491—21no—
180#490—21no—
181#489—21no—
182#489—21no—
183#484—21no—
184#481—21no—
185#477—21no—
186#475—21no—
187#462—21no—
188#460—21no—
189#451—21no—
190#448—21no—
191C4×Q16—22no—
192C4×SD16—22no—
193#431C22×C1311yescharacteristic
194#431C22×C1311yescharacteristic
195C2×C4⋊C8C22×C1311yescharacteristic
196#416—22no—
197C2×#97C22×C1311yescharacteristic
198#336—22no—
199Q8⋊C8—22no—
200D4⋊C8—22no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13#39211yescharacteristic
207C22×C13#46412yes—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—42no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13#45212yes—
218C4×C13#49511yescharacteristic
219C4×C13#49711yescharacteristic
220C2×#41—21no—
221C22×Q8D4×C1311yescharacteristic
222C2×Q16—22no—
223C2×SD16—22no—
224C22×C8—21no—
225C22×C8D4×C1312yes—
226C4⋊Q8D4×C1311yescharacteristic
227C4⋊Q8D4×C1311yescharacteristic
228C4⋊Q8D4×C1311yescharacteristic
229#127D4×C1311yescharacteristic
230#125—21no—
231#124—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234#121—21no—
235#121—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C1311yescharacteristic
247C2×C42—21no—
248C2×C42C23×C1311yescharacteristic
249#107—22no—
250#106—22no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255#103—22no—
256#103—22no—
257#103—22no—
258#103—22no—
259#103—22no—
260#102—22no—
261#102—22no—
262#102—22no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#97—21no—
266#97—21no—
267C4×C8D4×C1312yes—
268C4×C8D4×C1312yes—
269C2×C13—22no—
270C2×C13—161no—
271C2×C13#201011yescharacteristic
272C2×C13#201511yescharacteristic
273C2×C13#201711yescharacteristic
274#41—42no—
275#41—42no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—42no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4C2×D4×C1311yescharacteristic
290C22×C4C2×D4×C1311yescharacteristic
291C22×C4C13×#4111yescharacteristic
292Q16—44no—
293SD16—44no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—42no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C42—41no—
318C42—41no—
319C42C2×D4×C1311yescharacteristic
320C42C2×D4×C1311yescharacteristic
321C42C2×D4×C1311yescharacteristic
322C42C2×D4×C1311yescharacteristic
323C13#1003511yescharacteristic, direct product factor, Sylow
324C23—41no—
325C23C13×#12111yescharacteristic
326Q8—22no—
327Q8—22no—
328Q8—41no—
329Q8—41no—
330Q8—42no—
331Q8—42no—
332Q8—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—82no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4C13×#12011yescharacteristic
350C2×C4C13×#12011yescharacteristic
351C2×C4C13×#12011yescharacteristic
352C2×C4C13×#12111yescharacteristic
353C2×C4C13×#12111yescharacteristic
354C2×C4C13×#12711yescharacteristic
355C2×C4C13×#13512yes—
356C2×C4C13×#13712yes—
357C8—42no—
358C8—42no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22C13×#39211yescharacteristic
367C22C13×#46412yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4C13×#45212yes—
378C4C13×#49511yescharacteristic
379C4C13×#49711yescharacteristic
380C2—22no—
381C2—161no—
382C2C13×#201011yescharacteristic
383C2C13×#201511yescharacteristic
384C2C13×#201711yescharacteristic
subgroupG/H
centerC2×C4×C13#127
commutator, Frattini, cosocleC2×C42C23×C13
socleC22×C13#392
prime radicalC13×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3104C2semidirect
4. C13×#1985C2semidirect
5. C13×#1481C2semidirect
7. C13×#1275C2semidirect
82. #10035C13direct (N × H)
133. #3104C2×C13semidirect
135. #1985C2×C13semidirect
136. #1481C2×C13semidirect
138. #1275C2×C13semidirect
323. C13#10035direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31352
C13×#31042
C13×#31032
C13×#19852
C13×#14812
C13×#14802
C13×#12752
#1003513