Finite Group Databasebeta

← C13×#10263 #15696602

Subgroups — C13×#10263 #15696602

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#486C211yesmaximal, characteristic
2C2×C13×#462C211yesmaximal, characteristic, complemented
3C2×C13×#460C211yesmaximal, characteristic
4C13×#1984C211yesmaximal, characteristic, complemented
5C2×C13×#332C211yesmaximal, characteristic, complemented
6C2×C13×#331C211yesmaximal, characteristic
7C13×#1277C211yesmaximal, characteristic, complemented
8C22×C13×Q16—21no—
9C22×C13×SD16—21no—
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×#127C2211yescharacteristic
12C2×C4×Q8×C13C2211yescharacteristic
13C13×#486—22no—
14C13×#486—22no—
15C13×#462—22no—
16C13×#462—22no—
17C13×#460—22no—
18C13×#460—22no—
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×#103—21no—
23C2×C13×#102—22no—
24C2×C13×#102—21no—
25C2×C4×C8×C13C2211yescharacteristic
26C13×#336—22no—
27C13×#332—22no—
28C13×#331—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D411yescharacteristic
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C2×C13×Q16—24no—
35C2×C13×Q16—42no—
36C2×C13×Q16—42no—
37C2×C13×SD16—24no—
38C2×C13×SD16—42no—
39C2×C13×SD16—42no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13D412yes—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8—21no—
47C13×C4⋊Q8D412yes—
48C13×#127—21no—
49C13×#127—21no—
50C13×#127—21no—
51C13×#127D412yes—
52C4×Q8×C13—21no—
53C4×Q8×C13—21no—
54C4×Q8×C13—21no—
55C4×Q8×C13—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8D412yes—
67C13×C4⋊C8D412yes—
68C13×#103—24no—
69C13×#102—24no—
70C13×#102—28no—
71C4×C8×C13—21no—
72C4×C8×C13—21no—
73#10263C1311yesmaximal, characteristic, direct product factor, Sylow
74C24×C13—41no—
75C2×Q8×C13—21no—
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—22no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×Q8×C13D812yes—
87C2×D4×C13—22no—
88C2×D4×C13—22no—
89C2×D4×C13—22no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—42no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—42no—
99C2×D4×C13—82no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C13×Q16—48no—
107C13×SD16—48no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C2×C8×C13—22no—
111C2×C8×C13—22no—
112C2×C8×C13—22no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C2×C8×C13—41no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×C8×C13—42no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C42×C13—41no—
128C42×C13—41no—
129C42×C13C2×D411yescharacteristic
130C42×C13C2×D411yescharacteristic
131C42×C13C2×D411yescharacteristic
132C42×C13C2×D411yescharacteristic
133C2×#486C2×C1311yescharacteristic
134C2×#462C2×C1311yescharacteristic, complemented
135C2×#460C2×C1311yescharacteristic
136#1984C2×C1311yescharacteristic, complemented
137C2×#332C2×C1311yescharacteristic, complemented
138C2×#331C2×C1311yescharacteristic
139#1277C2×C1311yescharacteristic, complemented
140C23×C13—42no—
141C23×C13—82no—
142C23×C13—81no—
143C23×C13—81no—
144C23×C13—82no—
145C23×C13#12111yescharacteristic
146Q8×C13—22no—
147Q8×C13—22no—
148Q8×C13—41no—
149Q8×C13—41no—
150Q8×C13—42no—
151Q8×C13—42no—
152Q8×C13—81no—
153Q8×C13—81no—
154D4×C13—42no—
155D4×C13—42no—
156D4×C13—44no—
157D4×C13—82no—
158D4×C13—82no—
159D4×C13—81no—
160D4×C13—81no—
161D4×C13—81no—
162D4×C13—81no—
163C2×C4×C13—22no—
164C2×C4×C13—22no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12011yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12711yescharacteristic
178C2×C4×C13C2×D811yescharacteristic
179C2×C4×C13#13511yescharacteristic
180C2×C4×C13#13512yes—
181C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C13#13712yes—
184C8×C13—42no—
185C8×C13—42no—
186C8×C13—42no—
187C8×C13—81no—
188C22×Q16—21no—
189C22×SD16—21no—
190C2×C4⋊Q8C22×C1311yescharacteristic
191C2×#127C22×C1311yescharacteristic
192C2×C4×Q8C22×C1311yescharacteristic
193#486—22no—
194#486—22no—
195#462—22no—
196#462—22no—
197#460—22no—
198#460—22no—
199C2×C4⋊C8C22×C1311yescharacteristic
200C2×C4⋊C8C22×C1311yescharacteristic
201C2×C4⋊C8C22×C1311yescharacteristic
202C2×#103—21no—
203C2×#102—22no—
204C2×#102—21no—
205C2×C4×C8C22×C1311yescharacteristic
206#336—22no—
207#332—22no—
208#331—22no—
209C22×C13—82no—
210C22×C13—82no—
211C22×C13—82no—
212C22×C13—162no—
213C22×C13—162no—
214C22×C13#39211yescharacteristic
215C22×C13#46412yes—
216C22×C13#46611yescharacteristic
217C22×C13#46911yescharacteristic
218C22×C13#47112yes—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—42no—
222C4×C13—82no—
223C4×C13—81no—
224C4×C13#44711yescharacteristic
225C4×C13#44711yescharacteristic
226C4×C13#44911yescharacteristic
227C4×C13#44911yescharacteristic
228C4×C13#45212yes—
229C4×C13#49511yescharacteristic
230C4×C13#49711yescharacteristic
231C22×Q8—21no—
232C22×Q8D4×C1311yescharacteristic
233C22×D4—21no—
234C22×D4—21no—
235C22×D4—21no—
236C2×Q16—24no—
237C2×Q16—42no—
238C2×Q16—42no—
239C2×SD16—24no—
240C2×SD16—42no—
241C2×SD16—42no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8D4×C1312yes—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8D4×C1312yes—
250#127—21no—
251#127—21no—
252#127—21no—
253#127D4×C1312yes—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C1311yescharacteristic
262C2×C42—21no—
263C2×C42C23×C1311yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C1312yes—
269C4⋊C8D4×C1312yes—
270#103—24no—
271#102—24no—
272#102—28no—
273C4×C8—21no—
274C4×C8—21no—
275C2×C13—162no—
276C2×C13#168212yes—
277C2×C13#170212yes—
278C2×C13#199911yescharacteristic
279C2×C13#201511yescharacteristic
280C2×C13#201911yescharacteristic
281C24—41no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8C13×D812yes—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—82no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4C2×D4×C1311yescharacteristic
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C13×#4111yescharacteristic
313Q16—48no—
314SD16—48no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—42no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C42—41no—
335C42—41no—
336C42C2×D4×C1311yescharacteristic
337C42C2×D4×C1311yescharacteristic
338C42C2×D4×C1311yescharacteristic
339C42C2×D4×C1311yescharacteristic
340C13#1026311yescharacteristic, direct product factor, Sylow
341C23—42no—
342C23—82no—
343C23—81no—
344C23—81no—
345C23—82no—
346C23C13×#12111yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—82no—
359D4—82no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C13×#12011yescharacteristic
374C2×C4C13×#12011yescharacteristic
375C2×C4C13×#12011yescharacteristic
376C2×C4C13×#12111yescharacteristic
377C2×C4C13×#12111yescharacteristic
378C2×C4C13×#12711yescharacteristic
379C2×C4C2×C13×D811yescharacteristic
380C2×C4C13×#13511yescharacteristic
381C2×C4C13×#13512yes—
382C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
383C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C13×#13712yes—
385C8—42no—
386C8—42no—
387C8—42no—
388C8—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—162no—
393C22—162no—
394C22C13×#39211yescharacteristic
395C22C13×#46412yes—
396C22C13×#46611yescharacteristic
397C22C13×#46911yescharacteristic
398C22C13×#47112yes—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—82no—
403C4—81no—
404C4C13×#44711yescharacteristic
405C4C13×#44711yescharacteristic
406C4C13×#44911yescharacteristic
407C4C13×#44911yescharacteristic
408C4C13×#45212yes—
409C4C13×#49511yescharacteristic
410C4C13×#49711yescharacteristic
411C2—162no—
412C2C13×#168212yes—
413C2C13×#170212yes—
414C2C13×#199911yescharacteristic
415C2C13×#201511yescharacteristic
416C2C13×#201911yescharacteristic
subgroupG/H
center, socleC23×C13#121
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#462C2semidirect
4. C13×#1984C2semidirect
5. C2×C13×#332C2semidirect
7. C13×#1277C2semidirect
73. #10263C13direct (N × H)
134. C2×#462C2×C13semidirect
136. #1984C2×C13semidirect
137. C2×#332C2×C13semidirect
139. #1277C2×C13semidirect
340. C13#10263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4862
C2×C13×#4622
C2×C13×#4602
C13×#19842
C2×C13×#3322
C2×C13×#3312
C13×#12772
#1026313