Finite Group Databasebeta

← C13×#13311 #15699650

Subgroups — C13×#13311 #15699650

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#510C211yesmaximal, characteristic, complemented
2C13×#3067C211yesmaximal, characteristic
3C13×#3059C211yesmaximal, characteristic, complemented
4C2×C13×#362C211yesmaximal, characteristic, complemented
5C13×#2145C211yesmaximal, characteristic, complemented
6C13×#2117C211yesmaximal, characteristic, complemented
7C13×#1389C211yesmaximal, characteristic, complemented
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×Q16C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C13×#536—21no—
13C13×#510—22no—
14C13×#510—22no—
15C2×C13×Q32—21no—
16C2×C13×SD32—21no—
17C2×C13×M32C2211yescharacteristic
18C2×C13×M32C2211yescharacteristic
19C13×#473—21no—
20C13×#472—21no—
21C13×#471—22no—
22C13×#470—22no—
23C13×#467—22no—
24C2×C13×#108C2211yescharacteristic
25C13×#427C2211yescharacteristic
26C13×#419—21no—
27C13×#413—21no—
28C13×#362—22no—
29C13×#360—22no—
30C13×#350—22no—
31C2×C13×#41—21no—
32C2×C13×#41D411yescharacteristic
33C22×Q8×C13—21no—
34C13×#137—22no—
35C13×#137—41no—
36C13×AGL(1,ℤ/8)—22no—
37C13×AGL(1,ℤ/8)—41no—
38C13×#135—21no—
39C13×#135—21no—
40C13×#135—21no—
41C13×#135—21no—
42C13×#135—42no—
43C2×C13×Q16—21no—
44C2×C13×Q16—21no—
45C2×C13×Q16—21no—
46C2×C13×Q16—21no—
47C2×C13×Q16—21no—
48C2×C13×Q16D412yes—
49C2×C13×Q16D411yescharacteristic
50C2×C13×SD16—21no—
51C2×C13×D8D411yescharacteristic
52C13×#131—21no—
53C13×#131—21no—
54C13×#131—21no—
55C13×#131—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16D411yescharacteristic
59C22×C8×C13—21no—
60C22×C8×C13C2311yescharacteristic
61C13×C4⋊Q8—41no—
62C13×#124—41no—
63C13×#123—42no—
64C13×C22⋊Q8—24no—
65C13×#117—21no—
66C13×Q32—24no—
67C13×SD32—24no—
68C13×M32—21no—
69C13×M32—21no—
70C13×M32—21no—
71C13×M32D412yes—
72C2×C13×C16—21no—
73C2×C13×C16—21no—
74C13×#108—21no—
75C13×#108D412yes—
76C13×#107—21no—
77C13×#106D412yes—
78C13×#103—24no—
79C13×#101—22no—
80C13×#100—22no—
81#13311C1311yesmaximal, characteristic, direct product factor, Sylow
82C13×#41—21no—
83C13×#41—21no—
84C13×#41—21no—
85C13×#41—21no—
86C13×#41—41no—
87C13×#41—41no—
88C13×#41—41no—
89C13×#41—41no—
90C2×Q8×C13—21no—
91C2×Q8×C13—22no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×Q8×C13—41no—
95C2×Q8×C13—41no—
96C2×Q8×C13—41no—
97C2×Q8×C13D811yescharacteristic
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—41no—
101C2×D4×C13D811yescharacteristic
102C22×C4×C13—21no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13C2×D411yescharacteristic
106C13×Q16—22no—
107C13×Q16—21no—
108C13×Q16—22no—
109C13×Q16—21no—
110C13×Q16—42no—
111C13×Q16—41no—
112C13×Q16—41no—
113C13×SD16—42no—
114C13×SD16—42no—
115C13×SD16—41no—
116C13×SD16—41no—
117C13×D8—21no—
118C13×D8—21no—
119C13×D8—42no—
120C13×M16—21no—
121C13×M16—22no—
122C13×M16—21no—
123C13×M16—41no—
124C13×M16—41no—
125C13×M16—41no—
126C2×C8×C13—21no—
127C2×C8×C13—41no—
128C2×C8×C13—41no—
129C2×C8×C13—41no—
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13#4111yescharacteristic
136C13×C4⋊C4—22no—
137C13×C4⋊C4—44no—
138C13×C22⋊C4—44no—
139C13×C22⋊C4—41no—
140C42×C13—41no—
141C13×C16—22no—
142C13×C16—41no—
143C2×#510C2×C1311yescharacteristic, complemented
144#3067C2×C1311yescharacteristic
145#3059C2×C1311yescharacteristic, complemented
146C2×#362C2×C1311yescharacteristic, complemented
147#2145C2×C1311yescharacteristic, complemented
148#2117C2×C1311yescharacteristic, complemented
149#1389C2×C1311yescharacteristic, complemented
150C23×C13—21no—
151C23×C13—41no—
152C23×C13AGL(1,ℤ/8)11yescharacteristic
153Q8×C13—21no—
154Q8×C13—21no—
155Q8×C13—41no—
156Q8×C13—42no—
157Q8×C13—41no—
158Q8×C13—42no—
159Q8×C13—81no—
160Q8×C13—81no—
161D4×C13—21no—
162D4×C13—21no—
163D4×C13—41no—
164D4×C13—41no—
165D4×C13—41no—
166D4×C13—41no—
167D4×C13—81no—
168D4×C13—81no—
169C2×C4×C13—21no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13#12011yescharacteristic
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13C2×D811yescharacteristic
183C2×C4×C13#13511yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185C8×C13—41no—
186C8×C13—42no—
187C8×C13#12011yescharacteristic
188C8×C13#12111yescharacteristic
189C8×C13#12111yescharacteristic
190C8×C13#12711yescharacteristic
191#575—21no—
192C2×#135C22×C1311yescharacteristic
193C22×Q16C22×C1311yescharacteristic
194C2×#131C22×C1311yescharacteristic
195#536—21no—
196#510—22no—
197#510—22no—
198C2×Q32—21no—
199C2×SD32—21no—
200C2×M32C22×C1311yescharacteristic
201C2×M32C22×C1311yescharacteristic
202#473—21no—
203#472—21no—
204#471—22no—
205#470—22no—
206#467—22no—
207C2×#108C22×C1311yescharacteristic
208#427C22×C1311yescharacteristic
209#419—21no—
210#413—21no—
211#362—22no—
212#360—22no—
213#350—22no—
214C22×C13—41no—
215C22×C13—42no—
216C22×C13—41no—
217C22×C13—81no—
218C22×C13—161no—
219C22×C13#44711yescharacteristic
220C22×C13#44911yescharacteristic
221C22×C13#46911yescharacteristic
222C4×C13—41no—
223C4×C13—82no—
224C4×C13—81no—
225C4×C13—82no—
226C4×C13#39211yescharacteristic
227C4×C13#44711yescharacteristic
228C4×C13#44911yescharacteristic
229C4×C13#46611yescharacteristic
230C2×#41—21no—
231C2×#41D4×C1311yescharacteristic
232C22×Q8—21no—
233#137—22no—
234#137—41no—
235AGL(1,ℤ/8)—22no—
236AGL(1,ℤ/8)—41no—
237#135—21no—
238#135—21no—
239#135—21no—
240#135—21no—
241#135—42no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16D4×C1312yes—
248C2×Q16D4×C1311yescharacteristic
249C2×SD16—21no—
250C2×D8D4×C1311yescharacteristic
251#131—21no—
252#131—21no—
253#131—21no—
254#131—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16D4×C1311yescharacteristic
258C22×C8—21no—
259C22×C8C23×C1311yescharacteristic
260C4⋊Q8—41no—
261#124—41no—
262#123—42no—
263C22⋊Q8—24no—
264#117—21no—
265Q32—24no—
266SD32—24no—
267M32—21no—
268M32—21no—
269M32—21no—
270M32D4×C1312yes—
271C2×C16—21no—
272C2×C16—21no—
273#108—21no—
274#108D4×C1312yes—
275#107—21no—
276#106D4×C1312yes—
277#103—24no—
278#101—22no—
279#100—22no—
280C2×C13—21no—
281C2×C13—21no—
282C2×C13—21no—
283C2×C13—81no—
284C2×C13—161no—
285C2×C13#199911yescharacteristic
286#41—21no—
287#41—21no—
288#41—21no—
289#41—21no—
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8C13×D811yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4C13×D811yescharacteristic
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4C2×D4×C1311yescharacteristic
310Q16—22no—
311Q16—21no—
312Q16—22no—
313Q16—21no—
314Q16—42no—
315Q16—41no—
316Q16—41no—
317SD16—42no—
318SD16—42no—
319SD16—41no—
320SD16—41no—
321D8—21no—
322D8—21no—
323D8—42no—
324M16—21no—
325M16—22no—
326M16—21no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8C2×D4×C1311yescharacteristic
335C2×C8C2×D4×C1311yescharacteristic
336C2×C8C2×D4×C1311yescharacteristic
337C2×C8C2×D4×C1311yescharacteristic
338C2×C8C2×D4×C1311yescharacteristic
339C2×C8C13×#4111yescharacteristic
340C4⋊C4—22no—
341C4⋊C4—44no—
342C22⋊C4—44no—
343C22⋊C4—41no—
344C42—41no—
345C16—22no—
346C16—41no—
347C13#1331111yescharacteristic, direct product factor, Sylow
348C23—21no—
349C23—41no—
350C23C13×AGL(1,ℤ/8)11yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—41no—
354Q8—42no—
355Q8—41no—
356Q8—42no—
357Q8—81no—
358Q8—81no—
359D4—21no—
360D4—21no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—81no—
366D4—81no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4C13×#12011yescharacteristic
378C2×C4C13×#12011yescharacteristic
379C2×C4C13×#12111yescharacteristic
380C2×C4C2×C13×D811yescharacteristic
381C2×C4C13×#13511yescharacteristic
382C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
383C8—41no—
384C8—42no—
385C8C13×#12011yescharacteristic
386C8C13×#12111yescharacteristic
387C8C13×#12111yescharacteristic
388C8C13×#12711yescharacteristic
389C22—41no—
390C22—42no—
391C22—41no—
392C22—81no—
393C22—161no—
394C22C13×#44711yescharacteristic
395C22C13×#44911yescharacteristic
396C22C13×#46911yescharacteristic
397C4—41no—
398C4—82no—
399C4—81no—
400C4—82no—
401C4C13×#39211yescharacteristic
402C4C13×#44711yescharacteristic
403C4C13×#44911yescharacteristic
404C4C13×#46611yescharacteristic
405C2—21no—
406C2—21no—
407C2—21no—
408C2—81no—
409C2—161no—
410C2C13×#199911yescharacteristic
subgroupG/H
center, socleC2×C13#1999
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#510C2semidirect
3. C13×#3059C2semidirect
4. C2×C13×#362C2semidirect
5. C13×#2145C2semidirect
6. C13×#2117C2semidirect
7. C13×#1389C2semidirect
81. #13311C13direct (N × H)
143. C2×#510C2×C13semidirect
145. #3059C2×C13semidirect
146. C2×#362C2×C13semidirect
147. #2145C2×C13semidirect
148. #2117C2×C13semidirect
149. #1389C2×C13semidirect
347. C13#13311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5102
C13×#30672
C13×#30592
C2×C13×#3622
C13×#21452
C13×#21172
C13×#13892
#1331113