Finite Group Databasebeta

← C13×#13323 #15699662

Subgroups — C13×#13323 #15699662

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic, complemented
2C13×#3067C211yesmaximal, characteristic, complemented
3C2×C13×#472C211yesmaximal, characteristic, complemented
4C2×C13×#361C211yesmaximal, characteristic, complemented
5C13×#2143C211yesmaximal, characteristic, complemented
6C13×#2115C211yesmaximal, characteristic, complemented
7C13×#1388C211yesmaximal, characteristic, complemented
8C13×#575—21no—
9C2×C13×AGL(1,ℤ/8)—21no—
10C2×C13×#135C2211yescharacteristic
11C22×C13×D8C2211yescharacteristic
12C2×C13×#131C2211yescharacteristic
13C13×#509—22no—
14C13×#509—22no—
15C2×C13×SD32—21no—
16C2×C13×D16—21no—
17C2×C13×M32C2211yescharacteristic
18C2×C13×M32C2211yescharacteristic
19C13×#473—21no—
20C13×#472—22no—
21C13×#472—21no—
22C13×#472—22no—
23C13×#471—22no—
24C2×C13×#108C2211yescharacteristic
25C2×C13×#108C2211yescharacteristic
26C13×#413—21no—
27C2×C13×#100—21no—
28C13×#361—22no—
29C13×#359—22no—
30C13×#349—22no—
31C2×C13×#41—21no—
32C2×C13×#41D411yescharacteristic
33C22×D4×C13—21no—
34C13×#137—22no—
35C13×#137—41no—
36C13×AGL(1,ℤ/8)—22no—
37C13×AGL(1,ℤ/8)—24no—
38C13×AGL(1,ℤ/8)—42no—
39C13×AGL(1,ℤ/8)—41no—
40C13×#135—21no—
41C13×#135—21no—
42C13×#135—21no—
43C13×#135—21no—
44C13×#135—42no—
45C2×C13×Q16D411yescharacteristic
46C2×C13×SD16—21no—
47C2×C13×SD16—41no—
48C2×C13×D8—21no—
49C2×C13×D8—21no—
50C2×C13×D8—21no—
51C2×C13×D8—21no—
52C2×C13×D8—21no—
53C2×C13×D8—41no—
54C2×C13×D8D411yescharacteristic
55C2×C13×D8D412yes—
56C13×#131—21no—
57C13×#131—21no—
58C13×#131—21no—
59C13×#131—21no—
60C2×C13×M16—21no—
61C2×C13×M16—21no—
62C2×C13×M16—21no—
63C2×C13×M16D411yescharacteristic
64C22×C8×C13—21no—
65C22×C8×C13C2311yescharacteristic
66C13×SD32—24no—
67C13×D16—24no—
68C13×M32—21no—
69C13×M32—21no—
70C13×M32—21no—
71C13×M32D412yes—
72C2×C13×C16—21no—
73C2×C13×C16—21no—
74C13×#108—21no—
75C13×#108—21no—
76C13×#108D412yes—
77C13×#108D412yes—
78C13×#101—22no—
79C13×#100—24no—
80C13×#100—22no—
81#13323C1311yesmaximal, characteristic, direct product factor, Sylow
82C24×C13—41no—
83C13×#41—21no—
84C13×#41—21no—
85C13×#41—21no—
86C13×#41—21no—
87C13×#41—41no—
88C13×#41—41no—
89C13×#41—41no—
90C13×#41—41no—
91C2×Q8×C13—21no—
92C2×Q8×C13D811yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—22no—
95C2×D4×C13—21no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13D811yescharacteristic
103C22×C4×C13—21no—
104C22×C4×C13—41no—
105C22×C4×C13C2×D411yescharacteristic
106C13×Q16—21no—
107C13×Q16—21no—
108C13×Q16—42no—
109C13×SD16—42no—
110C13×SD16—44no—
111C13×SD16—42no—
112C13×SD16—41no—
113C13×SD16—41no—
114C13×D8—21no—
115C13×D8—22no—
116C13×D8—22no—
117C13×D8—21no—
118C13×D8—44no—
119C13×D8—42no—
120C13×D8—41no—
121C13×D8—41no—
122C13×M16—21no—
123C13×M16—21no—
124C13×M16—22no—
125C13×M16—22no—
126C13×M16—41no—
127C13×M16—41no—
128C13×M16—41no—
129C13×M16—41no—
130C2×C8×C13—21no—
131C2×C8×C13—41no—
132C2×C8×C13—41no—
133C2×C8×C13—41no—
134C2×C8×C13—41no—
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2×D411yescharacteristic
140C2×C8×C13#4111yescharacteristic
141C13×C16—22no—
142C13×C16—41no—
143C2×#509C2×C1311yescharacteristic, complemented
144#3067C2×C1311yescharacteristic, complemented
145C2×#472C2×C1311yescharacteristic, complemented
146C2×#361C2×C1311yescharacteristic, complemented
147#2143C2×C1311yescharacteristic, complemented
148#2115C2×C1311yescharacteristic, complemented
149#1388C2×C1311yescharacteristic, complemented
150C23×C13—21no—
151C23×C13—41no—
152C23×C13—42no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—162no—
156C23×C13#13511yescharacteristic
157Q8×C13—21no—
158Q8×C13—21no—
159Q8×C13—41no—
160Q8×C13—41no—
161D4×C13—21no—
162D4×C13—21no—
163D4×C13—41no—
164D4×C13—41no—
165D4×C13—42no—
166D4×C13—41no—
167D4×C13—42no—
168D4×C13—41no—
169D4×C13—81no—
170D4×C13—81no—
171D4×C13—81no—
172D4×C13—81no—
173C2×C4×C13—21no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
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×C13AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185C8×C13—41no—
186C8×C13—42no—
187C8×C13—42no—
188C8×C13#12011yescharacteristic
189C8×C13#12111yescharacteristic
190C8×C13#12111yescharacteristic
191C8×C13#12711yescharacteristic
192#575—21no—
193C2×AGL(1,ℤ/8)—21no—
194C2×#135C22×C1311yescharacteristic
195C22×D8C22×C1311yescharacteristic
196C2×#131C22×C1311yescharacteristic
197#509—22no—
198#509—22no—
199C2×SD32—21no—
200C2×D16—21no—
201C2×M32C22×C1311yescharacteristic
202C2×M32C22×C1311yescharacteristic
203#473—21no—
204#472—22no—
205#472—21no—
206#472—22no—
207#471—22no—
208C2×#108C22×C1311yescharacteristic
209C2×#108C22×C1311yescharacteristic
210#413—21no—
211C2×#100—21no—
212#361—22no—
213#359—22no—
214#349—22no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—82no—
220C22×C13—161no—
221C22×C13—162no—
222C22×C13—162no—
223C22×C13—162no—
224C22×C13#44911yescharacteristic
225C22×C13#44911yescharacteristic
226C22×C13#46611yescharacteristic
227C4×C13—41no—
228C4×C13—81no—
229C4×C13#39211yescharacteristic
230C4×C13#44711yescharacteristic
231C4×C13#44711yescharacteristic
232C4×C13#46911yescharacteristic
233C2×#41—21no—
234C2×#41D4×C1311yescharacteristic
235C22×D4—21no—
236#137—22no—
237#137—41no—
238AGL(1,ℤ/8)—24no—
239AGL(1,ℤ/8)—22no—
240AGL(1,ℤ/8)—42no—
241AGL(1,ℤ/8)—41no—
242#135—21no—
243#135—21no—
244#135—21no—
245#135—21no—
246#135—42no—
247C2×Q16D4×C1311yescharacteristic
248C2×SD16—21no—
249C2×SD16—41no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—41no—
256C2×D8D4×C1312yes—
257C2×D8D4×C1311yescharacteristic
258#131—21no—
259#131—21no—
260#131—21no—
261#131—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16D4×C1311yescharacteristic
266C22×C8—21no—
267C22×C8C23×C1311yescharacteristic
268SD32—24no—
269D16—24no—
270M32—21no—
271M32—21no—
272M32—21no—
273M32D4×C1312yes—
274C2×C16—21no—
275C2×C16—21no—
276#108—21no—
277#108—21no—
278#108D4×C1312yes—
279#108D4×C1312yes—
280#101—22no—
281#100—24no—
282#100—22no—
283C2×C13—21no—
284C2×C13—21no—
285C2×C13—21no—
286C2×C13—81no—
287C2×C13—161no—
288C2×C13—162no—
289C2×C13#199911yescharacteristic
290C24—41no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299C2×Q8—21no—
300C2×Q8C13×D811yescharacteristic
301C2×D4—21no—
302C2×D4—22no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4C13×D811yescharacteristic
311C22×C4—21no—
312C22×C4—41no—
313C22×C4C2×D4×C1311yescharacteristic
314Q16—21no—
315Q16—21no—
316Q16—42no—
317SD16—42no—
318SD16—44no—
319SD16—42no—
320SD16—41no—
321SD16—41no—
322D8—21no—
323D8—22no—
324D8—22no—
325D8—21no—
326D8—44no—
327D8—42no—
328D8—41no—
329D8—41no—
330M16—21no—
331M16—21no—
332M16—22no—
333M16—22no—
334M16—41no—
335M16—41no—
336M16—41no—
337M16—41no—
338C2×C8—21no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8C2×D4×C1311yescharacteristic
344C2×C8C2×D4×C1311yescharacteristic
345C2×C8C2×D4×C1311yescharacteristic
346C2×C8C2×D4×C1311yescharacteristic
347C2×C8C2×D4×C1311yescharacteristic
348C2×C8C13×#4111yescharacteristic
349C16—22no—
350C16—41no—
351C13#1332311yescharacteristic, direct product factor, Sylow
352C23—21no—
353C23—41no—
354C23—42no—
355C23—81no—
356C23—81no—
357C23—162no—
358C23C13×#13511yescharacteristic
359Q8—21no—
360Q8—21no—
361Q8—41no—
362Q8—41no—
363D4—21no—
364D4—21no—
365D4—41no—
366D4—41no—
367D4—42no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4C13×#12011yescharacteristic
382C2×C4C13×#12011yescharacteristic
383C2×C4C13×#12111yescharacteristic
384C2×C4C2×C13×D811yescharacteristic
385C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
386C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
387C8—41no—
388C8—42no—
389C8—42no—
390C8C13×#12011yescharacteristic
391C8C13×#12111yescharacteristic
392C8C13×#12111yescharacteristic
393C8C13×#12711yescharacteristic
394C22—41no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—82no—
399C22—161no—
400C22—162no—
401C22—162no—
402C22—162no—
403C22C13×#44911yescharacteristic
404C22C13×#44911yescharacteristic
405C22C13×#46611yescharacteristic
406C4—41no—
407C4—81no—
408C4C13×#39211yescharacteristic
409C4C13×#44711yescharacteristic
410C4C13×#44711yescharacteristic
411C4C13×#46911yescharacteristic
412C2—21no—
413C2—21no—
414C2—21no—
415C2—81no—
416C2—162no—
417C2—161no—
418C2C13×#199911yescharacteristic
subgroupG/H
center, socleC2×C13#1999
commutator, Frattini, cosocleC22×C8C23×C13
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×#509C2semidirect
2. C13×#3067C2semidirect
3. C2×C13×#472C2semidirect
4. C2×C13×#361C2semidirect
5. C13×#2143C2semidirect
6. C13×#2115C2semidirect
7. C13×#1388C2semidirect
81. #13323C13direct (N × H)
143. C2×#509C2×C13semidirect
144. #3067C2×C13semidirect
145. C2×#472C2×C13semidirect
146. C2×#361C2×C13semidirect
147. #2143C2×C13semidirect
148. #2115C2×C13semidirect
149. #1388C2×C13semidirect
351. C13#13323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5092
C13×#30672
C2×C13×#4722
C2×C13×#3612
C13×#21432
C13×#21152
C13×#13882
#1332313