Finite Group Databasebeta

← C13×#13310 #15699649

Subgroups — C13×#13310 #15699649

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 424 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
3C13×#3058C211yesmaximal, characteristic, complemented
4C2×C13×#361C211yesmaximal, characteristic, complemented
5C13×#2145C211yesmaximal, characteristic, complemented
6C13×#2117C211yesmaximal, characteristic, complemented
7C13×#1389C211yesmaximal, characteristic, complemented
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×D8C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C13×#535—21no—
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—21no—
21C13×#471—22no—
22C13×#469—22no—
23C13×#466—22no—
24C2×C13×#108C2211yescharacteristic
25C13×#427C2211yescharacteristic
26C13×#418—21no—
27C13×#413—21no—
28C13×#361—22no—
29C13×#360—22no—
30C13×#350—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)—41no—
38C13×#135—21no—
39C13×#135—21no—
40C13×#135—21no—
41C13×#135—21no—
42C13×#135—42no—
43C2×C13×Q16D411yescharacteristic, complemented
44C2×C13×SD16—21no—
45C2×C13×D8—21no—
46C2×C13×D8—21no—
47C2×C13×D8—21no—
48C2×C13×D8—21no—
49C2×C13×D8—21no—
50C2×C13×D8D412yes—
51C2×C13×D8D411yescharacteristic, complemented
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×#127—41no—
62C13×#124—41no—
63C13×#121—24no—
64C13×#120—42no—
65C13×#117—21no—
66C13×SD32—24no—
67C13×D16—24no—
68C13×M32—21no—
69C13×M32—21no—
70C13×M32—21no—
71C13×M32D412yescomplemented
72C2×C13×C16—21no—
73C2×C13×C16—21no—
74C13×#108—21no—
75C13×#108D412yescomplemented
76C13×#107—21no—
77C13×#106D412yes—
78C13×#102—24no—
79C13×#101—22no—
80C13×#100—22no—
81#13310C1311yesmaximal, 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—21no—
95C2×D4×C13—22no—
96C2×D4×C13—41no—
97C2×D4×C13—44no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13D811yescharacteristic
104C22×C4×C13—21no—
105C22×C4×C13—41no—
106C22×C4×C13C2×D411yescharacteristic
107C13×Q16—21no—
108C13×Q16—21no—
109C13×Q16—42no—
110C13×SD16—42no—
111C13×SD16—42no—
112C13×SD16—41no—
113C13×SD16—41no—
114C13×D8—21no—
115C13×D8—22no—
116C13×D8—22no—
117C13×D8—21no—
118C13×D8—42no—
119C13×D8—41no—
120C13×D8—41no—
121C13×M16—21no—
122C13×M16—22no—
123C13×M16—21no—
124C13×M16—41no—
125C13×M16—41no—
126C13×M16—41no—
127C2×C8×C13—21no—
128C2×C8×C13—41no—
129C2×C8×C13—41no—
130C2×C8×C13—41no—
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13#4111yescharacteristic
137C13×C4⋊C4—22no—
138C13×C22⋊C4—44no—
139C13×C22⋊C4—41no—
140C42×C13—41no—
141C13×C16—22no—
142C13×C16—41no—
143C2×#509C2×C1311yescharacteristic, complemented
144#3067C2×C1311yescharacteristic, complemented
145#3058C2×C1311yescharacteristic, complemented
146C2×#361C2×C1311yescharacteristic, complemented
147#2145C2×C1311yescharacteristic, complemented
148#2117C2×C1311yescharacteristic, complemented
149#1389C2×C1311yescharacteristic, complemented
150C23×C13—21no—
151C23×C13—42no—
152C23×C13—41no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—162no—
156C23×C13AGL(1,ℤ/8)11yescharacteristic
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—41no—
168D4×C13—42no—
169D4×C13—81no—
170D4×C13—81no—
171D4×C13—81no—
172D4×C13—81no—
173D4×C13—164no—
174C2×C4×C13—21no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—42no—
178C2×C4×C13—41no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13#12011yescharacteristic
182C2×C4×C13#12011yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13C2×D811yescharacteristic
185C2×C4×C13#13511yescharacteristic
186C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
187C8×C13—41no—
188C8×C13—42no—
189C8×C13#12011yescharacteristic
190C8×C13#12111yescharacteristic
191C8×C13#12111yescharacteristic
192C8×C13#12711yescharacteristic
193#575—21no—
194C2×#135C22×C1311yescharacteristic
195C22×D8C22×C1311yescharacteristic
196C2×#131C22×C1311yescharacteristic
197#535—21no—
198#509—22no—
199#509—22no—
200C2×SD32—21no—
201C2×D16—21no—
202C2×M32C22×C1311yescharacteristic
203C2×M32C22×C1311yescharacteristic
204#473—21no—
205#472—21no—
206#471—22no—
207#469—22no—
208#466—22no—
209C2×#108C22×C1311yescharacteristic
210#427C22×C1311yescharacteristic
211#418—21no—
212#413—21no—
213#361—22no—
214#360—22no—
215#350—22no—
216C22×C13—41no—
217C22×C13—42no—
218C22×C13—41no—
219C22×C13—84no—
220C22×C13—81no—
221C22×C13—82no—
222C22×C13—161no—
223C22×C13—162no—
224C22×C13—162no—
225C22×C13#44711yescharacteristic
226C22×C13#44911yescharacteristic
227C22×C13#46911yescharacteristic
228C4×C13—41no—
229C4×C13—82no—
230C4×C13—81no—
231C4×C13#39211yescharacteristic
232C4×C13#44711yescharacteristic
233C4×C13#44911yescharacteristic
234C4×C13#46611yescharacteristic
235C2×#41—21no—
236C2×#41D4×C1311yescharacteristic
237C22×D4—21no—
238#137—22no—
239#137—41no—
240AGL(1,ℤ/8)—22no—
241AGL(1,ℤ/8)—41no—
242#135—21no—
243#135—21no—
244#135—21no—
245#135—21no—
246#135—42no—
247C2×Q16D4×C1311yescharacteristic, complemented
248C2×SD16—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—21no—
254C2×D8D4×C1312yes—
255C2×D8D4×C1311yescharacteristic, complemented
256#131—21no—
257#131—21no—
258#131—21no—
259#131—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16D4×C1311yescharacteristic
263C22×C8—21no—
264C22×C8C23×C1311yescharacteristic
265#127—41no—
266#124—41no—
267#121—24no—
268#120—42no—
269#117—21no—
270SD32—24no—
271D16—24no—
272M32—21no—
273M32—21no—
274M32—21no—
275M32D4×C1312yescomplemented
276C2×C16—21no—
277C2×C16—21no—
278#108—21no—
279#108D4×C1312yescomplemented
280#107—21no—
281#106D4×C1312yes—
282#102—24no—
283#101—22no—
284#100—22no—
285C2×C13—21no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—81no—
289C2×C13—162no—
290C2×C13—161no—
291C2×C13#199911yescharacteristic
292C24—41no—
293#41—21no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×Q8C13×D811yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—44no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4C13×D811yescharacteristic
314C22×C4—21no—
315C22×C4—41no—
316C22×C4C2×D4×C1311yescharacteristic
317Q16—21no—
318Q16—21no—
319Q16—42no—
320SD16—42no—
321SD16—42no—
322SD16—41no—
323SD16—41no—
324D8—21no—
325D8—22no—
326D8—22no—
327D8—21no—
328D8—42no—
329D8—41no—
330D8—41no—
331M16—21no—
332M16—22no—
333M16—21no—
334M16—41no—
335M16—41no—
336M16—41no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8C2×D4×C1311yescharacteristic
342C2×C8C2×D4×C1311yescharacteristic
343C2×C8C2×D4×C1311yescharacteristic
344C2×C8C2×D4×C1311yescharacteristic
345C2×C8C2×D4×C1311yescharacteristic
346C2×C8C13×#4111yescharacteristic
347C4⋊C4—22no—
348C22⋊C4—44no—
349C22⋊C4—41no—
350C42—41no—
351C16—22no—
352C16—41no—
353C13#1331011yescharacteristic, direct product factor, Sylow
354C23—21no—
355C23—42no—
356C23—41no—
357C23—81no—
358C23—81no—
359C23—162no—
360C23C13×AGL(1,ℤ/8)11yescharacteristic
361Q8—21no—
362Q8—21no—
363Q8—41no—
364Q8—41no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—164no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C13×#12011yescharacteristic
386C2×C4C13×#12011yescharacteristic
387C2×C4C13×#12111yescharacteristic
388C2×C4C2×C13×D811yescharacteristic
389C2×C4C13×#13511yescharacteristic
390C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
391C8—41no—
392C8—42no—
393C8C13×#12011yescharacteristic
394C8C13×#12111yescharacteristic
395C8C13×#12111yescharacteristic
396C8C13×#12711yescharacteristic
397C22—41no—
398C22—42no—
399C22—41no—
400C22—84no—
401C22—81no—
402C22—82no—
403C22—161no—
404C22—162no—
405C22—162no—
406C22C13×#44711yescharacteristic
407C22C13×#44911yescharacteristic
408C22C13×#46911yescharacteristic
409C4—41no—
410C4—82no—
411C4—81no—
412C4C13×#39211yescharacteristic
413C4C13×#44711yescharacteristic
414C4C13×#44911yescharacteristic
415C4C13×#46611yescharacteristic
416C2—21no—
417C2—21no—
418C2—21no—
419C2—81no—
420C2—162no—
421C2—161no—
422C2C13×#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. C13×#3058C2semidirect
4. C2×C13×#361C2semidirect
5. C13×#2145C2semidirect
6. C13×#2117C2semidirect
7. C13×#1389C2semidirect
43. C2×C13×Q16D4semidirect
51. C2×C13×D8D4semidirect
71. C13×M32D4semidirect
75. C13×#108D4semidirect
81. #13310C13direct (N × H)
143. C2×#509C2×C13semidirect
144. #3067C2×C13semidirect
145. #3058C2×C13semidirect
146. C2×#361C2×C13semidirect
147. #2145C2×C13semidirect
148. #2117C2×C13semidirect
149. #1389C2×C13semidirect
247. C2×Q16D4×C13semidirect
255. C2×D8D4×C13semidirect
275. M32D4×C13semidirect
279. #108D4×C13semidirect
353. C13#13310direct (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
C13×#30582
C2×C13×#3612
C13×#21452
C13×#21172
C13×#13892
#1331013