Finite Group Databasebeta

← C13×#13317 #15699656

Subgroups — C13×#13317 #15699656

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×#510C211yesmaximal, characteristic, complemented
2C13×#3054C211yesmaximal, characteristic
3C2×C13×#470C211yesmaximal, characteristic, complemented
4C2×C13×#360C211yesmaximal, characteristic, complemented
5C13×#2141C211yesmaximal, characteristic, complemented
6C2×C13×#349C211yesmaximal, characteristic, complemented
7C13×#1386C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×Q16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C13×#525—21no—
12C2×C13×C22⋊Q8—21no—
13C13×#510—22no—
14C13×#510—22no—
15C2×C13×Q32—21no—
16C2×C13×SD32—21no—
17C2×C13×M32C2211yescharacteristic
18C2×C13×M32C2211yescharacteristic
19C13×#470—21no—
20C13×#470—22no—
21C13×#470—22no—
22C13×#469—21no—
23C13×#468—22no—
24C13×#427C2211yescharacteristic
25C2×C13×#106C2211yescharacteristic
26C13×#416—21no—
27C2×C13×#103—21no—
28C13×#360—22no—
29C13×#358—22no—
30C13×#349—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C23×C4×C13D411yescharacteristic
34C13×#135—21no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135—21no—
38C2×C13×Q16—21no—
39C2×C13×Q16—21no—
40C2×C13×Q16—21no—
41C2×C13×Q16—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16D411yescharacteristic
44C2×C13×Q16D412yescomplemented
45C2×C13×SD16—21no—
46C2×C13×D8D411yescharacteristic
47C2×C13×M16—21no—
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C22×C8×C13D411yescharacteristic
54C22×C8×C13C2311yescharacteristic
55C13×#123—41no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—42no—
59C13×#121—22no—
60C13×#120—41no—
61C4×D4×C13—42no—
62C13×#117—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—41no—
65C2×C13×C22⋊C4—41no—
66C13×Q32—24no—
67C13×SD32—24no—
68C13×M32—21no—
69C13×M32—21no—
70C13×M32—21no—
71C13×M32D412yescomplemented
72C2×C13×C16—21no—
73C2×C13×C16—21no—
74C13×#107D412yes—
75C13×#106—21no—
76C13×#106—21no—
77C13×#106D412yescomplemented
78C13×#103—24no—
79C13×#103—22no—
80C13×#102—22no—
81#13317C1311yesmaximal, characteristic, direct product factor, Sylow
82C24×C13D811yescharacteristic
83C13×#41—41no—
84C13×#41—41no—
85C13×#41—41no—
86C13×#41—41no—
87C2×Q8×C13—21no—
88C2×Q8×C13—22no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×D4×C13—21no—
95C2×D4×C13—42no—
96C2×D4×C13—41no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13D811yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C13×Q16—22no—
109C13×Q16—21no—
110C13×Q16—22no—
111C13×Q16—21no—
112C13×Q16—41no—
113C13×Q16—41no—
114C13×SD16—41no—
115C13×SD16—41no—
116C13×D8—21no—
117C13×D8—21no—
118C13×M16—41no—
119C13×M16—41no—
120C13×M16—41no—
121C13×M16—41no—
122C2×C8×C13—21no—
123C2×C8×C13—21no—
124C2×C8×C13—21no—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13#4111yescharacteristic
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—44no—
134C13×C4⋊C4—42no—
135C13×C4⋊C4—41no—
136C13×C22⋊C4—42no—
137C13×C22⋊C4—44no—
138C13×C22⋊C4—42no—
139C13×C22⋊C4—41no—
140C42×C13—41no—
141C13×C16—22no—
142C13×C16—41no—
143C2×#510C2×C1311yescharacteristic, complemented
144#3054C2×C1311yescharacteristic
145C2×#470C2×C1311yescharacteristic, complemented
146C2×#360C2×C1311yescharacteristic, complemented
147#2141C2×C1311yescharacteristic, complemented
148C2×#349C2×C1311yescharacteristic, complemented
149#1386C2×C1311yescharacteristic, complemented
150C23×C13—21no—
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—42no—
154C23×C13—41no—
155C23×C13C2×D811yescharacteristic
156Q8×C13—41no—
157Q8×C13—42no—
158Q8×C13—42no—
159Q8×C13—41no—
160Q8×C13—81no—
161Q8×C13—81no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—84no—
165D4×C13—81no—
166D4×C13—81no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—82no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C2×C4×C13—81no—
183C2×C4×C13#12011yescharacteristic
184C2×C4×C13#12011yescharacteristic
185C2×C4×C13#12111yescharacteristic
186C2×C4×C13#13511yescharacteristic
187C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
189C8×C13—41no—
190C8×C13#12011yescharacteristic
191C8×C13#12111yescharacteristic
192C8×C13#12111yescharacteristic
193C8×C13#12711yescharacteristic
194C2×#135C22×C1311yescharacteristic
195C22×Q16C22×C1311yescharacteristic
196C22×M16C22×C1311yescharacteristic
197#525—21no—
198C2×C22⋊Q8—21no—
199#510—22no—
200#510—22no—
201C2×Q32—21no—
202C2×SD32—21no—
203C2×M32C22×C1311yescharacteristic
204C2×M32C22×C1311yescharacteristic
205#470—21no—
206#470—22no—
207#470—22no—
208#469—21no—
209#468—22no—
210#427C22×C1311yescharacteristic
211C2×#106C22×C1311yescharacteristic
212#416—21no—
213C2×#103—21no—
214#360—22no—
215#358—22no—
216#349—22no—
217C22×C13—22no—
218C22×C13—42no—
219C22×C13—42no—
220C22×C13—41no—
221C22×C13—81no—
222C22×C13—82no—
223C22×C13—81no—
224C22×C13#44711yescharacteristic
225C22×C13#44711yescharacteristic
226C22×C13#46611yescharacteristic
227C4×C13—41no—
228C4×C13—82no—
229C4×C13—82no—
230C4×C13—81no—
231C4×C13—82no—
232C4×C13#39211yescharacteristic
233C4×C13#44911yescharacteristic
234C4×C13#44911yescharacteristic
235C4×C13#46911yescharacteristic
236C2×#41—21no—
237C22×Q8—21no—
238C23×C4D4×C1311yescharacteristic
239#135—21no—
240#135—21no—
241#135—21no—
242#135—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16D4×C1311yescharacteristic
249C2×Q16D4×C1312yescomplemented
250C2×SD16—21no—
251C2×D8D4×C1311yescharacteristic
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C22×C8D4×C1311yescharacteristic
259C22×C8C23×C1311yescharacteristic
260#123—41no—
261C22⋊Q8—24no—
262C22⋊Q8—22no—
263C22⋊Q8—42no—
264#121—22no—
265#120—41no—
266C4×D4—42no—
267#117—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—41no—
270C2×C22⋊C4—41no—
271Q32—24no—
272SD32—24no—
273M32—21no—
274M32—21no—
275M32—21no—
276M32D4×C1312yescomplemented
277C2×C16—21no—
278C2×C16—21no—
279#107D4×C1312yes—
280#106—21no—
281#106—21no—
282#106D4×C1312yescomplemented
283#103—24no—
284#103—22no—
285#102—22no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—81no—
289C2×C13—161no—
290C2×C13#199911yescharacteristic
291C2×C13#219112yes—
292C24C13×D811yescharacteristic
293#41—41no—
294#41—41no—
295#41—41no—
296#41—41no—
297C2×Q8—21no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4C13×D811yescharacteristic
317C22×C4C2×D4×C1311yescharacteristic
318Q16—22no—
319Q16—21no—
320Q16—22no—
321Q16—21no—
322Q16—41no—
323Q16—41no—
324SD16—41no—
325SD16—41no—
326D8—21no—
327D8—21no—
328M16—41no—
329M16—41no—
330M16—41no—
331M16—41no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8C2×D4×C1311yescharacteristic
336C2×C8C2×D4×C1311yescharacteristic
337C2×C8C2×D4×C1311yescharacteristic
338C2×C8C2×D4×C1311yescharacteristic
339C2×C8C2×D4×C1311yescharacteristic
340C2×C8C13×#4111yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—44no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C22⋊C4—42no—
347C22⋊C4—44no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C42—41no—
351C16—22no—
352C16—41no—
353C13#1331711yescharacteristic, direct product factor, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—42no—
358C23—41no—
359C23C2×C13×D811yescharacteristic
360Q8—41no—
361Q8—42no—
362Q8—42no—
363Q8—41no—
364Q8—81no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—84no—
369D4—81no—
370D4—81no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4C13×#12011yescharacteristic
388C2×C4C13×#12011yescharacteristic
389C2×C4C13×#12111yescharacteristic
390C2×C4C13×#13511yescharacteristic
391C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
392C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
393C8—41no—
394C8C13×#12011yescharacteristic
395C8C13×#12111yescharacteristic
396C8C13×#12111yescharacteristic
397C8C13×#12711yescharacteristic
398C22—22no—
399C22—42no—
400C22—41no—
401C22—42no—
402C22—81no—
403C22—81no—
404C22—82no—
405C22C13×#44711yescharacteristic
406C22C13×#44711yescharacteristic
407C22C13×#46611yescharacteristic
408C4—41no—
409C4—82no—
410C4—81no—
411C4—82no—
412C4—82no—
413C4C13×#39211yescharacteristic
414C4C13×#44911yescharacteristic
415C4C13×#44911yescharacteristic
416C4C13×#46911yescharacteristic
417C2—21no—
418C2—21no—
419C2—81no—
420C2—161no—
421C2C13×#199911yescharacteristic
422C2C13×#219112yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3054C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#510C2semidirect
3. C2×C13×#470C2semidirect
4. C2×C13×#360C2semidirect
5. C13×#2141C2semidirect
6. C2×C13×#349C2semidirect
7. C13×#1386C2semidirect
44. C2×C13×Q16D4semidirect
71. C13×M32D4semidirect
77. C13×#106D4semidirect
81. #13317C13direct (N × H)
143. C2×#510C2×C13semidirect
145. C2×#470C2×C13semidirect
146. C2×#360C2×C13semidirect
147. #2141C2×C13semidirect
148. C2×#349C2×C13semidirect
149. #1386C2×C13semidirect
249. C2×Q16D4×C13semidirect
276. M32D4×C13semidirect
282. #106D4×C13semidirect
353. C13#13317direct (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×#30542
C2×C13×#4702
C2×C13×#3602
C13×#21412
C2×C13×#3492
C13×#13862
#1331713