Finite Group Databasebeta

← C13×#10402 #15696741

Subgroups — C13×#10402 #15696741

Order 3328.

760 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2656C211yesmaximal, characteristic
2C13×#1874C212yesmaximal, complemented
3C2×C13×#327C212yesmaximal, complemented
4C13×#1444C211yesmaximal, characteristic, complemented
5C13×#1280C211yesmaximal, characteristic, complemented
6C2×C13×#121—21no—
7C2×C13×#121—21no—
8C2×C13×#121C2212yes—
9C22×C13×C4⋊C4—21no—
10C22×C13×C4⋊C4C2211yescharacteristic
11C2×C13×#102—22no—
12C2×C13×C22⋊C8C2212yes—
13C13×#399—22no—
14C13×#392—22no—
15C2×C13×#95—21no—
16C2×C13×#95C2211yescharacteristic
17C2×C13×#95C2211yescharacteristic
18C13×#340—22no—
19C13×#327—24no—
20C22×D4×C13—22no—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13D412yes—
24C23×C4×C13—21no—
25C23×C4×C13—21no—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C22×C8×C13—22no—
30C13×#121—22no—
31C13×#121—22no—
32C13×#121—22no—
33C13×#121—22no—
34C13×#121—42no—
35C13×#121—42no—
36C13×#121—42no—
37C13×#121—42no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—42no—
42C2×C13×C4⋊C4—42no—
43C2×C13×C4⋊C4—42no—
44C2×C13×C4⋊C4—42no—
45C2×C13×C4⋊C4D412yes—
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—22no—
49C13×#102—44no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—22no—
52C13×#95—22no—
53C13×#95—21no—
54C13×#95—42no—
55C13×#95D412yescomplemented
56#10402C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13—22no—
58C24×C13C2×D411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—42no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—81no—
72C2×D4×C13—81no—
73C2×D4×C13—81no—
74C2×D4×C13—81no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—22no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13D812yes—
101C22×C4×C13SD1612yes—
102C22×C4×C13C2×D412yes—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4112yes—
105C22×C4×C13#4111yescharacteristic
106C2×C8×C13—42no—
107C2×C8×C13—42no—
108C2×C8×C13—42no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—42no—
114C13×C4⋊C4—42no—
115C13×C4⋊C4—48no—
116C13×C22⋊C4—44no—
117C13×C22⋊C4—44no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—42no—
120#2656C2×C1311yescharacteristic
121#1874C2×C1312yescomplemented
122C2×#327C2×C1312yescomplemented
123#1444C2×C1311yescharacteristic, complemented
124#1280C2×C1311yescharacteristic, complemented
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—42no—
135C23×C13—42no—
136C23×C13#12011yescharacteristic
137C23×C13#12111yescharacteristic
138C23×C13#12411yescharacteristic
139C23×C13C2×D811yescharacteristic
140C23×C13C2×SD1611yescharacteristic
141C23×C13AGL(1,ℤ/8)11yescharacteristic
142C23×C13AGL(1,ℤ/8)11yescharacteristic
143D4×C13—44no—
144D4×C13—82no—
145D4×C13—84no—
146D4×C13—84no—
147D4×C13—82no—
148D4×C13—82no—
149D4×C13—82no—
150D4×C13—82no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—24no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C2×C4×C13—81no—
183C2×C4×C13#12112yes—
184C2×C4×C13#12312yes—
185C8×C13—82no—
186C2×#121—21no—
187C2×#121—21no—
188C2×#121C22×C1312yes—
189C22×C4⋊C4—21no—
190C22×C4⋊C4C22×C1311yescharacteristic
191C2×#102—22no—
192C2×C22⋊C8C22×C1312yes—
193#399—22no—
194#392—22no—
195C2×#95—21no—
196C2×#95C22×C1311yescharacteristic
197C2×#95C22×C1311yescharacteristic
198#340—22no—
199#327—24no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13—82no—
215C22×C13—82no—
216C22×C13—82no—
217C22×C13—82no—
218C22×C13—82no—
219C22×C13#39411yescharacteristic
220C22×C13#44711yescharacteristic
221C22×C13#45011yescharacteristic
222C22×C13#45311yescharacteristic
223C22×C13#45611yescharacteristic
224C22×C13B(4,𝔽2)11yescharacteristic
225C22×C13#45811yescharacteristic
226C22×C13#45911yescharacteristic
227C22×C13#46011yescharacteristic
228C22×C13#48611yescharacteristic
229C22×C13#49011yescharacteristic
230C4×C13—22no—
231C4×C13—22no—
232C4×C13—44no—
233C4×C13—42no—
234C4×C13—42no—
235C4×C13—82no—
236C4×C13—82no—
237C22×D4—22no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4D4×C1312yes—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4D4×C1311yescharacteristic
244C23×C4D4×C1311yescharacteristic
245C23×C4C23×C1311yescharacteristic
246C22×C8—22no—
247#121—22no—
248#121—22no—
249#121—22no—
250#121—22no—
251#121—42no—
252#121—42no—
253#121—42no—
254#121—42no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4D4×C1312yes—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266#102—44no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269#95—22no—
270#95—21no—
271#95—42no—
272#95D4×C1312yescomplemented
273C2×C13—21no—
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13—162no—
278C2×C13#159511yescharacteristic
279C2×C13#160411yescharacteristic
280C2×C13#161011yescharacteristic
281C2×C13#161311yescharacteristic
282C2×C13#203911yescharacteristic
283C2×C13#204111yescharacteristic
284C2×C13#204411yescharacteristic
285C24—22no—
286C24C2×D4×C1311yescharacteristic
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—81no—
300C2×D4—81no—
301C2×D4—81no—
302C2×D4—81no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4C13×D812yes—
329C22×C4C13×SD1612yes—
330C22×C4C2×D4×C1312yes—
331C22×C4C2×D4×C1311yescharacteristic
332C22×C4C13×#4112yes—
333C22×C4C13×#4111yescharacteristic
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—48no—
344C22⋊C4—44no—
345C22⋊C4—44no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C13#1040211yescharacteristic, direct product factor, Sylow
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23C13×#12011yescharacteristic
361C23C13×#12111yescharacteristic
362C23C13×#12411yescharacteristic
363C23C2×C13×D811yescharacteristic
364C23C2×C13×SD1611yescharacteristic
365C23C13×AGL(1,ℤ/8)11yescharacteristic
366C23C13×AGL(1,ℤ/8)11yescharacteristic
367D4—44no—
368D4—82no—
369D4—84no—
370D4—84no—
371D4—82no—
372D4—82no—
373D4—82no—
374D4—82no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C13×#12112yes—
408C2×C4C13×#12312yes—
409C8—82no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22C13×#39411yescharacteristic
430C22C13×#44711yescharacteristic
431C22C13×#45011yescharacteristic
432C22C13×#45311yescharacteristic
433C22C13×#45611yescharacteristic
434C22C13×B(4,𝔽2)11yescharacteristic
435C22C13×#45811yescharacteristic
436C22C13×#45911yescharacteristic
437C22C13×#46011yescharacteristic
438C22C13×#48611yescharacteristic
439C22C13×#49011yescharacteristic
440C4—22no—
441C4—22no—
442C4—44no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—82no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—162no—
452C2C13×#159511yescharacteristic
453C2C13×#160411yescharacteristic
454C2C13×#161011yescharacteristic
455C2C13×#161311yescharacteristic
456C2C13×#203911yescharacteristic
457C2C13×#204111yescharacteristic
458C2C13×#204411yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2656C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1874C2semidirect
3. C2×C13×#327C2semidirect
4. C13×#1444C2semidirect
5. C13×#1280C2semidirect
55. C13×#95D4semidirect
56. #10402C13direct (N × H)
121. #1874C2×C13semidirect
122. C2×#327C2×C13semidirect
123. #1444C2×C13semidirect
124. #1280C2×C13semidirect
272. #95D4×C13semidirect
348. C13#10402direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26562
C13×#18742
C2×C13×#3272
C13×#14442
C13×#12802
#1040213