Finite Group Databasebeta

← C13×#9969 #15696308

Subgroups — C13×#9969 #15696308

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#484C211yesmaximal, characteristic, complemented
2C2×C13×#481C211yesmaximal, characteristic
3C13×#2639C211yesmaximal, characteristic
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C2×C13×#327C211yesmaximal, characteristic
6C13×#1445C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C13×#484—22no—
12C13×#484—22no—
13C13×#481—22no—
14C13×#481—22no—
15C2×C13×#107—21no—
16C2×C13×#106—21no—
17C2×C13×#103—21no—
18C2×C13×#102—21no—
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C13×#400—21no—
22C13×#397—21no—
23C13×#394—21no—
24C13×#393—21no—
25C13×#386—22no—
26C2×C13×#95—22no—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C13×#328—22no—
30C13×#327—22no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13—21no—
36C23×C4×C13D412yes—
37C23×C4×C13C2311yescharacteristic
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C13×#121—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4D412yes—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C13×#107—24no—
62C13×#106—24no—
63C13×#103—24no—
64C13×#102—24no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8D412yes—
68C13×C22⋊C8D412yes—
69C13×#95—22no—
70C13×#95—22no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—44no—
76#9969C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13—21no—
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—42no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—42no—
88C2×D4×C13—42no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—41no—
102C22×C4×C13—42no—
103C22×C4×C13—42no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—42no—
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C2×C8×C13—22no—
115C2×C8×C13—22no—
116C2×C8×C13—42no—
117C2×C8×C13—42no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—82no—
133C13×C22⋊C4—82no—
134C2×#484C2×C1311yescharacteristic, complemented
135C2×#481C2×C1311yescharacteristic
136#2639C2×C1311yescharacteristic
137C2×#328C2×C1311yescharacteristic, complemented
138C2×#327C2×C1311yescharacteristic
139#1445C2×C1311yescharacteristic, complemented
140#1280C2×C1311yescharacteristic, complemented
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—22no—
144C23×C13—41no—
145C23×C13—42no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—42no—
149C23×C13#12011yescharacteristic
150C23×C13#12111yescharacteristic
151C23×C13#12711yescharacteristic
152C23×C13#13512yes—
153C23×C13#13712yes—
154Q8×C13—42no—
155Q8×C13—81no—
156D4×C13—42no—
157D4×C13—81no—
158D4×C13—82no—
159D4×C13—81no—
160D4×C13—81no—
161C2×C4×C13—22no—
162C2×C4×C13—22no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—44no—
168C2×C4×C13—42no—
169C2×C4×C13—44no—
170C2×C4×C13—44no—
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—42no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13—82no—
183C2×C4×C13—81no—
184C2×C4×C13—82no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13—81no—
188C2×C4×C13—82no—
189C2×C4×C13#12011yescharacteristic
190C2×C4×C13#12011yescharacteristic
191C2×C4×C13#12111yescharacteristic
192C2×C4×C13#12111yescharacteristic
193C8×C13—42no—
194C8×C13—42no—
195C2×C22⋊Q8C22×C1311yescharacteristic
196C2×#121C22×C1311yescharacteristic
197C22×C4⋊C4C22×C1311yescharacteristic
198#484—22no—
199#484—22no—
200#481—22no—
201#481—22no—
202C2×#107—21no—
203C2×#106—21no—
204C2×#103—21no—
205C2×#102—21no—
206C2×C22⋊C8C22×C1311yescharacteristic
207C2×C22⋊C8C22×C1311yescharacteristic
208#400—21no—
209#397—21no—
210#394—21no—
211#393—21no—
212#386—22no—
213C2×#95—22no—
214C2×#95C22×C1311yescharacteristic
215C2×#95C22×C1311yescharacteristic
216#328—22no—
217#327—22no—
218C22×C13—22no—
219C22×C13—22no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—82no—
227C22×C13—82no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13#39211yescharacteristic
232C22×C13#45212yes—
233C22×C13#45311yescharacteristic
234C22×C13#45411yescharacteristic
235C22×C13#45812yes—
236C22×C13#46412yes—
237C22×C13#49511yescharacteristic
238C22×C13#49711yescharacteristic
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—82no—
244C4×C13—82no—
245C4×C13—81no—
246C4×C13—82no—
247C4×C13—81no—
248C4×C13—81no—
249C22×Q8D4×C1311yescharacteristic
250C22×D4—21no—
251C22×D4D4×C1311yescharacteristic
252C23×C4—21no—
253C23×C4—21no—
254C23×C4D4×C1312yes—
255C23×C4C23×C1311yescharacteristic
256C22×C8—21no—
257C22×C8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C1312yes—
273C2×C4⋊C4D4×C1311yescharacteristic
274C2×C4⋊C4D4×C1311yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279#107—24no—
280#106—24no—
281#103—24no—
282#102—24no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8D4×C1312yes—
286C22⋊C8D4×C1312yes—
287#95—22no—
288#95—22no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—44no—
294C2×C13—21no—
295C2×C13—22no—
296C2×C13—21no—
297C2×C13—161no—
298C2×C13#161512yes—
299C2×C13#161812yes—
300C2×C13#200611yescharacteristic
301C2×C13#201511yescharacteristic
302C2×C13#202211yescharacteristic
303C24—21no—
304C24C2×D4×C1311yescharacteristic
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—42no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—42no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—42no—
334C22×C4C2×D4×C1311yescharacteristic
335C22×C4C2×D4×C1311yescharacteristic
336C22×C4C2×D4×C1311yescharacteristic
337C22×C4C2×D4×C1311yescharacteristic
338C22×C4C2×D4×C1311yescharacteristic
339C22×C4C13×#4111yescharacteristic
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—42no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—82no—
359C22⋊C4—82no—
360C13#996911yescharacteristic, direct product factor, Sylow
361C23—21no—
362C23—21no—
363C23—22no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23C13×#12011yescharacteristic
370C23C13×#12111yescharacteristic
371C23C13×#12711yescharacteristic
372C23C13×#13512yes—
373C23C13×#13712yes—
374Q8—42no—
375Q8—81no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—81no—
380D4—81no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—81no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—82no—
409C2×C4C13×#12011yescharacteristic
410C2×C4C13×#12011yescharacteristic
411C2×C4C13×#12111yescharacteristic
412C2×C4C13×#12111yescharacteristic
413C8—42no—
414C8—42no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—82no—
427C22—82no—
428C22C13×#39211yescharacteristic
429C22C13×#45212yes—
430C22C13×#45311yescharacteristic
431C22C13×#45411yescharacteristic
432C22C13×#45812yes—
433C22C13×#46412yes—
434C22C13×#49511yescharacteristic
435C22C13×#49711yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—81no—
442C4—82no—
443C4—81no—
444C4—81no—
445C4—82no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—161no—
450C2C13×#161512yes—
451C2C13×#161812yes—
452C2C13×#200611yescharacteristic
453C2C13×#201511yescharacteristic
454C2C13×#202211yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
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
1. C2×C13×#484C2semidirect
4. C2×C13×#328C2semidirect
6. C13×#1445C2semidirect
7. C13×#1280C2semidirect
76. #9969C13direct (N × H)
134. C2×#484C2×C13semidirect
137. C2×#328C2×C13semidirect
139. #1445C2×C13semidirect
140. #1280C2×C13semidirect
360. C13#9969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4842
C2×C13×#4812
C13×#26392
C2×C13×#3282
C2×C13×#3272
C13×#14452
C13×#12802
#996913