Finite Group Databasebeta

← C13×#12262 #15698601

Subgroups — C13×#12262 #15698601

Order 3328.

596 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2668C211yesmaximal, characteristic
2C13×#2029C211yesmaximal, characteristic, complemented
3C13×#1614C211yesmaximal, characteristic, complemented
4C13×#1596C211yesmaximal, characteristic, complemented
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic, complemented
7C13×#1316C211yesmaximal, characteristic, complemented
8C13×#543C2211yescharacteristic
9C2×C13×#121—21no—
10C2×C13×#120—21no—
11C13×#484—21no—
12C13×#450—21no—
13C13×#399C2211yescharacteristic
14C13×#397—21no—
15C13×#394—21no—
16C13×#392C2211yescharacteristic
17C13×#386—21no—
18C13×#386—21no—
19C13×#379—21no—
20C13×#379C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C25×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13D411yescharacteristic
32C23×C4×C13—21no—
33C2×C13×SD16—41no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—41no—
37C13×C22⋊Q8—41no—
38C13×#121—44no—
39C13×#120—44no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—41no—
52C2×C13×C22⋊C4—41no—
53C2×C13×C22⋊C4D411yescharacteristic
54C2×C13×C22⋊C4C2311yescharacteristic
55C13×#107—41no—
56C13×#103—41no—
57C13×#102—41no—
58C13×C22⋊C8—21no—
59C13×C22⋊C8—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64#12262C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13—21no—
67C24×C13—21no—
68C24×C13—21no—
69C24×C13—41no—
70C24×C13—42no—
71C24×C13—41no—
72C24×C13—81no—
73C24×C13C2×D411yescharacteristic
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×D4×C13—24no—
77C2×D4×C13—41no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C2×D4×C13—42no—
81C2×D4×C13—42no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—81no—
85C2×D4×C13—81no—
86C2×D4×C13—81no—
87C2×D4×C13—81no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—42no—
95C22×C4×C13—41no—
96C22×C4×C13—81no—
97C22×C4×C13—81no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C13×SD16—82no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—81no—
121C13×C22⋊C4—81no—
122C13×C22⋊C4—82no—
123C13×C22⋊C4—82no—
124#2668C2×C1311yescharacteristic
125#2029C2×C1311yescharacteristic, complemented
126#1614C2×C1311yescharacteristic, complemented
127#1596C2×C1311yescharacteristic, complemented
128#1352C2×C1311yescharacteristic, complemented
129#1343C2×C1311yescharacteristic, complemented
130#1316C2×C1311yescharacteristic, complemented
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—22no—
134C23×C13—22no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—42no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—81no—
153C23×C13—82no—
154C23×C13—81no—
155C23×C13—84no—
156C23×C13—82no—
157C23×C13—81no—
158C23×C13#12011yescharacteristic
159C23×C13#13511yescharacteristic
160C23×C13#13711yescharacteristic
161Q8×C13—81no—
162Q8×C13—81no—
163D4×C13—42no—
164D4×C13—84no—
165D4×C13—81no—
166D4×C13—82no—
167D4×C13—82no—
168D4×C13—84no—
169C2×C4×C13—22no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—84no—
188C2×C4×C13—81no—
189C2×C4×C13—81no—
190C2×C4×C13—81no—
191C2×C4×C13—81no—
192C2×C4×C13—81no—
193C8×C13—81no—
194C8×C13—81no—
195#543C22×C1311yescharacteristic
196C2×#121—21no—
197C2×#120—21no—
198#484—21no—
199#450—21no—
200#399C22×C1311yescharacteristic
201#397—21no—
202#394—21no—
203#392C22×C1311yescharacteristic
204#386—21no—
205#386—21no—
206#379—21no—
207#379C22×C1311yescharacteristic
208#342—21no—
209#342C22×C1311yescharacteristic
210#328—21no—
211#328—21no—
212#323C22×C1311yescharacteristic
213#323C22×C1311yescharacteristic
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—42no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—42no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—44no—
227C22×C13—42no—
228C22×C13—42no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13—82no—
235C22×C13—82no—
236C22×C13—82no—
237C22×C13—81no—
238C22×C13—81no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13#45211yescharacteristic
242C22×C13#45511yescharacteristic
243C22×C13B(4,𝔽2)11yescharacteristic
244C4×C13—42no—
245C4×C13—41no—
246C4×C13—41no—
247C4×C13—81no—
248C4×C13—81no—
249C4×C13—81no—
250C4×C13—81no—
251C4×C13—81no—
252C4×C13—161no—
253C25D4×C1311yescharacteristic
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4D4×C1311yescharacteristic
258C23×C4—21no—
259C2×SD16—41no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—41no—
263C22⋊Q8—41no—
264#121—44no—
265#120—44no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4D4×C1311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4D4×C1311yescharacteristic
280C2×C22⋊C4C23×C1311yescharacteristic
281#107—41no—
282#103—41no—
283#102—41no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286#95—21no—
287#95—21no—
288#95D4×C1311yescharacteristic
289#95D4×C1311yescharacteristic
290C2×C13—21no—
291C2×C13—21no—
292C2×C13—41no—
293C2×C13—41no—
294C2×C13—82no—
295C2×C13—82no—
296C2×C13#160611yescharacteristic
297C2×C13#219611yescharacteristic
298C2×C13#220011yescharacteristic
299C24—21no—
300C24—21no—
301C24—21no—
302C24—21no—
303C24—41no—
304C24—42no—
305C24—41no—
306C24—81no—
307C24C2×D4×C1311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×D4—24no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—81no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—81no—
331C22×C4—81no—
332C22×C4C2×D4×C1311yescharacteristic
333C22×C4C2×D4×C1311yescharacteristic
334SD16—82no—
335C2×C8—41no—
336C2×C8—41no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—81no—
355C22⋊C4—81no—
356C22⋊C4—82no—
357C22⋊C4—82no—
358C13#1226211yescharacteristic, direct product factor, Sylow
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—82no—
382C23—81no—
383C23—82no—
384C23—84no—
385C23—81no—
386C23C13×#12011yescharacteristic
387C23C13×#13511yescharacteristic
388C23C13×#13711yescharacteristic
389Q8—81no—
390Q8—81no—
391D4—42no—
392D4—84no—
393D4—81no—
394D4—82no—
395D4—82no—
396D4—84no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—84no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C8—81no—
422C8—81no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—41no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—44no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C13×#45211yescharacteristic
451C22C13×#45511yescharacteristic
452C22C13×B(4,𝔽2)11yescharacteristic
453C4—42no—
454C4—41no—
455C4—41no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—161no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—82no—
467C2—82no—
468C2C13×#160611yescharacteristic
469C2C13×#219611yescharacteristic
470C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2668C2
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2029C2semidirect
3. C13×#1614C2semidirect
4. C13×#1596C2semidirect
5. C13×#1352C2semidirect
6. C13×#1343C2semidirect
7. C13×#1316C2semidirect
64. #12262C13direct (N × H)
125. #2029C2×C13semidirect
126. #1614C2×C13semidirect
127. #1596C2×C13semidirect
128. #1352C2×C13semidirect
129. #1343C2×C13semidirect
130. #1316C2×C13semidirect
358. C13#12262direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26682
C13×#20292
C13×#16142
C13×#15962
C13×#13522
C13×#13432
C13×#13162
#1226213