Finite Group Databasebeta

← C13×#12137 #15698476

Subgroups — C13×#12137 #15698476

Order 3328.

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

normal subgroups only

This group has 446 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×#2826C211yesmaximal, characteristic, complemented
2C13×#2044C211yesmaximal, characteristic, complemented
3C13×#1613C211yesmaximal, characteristic, complemented
4C13×#1595C211yesmaximal, characteristic
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic, complemented
7C13×#1326C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C13×#481—21no—
10C13×#447—21no—
11C2×C13×#99—21no—
12C13×#400—21no—
13C13×#399C2211yescharacteristic
14C13×#397—21no—
15C13×#396—21no—
16C13×#394—21no—
17C13×#394—21no—
18C13×#392C2211yescharacteristic
19C13×#386—21no—
20C13×#386—21no—
21C13×#385C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C2×C13×D8—41no—
32C13×#123—41no—
33C13×#121—21no—
34C13×#121—21no—
35C13×#120—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
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—41no—
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4C2311yescharacteristic
50C13×#106—41no—
51C13×#102—41no—
52C13×#102—41no—
53C13×#99—42no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—41no—
61C13×#95D411yescharacteristic
62C13×#95D411yescharacteristic
63#12137C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C24×C13—21no—
66C24×C13C2×D411yescharacteristic
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—81no—
79C2×D4×C13—81no—
80C2×D4×C13—81no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—81no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C13×D8—82no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—81no—
99C13×C4⋊C4—81no—
100C13×C4⋊C4—81no—
101C13×C22⋊C4—21no—
102C13×C22⋊C4—21no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—81no—
109C13×C22⋊C4—81no—
110C13×C22⋊C4—81no—
111C13×C22⋊C4—81no—
112C13×C22⋊C4—81no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4—82no—
115#2826C2×C1311yescharacteristic, complemented
116#2044C2×C1311yescharacteristic, complemented
117#1613C2×C1311yescharacteristic, complemented
118#1595C2×C1311yescharacteristic
119#1352C2×C1311yescharacteristic, complemented
120#1343C2×C1311yescharacteristic, complemented
121#1326C2×C1311yescharacteristic, complemented
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—81no—
137C23×C13—81no—
138C23×C13#12011yescharacteristic
139C23×C13#13511yescharacteristic
140C23×C13AGL(1,ℤ/8)11yescharacteristic
141D4×C13—42no—
142D4×C13—81no—
143D4×C13—81no—
144D4×C13—81no—
145D4×C13—81no—
146D4×C13—81no—
147D4×C13—82no—
148D4×C13—82no—
149D4×C13—81no—
150D4×C13—81no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C8×C13—81no—
179C8×C13—81no—
180#534C22×C1311yescharacteristic
181#481—21no—
182#447—21no—
183C2×#99—21no—
184#400—21no—
185#399C22×C1311yescharacteristic
186#397—21no—
187#396—21no—
188#394—21no—
189#394—21no—
190#392C22×C1311yescharacteristic
191#386—21no—
192#386—21no—
193#385C22×C1311yescharacteristic
194#342C22×C1311yescharacteristic
195#327—21no—
196#327—21no—
197#323C22×C1311yescharacteristic
198#323C22×C1311yescharacteristic
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—82no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—161no—
220C22×C13#44911yescharacteristic
221C22×C13#45411yescharacteristic
222C22×C13B(4,𝔽2)11yescharacteristic
223C4×C13—41no—
224C4×C13—41no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13—81no—
228C4×C13—81no—
229C4×C13—81no—
230C4×C13—81no—
231C4×C13—161no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4D4×C1311yescharacteristic
235C23×C4D4×C1311yescharacteristic
236C2×D8—41no—
237#123—41no—
238#121—21no—
239#121—21no—
240#120—41no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C1311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—41no—
253C2×C22⋊C4D4×C1311yescharacteristic
254C2×C22⋊C4C23×C1311yescharacteristic
255#106—41no—
256#102—41no—
257#102—41no—
258#99—42no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—41no—
266#95D4×C1311yescharacteristic
267#95D4×C1311yescharacteristic
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—41no—
271C2×C13—41no—
272C2×C13—161no—
273C2×C13—161no—
274C2×C13#159711yescharacteristic
275C2×C13#220011yescharacteristic
276C2×C13#220011yescharacteristic
277C24—21no—
278C24—21no—
279C24C2×D4×C1311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—81no—
303C22×C4C2×D4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305D8—82no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C4⋊C4—81no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—81no—
322C22⋊C4—81no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—82no—
328C13#1213711yescharacteristic, direct product factor, Sylow
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—81no—
344C23—81no—
345C23C13×#12011yescharacteristic
346C23C13×#13511yescharacteristic
347C23C13×AGL(1,ℤ/8)11yescharacteristic
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—82no—
355D4—82no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C8—81no—
386C8—81no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—82no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—161no—
408C22C13×#44911yescharacteristic
409C22C13×#45411yescharacteristic
410C22C13×B(4,𝔽2)11yescharacteristic
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—161no—
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2—161no—
425C2—161no—
426C2C13×#159711yescharacteristic
427C2C13×#220011yescharacteristic
428C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#1595C2
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
1. C13×#2826C2semidirect
2. C13×#2044C2semidirect
3. C13×#1613C2semidirect
5. C13×#1352C2semidirect
6. C13×#1343C2semidirect
7. C13×#1326C2semidirect
63. #12137C13direct (N × H)
115. #2826C2×C13semidirect
116. #2044C2×C13semidirect
117. #1613C2×C13semidirect
119. #1352C2×C13semidirect
120. #1343C2×C13semidirect
121. #1326C2×C13semidirect
328. C13#12137direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28262
C13×#20442
C13×#16132
C13×#15952
C13×#13522
C13×#13432
C13×#13262
#1213713