Finite Group Databasebeta

← C13×#12243 #15698582

Subgroups — C13×#12243 #15698582

Order 3328.

464 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2693C211yesmaximal, characteristic
2C13×#2062C211yesmaximal, characteristic, complemented
3C13×#1608C211yesmaximal, characteristic, complemented
4C13×#1596C211yesmaximal, characteristic
5C13×#1344C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic
7C13×#1326C211yesmaximal, characteristic, complemented
8C13×#543C2211yescharacteristic
9C2×C13×#123—21no—
10C13×#483—21no—
11C13×#450—21no—
12C13×#400—21no—
13C13×#397C2211yescharacteristic
14C13×#396—21no—
15C13×#392C2211yescharacteristic
16C13×#386—21no—
17C13×#386—21no—
18C13×#385—21no—
19C13×#385C2211yescharacteristic
20C13×#380—21no—
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C2×C13×SD16—41no—
32C13×#123—42no—
33C13×#123—42no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—41no—
37C13×C22⋊Q8—41no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—41no—
42C2×C13×C4⋊C4D411yescharacteristic
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⋊C4D411yescharacteristic
51C2×C13×C22⋊C4C2311yescharacteristic
52C13×#106—41no—
53C13×#103—41no—
54C13×#102—41no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—41no—
62C13×#95D411yescharacteristic
63C13×#95D411yescharacteristic
64#12243C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13C2×D411yescharacteristic
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C2×D4×C13—41no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—81no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—42no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—42no—
86C22×C4×C13—81no—
87C22×C4×C13—81no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C13×SD16—82no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—81no—
101C13×C4⋊C4—82no—
102C13×C22⋊C4—21no—
103C13×C22⋊C4—22no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—81no—
112C13×C22⋊C4—81no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4SD1612yescomplemented
115#2693C2×C1311yescharacteristic
116#2062C2×C1311yescharacteristic, complemented
117#1608C2×C1311yescharacteristic, complemented
118#1596C2×C1311yescharacteristic
119#1344C2×C1311yescharacteristic, complemented
120#1343C2×C1311yescharacteristic
121#1326C2×C1311yescharacteristic, complemented
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—22no—
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#12011yescharacteristic
134C23×C13C2×SD1611yescharacteristic
135C23×C13AGL(1,ℤ/8)11yescharacteristic
136Q8×C13—81no—
137Q8×C13—81no—
138D4×C13—42no—
139D4×C13—81no—
140D4×C13—82no—
141D4×C13—82no—
142C2×C4×C13—22no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
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—84no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C8×C13—81no—
172C8×C13—81no—
173#543C22×C1311yescharacteristic
174C2×#123—21no—
175#483—21no—
176#450—21no—
177#400—21no—
178#397C22×C1311yescharacteristic
179#396—21no—
180#392C22×C1311yescharacteristic
181#386—21no—
182#386—21no—
183#385—21no—
184#385C22×C1311yescharacteristic
185#380—21no—
186#342—21no—
187#342C22×C1311yescharacteristic
188#328—21no—
189#328—21no—
190#323C22×C1311yescharacteristic
191#323C22×C1311yescharacteristic
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—42no—
199C22×C13—42no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—42no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13#45011yescharacteristic
209C22×C13#45611yescharacteristic
210C22×C13B(4,𝔽2)11yescharacteristic
211C4×C13—42no—
212C4×C13—41no—
213C4×C13—41no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—82no—
217C4×C13—81no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13—81no—
221C22×D4—21no—
222C22×D4D4×C1311yescharacteristic
223C23×C4—21no—
224C23×C4D4×C1311yescharacteristic
225C2×SD16—41no—
226#123—42no—
227#123—42no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—41no—
231C22⋊Q8—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C4⋊C4D4×C1311yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4D4×C1311yescharacteristic
245C2×C22⋊C4C23×C1311yescharacteristic
246#106—41no—
247#103—41no—
248#102—41no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—41no—
256#95D4×C1311yescharacteristic
257#95D4×C1311yescharacteristic
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—41no—
261C2×C13—41no—
262C2×C13—82no—
263C2×C13#160411yescharacteristic
264C2×C13#219711yescharacteristic
265C2×C13#220011yescharacteristic
266C24—21no—
267C24C2×D4×C1311yescharacteristic
268C2×Q8—21no—
269C2×Q8—21no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—81no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C1311yescharacteristic
290C22×C4C2×D4×C1311yescharacteristic
291SD16—82no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—81no—
302C4⋊C4—82no—
303C22⋊C4—21no—
304C22⋊C4—22no—
305C22⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C22⋊C4—81no—
315C22⋊C4C13×SD1612yescomplemented
316C13#1224311yescharacteristic, direct product factor, Sylow
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23C13×#12011yescharacteristic
329C23C2×C13×SD1611yescharacteristic
330C23C13×AGL(1,ℤ/8)11yescharacteristic
331Q8—81no—
332Q8—81no—
333D4—42no—
334D4—81no—
335D4—82no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—84no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C8—81no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22C13×#45011yescharacteristic
385C22C13×#45611yescharacteristic
386C22C13×B(4,𝔽2)11yescharacteristic
387C4—42no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—82no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—82no—
402C2C13×#160411yescharacteristic
403C2C13×#219711yescharacteristic
404C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#392C22
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×#2062C2semidirect
3. C13×#1608C2semidirect
5. C13×#1344C2semidirect
7. C13×#1326C2semidirect
64. #12243C13direct (N × H)
114. C13×C22⋊C4SD16semidirect
116. #2062C2×C13semidirect
117. #1608C2×C13semidirect
119. #1344C2×C13semidirect
121. #1326C2×C13semidirect
315. C22⋊C4C13×SD16semidirect
316. C13#12243direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26932
C13×#20622
C13×#16082
C13×#15962
C13×#13442
C13×#13432
C13×#13262
#1224313