Finite Group Databasebeta

← C13×#12263 #15698602

Subgroups — C13×#12263 #15698602

Order 3328.

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

normal subgroups only

This group has 438 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×#2760C211yesmaximal, characteristic
2C13×#2030C211yesmaximal, characteristic, complemented
3C13×#1602C211yesmaximal, characteristic, complemented
4C13×#1596C211yesmaximal, characteristic
5C13×#1351C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic
7C13×#1317C211yesmaximal, characteristic, complemented
8C13×#543C2211yescharacteristic
9C13×#451—21no—
10C13×#450—21no—
11C13×#401—21no—
12C13×#393—21no—
13C13×#393C2211yescharacteristic
14C13×#392C2211yescharacteristic
15C13×#386—21no—
16C13×#386—21no—
17C13×#386—21no—
18C13×#381—21no—
19C13×#381—21no—
20C13×#381C2211yescharacteristic
21C13×#342—21no—
22C13×#342C2211yescharacteristic
23C13×#328—21no—
24C13×#328—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13D411yescharacteristic
30C23×C4×C13—21no—
31C23×C4×C13D411yescharacteristic
32C2×C13×Q16—41no—
33C2×C13×SD16—41no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—41no—
37C13×C22⋊Q8—41no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
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⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C13×#103—41no—
48C13×#102—41no—
49C13×C22⋊C8—21no—
50C13×C22⋊C8—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—41no—
59C13×#95—41no—
60C13×#95D411yescharacteristic
61C13×#95D411yescharacteristic
62#12263C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C24×C13C2×D411yescharacteristic
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—41no—
68C2×Q8×C13—81no—
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—21no—
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—81no—
89C22×C4×C13—81no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C13×Q16—82no—
93C13×SD16—82no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C13×C22⋊C4—81no—
109C13×C22⋊C4—81no—
110C13×C22⋊C4—81no—
111#2760C2×C1311yescharacteristic
112#2030C2×C1311yescharacteristic, complemented
113#1602C2×C1311yescharacteristic, complemented
114#1596C2×C1311yescharacteristic
115#1351C2×C1311yescharacteristic, complemented
116#1343C2×C1311yescharacteristic
117#1317C2×C1311yescharacteristic, complemented
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—22no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13#12011yescharacteristic
130C23×C13#13511yescharacteristic
131C23×C13#13711yescharacteristic
132Q8×C13—42no—
133Q8×C13—81no—
134Q8×C13—81no—
135Q8×C13—81no—
136D4×C13—42no—
137D4×C13—81no—
138D4×C13—82no—
139D4×C13—82no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
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—84no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C8×C13—81no—
170C8×C13—81no—
171#543C22×C1311yescharacteristic
172#451—21no—
173#450—21no—
174#401—21no—
175#393—21no—
176#393C22×C1311yescharacteristic
177#392C22×C1311yescharacteristic
178#386—21no—
179#386—21no—
180#386—21no—
181#381—21no—
182#381—21no—
183#381C22×C1311yescharacteristic
184#342—21no—
185#342C22×C1311yescharacteristic
186#328—21no—
187#328—21no—
188#323C22×C1311yescharacteristic
189#323C22×C1311yescharacteristic
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—42no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13#45211yescharacteristic
207C22×C13#45511yescharacteristic
208C22×C13B(4,𝔽2)11yescharacteristic
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—81no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—161no—
219C22×Q8D4×C1311yescharacteristic
220C22×D4—21no—
221C22×D4D4×C1311yescharacteristic
222C23×C4—21no—
223C23×C4D4×C1311yescharacteristic
224C2×Q16—41no—
225C2×SD16—41no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—41no—
229C22⋊Q8—41no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4D4×C1311yescharacteristic
238C2×C22⋊C4C23×C1311yescharacteristic
239#103—41no—
240#102—41no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—41no—
251#95—41no—
252#95D4×C1311yescharacteristic
253#95D4×C1311yescharacteristic
254C2×C13—21no—
255C2×C13—21no—
256C2×C13—41no—
257C2×C13—41no—
258C2×C13—82no—
259C2×C13#160611yescharacteristic
260C2×C13#219711yescharacteristic
261C2×C13#220011yescharacteristic
262C24—21no—
263C24C2×D4×C1311yescharacteristic
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—41no—
267C2×Q8—81no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—81no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C1311yescharacteristic
290C22×C4C2×D4×C1311yescharacteristic
291Q16—82no—
292SD16—82no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C13#1226311yescharacteristic, direct product factor, Sylow
311C23—21no—
312C23—21no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C13×#12011yescharacteristic
323C23C13×#13511yescharacteristic
324C23C13×#13711yescharacteristic
325Q8—42no—
326Q8—81no—
327Q8—81no—
328Q8—81no—
329D4—42no—
330D4—81no—
331D4—82no—
332D4—82no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
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—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—84no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C8—81no—
363C8—81no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22C13×#45211yescharacteristic
381C22C13×#45511yescharacteristic
382C22C13×B(4,𝔽2)11yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—161no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—82no—
398C2C13×#160611yescharacteristic
399C2C13×#219711yescharacteristic
400C2C13×#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×#2030C2semidirect
3. C13×#1602C2semidirect
5. C13×#1351C2semidirect
7. C13×#1317C2semidirect
62. #12263C13direct (N × H)
112. #2030C2×C13semidirect
113. #1602C2×C13semidirect
115. #1351C2×C13semidirect
117. #1317C2×C13semidirect
310. C13#12263direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27602
C13×#20302
C13×#16022
C13×#15962
C13×#13512
C13×#13432
C13×#13172
#1226313