Finite Group Databasebeta

← C13×#32558 #15718897

Subgroups — C13×#32558 #15718897

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2580C212yesmaximal, complemented
2C13×#2101C212yesmaximal, complemented
3C13×#2086C211yesmaximal, characteristic, complemented
4C13×#2073C212yesmaximal, complemented
5C13×#2054C211yesmaximal, characteristic
6C13×#1985C211yesmaximal, characteristic, complemented
7C13×#1936C212yesmaximal, complemented
8C13×#1879C212yesmaximal
9C13×#1862C212yesmaximal, complemented
10C22×C13×D8C2211yescharacteristic
11C2×C4×Q8×C13C2211yescharacteristic
12C2×C4×D4×C13C2212yes—
13C2×C13×#107C2211yescharacteristic
14C2×C13×C4⋊C8C2211yescharacteristic
15C2×C13×#102C2212yes—
16C2×C13×#102C2212yes—
17C2×C13×#102C2212yes—
18C2×C13×#97C2211yescharacteristic
19C13×#399—22no—
20C13×#393—22no—
21C13×#390C2212yes—
22C13×#390C2212yes—
23C13×#389C2212yes—
24C13×#389C2212yes—
25C13×#385—22no—
26C13×#385—22no—
27C13×#382C2212yes—
28C13×#340C2211yescharacteristic
29C13×#340C2211yescharacteristic
30C13×#340C2212yes—
31C13×#340C2212yes—
32C13×#340C2212yes—
33C13×#336C2212yes—
34C13×#336C2212yes—
35C22×Q8×C13D411yescharacteristic
36C22×D4×C13C2312yes—
37C23×C4×C13—22no—
38C2×C13×D8—24no—
39C2×C13×D8—41no—
40C22×C8×C13C2312yes—
41C22×C8×C13C2311yescharacteristic
42C22×C8×C13C2311yescharacteristic
43C4×Q8×C13—41no—
44C4×Q8×C13—41no—
45C4×D4×C13—42no—
46C4×D4×C13—42no—
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D412yes—
51C2×C13×C4⋊C4C2312yes—
52C2×C13×C4⋊C4C2312yes—
53C2×C13×C4⋊C4C2312yes—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—22no—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C42×C13C2312yes—
60C2×C42×C13C2311yescharacteristic
61C13×#107—41no—
62C13×C4⋊C8—41no—
63C13×#102—24no—
64C13×#102—24no—
65C13×#102—42no—
66C13×#97—41no—
67C13×#95—22no—
68C13×#95—22no—
69C13×#95—22no—
70C13×#95—22no—
71#32558C1311yesmaximal, characteristic, direct product factor, Sylow
72C24×C13—22no—
73C2×Q8×C13—41no—
74C2×Q8×C13—42no—
75C2×D4×C13—22no—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C2×D4×C13#4114yes—
81C22×C4×C13—22no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—44no—
85C22×C4×C13—82no—
86C22×C4×C13—82no—
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2411yescharacteristic
92C13×D8—44no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—82no—
109C13×C4⋊C4—82no—
110C13×C22⋊C4—44no—
111C13×C22⋊C4—44no—
112C13×C22⋊C4—44no—
113C13×C22⋊C4—82no—
114C13×C22⋊C4—82no—
115C42×C13—21no—
116C42×C13—21no—
117C42×C13—22no—
118C42×C13—22no—
119#2580C2×C1312yescomplemented
120#2101C2×C1312yescomplemented
121#2086C2×C1311yescharacteristic, complemented
122#2073C2×C1312yescomplemented
123#2054C2×C1311yescharacteristic
124#1985C2×C1311yescharacteristic, complemented
125#1936C2×C1312yescomplemented
126#1879C2×C1312yes—
127#1862C2×C1312yescomplemented
128C23×C13—24no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—42no—
135C23×C13C22×D411yescharacteristic
136Q8×C13—44no—
137D4×C13—24no—
138D4×C13—24no—
139D4×C13—42no—
140D4×C13—42no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—21no—
149C2×C4×C13—22no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—88no—
162C2×C4×C13C2×#4112yes—
163C2×C4×C13H(5,𝔽2)11yescharacteristic
164C2×C4×C13H(5,𝔽2)11yescharacteristic
165C2×C4×C132−1+412yes—
166C8×C13—42no—
167C8×C13—41no—
168C8×C13—41no—
169C22×D8C22×C1311yescharacteristic
170C2×C4×Q8C22×C1311yescharacteristic
171C2×C4×D4C22×C1312yes—
172C2×#107C22×C1311yescharacteristic
173C2×C4⋊C8C22×C1311yescharacteristic
174C2×#102C22×C1312yes—
175C2×#102C22×C1312yes—
176C2×#102C22×C1312yes—
177C2×#97C22×C1311yescharacteristic
178#399—22no—
179#393—22no—
180#390C22×C1312yes—
181#390C22×C1312yes—
182#389C22×C1312yes—
183#389C22×C1312yes—
184#385—22no—
185#385—22no—
186#382C22×C1312yes—
187#340C22×C1311yescharacteristic
188#340C22×C1311yescharacteristic
189#340C22×C1312yes—
190#340C22×C1312yes—
191#340C22×C1312yes—
192#336C22×C1312yes—
193#336C22×C1312yes—
194C22×C13—44no—
195C22×C13—44no—
196C22×C13—44no—
197C22×C13—82no—
198C22×C13—82no—
199C22×C13—82no—
200C22×C13—82no—
201C22×C13#53411yescharacteristic
202C22×C13#54812yes—
203C22×C13#57512yes—
204C22×C13#57611yescharacteristic
205C22×C13#57611yescharacteristic
206C4×C13—42no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—42no—
210C4×C13—82no—
211C4×C13—82no—
212C4×C13—82no—
213C4×C13#53912yes—
214C4×C13#55111yescharacteristic
215C4×C13#56311yescharacteristic
216C22×Q8D4×C1311yescharacteristic
217C22×D4C23×C1312yes—
218C23×C4—22no—
219C2×D8—24no—
220C2×D8—41no—
221C22×C8C23×C1311yescharacteristic
222C22×C8C23×C1312yes—
223C22×C8C23×C1311yescharacteristic
224C4×Q8—41no—
225C4×Q8—41no—
226C4×D4—42no—
227C4×D4—42no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4D4×C1311yescharacteristic
231C2×C4⋊C4D4×C1312yes—
232C2×C4⋊C4C23×C1312yes—
233C2×C4⋊C4C23×C1312yes—
234C2×C4⋊C4C23×C1312yes—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C42C23×C1312yes—
241C2×C42C23×C1311yescharacteristic
242#107—41no—
243C4⋊C8—41no—
244#102—24no—
245#102—24no—
246#102—42no—
247#97—41no—
248#95—22no—
249#95—22no—
250#95—22no—
251#95—22no—
252C2×C13—84no—
253C2×C13#272811yescharacteristic
254C2×C13#319711yescharacteristic
255C2×C13#319911yescharacteristic
256C2×C13#337012yes—
257C2×C13#337012yes—
258C24—22no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4C13×#4114yes—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—44no—
271C22×C4—82no—
272C22×C4—82no—
273C22×C4C2×D4×C1312yes—
274C22×C4C2×D4×C1311yescharacteristic
275C22×C4C2×D4×C1312yes—
276C22×C4C2×D4×C1311yescharacteristic
277C22×C4C24×C1311yescharacteristic
278D8—44no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—82no—
295C4⋊C4—82no—
296C22⋊C4—44no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—82no—
300C22⋊C4—82no—
301C42—21no—
302C42—21no—
303C42—22no—
304C42—22no—
305C13#3255811yescharacteristic, direct product factor, Sylow
306C23—24no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23C22×D4×C1311yescharacteristic
314Q8—44no—
315D4—24no—
316D4—24no—
317D4—42no—
318D4—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—88no—
340C2×C4C2×C13×#4112yes—
341C2×C4C13×H(5,𝔽2)11yescharacteristic
342C2×C4C13×H(5,𝔽2)11yescharacteristic
343C2×C4C13×2−1+412yes—
344C8—42no—
345C8—41no—
346C8—41no—
347C22—44no—
348C22—44no—
349C22—44no—
350C22—82no—
351C22—82no—
352C22—82no—
353C22—82no—
354C22C13×#53411yescharacteristic
355C22C13×#54812yes—
356C22C13×#57512yes—
357C22C13×#57611yescharacteristic
358C22C13×#57611yescharacteristic
359C4—42no—
360C4—41no—
361C4—41no—
362C4—42no—
363C4—82no—
364C4—82no—
365C4—82no—
366C4C13×#53912yes—
367C4C13×#55111yescharacteristic
368C4C13×#56311yescharacteristic
369C2—84no—
370C2C13×#272811yescharacteristic
371C2C13×#319711yescharacteristic
372C2C13×#319911yescharacteristic
373C2C13×#337012yes—
374C2C13×#337012yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×C13×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2580C2semidirect
2. C13×#2101C2semidirect
3. C13×#2086C2semidirect
4. C13×#2073C2semidirect
6. C13×#1985C2semidirect
7. C13×#1936C2semidirect
9. C13×#1862C2semidirect
71. #32558C13direct (N × H)
119. #2580C2×C13semidirect
120. #2101C2×C13semidirect
121. #2086C2×C13semidirect
122. #2073C2×C13semidirect
124. #1985C2×C13semidirect
125. #1936C2×C13semidirect
127. #1862C2×C13semidirect
305. C13#32558direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25802
C13×#21012
C13×#20862
C13×#20732
C13×#20542
C13×#19852
C13×#19362
C13×#18792
C13×#18622
#3255813