Finite Group Databasebeta

← C13×#32537 #15718876

Subgroups — C13×#32537 #15718876

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2513C212yesmaximal, complemented
2C13×#2092C212yesmaximal, complemented
3C13×#2067C212yesmaximal, complemented
4C13×#2054C212yesmaximal
5C13×#1972C211yesmaximal, characteristic
6C13×#1949C212yesmaximal, complemented
7C13×#1944C211yesmaximal, characteristic, complemented
8C13×#1940C211yesmaximal, characteristic, complemented
9C13×#1925C212yesmaximal, complemented
10C22×C13×D8C2211yescharacteristic
11C2×C13×#107C2212yes—
12C2×C13×#107C2211yescharacteristic
13C2×C13×#106C2211yescharacteristic
14C2×C13×#106C2211yescharacteristic
15C2×C13×C4⋊C8C2212yes—
16C2×C13×C4⋊C8C2211yescharacteristic
17C2×C13×#102C2212yes—
18C2×C13×#102C2212yes—
19C2×C13×#102C2212yes—
20C2×C13×#97C2211yescharacteristic
21C13×#397—22no—
22C13×#397—22no—
23C13×#390C2212yes—
24C13×#390C2212yes—
25C13×#390C2212yes—
26C13×#389C2212yes—
27C13×#388—22no—
28C13×#388—22no—
29C13×#382C2212yes—
30C4×C13×C4⋊C4C2212yes—
31C4×C13×C4⋊C4C2211yescharacteristic
32C13×#340C2212yes—
33C13×#340C2212yes—
34C13×#336C2212yes—
35C22×D4×C13C2312yes—
36C2×C13×D8—22no—
37C2×C13×D8—41no—
38C2×C13×D8—41no—
39C22×C8×C13C2312yes—
40C22×C8×C13C2311yescharacteristic
41C22×C8×C13C2311yescharacteristic
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4D412yes—
44C2×C13×C4⋊C4C2312yes—
45C2×C13×C4⋊C4C2312yes—
46C2×C13×C4⋊C4C2312yes—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—22no—
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C42×C13—22no—
54C2×C42×C13C2312yes—
55C2×C42×C13C2311yescharacteristic
56C13×#107—41no—
57C13×#107—42no—
58C13×#106—22no—
59C13×#106—41no—
60C13×C4⋊C8—24no—
61C13×C4⋊C8—41no—
62C13×#102—24no—
63C13×#102—42no—
64C13×#102—42no—
65C13×#97—41no—
66C13×#95—22no—
67C13×#95—22no—
68C13×#95—22no—
69C13×#95—22no—
70C13×#95D411yescharacteristic
71C13×#95D411yescharacteristic
72#32537C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13—22no—
74C2×D4×C13—22no—
75C2×D4×C13—22no—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—22no—
82C22×C4×C13—22no—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2411yescharacteristic
88C13×D8—44no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13#4112yes—
97C2×C8×C13#4112yes—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—82no—
106C13×C22⋊C4—44no—
107C13×C22⋊C4—44no—
108C13×C22⋊C4—82no—
109C13×C22⋊C4—82no—
110C13×C22⋊C4—82no—
111C13×C22⋊C4—82no—
112C42×C13—22no—
113C42×C13—21no—
114C42×C13—21no—
115C42×C13—22no—
116C42×C13—82no—
117#2513C2×C1312yescomplemented
118#2092C2×C1312yescomplemented
119#2067C2×C1312yescomplemented
120#2054C2×C1312yes—
121#1972C2×C1311yescharacteristic
122#1949C2×C1312yescomplemented
123#1944C2×C1311yescharacteristic, complemented
124#1940C2×C1311yescharacteristic, complemented
125#1925C2×C1312yescomplemented
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13C22×D411yescharacteristic
134D4×C13—42no—
135D4×C13—42no—
136D4×C13—42no—
137D4×C13—42no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13C2×#4111yescharacteristic
158C2×C4×C13C2×#4111yescharacteristic
159C2×C4×C13H(5,𝔽2)11yescharacteristic
160C2×C4×C13H(5,𝔽2)11yescharacteristic
161C2×C4×C132−1+411yescharacteristic
162C2×C4×C132−1+411yescharacteristic
163C8×C13—22no—
164C8×C13—22no—
165C8×C13—42no—
166C22×D8C22×C1311yescharacteristic
167C2×#107C22×C1312yes—
168C2×#107C22×C1311yescharacteristic
169C2×#106C22×C1311yescharacteristic
170C2×#106C22×C1311yescharacteristic
171C2×C4⋊C8C22×C1312yes—
172C2×C4⋊C8C22×C1311yescharacteristic
173C2×#102C22×C1312yes—
174C2×#102C22×C1312yes—
175C2×#102C22×C1312yes—
176C2×#97C22×C1311yescharacteristic
177#397—22no—
178#397—22no—
179#390C22×C1312yes—
180#390C22×C1312yes—
181#390C22×C1312yes—
182#389C22×C1312yes—
183#388—22no—
184#388—22no—
185#382C22×C1312yes—
186C4×C4⋊C4C22×C1312yes—
187C4×C4⋊C4C22×C1311yescharacteristic
188#340C22×C1312yes—
189#340C22×C1312yes—
190#336C22×C1312yes—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13—82no—
195C22×C13—82no—
196C22×C13—82no—
197C22×C13—82no—
198C22×C13#53711yescharacteristic
199C22×C13#54711yescharacteristic
200C22×C13#55011yescharacteristic
201C22×C13#57512yes—
202C22×C13#57612yes—
203C4×C13—42no—
204C4×C13—42no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13—82no—
208C4×C13—82no—
209C4×C13—82no—
210C4×C13#53811yescharacteristic
211C4×C13#53911yescharacteristic
212C4×C13#55611yescharacteristic
213C4×C13#56311yescharacteristic
214C22×D4C23×C1312yes—
215C2×D8—22no—
216C2×D8—41no—
217C2×D8—41no—
218C22×C8C23×C1312yes—
219C22×C8C23×C1311yescharacteristic
220C22×C8C23×C1311yescharacteristic
221C2×C4⋊C4—22no—
222C2×C4⋊C4D4×C1312yes—
223C2×C4⋊C4C23×C1312yes—
224C2×C4⋊C4C23×C1312yes—
225C2×C4⋊C4C23×C1312yes—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C42—22no—
233C2×C42C23×C1312yes—
234C2×C42C23×C1311yescharacteristic
235#107—41no—
236#107—42no—
237#106—22no—
238#106—41no—
239C4⋊C8—24no—
240C4⋊C8—41no—
241#102—24no—
242#102—42no—
243#102—42no—
244#97—41no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95D4×C1311yescharacteristic
250#95D4×C1311yescharacteristic
251C2×C13—162no—
252C2×C13#272711yescharacteristic
253C2×C13#325611yescharacteristic
254C2×C13#325911yescharacteristic
255C2×C13#334712yes—
256C2×C13#340312yes—
257C24—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4C2×D4×C1312yes—
268C22×C4C2×D4×C1311yescharacteristic
269C22×C4C2×D4×C1312yes—
270C22×C4C2×D4×C1311yescharacteristic
271C22×C4C24×C1311yescharacteristic
272D8—44no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C13×#4112yes—
281C2×C8C13×#4112yes—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—82no—
290C22⋊C4—44no—
291C22⋊C4—44no—
292C22⋊C4—82no—
293C22⋊C4—82no—
294C22⋊C4—82no—
295C22⋊C4—82no—
296C42—22no—
297C42—21no—
298C42—21no—
299C42—22no—
300C42—82no—
301C13#3253711yescharacteristic, direct product factor, Sylow
302C23—42no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23C22×D4×C1311yescharacteristic
310D4—42no—
311D4—42no—
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4C2×C13×#4111yescharacteristic
334C2×C4C2×C13×#4111yescharacteristic
335C2×C4C13×H(5,𝔽2)11yescharacteristic
336C2×C4C13×H(5,𝔽2)11yescharacteristic
337C2×C4C13×2−1+411yescharacteristic
338C2×C4C13×2−1+411yescharacteristic
339C8—22no—
340C8—22no—
341C8—42no—
342C22—82no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—82no—
347C22—82no—
348C22—82no—
349C22C13×#53711yescharacteristic
350C22C13×#54711yescharacteristic
351C22C13×#55011yescharacteristic
352C22C13×#57512yes—
353C22C13×#57612yes—
354C4—42no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—82no—
359C4—82no—
360C4—82no—
361C4C13×#53811yescharacteristic
362C4C13×#53911yescharacteristic
363C4C13×#55611yescharacteristic
364C4C13×#56311yescharacteristic
365C2—162no—
366C2C13×#272711yescharacteristic
367C2C13×#325611yescharacteristic
368C2C13×#325911yescharacteristic
369C2C13×#334712yes—
370C2C13×#340312yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×C13×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2513C2semidirect
2. C13×#2092C2semidirect
3. C13×#2067C2semidirect
6. C13×#1949C2semidirect
7. C13×#1944C2semidirect
8. C13×#1940C2semidirect
9. C13×#1925C2semidirect
72. #32537C13direct (N × H)
117. #2513C2×C13semidirect
118. #2092C2×C13semidirect
119. #2067C2×C13semidirect
122. #1949C2×C13semidirect
123. #1944C2×C13semidirect
124. #1940C2×C13semidirect
125. #1925C2×C13semidirect
301. C13#32537direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25132
C13×#20922
C13×#20672
C13×#20542
C13×#19722
C13×#19492
C13×#19442
C13×#19402
C13×#19252
#3253713