Finite Group Databasebeta

← C13×#12962 #15699301

Subgroups — C13×#12962 #15699301

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2977C211yesmaximal, characteristic
2C13×#2120C211yesmaximal, characteristic
3C13×#1891C211yesmaximal, characteristic
4C13×#1868C211yesmaximal, characteristic, complemented
5C13×#1858C211yesmaximal, characteristic, complemented
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1392C211yesmaximal, characteristic, complemented
8C13×#568C2211yescharacteristic
9C13×#525C2211yescharacteristic
10C13×#435—21no—
11C13×#435—21no—
12C8×D4×C13—21no—
13C8×D4×C13—21no—
14C13×#433—21no—
15C13×#430—21no—
16C13×#424—21no—
17C13×#413C2211yescharacteristic
18C13×#413C2211yescharacteristic
19C13×#410C2211yescharacteristic
20C13×#408C2211yescharacteristic
21C13×#408C2211yescharacteristic
22C13×#407—21no—
23C2×C13×C22⋊C8—21no—
24C13×#352C412yes—
25C13×AΣL(1,𝔽16)C412yes—
26C13×#344—21no—
27C13×#344—21no—
28C13×#341—21no—
29C2×C13×#41C2311yescharacteristic
30C23×C4×C13D411yescharacteristic
31C13×#131—42no—
32C2×C13×M16—21no—
33C2×C13×M16—21no—
34C2×C13×M16—21no—
35C2×C13×M16—21no—
36C2×C13×M16—21no—
37C2×C13×M16D411yescharacteristic
38C2×C13×M16D411yescharacteristic
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13D411yescharacteristic
42C22×C8×C13D411yescharacteristic
43C13×#123C2×C411yescharacteristic
44C13×#123Q811yescharacteristic
45C13×C22⋊Q8—21no—
46C13×#121—21no—
47C13×#120C2×C411yescharacteristic
48C13×#120Q811yescharacteristic
49C4×D4×C13—21no—
50C4×D4×C13—21no—
51C13×#117—21no—
52C13×#117D411yescharacteristic
53C13×#108—42no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—42no—
57C13×#101—21no—
58C13×#101—21no—
59C13×#100—21no—
60C13×#100C2×C412yes—
61C13×#99—21no—
62C13×#99C2×C412yes—
63C13×C22⋊C8—21no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8—21no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—42no—
70C13×#97—21no—
71C4×C8×C13—21no—
72#12962C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13C4⋊C411yescharacteristic
74C13×#41—41no—
75C13×#41—41no—
76C2×Q8×C13#4111yescharacteristic
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13C22×C411yescharacteristic
80C2×D4×C13C2×Q811yescharacteristic
81C2×D4×C13#4111yescharacteristic
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C4⋊C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C13×M16—22no—
91C13×M16—22no—
92C13×M16—41no—
93C13×M16—41no—
94C13×M16—41no—
95C13×M16—41no—
96C13×M16—41no—
97C13×M16—41no—
98C13×M16—41no—
99C13×M16—41no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C2×C8×C13—81no—
112C2×C8×C13—81no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—41no—
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4C4⋊C411yescharacteristic
123C13×C22⋊C4C4⋊C411yescharacteristic
124C42×C13—21no—
125C42×C13—41no—
126#2977C2×C1311yescharacteristic
127#2120C2×C1311yescharacteristic
128#1891C2×C1311yescharacteristic
129#1868C2×C1311yescharacteristic, complemented
130#1858C2×C1311yescharacteristic, complemented
131#1395C2×C1311yescharacteristic, complemented
132#1392C2×C1311yescharacteristic, complemented
133C23×C13—21no—
134C23×C13—41no—
135C23×C13—42no—
136C23×C13C2×C4⋊C411yescharacteristic
137C23×C13C4×D411yescharacteristic
138C23×C13C22⋊Q811yescharacteristic
139Q8×C13—41no—
140D4×C13—41no—
141D4×C13—41no—
142D4×C13—41no—
143D4×C13—42no—
144D4×C13—42no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—81no—
159C2×C4×C13C4×D411yescharacteristic
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13C22⋊Q811yescharacteristic
162C2×C4×C13#12311yescharacteristic
163C8×C13—42no—
164C8×C13—42no—
165C8×C13—41no—
166C8×C13—41no—
167C8×C13—41no—
168C8×C13—41no—
169C8×C13—81no—
170#568C22×C1311yescharacteristic
171#525C22×C1311yescharacteristic
172#435—21no—
173#435—21no—
174C8×D4—21no—
175C8×D4—21no—
176#433—21no—
177#430—21no—
178#424—21no—
179#413C22×C1311yescharacteristic
180#413C22×C1311yescharacteristic
181#410C22×C1311yescharacteristic
182#408C22×C1311yescharacteristic
183#408C22×C1311yescharacteristic
184#407—21no—
185C2×C22⋊C8—21no—
186#352C4×C1312yes—
187AΣL(1,𝔽16)C4×C1312yes—
188#344—21no—
189#344—21no—
190#341—21no—
191C22×C13—22no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—42no—
200C22×C13—41no—
201C22×C13—81no—
202C22×C13#38511yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—82no—
210C4×C13B(4,𝔽2)11yescharacteristic
211C4×C13#45811yescharacteristic
212C2×#41C23×C1311yescharacteristic
213C23×C4D4×C1311yescharacteristic
214#131—42no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16D4×C1311yescharacteristic
221C2×M16D4×C1311yescharacteristic
222C22×C8—21no—
223C22×C8—21no—
224C22×C8D4×C1311yescharacteristic
225C22×C8D4×C1311yescharacteristic
226#123C2×C4×C1311yescharacteristic
227#123Q8×C1311yescharacteristic
228C22⋊Q8—21no—
229#121—21no—
230#120C2×C4×C1311yescharacteristic
231#120Q8×C1311yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234#117—21no—
235#117D4×C1311yescharacteristic
236#108—42no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—42no—
240#101—21no—
241#101—21no—
242#100—21no—
243#100C2×C4×C1312yes—
244#99—21no—
245#99C2×C4×C1312yes—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—42no—
253#97—21no—
254C4×C8—21no—
255C2×C13—21no—
256C2×C13—41no—
257C2×C13—41no—
258C2×C13—42no—
259C2×C13—41no—
260C2×C13#186711yescharacteristic
261C24C13×C4⋊C411yescharacteristic
262#41—41no—
263#41—41no—
264C2×Q8C13×#4111yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4C22×C4×C1311yescharacteristic
268C2×D4C2×Q8×C1311yescharacteristic
269C2×D4C13×#4111yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C13×C4⋊C411yescharacteristic
275C22×C4C2×D4×C1311yescharacteristic
276C22×C4C2×D4×C1311yescharacteristic
277C22×C4C2×D4×C1311yescharacteristic
278M16—22no—
279M16—22no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—41no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—81no—
300C2×C8—81no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—22no—
310C22⋊C4C13×C4⋊C411yescharacteristic
311C22⋊C4C13×C4⋊C411yescharacteristic
312C42—21no—
313C42—41no—
314C13#1296211yescharacteristic, direct product factor, Sylow
315C23—21no—
316C23—41no—
317C23—42no—
318C23C2×C13×C4⋊C411yescharacteristic
319C23C4×D4×C1311yescharacteristic
320C23C13×C22⋊Q811yescharacteristic
321Q8—41no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4C4×D4×C1311yescharacteristic
342C2×C4C13×#12011yescharacteristic
343C2×C4C13×C22⋊Q811yescharacteristic
344C2×C4C13×#12311yescharacteristic
345C8—42no—
346C8—42no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—41no—
362C22—81no—
363C22C13×#38511yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—82no—
371C4C13×B(4,𝔽2)11yescharacteristic
372C4C13×#45811yescharacteristic
373C2—21no—
374C2—41no—
375C2—42no—
376C2—41no—
377C2—41no—
378C2C13×#186711yescharacteristic
subgroupG/H
centerC4×C13B(4,𝔽2)
commutatorC2×D4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
socleC2×C13#1867
prime radicalC13×#525C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1868C2semidirect
5. C13×#1858C2semidirect
6. C13×#1395C2semidirect
7. C13×#1392C2semidirect
72. #12962C13direct (N × H)
129. #1868C2×C13semidirect
130. #1858C2×C13semidirect
131. #1395C2×C13semidirect
132. #1392C2×C13semidirect
314. C13#12962direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29772
C13×#21202
C13×#18912
C13×#18682
C13×#18582
C13×#13952
C13×#13922
#1296213