Finite Group Databasebeta

← C13×#10427 #15696766

Subgroups — C13×#10427 #15696766

Order 3328.

460 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2820C211yesmaximal, characteristic
2C13×#1992C211yesmaximal, characteristic, complemented
3C13×#1959C211yesmaximal, characteristic
4C13×#1847C211yesmaximal, characteristic, complemented
5C2×C13×#330C211yesmaximal, characteristic, complemented
6C2×C13×#329C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic, complemented
8C2×C13×#125C2211yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C2×C13×#107—21no—
11C2×C13×#106—21no—
12C2×C13×#103—21no—
13C2×C13×#102—21no—
14C2×C13×#97C2211yescharacteristic
15C2×C13×#97C2211yescharacteristic
16C2×C13×#97C2211yescharacteristic
17C13×#399—21no—
18C13×#397—21no—
19C13×#396—21no—
20C13×#396—21no—
21C13×#395—21no—
22C13×#394—21no—
23C13×#384C2211yescharacteristic
24C13×#382C2211yescharacteristic
25C13×#340—21no—
26C13×#340—21no—
27C13×#330—22no—
28C13×#329—22no—
29C22×Q8×C13D411yescharacteristic
30C22×D4×C13D411yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C13×#125—21no—
35C13×#125—21no—
36C13×#125—21no—
37C13×#125—21no—
38C13×#124—21no—
39C13×#124—21no—
40C13×#124—21no—
41C13×#124—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C42×C13C2311yescharacteristic
60C13×#107—42no—
61C13×#106—42no—
62C13×#103—42no—
63C13×#102—42no—
64C13×#97—21no—
65C13×#97—21no—
66C13×#97—21no—
67C13×#97—21no—
68C13×#97—21no—
69C13×#97D412yes—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74#10427C1311yesmaximal, characteristic, direct product factor, Sylow
75C24×C13—21no—
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—81no—
118C13×C4⋊C4—81no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—81no—
124C13×C22⋊C4—81no—
125C13×C22⋊C4—81no—
126C13×C22⋊C4—81no—
127C42×C13C2×D411yescharacteristic
128C42×C13#4111yescharacteristic
129C42×C13#4111yescharacteristic
130C42×C13#4111yescharacteristic
131#2820C2×C1311yescharacteristic
132#1992C2×C1311yescharacteristic, complemented
133#1959C2×C1311yescharacteristic
134#1847C2×C1311yescharacteristic, complemented
135C2×#330C2×C1311yescharacteristic, complemented
136C2×#329C2×C1311yescharacteristic
137#1295C2×C1311yescharacteristic, complemented
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13#12011yescharacteristic
146Q8×C13—42no—
147Q8×C13—81no—
148D4×C13—42no—
149D4×C13—81no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
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—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12311yescharacteristic
178C2×C4×C13#12311yescharacteristic
179C2×C4×C13#12411yescharacteristic
180C8×C13—24no—
181C8×C13—42no—
182C8×C13—42no—
183C2×#125C22×C1311yescharacteristic
184C2×#124C22×C1311yescharacteristic
185C2×#107—21no—
186C2×#106—21no—
187C2×#103—21no—
188C2×#102—21no—
189C2×#97C22×C1311yescharacteristic
190C2×#97C22×C1311yescharacteristic
191C2×#97C22×C1311yescharacteristic
192#399—21no—
193#397—21no—
194#396—21no—
195#396—21no—
196#395—21no—
197#394—21no—
198#384C22×C1311yescharacteristic
199#382C22×C1311yescharacteristic
200#340—21no—
201#340—21no—
202#330—22no—
203#329—22no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13#39411yescharacteristic
212C22×C13#45311yescharacteristic
213C22×C13#45311yescharacteristic
214C22×C13#45411yescharacteristic
215C22×C13#45511yescharacteristic
216C22×C13#45611yescharacteristic
217C22×C13#45611yescharacteristic
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13—81no—
228C4×C13—81no—
229C4×C13—161no—
230C22×Q8D4×C1311yescharacteristic
231C22×D4D4×C1311yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235#125—21no—
236#125—21no—
237#125—21no—
238#125—21no—
239#124—21no—
240#124—21no—
241#124—21no—
242#124—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C1311yescharacteristic
251C2×C4⋊C4D4×C1311yescharacteristic
252C2×C4⋊C4D4×C1311yescharacteristic
253C2×C4⋊C4D4×C1311yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42C23×C1311yescharacteristic
261#107—42no—
262#106—42no—
263#103—42no—
264#102—42no—
265#97—21no—
266#97—21no—
267#97—21no—
268#97—21no—
269#97—21no—
270#97D4×C1312yes—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275C2×C13—161no—
276C2×C13#165611yescharacteristic
277C2×C13#166011yescharacteristic
278C2×C13#166111yescharacteristic
279C2×C13#166411yescharacteristic
280C2×C13#203711yescharacteristic
281C2×C13#203811yescharacteristic
282C2×C13#203911yescharacteristic
283C24—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4C2×D4×C1311yescharacteristic
299C22×C4C2×D4×C1311yescharacteristic
300C22×C4C2×D4×C1311yescharacteristic
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C4⋊C4—81no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C42C2×D4×C1311yescharacteristic
336C42C13×#4111yescharacteristic
337C42C13×#4111yescharacteristic
338C42C13×#4111yescharacteristic
339C13#1042711yescharacteristic, direct product factor, Sylow
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C13×#12011yescharacteristic
348Q8—42no—
349Q8—81no—
350D4—42no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4C13×#12111yescharacteristic
377C2×C4C13×#12111yescharacteristic
378C2×C4C13×#12111yescharacteristic
379C2×C4C13×#12311yescharacteristic
380C2×C4C13×#12311yescharacteristic
381C2×C4C13×#12411yescharacteristic
382C8—24no—
383C8—42no—
384C8—42no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C13×#39411yescharacteristic
393C22C13×#45311yescharacteristic
394C22C13×#45311yescharacteristic
395C22C13×#45411yescharacteristic
396C22C13×#45511yescharacteristic
397C22C13×#45611yescharacteristic
398C22C13×#45611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—161no—
411C2—161no—
412C2C13×#165611yescharacteristic
413C2C13×#166011yescharacteristic
414C2C13×#166111yescharacteristic
415C2C13×#166411yescharacteristic
416C2C13×#203711yescharacteristic
417C2C13×#203811yescharacteristic
418C2C13×#203911yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1992C2semidirect
4. C13×#1847C2semidirect
5. C2×C13×#330C2semidirect
7. C13×#1295C2semidirect
74. #10427C13direct (N × H)
132. #1992C2×C13semidirect
134. #1847C2×C13semidirect
135. C2×#330C2×C13semidirect
137. #1295C2×C13semidirect
339. C13#10427direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28202
C13×#19922
C13×#19592
C13×#18472
C2×C13×#3302
C2×C13×#3292
C13×#12952
#1042713