Finite Group Databasebeta

← C13×#13322 #15699661

Subgroups — C13×#13322 #15699661

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×Q32C211yesmaximal, characteristic, complemented
2C2×C13×#473C211yesmaximal, characteristic
3C13×#3059C211yesmaximal, characteristic
4C2×C13×#362C211yesmaximal, characteristic, complemented
5C13×#2141C211yesmaximal, characteristic, complemented
6C2×C13×#350C211yesmaximal, characteristic
7C13×#1382C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C22×C13×Q16C2211yescharacteristic
10C22×C13×Q16C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C13×#536—21no—
13C2×C13×Q32—22no—
14C2×C13×Q32—22no—
15C2×C13×Q32—22no—
16C2×C13×M32C2211yescharacteristic
17C22×C13×C16C2211yescharacteristic
18C13×#473—22no—
19C13×#473—22no—
20C13×#470—22no—
21C13×#467—22no—
22C2×C13×#108C2211yescharacteristic
23C13×#427C2211yescharacteristic
24C13×#419—21no—
25C2×C13×#101—21no—
26C13×#362—22no—
27C13×#358—22no—
28C13×#350—22no—
29C2×C13×#41D411yescharacteristic
30C22×Q8×C13—21no—
31C22×Q8×C13—21no—
32C13×#137—24no—
33C13×#137—42no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16—21no—
38C2×C13×Q16—21no—
39C2×C13×Q16—21no—
40C2×C13×Q16—21no—
41C2×C13×Q16—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16—21no—
44C2×C13×Q16—41no—
45C2×C13×Q16D412yes—
46C2×C13×Q16D412yes—
47C2×C13×SD16—41no—
48C13×#131—21no—
49C13×#131—21no—
50C13×#131—21no—
51C13×#131—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16D411yescharacteristic
55C22×C8×C13—21no—
56C22×C8×C13C2311yescharacteristic
57C13×C4⋊Q8—41no—
58C13×#124—41no—
59C13×#123—42no—
60C13×C22⋊Q8—24no—
61C13×#117—21no—
62C13×Q32—28no—
63C13×M32—21no—
64C13×M32—21no—
65C2×C13×C16—21no—
66C2×C13×C16—21no—
67C2×C13×C16—21no—
68C2×C13×C16D412yes—
69C13×#108—21no—
70C13×#108D412yes—
71C13×#107D412yes—
72C13×#106—21no—
73C13×#103—24no—
74C13×#101—24no—
75#13322C1311yesmaximal, characteristic, direct product factor, Sylow
76C13×#41—21no—
77C13×#41—21no—
78C13×#41—21no—
79C13×#41—21no—
80C2×Q8×C13—22no—
81C2×Q8×C13—22no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×Q8×C13—41no—
87C2×Q8×C13—41no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13D811yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13D811yescharacteristic
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13C2×D411yescharacteristic
99C13×Q16—22no—
100C13×Q16—22no—
101C13×Q16—22no—
102C13×Q16—22no—
103C13×Q16—44no—
104C13×Q16—41no—
105C13×Q16—41no—
106C13×Q16—41no—
107C13×Q16—41no—
108C13×SD16—44no—
109C13×M16—21no—
110C13×M16—22no—
111C13×M16—21no—
112C13×M16—41no—
113C13×M16—41no—
114C13×M16—41no—
115C2×C8×C13—21no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×C8×C13—41no—
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2×D411yescharacteristic
122C2×C8×C13C2×D411yescharacteristic
123C2×C8×C13C2×D411yescharacteristic
124C2×C8×C13#4111yescharacteristic
125C13×C4⋊C4—22no—
126C13×C4⋊C4—44no—
127C13×C22⋊C4—44no—
128C13×C22⋊C4—41no—
129C42×C13—41no—
130C13×C16—22no—
131C13×C16—41no—
132C22×Q32C2×C1311yescharacteristic, complemented
133C2×#473C2×C1311yescharacteristic
134#3059C2×C1311yescharacteristic
135C2×#362C2×C1311yescharacteristic, complemented
136#2141C2×C1311yescharacteristic, complemented
137C2×#350C2×C1311yescharacteristic
138#1382C2×C1311yescharacteristic, complemented
139C23×C13—21no—
140C23×C13AGL(1,ℤ/8)11yescharacteristic
141Q8×C13—21no—
142Q8×C13—21no—
143Q8×C13—42no—
144Q8×C13—42no—
145Q8×C13—42no—
146Q8×C13—42no—
147Q8×C13—81no—
148Q8×C13—81no—
149Q8×C13—81no—
150Q8×C13—81no—
151D4×C13—21no—
152D4×C13—21no—
153D4×C13—41no—
154D4×C13—41no—
155C2×C4×C13—21no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13#12011yescharacteristic
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C8×C13—41no—
172C8×C13—42no—
173C8×C13#12011yescharacteristic
174C8×C13#12111yescharacteristic
175C8×C13#12111yescharacteristic
176C8×C13#12711yescharacteristic
177C2×#137—21no—
178C22×Q16C22×C1311yescharacteristic
179C22×Q16C22×C1311yescharacteristic
180C2×#131C22×C1311yescharacteristic
181#536—21no—
182C2×Q32—22no—
183C2×Q32—22no—
184C2×Q32—22no—
185C2×M32C22×C1311yescharacteristic
186C22×C16C22×C1311yescharacteristic
187#473—22no—
188#473—22no—
189#470—22no—
190#467—22no—
191C2×#108C22×C1311yescharacteristic
192#427C22×C1311yescharacteristic
193#419—21no—
194C2×#101—21no—
195#362—22no—
196#358—22no—
197#350—22no—
198C22×C13—22no—
199C22×C13—42no—
200C22×C13—41no—
201C22×C13#44711yescharacteristic
202C22×C13#44911yescharacteristic
203C22×C13#46911yescharacteristic
204C4×C13—41no—
205C4×C13—82no—
206C4×C13—82no—
207C4×C13—82no—
208C4×C13#39211yescharacteristic
209C4×C13#44711yescharacteristic
210C4×C13#44911yescharacteristic
211C4×C13#46611yescharacteristic
212C2×#41D4×C1311yescharacteristic
213C22×Q8—21no—
214C22×Q8—21no—
215#137—24no—
216#137—42no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—41no—
228C2×Q16D4×C1312yes—
229C2×Q16D4×C1312yes—
230C2×SD16—41no—
231#131—21no—
232#131—21no—
233#131—21no—
234#131—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16D4×C1311yescharacteristic
238C22×C8—21no—
239C22×C8C23×C1311yescharacteristic
240C4⋊Q8—41no—
241#124—41no—
242#123—42no—
243C22⋊Q8—24no—
244#117—21no—
245Q32—28no—
246M32—21no—
247M32—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16D4×C1312yes—
252#108—21no—
253#108D4×C1312yes—
254#107D4×C1312yes—
255#106—21no—
256#103—24no—
257#101—24no—
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—81no—
261C2×C13#199911yescharacteristic
262C2×C13#219512yes—
263#41—21no—
264#41—21no—
265#41—21no—
266#41—21no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8C13×D811yescharacteristic
280C2×D4—21no—
281C2×D4C13×D811yescharacteristic
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C1311yescharacteristic
286Q16—22no—
287Q16—22no—
288Q16—22no—
289Q16—22no—
290Q16—44no—
291Q16—41no—
292Q16—41no—
293Q16—41no—
294Q16—41no—
295SD16—44no—
296M16—21no—
297M16—22no—
298M16—21no—
299M16—41no—
300M16—41no—
301M16—41no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8C2×D4×C1311yescharacteristic
307C2×C8C2×D4×C1311yescharacteristic
308C2×C8C2×D4×C1311yescharacteristic
309C2×C8C2×D4×C1311yescharacteristic
310C2×C8C2×D4×C1311yescharacteristic
311C2×C8C13×#4111yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—44no—
314C22⋊C4—44no—
315C22⋊C4—41no—
316C42—41no—
317C16—22no—
318C16—41no—
319C13#1332211yescharacteristic, direct product factor, Sylow
320C23—21no—
321C23C13×AGL(1,ℤ/8)11yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C13×#12011yescharacteristic
347C2×C4C13×#12011yescharacteristic
348C2×C4C13×#12111yescharacteristic
349C2×C4C2×C13×D811yescharacteristic
350C2×C4C13×#13511yescharacteristic
351C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
352C8—41no—
353C8—42no—
354C8C13×#12011yescharacteristic
355C8C13×#12111yescharacteristic
356C8C13×#12111yescharacteristic
357C8C13×#12711yescharacteristic
358C22—22no—
359C22—41no—
360C22—42no—
361C22C13×#44711yescharacteristic
362C22C13×#44911yescharacteristic
363C22C13×#46911yescharacteristic
364C4—41no—
365C4—82no—
366C4—82no—
367C4—82no—
368C4C13×#39211yescharacteristic
369C4C13×#44711yescharacteristic
370C4C13×#44911yescharacteristic
371C4C13×#46611yescharacteristic
372C2—21no—
373C2—21no—
374C2—81no—
375C2C13×#199911yescharacteristic
376C2C13×#219512yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#41D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×Q32C2semidirect
4. C2×C13×#362C2semidirect
5. C13×#2141C2semidirect
7. C13×#1382C2semidirect
75. #13322C13direct (N × H)
132. C22×Q32C2×C13semidirect
135. C2×#362C2×C13semidirect
136. #2141C2×C13semidirect
138. #1382C2×C13semidirect
319. C13#13322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×Q322
C2×C13×#4732
C13×#30592
C2×C13×#3622
C13×#21412
C2×C13×#3502
C13×#13822
#1332213