Finite Group Databasebeta

← C13×#13321 #15699660

Subgroups — C13×#13321 #15699660

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×SD32C211yesmaximal, characteristic, complemented
2C2×C13×#473C211yesmaximal, characteristic, complemented
3C13×#3058C211yesmaximal, characteristic
4C2×C13×#361C211yesmaximal, characteristic, complemented
5C13×#2141C211yesmaximal, characteristic, complemented
6C2×C13×#350C211yesmaximal, characteristic, complemented
7C13×#1382C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C22×C13×Q16C2211yescharacteristic
10C22×C13×D8C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C13×#535—21no—
13C2×C13×SD32—22no—
14C2×C13×SD32—22no—
15C2×C13×SD32—22no—
16C2×C13×M32C2211yescharacteristic
17C22×C13×C16C2211yescharacteristic
18C13×#473—22no—
19C13×#473—22no—
20C13×#469—22no—
21C13×#466—22no—
22C2×C13×#108C2211yescharacteristic
23C13×#427C2211yescharacteristic
24C13×#418—21no—
25C2×C13×#101—21no—
26C13×#361—22no—
27C13×#358—22no—
28C13×#350—22no—
29C2×C13×#41D411yescharacteristic
30C22×Q8×C13—21no—
31C22×D4×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—41no—
40C2×C13×Q16D412yescomplemented
41C2×C13×SD16—41no—
42C2×C13×D8—21no—
43C2×C13×D8—21no—
44C2×C13×D8—21no—
45C2×C13×D8—21no—
46C2×C13×D8—21no—
47C2×C13×D8D412yes—
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×#127—41no—
58C13×#124—41no—
59C13×#121—24no—
60C13×#120—42no—
61C13×#117—21no—
62C13×SD32—28no—
63C13×M32—21no—
64C13×M32—21no—
65C2×C13×C16—21no—
66C2×C13×C16—21no—
67C2×C13×C16—21no—
68C2×C13×C16D412yescomplemented
69C13×#108—21no—
70C13×#108D412yescomplemented
71C13×#107D412yes—
72C13×#106—21no—
73C13×#102—24no—
74C13×#101—24no—
75#13321C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13—41no—
77C13×#41—21no—
78C13×#41—21no—
79C13×#41—21no—
80C13×#41—21no—
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×C13D811yescharacteristic
88C2×D4×C13—21no—
89C2×D4×C13—22no—
90C2×D4×C13—44no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13D811yescharacteristic
97C22×C4×C13—21no—
98C22×C4×C13—41no—
99C22×C4×C13C2×D411yescharacteristic
100C13×Q16—22no—
101C13×Q16—22no—
102C13×Q16—44no—
103C13×Q16—41no—
104C13×Q16—41no—
105C13×SD16—44no—
106C13×D8—22no—
107C13×D8—22no—
108C13×D8—41no—
109C13×D8—41no—
110C13×M16—21no—
111C13×M16—22no—
112C13×M16—21no—
113C13×M16—41no—
114C13×M16—41no—
115C13×M16—41no—
116C2×C8×C13—21no—
117C2×C8×C13—41no—
118C2×C8×C13—41no—
119C2×C8×C13—41no—
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2×D411yescharacteristic
122C2×C8×C13C2×D411yescharacteristic
123C2×C8×C13C2×D411yescharacteristic
124C2×C8×C13C2×D411yescharacteristic
125C2×C8×C13#4111yescharacteristic
126C13×C4⋊C4—22no—
127C13×C22⋊C4—44no—
128C13×C22⋊C4—41no—
129C42×C13—41no—
130C13×C16—22no—
131C13×C16—41no—
132C22×SD32C2×C1311yescharacteristic, complemented
133C2×#473C2×C1311yescharacteristic, complemented
134#3058C2×C1311yescharacteristic
135C2×#361C2×C1311yescharacteristic, complemented
136#2141C2×C1311yescharacteristic, complemented
137C2×#350C2×C1311yescharacteristic, complemented
138#1382C2×C1311yescharacteristic, complemented
139C23×C13—21no—
140C23×C13—42no—
141C23×C13—81no—
142C23×C13—81no—
143C23×C13—162no—
144C23×C13AGL(1,ℤ/8)11yescharacteristic
145Q8×C13—21no—
146Q8×C13—21no—
147Q8×C13—42no—
148Q8×C13—42no—
149Q8×C13—81no—
150Q8×C13—81no—
151D4×C13—21no—
152D4×C13—21no—
153D4×C13—41no—
154D4×C13—41no—
155D4×C13—42no—
156D4×C13—42no—
157D4×C13—81no—
158D4×C13—81no—
159D4×C13—164no—
160C2×C4×C13—21no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12011yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13#13511yescharacteristic
172C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
173C8×C13—41no—
174C8×C13—42no—
175C8×C13#12011yescharacteristic
176C8×C13#12111yescharacteristic
177C8×C13#12111yescharacteristic
178C8×C13#12711yescharacteristic
179C2×#137—21no—
180C22×Q16C22×C1311yescharacteristic
181C22×D8C22×C1311yescharacteristic
182C2×#131C22×C1311yescharacteristic
183#535—21no—
184C2×SD32—22no—
185C2×SD32—22no—
186C2×SD32—22no—
187C2×M32C22×C1311yescharacteristic
188C22×C16C22×C1311yescharacteristic
189#473—22no—
190#473—22no—
191#469—22no—
192#466—22no—
193C2×#108C22×C1311yescharacteristic
194#427C22×C1311yescharacteristic
195#418—21no—
196C2×#101—21no—
197#361—22no—
198#358—22no—
199#350—22no—
200C22×C13—22no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—84no—
204C22×C13—82no—
205C22×C13—162no—
206C22×C13—162no—
207C22×C13#44711yescharacteristic
208C22×C13#44911yescharacteristic
209C22×C13#46911yescharacteristic
210C4×C13—41no—
211C4×C13—82no—
212C4×C13—82no—
213C4×C13#39211yescharacteristic
214C4×C13#44711yescharacteristic
215C4×C13#44911yescharacteristic
216C4×C13#46611yescharacteristic
217C2×#41D4×C1311yescharacteristic
218C22×Q8—21no—
219C22×D4—21no—
220#137—24no—
221#137—42no—
222C2×Q16—21no—
223C2×Q16—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—41no—
228C2×Q16D4×C1312yescomplemented
229C2×SD16—41no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8D4×C1312yes—
236#131—21no—
237#131—21no—
238#131—21no—
239#131—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16D4×C1311yescharacteristic
243C22×C8—21no—
244C22×C8C23×C1311yescharacteristic
245#127—41no—
246#124—41no—
247#121—24no—
248#120—42no—
249#117—21no—
250SD32—28no—
251M32—21no—
252M32—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16D4×C1312yescomplemented
257#108—21no—
258#108D4×C1312yescomplemented
259#107D4×C1312yes—
260#106—21no—
261#102—24no—
262#101—24no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13—81no—
266C2×C13—162no—
267C2×C13#199911yescharacteristic
268C2×C13#219412yes—
269C24—41no—
270#41—21no—
271#41—21no—
272#41—21no—
273#41—21no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8C13×D811yescharacteristic
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—44no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4C13×D811yescharacteristic
290C22×C4—21no—
291C22×C4—41no—
292C22×C4C2×D4×C1311yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—44no—
296Q16—41no—
297Q16—41no—
298SD16—44no—
299D8—22no—
300D8—22no—
301D8—41no—
302D8—41no—
303M16—21no—
304M16—22no—
305M16—21no—
306M16—41no—
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8C2×D4×C1311yescharacteristic
314C2×C8C2×D4×C1311yescharacteristic
315C2×C8C2×D4×C1311yescharacteristic
316C2×C8C2×D4×C1311yescharacteristic
317C2×C8C2×D4×C1311yescharacteristic
318C2×C8C13×#4111yescharacteristic
319C4⋊C4—22no—
320C22⋊C4—44no—
321C22⋊C4—41no—
322C42—41no—
323C16—22no—
324C16—41no—
325C13#1332111yescharacteristic, direct product factor, Sylow
326C23—21no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—162no—
331C23C13×AGL(1,ℤ/8)11yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—81no—
345D4—81no—
346D4—164no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4C13×#12011yescharacteristic
355C2×C4C13×#12011yescharacteristic
356C2×C4C13×#12111yescharacteristic
357C2×C4C2×C13×D811yescharacteristic
358C2×C4C13×#13511yescharacteristic
359C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
360C8—41no—
361C8—42no—
362C8C13×#12011yescharacteristic
363C8C13×#12111yescharacteristic
364C8C13×#12111yescharacteristic
365C8C13×#12711yescharacteristic
366C22—22no—
367C22—41no—
368C22—42no—
369C22—82no—
370C22—84no—
371C22—162no—
372C22—162no—
373C22C13×#44711yescharacteristic
374C22C13×#44911yescharacteristic
375C22C13×#46911yescharacteristic
376C4—41no—
377C4—82no—
378C4—82no—
379C4C13×#39211yescharacteristic
380C4C13×#44711yescharacteristic
381C4C13×#44911yescharacteristic
382C4C13×#46611yescharacteristic
383C2—21no—
384C2—21no—
385C2—81no—
386C2—162no—
387C2C13×#199911yescharacteristic
388C2C13×#219412yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3058C2
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×SD32C2semidirect
2. C2×C13×#473C2semidirect
4. C2×C13×#361C2semidirect
5. C13×#2141C2semidirect
6. C2×C13×#350C2semidirect
7. C13×#1382C2semidirect
40. C2×C13×Q16D4semidirect
68. C2×C13×C16D4semidirect
70. C13×#108D4semidirect
75. #13321C13direct (N × H)
132. C22×SD32C2×C13semidirect
133. C2×#473C2×C13semidirect
135. C2×#361C2×C13semidirect
136. #2141C2×C13semidirect
137. C2×#350C2×C13semidirect
138. #1382C2×C13semidirect
228. C2×Q16D4×C13semidirect
256. C2×C16D4×C13semidirect
258. #108D4×C13semidirect
325. C13#13321direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×SD322
C2×C13×#4732
C13×#30582
C2×C13×#3612
C13×#21412
C2×C13×#3502
C13×#13822
#1332113