Finite Group Databasebeta

← C13×#13028 #15699367

Subgroups — C13×#13028 #15699367

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#510C211yesmaximal, characteristic
2C2×C13×#443C211yesmaximal, characteristic
3C2×C13×#362C211yesmaximal, characteristic, complemented
4C13×#2139C211yesmaximal, characteristic
5C13×#1969C211yesmaximal, characteristic, complemented
6C13×#1387C211yesmaximal, characteristic, complemented
7C13×#1376C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×Q16C2211yescharacteristic
10C2×C13×#131—21no—
11C13×#510—22no—
12C13×#510C414yescomplemented
13C2×C13×Q32—21no—
14C2×C13×SD32—21no—
15C2×C13×M32C2211yescharacteristic
16C2×C13×M32C2211yescharacteristic
17C13×#443—22no—
18C13×#443—22no—
19C2×C13×#108C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#104—21no—
22C2×C13×#103—21no—
23C2×C4×C8×C13C2211yescharacteristic
24C13×#391—21no—
25C13×#362—22no—
26C13×#358—21no—
27C13×#357—21no—
28C2×C13×#41—21no—
29C22×Q8×C13—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135C2×C412yes—
33C13×#135D412yes—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16—21no—
38C2×C13×Q16—21no—
39C2×C13×Q16C2×C412yes—
40C2×C13×Q16D411yescharacteristic
41C2×C13×SD16—21no—
42C2×C13×D8D411yescharacteristic
43C13×#131—24no—
44C13×#131—42no—
45C2×C13×M16—21no—
46C2×C13×M16—41no—
47C22×C8×C13—41no—
48C22×C8×C13D411yescharacteristic
49C22×C8×C13C2311yescharacteristic
50C2×C13×C4⋊C4—21no—
51C2×C42×C13D411yescharacteristic
52C13×Q32—24no—
53C13×SD32—24no—
54C13×M32—21no—
55C13×M32—21no—
56C13×M32—21no—
57C13×M32C2×C412yes—
58C2×C13×C16—21no—
59C2×C13×C16—21no—
60C13×#108—21no—
61C13×#108D412yes—
62C13×#107—21no—
63C13×#107—21no—
64C13×#104—24no—
65C13×#103—41no—
66C13×#103—41no—
67C4×C8×C13—21no—
68C4×C8×C13—21no—
69C13×#95—42no—
70#13028C1311yesmaximal, characteristic, direct product factor, Sylow
71C13×#41—22no—
72C13×#41—22no—
73C13×#41—41no—
74C13×#41—41no—
75C2×Q8×C13—22no—
76C2×Q8×C13—21no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13C2×D411yescharacteristic
89C13×Q16—22no—
90C13×Q16—22no—
91C13×Q16—21no—
92C13×Q16—41no—
93C13×Q16—41no—
94C13×Q16C22⋊C412yes—
95C13×SD16—22no—
96C13×SD16—22no—
97C13×D8—21no—
98C13×D8C22⋊C412yes—
99C13×M16—22no—
100C13×M16—44no—
101C13×M16—41no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—44no—
105C2×C8×C13—41no—
106C2×C8×C13D811yescharacteristic
107C2×C8×C13D811yescharacteristic
108C2×C8×C13C22×C411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13#4111yescharacteristic
113C2×C8×C13#4111yescharacteristic
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C42×C13—21no—
117C42×C13—21no—
118C13×C16—22no—
119C13×C16—41no—
120C2×#510C2×C1311yescharacteristic
121C2×#443C2×C1311yescharacteristic
122C2×#362C2×C1311yescharacteristic, complemented
123#2139C2×C1311yescharacteristic
124#1969C2×C1311yescharacteristic, complemented
125#1387C2×C1311yescharacteristic, complemented
126#1376C2×C1311yescharacteristic, complemented
127C23×C13—41no—
128C23×C13AGL(1,ℤ/8)11yescharacteristic
129Q8×C13—22no—
130Q8×C13—41no—
131Q8×C13—42no—
132Q8×C13—42no—
133Q8×C13—81no—
134Q8×C13—81no—
135D4×C13—22no—
136D4×C13—42no—
137D4×C13—42no—
138D4×C13—41no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—82no—
149C2×C4×C13—81no—
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13#13511yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C8×C13—21no—
157C8×C13—21no—
158C8×C13—42no—
159C8×C13C2×C22⋊C411yescharacteristic
160C8×C13C4×D411yescharacteristic
161C8×C13#12111yescharacteristic
162C8×C13#12311yescharacteristic
163C2×#135C22×C1311yescharacteristic
164C22×Q16C22×C1311yescharacteristic
165C2×#131—21no—
166#510—22no—
167#510C4×C1314yescomplemented
168C2×Q32—21no—
169C2×SD32—21no—
170C2×M32C22×C1311yescharacteristic
171C2×M32C22×C1311yescharacteristic
172#443—22no—
173#443—22no—
174C2×#108C22×C1311yescharacteristic
175C2×#107C22×C1311yescharacteristic
176C2×#104—21no—
177C2×#103—21no—
178C2×C4×C8C22×C1311yescharacteristic
179#391—21no—
180#362—22no—
181#358—21no—
182#357—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—42no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#44211yescharacteristic
189C22×C13#44911yescharacteristic
190C22×C13#45911yescharacteristic
191C4×C13—42no—
192C4×C13—42no—
193C4×C13—82no—
194C4×C13—161no—
195C4×C13#38611yescharacteristic
196C4×C13C4×D811yescharacteristic
197C4×C13#44711yescharacteristic
198C4×C13#46311yescharacteristic
199C2×#41—21no—
200C22×Q8—21no—
201#135—21no—
202#135—21no—
203#135C2×C4×C1312yes—
204#135D4×C1312yes—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16C2×C4×C1312yes—
211C2×Q16D4×C1311yescharacteristic
212C2×SD16—21no—
213C2×D8D4×C1311yescharacteristic
214#131—24no—
215#131—42no—
216C2×M16—21no—
217C2×M16—41no—
218C22×C8—41no—
219C22×C8D4×C1311yescharacteristic
220C22×C8C23×C1311yescharacteristic
221C2×C4⋊C4—21no—
222C2×C42D4×C1311yescharacteristic
223Q32—24no—
224SD32—24no—
225M32—21no—
226M32—21no—
227M32—21no—
228M32C2×C4×C1312yes—
229C2×C16—21no—
230C2×C16—21no—
231#108—21no—
232#108D4×C1312yes—
233#107—21no—
234#107—21no—
235#104—24no—
236#103—41no—
237#103—41no—
238C4×C8—21no—
239C4×C8—21no—
240#95—42no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13—82no—
244C2×C13#187911yescharacteristic
245C2×C13#221211yescharacteristic
246C2×C13#221411yescharacteristic
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—22no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C1311yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—21no—
268Q16—41no—
269Q16—41no—
270Q16C13×C22⋊C412yes—
271SD16—22no—
272SD16—22no—
273D8—21no—
274D8C13×C22⋊C412yes—
275M16—22no—
276M16—44no—
277M16—41no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—44no—
281C2×C8—41no—
282C2×C8C13×D811yescharacteristic
283C2×C8C13×D811yescharacteristic
284C2×C8C22×C4×C1311yescharacteristic
285C2×C8C2×D4×C1311yescharacteristic
286C2×C8C2×D4×C1311yescharacteristic
287C2×C8C2×D4×C1311yescharacteristic
288C2×C8C13×#4111yescharacteristic
289C2×C8C13×#4111yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—41no—
292C42—21no—
293C42—21no—
294C16—22no—
295C16—41no—
296C13#1302811yescharacteristic, direct product factor, Sylow
297C23—41no—
298C23C13×AGL(1,ℤ/8)11yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—81no—
304Q8—81no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—81no—
320C2×C4C4×D4×C1311yescharacteristic
321C2×C4C13×#12011yescharacteristic
322C2×C4C13×#12111yescharacteristic
323C2×C4C2×C13×D811yescharacteristic
324C2×C4C13×#13511yescharacteristic
325C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8C2×C13×C22⋊C411yescharacteristic
330C8C4×D4×C1311yescharacteristic
331C8C13×#12111yescharacteristic
332C8C13×#12311yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22C13×#44211yescharacteristic
339C22C13×#44911yescharacteristic
340C22C13×#45911yescharacteristic
341C4—42no—
342C4—42no—
343C4—82no—
344C4—161no—
345C4C13×#38611yescharacteristic
346C4C4×C13×D811yescharacteristic
347C4C13×#44711yescharacteristic
348C4C13×#46311yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2C13×#187911yescharacteristic
353C2C13×#221211yescharacteristic
354C2C13×#221411yescharacteristic
subgroupG/H
center, socleC22×C13#459
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#362C2semidirect
5. C13×#1969C2semidirect
6. C13×#1387C2semidirect
7. C13×#1376C2semidirect
12. C13×#510C4semidirect
70. #13028C13direct (N × H)
122. C2×#362C2×C13semidirect
124. #1969C2×C13semidirect
125. #1387C2×C13semidirect
126. #1376C2×C13semidirect
167. #510C4×C13semidirect
296. C13#13028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5102
C2×C13×#4432
C2×C13×#3622
C13×#21392
C13×#19692
C13×#13872
C13×#13762
#1302813