Finite Group Databasebeta

← C13×#13072 #15699411

Subgroups — C13×#13072 #15699411

Order 3328.

458 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#504C211yesmaximal, characteristic
2C2×C13×#473C211yesmaximal, characteristic
3C2×C13×#362C211yesmaximal, characteristic, complemented
4C2×C13×#358C211yesmaximal, characteristic, complemented
5C13×#1816C211yesmaximal, characteristic
6C13×#1387C211yesmaximal, characteristic, complemented
7C13×#1381C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C22×C13×Q16C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C13×#504—22no—
12C13×#504—22no—
13C2×C13×M32—21no—
14C2×C13×M32C2211yescharacteristic
15C22×C13×C16—21no—
16C22×C13×C16C2211yescharacteristic
17C13×#473—22no—
18C13×#473C414yescomplemented
19C2×C13×#108C2211yescharacteristic
20C2×C13×#108C2211yescharacteristic
21C2×C13×#107C2211yescharacteristic
22C13×#417—21no—
23C2×C13×#101—21no—
24C13×#362—22no—
25C13×#358—21no—
26C13×#358—21no—
27C13×#343—21no—
28C2×C13×#41D411yescharacteristic
29C22×Q8×C13—21no—
30C13×#137—24no—
31C13×#137—42no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16—41no—
38C2×C13×Q16C2×C412yes—
39C2×C13×SD16—41no—
40C13×#131—21no—
41C13×#131—21no—
42C13×#131C2×C412yes—
43C13×#131D412yes—
44C2×C13×M16—21no—
45C2×C13×M16—21no—
46C2×C13×M16—21no—
47C2×C13×M16D411yescharacteristic
48C22×C8×C13—21no—
49C22×C8×C13C2311yescharacteristic
50C2×C13×C4⋊C4—21no—
51C13×M32—24no—
52C13×M32—21no—
53C13×M32D412yes—
54C2×C13×C16—24no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C2×C13×C16D411yescharacteristic
59C2×C13×C16D411yescharacteristic
60C13×#108—21no—
61C13×#108—21no—
62C13×#108—21no—
63C13×#108C2×C412yes—
64C13×#107—21no—
65C13×#107—21no—
66C13×#103—41no—
67C13×#102—41no—
68C13×#101—24no—
69#13072C1311yesmaximal, characteristic, direct product factor, Sylow
70C13×#41—21no—
71C13×#41—21no—
72C13×#41C22⋊C412yes—
73C13×#41SD1612yes—
74C2×Q8×C13—22no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13D811yescharacteristic
81C2×D4×C13—21no—
82C2×D4×C13D811yescharacteristic
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C13×Q16—22no—
88C13×Q16—22no—
89C13×Q16—44no—
90C13×Q16—41no—
91C13×Q16—41no—
92C13×SD16—44no—
93C13×M16—21no—
94C13×M16—22no—
95C13×M16—22no—
96C13×M16—22no—
97C13×M16—41no—
98C13×M16—41no—
99C13×M16—41no—
100C13×M16C22⋊C412yes—
101C2×C8×C13—21no—
102C2×C8×C13—22no—
103C2×C8×C13—22no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13C22×C411yescharacteristic
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13#4111yescharacteristic
111C2×C8×C13#4111yescharacteristic
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C16—21no—
115C13×C16—22no—
116C13×C16—21no—
117C2×#504C2×C1311yescharacteristic
118C2×#473C2×C1311yescharacteristic
119C2×#362C2×C1311yescharacteristic, complemented
120C2×#358C2×C1311yescharacteristic, complemented
121#1816C2×C1311yescharacteristic
122#1387C2×C1311yescharacteristic, complemented
123#1381C2×C1311yescharacteristic, complemented
124C23×C13—21no—
125C23×C13#13511yescharacteristic
126Q8×C13—21no—
127Q8×C13—42no—
128Q8×C13—42no—
129Q8×C13—81no—
130Q8×C13—81no—
131Q8×C13#10212yes—
132D4×C13—22no—
133D4×C13—22no—
134D4×C13—21no—
135D4×C13#10212yes—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—42no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—161no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13C2×D811yescharacteristic
148C2×C4×C13C2×SD1611yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C8×C13—22no—
151C8×C13—42no—
152C8×C13—81no—
153C8×C13C4×D411yescharacteristic
154C8×C13C4×D411yescharacteristic
155C8×C13#12011yescharacteristic
156C8×C13#12311yescharacteristic
157C2×#137—21no—
158C22×Q16C22×C1311yescharacteristic
159C2×#131C22×C1311yescharacteristic
160#504—22no—
161#504—22no—
162C2×M32—21no—
163C2×M32C22×C1311yescharacteristic
164C22×C16—21no—
165C22×C16C22×C1311yescharacteristic
166#473—22no—
167#473C4×C1314yescomplemented
168C2×#108C22×C1311yescharacteristic
169C2×#108C22×C1311yescharacteristic
170C2×#107C22×C1311yescharacteristic
171#417—21no—
172C2×#101—21no—
173#362—22no—
174#358—21no—
175#358—21no—
176#343—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13#41611yescharacteristic
183C22×C13#46511yescharacteristic
184C22×C13#46611yescharacteristic
185C4×C13—22no—
186C4×C13—82no—
187C4×C13—161no—
188C4×C13#38611yescharacteristic
189C4×C13C2×#10211yescharacteristic
190C4×C13#46511yescharacteristic
191C4×C13#46611yescharacteristic
192C2×#41D4×C1311yescharacteristic
193C22×Q8—21no—
194#137—24no—
195#137—42no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—41no—
202C2×Q16C2×C4×C1312yes—
203C2×SD16—41no—
204#131—21no—
205#131—21no—
206#131C2×C4×C1312yes—
207#131D4×C1312yes—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—21no—
211C2×M16D4×C1311yescharacteristic
212C22×C8—21no—
213C22×C8C23×C1311yescharacteristic
214C2×C4⋊C4—21no—
215M32—24no—
216M32—21no—
217M32D4×C1312yes—
218C2×C16—24no—
219C2×C16—21no—
220C2×C16—21no—
221C2×C16—21no—
222C2×C16D4×C1311yescharacteristic
223C2×C16D4×C1311yescharacteristic
224#108—21no—
225#108—21no—
226#108—21no—
227#108C2×C4×C1312yes—
228#107—21no—
229#107—21no—
230#103—41no—
231#102—41no—
232#101—24no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—42no—
236C2×C13#189311yescharacteristic
237C2×C13#222211yescharacteristic
238C2×C13#222311yescharacteristic
239#41—21no—
240#41—21no—
241#41C13×C22⋊C412yes—
242#41C13×SD1612yes—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8C13×D811yescharacteristic
250C2×D4—21no—
251C2×D4C13×D811yescharacteristic
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C2×D4×C1311yescharacteristic
256Q16—22no—
257Q16—22no—
258Q16—44no—
259Q16—41no—
260Q16—41no—
261SD16—44no—
262M16—21no—
263M16—22no—
264M16—22no—
265M16—22no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16C13×C22⋊C412yes—
270C2×C8—21no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8C22×C4×C1311yescharacteristic
276C2×C8C2×D4×C1311yescharacteristic
277C2×C8C2×D4×C1311yescharacteristic
278C2×C8C2×D4×C1311yescharacteristic
279C2×C8C13×#4111yescharacteristic
280C2×C8C13×#4111yescharacteristic
281C4⋊C4—41no—
282C4⋊C4—41no—
283C16—21no—
284C16—22no—
285C16—21no—
286C13#1307211yescharacteristic, direct product factor, Sylow
287C23—21no—
288C23C13×#13511yescharacteristic
289Q8—21no—
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8C13×#10212yes—
295D4—22no—
296D4—22no—
297D4—21no—
298D4C13×#10212yes—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—161no—
307C2×C4C2×C13×C22⋊C411yescharacteristic
308C2×C4C13×#12111yescharacteristic
309C2×C4C13×#12111yescharacteristic
310C2×C4C2×C13×D811yescharacteristic
311C2×C4C2×C13×SD1611yescharacteristic
312C2×C4C13×#13511yescharacteristic
313C8—22no—
314C8—42no—
315C8—81no—
316C8C4×D4×C1311yescharacteristic
317C8C4×D4×C1311yescharacteristic
318C8C13×#12011yescharacteristic
319C8C13×#12311yescharacteristic
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22C13×#41611yescharacteristic
326C22C13×#46511yescharacteristic
327C22C13×#46611yescharacteristic
328C4—22no—
329C4—82no—
330C4—161no—
331C4C13×#38611yescharacteristic
332C4C2×C13×#10211yescharacteristic
333C4C13×#46511yescharacteristic
334C4C13×#46611yescharacteristic
335C2—21no—
336C2—21no—
337C2—42no—
338C2C13×#189311yescharacteristic
339C2C13×#222211yescharacteristic
340C2C13×#222311yescharacteristic
subgroupG/H
center, socleC22×C13#466
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#41D4
LCSG ▷ C2×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
3. C2×C13×#362C2semidirect
4. C2×C13×#358C2semidirect
6. C13×#1387C2semidirect
7. C13×#1381C2semidirect
18. C13×#473C4semidirect
69. #13072C13direct (N × H)
119. C2×#362C2×C13semidirect
120. C2×#358C2×C13semidirect
122. #1387C2×C13semidirect
123. #1381C2×C13semidirect
167. #473C4×C13semidirect
286. C13#13072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5042
C2×C13×#4732
C2×C13×#3622
C2×C13×#3582
C13×#18162
C13×#13872
C13×#13812
#1307213