Finite Group Databasebeta

← C13×#19265 #15705604

Subgroups — C13×#19265 #15705604

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3170C211yesmaximal, characteristic
2C13×#3113C212yesmaximal
3C2×C8×Q8×C13C211yesmaximal, characteristic
4C13×#1680C214yesmaximal, complemented
5C13×#1674C212yesmaximal, complemented
6C13×#1670C212yesmaximal, complemented
7C13×#1568C211yesmaximal, characteristic
8C13×#1552C212yesmaximal
9C13×#533C2212yes—
10C2×C4×Q8×C13C2211yescharacteristic
11C13×#500C2211yescharacteristic
12C13×#494C2211yescharacteristic
13C13×#487C2212yes—
14C13×#483—22no—
15C13×#475C2214yes—
16C13×#467—21no—
17C13×#467—21no—
18C13×#462C2214yes—
19C13×#451—22no—
20C8×Q8×C13—21no—
21C8×Q8×C13—21no—
22C8×Q8×C13C2212yes—
23C8×Q8×C13C2212yes—
24C13×#441—24no—
25C4×C13×Q16—21no—
26C4×C13×Q16—21no—
27C13×#432C2212yes—
28C2×C13×C4⋊C8—21no—
29C2×C13×C4⋊C8C2211yescharacteristic
30C2×C4×C8×C13—21no—
31C2×C4×C8×C13C2211yescharacteristic
32C13×#335C2212yes—
33C13×#334C2212yes—
34C13×#332C2214yes—
35C13×#332C2214yes—
36C22×Q8×C13D411yescharacteristic
37C2×C13×Q16—24no—
38C2×C13×Q16—21no—
39C2×C13×Q16—21no—
40C22×C8×C13—21no—
41C22×C8×C13D411yescharacteristic
42C22×C8×C13D411yescharacteristic
43C13×C4⋊Q8C2312yes—
44C13×C4⋊Q8C2312yes—
45C13×#125—22no—
46C13×C22⋊Q8—22no—
47C13×C22⋊Q8—22no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—22no—
51C4×Q8×C13—22no—
52C4×Q8×C13D412yes—
53C4×Q8×C13C2312yes—
54C13×#117—22no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59C13×#107—21no—
60C13×#107—21no—
61C13×#106—24no—
62C13×C4⋊C8—22no—
63C13×C4⋊C8—22no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8C2312yes—
66C13×C4⋊C8C2314yes—
67C13×#103—24no—
68C13×#103—22no—
69C13×#103—22no—
70C13×#103—24no—
71C13×C22⋊C8—22no—
72C13×#97—22no—
73C4×C8×C13—22no—
74C4×C8×C13—22no—
75C4×C8×C13D411yescharacteristic
76C4×C8×C13D411yescharacteristic
77C4×C8×C13C2311yescharacteristic
78C4×C8×C13C2311yescharacteristic
79#19265C1311yesmaximal, characteristic, direct product factor, Sylow
80C2×Q8×C13—24no—
81C2×Q8×C13—21no—
82C2×Q8×C13—22no—
83C2×Q8×C13—22no—
84C2×Q8×C13C2×D412yes—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13#4111yescharacteristic
90C13×Q16—42no—
91C13×Q16—48no—
92C13×Q16—42no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—24no—
96C2×C8×C13—41no—
97C2×C8×C13—42no—
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C13×C4⋊C4—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4C2×D412yes—
112C13×C22⋊C4—42no—
113C42×C13—22no—
114C42×C13—22no—
115C42×C13—42no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13C2411yescharacteristic
120#3170C2×C1311yescharacteristic
121#3113C2×C1312yes—
122C2×C8×Q8C2×C1311yescharacteristic
123#1680C2×C1314yescomplemented
124#1674C2×C1312yescomplemented
125#1670C2×C1312yescomplemented
126#1568C2×C1311yescharacteristic
127#1552C2×C1312yes—
128C23×C13#12111yescharacteristic
129Q8×C13—24no—
130Q8×C13—22no—
131Q8×C13—44no—
132Q8×C13—42no—
133Q8×C13—42no—
134Q8×C13#13514yes—
135C2×C4×C13—24no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13C22×D411yescharacteristic
149C2×C4×C13C22×D411yescharacteristic
150C2×C4×C13C2×#4111yescharacteristic
151C8×C13—21no—
152C8×C13—21no—
153C8×C13—21no—
154C8×C13—44no—
155C8×C13—42no—
156C8×C13#13712yes—
157#533C22×C1312yes—
158C2×C4×Q8C22×C1311yescharacteristic
159#500C22×C1311yescharacteristic
160#494C22×C1311yescharacteristic
161#487C22×C1312yes—
162#483—22no—
163#475C22×C1314yes—
164#467—21no—
165#467—21no—
166#462C22×C1314yes—
167#451—22no—
168C8×Q8—21no—
169C8×Q8—21no—
170C8×Q8C22×C1312yes—
171C8×Q8C22×C1312yes—
172#441—24no—
173C4×Q16—21no—
174C4×Q16—21no—
175#432C22×C1312yes—
176C2×C4⋊C8—21no—
177C2×C4⋊C8C22×C1311yescharacteristic
178C2×C4×C8—21no—
179C2×C4×C8C22×C1311yescharacteristic
180#335C22×C1312yes—
181#334C22×C1312yes—
182#332C22×C1314yes—
183#332C22×C1314yes—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13#47312yes—
187C22×C13C2×#12111yescharacteristic
188C4×C13—21no—
189C4×C13—24no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—42no—
194C4×C13—82no—
195C4×C13—82no—
196C4×C13C2×#13512yes—
197C4×C13C2×#13711yescharacteristic
198C4×C13#57511yescharacteristic
199C22×Q8D4×C1311yescharacteristic
200C2×Q16—24no—
201C2×Q16—21no—
202C2×Q16—21no—
203C22×C8—21no—
204C22×C8D4×C1311yescharacteristic
205C22×C8D4×C1311yescharacteristic
206C4⋊Q8C23×C1312yes—
207C4⋊Q8C23×C1312yes—
208#125—22no—
209C22⋊Q8—22no—
210C22⋊Q8—22no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8D4×C1312yes—
216C4×Q8C23×C1312yes—
217#117—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4×C1311yescharacteristic
220C2×C42—21no—
221C2×C42C23×C1311yescharacteristic
222#107—21no—
223#107—21no—
224#106—24no—
225C4⋊C8—22no—
226C4⋊C8—22no—
227C4⋊C8—21no—
228C4⋊C8C23×C1312yes—
229C4⋊C8C23×C1314yes—
230#103—24no—
231#103—22no—
232#103—22no—
233#103—24no—
234C22⋊C8—22no—
235#97—22no—
236C4×C8—22no—
237C4×C8—22no—
238C4×C8D4×C1311yescharacteristic
239C4×C8D4×C1311yescharacteristic
240C4×C8C23×C1311yescharacteristic
241C4×C8C23×C1311yescharacteristic
242C2×C13—22no—
243C2×C13#303711yescharacteristic
244C2×C13#305011yescharacteristic
245C2×C13C2×#47311yescharacteristic
246C2×Q8—24no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—22no—
250C2×Q8C2×D4×C1312yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4×C1311yescharacteristic
254C22×C4C2×D4×C1311yescharacteristic
255C22×C4C13×#4111yescharacteristic
256Q16—42no—
257Q16—48no—
258Q16—42no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—24no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8C2×D4×C1311yescharacteristic
265C2×C8C2×D4×C1311yescharacteristic
266C2×C8C2×D4×C1311yescharacteristic
267C2×C8C2×D4×C1311yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4C2×D4×C1312yes—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42C2×D4×C1311yescharacteristic
283C42C2×D4×C1311yescharacteristic
284C42C13×#4111yescharacteristic
285C42C24×C1311yescharacteristic
286C13#1926511yescharacteristic, direct product factor, Sylow
287C23C13×#12111yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—44no—
291Q8—42no—
292Q8—42no—
293Q8C13×#13514yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4C13×#12111yescharacteristic
305C2×C4C13×#12111yescharacteristic
306C2×C4C13×#12111yescharacteristic
307C2×C4C22×D4×C1311yescharacteristic
308C2×C4C22×D4×C1311yescharacteristic
309C2×C4C2×C13×#4111yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8—44no—
314C8—42no—
315C8C13×#13712yes—
316C22—21no—
317C22—21no—
318C22C13×#47312yes—
319C22C2×C13×#12111yescharacteristic
320C4—21no—
321C4—24no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—82no—
327C4—82no—
328C4C2×C13×#13512yes—
329C4C2×C13×#13711yescharacteristic
330C4C13×#57511yescharacteristic
331C2—22no—
332C2C13×#303711yescharacteristic
333C2C13×#305011yescharacteristic
334C2C2×C13×#47311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#121
commutator, Frattini, cosocleC42C24×C13
prime radicalC23×C13#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1680C2semidirect
5. C13×#1674C2semidirect
6. C13×#1670C2semidirect
79. #19265C13direct (N × H)
123. #1680C2×C13semidirect
124. #1674C2×C13semidirect
125. #1670C2×C13semidirect
286. C13#19265direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31702
C13×#31132
C2×C8×Q8×C132
C13×#16802
C13×#16742
C13×#16702
C13×#15682
C13×#15522
#1926513