Finite Group Databasebeta

← C13×#19150 #15705489

Subgroups — C13×#19150 #15705489

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3160C211yesmaximal, characteristic
2C13×#3104C212yesmaximal
3C2×C13×#446C211yesmaximal, characteristic
4C13×#1696C212yesmaximal, complemented
5C13×#1694C212yesmaximal, complemented
6C13×#1692C214yesmaximal, complemented
7C13×#1564C211yesmaximal, characteristic
8C13×#1542C212yesmaximal
9C13×#533C2212yes—
10C2×C4×Q8×C13C2211yescharacteristic
11C13×#500C2211yescharacteristic
12C13×#500C2211yescharacteristic
13C13×#499—21no—
14C13×#499—21no—
15C13×#498C2212yes—
16C13×#484—22no—
17C13×#477C2214yes—
18C13×#462C2214yes—
19C13×#451—22no—
20C13×#446—21no—
21C13×#446—21no—
22C13×#446C2212yes—
23C13×#446C2212yes—
24C4×C13×Q16—24no—
25C13×#431C2212yes—
26C13×#427—21no—
27C13×#427—21no—
28C2×C13×C4⋊C8—21no—
29C2×C13×C4⋊C8C2211yescharacteristic
30C2×C13×#97—21no—
31C2×C4×C8×C13C2211yescharacteristic
32C13×#335C2212yes—
33C13×#334C2212yes—
34C13×#333C2214yes—
35C13×#332C2214yes—
36C22×Q8×C13D411yescharacteristic
37C2×C13×Q16—24no—
38C22×C8×C13—21no—
39C22×C8×C13D411yescharacteristic
40C22×C8×C13D411yescharacteristic
41C13×C4⋊Q8C2312yes—
42C13×C4⋊Q8C2312yes—
43C13×#125—22no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—22no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—22no—
49C4×Q8×C13—22no—
50C4×Q8×C13D412yes—
51C4×Q8×C13C2312yes—
52C13×#117—22no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C42×C13—21no—
56C2×C42×C13C2311yescharacteristic
57C13×#107—21no—
58C13×#107—21no—
59C13×#107—21no—
60C13×#107—21no—
61C13×#107—24no—
62C13×#106—22no—
63C13×#106—22no—
64C13×C4⋊C8—22no—
65C13×C4⋊C8—22no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8C2312yes—
68C13×C4⋊C8C2314yes—
69C13×#103—24no—
70C13×#103—24no—
71C13×C22⋊C8—22no—
72C13×#97—22no—
73C13×#97—22no—
74C4×C8×C13—22no—
75C4×C8×C13D411yescharacteristic
76C4×C8×C13D411yescharacteristic
77C4×C8×C13C2311yescharacteristic
78C4×C8×C13C2311yescharacteristic
79#19150C1311yesmaximal, characteristic, direct product factor, Sylow
80C2×Q8×C13—21no—
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13—42no—
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—48no—
91C2×C8×C13—22no—
92C2×C8×C13—24no—
93C2×C8×C13—22no—
94C2×C8×C13—42no—
95C2×C8×C13Q1614yescomplemented
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C13×C4⋊C4—22no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4C2×D412yes—
110C13×C22⋊C4—42no—
111C42×C13—22no—
112C42×C13—22no—
113C42×C13—42no—
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13#4111yescharacteristic
117C42×C13C2411yescharacteristic
118#3160C2×C1311yescharacteristic
119#3104C2×C1312yes—
120C2×#446C2×C1311yescharacteristic
121#1696C2×C1312yescomplemented
122#1694C2×C1312yescomplemented
123#1692C2×C1314yescomplemented
124#1564C2×C1311yescharacteristic
125#1542C2×C1312yes—
126C23×C13#12111yescharacteristic
127Q8×C13—24no—
128Q8×C13—42no—
129Q8×C13—44no—
130Q8×C13—82no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13C2×Q1612yes—
143C2×C4×C13#13712yes—
144C2×C4×C13C22×D411yescharacteristic
145C2×C4×C13C22×D411yescharacteristic
146C2×C4×C13C2×#4111yescharacteristic
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—42no—
150C8×C13—44no—
151C8×C13C2×Q1612yes—
152C8×C13C2×Q1612yes—
153#533C22×C1312yes—
154C2×C4×Q8C22×C1311yescharacteristic
155#500C22×C1311yescharacteristic
156#500C22×C1311yescharacteristic
157#499—21no—
158#499—21no—
159#498C22×C1312yes—
160#484—22no—
161#477C22×C1314yes—
162#462C22×C1314yes—
163#451—22no—
164#446—21no—
165#446—21no—
166#446C22×C1312yes—
167#446C22×C1312yes—
168C4×Q16—24no—
169#431C22×C1312yes—
170#427—21no—
171#427—21no—
172C2×C4⋊C8—21no—
173C2×C4⋊C8C22×C1311yescharacteristic
174C2×#97—21no—
175C2×C4×C8C22×C1311yescharacteristic
176#335C22×C1312yes—
177#334C22×C1312yes—
178#333C22×C1314yes—
179#332C22×C1314yes—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13#46212yes—
183C22×C13C2×#12111yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13—42no—
189C4×C13—82no—
190C4×C13—82no—
191C4×C13#46212yes—
192C4×C13C22×Q1611yescharacteristic
193C4×C13C2×#13711yescharacteristic
194C4×C13#57512yes—
195C22×Q8D4×C1311yescharacteristic
196C2×Q16—24no—
197C22×C8—21no—
198C22×C8D4×C1311yescharacteristic
199C22×C8D4×C1311yescharacteristic
200C4⋊Q8C23×C1312yes—
201C4⋊Q8C23×C1312yes—
202#125—22no—
203C22⋊Q8—22no—
204C22⋊Q8—22no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8D4×C1312yes—
210C4×Q8C23×C1312yes—
211#117—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4D4×C1311yescharacteristic
214C2×C42—21no—
215C2×C42C23×C1311yescharacteristic
216#107—21no—
217#107—21no—
218#107—21no—
219#107—21no—
220#107—24no—
221#106—22no—
222#106—22no—
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—21no—
226C4⋊C8C23×C1312yes—
227C4⋊C8C23×C1314yes—
228#103—24no—
229#103—24no—
230C22⋊C8—22no—
231#97—22no—
232#97—22no—
233C4×C8—22no—
234C4×C8D4×C1311yescharacteristic
235C4×C8D4×C1311yescharacteristic
236C4×C8C23×C1311yescharacteristic
237C4×C8C23×C1311yescharacteristic
238C2×C13—22no—
239C2×C13C2×#46211yescharacteristic
240C2×C13#305411yescharacteristic
241C2×C13#306711yescharacteristic
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—42no—
246C2×Q8C2×D4×C1312yes—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4C2×D4×C1311yescharacteristic
250C22×C4C2×D4×C1311yescharacteristic
251C22×C4C13×#4111yescharacteristic
252Q16—48no—
253C2×C8—22no—
254C2×C8—24no—
255C2×C8—22no—
256C2×C8—42no—
257C2×C8C13×Q1614yescomplemented
258C2×C8C2×D4×C1311yescharacteristic
259C2×C8C2×D4×C1311yescharacteristic
260C2×C8C2×D4×C1311yescharacteristic
261C2×C8C2×D4×C1311yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4C2×D4×C1312yes—
272C22⋊C4—42no—
273C42—22no—
274C42—22no—
275C42—42no—
276C42C2×D4×C1311yescharacteristic
277C42C2×D4×C1311yescharacteristic
278C42C13×#4111yescharacteristic
279C42C24×C1311yescharacteristic
280C13#1915011yescharacteristic, direct product factor, Sylow
281C23C13×#12111yescharacteristic
282Q8—24no—
283Q8—42no—
284Q8—44no—
285Q8—82no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4C13×#12111yescharacteristic
295C2×C4C13×#12111yescharacteristic
296C2×C4C13×#12111yescharacteristic
297C2×C4C2×C13×Q1612yes—
298C2×C4C13×#13712yes—
299C2×C4C22×D4×C1311yescharacteristic
300C2×C4C22×D4×C1311yescharacteristic
301C2×C4C2×C13×#4111yescharacteristic
302C8—21no—
303C8—21no—
304C8—42no—
305C8—44no—
306C8C2×C13×Q1612yes—
307C8C2×C13×Q1612yes—
308C22—21no—
309C22—21no—
310C22C13×#46212yes—
311C22C2×C13×#12111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—82no—
318C4—82no—
319C4C13×#46212yes—
320C4C22×C13×Q1611yescharacteristic
321C4C2×C13×#13711yescharacteristic
322C4C13×#57512yes—
323C2—22no—
324C2C2×C13×#46211yescharacteristic
325C2C13×#305411yescharacteristic
326C2C13×#306711yescharacteristic
subgroupG/H
centerC2×C4×C13#121
commutator, Frattini, cosocleC42C24×C13
socleC22×C13C2×#121
prime radicalC23×C13#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1696C2semidirect
5. C13×#1694C2semidirect
6. C13×#1692C2semidirect
79. #19150C13direct (N × H)
95. C2×C8×C13Q16semidirect
121. #1696C2×C13semidirect
122. #1694C2×C13semidirect
123. #1692C2×C13semidirect
257. C2×C8C13×Q16semidirect
280. C13#19150direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31602
C13×#31042
C2×C13×#4462
C13×#16962
C13×#16942
C13×#16922
C13×#15642
C13×#15422
#1915013