Finite Group Databasebeta

← C13×#33632 #15719971

Subgroups — C13×#33632 #15719971

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3164C211yesmaximal, characteristic
2C13×#2950C211yesmaximal, characteristic
3C13×#2229C212yesmaximal, complemented
4C13×#2229C212yesmaximal, complemented
5C13×#2227C212yesmaximal, complemented
6C13×#2225C212yesmaximal, complemented
7C13×#2159C211yesmaximal, characteristic
8C13×#2158C211yesmaximal, characteristic
9C13×#2151C211yesmaximal, characteristic
10C13×#2141C211yesmaximal, characteristic
11C2×C13×#358C211yesmaximal, characteristic
12C22×C13×Q16C2211yescharacteristic
13C13×#544—21no—
14C13×#519—21no—
15C2×C13×M32C2211yescharacteristic
16C22×C13×C16C2211yescharacteristic
17C13×#501—22no—
18C13×#500C2212yes—
19C13×#499C2212yes—
20C13×#441—22no—
21C4×C13×Q16C2212yes—
22C4×C13×Q16C2212yes—
23C13×#428—21no—
24C13×#427C2211yescharacteristic
25C13×#427C2211yescharacteristic
26C2×C13×#107C2211yescharacteristic
27C13×#419—21no—
28C13×#405C2211yescharacteristic
29C13×#367C2211yescharacteristic
30C13×#367C2211yescharacteristic
31C13×#367C2212yes—
32C13×#366C2211yescharacteristic
33C13×#366C2211yescharacteristic
34C13×#366C2212yes—
35C13×C4⋊C16C2212yes—
36C13×C4⋊C16C2212yes—
37C13×#358C2212yes—
38C13×#358C2212yes—
39C13×#358C2212yes—
40C13×#358C2212yes—
41C22×Q8×C13—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16—22no—
44C2×C13×Q16Q814yescomplemented
45C2×C13×Q16C2312yes—
46C2×C13×M16D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×C4⋊Q8—22no—
49C13×C4⋊Q8—41no—
50C13×#125—22no—
51C13×#125—41no—
52C13×C22⋊Q8—42no—
53C4×Q8×C13—22no—
54C4×Q8×C13—22no—
55C4×Q8×C13—41no—
56C4×Q8×C13—41no—
57C13×#117—21no—
58C13×#117—21no—
59C13×#117—42no—
60C13×#117D411yescharacteristic
61C2×C13×C4⋊C4—21no—
62C13×M32—22no—
63C2×C13×C16—22no—
64C2×C13×C16C2311yescharacteristic
65C2×C13×C16C2312yes—
66C2×C13×C16C2311yescharacteristic
67C13×#107—21no—
68C13×#107—22no—
69C13×#107C2312yes—
70C13×#107C2311yescharacteristic
71C13×#107C2311yescharacteristic
72C13×#107C2311yescharacteristic
73C13×#107C2311yescharacteristic
74C13×#106—21no—
75C13×#106—21no—
76C13×#106—22no—
77C13×#103—22no—
78C13×#103—22no—
79C13×#97D412yes—
80C4×C8×C13C2312yes—
81#33632C1311yesmaximal, characteristic, direct product factor, Sylow
82C2×Q8×C13—24no—
83C2×Q8×C13—22no—
84C2×Q8×C13—41no—
85C2×Q8×C13—42no—
86C2×Q8×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C13×Q16—24no—
91C13×Q16—22no—
92C13×Q16C2×Q814yes—
93C13×M16—22no—
94C2×C8×C13C2×D412yes—
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2×Q812yes—
97C2×C8×C13#4112yes—
98C2×C8×C13C2411yescharacteristic
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4D811yescharacteristic
111C13×C4⋊C4D811yescharacteristic
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4D812yes—
115C42×C13—41no—
116C42×C13—41no—
117C42×C13—42no—
118C42×C13—42no—
119C42×C13C2×D412yes—
120C13×C16—21no—
121C13×C16—21no—
122C13×C16—22no—
123#3164C2×C1311yescharacteristic
124#2950C2×C1311yescharacteristic
125#2229C2×C1312yescomplemented
126#2229C2×C1312yescomplemented
127#2227C2×C1312yescomplemented
128#2225C2×C1312yescomplemented
129#2159C2×C1311yescharacteristic
130#2158C2×C1311yescharacteristic
131#2151C2×C1311yescharacteristic
132#2141C2×C1311yescharacteristic
133C2×#358C2×C1311yescharacteristic
134C23×C13C2×D811yescharacteristic
135Q8×C13—24no—
136Q8×C13—42no—
137Q8×C13—44no—
138Q8×C13—162no—
139C2×C4×C13—42no—
140C2×C4×C13—44no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—161no—
147C2×C4×C13C22⋊Q812yes—
148C2×C4×C13C2×D812yes—
149C2×C4×C13C2×D812yes—
150C2×C4×C13C2×D811yescharacteristic
151C2×C4×C13#13712yes—
152C2×C4×C13C22×D411yescharacteristic
153C8×C13—22no—
154C8×C13C22⋊Q812yes—
155C8×C13C22×Q811yescharacteristic
156C8×C13C2×#4111yescharacteristic
157C22×Q16C22×C1311yescharacteristic
158#544—21no—
159#519—21no—
160C2×M32C22×C1311yescharacteristic
161C22×C16C22×C1311yescharacteristic
162#501—22no—
163#500C22×C1312yes—
164#499C22×C1312yes—
165#441—22no—
166C4×Q16C22×C1312yes—
167C4×Q16C22×C1312yes—
168#428—21no—
169#427C22×C1311yescharacteristic
170#427C22×C1311yescharacteristic
171C2×#107C22×C1311yescharacteristic
172#419—21no—
173#405C22×C1311yescharacteristic
174#367C22×C1311yescharacteristic
175#367C22×C1311yescharacteristic
176#367C22×C1312yes—
177#366C22×C1311yescharacteristic
178#366C22×C1311yescharacteristic
179#366C22×C1312yes—
180C4⋊C16C22×C1312yes—
181C4⋊C16C22×C1312yes—
182#358C22×C1312yes—
183#358C22×C1312yes—
184#358C22×C1312yes—
185#358C22×C1312yes—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#47412yes—
189C22×C13C22×D811yescharacteristic
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—44no—
193C4×C13—81no—
194C4×C13—82no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13#47412yes—
199C4×C13C2×C22⋊Q811yescharacteristic
200C4×C13C2×#13711yescharacteristic
201C22×Q8—21no—
202C2×Q16—21no—
203C2×Q16—22no—
204C2×Q16Q8×C1314yescomplemented
205C2×Q16C23×C1312yes—
206C2×M16D4×C1311yescharacteristic
207C22×C8C23×C1311yescharacteristic
208C4⋊Q8—22no—
209C4⋊Q8—41no—
210#125—22no—
211#125—41no—
212C22⋊Q8—42no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8—41no—
216C4×Q8—41no—
217#117—21no—
218#117—21no—
219#117—42no—
220#117D4×C1311yescharacteristic
221C2×C4⋊C4—21no—
222M32—22no—
223C2×C16—22no—
224C2×C16C23×C1311yescharacteristic
225C2×C16C23×C1312yes—
226C2×C16C23×C1311yescharacteristic
227#107—21no—
228#107—22no—
229#107C23×C1312yes—
230#107C23×C1311yescharacteristic
231#107C23×C1311yescharacteristic
232#107C23×C1311yescharacteristic
233#107C23×C1311yescharacteristic
234#106—21no—
235#106—21no—
236#106—22no—
237#103—22no—
238#103—22no—
239#97D4×C1312yes—
240C4×C8C23×C1312yes—
241C2×C13—22no—
242C2×C13C2×#47411yescharacteristic
243C2×C13#341611yescharacteristic
244C2×C13#341711yescharacteristic
245C2×Q8—24no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C1311yescharacteristic
253Q16—24no—
254Q16—22no—
255Q16C2×Q8×C1314yes—
256M16—22no—
257C2×C8C2×D4×C1312yes—
258C2×C8C2×D4×C1311yescharacteristic
259C2×C8C2×Q8×C1312yes—
260C2×C8C13×#4112yes—
261C2×C8C24×C1311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4C13×D811yescharacteristic
274C4⋊C4C13×D811yescharacteristic
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4C13×D812yes—
278C42—41no—
279C42—41no—
280C42—42no—
281C42—42no—
282C42C2×D4×C1312yes—
283C16—21no—
284C16—21no—
285C16—22no—
286C13#3363211yescharacteristic, direct product factor, Sylow
287C23C2×C13×D811yescharacteristic
288Q8—24no—
289Q8—44no—
290Q8—42no—
291Q8—162no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—161no—
300C2×C4C13×C22⋊Q812yes—
301C2×C4C2×C13×D812yes—
302C2×C4C2×C13×D812yes—
303C2×C4C2×C13×D811yescharacteristic
304C2×C4C13×#13712yes—
305C2×C4C22×D4×C1311yescharacteristic
306C8—22no—
307C8C13×C22⋊Q812yes—
308C8C22×Q8×C1311yescharacteristic
309C8C2×C13×#4111yescharacteristic
310C22—21no—
311C22—21no—
312C22C13×#47412yes—
313C22C22×C13×D811yescharacteristic
314C4—22no—
315C4—22no—
316C4—44no—
317C4—81no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4C13×#47412yes—
323C4C2×C13×C22⋊Q811yescharacteristic
324C4C2×C13×#13711yescharacteristic
325C2—22no—
326C2C2×C13×#47411yescharacteristic
327C2C13×#341611yescharacteristic
328C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC23×C13C2×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2229C2semidirect
4. C13×#2229C2semidirect
5. C13×#2227C2semidirect
6. C13×#2225C2semidirect
44. C2×C13×Q16Q8semidirect
81. #33632C13direct (N × H)
125. #2229C2×C13semidirect
126. #2229C2×C13semidirect
127. #2227C2×C13semidirect
128. #2225C2×C13semidirect
204. C2×Q16Q8×C13semidirect
286. C13#33632direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31642
C13×#29502
C13×#22292
C13×#22272
C13×#22252
C13×#21592
C13×#21582
C13×#21512
C13×#21412
C2×C13×#3582
#3363213