Finite Group Databasebeta

← C13×#33866 #15720205

Subgroups — C13×#33866 #15720205

Order 3328.

548 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3338C211yesmaximal, characteristic
2D4×C13×Q16C211yesmaximal, characteristic
3C13×#2241C211yesmaximal, characteristic, complemented
4C13×#2236C212yesmaximal, complemented
5C13×#2227C211yesmaximal, characteristic, complemented
6C13×#2216C212yesmaximal, complemented
7C13×#2209C211yesmaximal, characteristic, complemented
8C13×#2188C212yesmaximal, complemented
9C4×C13×Q32C211yesmaximal, characteristic, complemented
10D4×C13×C16C211yesmaximal, characteristic
11C2×C13×#358C212yesmaximal, complemented
12C22×C13×Q16C2212yes—
13C13×#554—21no—
14D4×Q8×C13—21no—
15C2×C13×Q32C2211yescharacteristic
16C2×C13×Q32C2212yes—
17C22×C13×C16C2212yes—
18C13×#500C2211yescharacteristic
19C13×#494C2211yescharacteristic
20C13×#484—22no—
21C13×#477—21no—
22C13×#467C2212yes—
23C13×#467C2212yes—
24C13×#462—21no—
25C13×#451—22no—
26C4×C13×Q16C2211yescharacteristic
27C4×C13×Q16C2211yescharacteristic
28C8×D4×C13C2211yescharacteristic
29C2×C13×#107C2212yes—
30C13×#366C2211yescharacteristic
31C13×#366C2212yes—
32C13×C4⋊C16C2211yescharacteristic
33C13×#358C2212yes—
34C13×#358C2212yes—
35C13×#358C2211yescharacteristic
36C13×#358C2212yes—
37C13×#358C2212yes—
38C13×#358C2211yescharacteristic
39C13×C22⋊C16C2212yes—
40C4×C13×C16C2211yescharacteristic
41C22×Q8×C13—22no—
42C2×C13×Q16—24no—
43C2×C13×Q16—22no—
44C2×C13×Q16—21no—
45C2×C13×Q16—42no—
46C2×C13×Q16C2312yes—
47C2×C13×Q16C2311yescharacteristic
48C2×C13×Q16C2311yescharacteristic
49C22×C8×C13C2312yes—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8—21no—
52C13×C4⋊Q8—41no—
53C13×#125—41no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—42no—
57C13×C22⋊Q8—42no—
58C4×Q8×C13—21no—
59C4×Q8×C13—21no—
60C4×D4×C13—41no—
61C4×D4×C13—41no—
62C4×D4×C13D411yescharacteristic
63C2×C13×C4⋊C4—22no—
64C13×Q32—22no—
65C13×Q32—42no—
66C2×C13×C16—42no—
67C2×C13×C16C2311yescharacteristic
68C2×C13×C16C2311yescharacteristic
69C2×C13×C16C2312yes—
70C13×#107—22no—
71C13×#107—21no—
72C13×#107C2311yescharacteristic
73C13×#107C2312yes—
74C13×#107C2311yescharacteristic
75C13×C4⋊C8D411yescharacteristic
76C13×#103—21no—
77C13×#103—21no—
78C13×#103—22no—
79C13×#103—22no—
80C13×C22⋊C8D412yes—
81C4×C8×C13C2311yescharacteristic
82#33866C1311yesmaximal, characteristic, direct product factor, Sylow
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13—22no—
86C2×Q8×C13—44no—
87C2×Q8×C13—42no—
88C2×Q8×C13—41no—
89C2×Q8×C13—82no—
90C2×D4×C13D811yescharacteristic
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13C2×D412yes—
94C13×Q16—21no—
95C13×Q16—22no—
96C13×Q16—21no—
97C13×Q16—21no—
98C13×Q16—22no—
99C13×Q16—44no—
100C13×Q16—81no—
101C13×Q16#4112yes—
102C2×C8×C13—22no—
103C2×C8×C13—22no—
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13C2×D412yes—
106C2×C8×C13C2411yescharacteristic
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—42no—
116C13×C4⋊C4—42no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4D811yescharacteristic
119C13×C22⋊C4—42no—
120C13×C22⋊C4—42no—
121C13×C22⋊C4D812yes—
122C42×C13—41no—
123C42×C13—41no—
124C42×C13C2×D411yescharacteristic
125C13×C16—21no—
126C13×C16—21no—
127C13×C16—22no—
128#3338C2×C1311yescharacteristic
129D4×Q16C2×C1311yescharacteristic
130#2241C2×C1311yescharacteristic, complemented
131#2236C2×C1312yescomplemented
132#2227C2×C1311yescharacteristic, complemented
133#2216C2×C1312yescomplemented
134#2209C2×C1311yescharacteristic, complemented
135#2188C2×C1312yescomplemented
136C4×Q32C2×C1311yescharacteristic, complemented
137D4×C16C2×C1311yescharacteristic
138C2×#358C2×C1312yescomplemented
139C23×C13C2×D812yes—
140Q8×C13—22no—
141Q8×C13—41no—
142Q8×C13—42no—
143Q8×C13—41no—
144Q8×C13—42no—
145Q8×C13—41no—
146Q8×C13—84no—
147Q8×C13—161no—
148D4×C13Q3214yescomplemented
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—84no—
158C2×C4×C13—162no—
159C2×C4×C13C2×D811yescharacteristic
160C2×C4×C13C2×D812yes—
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C8×C13—22no—
164C8×C13—21no—
165C8×C13C2×#4111yescharacteristic
166C8×C13H(5,𝔽2)11yescharacteristic
167C22×Q16C22×C1312yes—
168#554—21no—
169D4×Q8—21no—
170C2×Q32C22×C1311yescharacteristic
171C2×Q32C22×C1312yes—
172C22×C16C22×C1312yes—
173#500C22×C1311yescharacteristic
174#494C22×C1311yescharacteristic
175#484—22no—
176#477—21no—
177#467C22×C1312yes—
178#467C22×C1312yes—
179#462—21no—
180#451—22no—
181C4×Q16C22×C1311yescharacteristic
182C4×Q16C22×C1311yescharacteristic
183C8×D4C22×C1311yescharacteristic
184C2×#107C22×C1312yes—
185#366C22×C1311yescharacteristic
186#366C22×C1312yes—
187C4⋊C16C22×C1311yescharacteristic
188#358C22×C1311yescharacteristic
189#358C22×C1312yes—
190#358C22×C1312yes—
191#358C22×C1312yes—
192#358C22×C1311yescharacteristic
193#358C22×C1312yes—
194C22⋊C16C22×C1312yes—
195C4×C16C22×C1311yescharacteristic
196C22×C13—22no—
197C22×C13—22no—
198C22×C13C2×Q3214yes—
199C22×C13C22×D811yescharacteristic
200C4×C13—21no—
201C4×C13—22no—
202C4×C13—42no—
203C4×C13—81no—
204C4×C13—81no—
205C4×C13—82no—
206C4×C13—82no—
207C4×C13—81no—
208C4×C13C2×Q3212yes—
209C4×C13#54611yescharacteristic
210C4×C13#57711yescharacteristic
211C22×Q8—22no—
212C2×Q16—24no—
213C2×Q16—22no—
214C2×Q16—21no—
215C2×Q16—42no—
216C2×Q16C23×C1312yes—
217C2×Q16C23×C1311yescharacteristic
218C2×Q16C23×C1311yescharacteristic
219C22×C8C23×C1312yes—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—41no—
223#125—41no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8—42no—
227C22⋊Q8—42no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—41no—
231C4×D4—41no—
232C4×D4D4×C1311yescharacteristic
233C2×C4⋊C4—22no—
234Q32—22no—
235Q32—42no—
236C2×C16—42no—
237C2×C16C23×C1311yescharacteristic
238C2×C16C23×C1311yescharacteristic
239C2×C16C23×C1312yes—
240#107—22no—
241#107—21no—
242#107C23×C1311yescharacteristic
243#107C23×C1312yes—
244#107C23×C1311yescharacteristic
245C4⋊C8D4×C1311yescharacteristic
246#103—21no—
247#103—21no—
248#103—22no—
249#103—22no—
250C22⋊C8D4×C1312yes—
251C4×C8C23×C1311yescharacteristic
252C2×C13—24no—
253C2×C13#329411yescharacteristic
254C2×C13C22×Q3211yescharacteristic
255C2×C13#341611yescharacteristic
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—44no—
260C2×Q8—42no—
261C2×Q8—41no—
262C2×Q8—82no—
263C2×D4C13×D811yescharacteristic
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C2×D4×C1312yes—
267Q16—21no—
268Q16—22no—
269Q16—21no—
270Q16—21no—
271Q16—22no—
272Q16—44no—
273Q16—81no—
274Q16C13×#4112yes—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8C2×D4×C1311yescharacteristic
278C2×C8C2×D4×C1312yes—
279C2×C8C24×C1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—42no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4C13×D811yescharacteristic
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4C13×D812yes—
295C42—41no—
296C42—41no—
297C42C2×D4×C1311yescharacteristic
298C16—21no—
299C16—21no—
300C16—22no—
301C13#3386611yescharacteristic, direct product factor, Sylow
302C23C2×C13×D812yes—
303Q8—22no—
304Q8—41no—
305Q8—42no—
306Q8—41no—
307Q8—42no—
308Q8—41no—
309Q8—84no—
310Q8—161no—
311D4C13×Q3214yescomplemented
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—162no—
322C2×C4C2×C13×D811yescharacteristic
323C2×C4C2×C13×D812yes—
324C2×C4C2×C13×D811yescharacteristic
325C2×C4C22×D4×C1311yescharacteristic
326C8—22no—
327C8—21no—
328C8C2×C13×#4111yescharacteristic
329C8C13×H(5,𝔽2)11yescharacteristic
330C22—22no—
331C22—22no—
332C22C2×C13×Q3214yes—
333C22C22×C13×D811yescharacteristic
334C4—22no—
335C4—21no—
336C4—42no—
337C4—82no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—82no—
342C4C2×C13×Q3212yes—
343C4C13×#54611yescharacteristic
344C4C13×#57711yescharacteristic
345C2—24no—
346C2C13×#329411yescharacteristic
347C2C22×C13×Q3211yescharacteristic
348C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC2×D4×C13D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2241C2semidirect
4. C13×#2236C2semidirect
5. C13×#2227C2semidirect
6. C13×#2216C2semidirect
7. C13×#2209C2semidirect
8. C13×#2188C2semidirect
9. C4×C13×Q32C2semidirect
11. C2×C13×#358C2semidirect
82. #33866C13direct (N × H)
130. #2241C2×C13semidirect
131. #2236C2×C13semidirect
132. #2227C2×C13semidirect
133. #2216C2×C13semidirect
134. #2209C2×C13semidirect
135. #2188C2×C13semidirect
136. C4×Q32C2×C13semidirect
138. C2×#358C2×C13semidirect
148. D4×C13Q32semidirect
301. C13#33866direct (N × H)
311. D4C13×Q32semidirect

Maximal subgroups

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

subgroupindex
C13×#33382
D4×C13×Q162
C13×#22412
C13×#22362
C13×#22272
C13×#22162
C13×#22092
C13×#21882
C4×C13×Q322
D4×C13×C162
C2×C13×#3582
#3386613