Finite Group Databasebeta

← C13×#13033 #15699372

Subgroups — C13×#13033 #15699372

Order 3328.

498 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic
2C13×#2948C211yesmaximal, characteristic, complemented
3C13×#2145C211yesmaximal, characteristic, complemented
4C13×#2140C211yesmaximal, characteristic, complemented
5C13×#1976C211yesmaximal, characteristic, complemented
6C13×#1384C211yesmaximal, characteristic, complemented
7C13×#1378C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×D8C2211yescharacteristic
10C13×#518—21no—
11C13×#509—22no—
12C13×#509—22no—
13C2×C13×SD32C412yescomplemented
14C2×C13×D16C412yescomplemented
15C2×C13×M32C2211yescharacteristic
16C2×C13×M32C2211yescharacteristic
17C13×#442—22no—
18C4×C13×D8—22no—
19C13×#427C2211yescharacteristic
20C13×#427C2211yescharacteristic
21C13×#421—21no—
22C13×#418—21no—
23C13×#410—21no—
24C13×#405C2211yescharacteristic
25C13×#360—22no—
26C13×#357—22no—
27C2×C13×#41—21no—
28C22×D4×C13—21no—
29C13×#135—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135—21no—
33C2×C13×Q16C2×C411yescharacteristic, complemented
34C2×C13×SD16—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8C2×C412yes—
39C2×C13×D8C2×C411yescharacteristic, complemented
40C2×C13×D8D412yes—
41C2×C13×D8D412yes—
42C2×C13×M16D411yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C4×D4×C13—24no—
45C4×D4×C13—42no—
46C13×#117—21no—
47C13×#117—21no—
48C13×#117D411yescharacteristic
49C2×C13×C22⋊C4—42no—
50C13×SD32—24no—
51C13×D16—24no—
52C13×M32—21no—
53C13×M32—21no—
54C13×M32—21no—
55C13×M32—21no—
56C2×C13×C16—21no—
57C2×C13×C16C2×C412yescomplemented
58C13×#107—21no—
59C13×#107—21no—
60C13×#106—21no—
61C13×#106D412yes—
62C13×#104—42no—
63C13×#102—24no—
64C13×#99—42no—
65C13×#97—21no—
66C4×C8×C13—21no—
67#13033C1311yesmaximal, characteristic, direct product factor, Sylow
68C24×C13—41no—
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C13×#41—41no—
73C2×Q8×C13—21no—
74C2×D4×C13—22no—
75C2×D4×C13—21no—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C22×C4×C13—44no—
83C22×C4×C13—41no—
84C22×C4×C13C2×D411yescharacteristic
85C13×Q16—21no—
86C13×Q16—21no—
87C13×SD16—41no—
88C13×SD16—41no—
89C13×D8—21no—
90C13×D8—22no—
91C13×D8—21no—
92C13×D8—22no—
93C13×D8—22no—
94C13×D8C22⋊C414yes—
95C13×M16—21no—
96C13×M16—21no—
97C2×C8×C13—21no—
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—41no—
107C13×C22⋊C4—44no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4D812yes—
111C42×C13—21no—
112C42×C13—41no—
113C42×C13—41no—
114C13×C16—22no—
115C13×C16—41no—
116C2×#509C2×C1311yescharacteristic
117#2948C2×C1311yescharacteristic, complemented
118#2145C2×C1311yescharacteristic, complemented
119#2140C2×C1311yescharacteristic, complemented
120#1976C2×C1311yescharacteristic, complemented
121#1384C2×C1311yescharacteristic, complemented
122#1378C2×C1311yescharacteristic, complemented
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—41no—
127C23×C13—162no—
128C23×C13C2×D811yescharacteristic
129Q8×C13—41no—
130Q8×C13—41no—
131D4×C13—24no—
132D4×C13—41no—
133D4×C13—42no—
134D4×C13—41no—
135D4×C13—42no—
136D4×C13—42no—
137D4×C13—81no—
138D4×C13—81no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—164no—
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C8×C13—41no—
153C8×C13C2×C22⋊C411yescharacteristic
154C8×C13C4×D411yescharacteristic
155C8×C13#12111yescharacteristic
156C8×C13#12311yescharacteristic
157C2×#135C22×C1311yescharacteristic
158C22×D8C22×C1311yescharacteristic
159#518—21no—
160#509—22no—
161#509—22no—
162C2×SD32C4×C1312yescomplemented
163C2×D16C4×C1312yescomplemented
164C2×M32C22×C1311yescharacteristic
165C2×M32C22×C1311yescharacteristic
166#442—22no—
167C4×D8—22no—
168#427C22×C1311yescharacteristic
169#427C22×C1311yescharacteristic
170#421—21no—
171#418—21no—
172#410—21no—
173#405C22×C1311yescharacteristic
174#360—22no—
175#357—22no—
176C22×C13—41no—
177C22×C13—44no—
178C22×C13—84no—
179C22×C13—81no—
180C22×C13—162no—
181C22×C13—162no—
182C22×C13—161no—
183C22×C13C4×D811yescharacteristic
184C22×C13#44711yescharacteristic
185C22×C13#45911yescharacteristic
186C4×C13—42no—
187C4×C13—82no—
188C4×C13—81no—
189C4×C13—161no—
190C4×C13#38611yescharacteristic
191C4×C13#44211yescharacteristic
192C4×C13#44911yescharacteristic
193C4×C13#46311yescharacteristic
194C2×#41—21no—
195C22×D4—21no—
196#135—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200C2×Q16C2×C4×C1311yescharacteristic, complemented
201C2×SD16—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8C2×C4×C1312yes—
206C2×D8C2×C4×C1311yescharacteristic, complemented
207C2×D8D4×C1312yes—
208C2×D8D4×C1312yes—
209C2×M16D4×C1311yescharacteristic
210C22×C8C23×C1311yescharacteristic
211C4×D4—24no—
212C4×D4—42no—
213#117—21no—
214#117—21no—
215#117D4×C1311yescharacteristic
216C2×C22⋊C4—42no—
217SD32—24no—
218D16—24no—
219M32—21no—
220M32—21no—
221M32—21no—
222M32—21no—
223C2×C16—21no—
224C2×C16C2×C4×C1312yescomplemented
225#107—21no—
226#107—21no—
227#106—21no—
228#106D4×C1312yes—
229#104—42no—
230#102—24no—
231#99—42no—
232#97—21no—
233C4×C8—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—84no—
238C2×C13—161no—
239C2×C13#187911yescharacteristic
240C24—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—44no—
255C22×C4—41no—
256C22×C4C2×D4×C1311yescharacteristic
257Q16—21no—
258Q16—21no—
259SD16—41no—
260SD16—41no—
261D8—21no—
262D8—22no—
263D8—21no—
264D8—22no—
265D8—22no—
266D8C13×C22⋊C414yes—
267M16—21no—
268M16—21no—
269C2×C8—21no—
270C2×C8C22×C4×C1311yescharacteristic
271C2×C8C2×D4×C1311yescharacteristic
272C2×C8C2×D4×C1311yescharacteristic
273C2×C8C2×D4×C1311yescharacteristic
274C2×C8C13×#4111yescharacteristic
275C2×C8C13×#4111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C22⋊C4—44no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4C13×D812yes—
283C42—21no—
284C42—41no—
285C42—41no—
286C16—22no—
287C16—41no—
288C13#1303311yescharacteristic, direct product factor, Sylow
289C23—42no—
290C23—42no—
291C23—42no—
292C23—41no—
293C23—162no—
294C23C2×C13×D811yescharacteristic
295Q8—41no—
296Q8—41no—
297D4—24no—
298D4—41no—
299D4—42no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—164no—
312C2×C4C4×D4×C1311yescharacteristic
313C2×C4C13×#12011yescharacteristic
314C2×C4C13×#12111yescharacteristic
315C2×C4C13×#13511yescharacteristic
316C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
317C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
318C8—41no—
319C8C2×C13×C22⋊C411yescharacteristic
320C8C4×D4×C1311yescharacteristic
321C8C13×#12111yescharacteristic
322C8C13×#12311yescharacteristic
323C22—41no—
324C22—44no—
325C22—84no—
326C22—81no—
327C22—162no—
328C22—162no—
329C22—161no—
330C22C4×C13×D811yescharacteristic
331C22C13×#44711yescharacteristic
332C22C13×#45911yescharacteristic
333C4—42no—
334C4—82no—
335C4—81no—
336C4—161no—
337C4C13×#38611yescharacteristic
338C4C13×#44211yescharacteristic
339C4C13×#44911yescharacteristic
340C4C13×#46311yescharacteristic
341C2—21no—
342C2—21no—
343C2—21no—
344C2—84no—
345C2—161no—
346C2C13×#187911yescharacteristic
subgroupG/H
center, socleC2×C13#1879
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2948C2semidirect
3. C13×#2145C2semidirect
4. C13×#2140C2semidirect
5. C13×#1976C2semidirect
6. C13×#1384C2semidirect
7. C13×#1378C2semidirect
13. C2×C13×SD32C4semidirect
14. C2×C13×D16C4semidirect
33. C2×C13×Q16C2×C4semidirect
39. C2×C13×D8C2×C4semidirect
57. C2×C13×C16C2×C4semidirect
67. #13033C13direct (N × H)
117. #2948C2×C13semidirect
118. #2145C2×C13semidirect
119. #2140C2×C13semidirect
120. #1976C2×C13semidirect
121. #1384C2×C13semidirect
122. #1378C2×C13semidirect
162. C2×SD32C4×C13semidirect
163. C2×D16C4×C13semidirect
200. C2×Q16C2×C4×C13semidirect
206. C2×D8C2×C4×C13semidirect
224. C2×C16C2×C4×C13semidirect
288. C13#13033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5092
C13×#29482
C13×#21452
C13×#21402
C13×#19762
C13×#13842
C13×#13782
#1303313