Finite Group Databasebeta

← C13×#13250 #15699589

Subgroups — C13×#13250 #15699589

Order 3328.

408 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
1C2×C13×#510C211yesmaximal, characteristic
2C2×C13×#365C211yesmaximal, characteristic, complemented
3C2×C13×#362C211yesmaximal, characteristic, complemented
4C2×C13×#360C211yesmaximal, characteristic
5C2×C13×#347C211yesmaximal, characteristic, complemented
6C13×#1975C211yesmaximal, characteristic
7C13×#1971C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×Q16C2211yescharacteristic
10C13×#510—22no—
11C13×#510—22no—
12C2×C13×Q32C412yescomplemented
13C2×C13×SD32C412yescomplemented
14C2×C13×M32C2211yescharacteristic
15C2×C13×M32C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17C2×C13×#106C2211yescharacteristic
18C2×C13×#104—21no—
19C2×C13×#103—21no—
20C13×#408—21no—
21C2×C13×#97C2211yescharacteristic
22C13×#391—21no—
23C13×#365—22no—
24C13×#362—22no—
25C13×#360—22no—
26C13×#347—22no—
27C2×C13×#41—21no—
28C22×Q8×C13—21no—
29C13×#135—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16—21no—
38C2×C13×Q16C2×C412yes—
39C2×C13×Q16C2×C411yescharacteristic
40C2×C13×SD16—21no—
41C2×C13×D8C2×C411yescharacteristic
42C2×C13×M16—21no—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C2×C13×C4⋊C4—21no—
46C2×C42×C13D411yescharacteristic
47C13×Q32—24no—
48C13×SD32—24no—
49C13×M32—21no—
50C13×M32D412yes—
51C13×M32D412yes—
52C13×M32D412yes—
53C2×C13×C16—21no—
54C2×C13×C16C2×C412yes—
55C13×#108—21no—
56C13×#108—21no—
57C13×#106—21no—
58C13×#106—21no—
59C13×#104—42no—
60C13×#103—42no—
61C13×C22⋊C8—42no—
62C13×#97—21no—
63C13×#97—21no—
64C13×#95—42no—
65#13250C1311yesmaximal, characteristic, direct product factor, Sylow
66C13×#41—41no—
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C2×Q8×C13—21no—
71C2×Q8×C13—22no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×D4×C13—21no—
78C2×D4×C13—41no—
79C22×C4×C13—21no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C13×Q16—22no—
85C13×Q16—21no—
86C13×Q16—22no—
87C13×Q16—21no—
88C13×Q16—41no—
89C13×Q16—41no—
90C13×SD16—41no—
91C13×SD16—41no—
92C13×D8—21no—
93C13×D8—21no—
94C13×M16—41no—
95C13×M16—41no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—41no—
100C2×C8×C13C22×C411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D411yescharacteristic
104C2×C8×C13#4111yescharacteristic
105C2×C8×C13#4111yescharacteristic
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C42×C13—21no—
109C42×C13—21no—
110C13×C16—22no—
111C13×C16C22⋊C414yes—
112C2×#510C2×C1311yescharacteristic
113C2×#365C2×C1311yescharacteristic, complemented
114C2×#362C2×C1311yescharacteristic, complemented
115C2×#360C2×C1311yescharacteristic
116C2×#347C2×C1311yescharacteristic, complemented
117#1975C2×C1311yescharacteristic
118#1971C2×C1311yescharacteristic, complemented
119C23×C13—41no—
120C23×C13AGL(1,ℤ/8)11yescharacteristic
121Q8×C13—41no—
122Q8×C13—42no—
123Q8×C13—42no—
124Q8×C13—41no—
125Q8×C13—81no—
126Q8×C13—81no—
127D4×C13—41no—
128D4×C13—41no—
129D4×C13—81no—
130D4×C13—81no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13—82no—
140C2×C4×C13—81no—
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12711yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C8×C13—41no—
148C8×C13—81no—
149C8×C13C2×C22⋊C411yescharacteristic
150C8×C13C4×D411yescharacteristic
151C8×C13#12111yescharacteristic
152C8×C13#12411yescharacteristic
153C2×#135C22×C1311yescharacteristic
154C22×Q16C22×C1311yescharacteristic
155#510—22no—
156#510—22no—
157C2×Q32C4×C1312yescomplemented
158C2×SD32C4×C1312yescomplemented
159C2×M32C22×C1311yescharacteristic
160C2×M32C22×C1311yescharacteristic
161C2×#108C22×C1311yescharacteristic
162C2×#106C22×C1311yescharacteristic
163C2×#104—21no—
164C2×#103—21no—
165#408—21no—
166C2×#97C22×C1311yescharacteristic
167#391—21no—
168#365—22no—
169#362—22no—
170#360—22no—
171#347—22no—
172C22×C13—22no—
173C22×C13—82no—
174C22×C13—81no—
175C22×C13#44211yescharacteristic
176C22×C13#46911yescharacteristic
177C22×C13#49611yescharacteristic
178C4×C13—81no—
179C4×C13—81no—
180C4×C13—82no—
181C4×C13—161no—
182C4×C13#39011yescharacteristic
183C4×C13#44211yescharacteristic
184C4×C13#46911yescharacteristic
185C4×C13#49611yescharacteristic
186C2×#41—21no—
187C22×Q8—21no—
188#135—21no—
189#135—21no—
190#135—21no—
191#135—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16C2×C4×C1312yes—
198C2×Q16C2×C4×C1311yescharacteristic
199C2×SD16—21no—
200C2×D8C2×C4×C1311yescharacteristic
201C2×M16—21no—
202C22×C8D4×C1311yescharacteristic
203C22×C8C23×C1311yescharacteristic
204C2×C4⋊C4—21no—
205C2×C42D4×C1311yescharacteristic
206Q32—24no—
207SD32—24no—
208M32—21no—
209M32D4×C1312yes—
210M32D4×C1312yes—
211M32D4×C1312yes—
212C2×C16—21no—
213C2×C16C2×C4×C1312yes—
214#108—21no—
215#108—21no—
216#106—21no—
217#106—21no—
218#104—42no—
219#103—42no—
220C22⋊C8—42no—
221#97—21no—
222#97—21no—
223#95—42no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—161no—
227C2×C13#197211yescharacteristic
228C2×C13#218012yes—
229#41—41no—
230#41—41no—
231#41—41no—
232#41—41no—
233C2×Q8—21no—
234C2×Q8—22no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×D4—21no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4C2×D4×C1311yescharacteristic
247Q16—22no—
248Q16—21no—
249Q16—22no—
250Q16—21no—
251Q16—41no—
252Q16—41no—
253SD16—41no—
254SD16—41no—
255D8—21no—
256D8—21no—
257M16—41no—
258M16—41no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8C22×C4×C1311yescharacteristic
264C2×C8C2×D4×C1311yescharacteristic
265C2×C8C2×D4×C1311yescharacteristic
266C2×C8C2×D4×C1311yescharacteristic
267C2×C8C13×#4111yescharacteristic
268C2×C8C13×#4111yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C42—21no—
272C42—21no—
273C16—22no—
274C16C13×C22⋊C414yes—
275C13#1325011yescharacteristic, direct product factor, Sylow
276C23—41no—
277C23C13×AGL(1,ℤ/8)11yescharacteristic
278Q8—41no—
279Q8—42no—
280Q8—42no—
281Q8—41no—
282Q8—81no—
283Q8—81no—
284D4—41no—
285D4—41no—
286D4—81no—
287D4—81no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4C4×D4×C1311yescharacteristic
299C2×C4C13×#12111yescharacteristic
300C2×C4C13×#12711yescharacteristic
301C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
302C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
303C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
304C8—41no—
305C8—81no—
306C8C2×C13×C22⋊C411yescharacteristic
307C8C4×D4×C1311yescharacteristic
308C8C13×#12111yescharacteristic
309C8C13×#12411yescharacteristic
310C22—22no—
311C22—82no—
312C22—81no—
313C22C13×#44211yescharacteristic
314C22C13×#46911yescharacteristic
315C22C13×#49611yescharacteristic
316C4—81no—
317C4—81no—
318C4—82no—
319C4—161no—
320C4C13×#39011yescharacteristic
321C4C13×#44211yescharacteristic
322C4C13×#46911yescharacteristic
323C4C13×#49611yescharacteristic
324C2—21no—
325C2—21no—
326C2—161no—
327C2C13×#197211yescharacteristic
328C2C13×#218012yes—
subgroupG/H
center, socleC22×C13#442
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#365C2semidirect
3. C2×C13×#362C2semidirect
5. C2×C13×#347C2semidirect
7. C13×#1971C2semidirect
12. C2×C13×Q32C4semidirect
13. C2×C13×SD32C4semidirect
65. #13250C13direct (N × H)
113. C2×#365C2×C13semidirect
114. C2×#362C2×C13semidirect
116. C2×#347C2×C13semidirect
118. #1971C2×C13semidirect
157. C2×Q32C4×C13semidirect
158. C2×SD32C4×C13semidirect
275. C13#13250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5102
C2×C13×#3652
C2×C13×#3622
C2×C13×#3602
C2×C13×#3472
C13×#19752
C13×#19712
#1325013