Finite Group Databasebeta

← C13×#13443 #15699782

Subgroups — C13×#13443 #15699782

Order 3328.

378 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#510C211yesmaximal, characteristic
2C13×#2153C211yesmaximal, characteristic, complemented
3C13×#2148C211yesmaximal, characteristic
4C13×#2141C211yesmaximal, characteristic, complemented
5C13×#1979C211yesmaximal, characteristic, complemented
6C13×#1976C211yesmaximal, characteristic
7C13×#1389C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×Q16C2211yescharacteristic
10C13×#510—22no—
11C13×#510—22no—
12C2×C13×Q32—21no—
13C2×C13×SD32—21no—
14C2×C13×M32C2211yescharacteristic
15C2×C13×M32C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17C13×#427C2211yescharacteristic
18C13×#421—21no—
19C13×#419—21no—
20C2×C13×#101—21no—
21C13×#410—21no—
22C13×#405C2211yescharacteristic
23C13×#364—22no—
24C13×#362—21no—
25C13×#361—21no—
26C13×#358—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×Q16D412yes—
39C2×C13×Q16D411yescharacteristic
40C2×C13×SD16—21no—
41C2×C13×D8D411yescharacteristic
42C2×C13×M16—21no—
43C2×C13×M16D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C13×#117—21no—
46C13×#117D411yescharacteristic
47C13×Q32—24no—
48C13×SD32—24no—
49C13×M32—21no—
50C13×M32—21no—
51C13×M32—21no—
52C13×M32D412yes—
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C13×#108—21no—
56C13×#108—21no—
57C13×#107—21no—
58C13×#106—21no—
59C13×#104—42no—
60C13×#103—42no—
61C13×#101—42no—
62C13×#99—42no—
63C13×#97—21no—
64C4×C8×C13—21no—
65#13443C1311yesmaximal, 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—41no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C13×Q16—22no—
83C13×Q16—21no—
84C13×Q16—22no—
85C13×Q16—21no—
86C13×Q16—41no—
87C13×Q16—41no—
88C13×SD16—41no—
89C13×SD16—41no—
90C13×D8—21no—
91C13×D8—21no—
92C13×M16—21no—
93C13×M16—41no—
94C13×M16—41no—
95C13×M16D812yes—
96C2×C8×C13—21no—
97C2×C8×C13—41no—
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C13×C4⋊C4—21no—
105C13×C4⋊C4—41no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—41no—
108C42×C13—21no—
109C42×C13—41no—
110C13×C16—22no—
111C13×C16—41no—
112C2×#510C2×C1311yescharacteristic
113#2153C2×C1311yescharacteristic, complemented
114#2148C2×C1311yescharacteristic
115#2141C2×C1311yescharacteristic, complemented
116#1979C2×C1311yescharacteristic, complemented
117#1976C2×C1311yescharacteristic
118#1389C2×C1311yescharacteristic, complemented
119C23×C13—41no—
120C23×C13AGL(1,ℤ/8)11yescharacteristic
121Q8×C13—41no—
122Q8×C13—42no—
123Q8×C13—41no—
124Q8×C13—42no—
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—41no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13C2×D811yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C8×C13—22no—
146C8×C13—81no—
147C8×C13#12011yescharacteristic
148C8×C13#12311yescharacteristic
149C8×C13#12311yescharacteristic
150C8×C13#12411yescharacteristic
151C2×#135C22×C1311yescharacteristic
152C22×Q16C22×C1311yescharacteristic
153#510—22no—
154#510—22no—
155C2×Q32—21no—
156C2×SD32—21no—
157C2×M32C22×C1311yescharacteristic
158C2×M32C22×C1311yescharacteristic
159C2×#108C22×C1311yescharacteristic
160#427C22×C1311yescharacteristic
161#421—21no—
162#419—21no—
163C2×#101—21no—
164#410—21no—
165#405C22×C1311yescharacteristic
166#364—22no—
167#362—21no—
168#361—21no—
169#358—22no—
170C22×C13—41no—
171C22×C13—81no—
172C22×C13—161no—
173C22×C13#45911yescharacteristic
174C22×C13#46311yescharacteristic
175C22×C13#46911yescharacteristic
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—82no—
179C4×C13—161no—
180C4×C13#39411yescharacteristic
181C4×C13#45911yescharacteristic
182C4×C13#46311yescharacteristic
183C4×C13#46611yescharacteristic
184C2×#41—21no—
185C22×Q8—21no—
186#135—21no—
187#135—21no—
188#135—21no—
189#135—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16D4×C1312yes—
196C2×Q16D4×C1311yescharacteristic
197C2×SD16—21no—
198C2×D8D4×C1311yescharacteristic
199C2×M16—21no—
200C2×M16D4×C1311yescharacteristic
201C22×C8C23×C1311yescharacteristic
202#117—21no—
203#117D4×C1311yescharacteristic
204Q32—24no—
205SD32—24no—
206M32—21no—
207M32—21no—
208M32—21no—
209M32D4×C1312yes—
210C2×C16—21no—
211C2×C16—21no—
212#108—21no—
213#108—21no—
214#107—21no—
215#106—21no—
216#104—42no—
217#103—42no—
218#101—42no—
219#99—42no—
220#97—21no—
221C4×C8—21no—
222C2×C13—21no—
223C2×C13—21no—
224C2×C13—21no—
225C2×C13—161no—
226C2×C13#205411yescharacteristic
227#41—41no—
228#41—41no—
229#41—41no—
230#41—41no—
231C2×Q8—21no—
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×D4—21no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×D4×C1311yescharacteristic
243Q16—22no—
244Q16—21no—
245Q16—22no—
246Q16—21no—
247Q16—41no—
248Q16—41no—
249SD16—41no—
250SD16—41no—
251D8—21no—
252D8—21no—
253M16—21no—
254M16—41no—
255M16—41no—
256M16C13×D812yes—
257C2×C8—21no—
258C2×C8—41no—
259C2×C8C2×D4×C1311yescharacteristic
260C2×C8C2×D4×C1311yescharacteristic
261C2×C8C2×D4×C1311yescharacteristic
262C2×C8C13×#4111yescharacteristic
263C2×C8C13×#4111yescharacteristic
264C2×C8C13×#4111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—41no—
267C22⋊C4—21no—
268C22⋊C4—41no—
269C42—21no—
270C42—41no—
271C16—22no—
272C16—41no—
273C13#1344311yescharacteristic, direct product factor, Sylow
274C23—41no—
275C23C13×AGL(1,ℤ/8)11yescharacteristic
276Q8—41no—
277Q8—42no—
278Q8—41no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—41no—
283D4—41no—
284D4—81no—
285D4—81no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4C13×#12111yescharacteristic
295C2×C4C13×#12111yescharacteristic
296C2×C4C13×#12111yescharacteristic
297C2×C4C2×C13×D811yescharacteristic
298C2×C4C13×#13511yescharacteristic
299C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
300C8—22no—
301C8—81no—
302C8C13×#12011yescharacteristic
303C8C13×#12311yescharacteristic
304C8C13×#12311yescharacteristic
305C8C13×#12411yescharacteristic
306C22—41no—
307C22—81no—
308C22—161no—
309C22C13×#45911yescharacteristic
310C22C13×#46311yescharacteristic
311C22C13×#46911yescharacteristic
312C4—81no—
313C4—81no—
314C4—82no—
315C4—161no—
316C4C13×#39411yescharacteristic
317C4C13×#45911yescharacteristic
318C4C13×#46311yescharacteristic
319C4C13×#46611yescharacteristic
320C2—21no—
321C2—21no—
322C2—21no—
323C2—161no—
324C2C13×#205411yescharacteristic
subgroupG/H
center, socleC2×C13#2054
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#135C22
LCSG ▷ C22×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×#2153C2semidirect
4. C13×#2141C2semidirect
5. C13×#1979C2semidirect
7. C13×#1389C2semidirect
65. #13443C13direct (N × H)
113. #2153C2×C13semidirect
115. #2141C2×C13semidirect
116. #1979C2×C13semidirect
118. #1389C2×C13semidirect
273. C13#13443direct (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
C13×#21532
C13×#21482
C13×#21412
C13×#19792
C13×#19762
C13×#13892
#1344313