Finite Group Databasebeta

← C13×#13403 #15699742

Subgroups — C13×#13403 #15699742

Order 3328.

384 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#473C211yesmaximal, characteristic
2C13×#2155C211yesmaximal, characteristic, complemented
3C2×C13×#362C211yesmaximal, characteristic, complemented
4C13×#2141C211yesmaximal, characteristic, complemented
5C13×#2115C211yesmaximal, characteristic
6C13×#1814C211yesmaximal, characteristic
7C13×#1388C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C22×C13×Q16C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C2×C13×M32C2211yescharacteristic
12C2×C13×M32C2211yescharacteristic
13C13×#473—22no—
14C13×#473—22no—
15C2×C13×#108C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17C13×#427C2211yescharacteristic
18C13×#421—21no—
19C2×C13×#101—21no—
20C13×#365—22no—
21C13×#362—22no—
22C13×#358—22no—
23C13×#349—22no—
24C13×#344—21no—
25C2×C13×#41D411yescharacteristic
26C22×Q8×C13—21no—
27C13×#137—24no—
28C13×#137—42no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—41no—
35C2×C13×Q16D412yes—
36C2×C13×SD16—41no—
37C13×#131—21no—
38C13×#131—21no—
39C13×#131—21no—
40C13×#131—21no—
41C2×C13×M16—21no—
42C2×C13×M16—21no—
43C2×C13×M16—21no—
44C2×C13×M16D411yescharacteristic
45C22×C8×C13—21no—
46C22×C8×C13C2311yescharacteristic
47C13×#117—21no—
48C13×M32—21no—
49C13×M32—21no—
50C13×M32—21no—
51C13×M32D412yes—
52C2×C13×C16—21no—
53C2×C13×C16—21no—
54C13×#108—21no—
55C13×#108—21no—
56C13×#108—21no—
57C13×#108D412yes—
58C13×#107—21no—
59C13×#106—21no—
60C13×#104—42no—
61C13×#101—24no—
62#13403C1311yesmaximal, characteristic, direct product factor, Sylow
63C13×#41—21no—
64C13×#41—21no—
65C13×#41—21no—
66C13×#41—21no—
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13SD1611yescharacteristic
74C2×D4×C13—21no—
75C2×D4×C13SD1611yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C13×Q16—22no—
80C13×Q16—22no—
81C13×Q16—44no—
82C13×Q16—41no—
83C13×Q16—41no—
84C13×SD16—44no—
85C13×M16—21no—
86C13×M16—22no—
87C13×M16—21no—
88C13×M16—41no—
89C13×M16—41no—
90C13×M16—41no—
91C13×M16—41no—
92C13×M16—41no—
93C2×C8×C13—21no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
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—41no—
105C13×C22⋊C4—41no—
106C42×C13—41no—
107C13×C16—22no—
108C13×C16—41no—
109C2×#473C2×C1311yescharacteristic
110#2155C2×C1311yescharacteristic, complemented
111C2×#362C2×C1311yescharacteristic, complemented
112#2141C2×C1311yescharacteristic, complemented
113#2115C2×C1311yescharacteristic
114#1814C2×C1311yescharacteristic
115#1388C2×C1311yescharacteristic, complemented
116C23×C13—21no—
117C23×C13#13511yescharacteristic
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13—81no—
123Q8×C13—81no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—41no—
127D4×C13—41no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12311yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C8×C13—41no—
142C8×C13—42no—
143C8×C13—81no—
144C8×C13#12111yescharacteristic
145C8×C13#12111yescharacteristic
146C8×C13#12311yescharacteristic
147C8×C13#12411yescharacteristic
148C2×#137—21no—
149C22×Q16C22×C1311yescharacteristic
150C2×#131C22×C1311yescharacteristic
151C2×M32C22×C1311yescharacteristic
152C2×M32C22×C1311yescharacteristic
153#473—22no—
154#473—22no—
155C2×#108C22×C1311yescharacteristic
156C2×#108C22×C1311yescharacteristic
157#427C22×C1311yescharacteristic
158#421—21no—
159C2×#101—21no—
160#365—22no—
161#362—22no—
162#358—22no—
163#349—22no—
164#344—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—81no—
168C22×C13#44911yescharacteristic
169C22×C13#46511yescharacteristic
170C22×C13#48211yescharacteristic
171C4×C13—41no—
172C4×C13—82no—
173C4×C13—161no—
174C4×C13#39411yescharacteristic
175C4×C13#45011yescharacteristic
176C4×C13#46911yescharacteristic
177C4×C13#48111yescharacteristic
178C2×#41D4×C1311yescharacteristic
179C22×Q8—21no—
180#137—24no—
181#137—42no—
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×Q16—21no—
186C2×Q16—21no—
187C2×Q16—41no—
188C2×Q16D4×C1312yes—
189C2×SD16—41no—
190#131—21no—
191#131—21no—
192#131—21no—
193#131—21no—
194C2×M16—21no—
195C2×M16—21no—
196C2×M16—21no—
197C2×M16D4×C1311yescharacteristic
198C22×C8—21no—
199C22×C8C23×C1311yescharacteristic
200#117—21no—
201M32—21no—
202M32—21no—
203M32—21no—
204M32D4×C1312yes—
205C2×C16—21no—
206C2×C16—21no—
207#108—21no—
208#108—21no—
209#108—21no—
210#108D4×C1312yes—
211#107—21no—
212#106—21no—
213#104—42no—
214#101—24no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—81no—
219C2×C13#203411yescharacteristic
220#41—21no—
221#41—21no—
222#41—21no—
223#41—21no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8C13×SD1611yescharacteristic
231C2×D4—21no—
232C2×D4C13×SD1611yescharacteristic
233C22×C4—21no—
234C22×C4—41no—
235C22×C4C2×D4×C1311yescharacteristic
236Q16—22no—
237Q16—22no—
238Q16—44no—
239Q16—41no—
240Q16—41no—
241SD16—44no—
242M16—21no—
243M16—22no—
244M16—21no—
245M16—41no—
246M16—41no—
247M16—41no—
248M16—41no—
249M16—41no—
250C2×C8—21no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8C2×D4×C1311yescharacteristic
256C2×C8C2×D4×C1311yescharacteristic
257C2×C8C2×D4×C1311yescharacteristic
258C2×C8C13×#4111yescharacteristic
259C2×C8C13×#4111yescharacteristic
260C2×C8C13×#4111yescharacteristic
261C4⋊C4—41no—
262C22⋊C4—41no—
263C42—41no—
264C16—22no—
265C16—41no—
266C13#1340311yescharacteristic, direct product factor, Sylow
267C23—21no—
268C23C13×#13511yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—42no—
272Q8—42no—
273Q8—81no—
274Q8—81no—
275D4—21no—
276D4—21no—
277D4—41no—
278D4—41no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4C13×#12011yescharacteristic
287C2×C4C13×#12111yescharacteristic
288C2×C4C13×#12311yescharacteristic
289C2×C4C2×C13×SD1611yescharacteristic
290C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
291C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
292C8—41no—
293C8—42no—
294C8—81no—
295C8C13×#12111yescharacteristic
296C8C13×#12111yescharacteristic
297C8C13×#12311yescharacteristic
298C8C13×#12411yescharacteristic
299C22—41no—
300C22—41no—
301C22—81no—
302C22C13×#44911yescharacteristic
303C22C13×#46511yescharacteristic
304C22C13×#48211yescharacteristic
305C4—41no—
306C4—82no—
307C4—161no—
308C4C13×#39411yescharacteristic
309C4C13×#45011yescharacteristic
310C4C13×#46911yescharacteristic
311C4C13×#48111yescharacteristic
312C2—21no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2C13×#203411yescharacteristic
subgroupG/H
center, socleC2×C13#2034
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#41D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2155C2semidirect
3. C2×C13×#362C2semidirect
4. C13×#2141C2semidirect
7. C13×#1388C2semidirect
62. #13403C13direct (N × H)
110. #2155C2×C13semidirect
111. C2×#362C2×C13semidirect
112. #2141C2×C13semidirect
115. #1388C2×C13semidirect
266. C13#13403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4732
C13×#21552
C2×C13×#3622
C13×#21412
C13×#21152
C13×#18142
C13×#13882
#1340313