Finite Group Databasebeta

← C13×#13027 #15699366

Subgroups — C13×#13027 #15699366

Order 3328.

484 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3414C211yesmaximal, characteristic
2C4×C13×#135C211yesmaximal, characteristic, complemented
3C13×#2145C211yesmaximal, characteristic, complemented
4C13×#2143C211yesmaximal, characteristic, complemented
5C13×#1974C211yesmaximal, characteristic, complemented
6C13×#1389C211yesmaximal, characteristic, complemented
7C13×#1376C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C2×C13×#135C2211yescharacteristic
10C4×C13×#41—21no—
11C13×#510—21no—
12C13×#510C412yescomplemented
13C13×#509—21no—
14C13×#509C412yescomplemented
15C13×#508—22no—
16C2×C13×M32C2211yescharacteristic
17C2×C13×M32C2211yescharacteristic
18C4×C13×Q16—21no—
19C4×C13×SD16—22no—
20C4×C13×D8—21no—
21C2×C13×#108C2211yescharacteristic
22C13×#427C2211yescharacteristic
23C2×C13×#104—21no—
24C13×#416—21no—
25C13×#408—21no—
26C2×C4×C8×C13C2211yescharacteristic
27C13×#360—22no—
28C13×#359—22no—
29C2×C13×#41—21no—
30C2×C13×#41—21no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135—21no—
34C13×#135—21no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135C2×C412yes—
38C13×#135D412yes—
39C2×C13×Q16C2×C411yescharacteristic, complemented
40C2×C13×Q16D411yescharacteristic
41C2×C13×SD16—21no—
42C2×C13×SD16—21no—
43C2×C13×D8C2×C411yescharacteristic, complemented
44C2×C13×D8D411yescharacteristic
45C2×C13×M16—21no—
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C4×Q8×C13—22no—
49C4×D4×C13—22no—
50C4×D4×C13—42no—
51C13×#117—21no—
52C13×#117—41no—
53C2×C42×C13—41no—
54C2×C42×C13D411yescharacteristic
55C13×Q32—22no—
56C13×SD32—22no—
57C13×SD32—22no—
58C13×D16—22no—
59C13×M32—21no—
60C13×M32—21no—
61C13×M32—21no—
62C13×M32C2×C412yescomplemented
63C2×C13×C16—21no—
64C2×C13×C16—21no—
65C13×#108—21no—
66C13×#108—21no—
67C13×#107—21no—
68C13×#106D412yes—
69C13×#104—41no—
70C13×#104—41no—
71C13×#103—22no—
72C13×#102—22no—
73C13×C22⋊C8—42no—
74C4×C8×C13—21no—
75C4×C8×C13—21no—
76#13027C1311yesmaximal, characteristic, direct product factor, Sylow
77C13×#41—22no—
78C13×#41—22no—
79C13×#41—41no—
80C13×#41—41no—
81C13×#41—41no—
82C13×#41—41no—
83C13×#41—41no—
84C13×#41—41no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C22×C4×C13—21no—
92C22×C4×C13—42no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13C2×D411yescharacteristic
96C13×Q16—21no—
97C13×Q16—21no—
98C13×Q16—21no—
99C13×Q16C22⋊C412yes—
100C13×SD16—22no—
101C13×SD16—22no—
102C13×SD16—41no—
103C13×SD16—41no—
104C13×D8—21no—
105C13×D8—21no—
106C13×D8—21no—
107C13×D8C22⋊C412yes—
108C13×M16—41no—
109C13×M16—41no—
110C2×C8×C13—21no—
111C2×C8×C13—21no—
112C2×C8×C13—21no—
113C2×C8×C13—41no—
114C2×C8×C13C22×C411yescharacteristic
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13#4111yescharacteristic
119C2×C8×C13#4111yescharacteristic
120C13×C4⋊C4—22no—
121C13×C4⋊C4—42no—
122C13×C22⋊C4—42no—
123C13×C22⋊C4—41no—
124C42×C13—21no—
125C42×C13—42no—
126C42×C13—41no—
127C42×C13D811yescharacteristic
128C42×C13D811yescharacteristic
129C13×C16—22no—
130C13×C16—41no—
131#3414C2×C1311yescharacteristic
132C4×#135C2×C1311yescharacteristic, complemented
133#2145C2×C1311yescharacteristic, complemented
134#2143C2×C1311yescharacteristic, complemented
135#1974C2×C1311yescharacteristic, complemented
136#1389C2×C1311yescharacteristic, complemented
137#1376C2×C1311yescharacteristic, complemented
138C23×C13—41no—
139C23×C13—41no—
140C23×C13AGL(1,ℤ/8)11yescharacteristic
141Q8×C13—22no—
142Q8×C13—41no—
143Q8×C13—41no—
144Q8×C13—41no—
145D4×C13—22no—
146D4×C13—42no—
147D4×C13—42no—
148D4×C13—41no—
149D4×C13—41no—
150D4×C13—41no—
151D4×C13—81no—
152D4×C13—81no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—42no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—84no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13C4×D411yescharacteristic
165C2×C4×C13#12011yescharacteristic
166C2×C4×C13#12111yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
170C8×C13—41no—
171C8×C13—81no—
172C8×C13C2×C22⋊C411yescharacteristic
173C8×C13C4×D411yescharacteristic
174C8×C13#12111yescharacteristic
175C8×C13#12311yescharacteristic
176C2×#135C22×C1311yescharacteristic
177C2×#135C22×C1311yescharacteristic
178C4×#41—21no—
179#510—21no—
180#510C4×C1312yescomplemented
181#509—21no—
182#509C4×C1312yescomplemented
183#508—22no—
184C2×M32C22×C1311yescharacteristic
185C2×M32C22×C1311yescharacteristic
186C4×Q16—21no—
187C4×SD16—22no—
188C4×D8—21no—
189C2×#108C22×C1311yescharacteristic
190#427C22×C1311yescharacteristic
191C2×#104—21no—
192#416—21no—
193#408—21no—
194C2×C4×C8C22×C1311yescharacteristic
195#360—22no—
196#359—22no—
197C22×C13—41no—
198C22×C13—42no—
199C22×C13—82no—
200C22×C13—82no—
201C22×C13—81no—
202C22×C13#44211yescharacteristic
203C22×C13#44711yescharacteristic
204C22×C13#46311yescharacteristic
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—42no—
208C4×C13—82no—
209C4×C13—81no—
210C4×C13#38611yescharacteristic
211C4×C13C4×D811yescharacteristic
212C4×C13#44911yescharacteristic
213C4×C13#45911yescharacteristic
214C2×#41—21no—
215C2×#41—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135—21no—
221#135—21no—
222#135C2×C4×C1312yes—
223#135D4×C1312yes—
224C2×Q16C2×C4×C1311yescharacteristic, complemented
225C2×Q16D4×C1311yescharacteristic
226C2×SD16—21no—
227C2×SD16—21no—
228C2×D8C2×C4×C1311yescharacteristic, complemented
229C2×D8D4×C1311yescharacteristic
230C2×M16—21no—
231C22×C8D4×C1311yescharacteristic
232C22×C8C23×C1311yescharacteristic
233C4×Q8—22no—
234C4×D4—22no—
235C4×D4—42no—
236#117—21no—
237#117—41no—
238C2×C42—41no—
239C2×C42D4×C1311yescharacteristic
240Q32—22no—
241SD32—22no—
242SD32—22no—
243D16—22no—
244M32—21no—
245M32—21no—
246M32—21no—
247M32C2×C4×C1312yescomplemented
248C2×C16—21no—
249C2×C16—21no—
250#108—21no—
251#108—21no—
252#107—21no—
253#106D4×C1312yes—
254#104—41no—
255#104—41no—
256#103—22no—
257#102—22no—
258C22⋊C8—42no—
259C4×C8—21no—
260C4×C8—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—82no—
265C2×C13—161no—
266C2×C13#187911yescharacteristic
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C22×C4—21no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C1311yescharacteristic
286Q16—21no—
287Q16—21no—
288Q16—21no—
289Q16C13×C22⋊C412yes—
290SD16—22no—
291SD16—22no—
292SD16—41no—
293SD16—41no—
294D8—21no—
295D8—21no—
296D8—21no—
297D8C13×C22⋊C412yes—
298M16—41no—
299M16—41no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8C22×C4×C1311yescharacteristic
305C2×C8C2×D4×C1311yescharacteristic
306C2×C8C2×D4×C1311yescharacteristic
307C2×C8C2×D4×C1311yescharacteristic
308C2×C8C13×#4111yescharacteristic
309C2×C8C13×#4111yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C42—21no—
315C42—42no—
316C42—41no—
317C42C13×D811yescharacteristic
318C42C13×D811yescharacteristic
319C16—22no—
320C16—41no—
321C13#1302711yescharacteristic, direct product factor, Sylow
322C23—41no—
323C23—41no—
324C23C13×AGL(1,ℤ/8)11yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—81no—
336D4—81no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—84no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4C4×D4×C1311yescharacteristic
349C2×C4C13×#12011yescharacteristic
350C2×C4C13×#12111yescharacteristic
351C2×C4C2×C13×D811yescharacteristic
352C2×C4C13×#13511yescharacteristic
353C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
354C8—41no—
355C8—81no—
356C8C2×C13×C22⋊C411yescharacteristic
357C8C4×D4×C1311yescharacteristic
358C8C13×#12111yescharacteristic
359C8C13×#12311yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—81no—
365C22C13×#44211yescharacteristic
366C22C13×#44711yescharacteristic
367C22C13×#46311yescharacteristic
368C4—22no—
369C4—41no—
370C4—42no—
371C4—82no—
372C4—81no—
373C4C13×#38611yescharacteristic
374C4C4×C13×D811yescharacteristic
375C4C13×#44911yescharacteristic
376C4C13×#45911yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2C13×#187911yescharacteristic
subgroupG/H
centerC4×C13#459
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
socleC2×C13#1879
prime radicalC13×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C13×#135C2semidirect
3. C13×#2145C2semidirect
4. C13×#2143C2semidirect
5. C13×#1974C2semidirect
6. C13×#1389C2semidirect
7. C13×#1376C2semidirect
12. C13×#510C4semidirect
14. C13×#509C4semidirect
39. C2×C13×Q16C2×C4semidirect
43. C2×C13×D8C2×C4semidirect
62. C13×M32C2×C4semidirect
76. #13027C13direct (N × H)
132. C4×#135C2×C13semidirect
133. #2145C2×C13semidirect
134. #2143C2×C13semidirect
135. #1974C2×C13semidirect
136. #1389C2×C13semidirect
137. #1376C2×C13semidirect
180. #510C4×C13semidirect
182. #509C4×C13semidirect
224. C2×Q16C2×C4×C13semidirect
228. C2×D8C2×C4×C13semidirect
247. M32C2×C4×C13semidirect
321. C13#13027direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34142
C4×C13×#1352
C13×#21452
C13×#21432
C13×#19742
C13×#13892
C13×#13762
#1302713