Finite Group Databasebeta

← C13×#13249 #15699588

Subgroups — C13×#13249 #15699588

Order 3328.

444 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic
2C2×C13×#365C211yesmaximal, characteristic, complemented
3C2×C13×#361C211yesmaximal, characteristic, complemented
4C2×C13×#360C211yesmaximal, characteristic, complemented
5C2×C13×#347C211yesmaximal, characteristic, complemented
6C13×#1975C211yesmaximal, characteristic, complemented
7C13×#1972C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×D8C2211yescharacteristic
10C13×#509—22no—
11C13×#509—22no—
12C2×C13×SD32C412yescomplemented
13C2×C13×D16C412yescomplemented
14C2×C13×M32C2211yescharacteristic
15C2×C13×M32C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17C2×C13×#106C2211yescharacteristic
18C2×C13×#104—21no—
19C2×C13×#102—21no—
20C13×#408—21no—
21C2×C13×#97C2211yescharacteristic
22C13×#390—21no—
23C13×#365—22no—
24C13×#361—22no—
25C13×#360—22no—
26C13×#347—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
34C2×C13×SD16—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8—21no—
39C2×C13×D8—21no—
40C2×C13×D8C2×C411yescharacteristic
41C2×C13×D8C2×C412yes—
42C2×C13×M16—21no—
43C22×C8×C13D411yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C2×C13×C4⋊C4—21no—
46C2×C13×C22⋊C4—42no—
47C2×C42×C13D411yescharacteristic
48C13×SD32—24no—
49C13×D16—24no—
50C13×M32—21no—
51C13×M32D412yes—
52C13×M32D412yes—
53C13×M32D412yes—
54C2×C13×C16—21no—
55C2×C13×C16C2×C412yes—
56C13×#108—21no—
57C13×#108—21no—
58C13×#106—21no—
59C13×#106—21no—
60C13×#104—42no—
61C13×#102—42no—
62C13×C22⋊C8—42no—
63C13×#97—21no—
64C13×#97—21no—
65#13249C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—41no—
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C2×Q8×C13—21no—
72C2×D4×C13—22no—
73C2×D4×C13—21no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C22×C4×C13—21no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C13×Q16—21no—
85C13×Q16—21no—
86C13×SD16—41no—
87C13×SD16—41no—
88C13×D8—21no—
89C13×D8—22no—
90C13×D8—22no—
91C13×D8—21no—
92C13×D8—41no—
93C13×D8—41no—
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—
108C13×C22⋊C4—84no—
109C42×C13—21no—
110C42×C13—21no—
111C13×C16—22no—
112C13×C16C22⋊C414yescomplemented
113C2×#509C2×C1311yescharacteristic
114C2×#365C2×C1311yescharacteristic, complemented
115C2×#361C2×C1311yescharacteristic, complemented
116C2×#360C2×C1311yescharacteristic, complemented
117C2×#347C2×C1311yescharacteristic, complemented
118#1975C2×C1311yescharacteristic, complemented
119#1972C2×C1311yescharacteristic, complemented
120C23×C13—41no—
121C23×C13—42no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13AGL(1,ℤ/8)11yescharacteristic
127Q8×C13—41no—
128Q8×C13—41no—
129D4×C13—42no—
130D4×C13—41no—
131D4×C13—42no—
132D4×C13—41no—
133D4×C13—81no—
134D4×C13—81no—
135D4×C13—81no—
136D4×C13—81no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—82no—
143C2×C4×C13—81no—
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12711yescharacteristic
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C8×C13—41no—
151C8×C13—81no—
152C8×C13C2×C22⋊C411yescharacteristic
153C8×C13C4×D411yescharacteristic
154C8×C13#12111yescharacteristic
155C8×C13#12411yescharacteristic
156C2×#135C22×C1311yescharacteristic
157C22×D8C22×C1311yescharacteristic
158#509—22no—
159#509—22no—
160C2×SD32C4×C1312yescomplemented
161C2×D16C4×C1312yescomplemented
162C2×M32C22×C1311yescharacteristic
163C2×M32C22×C1311yescharacteristic
164C2×#108C22×C1311yescharacteristic
165C2×#106C22×C1311yescharacteristic
166C2×#104—21no—
167C2×#102—21no—
168#408—21no—
169C2×#97C22×C1311yescharacteristic
170#390—21no—
171#365—22no—
172#361—22no—
173#360—22no—
174#347—22no—
175C22×C13—22no—
176C22×C13—82no—
177C22×C13—84no—
178C22×C13—81no—
179C22×C13—82no—
180C22×C13—162no—
181C22×C13—161no—
182C22×C13—161no—
183C22×C13#44211yescharacteristic
184C22×C13#46911yescharacteristic
185C22×C13#49611yescharacteristic
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—161no—
189C4×C13#39011yescharacteristic
190C4×C13#44211yescharacteristic
191C4×C13#46911yescharacteristic
192C4×C13#49611yescharacteristic
193C2×#41—21no—
194C22×D4—21no—
195#135—21no—
196#135—21no—
197#135—21no—
198#135—21no—
199C2×Q16C2×C4×C1311yescharacteristic
200C2×SD16—21no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8C2×C4×C1312yes—
207C2×D8C2×C4×C1311yescharacteristic
208C2×M16—21no—
209C22×C8D4×C1311yescharacteristic
210C22×C8C23×C1311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C22⋊C4—42no—
213C2×C42D4×C1311yescharacteristic
214SD32—24no—
215D16—24no—
216M32—21no—
217M32D4×C1312yes—
218M32D4×C1312yes—
219M32D4×C1312yes—
220C2×C16—21no—
221C2×C16C2×C4×C1312yes—
222#108—21no—
223#108—21no—
224#106—21no—
225#106—21no—
226#104—42no—
227#102—42no—
228C22⋊C8—42no—
229#97—21no—
230#97—21no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—161no—
234C2×C13—162no—
235C2×C13#197211yescharacteristic
236C2×C13AGL(1,ℤ/16)12yes—
237C24—41no—
238#41—41no—
239#41—41no—
240#41—41no—
241#41—41no—
242C2×Q8—21no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C1311yescharacteristic
255Q16—21no—
256Q16—21no—
257SD16—41no—
258SD16—41no—
259D8—21no—
260D8—22no—
261D8—22no—
262D8—21no—
263D8—41no—
264D8—41no—
265M16—41no—
266M16—41no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—41no—
271C2×C8C22×C4×C1311yescharacteristic
272C2×C8C2×D4×C1311yescharacteristic
273C2×C8C2×D4×C1311yescharacteristic
274C2×C8C2×D4×C1311yescharacteristic
275C2×C8C13×#4111yescharacteristic
276C2×C8C13×#4111yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—41no—
279C22⋊C4—84no—
280C42—21no—
281C42—21no—
282C16—22no—
283C16C13×C22⋊C414yescomplemented
284C13#1324911yescharacteristic, direct product factor, Sylow
285C23—41no—
286C23—42no—
287C23—82no—
288C23—82no—
289C23—81no—
290C23—81no—
291C23C13×AGL(1,ℤ/8)11yescharacteristic
292Q8—41no—
293Q8—41no—
294D4—42no—
295D4—41no—
296D4—42no—
297D4—41no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—82no—
308C2×C4—81no—
309C2×C4C4×D4×C1311yescharacteristic
310C2×C4C13×#12111yescharacteristic
311C2×C4C13×#12711yescharacteristic
312C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
313C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
314C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
315C8—41no—
316C8—81no—
317C8C2×C13×C22⋊C411yescharacteristic
318C8C4×D4×C1311yescharacteristic
319C8C13×#12111yescharacteristic
320C8C13×#12411yescharacteristic
321C22—22no—
322C22—82no—
323C22—84no—
324C22—81no—
325C22—82no—
326C22—162no—
327C22—161no—
328C22—161no—
329C22C13×#44211yescharacteristic
330C22C13×#46911yescharacteristic
331C22C13×#49611yescharacteristic
332C4—81no—
333C4—81no—
334C4—161no—
335C4C13×#39011yescharacteristic
336C4C13×#44211yescharacteristic
337C4C13×#46911yescharacteristic
338C4C13×#49611yescharacteristic
339C2—21no—
340C2—21no—
341C2—162no—
342C2—161no—
343C2C13×#197211yescharacteristic
344C2C13×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C13#442
commutatorC2×C8C22×C4×C13
Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#509C2
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×#361C2semidirect
4. C2×C13×#360C2semidirect
5. C2×C13×#347C2semidirect
6. C13×#1975C2semidirect
7. C13×#1972C2semidirect
12. C2×C13×SD32C4semidirect
13. C2×C13×D16C4semidirect
65. #13249C13direct (N × H)
112. C13×C16C22⋊C4semidirect
114. C2×#365C2×C13semidirect
115. C2×#361C2×C13semidirect
116. C2×#360C2×C13semidirect
117. C2×#347C2×C13semidirect
118. #1975C2×C13semidirect
119. #1972C2×C13semidirect
160. C2×SD32C4×C13semidirect
161. C2×D16C4×C13semidirect
283. C16C13×C22⋊C4semidirect
284. C13#13249direct (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
C2×C13×#3652
C2×C13×#3612
C2×C13×#3602
C2×C13×#3472
C13×#19752
C13×#19722
#1324913