Finite Group Databasebeta

← #13125035

Subgroups — #13125035

Order 1664.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#520C211yesmaximal, characteristic, complemented
2#11719240C211yesmaximal, characteristic, complemented
3#11718899C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718688C211yesmaximal, characteristic, complemented
6#11718687C211yesmaximal, characteristic, complemented
7C4×#6106C211yesmaximal, characteristic, complemented
8#11718683C211yesmaximal, characteristic, complemented
9#11718676C211yesmaximal, characteristic, complemented
10#11718675C211yesmaximal, characteristic, complemented
11C4×#6104C211yesmaximal, characteristic, complemented
12#11718670C211yesmaximal, characteristic, complemented
13#11718661C211yesmaximal, characteristic, complemented
14#11718629C211yesmaximal, characteristic, complemented
15#11718628C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13—21no—
21C4×D4×C13C2211yescharacteristic
22C4×D4×C13C2211yescharacteristic
23C13×#117—21no—
24C13×#117C2211yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6104C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88184C2211yescharacteristic
33#88148—21no—
34#88148—21no—
35#88138—21no—
36#88138—21no—
37#88128C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88124C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88049C2211yescharacteristic
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52C2311yescharacteristic
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4D411yescharacteristic
81C13×C4⋊C4D411yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4D411yescharacteristic
87C13×C22⋊C4D411yescharacteristic
88C42×C13—21no—
89C42×C13—21no—
90C42×C13C2311yescharacteristic
91C42×C13C2311yescharacteristic
92#6106—22no—
93#6106—22no—
94#6104—22no—
95#6104—22no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3119—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112C22×D13—21no—
113Q8×C13—21no—
114Q8×C13#4112yes—
115D4×C13—24no—
116D4×C13—21no—
117D4×C13#4112yes—
118C2×C4×C13—24no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—81no—
134C22⋊D13—81no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137D52—21no—
138D52—21no—
139D52—21no—
140D52—21no—
141D52—81no—
142D52—81no—
143C4×D13—81no—
144C4×D13—81no—
145#1055—21no—
146#1055—21no—
147#1055—21no—
148#1055—21no—
149#540—131no—
150#520D1311yescharacteristic, complemented
151#481—131no—
152#480—131no—
153#479—131no—
154#478—131no—
155#460—131no—
156#459—131no—
157#449—131no—
158#449—131no—
159#442—131no—
160#440—131no—
161C4×SD16—131no—
162C4×D8—131no—
163#433—131no—
164C22×C13—21no—
165C22×C13—22no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13C22×D411yescharacteristic
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13C2×#4111yescharacteristic
187Dic13—41no—
188Dic13—41no—
189C2×#41C2×D1311yescharacteristic
190C2×SD16—131no—
191C2×SD16—131no—
192C2×D8—131no—
193C2×D8—131no—
194#127—131no—
195#125—131no—
196#123—261no—
197#123—261no—
198#121—131no—
199#121—131no—
200#121—261no—
201#121—261no—
202C4×Q8C2×D1311yescharacteristic
203C4×Q8C2×D1311yescharacteristic
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—131no—
207C4×D4—131no—
208C4×D4C2×D1311yescharacteristic
209C4×D4C2×D1311yescharacteristic
210#117—21no—
211#117C2×D1311yescharacteristic
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×D1311yescharacteristic
214#107—131no—
215#107—131no—
216#106—131no—
217#106—131no—
218C4⋊C8—131no—
219C4⋊C8—131no—
220#103—131no—
221#103—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8—131no—
229C22⋊C8—131no—
230#97—131no—
231C4×C8—131no—
232C2×C13—41no—
233C2×C13—42no—
234C2×C13#52511yescharacteristic
235C2×C13#57611yescharacteristic
236C2×C13#57711yescharacteristic
237D13—81no—
238D13—81no—
239#41—22no—
240#41—22no—
241C2×Q8C22×D1311yescharacteristic
242C2×D4—21no—
243C2×D4—131no—
244C2×D4—131no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4—261no—
249C2×D4C22×D1311yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4C22×D1311yescharacteristic
257SD16—262no—
258SD16—262no—
259D8—262no—
260D8—262no—
261C2×C8—131no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—131no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—131no—
269C4⋊C4—131no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4C22⋊D1311yescharacteristic
273C4⋊C4C22⋊D1311yescharacteristic
274C4⋊C4C22×D1311yescharacteristic
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4C22⋊D1311yescharacteristic
283C22⋊C4C22⋊D1311yescharacteristic
284C42—21no—
285C42—21no—
286C42C22×D1311yescharacteristic
287C42C22×D1311yescharacteristic
288C13#311911yescharacteristic, complemented, Sylow
289C23—21no—
290C23—261no—
291C23—261no—
292C23C2×C22⋊D1311yescharacteristic
293Q8—21no—
294Q8#612712yes—
295D4—24no—
296D4—21no—
297D4—261no—
298D4—261no—
299D4—261no—
300D4—261no—
301D4—1041no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305D4#612712yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—1041no—
318C2×C4—1041no—
319C2×C4C2×C22⋊D1311yescharacteristic
320C2×C4C2×C22⋊D1311yescharacteristic
321C2×C4C2×C22⋊D1311yescharacteristic
322C2×C4C2×C22⋊D1311yescharacteristic
323C2×C4C2×C22⋊D1311yescharacteristic
324C2×C4C23×D1311yescharacteristic
325C8—261no—
326C8—261no—
327C8—261no—
328C8—261no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—521no—
336C22—521no—
337C22—521no—
338C22—521no—
339C22—521no—
340C22—521no—
341C22C22×C22⋊D1311yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—521no—
351C4—521no—
352C4C2×#612711yescharacteristic
353C4C2×#612711yescharacteristic
354C2—41no—
355C2—42no—
356C2—1041no—
357C2—1041no—
358C2#1171949611yescharacteristic
359C2#1171954011yescharacteristic
360C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#520C2
socleC22×C13C22×D4
hypercenter#520D13
hypocenterC13#3119
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C13×#520C2semidirect
2. #11719240C2semidirect
3. #11718899C2semidirect
4. #11718899C2semidirect
5. #11718688C2semidirect
6. #11718687C2semidirect
7. C4×#6106C2semidirect
8. #11718683C2semidirect
9. #11718676C2semidirect
10. #11718675C2semidirect
11. C4×#6104C2semidirect
12. #11718670C2semidirect
13. #11718661C2semidirect
14. #11718629C2semidirect
15. #11718628C2semidirect
150. #520D13semidirect
288. C13#3119semidirect

Maximal subgroups

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

subgroupindex
C13×#5202
#117192402
#117188992
#117186882
#117186872
C4×#61062
#117186832
#117186762
#117186752
C4×#61042
#117186702
#117186612
#117186292
#117186282
#311913