Finite Group Databasebeta

← C13×#32976 #15719315

Subgroups — C13×#32976 #15719315

Order 3328.

1382 conjugacy classes of subgroups; only the 298 normal subgroups are shown.

normal subgroups only

This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 298 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C13×H(5,𝔽2)C211yesmaximal, characteristic
2C13×#2487C213yesmaximal, complemented
3C13×#1867C216yesmaximal, complemented
4C13×#1799C213yesmaximal, complemented
5C13×#1790C212yesmaximal
6C2×C13×H(5,𝔽2)C2211yescharacteristic
7C13×#520—23no—
8C13×#518—23no—
9C13×#518C2213yes—
10C4×C13×#41—23no—
11C2×C4×D4×C13—23no—
12C2×C4×D4×C13C2213yes—
13C22×C13×C4⋊C4C2211yescharacteristic, complemented
14C2×C13×#99C2216yes—
15C13×#400—23no—
16C13×#399—23no—
17C13×#389—23no—
18C13×#386C2216yes—
19C13×#385C2216yescomplemented
20C13×#380—23no—
21C13×#380C2213yescomplemented
22C13×#342C2216yescomplemented
23C13×H(5,𝔽2)—26no—
24C13×H(5,𝔽2)Q814yes—
25C2×C13×#41—23no—
26C22×D4×C13—23no—
27C22×D4×C13C2313yes—
28C23×C4×C13—21no—
29C23×C4×C13D413yes—
30C23×C4×C13C2312yes—
31C23×C4×C13C2311yescharacteristic
32C4×Q8×C13—21no—
33C4×Q8×C13—23no—
34C4×D4×C13—23no—
35C4×D4×C13—26no—
36C4×D4×C13—23no—
37C4×D4×C13—26no—
38C4×D4×C13—26no—
39C4×D4×C13—26no—
40C4×D4×C13—26no—
41C13×#117—26no—
42C13×#117—23no—
43C2×C13×C4⋊C4—23no—
44C2×C13×C4⋊C4—23no—
45C2×C13×C4⋊C4—23no—
46C2×C13×C4⋊C4—23no—
47C2×C13×C4⋊C4—26no—
48C2×C13×C4⋊C4D413yes—
49C2×C13×C22⋊C4—23no—
50C2×C13×C22⋊C4—23no—
51C2×C13×C22⋊C4—26no—
52C2×C13×C22⋊C4D413yes—
53C2×C13×C22⋊C4C2316yes—
54C2×C13×C22⋊C4C2313yes—
55C2×C42×C13—23no—
56C2×C42×C13D413yes—
57C13×#99—212no—
58C13×#95—26no—
59C13×#95—23no—
60C13×#95—26no—
61#32976C1311yesmaximal, characteristic, direct product factor, Sylow
62C24×C13—21no—
63C24×C13C2×D413yes—
64C24×C13C2411yescharacteristic
65C13×#41—212no—
66C13×#41—212no—
67C2×Q8×C13—21no—
68C2×D4×C13—23no—
69C2×D4×C13—212no—
70C2×D4×C13—212no—
71C2×D4×C13—26no—
72C2×D4×C13—26no—
73C2×D4×C13C2×Q816yes—
74C2×D4×C13#4116yes—
75C22×C4×C13—23no—
76C22×C4×C13—23no—
77C22×C4×C13—23no—
78C22×C4×C13—23no—
79C22×C4×C13—23no—
80C22×C4×C13—26no—
81C22×C4×C13—26no—
82C22×C4×C13—42no—
83C22×C4×C13—46no—
84C22×C4×C13—82no—
85C22×C4×C13—82no—
86C22×C4×C13C2×D413yes—
87C22×C4×C13C2×D413yes—
88C22×C4×C13C2×D413yes—
89C22×C4×C13C2×D413yes—
90C22×C4×C13C2×D413yes—
91C13×C4⋊C4—23no—
92C13×C4⋊C4—23no—
93C13×C4⋊C4—26no—
94C13×C4⋊C4—46no—
95C13×C4⋊C4—43no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—86no—
98C13×C22⋊C4—26no—
99C13×C22⋊C4—26no—
100C13×C22⋊C4—26no—
101C13×C22⋊C4—212no—
102C13×C22⋊C4—86no—
103C42×C13—26no—
104C42×C13—23no—
105C42×C13—23no—
106C4×H(5,𝔽2)C2×C1311yescharacteristic
107#2487C2×C1313yescomplemented
108#1867C2×C1316yescomplemented
109#1799C2×C1313yescomplemented
110#1790C2×C1312yes—
111C23×C13—24no—
112C23×C13—23no—
113C23×C13—23no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—43no—
117C23×C13—43no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13C22⋊Q816yes—
121C23×C13C22×D413yes—
122C23×C13C22×Q811yescharacteristic
123C23×C13C2×#4113yes—
124Q8×C13—24no—
125D4×C13—212no—
126D4×C13—212no—
127D4×C13—212no—
128C2×C4×C13—212no—
129C2×C4×C13—23no—
130C2×C4×C13—23no—
131C2×C4×C13—26no—
132C2×C4×C13—23no—
133C2×C4×C13—23no—
134C2×C4×C13—43no—
135C2×C4×C13—46no—
136C2×C4×C13—43no—
137C2×C4×C13—43no—
138C2×C4×C13—46no—
139C2×C4×C13—46no—
140C2×C4×C13—46no—
141C2×C4×C13—46no—
142C2×C4×C13—42no—
143C2×C4×C13—46no—
144C2×C4×C13—83no—
145C2×C4×C13—83no—
146C2×C4×C13—83no—
147C2×C4×C13#12013yes—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13C22⋊Q816yes—
150C2×H(5,𝔽2)C22×C1311yescharacteristic
151#520—23no—
152#518—23no—
153#518C22×C1313yes—
154C4×#41—23no—
155C2×C4×D4—23no—
156C2×C4×D4C22×C1313yes—
157C22×C4⋊C4C22×C1311yescharacteristic, complemented
158C2×#99C22×C1316yes—
159#400—23no—
160#399—23no—
161#389—23no—
162#386C22×C1316yes—
163#385C22×C1316yescomplemented
164#380—23no—
165#380C22×C1313yescomplemented
166#342C22×C1316yescomplemented
167C22×C13—23no—
168C22×C13—23no—
169C22×C13—26no—
170C22×C13—41no—
171C22×C13—43no—
172C22×C13—46no—
173C22×C13—43no—
174C22×C13—43no—
175C22×C13—83no—
176C22×C13—84no—
177C22×C13C2×#12011yescharacteristic
178C22×C13C2×C22⋊Q813yes—
179C22×C13#52513yes—
180C4×C13—26no—
181C4×C13—23no—
182C4×C13—43no—
183C4×C13—43no—
184C4×C13—86no—
185C4×C13—82no—
186C4×C13#45812yes—
187H(5,𝔽2)—26no—
188H(5,𝔽2)Q8×C1314yes—
189C2×#41—23no—
190C22×D4—23no—
191C22×D4C23×C1313yes—
192C23×C4—21no—
193C23×C4D4×C1313yes—
194C23×C4C23×C1312yes—
195C23×C4C23×C1311yescharacteristic
196C4×Q8—21no—
197C4×Q8—23no—
198C4×D4—23no—
199C4×D4—26no—
200C4×D4—23no—
201C4×D4—26no—
202C4×D4—26no—
203C4×D4—26no—
204C4×D4—26no—
205#117—26no—
206#117—23no—
207C2×C4⋊C4—23no—
208C2×C4⋊C4—23no—
209C2×C4⋊C4—23no—
210C2×C4⋊C4—23no—
211C2×C4⋊C4—26no—
212C2×C4⋊C4D4×C1313yes—
213C2×C22⋊C4—23no—
214C2×C22⋊C4—23no—
215C2×C22⋊C4—26no—
216C2×C22⋊C4D4×C1313yes—
217C2×C22⋊C4C23×C1316yes—
218C2×C22⋊C4C23×C1313yes—
219C2×C42—23no—
220C2×C42D4×C1313yes—
221#99—212no—
222#95—26no—
223#95—23no—
224#95—26no—
225C2×C13—23no—
226C2×C13—23no—
227C2×C13—46no—
228C2×C13#284811yescharacteristic
229C2×C13C2×#45811yescharacteristic
230C2×C13#302711yescharacteristic
231C24—21no—
232C24C2×D4×C1313yes—
233C24C24×C1311yescharacteristic
234#41—212no—
235#41—212no—
236C2×Q8—21no—
237C2×D4—23no—
238C2×D4—212no—
239C2×D4—212no—
240C2×D4—26no—
241C2×D4—26no—
242C2×D4C2×Q8×C1316yes—
243C2×D4C13×#4116yes—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—42no—
252C22×C4—46no—
253C22×C4—82no—
254C22×C4—82no—
255C22×C4C2×D4×C1313yes—
256C22×C4C2×D4×C1313yes—
257C22×C4C2×D4×C1313yes—
258C22×C4C2×D4×C1313yes—
259C22×C4C2×D4×C1313yes—
260C4⋊C4—23no—
261C4⋊C4—23no—
262C4⋊C4—26no—
263C4⋊C4—46no—
264C4⋊C4—43no—
265C4⋊C4—41no—
266C4⋊C4—86no—
267C22⋊C4—26no—
268C22⋊C4—26no—
269C22⋊C4—26no—
270C22⋊C4—212no—
271C22⋊C4—86no—
272C42—26no—
273C42—23no—
274C42—23no—
275C13#3297611yescharacteristic, direct product factor, Sylow
276C23—24no—
277C23—23no—
278C23—23no—
279C23—41no—
280C23—41no—
281C23—43no—
282C23—43no—
283C23—81no—
284C23—81no—
285C23C13×C22⋊Q816yes—
286C23C22×D4×C1313yes—
287C23C22×Q8×C1311yescharacteristic
288C23C2×C13×#4113yes—
289Q8—24no—
290D4—212no—
291D4—212no—
292D4—212no—
293C2×C4—212no—
294C2×C4—23no—
295C2×C4—23no—
296C2×C4—26no—
297C2×C4—23no—
298C2×C4—23no—
299C2×C4—43no—
300C2×C4—46no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—46no—
304C2×C4—46no—
305C2×C4—46no—
306C2×C4—46no—
307C2×C4—42no—
308C2×C4—46no—
309C2×C4—83no—
310C2×C4—83no—
311C2×C4—83no—
312C2×C4C13×#12013yes—
313C2×C4C13×#12011yescharacteristic
314C2×C4C13×C22⋊Q816yes—
315C22—23no—
316C22—23no—
317C22—26no—
318C22—41no—
319C22—43no—
320C22—46no—
321C22—43no—
322C22—43no—
323C22—83no—
324C22—84no—
325C22C2×C13×#12011yescharacteristic
326C22C2×C13×C22⋊Q813yes—
327C22C13×#52513yes—
328C4—23no—
329C4—26no—
330C4—43no—
331C4—43no—
332C4—86no—
333C4—82no—
334C4C13×#45812yes—
335C2—23no—
336C2—23no—
337C2—46no—
338C2C13×#284811yescharacteristic
339C2C2×C13×#45811yescharacteristic
340C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×H(5,𝔽2)C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2487C2semidirect
3. C13×#1867C2semidirect
4. C13×#1799C2semidirect
13. C22×C13×C4⋊C4C22semidirect
19. C13×#385C22semidirect
21. C13×#380C22semidirect
22. C13×#342C22semidirect
61. #32976C13direct (N × H)
107. #2487C2×C13semidirect
108. #1867C2×C13semidirect
109. #1799C2×C13semidirect
157. C22×C4⋊C4C22×C13semidirect
163. #385C22×C13semidirect
165. #380C22×C13semidirect
166. #342C22×C13semidirect
275. C13#32976direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C13×H(5,𝔽2)2
C13×#24872
C13×#18672
C13×#17992
C13×#17902
#3297613