Finite Group Databasebeta

← C13×#9500 #15695839

Subgroups — C13×#9500 #15695839

Order 3328.

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C13×#2483C211yesmaximal, characteristic
2C13×#2312C211yesmaximal, characteristic
3C13×#1819C211yesmaximal, characteristic
4C13×#1819C212yesmaximal
5C13×#1304C212yesmaximal
6C22×C13×C22⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#397—22no—
9C13×#388—24no—
10C13×#385—21no—
11C13×#385C412yescomplemented
12C13×#381—21no—
13C13×#381C412yescomplemented
14C13×#380—21no—
15C13×#379C2212yes—
16C13×#379C2211yescharacteristic
17C13×#379C2212yes—
18C4×C13×C22⋊C4—21no—
19C13×#342—24no—
20C13×#342—22no—
21C25×C13C2311yescharacteristic
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4C2×C412yes—
42C2×C13×C22⋊C4C2×C412yes—
43C2×C13×C22⋊C4D412yes—
44C2×C13×C22⋊C4D414yes—
45C2×C42×C13—22no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95—22no—
50C13×#95—22no—
51#9500C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—42no—
53C24×C13—42no—
54C24×C13—81no—
55C24×C13C22×C411yescharacteristic
56C24×C13C2×D411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C24×C13C2×D412yes—
59C24×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—24no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C412yes—
76C22×C4×C13C22⋊C412yes—
77C13×C4⋊C4—82no—
78C13×C4⋊C4—82no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—44no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—44no—
88C13×C22⋊C4—44no—
89C13×C22⋊C4—44no—
90C13×C22⋊C4—82no—
91C13×C22⋊C4—81no—
92C13×C22⋊C4—82no—
93C42×C13—82no—
94#2483C2×C1311yescharacteristic
95#2312C2×C1311yescharacteristic
96#1819C2×C1312yes—
97#1819C2×C1311yescharacteristic
98#1304C2×C1312yes—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—22no—
102C23×C13—22no—
103C23×C13—24no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—41no—
111C23×C13—42no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—88no—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13C4×D412yes—
117C23×C13#12011yescharacteristic
118C23×C13#12112yes—
119C23×C13#12311yescharacteristic
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—42no—
129C2×C4×C13—44no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—44no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—82no—
139C2×C4×C13—82no—
140C2×C4×C13—82no—
141C2×C4×C13—82no—
142C2×C4×C13—82no—
143C22×C22⋊C4C22×C1311yescharacteristic
144C22×C22⋊C4C22×C1311yescharacteristic
145#397—22no—
146#388—24no—
147#385—21no—
148#385C4×C1312yescomplemented
149#381—21no—
150#381C4×C1312yescomplemented
151#380—21no—
152#379C22×C1312yes—
153#379C22×C1311yescharacteristic
154#379C22×C1312yes—
155C4×C22⋊C4—21no—
156#342—24no—
157#342—22no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—21no—
171C22×C13—44no—
172C22×C13—44no—
173C22×C13—84no—
174C22×C13—82no—
175C22×C13—84no—
176C22×C13#38611yescharacteristic
177C22×C13#41012yes—
178C22×C13#45812yes—
179C4×C13—42no—
180C4×C13—42no—
181C4×C13—84no—
182C4×C13—82no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13—162no—
186C25C23×C1311yescharacteristic
187C23×C4C2×C4×C1311yescharacteristic
188C23×C4C2×C4×C1311yescharacteristic
189C23×C4D4×C1311yescharacteristic
190C23×C4D4×C1311yescharacteristic
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4C2×C4×C1312yes—
207C2×C22⋊C4C2×C4×C1312yes—
208C2×C22⋊C4D4×C1312yes—
209C2×C22⋊C4D4×C1314yes—
210C2×C42—22no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95—22no—
216C2×C13—22no—
217C2×C13—22no—
218C2×C13—42no—
219C2×C13—41no—
220C2×C13—42no—
221C2×C13#189011yescharacteristic
222C2×C13#189911yescharacteristic
223C2×C13#191311yescharacteristic
224C24—42no—
225C24—42no—
226C24—81no—
227C24C22×C4×C1311yescharacteristic
228C24C2×D4×C1311yescharacteristic
229C24C2×D4×C1311yescharacteristic
230C24C2×D4×C1312yes—
231C24C13×#4112yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4C13×C22⋊C412yes—
248C22×C4C13×C22⋊C412yes—
249C4⋊C4—82no—
250C4⋊C4—82no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—44no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—42no—
259C22⋊C4—44no—
260C22⋊C4—44no—
261C22⋊C4—44no—
262C22⋊C4—82no—
263C22⋊C4—81no—
264C22⋊C4—82no—
265C42—82no—
266C13#950011yescharacteristic, direct product factor, Sylow
267C23—22no—
268C23—22no—
269C23—22no—
270C23—22no—
271C23—24no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23—41no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—88no—
283C23C2×C13×C22⋊C411yescharacteristic
284C23C4×D4×C1312yes—
285C23C13×#12011yescharacteristic
286C23C13×#12112yes—
287C23C13×#12311yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22C13×#38611yescharacteristic
330C22C13×#41012yes—
331C22C13×#45812yes—
332C4—42no—
333C4—42no—
334C4—84no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—162no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—41no—
343C2—42no—
344C2C13×#189011yescharacteristic
345C2C13×#189911yescharacteristic
346C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC24C22×C4×C13
Frattini, cosocleC25C23×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
11. C13×#385C4semidirect
13. C13×#381C4semidirect
51. #9500C13direct (N × H)
148. #385C4×C13semidirect
150. #381C4×C13semidirect
266. C13#9500direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24832
C13×#23122
C13×#18192
C13×#13042
#950013