Finite Group Databasebeta

← C13×#13299 #15699638

Subgroups — C13×#13299 #15699638

Order 3328.

500 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2563C211yesmaximal, characteristic
2C13×#1799C211yesmaximal, characteristic
3C4×C13×#99C211yesmaximal, characteristic
4C13×#1393C214yesmaximal
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C2×C13×#99C2212yes—
8C2×C13×#99C2212yes—
9C13×#393—21no—
10C13×#393—21no—
11C13×#390C2212yes—
12C13×#382C412yescomplemented
13C13×#380—21no—
14C13×#380—21no—
15C13×#380—21no—
16C4×C13×C4⋊C4C411yescharacteristic, complemented
17C4×C13×C22⋊C4—21no—
18C13×#342—21no—
19C13×#342—21no—
20C22×Q8×C13—21no—
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×C4⋊Q8—41no—
25C13×C4⋊Q8—41no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13—41no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C412yes—
42C13×#99—22no—
43C13×#99—24no—
44C13×#99Q814yescomplemented
45C13×#95—21no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—41no—
49C13×#95—41no—
50#13299C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C2×D411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×Q8×C13—42no—
54C2×Q8×C13—82no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13C2×Q812yes—
58C2×D4×C13#4112yes—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—82no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—82no—
87C13×C22⋊C4—82no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—42no—
91C42×C13—82no—
92#2563C2×C1311yescharacteristic
93#1799C2×C1311yescharacteristic
94C4×#99C2×C1311yescharacteristic
95#1393C2×C1314yes—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13C22⋊Q812yes—
106C23×C13#12411yescharacteristic
107C23×C13C4⋊Q811yescharacteristic
108Q8×C13—84no—
109D4×C13—42no—
110D4×C13—42no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—44no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—82no—
132C2×C4×C13—82no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13#9911yescharacteristic
138C2×C4×C13C4×Q812yes—
139C2×C4⋊Q8C4×C1311yescharacteristic, complemented
140C2×C4×D4C22×C1311yescharacteristic
141C2×#99C22×C1312yes—
142C2×#99C22×C1312yes—
143#393—21no—
144#393—21no—
145#390C22×C1312yes—
146#382C4×C1312yescomplemented
147#380—21no—
148#380—21no—
149#380—21no—
150C4×C4⋊C4C4×C1311yescharacteristic, complemented
151C4×C22⋊C4—21no—
152#342—21no—
153#342—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—22no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13#39111yescharacteristic
169C22×C13C2×#9911yescharacteristic
170C22×C13#41011yescharacteristic
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—82no—
177C4×C13—84no—
178C4×C13—82no—
179C4×C13—162no—
180C4×C13#35412yes—
181C22×Q8—21no—
182C22×D4C23×C1311yescharacteristic
183C23×C4D4×C1311yescharacteristic
184C23×C4D4×C1311yescharacteristic
185C4⋊Q8—41no—
186C4⋊Q8—41no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4C2×C4×C1312yes—
193C2×C4⋊C4C2×C4×C1311yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4D4×C1311yescharacteristic
199C2×C22⋊C4D4×C1311yescharacteristic
200C2×C42—41no—
201C2×C42C2×C4×C1311yescharacteristic
202C2×C42C2×C4×C1312yes—
203#99—22no—
204#99—24no—
205#99Q8×C1314yescomplemented
206#95—21no—
207#95—22no—
208#95—22no—
209#95—41no—
210#95—41no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—42no—
214C2×C13—41no—
215C2×C13—41no—
216C2×C13#199611yescharacteristic
217C2×C13C2×#35411yescharacteristic
218C2×C13#212811yescharacteristic
219C24C2×D4×C1311yescharacteristic
220C24C2×D4×C1311yescharacteristic
221C2×Q8—42no—
222C2×Q8—82no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4C2×Q8×C1312yes—
226C2×D4C13×#4112yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C13×C22⋊C411yescharacteristic
238C22×C4C13×C22⋊C411yescharacteristic
239C22×C4C13×C22⋊C411yescharacteristic
240C22×C4C13×C22⋊C411yescharacteristic
241C22×C4C22×C4×C1311yescharacteristic
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—82no—
248C22⋊C4—24no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—82no—
255C22⋊C4—82no—
256C42—21no—
257C42—21no—
258C42—42no—
259C42—82no—
260C13#1329911yescharacteristic, direct product factor, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23C2×C13×C22⋊C411yescharacteristic
270C23C13×C22⋊Q812yes—
271C23C13×#12411yescharacteristic
272C23C13×C4⋊Q811yescharacteristic
273Q8—84no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4C13×#9911yescharacteristic
302C2×C4C13×#9911yescharacteristic
303C2×C4C4×Q8×C1312yes—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—81no—
318C22C13×#39111yescharacteristic
319C22C2×C13×#9911yescharacteristic
320C22C13×#41011yescharacteristic
321C4—22no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—82no—
327C4—84no—
328C4—82no—
329C4—162no—
330C4C13×#35412yes—
331C2—21no—
332C2—21no—
333C2—42no—
334C2—41no—
335C2—41no—
336C2C13×#199611yescharacteristic
337C2C2×C13×#35411yescharacteristic
338C2C13×#212811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
12. C13×#382C4semidirect
16. C4×C13×C4⋊C4C4semidirect
44. C13×#99Q8semidirect
50. #13299C13direct (N × H)
139. C2×C4⋊Q8C4×C13semidirect
146. #382C4×C13semidirect
150. C4×C4⋊C4C4×C13semidirect
205. #99Q8×C13semidirect
260. C13#13299direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25632
C13×#17992
C4×C13×#992
C13×#13932
#1329913