Finite Group Databasebeta

← C13×#12966 #15699305

Subgroups — C13×#12966 #15699305

Order 3328.

580 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2380C211yesmaximal, characteristic
2C2×C13×#353C211yesmaximal, characteristic
3C13×#1887C211yesmaximal, characteristic
4C13×#1867C212yesmaximal, complemented
5C13×#1390C212yesmaximal, complemented
6C2×C13×#127C2211yescharacteristic
7C13×#518C2211yescharacteristic
8C13×#418—21no—
9C2×C13×#100C2211yescharacteristic
10C2×C13×#99C2212yes—
11C13×#386—21no—
12C13×#386—22no—
13C13×#386—22no—
14C13×#386C2212yes—
15C13×#385—22no—
16C13×#383—21no—
17C13×#353C414yescomplemented
18C13×#342—22no—
19C13×#339—21no—
20C22×D4×C13—22no—
21C22×D4×C13D411yescharacteristic
22C22×D4×C13C2311yescharacteristic
23C23×C4×C13—21no—
24C23×C4×C13D412yes—
25C2×C13×M16—21no—
26C13×#127—22no—
27C13×#127C2×C412yes—
28C13×#127Q812yes—
29C4×D4×C13—42no—
30C13×#117—21no—
31C2×C13×C4⋊C4—42no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4D412yes—
38C2×C42×C13D411yescharacteristic
39C13×#102—42no—
40C13×#100—22no—
41C13×#99—22no—
42C13×#99C2×C414yescomplemented
43C13×#95—21no—
44C13×#95—22no—
45C13×#95—21no—
46C13×#95—22no—
47C13×#95—42no—
48#12966C1311yesmaximal, characteristic, direct product factor, Sylow
49C24×C13—21no—
50C24×C13C2×D412yes—
51C2×D4×C13—24no—
52C2×D4×C13—24no—
53C2×D4×C13—21no—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—82no—
59C2×D4×C13—82no—
60C2×D4×C13C4⋊C412yescomplemented
61C2×D4×C13C22×C411yescharacteristic
62C2×D4×C13C2×Q811yescharacteristic
63C2×D4×C13#4112yes—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—82no—
72C22×C4×C13—82no—
73C22×C4×C13—81no—
74C22×C4×C13C2×D411yescharacteristic
75C13×M16—41no—
76C13×M16—41no—
77C2×C8×C13—41no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—84no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—82no—
86C13×C22⋊C4—82no—
87C13×C22⋊C4—81no—
88C42×C13—21no—
89C42×C13—41no—
90C42×C13C4⋊C412yescomplemented
91#2380C2×C1311yescharacteristic
92C2×#353C2×C1311yescharacteristic
93#1887C2×C1311yescharacteristic
94#1867C2×C1312yescomplemented
95#1390C2×C1312yescomplemented
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C4×D412yes—
106C23×C13#12011yescharacteristic
107C23×C13C22⋊Q812yes—
108D4×C13—41no—
109D4×C13—41no—
110D4×C13—42no—
111D4×C13—42no—
112D4×C13—81no—
113D4×C13—84no—
114D4×C13—84no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—42no—
119C2×C4×C13—44no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—44no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13—84no—
131C2×C4×C13—82no—
132C2×C4×C13—82no—
133C2×C4×C13—82no—
134C2×C4×C13C2×C4⋊C411yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C8×C13—81no—
137C2×#127C22×C1311yescharacteristic
138#518C22×C1311yescharacteristic
139#418—21no—
140C2×#100C22×C1311yescharacteristic
141C2×#99C22×C1312yes—
142#386—21no—
143#386—22no—
144#386—22no—
145#386C22×C1312yes—
146#385—22no—
147#383—21no—
148#353C4×C1314yescomplemented
149#342—22no—
150#339—21no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13—22no—
154C22×C13—42no—
155C22×C13—42no—
156C22×C13—44no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—82no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—82no—
164C22×C13#38511yescharacteristic
165C22×C13B(4,𝔽2)11yescharacteristic
166C22×C13#45811yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—42no—
170C4×C13—82no—
171C4×C13—84no—
172C4×C13—82no—
173C4×C13—82no—
174C22×D4—22no—
175C22×D4D4×C1311yescharacteristic
176C22×D4C23×C1311yescharacteristic
177C23×C4—21no—
178C23×C4D4×C1312yes—
179C2×M16—21no—
180#127—22no—
181#127C2×C4×C1312yes—
182#127Q8×C1312yes—
183C4×D4—42no—
184#117—21no—
185C2×C4⋊C4—42no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4D4×C1312yes—
192C2×C42D4×C1311yescharacteristic
193#102—42no—
194#100—22no—
195#99—22no—
196#99C2×C4×C1314yescomplemented
197#95—21no—
198#95—22no—
199#95—21no—
200#95—22no—
201#95—42no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13—42no—
205C2×C13—42no—
206C2×C13—82no—
207C2×C13#186711yescharacteristic
208C2×C13#220012yes—
209C24—21no—
210C24C2×D4×C1312yes—
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—21no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4C13×C4⋊C412yescomplemented
221C2×D4C22×C4×C1311yescharacteristic
222C2×D4C2×Q8×C1311yescharacteristic
223C2×D4C13×#4112yes—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—82no—
232C22×C4—82no—
233C22×C4—81no—
234C22×C4C2×D4×C1311yescharacteristic
235M16—41no—
236M16—41no—
237C2×C8—41no—
238C4⋊C4—22no—
239C4⋊C4—84no—
240C22⋊C4—24no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—82no—
246C22⋊C4—82no—
247C22⋊C4—81no—
248C42—21no—
249C42—41no—
250C42C13×C4⋊C412yescomplemented
251C13#1296611yescharacteristic, direct product factor, Sylow
252C23—22no—
253C23—22no—
254C23—22no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—41no—
260C23—41no—
261C23C4×D4×C1312yes—
262C23C13×#12011yescharacteristic
263C23C13×C22⋊Q812yes—
264D4—41no—
265D4—41no—
266D4—42no—
267D4—42no—
268D4—81no—
269D4—84no—
270D4—84no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—84no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C2×C13×C4⋊C411yescharacteristic
291C2×C4C13×#12311yescharacteristic
292C8—81no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—82no—
303C22—81no—
304C22—81no—
305C22—82no—
306C22C13×#38511yescharacteristic
307C22C13×B(4,𝔽2)11yescharacteristic
308C22C13×#45811yescharacteristic
309C4—21no—
310C4—21no—
311C4—42no—
312C4—82no—
313C4—84no—
314C4—82no—
315C4—82no—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2—82no—
321C2C13×#186711yescharacteristic
322C2C13×#220012yes—
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutatorC2×D4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#127C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1867C2semidirect
5. C13×#1390C2semidirect
17. C13×#353C4semidirect
42. C13×#99C2×C4semidirect
48. #12966C13direct (N × H)
60. C2×D4×C13C4⋊C4semidirect
90. C42×C13C4⋊C4semidirect
94. #1867C2×C13semidirect
95. #1390C2×C13semidirect
148. #353C4×C13semidirect
196. #99C2×C4×C13semidirect
220. C2×D4C13×C4⋊C4semidirect
250. C42C13×C4⋊C4semidirect
251. C13#12966direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23802
C2×C13×#3532
C13×#18872
C13×#18672
C13×#13902
#1296613