Finite Group Databasebeta

← C13×#9982 #15696321

Subgroups — C13×#9982 #15696321

Order 3328.

722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3007C212yesmaximal
2C13×#2817C211yesmaximal, characteristic, complemented
3C13×#1782C211yesmaximal, characteristic
4C13×#1511C212yesmaximal, complemented
5C13×#1306C211yesmaximal, characteristic, complemented
6C22×C13×#41C2211yescharacteristic
7C2×C13×#137—22no—
8C2×C13×C22⋊Q8C2212yes—
9C13×#452—24no—
10C13×#451—22no—
11C13×#450—22no—
12C13×#417—22no—
13C2×C13×#99—22no—
14C13×#407C2212yes—
15C13×#400—22no—
16C13×#397—22no—
17C13×#395—22no—
18C13×#381C2211yescharacteristic
19C13×#381C2211yescharacteristic
20C13×#328—24no—
21C2×C13×#41—22no—
22C2×C13×#41—22no—
23C2×C13×#41—44no—
24C22×Q8×C13D412yes—
25C22×Q8×C13D411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13D411yescharacteristic
28C23×C4×C13—21no—
29C23×C4×C13C2311yescharacteristic
30C13×#137—48no—
31C2×C13×Q16—24no—
32C2×C13×SD16—24no—
33C2×C13×M16—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4D412yes—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4D412yes—
44C13×#103—24no—
45C13×#102—24no—
46C13×#99—44no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8D414yes—
49C13×#95—24no—
50C13×#95—22no—
51C13×#95—22no—
52C13×#95—22no—
53#9982C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—21no—
55C24×C13C2×D411yescharacteristic
56C13×#41—28no—
57C13×#41—44no—
58C13×#41—44no—
59C13×#41—44no—
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—22no—
63C2×Q8×C13—42no—
64C2×Q8×C13—44no—
65C2×D4×C13—24no—
66C2×D4×C13—22no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13#4111yescharacteristic
84C13×Q16—48no—
85C13×SD16—48no—
86C13×M16—44no—
87C2×C8×C13—24no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—82no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97#3007C2×C1312yes—
98#2817C2×C1311yescharacteristic, complemented
99#1782C2×C1311yescharacteristic
100#1511C2×C1312yescomplemented
101#1306C2×C1311yescharacteristic, complemented
102C23×C13—22no—
103C23×C13—22no—
104C23×C13—42no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—82no—
108C23×C13#12011yescharacteristic
109C23×C13#12111yescharacteristic
110C23×C13#12711yescharacteristic
111Q8×C13—24no—
112Q8×C13—42no—
113Q8×C13—44no—
114Q8×C13—82no—
115D4×C13—24no—
116D4×C13—42no—
117D4×C13—44no—
118D4×C13—44no—
119C2×C4×C13—24no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—48no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—44no—
128C2×C4×C13—44no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—81no—
134C2×C4×C13—82no—
135C2×C4×C13#12012yes—
136C2×C4×C13#12112yes—
137C8×C13—44no—
138C22×#41C22×C1311yescharacteristic
139C2×#137—22no—
140C2×C22⋊Q8C22×C1312yes—
141#452—24no—
142#451—22no—
143#450—22no—
144#417—22no—
145C2×#99—22no—
146#407C22×C1312yes—
147#400—22no—
148#397—22no—
149#395—22no—
150#381C22×C1311yescharacteristic
151#381C22×C1311yescharacteristic
152#328—24no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—42no—
159C22×C13—82no—
160C22×C13—82no—
161C22×C13—82no—
162C22×C13—82no—
163C22×C13#39211yescharacteristic
164C22×C13B(4,𝔽2)12yes—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—42no—
168C4×C13—82no—
169C4×C13—82no—
170C4×C13—82no—
171C4×C13—161no—
172C2×#41—22no—
173C2×#41—22no—
174C2×#41—44no—
175C22×Q8D4×C1312yes—
176C22×Q8D4×C1311yescharacteristic
177C22×D4—21no—
178C22×D4D4×C1311yescharacteristic
179C23×C4—21no—
180C23×C4C23×C1311yescharacteristic
181#137—48no—
182C2×Q16—24no—
183C2×SD16—24no—
184C2×M16—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4D4×C1312yes—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4D4×C1312yes—
195#103—24no—
196#102—24no—
197#99—44no—
198C22⋊C8—22no—
199C22⋊C8D4×C1314yes—
200#95—24no—
201#95—22no—
202#95—22no—
203#95—22no—
204C2×C13—22no—
205C2×C13—41no—
206C2×C13—41no—
207C2×C13—82no—
208C2×C13#200912yes—
209C2×C13#202111yescharacteristic
210C24—21no—
211C24C2×D4×C1311yescharacteristic
212#41—28no—
213#41—44no—
214#41—44no—
215#41—44no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—42no—
220C2×Q8—44no—
221C2×D4—24no—
222C2×D4—22no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—41no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4C2×D4×C1312yes—
237C22×C4C2×D4×C1311yescharacteristic
238C22×C4C2×D4×C1312yes—
239C22×C4C13×#4111yescharacteristic
240Q16—48no—
241SD16—48no—
242M16—44no—
243C2×C8—24no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—82no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C13#998211yescharacteristic, direct product factor, Sylow
254C23—22no—
255C23—22no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—82no—
260C23C13×#12011yescharacteristic
261C23C13×#12111yescharacteristic
262C23C13×#12711yescharacteristic
263Q8—24no—
264Q8—42no—
265Q8—44no—
266Q8—82no—
267D4—24no—
268D4—42no—
269D4—44no—
270D4—44no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—48no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—81no—
286C2×C4—82no—
287C2×C4C13×#12012yes—
288C2×C4C13×#12112yes—
289C8—44no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—42no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22C13×#39211yescharacteristic
301C22C13×B(4,𝔽2)12yes—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—82no—
306C4—82no—
307C4—82no—
308C4—161no—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2C13×#200912yes—
314C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC22×C13×#41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2817C2semidirect
4. C13×#1511C2semidirect
5. C13×#1306C2semidirect
53. #9982C13direct (N × H)
98. #2817C2×C13semidirect
100. #1511C2×C13semidirect
101. #1306C2×C13semidirect
253. C13#9982direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30072
C13×#28172
C13×#17822
C13×#15112
C13×#13062
#998213