Finite Group Databasebeta

← C13×#13608 #15699947

Subgroups — C13×#13608 #15699947

Order 3328.

308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3223C211yesmaximal, characteristic
2C13×#2133C211yesmaximal, characteristic
3C13×#2129C211yesmaximal, characteristic
4C13×#1414C212yesmaximal, complemented
5C13×#1407C212yesmaximal, complemented
6C13×#541C411yescharacteristic, complemented
7C13×#536C2211yescharacteristic
8C13×#497C2211yescharacteristic
9C13×#494C411yescharacteristic, complemented
10C13×#491C411yescharacteristic, complemented
11C13×#488C2211yescharacteristic
12C13×#464—21no—
13C13×#462—21no—
14C13×#452—21no—
15C13×#451—21no—
16C13×#433C411yescharacteristic, complemented
17C2×C13×#101—21no—
18C13×#410—21no—
19C13×#356—21no—
20C13×#355C2212yes—
21C13×#354—21no—
22C13×#354C2212yes—
23C2×C13×#41D411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C2×C13×Q16—21no—
26C2×C13×Q16—21no—
27C2×C13×Q16—21no—
28C2×C13×SD16—21no—
29C2×C13×M16—41no—
30C13×C4⋊Q8C2×C411yescharacteristic
31C13×C4⋊Q8C2×C411yescharacteristic
32C13×C4⋊Q8D411yescharacteristic
33C13×#126—41no—
34C13×#125—41no—
35C13×#125C2×C411yescharacteristic
36C13×#124D411yescharacteristic
37C13×#124C2311yescharacteristic
38C13×#123—41no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—41no—
41C4×Q8×C13—21no—
42C13×#117—41no—
43C13×#117C2×C411yescharacteristic
44C13×C4⋊C8—21no—
45C13×#103—21no—
46C13×#103—21no—
47C13×#103—21no—
48C13×#102—21no—
49C13×#101—22no—
50C13×#101—41no—
51C13×#99—22no—
52C13×#99—41no—
53C13×C22⋊C8—21no—
54C13×#97C2×C411yescharacteristic
55C4×C8×C13C2×C411yescharacteristic
56#13608C1311yesmaximal, characteristic, direct product factor, Sylow
57C13×#41—81no—
58C2×Q8×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—81no—
61C2×Q8×C13C22⋊C411yescharacteristic
62C2×Q8×C13C22⋊C411yescharacteristic
63C2×Q8×C13C2×D411yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C2×D411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C13×Q16—81no—
70C13×Q16—81no—
71C13×Q16—81no—
72C13×SD16—81no—
73C13×M16—42no—
74C13×M16—81no—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—81no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—81no—
87C13×C22⋊C4—21no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—42no—
92C42×C13—41no—
93C42×C13—81no—
94C42×C13C22⋊C411yescharacteristic
95C42×C13C22×C411yescharacteristic
96#3223C2×C1311yescharacteristic
97#2133C2×C1311yescharacteristic
98#2129C2×C1311yescharacteristic
99#1414C2×C1312yescomplemented
100#1407C2×C1312yescomplemented
101C23×C13—21no—
102C23×C13#9911yescharacteristic
103Q8×C13—41no—
104Q8×C13—41no—
105Q8×C13—41no—
106Q8×C13—41no—
107Q8×C13—41no—
108Q8×C13—81no—
109D4×C13—41no—
110D4×C13—81no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—82no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13C2×C22⋊C411yescharacteristic
126C8×C13—41no—
127C8×C13—41no—
128C8×C13—82no—
129#541C4×C1311yescharacteristic, complemented
130#536C22×C1311yescharacteristic
131#497C22×C1311yescharacteristic
132#494C4×C1311yescharacteristic, complemented
133#491C4×C1311yescharacteristic, complemented
134#488C22×C1311yescharacteristic
135#464—21no—
136#462—21no—
137#452—21no—
138#451—21no—
139#433C4×C1311yescharacteristic, complemented
140C2×#101—21no—
141#410—21no—
142#356—21no—
143#355C22×C1312yes—
144#354—21no—
145#354C22×C1312yes—
146C22×C13—21no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—81no—
150C22×C13C2×#9911yescharacteristic
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—81no—
159C4×C13—81no—
160C4×C13—162no—
161C2×#41D4×C1311yescharacteristic
162C22×Q8D4×C1311yescharacteristic
163C2×Q16—21no—
164C2×Q16—21no—
165C2×Q16—21no—
166C2×SD16—21no—
167C2×M16—41no—
168C4⋊Q8C2×C4×C1311yescharacteristic
169C4⋊Q8C2×C4×C1311yescharacteristic
170C4⋊Q8D4×C1311yescharacteristic
171#126—41no—
172#125—41no—
173#125C2×C4×C1311yescharacteristic
174#124D4×C1311yescharacteristic
175#124C23×C1311yescharacteristic
176#123—41no—
177C22⋊Q8—21no—
178C22⋊Q8—41no—
179C4×Q8—21no—
180#117—41no—
181#117C2×C4×C1311yescharacteristic
182C4⋊C8—21no—
183#103—21no—
184#103—21no—
185#103—21no—
186#102—21no—
187#101—22no—
188#101—41no—
189#99—22no—
190#99—41no—
191C22⋊C8—21no—
192#97C2×C4×C1311yescharacteristic
193C4×C8C2×C4×C1311yescharacteristic
194C2×C13—21no—
195C2×C13—41no—
196C2×C13—81no—
197C2×C13#212711yescharacteristic
198#41—81no—
199C2×Q8—21no—
200C2×Q8—21no—
201C2×Q8—81no—
202C2×Q8C13×C22⋊C411yescharacteristic
203C2×Q8C13×C22⋊C411yescharacteristic
204C2×Q8C2×D4×C1311yescharacteristic
205C2×D4—21no—
206C2×D4C2×D4×C1311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C13×C22⋊C411yescharacteristic
210Q16—81no—
211Q16—81no—
212Q16—81no—
213SD16—81no—
214M16—42no—
215M16—81no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—81no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—81no—
228C22⋊C4—21no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—42no—
233C42—41no—
234C42—81no—
235C42C13×C22⋊C411yescharacteristic
236C42C22×C4×C1311yescharacteristic
237C13#1360811yescharacteristic, direct product factor, Sylow
238C23—21no—
239C23C13×#9911yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—41no—
245Q8—81no—
246D4—41no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4C13×#9911yescharacteristic
262C2×C4C2×C13×C22⋊C411yescharacteristic
263C8—41no—
264C8—41no—
265C8—82no—
266C22—21no—
267C22—41no—
268C22—41no—
269C22—81no—
270C22C2×C13×#9911yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—81no—
279C4—81no—
280C4—162no—
281C2—21no—
282C2—41no—
283C2—81no—
284C2C13×#212711yescharacteristic
subgroupG/H
center, socleC2×C13#2127
commutatorC42C22×C4×C13
Frattini, cosocle#124C23×C13
prime radicalC2×C13×#41D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#536 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1414C2semidirect
5. C13×#1407C2semidirect
6. C13×#541C4semidirect
9. C13×#494C4semidirect
10. C13×#491C4semidirect
16. C13×#433C4semidirect
56. #13608C13direct (N × H)
99. #1414C2×C13semidirect
100. #1407C2×C13semidirect
129. #541C4×C13semidirect
132. #494C4×C13semidirect
133. #491C4×C13semidirect
139. #433C4×C13semidirect
237. C13#13608direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32232
C13×#21332
C13×#21292
C13×#14142
C13×#14072
#1360813