Finite Group Databasebeta

← C13×#13227 #15699566

Subgroups — C13×#13227 #15699566

Order 3328.

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

normal subgroups only

This group has 472 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×#2546C211yesmaximal, characteristic
2C2×C13×#356C214yesmaximal
3C13×#1801C211yesmaximal, characteristic
4C4×C13×#101C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C4⋊Q8C2212yes—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#423—21no—
9C2×C13×#101C2212yes—
10C2×C13×#101C2212yes—
11C4×C13×M16—21no—
12C13×#398—21no—
13C13×#398—21no—
14C13×#391C412yes—
15C13×#389—21no—
16C13×#389—21no—
17C4×C13×C4⋊C4C411yescharacteristic
18C13×#356—28no—
19C13×#343—21no—
20C13×#343—21no—
21C22×Q8×C13C2×C412yes—
22C22×Q8×C13C2311yescharacteristic
23C2×C13×M16—22no—
24C2×C13×M16—22no—
25C13×C4⋊Q8—24no—
26C13×C4⋊Q8—24no—
27C13×C4⋊Q8—41no—
28C13×C4⋊Q8—41no—
29C4×Q8×C13—41no—
30C4×Q8×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C42×C13C2×C412yes—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C13×C4⋊C8—41no—
44C13×C4⋊C8—41no—
45C13×#101—22no—
46C13×#101—24no—
47C13×#101D414yes—
48C13×#97—41no—
49C4×C8×C13—41no—
50C13×#95—21no—
51C13×#95—22no—
52C13×#95—22no—
53#13227C1311yesmaximal, characteristic, direct product factor, Sylow
54C2×Q8×C13—24no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13—42no—
58C2×Q8×C13—42no—
59C2×Q8×C13C2×D412yes—
60C2×Q8×C13#4112yes—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×M16—24no—
71C13×M16—42no—
72C13×M16—42no—
73C13×M16—42no—
74C2×C8×C13—42no—
75C2×C8×C13—42no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—44no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—24no—
93#2546C2×C1311yescharacteristic
94C2×#356C2×C1314yes—
95#1801C2×C1311yescharacteristic
96C4×#101C2×C1311yescharacteristic
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—42no—
99Q8×C13—42no—
100Q8×C13—84no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—24no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12112yes—
124C2×C4×C13#12411yescharacteristic
125C2×C4×C13#12711yescharacteristic
126C8×C13—44no—
127C8×C13—82no—
128C2×C4⋊Q8C4×C1311yescharacteristic
129C2×C4⋊Q8C22×C1312yes—
130C2×C4×Q8C22×C1311yescharacteristic
131#423—21no—
132C2×#101C22×C1312yes—
133C2×#101C22×C1312yes—
134C4×M16—21no—
135#398—21no—
136#398—21no—
137#391C4×C1312yes—
138#389—21no—
139#389—21no—
140C4×C4⋊C4C4×C1311yescharacteristic
141#356—28no—
142#343—21no—
143#343—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13#39011yescharacteristic
147C22×C13C2×#9911yescharacteristic
148C22×C13#41011yescharacteristic
149C4×C13—21no—
150C4×C13—22no—
151C4×C13—21no—
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—44no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—82no—
159C4×C13#35612yescomplemented
160C22×Q8C2×C4×C1312yes—
161C22×Q8C23×C1311yescharacteristic
162C2×M16—22no—
163C2×M16—22no—
164C4⋊Q8—24no—
165C4⋊Q8—24no—
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4C2×C4×C1311yescharacteristic
176C2×C4⋊C4D4×C1311yescharacteristic
177C2×C4⋊C4D4×C1311yescharacteristic
178C2×C42C2×C4×C1312yes—
179C2×C42C2×C4×C1311yescharacteristic
180C2×C42D4×C1311yescharacteristic
181C2×C42D4×C1311yescharacteristic
182C4⋊C8—41no—
183C4⋊C8—41no—
184#101—22no—
185#101—24no—
186#101D4×C1314yes—
187#97—41no—
188C4×C8—41no—
189#95—21no—
190#95—22no—
191#95—22no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13#196411yescharacteristic
195C2×C13C2×#35611yescharacteristic
196C2×C13#213511yescharacteristic
197C2×Q8—24no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8C2×D4×C1312yes—
203C2×Q8C13×#4112yes—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4C13×C22⋊C411yescharacteristic
207C22×C4C13×C22⋊C411yescharacteristic
208C22×C4C13×C22⋊C411yescharacteristic
209C22×C4C13×C22⋊C411yescharacteristic
210C22×C4C22×C4×C1311yescharacteristic
211C22×C4C2×D4×C1311yescharacteristic
212C22×C4C2×D4×C1311yescharacteristic
213M16—24no—
214M16—42no—
215M16—42no—
216M16—42no—
217C2×C8—42no—
218C2×C8—42no—
219C4⋊C4—24no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—24no—
236C13#1322711yescharacteristic, direct product factor, Sylow
237C23C2×C13×C22⋊C411yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—84no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4C13×#9911yescharacteristic
261C2×C4C13×#9911yescharacteristic
262C2×C4C4×D4×C1312yes—
263C2×C4C13×#12112yes—
264C2×C4C13×#12411yescharacteristic
265C2×C4C13×#12711yescharacteristic
266C8—44no—
267C8—82no—
268C22—21no—
269C22—21no—
270C22C13×#39011yescharacteristic
271C22C2×C13×#9911yescharacteristic
272C22C13×#41011yescharacteristic
273C4—21no—
274C4—22no—
275C4—21no—
276C4—22no—
277C4—21no—
278C4—44no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—82no—
283C4C13×#35612yescomplemented
284C2—21no—
285C2—21no—
286C2C13×#196411yescharacteristic
287C2C2×C13×#35611yescharacteristic
288C2C13×#213511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC23×C13C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
53. #13227C13direct (N × H)
159. C4×C13#356semidirect
236. C13#13227direct (N × H)
283. C4C13×#356semidirect

Maximal subgroups

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

subgroupindex
C13×#25462
C2×C13×#3562
C13×#18012
C4×C13×#1012
#1322713