Finite Group Databasebeta

← D13×#2030 #15890317

Subgroups — D13×#2030 #15890317

Order 3328.

1482 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 217 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
1D13×#543C211yesmaximal, characteristic
2D13×#381C213yesmaximal
3#13116004C213yesmaximal, complemented
4#13116003C213yesmaximal, complemented
5#13116002C211yesmaximal, characteristic, complemented
6D13×#342C213yesmaximal
7C13×#2030C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C13×#543C2211yescharacteristic
10#11719339—26no—
11D13×C22⋊Q8—26no—
12C2×C22⋊C4×D13C2213yes—
13C2×C22⋊C4×D13C2213yes—
14#11719188C2213yes—
15C13×#381C2213yes—
16#11718872C2213yes—
17#11718604C2213yes—
18#11718604C2213yes—
19#11718325—26no—
20D13×#95—26no—
21C13×#342C2213yes—
22#11718119C2216yes—
23#11718118C2213yes—
24C24×D13C2311yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13C2311yescharacteristic
27C2×Q8×D13—22no—
28C22×C4×D13—23no—
29C22×C4×D13—23no—
30C22×C4×D13—26no—
31C22×C4×D13—23no—
32C22×C4×D13D416yes—
33C22×C4×D13Q814yescomplemented
34C13×C22⋊Q8—26no—
35C2×C13×C22⋊C4C2313yes—
36C2×C13×C22⋊C4C2313yes—
37C2×C22⋊Dic13C2313yes—
38C2×C22⋊Dic13C2313yes—
39#88200—26no—
40C2×#6103—23no—
41C2×#6103D416yes—
42#88178—26no—
43#88151—26no—
44#88150—212no—
45C4⋊C4×D13—26no—
46C22⋊C4×D13—26no—
47C22⋊C4×D13—26no—
48C22⋊C4×D13—212no—
49#88132—212no—
50C13×#95—26no—
51#88071—26no—
52#88071—26no—
53#88071—26no—
54C2×#2030—131nomaximal, Sylow
55C24×C13C2411yescharacteristic
56C23×D13—44no—
57C23×D13C2×D413yes—
58C23×D13C2×D413yes—
59C23×D13C2×Q812yes—
60C23×D13#4116yes—
61C2×Q8×C13—22no—
62C22×C4×C13—23no—
63C22×C4×C13—23no—
64C22×C4×C13—23no—
65C22×C4×C13C2×D416yes—
66C22×C4×C13C2×Q812yescomplemented
67C22×Dic13—23no—
68C22×Dic13—23no—
69C22×Dic13—23no—
70C22×Dic13C2×D416yes—
71C22×Dic13C2×Q812yescomplemented
72Q8×D13—84no—
73C2×C4×D13—26no—
74C2×C4×D13—212no—
75C2×C4×D13—212no—
76C2×C4×D13—26no—
77C2×C4×D13—43no—
78C2×C4×D13—41no—
79C2×C4×D13—46no—
80C2×C4×D13—46no—
81C2×C4×D13—412no—
82C2×C4×D13—412no—
83C2×C4×D13—46no—
84C2×Dic26—26no—
85C13×C4⋊C4—26no—
86C13×C22⋊C4—26no—
87C13×C22⋊C4—26no—
88C22⋊Dic13—26no—
89C22⋊Dic13—26no—
90#6103—212no—
91#6103—46no—
92C4⋊Dic13—26no—
93#6101—212no—
94C2×#543—131no—
95C2×#381—133no—
96#2030—133no—
97#2030—133no—
98#2030—131no—
99#2030D1311yescharacteristic, direct product factor
100C2×#342—133no—
101C23×C13—42no—
102C23×C13C22×D413yes—
103C23×C13C22×Q811yescharacteristic
104C23×C13C2×#4113yes—
105C22×D13—212no—
106C22×D13—44no—
107C22×D13—412no—
108C22×D13—46no—
109C22×D13#12013yes—
110C22×D13#12011yescharacteristic
111C22×D13C22⋊Q816yes—
112C22×D13C22⋊Q816yes—
113C22×D13#12416yes—
114C22×D13#12416yes—
115Q8×C13—82no—
116C2×C4×C13—26no—
117C2×C4×C13—26no—
118C2×C4×C13—41no—
119C2×C4×C13—43no—
120C2×C4×C13—46no—
121C2×C4×C13—46no—
122C2×C4×C13—43no—
123C2×Dic13—26no—
124C2×Dic13—26no—
125C2×Dic13—41no—
126C2×Dic13—43no—
127C2×Dic13—46no—
128C2×Dic13—46no—
129C2×Dic13—43no—
130C4×D13—412no—
131C4×D13—44no—
132C4×D13—412no—
133C4×D13—86no—
134C4×D13—812no—
135Dic26—86no—
136C24×C4—131no—
137#543—133no—
138#543—266no—
139#543C2×D1311yescharacteristic
140C2×C22⋊Q8—266no—
141C22×C22⋊C4—133no—
142C22×C22⋊C4—133no—
143#381—133no—
144#381—133no—
145#381—133no—
146#381—266no—
147#381C2×D1313yes—
148C2×#95—266no—
149#342—133no—
150#342—136no—
151#342C2×D1313yes—
152C22×C13—26no—
153C22×C13—41no—
154C22×C13—43no—
155C22×C13C2×#12011yescharacteristic
156C22×C13C2×C22⋊Q813yes—
157C22×C13C2×#12413yes—
158C2×D13—26no—
159C2×D13—212no—
160C2×D13—212no—
161C2×D13—46no—
162C2×D13—46no—
163C2×D13#39316yes—
164C2×D13#39312yes—
165C2×D13#45814yes—
166C4×C13—42no—
167C4×C13—46no—
168C4×C13—83no—
169Dic13—42no—
170Dic13—46no—
171Dic13—83no—
172C25—131no—
173C22×Q8—262no—
174C23×C4—131no—
175C23×C4—134no—
176C23×C4—136no—
177C23×C4—263no—
178C23×C4—263no—
179C23×C4—266no—
180C23×C4—263no—
181C23×C4C22×D1311yescharacteristic
182C22⋊Q8—26no—
183C22⋊Q8—2612no—
184C22⋊Q8—2612no—
185C22⋊Q8—266no—
186C22⋊Q8—266no—
187C22⋊Q8—266no—
188C2×C4⋊C4—266no—
189C2×C22⋊C4—133no—
190C2×C22⋊C4—136no—
191C2×C22⋊C4—133no—
192C2×C22⋊C4—266no—
193C2×C22⋊C4—266no—
194C2×C22⋊C4—2612no—
195C2×C22⋊C4—263no—
196C2×C22⋊C4C22×D1313yes—
197C2×C22⋊C4C22×D1313yes—
198#95—26no—
199#95—266no—
200#95—266no—
201#95—266no—
202C2×C13—23no—
203C2×C13—23no—
204C2×C13C2×#39311yescharacteristic
205C2×C13C2×#45812yes—
206D13—26no—
207D13#203014yesdirect product factor
208C24—133no—
209C24—133no—
210C24—132no—
211C24—136no—
212C24—524no—
213C24C23×D1311yescharacteristic
214C2×Q8—22no—
215C2×Q8—266no—
216C2×Q8—1044no—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—132no—
221C22×C4—136no—
222C22×C4—266no—
223C22×C4—2612no—
224C22×C4—2612no—
225C22×C4—266no—
226C22×C4—263no—
227C22×C4—263no—
228C22×C4—263no—
229C22×C4—521no—
230C22×C4—523no—
231C22×C4—526no—
232C22×C4—526no—
233C22×C4—5212no—
234C22×C4—526no—
235C22×C4—5212no—
236C22×C4D4×D1316yes—
237C22×C4Q8×D1312yescomplemented
238C4⋊C4—26no—
239C4⋊C4—2612no—
240C4⋊C4—266no—
241C22⋊C4—26no—
242C22⋊C4—26no—
243C22⋊C4—2612no—
244C22⋊C4—266no—
245C22⋊C4—266no—
246C22⋊C4—526no—
247C13C2×#203011yescharacteristic, complemented, Sylow
248C23—42no—
249C23—131no—
250C23—133no—
251C23—136no—
252C23—136no—
253C23—136no—
254C23—136no—
255C23—2612no—
256C23—526no—
257C23—524no—
258C23—5212no—
259C23C2×D4×D1313yes—
260C23C2×Q8×D1311yescharacteristic
261C23#41×D1313yes—
262Q8—82no—
263Q8—1046no—
264C2×C4—26no—
265C2×C4—26no—
266C2×C4—41no—
267C2×C4—43no—
268C2×C4—46no—
269C2×C4—46no—
270C2×C4—43no—
271C2×C4—266no—
272C2×C4—266no—
273C2×C4—524no—
274C2×C4—5212no—
275C2×C4—5212no—
276C2×C4—521no—
277C2×C4—523no—
278C2×C4—526no—
279C2×C4—526no—
280C2×C4—523no—
281C2×C4—1046no—
282C2×C4—10412no—
283C22—26no—
284C22—41no—
285C22—43no—
286C22—132no—
287C22—134no—
288C22—136no—
289C22—2612no—
290C22—2612no—
291C22—266no—
292C22—526no—
293C22—526no—
294C22D13×#12011yescharacteristic
295C22D13×C22⋊Q813yes—
296C22D13×#12413yes—
297C4—42no—
298C4—46no—
299C4—83no—
300C4—522no—
301C4—526no—
302C4—1043no—
303C2—23no—
304C2—23no—
305C2—134no—
306C2—266no—
307C2D13×#39311yescharacteristic
308C2D13×#45812yes—
subgroupG/H
centerC22D13×#120
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC13×#2030C2
socleC22×C13C2×#120
prime radicalC24×D13C23
hypercenter#2030D13
hypocenterC13C2×#2030
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
3. #13116004C2semidirect
4. #13116003C2semidirect
5. #13116002C2semidirect
7. C13×#2030C2semidirect
33. C22×C4×D13Q8semidirect
66. C22×C4×C13C2×Q8semidirect
71. C22×Dic13C2×Q8semidirect
99. #2030D13direct (N × H)
207. D13#2030direct (N × H)
237. C22×C4Q8×D13semidirect
247. C13C2×#2030semidirect

Maximal subgroups

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

subgroupindex
D13×#5432
D13×#3812
#131160042
#131160032
#131160022
D13×#3422
C13×#20302
C2×#203013