Finite Group Databasebeta

← D13×#1705 #15850554

Subgroups — D13×#1705 #15850554

Order 3328.

994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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×#498C213yesmaximal, complemented
2D13×#492C213yesmaximal
3#13114424C213yesmaximal, complemented
4#13114423C211yesmaximal, characteristic, complemented
5#13114422C213yesmaximal, complemented
6C82×D13C211yesmaximal, characteristic, complemented
7C13×#1705C211yesmaximal, characteristic, complemented
8C2×SD16×D13—26no—
9D13×C4⋊Q8C2213yes—
10D13×#127C2211yescharacteristic
11C13×#498C2213yescomplemented
12C13×#492C2213yes—
13#11718836—26no—
14#11718746C2213yes—
15#11718740C2216yescomplemented
16#11718737C2213yes—
17D13×#106—26no—
18#11718516—26no—
19#11718354C2213yes—
20C4×C8×D13C2213yes—
21#11718341C2213yescomplemented
22C82×C13C2211yescharacteristic, complemented
23C8×#1055C2213yescomplemented
24C2×Q8×D13—23no—
25C2×D4×D13—23no—
26C2×C13×SD16—26no—
27C13×C4⋊Q8C2313yes—
28C13×#127C2311yescharacteristic
29#88198—23no—
30C2×#6106—26no—
31#88194—23no—
32C2×#6105—26no—
33SD16×D13—424no—
34C2×#6095—26no—
35C2×C8×D13D416yes—
36C4⋊C4×D13—26no—
37#88142—26no—
38#88128C2311yescharacteristic
39C42×D13C2311yescharacteristic
40#88123C2313yes—
41C13×#106—26no—
42C4×C8×C13C2313yes—
43#88057—26no—
44C8×Dic13D416yes—
45#88048—212no—
46C4×#1055C2313yes—
47C2×#1705—131nomaximal, Sylow
48C23×D13—41no—
49C2×Q8×C13—23no—
50C2×D4×C13—23no—
51C2×C22⋊D13—43no—
52Q8×D13—412no—
53D4×D13—412no—
54C2×D52—23no—
55C2×C4×D13—43no—
56C2×C4×D13C2×D413yes—
57C2×Dic26—23no—
58C2×Dic26—43no—
59C13×SD16—412no—
60C2×C8×C13C2×D416yes—
61C13×C4⋊C4—26no—
62C42×C13C2411yescharacteristic
63#6106—412no—
64#6105—412no—
65C4⋊Dic13—26no—
66#6101—46no—
67C4×Dic13C2×D413yes—
68C2×#1055C2×D416yes—
69#6095—412no—
70C8×D13SD16124yescomplemented
71C2×#498—133no—
72C2×#492—133no—
73#1705—133no—
74#1705—133no—
75#1705—131no—
76#1705D1311yescharacteristic, direct product factor
77C2×C82—131no—
78C23×C13—41no—
79C22×D13—41no—
80C22×D13—86no—
81C22×D13#12711yescharacteristic
82Q8×C13—46no—
83D4×C13—46no—
84C2×C4×C13—43no—
85C2×C4×C13C22×D413yes—
86C22⋊D13—86no—
87C2×Dic13—43no—
88C2×Dic13#12713yes—
89D52—46no—
90C4×D13—86no—
91C4×D13C2×SD16112yes—
92Dic26—46no—
93Dic26—86no—
94C8×C13C2×SD16112yescomplemented
95#1055C2×SD16112yescomplemented
96C22×SD16—266no—
97C2×C4⋊Q8—133no—
98C2×#127—131no—
99#498—136no—
100#498—133no—
101#498—266no—
102#498C2×D1313yescomplemented
103#492—133no—
104#492—133no—
105#492—133no—
106#492—266no—
107#492C2×D1313yes—
108C2×#106—266no—
109C2×C4×C8—133no—
110C82—133no—
111C82C2×D1311yescharacteristic, complemented
112C22×C13—83no—
113C22×C13C2×#12711yescharacteristic
114C2×D13—83no—
115C2×D13—164no—
116C2×D13#49216yes—
117C4×C13—83no—
118C4×C13C22×SD1616yes—
119Dic13—83no—
120Dic13#49216yes—
121C22×Q8—263no—
122C22×D4—263no—
123C2×SD16—26no—
124C2×SD16—266no—
125C2×SD16—266no—
126C2×SD16—266no—
127C2×SD16—5224no—
128C22×C8—136no—
129C4⋊Q8—133no—
130C4⋊Q8—266no—
131C4⋊Q8—263no—
132C4⋊Q8C22×D1313yes—
133#127—131no—
134#127—263no—
135#127C22×D1311yescharacteristic
136C2×C4⋊C4—266no—
137C2×C42—131no—
138#106—26no—
139#106—2612no—
140#106—266no—
141C4×C8—136no—
142C4×C8—133no—
143C4×C8C22×D1313yes—
144C2×C13—161no—
145C2×C13C2×#49213yes—
146D13—161no—
147D13#170514yesdirect product factor
148C24—521no—
149C2×Q8—23no—
150C2×Q8—263no—
151C2×Q8—523no—
152C2×Q8—5212no—
153C2×D4—23no—
154C2×D4—263no—
155C2×D4—5212no—
156C2×D4—523no—
157C22×C4—133no—
158C22×C4—523no—
159SD16—412no—
160SD16—5212no—
161SD16—5212no—
162SD16—5212no—
163C2×C8—136no—
164C2×C8—1324no—
165C2×C8D4×D1316yes—
166C4⋊C4—26no—
167C4⋊C4—266no—
168C4⋊C4—526no—
169C42—133no—
170C42C23×D1311yescharacteristic
171C13C2×#170511yescharacteristic, complemented, Sylow
172C23—41no—
173C23—131no—
174C23—521no—
175C23—1046no—
176Q8—46no—
177Q8—526no—
178Q8—1046no—
179D4—46no—
180D4—526no—
181D4—1046no—
182C2×C4—43no—
183C2×C4—133no—
184C2×C4—1312no—
185C2×C4—523no—
186C2×C4—1046no—
187C2×C4C2×D4×D1313yes—
188C8—1312no—
189C8SD16×D13112yescomplemented
190C22—83no—
191C22—136no—
192C22—1043no—
193C22—2084no—
194C22D13×#12711yescharacteristic
195C4—83no—
196C4—136no—
197C4—1043no—
198C4C2×SD16×D1316yes—
199C2—134no—
200C2—161no—
201C2—2081no—
202C2D13×#49213yes—
subgroupG/H
centerC22D13×#127
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#1705C2
socleC22×C13C2×#127
prime radicalD13×#127C22
hypercenter#1705D13
hypocenterC13C2×#1705
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #1705

Complements

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

NH ≅ G/Ntype
1. D13×#498C2semidirect
3. #13114424C2semidirect
4. #13114423C2semidirect
5. #13114422C2semidirect
6. C82×D13C2semidirect
7. C13×#1705C2semidirect
11. C13×#498C22semidirect
15. #11718740C22semidirect
21. #11718341C22semidirect
22. C82×C13C22semidirect
23. C8×#1055C22semidirect
70. C8×D13SD16semidirect
76. #1705D13direct (N × H)
94. C8×C13C2×SD16semidirect
95. #1055C2×SD16semidirect
102. #498C2×D13semidirect
111. C82C2×D13semidirect
147. D13#1705direct (N × H)
171. C13C2×#1705semidirect
189. C8SD16×D13semidirect

Maximal subgroups

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

subgroupindex
D13×#4982
D13×#4922
#131144242
#131144232
#131144222
C82×D132
C13×#17052
C2×#170513