Finite Group Databasebeta

← D13⋊#360 #13131154

Subgroups — D13⋊#360 #13131154

Order 1664.

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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×#135C211yesmaximal, characteristic
2C2×#88101C211yesmaximal, characteristic, complemented
3D13⋊M32C211yesmaximal, characteristic, complemented
4#11718279C212yesmaximal, complemented
5#11718275C212yesmaximal, complemented
6#41×D13—21no—
7C2×C4⋊#261—21no—
8C13×#135C411yescharacteristic, complemented
9#88204—21no—
10#88173C2211yescharacteristic
11Q16×D13C411yescharacteristic, complemented
12#88170—21no—
13SD16×D13—21no—
14#88166C2211yescharacteristic
15D8×D13C411yescharacteristic, complemented
16#88158C411yescharacteristic, complemented
17C2×C8×D13C2211yescharacteristic
18#88106—21no—
19#88101—21no—
20#88101C2212yescomplemented
21#88098C2212yescomplemented
22D13⋊C16—21no—
23C22×#261—41no—
24C13×#41—21no—
25#6131—21no—
26Q8×D13—21no—
27#6129—21no—
28#6129—41no—
29D4×D13—21no—
30D4×D13—41no—
31#6127—21no—
32#6127—41no—
33C2×C4×D13—41no—
34C2×C4×D13D411yescharacteristic
35C4⋊#261—22no—
36C4⋊#261—41no—
37C13×Q16C2×C411yescharacteristic, complemented
38C13×SD16—21no—
39C13×D8C2×C411yescharacteristic, complemented
40C2×C8×C13C2×C411yescharacteristic
41#6107—21no—
42#6106—21no—
43#6105—21no—
44#6104—21no—
45C2×#1055D411yescharacteristic
46Dic52C2×C411yescharacteristic, complemented
47D104C2×C411yescharacteristic, complemented
48#6095—21no—
49C8×D13C2×C411yescharacteristic
50C8×D13D411yescharacteristic
51C8×D13D411yescharacteristic
52C8×D13C2311yescharacteristic
53#6092—22no—
54C2×#360—131nomaximal, Sylow
55C22×D13—41no—
56C22×D13D811yescharacteristic
57C2×#261—42no—
58C2×#261—82no—
59Q8×C13—21no—
60D4×C13—21no—
61D4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13C22⋊C411yescharacteristic
64C22⋊D13—41no—
65C22⋊D13—41no—
66C22⋊D13—41no—
67C2×Dic13—41no—
68C2×Dic13SD1611yescharacteristic
69D52—21no—
70D52—41no—
71C4×D13—41no—
72C4×D13—41no—
73C4×D13—41no—
74C4×D13C22⋊C411yescharacteristic
75C4×D13D811yescharacteristic
76C4×D13SD1611yescharacteristic
77C4×D13C2×D411yescharacteristic
78Dic26—21no—
79Dic26—41no—
80C8×C13C22⋊C411yescharacteristic
81C8×C13C22×C411yescharacteristic
82#1055C22⋊C411yescharacteristic
83#1055C2×D411yescharacteristic
84C2×#135—131no—
85C2×M32—131no—
86C2×#106—131no—
87#360—132no—
88#360—132no—
89C22×C13—41no—
90C22×C13#10211yescharacteristic
91C2×D13—22no—
92C2×D13—41no—
93C2×D13—82no—
94C2×D13#10211yescharacteristic
95C2×D13C2×D811yescharacteristic
96#261—82no—
97C4×C13—41no—
98C4×C13#10211yescharacteristic
99C4×C13C2×C22⋊C411yescharacteristic
100Dic13—41no—
101Dic13#10211yescharacteristic
102Dic13C2×SD1611yescharacteristic
103C2×#41—261no—
104#135—131no—
105#135—131no—
106#135—131no—
107#135—261no—
108#135—261no—
109#135#26111yescharacteristic, complemented
110C2×Q16—131no—
111C2×SD16—261no—
112C2×D8—131no—
113C22×C8—131no—
114C2×C4⋊C4—261no—
115M32—132no—
116M32—261no—
117C2×C16—261no—
118#106—132no—
119#106—261no—
120C2×C13—21no—
121C2×C13—81no—
122C2×C13C2×#10211yescharacteristic
123D13—21no—
124D13—81no—
125D13#36012yescomplemented
126#41—21no—
127#41—261no—
128#41—261no—
129#41—261no—
130#41—521no—
131#41—521no—
132C2×Q8—261no—
133C2×D4—261no—
134C2×D4—521no—
135C22×C4—131no—
136C22×C4—521no—
137C22×C4—521no—
138Q16—131no—
139Q16—261no—
140Q16C2×#26111yescharacteristic, complemented
141SD16—21no—
142SD16—261no—
143SD16—261no—
144SD16—261no—
145D8—131no—
146D8—261no—
147D8C2×#26111yescharacteristic, complemented
148C2×C8—131no—
149C2×C8—131no—
150C2×C8—131no—
151C2×C8—131no—
152C2×C8—131no—
153C2×C8C2×#26111yescharacteristic
154C4⋊C4—262no—
155C4⋊C4—521no—
156C16—262no—
157C13C2×#36011yescharacteristic, complemented, Sylow
158C23—131no—
159C23—521no—
160Q8—21no—
161Q8—261no—
162Q8—521no—
163D4—21no—
164D4—41no—
165D4—261no—
166D4—521no—
167D4—521no—
168D4—521no—
169D4—521no—
170C2×C4—41no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—131no—
175C2×C4—131no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4—522no—
181C2×C4—1042no—
182C2×C4C22⋊#26111yescharacteristic
183C8—131no—
184C8—131no—
185C8C22⋊#26111yescharacteristic
186C8C22×#26111yescharacteristic
187C22—41no—
188C22—131no—
189C22—131no—
190C22—262no—
191C22—521no—
192C22—1042no—
193C22#8811511yescharacteristic
194C4—41no—
195C4—131no—
196C4—131no—
197C4—521no—
198C4—1042no—
199C4#8811511yescharacteristic
200C4C2×C22⋊#26111yescharacteristic
201C2—21no—
202C2—81no—
203C2—132no—
204C2—261no—
205C2—1041no—
206C2C2×#8811511yescharacteristic
subgroupG/H
centerC2C2×#88115
commutatorC8×C13C22×C4
FrattiniC8C22×#261
FittingC13×#135C4
socleC2×C13C2×#102
prime radicalD13×#135C2
cosocleC8×D13C23
hypercenter#135#261
hypocenterC13C2×#360
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. C2×#88101C2semidirect
3. D13⋊M32C2semidirect
4. #11718279C2semidirect
5. #11718275C2semidirect
8. C13×#135C4semidirect
11. Q16×D13C4semidirect
15. D8×D13C4semidirect
16. #88158C4semidirect
20. #88101C22semidirect
21. #88098C22semidirect
37. C13×Q16C2×C4semidirect
39. C13×D8C2×C4semidirect
46. Dic52C2×C4semidirect
47. D104C2×C4semidirect
109. #135#261semidirect
125. D13#360semidirect
140. Q16C2×#261semidirect
147. D8C2×#261semidirect
157. C13C2×#360semidirect

Maximal subgroups

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

subgroupindex
D13×#1352
C2×#881012
D13⋊M322
#117182792
#117182752
C2×#36013