Finite Group Databasebeta

← C13×#10336 #15696675

Subgroups — C13×#10336 #15696675

Order 3328.

1566 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2403C213yesmaximal, complemented
2C13×#1781C213yesmaximal, complemented
3C13×#1304C211yesmaximal, characteristic, complemented
4C23×D4×C13C2213yes—
5C2×C13×#120—26no—
6C2×C13×#99—26no—
7C13×#392—26no—
8C13×#386—26no—
9C13×#379C2211yescharacteristic
10C13×#379C2213yes—
11C25×C13D413yescomplemented
12C25×C13C2311yescharacteristic
13C22×D4×C13—26no—
14C22×D4×C13—23no—
15C22×D4×C13—26no—
16C22×D4×C13—23no—
17C22×D4×C13—26no—
18C22×D4×C13—412no—
19C23×C4×C13D413yescomplemented
20C13×#120—424no—
21C2×C13×C22⋊C4—212no—
22C2×C13×C22⋊C4—26no—
23C2×C13×C22⋊C4—23no—
24C2×C13×C22⋊C4D416yescomplemented
25C13×#99—412no—
26C13×#95—26no—
27#10336C1311yesmaximal, characteristic, direct product factor, Sylow
28C24×C13—26no—
29C24×C13—23no—
30C24×C13—46no—
31C24×C13—46no—
32C24×C13—412no—
33C24×C13C2×D413yes—
34C24×C13C2×D413yes—
35C24×C13#4111yescharacteristic
36C2×D4×C13—212no—
37C2×D4×C13—224no—
38C2×D4×C13—412no—
39C2×D4×C13—46no—
40C2×D4×C13—412no—
41C2×D4×C13—46no—
42C2×D4×C13—412no—
43C2×D4×C13—46no—
44C2×D4×C13—43no—
45C2×D4×C13—46no—
46C2×D4×C13—43no—
47C2×D4×C13—424no—
48C2×D4×C13—86no—
49C22×C4×C13—26no—
50C22×C4×C13—23no—
51C22×C4×C13—26no—
52C22×C4×C13—46no—
53C22×C4×C13—41no—
54C13×C22⋊C4—424no—
55C13×C22⋊C4—412no—
56C13×C22⋊C4—46no—
57C13×C22⋊C4—46no—
58#2403C2×C1313yescomplemented
59#1781C2×C1313yescomplemented
60#1304C2×C1311yescharacteristic, complemented
61C23×C13—212no—
62C23×C13—26no—
63C23×C13—212no—
64C23×C13—26no—
65C23×C13—43no—
66C23×C13—46no—
67C23×C13—43no—
68C23×C13—412no—
69C23×C13—46no—
70C23×C13—43no—
71C23×C13—43no—
72C23×C13—412no—
73C23×C13—86no—
74C23×C13—88no—
75C23×C13—824no—
76C23×C13#12013yes—
77C23×C13#12113yes—
78C23×C13#12711yescharacteristic
79D4×C13—412no—
80D4×C13—424no—
81D4×C13—412no—
82D4×C13—824no—
83C2×C4×C13—212no—
84C2×C4×C13—26no—
85C2×C4×C13—46no—
86C2×C4×C13—43no—
87C2×C4×C13—43no—
88C2×C4×C13—412no—
89C2×C4×C13—46no—
90C2×C4×C13—83no—
91C23×D4C22×C1313yes—
92C2×#120—26no—
93C2×#99—26no—
94#392—26no—
95#386—26no—
96#379C22×C1311yescharacteristic
97#379C22×C1313yes—
98C22×C13—26no—
99C22×C13—23no—
100C22×C13—23no—
101C22×C13—26no—
102C22×C13—412no—
103C22×C13—424no—
104C22×C13—46no—
105C22×C13—86no—
106C22×C13—812no—
107C22×C13—82no—
108C22×C13—86no—
109C22×C13—86no—
110C22×C13—86no—
111C22×C13#39211yescharacteristic
112C22×C13B(4,𝔽2)16yes—
113C4×C13—46no—
114C4×C13—86no—
115C4×C13—161no—
116C25D4×C1313yescomplemented
117C25C23×C1311yescharacteristic
118C22×D4—26no—
119C22×D4—23no—
120C22×D4—26no—
121C22×D4—23no—
122C22×D4—26no—
123C22×D4—412no—
124C23×C4D4×C1313yescomplemented
125#120—424no—
126C2×C22⋊C4—212no—
127C2×C22⋊C4—26no—
128C2×C22⋊C4—23no—
129C2×C22⋊C4D4×C1316yescomplemented
130#99—412no—
131#95—26no—
132C2×C13—26no—
133C2×C13—41no—
134C2×C13—43no—
135C2×C13—86no—
136C2×C13#202113yes—
137C24—26no—
138C24—23no—
139C24—46no—
140C24—46no—
141C24—412no—
142C24C2×D4×C1313yes—
143C24C2×D4×C1313yes—
144C24C13×#4111yescharacteristic
145C2×D4—212no—
146C2×D4—224no—
147C2×D4—412no—
148C2×D4—46no—
149C2×D4—412no—
150C2×D4—46no—
151C2×D4—412no—
152C2×D4—46no—
153C2×D4—43no—
154C2×D4—46no—
155C2×D4—43no—
156C2×D4—424no—
157C2×D4—86no—
158C22×C4—26no—
159C22×C4—23no—
160C22×C4—26no—
161C22×C4—46no—
162C22×C4—41no—
163C22⋊C4—424no—
164C22⋊C4—412no—
165C22⋊C4—46no—
166C22⋊C4—46no—
167C13#1033611yescharacteristic, direct product factor, Sylow
168C23—212no—
169C23—26no—
170C23—212no—
171C23—26no—
172C23—43no—
173C23—46no—
174C23—43no—
175C23—412no—
176C23—46no—
177C23—43no—
178C23—43no—
179C23—412no—
180C23—86no—
181C23—88no—
182C23—824no—
183C23C13×#12013yes—
184C23C13×#12113yes—
185C23C13×#12711yescharacteristic
186D4—412no—
187D4—424no—
188D4—412no—
189D4—824no—
190C2×C4—212no—
191C2×C4—26no—
192C2×C4—46no—
193C2×C4—43no—
194C2×C4—43no—
195C2×C4—412no—
196C2×C4—46no—
197C2×C4—83no—
198C22—26no—
199C22—23no—
200C22—23no—
201C22—26no—
202C22—412no—
203C22—424no—
204C22—46no—
205C22—86no—
206C22—812no—
207C22—82no—
208C22—86no—
209C22—86no—
210C22—86no—
211C22C13×#39211yescharacteristic
212C22C13×B(4,𝔽2)16yes—
213C4—46no—
214C4—86no—
215C4—161no—
216C2—26no—
217C2—41no—
218C2—43no—
219C2—86no—
220C2C13×#202113yes—
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC25C23×C13
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2403C2semidirect
2. C13×#1781C2semidirect
3. C13×#1304C2semidirect
11. C25×C13D4semidirect
19. C23×C4×C13D4semidirect
24. C2×C13×C22⋊C4D4semidirect
27. #10336C13direct (N × H)
58. #2403C2×C13semidirect
59. #1781C2×C13semidirect
60. #1304C2×C13semidirect
116. C25D4×C13semidirect
124. C23×C4D4×C13semidirect
129. C2×C22⋊C4D4×C13semidirect
167. C13#10336direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24032
C13×#17812
C13×#13042
#1033613