Finite Group Databasebeta

← C13×#1614 #13110672

Subgroups — C13×#1614 #13110672

Order 1664.

236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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×#543C211yesmaximal, characteristic
2C13×#484C212yesmaximal, complemented
3C13×#399C211yesmaximal, characteristic
4C13×#328C212yesmaximal, complemented
5C13×#323C211yesmaximal, characteristic
6C13×C22⋊Q8—22no—
7C13×C22⋊Q8—21no—
8C13×C22⋊Q8—22no—
9C13×C22⋊Q8C2212yes—
10C2×C13×C4⋊C4—21no—
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C22⋊C4—21no—
13C2×C13×C22⋊C4—21no—
14C2×C13×C22⋊C4C2211yescharacteristic
15C13×#107—22no—
16C13×#103—22no—
17C13×C22⋊C8C2212yes—
18C13×#95C2211yescharacteristic
19C24×C13D411yescharacteristic
20C2×Q8×C13—21no—
21C2×Q8×C13D412yes—
22C22×C4×C13—21no—
23C22×C4×C13—21no—
24C22×C4×C13—21no—
25C22×C4×C13—21no—
26C22×C4×C13D411yescharacteristic
27C22×C4×C13C2311yescharacteristic
28C2×C8×C13—22no—
29C13×C4⋊C4—21no—
30C13×C4⋊C4—22no—
31C13×C4⋊C4—22no—
32C13×C4⋊C4—22no—
33C13×C4⋊C4—42no—
34C13×C4⋊C4D412yes—
35C13×C22⋊C4—22no—
36C13×C22⋊C4—22no—
37C13×C22⋊C4—22no—
38C13×C22⋊C4—42no—
39#1614C1311yesmaximal, characteristic, direct product factor, Sylow
40C23×C13—21no—
41C23×C13—21no—
42C23×C13—41no—
43C23×C13—41no—
44C23×C13Q1612yes—
45C23×C13C2×D411yescharacteristic
46Q8×C13—42no—
47Q8×C13—81no—
48C2×C4×C13—22no—
49C2×C4×C13—22no—
50C2×C4×C13—21no—
51C2×C4×C13—22no—
52C2×C4×C13—41no—
53C2×C4×C13—41no—
54C2×C4×C13—41no—
55C2×C4×C13—41no—
56C2×C4×C13—41no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13—81no—
60C2×C4×C13—81no—
61C2×C4×C13C2×D412yes—
62C8×C13—42no—
63#543C2×C1311yescharacteristic
64#484C2×C1312yescomplemented
65#399C2×C1311yescharacteristic
66#328C2×C1312yescomplemented
67#323C2×C1311yescharacteristic
68C22×C13—21no—
69C22×C13—21no—
70C22×C13—22no—
71C22×C13—42no—
72C22×C13—41no—
73C22×C13—41no—
74C22×C13—81no—
75C22×C13#12011yescharacteristic
76C22×C13C2×Q1611yescharacteristic
77C22×C13#13711yescharacteristic
78C4×C13—22no—
79C4×C13—42no—
80C4×C13—41no—
81C4×C13—42no—
82C4×C13—42no—
83C4×C13—81no—
84C22⋊Q8—22no—
85C22⋊Q8—21no—
86C22⋊Q8—22no—
87C22⋊Q8C22×C1312yes—
88C2×C4⋊C4—21no—
89C2×C4⋊C4C22×C1311yescharacteristic
90C2×C22⋊C4—21no—
91C2×C22⋊C4—21no—
92C2×C22⋊C4C22×C1311yescharacteristic
93#107—22no—
94#103—22no—
95C22⋊C8C22×C1312yes—
96#95C22×C1311yescharacteristic
97C2×C13—21no—
98C2×C13—21no—
99C2×C13—42no—
100C2×C13#45111yescharacteristic
101C2×C13#45311yescharacteristic
102C2×C13#45811yescharacteristic
103C24D4×C1311yescharacteristic
104C2×Q8—21no—
105C2×Q8D4×C1312yes—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4D4×C1311yescharacteristic
111C22×C4C23×C1311yescharacteristic
112C2×C8—22no—
113C4⋊C4—21no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—42no—
118C4⋊C4D4×C1312yes—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—42no—
123C13#161411yescharacteristic, direct product factor, Sylow
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23C13×Q1612yes—
129C23C2×D4×C1311yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4C2×D4×C1312yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22C13×#12011yescharacteristic
155C22C2×C13×Q1611yescharacteristic
156C22C13×#13711yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—42no—
161C4—42no—
162C4—81no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2C13×#45111yescharacteristic
167C2C13×#45311yescharacteristic
168C2C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13#120
commutator, Frattini, cosocleC22×C4C23×C13
prime radicalC24×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#484C2semidirect
4. C13×#328C2semidirect
39. #1614C13direct (N × H)
64. #484C2×C13semidirect
66. #328C2×C13semidirect
123. C13#1614direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5432
C13×#4842
C13×#3992
C13×#3282
C13×#3232
#161413