Finite Group Databasebeta

← C13×#10428 #15696767

Subgroups — C13×#10428 #15696767

Order 3328.

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

normal subgroups only

This group has 386 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×#2822C211yesmaximal, characteristic
2C13×#1992C212yesmaximal
3C13×#1836C211yesmaximal, characteristic
4C2×C13×#330C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×#125C2212yes—
7C2×C13×#97C2212yes—
8C2×C13×#97C2211yescharacteristic
9C13×#400—22no—
10C13×#398—22no—
11C13×#398—22no—
12C13×#384C2211yescharacteristic
13C13×#382C2211yescharacteristic
14C13×#340—22no—
15C13×#340—22no—
16C13×#340—22no—
17C13×#330—24no—
18C22×C8×C13—22no—
19C22×C8×C13—21no—
20C13×#125—22no—
21C13×#125—22no—
22C13×#125—22no—
23C13×#125—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D412yes—
32C2×C42×C13C2311yescharacteristic
33C13×#97—22no—
34C13×#97—21no—
35C13×#97—22no—
36C13×#97D412yes—
37C13×#95—24no—
38C13×#95—22no—
39C13×#95—22no—
40#10428C1311yesmaximal, characteristic, direct product factor, Sylow
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—41no—
45C22×C4×C13C2×D412yes—
46C22×C4×C13C2×D411yescharacteristic
47C2×C8×C13—24no—
48C2×C8×C13—22no—
49C2×C8×C13—42no—
50C2×C8×C13—41no—
51C2×C8×C13—41no—
52C2×C8×C13—42no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—44no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—82no—
65C42×C13C2×D411yescharacteristic
66C42×C13#4111yescharacteristic
67C42×C13#4112yes—
68#2822C2×C1311yescharacteristic
69#1992C2×C1312yes—
70#1836C2×C1311yescharacteristic
71C2×#330C2×C1312yes—
72#1295C2×C1311yescharacteristic
73C23×C13#12011yescharacteristic
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—81no—
88C2×C4×C13—82no—
89C2×C4×C13#12112yes—
90C2×C4×C13#12111yescharacteristic
91C2×C4×C13#12312yes—
92C2×C4×C13#12411yescharacteristic
93C8×C13—44no—
94C8×C13—42no—
95C2×#125C22×C1312yes—
96C2×#97C22×C1312yes—
97C2×#97C22×C1311yescharacteristic
98#400—22no—
99#398—22no—
100#398—22no—
101#384C22×C1311yescharacteristic
102#382C22×C1311yescharacteristic
103#340—22no—
104#340—22no—
105#340—22no—
106#330—24no—
107C22×C13#39411yescharacteristic
108C22×C13#45411yescharacteristic
109C22×C13#45412yes—
110C22×C13#45511yescharacteristic
111C22×C13#45612yes—
112C4×C13—22no—
113C4×C13—22no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—82no—
117C4×C13—82no—
118C4×C13—82no—
119C4×C13—161no—
120C22×C8—22no—
121C22×C8—21no—
122#125—22no—
123#125—22no—
124#125—22no—
125#125—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4D4×C1312yes—
132C2×C4⋊C4D4×C1312yes—
133C2×C4⋊C4D4×C1312yes—
134C2×C42C23×C1311yescharacteristic
135#97—22no—
136#97—21no—
137#97—22no—
138#97D4×C1312yes—
139#95—24no—
140#95—22no—
141#95—22no—
142C2×C13#165811yescharacteristic
143C2×C13#166311yescharacteristic
144C2×C13#166412yes—
145C2×C13#203812yes—
146C2×C13#204011yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4C2×D4×C1312yes—
152C22×C4C2×D4×C1311yescharacteristic
153C2×C8—24no—
154C2×C8—22no—
155C2×C8—42no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—42no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—82no—
171C42C2×D4×C1311yescharacteristic
172C42C13×#4111yescharacteristic
173C42C13×#4112yes—
174C13#1042811yescharacteristic, direct product factor, Sylow
175C23C13×#12011yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C13×#12112yes—
192C2×C4C13×#12111yescharacteristic
193C2×C4C13×#12312yes—
194C2×C4C13×#12411yescharacteristic
195C8—44no—
196C8—42no—
197C22C13×#39411yescharacteristic
198C22C13×#45412yes—
199C22C13×#45411yescharacteristic
200C22C13×#45511yescharacteristic
201C22C13×#45612yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C13×#165811yescharacteristic
211C2C13×#166311yescharacteristic
212C2C13×#166412yes—
213C2C13×#203812yes—
214C2C13×#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
40. #10428C13direct (N × H)
174. C13#10428direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28222
C13×#19922
C13×#18362
C2×C13×#3302
C13×#12952
#1042813