Finite Group Databasebeta

← C13×#10227 #15696566

Subgroups — C13×#10227 #15696566

Order 3328.

466 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3229C212yesmaximal
2C13×#3162C211yesmaximal, characteristic
3C13×#1960C211yesmaximal, characteristic
4C13×#1518C212yesmaximal
5C13×#1281C211yesmaximal, characteristic
6C13×#533C2212yes—
7C2×C13×C4⋊Q8C2211yescharacteristic
8C13×#501—22no—
9C13×#501—22no—
10C13×#498—22no—
11C13×#487—22no—
12C13×#483—24no—
13C13×#475—24no—
14C13×#431C2212yes—
15C13×#427—22no—
16C2×C13×#103—22no—
17C2×C13×#97C2211yescharacteristic
18C13×#382C2211yescharacteristic
19C13×#328—24no—
20C22×Q8×C13—21no—
21C22×C8×C13D412yes—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8D412yes—
25C13×C4⋊Q8D412yes—
26C13×C4⋊Q8D412yes—
27C13×#125—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C4×Q8×C13—22no—
31C4×Q8×C13—22no—
32C13×#117—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—21no—
35C2×C42×C13C2311yescharacteristic
36C13×#107—24no—
37C13×#106—22no—
38C13×#106—22no—
39C13×#106—28no—
40C13×C4⋊C8—22no—
41C13×#103—28no—
42C13×#103—44no—
43C13×C22⋊C8D414yes—
44C13×#97—22no—
45C4×C8×C13—22no—
46C13×#95—22no—
47#10227C1311yesmaximal, characteristic, direct product factor, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—41no—
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C2×C8×C13—22no—
59C2×C8×C13—22no—
60C2×C8×C13—24no—
61C2×C8×C13SD1614yes—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C22⋊C4—42no—
72C42×C13—42no—
73C42×C13C2×D412yes—
74C42×C13C2×D411yescharacteristic
75C42×C13#4111yescharacteristic
76#3229C2×C1312yes—
77#3162C2×C1311yescharacteristic
78#1960C2×C1311yescharacteristic
79#1518C2×C1312yes—
80#1281C2×C1311yescharacteristic
81C23×C13#12711yescharacteristic
82Q8×C13—44no—
83Q8×C13—44no—
84Q8×C13—82no—
85Q8×C13—82no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—81no—
91C2×C4×C13—81no—
92C2×C4×C13—82no—
93C2×C4×C13—81no—
94C2×C4×C13#12012yes—
95C2×C4×C13#12011yescharacteristic
96C2×C4×C13#12112yes—
97C2×C4×C13#12111yescharacteristic
98C2×C4×C13C2×SD1612yes—
99C2×C4×C13#13712yes—
100C8×C13—24no—
101C8×C13—44no—
102#533C22×C1312yes—
103C2×C4⋊Q8C22×C1311yescharacteristic
104#501—22no—
105#501—22no—
106#498—22no—
107#487—22no—
108#483—24no—
109#475—24no—
110#431C22×C1312yes—
111#427—22no—
112C2×#103—22no—
113C2×#97C22×C1311yescharacteristic
114#382C22×C1311yescharacteristic
115#328—24no—
116C22×C13—22no—
117C22×C13#39211yescharacteristic
118C22×C13#49211yescharacteristic
119C22×C13#49711yescharacteristic
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—82no—
123C4×C13—82no—
124C4×C13—82no—
125C4×C13—161no—
126C4×C13#44812yes—
127C4×C13#46112yes—
128C22×Q8—21no—
129C22×C8D4×C1312yes—
130C4⋊Q8—22no—
131C4⋊Q8—21no—
132C4⋊Q8D4×C1312yes—
133C4⋊Q8D4×C1312yes—
134C4⋊Q8D4×C1312yes—
135#125—22no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140#117—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C42C23×C1311yescharacteristic
144#107—24no—
145#106—22no—
146#106—22no—
147#106—28no—
148C4⋊C8—22no—
149#103—28no—
150#103—44no—
151C22⋊C8D4×C1314yes—
152#97—22no—
153C4×C8—22no—
154#95—22no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#200912yes—
158C2×C13#201311yescharacteristic
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—41no—
163C2×Q8—42no—
164C2×Q8—42no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4C2×D4×C1312yes—
168C22×C4C2×D4×C1311yescharacteristic
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—24no—
172C2×C8C13×SD1614yes—
173C4⋊C4—24no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—42no—
184C42C2×D4×C1312yes—
185C42C2×D4×C1311yescharacteristic
186C42C13×#4111yescharacteristic
187C13#1022711yescharacteristic, direct product factor, Sylow
188C23C13×#12711yescharacteristic
189Q8—44no—
190Q8—44no—
191Q8—82no—
192Q8—82no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—82no—
200C2×C4—81no—
201C2×C4C13×#12012yes—
202C2×C4C13×#12011yescharacteristic
203C2×C4C13×#12112yes—
204C2×C4C13×#12111yescharacteristic
205C2×C4C2×C13×SD1612yes—
206C2×C4C13×#13712yes—
207C8—24no—
208C8—44no—
209C22—22no—
210C22C13×#39211yescharacteristic
211C22C13×#49211yescharacteristic
212C22C13×#49711yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4—161no—
219C4C13×#44812yes—
220C4C13×#46112yes—
221C2—21no—
222C2—21no—
223C2C13×#200912yes—
224C2C13×#201311yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
47. #10227C13direct (N × H)
187. C13#10227direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32292
C13×#31622
C13×#19602
C13×#15182
C13×#12812
#1022713