Finite Group Databasebeta

← C13×#10359 #15696698

Subgroups — C13×#10359 #15696698

Order 3328.

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

normal subgroups only

This group has 400 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×#2844C211yesmaximal, characteristic
2C13×#1993C212yesmaximal
3C13×#1960C211yesmaximal, characteristic
4C13×#1295C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#103—21no—
8C2×C13×#103—21no—
9C2×C13×#97C2212yes—
10C2×C13×#97C2211yescharacteristic
11C13×#400—22no—
12C13×#400—21no—
13C13×#395—22no—
14C13×#395—21no—
15C13×#382C2212yes—
16C13×#382C2211yescharacteristic
17C13×#340—22no—
18C13×#340—22no—
19C22×Q8×C13—21no—
20C22×Q8×C13—21no—
21C22×C8×C13—22no—
22C22×C8×C13—21no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—21no—
25C13×C4⋊Q8Q812yescomplemented
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C13×#103—42no—
35C13×#103—42no—
36C13×#97—22no—
37C13×#97—22no—
38C13×#97—22no—
39C13×#95—22no—
40C13×#95—21no—
41C13×#95—21no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—22no—
45#10359C1311yesmaximal, characteristic, direct product factor, Sylow
46C2×Q8×C13—22no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13—81no—
53C2×Q8×C13—82no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13C2×D412yes—
60C22×C4×C13C2×D411yescharacteristic
61C2×C8×C13—22no—
62C2×C8×C13—24no—
63C2×C8×C13—41no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C2×C8×C13—41no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—81no—
74C13×C4⋊C4—82no—
75C42×C13C2×Q811yescharacteristic
76C42×C13#4112yes—
77C42×C13#4111yescharacteristic
78#2844C2×C1311yescharacteristic
79#1993C2×C1312yes—
80#1960C2×C1311yescharacteristic
81#1295C2×C1311yescharacteristic
82#1295C2×C1312yes—
83C23×C13#12011yescharacteristic
84Q8×C13—42no—
85Q8×C13—42no—
86Q8×C13—81no—
87Q8×C13—81no—
88Q8×C13—84no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—42no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—81no—
105C2×C4×C13—81no—
106C2×C4×C13C22⋊Q812yes—
107C2×C4×C13C22⋊Q811yescharacteristic
108C2×C4×C13#12412yes—
109C2×C4×C13#12411yescharacteristic
110C8×C13—42no—
111C8×C13—44no—
112C2×C4⋊Q8C22×C1311yescharacteristic
113C2×#103—21no—
114C2×#103—21no—
115C2×#97C22×C1311yescharacteristic
116C2×#97C22×C1312yes—
117#400—22no—
118#400—21no—
119#395—22no—
120#395—21no—
121#382C22×C1311yescharacteristic
122#382C22×C1312yes—
123#340—22no—
124#340—22no—
125C22×C13#39311yescharacteristic
126C22×C13#45311yescharacteristic
127C22×C13#45411yescharacteristic
128C22×C13#45512yes—
129C22×C13#45612yes—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—81no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13—82no—
138C4×C13—82no—
139C22×Q8—21no—
140C22×Q8—21no—
141C22×C8—22no—
142C22×C8—21no—
143C4⋊Q8—22no—
144C4⋊Q8—21no—
145C4⋊Q8Q8×C1312yescomplemented
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4D4×C1312yes—
150C2×C4⋊C4D4×C1312yes—
151C2×C4⋊C4D4×C1311yescharacteristic
152C2×C4⋊C4D4×C1311yescharacteristic
153C2×C42C23×C1311yescharacteristic
154#103—42no—
155#103—42no—
156#97—22no—
157#97—22no—
158#97—22no—
159#95—22no—
160#95—21no—
161#95—21no—
162#95—22no—
163#95—22no—
164#95—22no—
165C2×C13#165911yescharacteristic
166C2×C13#166011yescharacteristic
167C2×C13#166412yes—
168C2×C13#202711yescharacteristic
169C2×C13#202812yes—
170C2×Q8—22no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—81no—
177C2×Q8—82no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4C2×D4×C1312yes—
184C22×C4C2×D4×C1311yescharacteristic
185C2×C8—22no—
186C2×C8—24no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—41no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—82no—
199C42C2×Q8×C1311yescharacteristic
200C42C13×#4112yes—
201C42C13×#4111yescharacteristic
202C13#1035911yescharacteristic, direct product factor, Sylow
203C23C13×#12011yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—84no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4C13×C22⋊Q812yes—
227C2×C4C13×C22⋊Q811yescharacteristic
228C2×C4C13×#12412yes—
229C2×C4C13×#12411yescharacteristic
230C8—42no—
231C8—44no—
232C22C13×#39311yescharacteristic
233C22C13×#45311yescharacteristic
234C22C13×#45411yescharacteristic
235C22C13×#45512yes—
236C22C13×#45612yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—81no—
243C4—82no—
244C4—81no—
245C4—82no—
246C2C13×#165911yescharacteristic
247C2C13×#166011yescharacteristic
248C2C13×#166412yes—
249C2C13×#202711yescharacteristic
250C2C13×#202812yes—
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
25. C13×C4⋊Q8Q8semidirect
45. #10359C13direct (N × H)
145. C4⋊Q8Q8×C13semidirect
202. C13#10359direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28442
C13×#19932
C13×#19602
C13×#12952
#1035913