Finite Group Databasebeta

← C13×#13428 #15699767

Subgroups — C13×#13428 #15699767

Order 3328.

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2734C211yesmaximal, characteristic
2C2×C13×#356C212yesmaximal
3C13×#1886C212yesmaximal
4C13×#1857C211yesmaximal, characteristic
5C13×#1394C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2212yes—
7C13×#519C2211yescharacteristic
8C13×#428—21no—
9C13×#419—22no—
10C2×C13×#101C2212yes—
11C2×C13×#101C2211yescharacteristic
12C13×#398—21no—
13C13×#395—22no—
14C13×#391C2211yescharacteristic
15C13×#389—21no—
16C13×#387—22no—
17C13×#356—24no—
18C13×#339—21no—
19C13×#339—22no—
20C22×Q8×C13D412yes—
21C22×Q8×C13C2311yescharacteristic
22C2×C13×M16—21no—
23C2×C13×M16—22no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—22no—
27C13×C4⋊Q8—22no—
28C4×Q8×C13—41no—
29C4×Q8×C13—41no—
30C13×#117—22no—
31C13×#117—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C42×C13D412yes—
39C2×C42×C13D411yescharacteristic
40C13×#107—41no—
41C13×#106—41no—
42C13×#103—42no—
43C13×#103—42no—
44C13×#101—21no—
45C13×#101—22no—
46C13×#101—22no—
47C13×#101D412yes—
48C13×#95—21no—
49C13×#95—22no—
50C13×#95—22no—
51C13×#95—22no—
52#13428C1311yesmaximal, characteristic, direct product factor, Sylow
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13—42no—
58C2×Q8×C13—42no—
59C2×Q8×C13C2×D411yescharacteristic
60C2×Q8×C13#4111yescharacteristic
61C2×Q8×C13#4112yes—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C13×M16—22no—
69C13×M16—41no—
70C13×M16—42no—
71C13×M16—42no—
72C2×C8×C13—41no—
73C2×C8×C13—42no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—81no—
85C13×C4⋊C4—81no—
86C13×C22⋊C4—41no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13—42no—
92#2734C2×C1311yescharacteristic
93C2×#356C2×C1312yes—
94#1886C2×C1312yes—
95#1857C2×C1311yescharacteristic
96#1394C2×C1311yescharacteristic
97C23×C13#12011yescharacteristic
98Q8×C13—41no—
99Q8×C13—41no—
100Q8×C13—42no—
101Q8×C13—44no—
102Q8×C13—82no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—24no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13#12112yes—
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12312yes—
123C2×C4×C13#12411yescharacteristic
124C8×C13—42no—
125C8×C13—82no—
126C2×C4⋊Q8C22×C1312yes—
127#519C22×C1311yescharacteristic
128#428—21no—
129#419—22no—
130C2×#101C22×C1312yes—
131C2×#101C22×C1311yescharacteristic
132#398—21no—
133#395—22no—
134#391C22×C1311yescharacteristic
135#389—21no—
136#387—22no—
137#356—24no—
138#339—21no—
139#339—22no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#39411yescharacteristic
143C22×C13B(4,𝔽2)11yescharacteristic
144C22×C13#45811yescharacteristic
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—21no—
149C4×C13—44no—
150C4×C13—42no—
151C4×C13—81no—
152C4×C13—81no—
153C4×C13—81no—
154C4×C13—82no—
155C22×Q8D4×C1312yes—
156C22×Q8C23×C1311yescharacteristic
157C2×M16—21no—
158C2×M16—22no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4×Q8—41no—
164C4×Q8—41no—
165#117—22no—
166#117—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4D4×C1311yescharacteristic
173C2×C42D4×C1312yes—
174C2×C42D4×C1311yescharacteristic
175#107—41no—
176#106—41no—
177#103—42no—
178#103—42no—
179#101—21no—
180#101—22no—
181#101—22no—
182#101D4×C1312yes—
183#95—21no—
184#95—22no—
185#95—22no—
186#95—22no—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13#204411yescharacteristic
190C2×C13#220311yescharacteristic
191C2×C13#220511yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8C2×D4×C1311yescharacteristic
199C2×Q8C13×#4111yescharacteristic
200C2×Q8C13×#4112yes—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4C2×D4×C1312yes—
206C22×C4C2×D4×C1311yescharacteristic
207M16—22no—
208M16—41no—
209M16—42no—
210M16—42no—
211C2×C8—41no—
212C2×C8—42no—
213C4⋊C4—24no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C22⋊C4—41no—
226C42—22no—
227C42—22no—
228C42—41no—
229C42—41no—
230C42—42no—
231C13#1342811yescharacteristic, direct product factor, Sylow
232C23C13×#12011yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4C13×#12112yes—
256C2×C4C13×#12111yescharacteristic
257C2×C4C13×#12312yes—
258C2×C4C13×#12411yescharacteristic
259C8—42no—
260C8—82no—
261C22—21no—
262C22—21no—
263C22C13×#39411yescharacteristic
264C22C13×B(4,𝔽2)11yescharacteristic
265C22C13×#45811yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—81no—
275C4—81no—
276C2—21no—
277C2—21no—
278C2C13×#204411yescharacteristic
279C2C13×#220311yescharacteristic
280C2C13×#220511yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C13
prime radicalC23×C13#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
52. #13428C13direct (N × H)
231. C13#13428direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27342
C2×C13×#3562
C13×#18862
C13×#18572
C13×#13942
#1342813