Finite Group Databasebeta

← C13×#7803 #15694142

Subgroups — C13×#7803 #15694142

Order 3328.

338 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2810C211yesmaximal, characteristic
2C13×#2099C211yesmaximal, characteristic
3C13×#2084C211yesmaximal, characteristic
4C13×#2083C211yesmaximal, characteristic
5C13×#1271C211yesmaximal, characteristic
6C13×#1271C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C2×C13×#107—21no—
9C2×C13×#106—21no—
10C13×#400—21no—
11C13×#400—21no—
12C13×#400—21no—
13C13×#389C2211yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#389C2211yescharacteristic
16C13×#387—21no—
17C13×#387—21no—
18C13×#387—21no—
19C13×#384C2211yescharacteristic
20C13×#340—21no—
21C13×#340—21no—
22C13×#340—21no—
23C13×#340—21no—
24C13×#336C2211yescharacteristic
25C13×#336C2211yescharacteristic
26C13×#336C2211yescharacteristic
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13C2311yescharacteristic
44C13×#107—42no—
45C13×#106—42no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#7803C1311yesmaximal, characteristic, direct product factor, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C2×C8×C13—22no—
68C2×C8×C13—22no—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C42×C13—41no—
97C42×C13—81no—
98#2810C2×C1311yescharacteristic
99#2099C2×C1311yescharacteristic
100#2084C2×C1311yescharacteristic
101#2083C2×C1311yescharacteristic
102#1271C2×C1311yescharacteristic
103#1271C2×C1311yescharacteristic
104#1271C2×C1311yescharacteristic
105C23×C13#12011yescharacteristic
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C8×C13—42no—
140C8×C13—42no—
141C8×C13—81no—
142C2×#107—21no—
143C2×#106—21no—
144#400—21no—
145#400—21no—
146#400—21no—
147#389C22×C1311yescharacteristic
148#389C22×C1311yescharacteristic
149#389C22×C1311yescharacteristic
150#387—21no—
151#387—21no—
152#387—21no—
153#384C22×C1311yescharacteristic
154#340—21no—
155#340—21no—
156#340—21no—
157#340—21no—
158#336C22×C1311yescharacteristic
159#336C22×C1311yescharacteristic
160#336C22×C1311yescharacteristic
161C22×C13#44911yescharacteristic
162C22×C13#44911yescharacteristic
163C22×C13#45211yescharacteristic
164C22×C13#45411yescharacteristic
165C22×C13#45611yescharacteristic
166C22×C13#45611yescharacteristic
167C22×C13#45811yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—81no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180C4×C13—161no—
181C22×C8—21no—
182C22×C8—21no—
183C22×C8—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4D4×C1311yescharacteristic
191C2×C4⋊C4D4×C1311yescharacteristic
192C2×C4⋊C4D4×C1311yescharacteristic
193C2×C4⋊C4D4×C1311yescharacteristic
194C2×C4⋊C4D4×C1311yescharacteristic
195C2×C4⋊C4D4×C1311yescharacteristic
196C2×C42—21no—
197C2×C42C23×C1311yescharacteristic
198#107—42no—
199#106—42no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C13#160911yescharacteristic
211C2×C13#160911yescharacteristic
212C2×C13#161511yescharacteristic
213C2×C13#162811yescharacteristic
214C2×C13#165011yescharacteristic
215C2×C13#165211yescharacteristic
216C2×C13#166311yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4C2×D4×C1311yescharacteristic
225C22×C4C2×D4×C1311yescharacteristic
226C22×C4C2×D4×C1311yescharacteristic
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C42—41no—
257C42—81no—
258C13#780311yescharacteristic, direct product factor, Sylow
259C23C13×#12011yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C13×#13511yescharacteristic
288C2×C4C13×#13511yescharacteristic
289C2×C4C13×#13511yescharacteristic
290C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
291C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
292C2×C4C13×#13711yescharacteristic
293C8—42no—
294C8—42no—
295C8—81no—
296C22C13×#44911yescharacteristic
297C22C13×#44911yescharacteristic
298C22C13×#45211yescharacteristic
299C22C13×#45411yescharacteristic
300C22C13×#45611yescharacteristic
301C22C13×#45611yescharacteristic
302C22C13×#45811yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—161no—
316C2C13×#160911yescharacteristic
317C2C13×#160911yescharacteristic
318C2C13×#161511yescharacteristic
319C2C13×#162811yescharacteristic
320C2C13×#165011yescharacteristic
321C2C13×#165211yescharacteristic
322C2C13×#166311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
56. #7803C13direct (N × H)
258. C13#7803direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28102
C13×#20992
C13×#20842
C13×#20832
C13×#12712
#780313