Finite Group Databasebeta

← C13×#10321 #15696660

Subgroups — C13×#10321 #15696660

Order 3328.

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

normal subgroups only

This group has 726 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×#3186C211yesmaximal, characteristic
2C13×#2854C212yesmaximal, complemented
3C13×#1817C211yesmaximal, characteristic, complemented
4C13×#1519C212yesmaximal, complemented
5C13×#1289C211yesmaximal, characteristic, complemented
6C2×C13×#123—22no—
7C2×C13×#121C2212yes—
8C22×C42×C13C2211yescharacteristic
9C13×#480—22no—
10C13×#466—22no—
11C13×#447—22no—
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×C13×C22⋊C8C2211yescharacteristic
14C13×#390—22no—
15C13×#389—22no—
16C13×#388—24no—
17C13×#386—22no—
18C13×#380C2212yes—
19C13×#336—22no—
20C13×#327—24no—
21C22×D4×C13—22no—
22C22×D4×C13D412yes—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C2×C13×D8—22no—
27C22×C8×C13—21no—
28C22×C8×C13D412yes—
29C13×#123—44no—
30C13×#123—44no—
31C13×#121—22no—
32C13×#121—22no—
33C13×#121—22no—
34C13×#121—22no—
35C2×C13×C4⋊C4—24no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4D412yes—
38C2×C13×C22⋊C4—24no—
39C2×C13×C22⋊C4—24no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C42×C13—22no—
43C2×C42×C13—22no—
44C2×C42×C13—21no—
45C2×C42×C13—21no—
46C13×#107—22no—
47C13×#102—24no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C13×#95—24no—
51C13×#95D414yes—
52#10321C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13—22no—
54C24×C13C2×D411yescharacteristic
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13—44no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—24no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13D812yescomplemented
75C22×C4×C13C2×D412yes—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D412yes—
78C22×C4×C13#4111yescharacteristic
79C13×D8—82no—
80C2×C8×C13—22no—
81C2×C8×C13—42no—
82C2×C8×C13—42no—
83C2×C8×C13—41no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—44no—
87C13×C4⋊C4—48no—
88C13×C22⋊C4—48no—
89C13×C22⋊C4—48no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C42×C13—41no—
95C42×C13—42no—
96C42×C13—41no—
97#3186C2×C1311yescharacteristic
98#2854C2×C1312yescomplemented
99#1817C2×C1311yescharacteristic, complemented
100#1519C2×C1312yescomplemented
101#1289C2×C1311yescharacteristic, complemented
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—44no—
105C23×C13—44no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13#12012yes—
110C23×C13#12111yescharacteristic
111C23×C13C2×D811yescharacteristic
112C23×C13#13511yescharacteristic
113C23×C13AGL(1,ℤ/8)12yes—
114D4×C13—44no—
115D4×C13—82no—
116D4×C13—82no—
117D4×C13—82no—
118D4×C13—82no—
119D4×C13—82no—
120C2×C4×C13—24no—
121C2×C4×C13—22no—
122C2×C4×C13—24no—
123C2×C4×C13—22no—
124C2×C4×C13—24no—
125C2×C4×C13—22no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—42no—
137C2×C4×C13—44no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13#12112yes—
142C2×C4×C13#12711yescharacteristic
143C8×C13—42no—
144C8×C13—81no—
145C2×#123—22no—
146C2×#121C22×C1312yes—
147C22×C42C22×C1311yescharacteristic
148#480—22no—
149#466—22no—
150#447—22no—
151C2×C22⋊C8C22×C1311yescharacteristic
152C2×C22⋊C8C22×C1311yescharacteristic
153#390—22no—
154#389—22no—
155#388—24no—
156#386—22no—
157#380C22×C1312yes—
158#336—22no—
159#327—24no—
160C22×C13—22no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—42no—
167C22×C13—84no—
168C22×C13—84no—
169C22×C13—82no—
170C22×C13—82no—
171C22×C13—82no—
172C22×C13#39211yescharacteristic
173C22×C13#44712yes—
174C22×C13#44912yes—
175C22×C13#46611yescharacteristic
176C22×C13#46911yescharacteristic
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—42no—
180C4×C13—42no—
181C4×C13—84no—
182C4×C13—82no—
183C4×C13#45812yes—
184C22×D4—22no—
185C22×D4D4×C1312yes—
186C23×C4D4×C1311yescharacteristic
187C23×C4D4×C1311yescharacteristic
188C23×C4C23×C1311yescharacteristic
189C2×D8—22no—
190C22×C8—21no—
191C22×C8D4×C1312yes—
192#123—44no—
193#123—44no—
194#121—22no—
195#121—22no—
196#121—22no—
197#121—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4D4×C1312yes—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C42—21no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—21no—
209#107—22no—
210#102—24no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213#95—24no—
214#95D4×C1314yes—
215C2×C13—22no—
216C2×C13—22no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13—162no—
220C2×C13#199911yescharacteristic
221C2×C13#201011yescharacteristic
222C2×C13#202211yescharacteristic
223C24—22no—
224C24C2×D4×C1311yescharacteristic
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—44no—
228C2×D4—42no—
229C2×D4—42no—
230C2×D4—42no—
231C2×D4—42no—
232C2×D4—42no—
233C2×D4—42no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4C13×D812yescomplemented
245C22×C4C2×D4×C1312yes—
246C22×C4C2×D4×C1311yescharacteristic
247C22×C4C2×D4×C1312yes—
248C22×C4C13×#4111yescharacteristic
249D8—82no—
250C2×C8—22no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—41no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—48no—
257C4⋊C4—44no—
258C22⋊C4—48no—
259C22⋊C4—48no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C42—41no—
265C42—42no—
266C42—41no—
267C13#1032111yescharacteristic, direct product factor, Sylow
268C23—41no—
269C23—41no—
270C23—44no—
271C23—44no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23C13×#12012yes—
276C23C13×#12111yescharacteristic
277C23C2×C13×D811yescharacteristic
278C23C13×#13511yescharacteristic
279C23C13×AGL(1,ℤ/8)12yes—
280D4—44no—
281D4—82no—
282D4—82no—
283D4—82no—
284D4—82no—
285D4—82no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4C13×#12011yescharacteristic
307C2×C4C13×#12112yes—
308C2×C4C13×#12711yescharacteristic
309C8—42no—
310C8—81no—
311C22—22no—
312C22—21no—
313C22—22no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—84no—
319C22—84no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22C13×#39211yescharacteristic
324C22C13×#44712yes—
325C22C13×#44912yes—
326C22C13×#46611yescharacteristic
327C22C13×#46911yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—42no—
332C4—84no—
333C4—82no—
334C4C13×#45812yes—
335C2—22no—
336C2—22no—
337C2—21no—
338C2—21no—
339C2—162no—
340C2C13×#199911yescharacteristic
341C2C13×#201011yescharacteristic
342C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#3186C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2854C2semidirect
3. C13×#1817C2semidirect
4. C13×#1519C2semidirect
5. C13×#1289C2semidirect
52. #10321C13direct (N × H)
74. C22×C4×C13D8semidirect
98. #2854C2×C13semidirect
99. #1817C2×C13semidirect
100. #1519C2×C13semidirect
101. #1289C2×C13semidirect
244. C22×C4C13×D8semidirect
267. C13#10321direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31862
C13×#28542
C13×#18172
C13×#15192
C13×#12892
#1032113