Finite Group Databasebeta

← C13×C22⋊#401 #15701166

Subgroups — C13×C22⋊#401 #15701166

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#401C211yesmaximal, characteristic, complemented
2C22×C13×#95C211yesmaximal, characteristic
3C13×#1443C213yesmaximal, complemented
4C13×#1443C213yesmaximal, complemented
5C13×#1443C211yesmaximal, characteristic, complemented
6C13×C22⋊#95C213yesmaximal
7C13×C22⋊#95C213yesmaximal
8C24×C4×C13C2213yes—
9C22×C13×C22⋊C4C2213yes—
10C22×C13×C22⋊C4C2211yescharacteristic
11C13×#401—24no—
12C2×C13×#95—24no—
13C2×C13×#95C2213yes—
14C2×C13×#95C2213yes—
15C2×C13×#95C2213yes—
16C2×C13×#95C2213yes—
17C2×C13×#95C2213yes—
18C2×C13×#95C2213yes—
19C2×C13×#95C2213yes—
20C2×C13×#95C2213yes—
21C2×C13×#95C2213yes—
22C2×C13×#95C2211yescharacteristic
23C25×C13C2311yescharacteristic
24C23×C4×C13—26no—
25C23×C4×C13—26no—
26C23×C4×C13—26no—
27C23×C4×C13—26no—
28C23×C4×C13—26no—
29C23×C4×C13—43no—
30C23×C4×C13—43no—
31C23×C4×C13C2311yescharacteristic
32C23×C4×C13C2313yes—
33C23×C4×C13C2313yes—
34C23×C4×C13C2311yescharacteristic
35C23×C4×C13C2313yes—
36C23×C4×C13C2313yes—
37C2×C13×C22⋊C4—26no—
38C2×C13×C22⋊C4—26no—
39C2×C13×C22⋊C4—26no—
40C2×C13×C22⋊C4—26no—
41C13×#95—26no—
42C13×#95—26no—
43C13×#95—26no—
44C13×#95—26no—
45C13×#95—26no—
46C13×#95—43no—
47C13×#95—43no—
48C13×#95—43no—
49C13×#95—43no—
50C13×#95D414yes—
51C22⋊#401C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C24×C13—23no—
54C24×C13—23no—
55C24×C13—21no—
56C24×C13#4112yes—
57C24×C13#4116yes—
58C24×C13#4116yes—
59C24×C13C2411yescharacteristic
60C22×C4×C13—224no—
61C22×C4×C13—23no—
62C22×C4×C13—23no—
63C22×C4×C13—23no—
64C22×C4×C13—23no—
65C22×C4×C13—23no—
66C22×C4×C13—23no—
67C22×C4×C13—23no—
68C22×C4×C13—23no—
69C22×C4×C13—23no—
70C22×C4×C13—23no—
71C22×C4×C13—23no—
72C22×C4×C13—23no—
73C22×C4×C13—21no—
74C22×C4×C13—23no—
75C22×C4×C13—23no—
76C22×C4×C13—23no—
77C22×C4×C13—23no—
78C22×C4×C13—23no—
79C22×C4×C13—23no—
80C22×C4×C13—23no—
81C22×C4×C13—23no—
82C22×C4×C13—23no—
83C22×C4×C13—23no—
84C22×C4×C13—23no—
85C22×C4×C13—23no—
86C22×C4×C13—23no—
87C22×C4×C13—23no—
88C22×C4×C13—23no—
89C22×C4×C13—23no—
90C22×C4×C13—23no—
91C22×C4×C13—21no—
92C22×C4×C13—23no—
93C22×C4×C13—412no—
94C22×C4×C13—412no—
95C22×C4×C13—412no—
96C22×C4×C13—412no—
97C22×C4×C13—412no—
98C22×C4×C13—412no—
99C22×C4×C13C2×D416yes—
100C22×C4×C13#4116yes—
101C13×C22⋊C4—44no—
102C13×C22⋊C4—412no—
103C2×#401C2×C1311yescharacteristic, complemented
104C22×#95C2×C1311yescharacteristic
105#1443C2×C1313yescomplemented
106#1443C2×C1313yescomplemented
107#1443C2×C1311yescharacteristic, complemented
108C22⋊#95C2×C1313yes—
109C22⋊#95C2×C1313yes—
110C23×C13—26no—
111C23×C13—26no—
112C23×C13—26no—
113C23×C13—26no—
114C23×C13—26no—
115C23×C13—22no—
116C23×C13—26no—
117C23×C13—26no—
118C23×C13—26no—
119C23×C13—26no—
120C23×C13#12614yes—
121C23×C13#126112yes—
122C23×C13#126112yes—
123C23×C13C22×D411yescharacteristic
124C23×C13C2×#4113yes—
125C23×C13C2×#4113yes—
126C23×C13C2×#4113yes—
127C23×C13C2×#4111yescharacteristic
128C23×C13H(5,𝔽2)13yes—
129C23×C132−1+411yescharacteristic
130C2×C4×C13—26no—
131C2×C4×C13—26no—
132C2×C4×C13—26no—
133C2×C4×C13—26no—
134C2×C4×C13—26no—
135C2×C4×C13—26no—
136C2×C4×C13—448no—
137C2×C4×C13—43no—
138C2×C4×C13—43no—
139C2×C4×C13—43no—
140C2×C4×C13—43no—
141C2×C4×C13—43no—
142C2×C4×C13—43no—
143C2×C4×C13—43no—
144C2×C4×C13—43no—
145C2×C4×C13—43no—
146C2×C4×C13—43no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—43no—
150C2×C4×C13—43no—
151C2×C4×C13—43no—
152C2×C4×C13—43no—
153C2×C4×C13—43no—
154C2×C4×C13—43no—
155C2×C4×C13—43no—
156C2×C4×C13—43no—
157C2×C4×C13—43no—
158C2×C4×C13—43no—
159C2×C4×C13—43no—
160C2×C4×C13—43no—
161C2×C4×C13—43no—
162C2×C4×C13—43no—
163C2×C4×C13—43no—
164C2×C4×C13—43no—
165C24×C4C22×C1313yes—
166C22×C22⋊C4C22×C1313yes—
167C22×C22⋊C4C22×C1311yescharacteristic
168#401—24no—
169C2×#95—24no—
170C2×#95C22×C1313yes—
171C2×#95C22×C1313yes—
172C2×#95C22×C1313yes—
173C2×#95C22×C1313yes—
174C2×#95C22×C1313yes—
175C2×#95C22×C1313yes—
176C2×#95C22×C1313yes—
177C2×#95C22×C1313yes—
178C2×#95C22×C1313yes—
179C2×#95C22×C1311yescharacteristic
180C22×C13—24no—
181C22×C13—24no—
182C22×C13—212no—
183C22×C13—212no—
184C22×C13—212no—
185C22×C13—212no—
186C22×C13#40118yescomplemented
187C22×C13#52513yes—
188C22×C13C2×#12611yescharacteristic
189C22×C13C2×#12613yes—
190C22×C13C2×#12613yes—
191C22×C13#52913yes—
192C22×C13#53813yes—
193C22×C13#53913yes—
194C22×C13#54613yes—
195C22×C13#54811yescharacteristic
196C22×C13#55113yes—
197C22×C13#55113yes—
198C22×C13#55213yes—
199C22×C13#55313yes—
200C4×C13—46no—
201C4×C13—46no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—83no—
205C4×C13—83no—
206C25C23×C1311yescharacteristic
207C23×C4—26no—
208C23×C4—26no—
209C23×C4—26no—
210C23×C4—26no—
211C23×C4—26no—
212C23×C4—43no—
213C23×C4—43no—
214C23×C4C23×C1311yescharacteristic
215C23×C4C23×C1313yes—
216C23×C4C23×C1313yes—
217C23×C4C23×C1311yescharacteristic
218C23×C4C23×C1313yes—
219C23×C4C23×C1313yes—
220C2×C22⋊C4—26no—
221C2×C22⋊C4—26no—
222C2×C22⋊C4—26no—
223C2×C22⋊C4—26no—
224#95—26no—
225#95—26no—
226#95—26no—
227#95—26no—
228#95—26no—
229#95—43no—
230#95—43no—
231#95—43no—
232#95—43no—
233#95D4×C1314yes—
234C2×C13—28no—
235C2×C13C2×#40111yescharacteristic
236C2×C13#248013yes—
237C2×C13#248113yes—
238C2×C13#249313yes—
239C2×C13#251013yes—
240C2×C13#264311yescharacteristic
241C2×C13#285211yescharacteristic
242C24—21no—
243C24—23no—
244C24—23no—
245C24—21no—
246C24C13×#4112yes—
247C24C13×#4116yes—
248C24C13×#4116yes—
249C24C24×C1311yescharacteristic
250C22×C4—224no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—21no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4—23no—
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—23no—
280C22×C4—23no—
281C22×C4—21no—
282C22×C4—23no—
283C22×C4—412no—
284C22×C4—412no—
285C22×C4—412no—
286C22×C4—412no—
287C22×C4—412no—
288C22×C4—412no—
289C22×C4C2×D4×C1316yes—
290C22×C4C13×#4116yes—
291C22⋊C4—412no—
292C22⋊C4—44no—
293C13C22⋊#40111yescharacteristic, direct product factor, Sylow
294C23—26no—
295C23—26no—
296C23—26no—
297C23—26no—
298C23—26no—
299C23—22no—
300C23—26no—
301C23—26no—
302C23—26no—
303C23—26no—
304C23C13×#126112yes—
305C23C13×#12614yes—
306C23C13×#126112yes—
307C23C22×D4×C1311yescharacteristic
308C23C2×C13×#4113yes—
309C23C2×C13×#4113yes—
310C23C2×C13×#4113yes—
311C23C2×C13×#4111yescharacteristic
312C23C13×H(5,𝔽2)13yes—
313C23C13×2−1+411yescharacteristic
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—448no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4—43no—
339C2×C4—43no—
340C2×C4—43no—
341C2×C4—43no—
342C2×C4—43no—
343C2×C4—43no—
344C2×C4—43no—
345C2×C4—43no—
346C2×C4—43no—
347C2×C4—43no—
348C2×C4—43no—
349C22—212no—
350C22—24no—
351C22—24no—
352C22—212no—
353C22—212no—
354C22—212no—
355C22C13×#40118yescomplemented
356C22C13×#52513yes—
357C22C2×C13×#12613yes—
358C22C2×C13×#12611yescharacteristic
359C22C2×C13×#12613yes—
360C22C13×#52913yes—
361C22C13×#53813yes—
362C22C13×#53913yes—
363C22C13×#54613yes—
364C22C13×#54811yescharacteristic
365C22C13×#55113yes—
366C22C13×#55113yes—
367C22C13×#55213yes—
368C22C13×#55313yes—
369C4—46no—
370C4—46no—
371C4—83no—
372C4—81no—
373C4—81no—
374C4—83no—
375C2—28no—
376C2C2×C13×#40111yescharacteristic
377C2C13×#248013yes—
378C2C13×#248113yes—
379C2C13×#249313yes—
380C2C13×#251013yes—
381C2C13×#264311yescharacteristic
382C2C13×#285211yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#401C2semidirect
3. C13×#1443C2semidirect
4. C13×#1443C2semidirect
5. C13×#1443C2semidirect
51. C22⋊#401C13direct (N × H)
103. C2×#401C2×C13semidirect
105. #1443C2×C13semidirect
106. #1443C2×C13semidirect
107. #1443C2×C13semidirect
186. C22×C13#401semidirect
293. C13C22⋊#401direct (N × H)
355. C22C13×#401semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#4012
C22×C13×#952
C13×#14432
C13×C22⋊#952
C22⋊#40113