Finite Group Databasebeta

← #72242003

Subgroups — #72242003

Order 5616.

420 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C2×C3×C3⋊AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
2C2×C3×C3⋊AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×D13⋊C3C211yesmaximal, characteristic
4#14273015C311yesmaximal, characteristic, complemented
5(C2×D3)⋊AGL(1,𝔽13)—31nomaximal
6(C2×D3)⋊AGL(1,𝔽13)—31nomaximal
7C2×C3⋊(C3⋊(D13⋊C3))C411yescharacteristic, complemented
8C2×C3⋊D3×C13⋊C3C411yescharacteristic, complemented
9C2×C32×D13⋊C3C2211yescharacteristic
10C3⋊D3×D13⋊C3—21no—
11C3⋊D3×D13⋊C3—21no—
12C3×C3⋊AGL(1,𝔽13)—21no—
13C3×C3⋊AGL(1,𝔽13)—21no—
14C2×C3⋊D3×D13C2×C311yescharacteristic
15C2×C3×C3⋊#261C2×C311yescharacteristic, complemented
16C2×C3×C3⋊#261C2×C311yescharacteristic, complemented
17C2×D3×D13⋊C3—31no—
18C2×D3×D13⋊C3—31no—
19C2×D3×D13⋊C3—61no—
20C2×C3⋊AGL(1,𝔽13)—21no—
21C2×C3⋊AGL(1,𝔽13)—21no—
22C2×C3⋊AGL(1,𝔽13)D311yescharacteristic, complemented
23C2×C3⋊AGL(1,𝔽13)D311yescharacteristic, complemented
24C2×C3×AGL(1,𝔽13)—31no—
25C2×C3×AGL(1,𝔽13)—31no—
26C2×C32×C13⋊C3C2×C411yescharacteristic
27C3⋊(C3⋊(D13⋊C3))—21no—
28C3⋊D3×C13⋊C3—21no—
29C32×D13⋊C3D411yescharacteristic
30C32×D13⋊C3D411yescharacteristic
31(C2×D3)⋊#261—31no—
32(C2×D3)⋊#261—31no—
33(C22⋊#261)⋊C3—91no—
34C2×C3⋊D39C3×C411yescharacteristic, complemented
35C2×C13×C3⋊D3C3×C411yescharacteristic, complemented
36C2×C32×D13C22×C311yescharacteristic
37C3⋊D3×D13—21no—
38C3⋊D3×D13—21no—
39C3×C3⋊#261—21no—
40C3×C3⋊#261—21no—
41C2×C3⋊(D13⋊C3)—31no—
42C2×C3⋊(D13⋊C3)—31no—
43C2×C3⋊(D13⋊C3)—61no—
44C2×D3×C13⋊C3—31no—
45C2×D3×C13⋊C3—31no—
46C2×D3×C13⋊C3—61no—
47C2×C3×D13⋊C3—21no—
48C2×C3×D13⋊C3—21no—
49C2×C3×D13⋊C3—21no—
50C2×C3×D13⋊C3—41no—
51C2×C3×D13⋊C3C2×D311yescharacteristic
52C2×C3×D13⋊C3C2×D311yescharacteristic
53D3×D13⋊C3—61no—
54D3×D13⋊C3—61no—
55D3×D13⋊C3—61no—
56D3×D13⋊C3—61no—
57D3×D13⋊C3—61no—
58D3×D13⋊C3—61no—
59D3×D13⋊C3—61no—
60D3×D13⋊C3—61no—
61C3⋊AGL(1,𝔽13)—21no—
62C3⋊AGL(1,𝔽13)—21no—
63C3⋊AGL(1,𝔽13)—21no—
64C3⋊AGL(1,𝔽13)—21no—
65C3⋊AGL(1,𝔽13)—21no—
66C3⋊AGL(1,𝔽13)—21no—
67C3×AGL(1,𝔽13)—61no—
68C3×AGL(1,𝔽13)—61no—
69C3×#3722—131nomaximal, Hall
70C32×C13⋊C3C22⋊C411yescharacteristic, complemented, Hall
71C2×D3×D13—31no—
72C2×D3×D13—31no—
73C2×D3×D13—61no—
74C2×C3⋊#261C3×D311yescharacteristic, complemented
75C2×C3⋊#261C3×D311yescharacteristic, complemented
76C2×C3×#261—31no—
77C2×C3×#261—31no—
78C22×D13⋊C3—91no—
79C2×AGL(1,𝔽13)—31no—
80C2×AGL(1,𝔽13)—31no—
81C2×AGL(1,𝔽13)—61no—
82C2×AGL(1,𝔽13)—61no—
83C2×C32×C13C2×C3×C411yescharacteristic
84C3⋊D39—21no—
85C13×C3⋊D3—21no—
86C32×D13C3×D411yescharacteristic
87C32×D13C3×D411yescharacteristic
88C2×C3×C13⋊C3—21no—
89C2×C3×C13⋊C3—21no—
90C2×C3×C13⋊C3—21no—
91C2×C3×C13⋊C3—41no—
92C2×C3×C13⋊C3C4×D311yescharacteristic
93C2×C3×C13⋊C3C4×D311yescharacteristic
94C3⋊(D13⋊C3)—61no—
95C3⋊(D13⋊C3)—61no—
96C3⋊(D13⋊C3)—61no—
97C3⋊(D13⋊C3)—61no—
98D3×C13⋊C3—61no—
99D3×C13⋊C3—61no—
100D3×C13⋊C3—61no—
101D3×C13⋊C3—61no—
102C3×D13⋊C3—21no—
103C3×D13⋊C3—21no—
104C3×D13⋊C3—21no—
105C3×D13⋊C3—21no—
106C3×D13⋊C3—21no—
107C3×D13⋊C3—21no—
108C3×D13⋊C3—41no—
109C3×D13⋊C3—41no—
110C3×D13⋊C3D1211yescharacteristic
111C3×D13⋊C3D1211yescharacteristic
112C3×D13⋊C3#6711yescharacteristic
113C3×D13⋊C3#6711yescharacteristic
114C22×C3×C3⋊D3—131no—
115C2×C32×Dic3—131no—
116C2×C32×Dic3—131no—
117C22⋊#261—91noHall
118C2×D39—31no—
119C2×D39—31no—
120C2×D39—61no—
121C2×D3×C13—31no—
122C2×D3×C13—31no—
123C2×D3×C13—61no—
124C2×C3×D13—21no—
125C2×C3×D13C2×C3×D311yescharacteristic
126C2×C3×D13C2×C3×D311yescharacteristic
127C22×C13⋊C3—91no—
128D3×D13—61no—
129D3×D13—61no—
130D3×D13—61no—
131D3×D13—61no—
132D3×D13—61no—
133D3×D13—61no—
134D3×D13—61no—
135D3×D13—61no—
136C3⋊#261—21no—
137C3⋊#261—21no—
138C3×#261—61no—
139C3×#261—61no—
140C2×D13⋊C3—21no—
141C2×D13⋊C3—21no—
142C2×D13⋊C3—41no—
143C2×D13⋊C3—91no—
144C2×D13⋊C3—181no—
145C2×D13⋊C3—181no—
146C2×D13⋊C3D3211yescharacteristic
147AGL(1,𝔽13)—61no—
148AGL(1,𝔽13)—61no—
149AGL(1,𝔽13)—61no—
150AGL(1,𝔽13)—61no—
151AGL(1,𝔽13)—61no—
152AGL(1,𝔽13)—61no—
153C3×(C2×D3)⋊C4—391no—
154C3×(C2×D3)⋊C4—391no—
155#3722—131no—
156C32×C13C3×C22⋊C411yescharacteristic, complemented
157C3×C13⋊C3—21no—
158C3×C13⋊C3—21no—
159C3×C13⋊C3—21no—
160C3×C13⋊C3—41no—
161C3×C13⋊C3(C2×D3)⋊C411yescharacteristic, complemented
162C3×C13⋊C3(C2×D3)⋊C411yescharacteristic, complemented
163C22×C33—131no—
164C2×C3×C3⋊D3—131no—
165C2×C3×C3⋊D3—261no—
166C2×C3×C3⋊D3—261no—
167C2×C3×C3⋊D3—521no—
168C32×Dic3—261no—
169C32×Dic3—261no—
170C22×D13—91no—
171C2×#261—31no—
172C2×#261—31no—
173C2×C3×C13—21no—
174C2×C3×C13C3×C4×D311yescharacteristic
175C2×C3×C13C3×C4×D311yescharacteristic
176D39—61no—
177D39—61no—
178D39—61no—
179D39—61no—
180C3×D13—21no—
181C3×D13—21no—
182C3×D13C3×D1211yescharacteristic
183C3×D13C3×D1211yescharacteristic
184C3×D13C3×#6711yescharacteristic
185C3×D13C3×#6711yescharacteristic
186D3×C13—61no—
187D3×C13—61no—
188D3×C13—61no—
189D3×C13—61no—
190C2×C13⋊C3—21no—
191C2×C13⋊C3—21no—
192C2×C13⋊C3—41no—
193C2×C13⋊C3—181no—
194C2×C13⋊C3#62411yescharacteristic
195D13⋊C3—21no—
196D13⋊C3—21no—
197D13⋊C3—21no—
198D13⋊C3—21no—
199D13⋊C3—41no—
200D13⋊C3—41no—
201D13⋊C3—181no—
202D13⋊C3#62611yescharacteristic
203D13⋊C3#62611yescharacteristic
204C22×C3⋊D3—131no—
205C22×C3×D3—391no—
206C22×C3×D3—391no—
207C22×C3×D3—781no—
208C2×C32×C4—391no—
209C2×C32×C4—391no—
210C2×C3×Dic3—131no—
211C2×C3×Dic3—131no—
212C2×C3×Dic3—131no—
213C2×C3×Dic3—131no—
214C2×C3×Dic3—261no—
215C2×C3×Dic3—261no—
216C2×C33—131no—
217C2×C33—131no—
218C2×C33—521no—
219C3×C3⋊D3—261no—
220C3×C3⋊D3—521no—
221C22×C13—91no—
222C2×D13—91no—
223C2×D13—181no—
224C2×D13—181no—
225C2×D13C3×D3211yescharacteristic
226#261—61no—
227#261—61no—
228C3×C22⋊C4—1171no—
229(C2×D3)⋊C4—391no—
230(C2×D3)⋊C4—391no—
231C3×C13—21no—
232C3×C13C3×(C2×D3)⋊C411yescharacteristic, complemented
233C3×C13C3×(C2×D3)⋊C411yescharacteristic, complemented
234C13⋊C3—21no—
235C13⋊C3—21no—
236C13⋊C3—41no—
237C13⋊C3#372211yescharacteristic, complemented
238C22×C32—131no—
239C22×C32—131no—
240C22×C32—131no—
241C22×C32—261no—
242C22×C32—261no—
243C22×C32—261no—
244C22×C32—521no—
245C2×C3⋊D3—131no—
246C2×C3⋊D3—261no—
247C2×C3⋊D3—261no—
248C2×C3⋊D3AGL(1,𝔽13)11yescharacteristic, complemented
249C2×C3×D3—391no—
250C2×C3×D3—391no—
251C2×C3×D3—781no—
252C2×C3×D3—781no—
253C2×C3×D3—781no—
254C2×C3×D3—781no—
255C2×C3×D3—781no—
256C2×C3×D3—781no—
257C2×C3×D3—781no—
258C2×C3×D3—781no—
259C2×C3×D3—781no—
260C2×C3×D3—1561no—
261C2×C3×D3—1561no—
262C2×C3×D3—1561no—
263C32×C4—781no—
264C32×C4—781no—
265C3×Dic3—261no—
266C3×Dic3—261no—
267C3×Dic3—261no—
268C3×Dic3—261no—
269C3×Dic3—261no—
270C3×Dic3—261no—
271C3×Dic3—261no—
272C3×Dic3—261no—
273C33—521noSylow
274C2×C13—181no—
275C2×C13C3×#62411yescharacteristic
276D13—181no—
277D13C3×#62611yescharacteristic
278D13C3×#62611yescharacteristic
279C23×C3—1171no—
280C22×D3—391no—
281C22×D3—391no—
282C22×D3—781no—
283C2×C3×C4—391no—
284C2×C3×C4—391no—
285C2×C3×C4—391no—
286C2×C3×C4—391no—
287C2×C3×C4—781no—
288C2×C3×C4—781no—
289C2×Dic3—131no—
290C2×Dic3—131no—
291C2×C32—131no—
292C2×C32—131no—
293C2×C32—131no—
294C2×C32—131no—
295C2×C32—131no—
296C2×C32—131no—
297C2×C32—261no—
298C2×C32—261no—
299C2×C32—261no—
300C2×C32—261no—
301C2×C32—261no—
302C2×C32—261no—
303C2×C32—521no—
304C2×C32—521no—
305C2×C32—521no—
306C2×C32—521no—
307C2×C32—521no—
308C2×C32—1041no—
309C2×C32—1041no—
310C2×C32—1041no—
311C2×C32C2×AGL(1,𝔽13)11yescharacteristic
312C3⋊D3—21no—
313C3⋊D3—261no—
314C3×D3—781no—
315C3×D3—781no—
316C3×D3—781no—
317C3×D3—781no—
318C3×D3—1561no—
319C3×D3—1561no—
320C3×D3—1561no—
321C3×D3—1561no—
322C22⋊C4—1171noSylow
323C13C3×#372211yescharacteristic, complemented, Sylow
324C22×C3—131no—
325C22×C3—131no—
326C22×C3—131no—
327C22×C3—261no—
328C22×C3—261no—
329C22×C3—261no—
330C22×C3—521no—
331C22×C3—1171no—
332C22×C3—4681no—
333C22×C3—2341no—
334C22×C3—2341no—
335C2×D3—31no—
336C2×D3—31no—
337C2×D3—61no—
338C2×D3—391no—
339C2×D3—391no—
340C2×D3—781no—
341C2×D3—781no—
342C2×D3—781no—
343C2×D3—781no—
344C2×D3—781no—
345C2×D3—781no—
346C2×D3—781no—
347C2×D3—781no—
348C2×D3—781no—
349C3×C4—781no—
350C3×C4—781no—
351C3×C4—781no—
352C3×C4—781no—
353C3×C4—781no—
354C3×C4—781no—
355C3×C4—781no—
356C3×C4—781no—
357Dic3—261no—
358Dic3—261no—
359C32—521no—
360C32—521no—
361C32—521no—
362C32—1041no—
363C32—1041no—
364C32—1041no—
365C32(C22⋊#261)⋊C311yescharacteristic, complemented
366C23—1171no—
367C2×C4—391no—
368C2×C4—391no—
369C2×C3—21no—
370C2×C3—131no—
371C2×C3—131no—
372C2×C3—131no—
373C2×C3—131no—
374C2×C3—131no—
375C2×C3—131no—
376C2×C3—261no—
377C2×C3—261no—
378C2×C3—261no—
379C2×C3—261no—
380C2×C3—261no—
381C2×C3—261no—
382C2×C3—521no—
383C2×C3—521no—
384C2×C3—521no—
385C2×C3—1041no—
386C2×C3—1041no—
387C2×C3—1041no—
388C2×C3—4681no—
389C2×C3—2341no—
390C2×C3D3×AGL(1,𝔽13)11yescharacteristic
391C2×C3D3×AGL(1,𝔽13)11yescharacteristic
392D3—61no—
393D3—61no—
394D3—61no—
395D3—61no—
396D3—781no—
397D3—781no—
398D3—781no—
399D3—781no—
400C22—91no—
401C22—131no—
402C22—1171no—
403C22—2341no—
404C22—2341no—
405C4—781no—
406C4—781no—
407C3—21no—
408C3—521no—
409C3—1041no—
410C3—1041no—
411C3—1041no—
412C3(C2×D3)⋊AGL(1,𝔽13)11yescharacteristic, complemented
413C3(C2×D3)⋊AGL(1,𝔽13)11yescharacteristic, complemented
414C2—131no—
415C2—131no—
416C2—181no—
417C2—2341no—
418C2#7222063511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#72220635
commutator, Fitting, socleC2×C32×C13C2×C3×C4
prime radicalC2×C3⋊D3×D13⋊C3C2
cosocleC2×C32×D13C22×C3
hypocenterC32×C13C3×C22⋊C4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊AGL(1,𝔽13)C2semidirect
2. C2×C3×C3⋊AGL(1,𝔽13)C2semidirect
4. #14273015C3semidirect
7. C2×C3⋊(C3⋊(D13⋊C3))C4semidirect
8. C2×C3⋊D3×C13⋊C3C4semidirect
15. C2×C3×C3⋊#261C2×C3semidirect
16. C2×C3×C3⋊#261C2×C3semidirect
22. C2×C3⋊AGL(1,𝔽13)D3semidirect
23. C2×C3⋊AGL(1,𝔽13)D3semidirect
34. C2×C3⋊D39C3×C4semidirect
35. C2×C13×C3⋊D3C3×C4semidirect
70. C32×C13⋊C3C22⋊C4semidirect
74. C2×C3⋊#261C3×D3semidirect
75. C2×C3⋊#261C3×D3semidirect
156. C32×C13C3×C22⋊C4semidirect
161. C3×C13⋊C3(C2×D3)⋊C4semidirect
162. C3×C13⋊C3(C2×D3)⋊C4semidirect
232. C3×C13C3×(C2×D3)⋊C4semidirect
233. C3×C13C3×(C2×D3)⋊C4semidirect
237. C13⋊C3#3722semidirect
248. C2×C3⋊D3AGL(1,𝔽13)semidirect
323. C13C3×#3722semidirect
365. C32(C22⋊#261)⋊C3semidirect
412. C3(C2×D3)⋊AGL(1,𝔽13)semidirect
413. C3(C2×D3)⋊AGL(1,𝔽13)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊AGL(1,𝔽13)2
C2×C3⋊D3×D13⋊C32
#142730153
(C2×D3)⋊AGL(1,𝔽13)3
C3×#372213