Finite Group Databasebeta

← D53×#1314 #27293149

Subgroups — D53×#1314 #27293149

Order 13568.

682 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 121 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×C22⋊C8×D53C211yesmaximal, characteristic
2C22⋊C16×D53C212yesmaximal, complemented
3#20272639C211yesmaximal, characteristic, complemented
4#20272638C212yesmaximal, complemented
5C53×#1314C211yesmaximal, characteristic, complemented
6C23×C4×D53C411yescharacteristic
7C22×C8×D53C411yescharacteristic
8C22×C8×D53C2211yescharacteristic
9C2×C16×D53—22no—
10C2×C22⋊#88322C411yescharacteristic
11C2×#13133129C411yescharacteristic
12C2×#13133129C2211yescharacteristic
13C22⋊C8×D53—22no—
14C22⋊C8×D53—22no—
15C22⋊#11719908C2212yescomplemented
16#16810402—22no—
17C2×C22⋊C8×C53C2211yescharacteristic
18C53×C22⋊C16C2212yescomplemented
19C24×D53C811yescharacteristic
20C23×Dic53C811yescharacteristic
21C22×C4×D53—21no—
22C22×C4×D53—21no—
23C22×C4×D53—21no—
24C22×C4×D53—21no—
25C22×C4×D53—42no—
26C22×C4×D53—42no—
27C22×C4×D53C811yescharacteristic
28C22×C4×D53C811yescharacteristic
29C22×C4×D53C2×C411yescharacteristic
30C22×C4×D53C2×C411yescharacteristic
31C22×#88322C2×C411yescharacteristic
32C22×#88322C2×C411yescharacteristic
33C2×C8×D53—21no—
34C2×C8×D53—21no—
35C2×C8×D53—42no—
36C2×C8×D53—42no—
37C2×C8×D53D412yes—
38C2×C8×D53D412yes—
39C2×#11719908—22no—
40C16×D53—44no—
41C22⋊#88322—22no—
42#13133129—22no—
43#13133129—22no—
44C23×C4×C53C2×C411yescharacteristic
45C22×C8×C53C2×C411yescharacteristic
46C22×C8×C53C2311yescharacteristic
47C2×C16×C53—22no—
48C22⋊C8×C53—22no—
49C24×C53C2×C811yescharacteristic
50C23×D53—21no—
51C23×D53—21no—
52C23×D53—22no—
53C23×D53—42no—
54C23×D53—42no—
55C23×D53C1614yescomplemented
56C23×D53C2×C811yescharacteristic
57C23×D53C2×C811yescharacteristic
58C22×C4×C53—21no—
59C22×C4×C53—21no—
60C22×C4×C53—41no—
61C22×C4×C53—41no—
62C22×C4×C53C2×C811yescharacteristic
63C22×C4×C53C22×C411yescharacteristic
64C22×Dic53—21no—
65C22×Dic53—21no—
66C22×Dic53—42no—
67C22×Dic53C2×C811yescharacteristic
68C22×Dic53C2×C811yescharacteristic
69C2×C4×D53—22no—
70C2×C4×D53—22no—
71C2×C4×D53—21no—
72C2×C4×D53—21no—
73C2×C4×D53—21no—
74C2×C4×D53—21no—
75C2×C4×D53—21no—
76C2×C4×D53—21no—
77C2×C4×D53—44no—
78C2×C4×D53—42no—
79C2×C4×D53—42no—
80C2×C4×D53—44no—
81C2×C4×D53—42no—
82C2×C4×D53—42no—
83C2×C4×D53—42no—
84C2×C4×D53—41no—
85C2×C4×D53—41no—
86C2×C4×D53—42no—
87C2×C4×D53C22⋊C411yescharacteristic
88C2×C4×D53C22⋊C411yescharacteristic
89C2×C4×D53M1611yescharacteristic
90C2×C4×D53M1611yescharacteristic
91C2×C8×C53—21no—
92C2×C8×C53—41no—
93C2×C8×C53—41no—
94C2×C8×C53C2×D412yes—
95C2×#88322—21no—
96C2×#88322—41no—
97C2×#88322—41no—
98C2×#88322C22⋊C412yes—
99C8×D53—24no—
100C8×D53—42no—
101C8×D53—42no—
102C8×D53—42no—
103C16×C53—42no—
104#11719908—42no—
105C23×C53—21no—
106C23×C53—21no—
107C23×C53—41no—
108C23×C53—41no—
109C23×C53C2×C1612yescomplemented
110C23×C53C22×C811yescharacteristic
111C22×D53—22no—
112C22×D53—22no—
113C22×D53—21no—
114C22×D53—21no—
115C22×D53—24no—
116C22×D53—24no—
117C22×D53—42no—
118C22×D53—42no—
119C22×D53—48no—
120C22×D53—48no—
121C22×D53—42no—
122C22×D53—42no—
123C22×D53—41no—
124C22×D53—41no—
125C22×D53C22⋊C811yescharacteristic
126C22×D53C22⋊C811yescharacteristic
127C22×D53C2×C1612yes—
128C22×D53C2×C1612yescomplemented
129C22×D53M3212yes—
130C2×C4×C53—21no—
131C2×C4×C53—21no—
132C2×C4×C53—21no—
133C2×C4×C53—42no—
134C2×C4×C53—41no—
135C2×C4×C53—41no—
136C2×C4×C53—41no—
137C2×C4×C53C2×C22⋊C411yescharacteristic
138C2×C4×C53C2×M1611yescharacteristic
139C2×Dic53—22no—
140C2×Dic53—21no—
141C2×Dic53—42no—
142C2×Dic53—42no—
143C2×Dic53—41no—
144C2×Dic53C22⋊C811yescharacteristic
145C2×Dic53C22⋊C811yescharacteristic
146C4×D53—22no—
147C4×D53—21no—
148C4×D53—21no—
149C4×D53—22no—
150C4×D53—42no—
151C4×D53—42no—
152C4×D53—42no—
153C4×D53—42no—
154C4×D53—41no—
155C4×D53—41no—
156C4×D53—42no—
157C4×D53#9912yes—
158C4×D53#10012yes—
159C8×C53—22no—
160C8×C53—41no—
161#88322—22no—
162#88322—41no—
163C2×#1314—531nomaximal, Sylow
164C22×C53—21no—
165C22×C53—21no—
166C22×C53—22no—
167C22×C53—42no—
168C22×C53—42no—
169C22×C53—41no—
170C22×C53—41no—
171C22×C53C2×C22⋊C811yescharacteristic
172C22×C53C22×C1611yescharacteristic
173C22×C53C2×M3211yescharacteristic
174C2×D53—21no—
175C2×D53—21no—
176C2×D53—24no—
177C2×D53—24no—
178C2×D53—22no—
179C2×D53—48no—
180C2×D53—42no—
181C2×D53—41no—
182C2×D53—41no—
183C2×D53—48no—
184C2×D53—42no—
185C2×D53#32312yes—
186C2×D53C22⋊C1612yes—
187C2×D53C22⋊C1612yes—
188C2×D53#34912yes—
189C4×C53—21no—
190C4×C53—41no—
191C4×C53C2×#9911yescharacteristic
192C4×C53C2×#10011yescharacteristic
193Dic53—21no—
194Dic53—41no—
195Dic53#32312yes—
196C22×C22⋊C8—531no—
197C2×C22⋊C16—532no—
198#1314—531no—
199#1314—532no—
200#1314D5311yescharacteristic, direct product factor
201C2×C53—21no—
202C2×C53—21no—
203C2×C53—42no—
204C2×C53C2×#32311yescharacteristic
205C2×C53C2×C22⋊C1611yescharacteristic
206C2×C53C2×#34911yescharacteristic
207D53—22no—
208D53—42no—
209D53#131414yesdirect product factor
210C24×C4—531no—
211C23×C8—531no—
212C23×C8—531no—
213C22×C16—1062no—
214C2×C22⋊C8—531no—
215C2×C22⋊C8—531no—
216C2×C22⋊C8—531no—
217C2×C22⋊C8—1062no—
218C2×C22⋊C8—1062no—
219C2×C22⋊C8C2×D5311yescharacteristic
220C22⋊C16—532no—
221C22⋊C16—1062no—
222C22⋊C16C2×D5312yescomplemented
223C53C2×#131411yescharacteristic, complemented, Sylow
224C25—531no—
225C23×C4—531no—
226C23×C4—531no—
227C23×C4—531no—
228C23×C4—531no—
229C23×C4—531no—
230C23×C4—1061no—
231C23×C4—1061no—
232C23×C4—1061no—
233C23×C4—1061no—
234C23×C4—2122no—
235C23×C4—2122no—
236C23×C4C4×D5311yescharacteristic
237C22×C8—531no—
238C22×C8—532no—
239C22×C8—532no—
240C22×C8—531no—
241C22×C8—1061no—
242C22×C8—1061no—
243C22×C8—2122no—
244C22×C8—2122no—
245C22×C8C4×D5311yescharacteristic
246C22×C8C22×D5311yescharacteristic
247C2×C16—22no—
248C2×C16—1062no—
249C2×C16—2124no—
250C22⋊C8—22no—
251C22⋊C8—1062no—
252C22⋊C8—1062no—
253C22⋊C8—1062no—
254C24—531no—
255C24—534no—
256C24—531no—
257C24—1061no—
258C24—1061no—
259C24—1062no—
260C24—2122no—
261C24—2122no—
262C24C8×D5311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—531no—
268C22×C4—531no—
269C22×C4—531no—
270C22×C4—531no—
271C22×C4—531no—
272C22×C4—531no—
273C22×C4—1062no—
274C22×C4—1062no—
275C22×C4—1061no—
276C22×C4—1061no—
277C22×C4—1061no—
278C22×C4—1061no—
279C22×C4—1061no—
280C22×C4—1061no—
281C22×C4—1061no—
282C22×C4—1061no—
283C22×C4—2121no—
284C22×C4—2121no—
285C22×C4—2122no—
286C22×C4—2122no—
287C22×C4—2124no—
288C22×C4—2124no—
289C22×C4—2122no—
290C22×C4—2122no—
291C22×C4—2122no—
292C22×C4—2122no—
293C22×C4—2122no—
294C22×C4C8×D5311yescharacteristic
295C22×C4C2×C4×D5311yescharacteristic
296C2×C8—21no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—532no—
300C2×C8—1064no—
301C2×C8—1061no—
302C2×C8—2122no—
303C2×C8—2122no—
304C2×C8—2122no—
305C2×C8—2121no—
306C2×C8—2121no—
307C2×C8D4×D5312yes—
308C16—42no—
309C16—2122no—
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—531no—
315C23—532no—
316C23—532no—
317C23—531no—
318C23—532no—
319C23—1062no—
320C23—1062no—
321C23—1064no—
322C23—1064no—
323C23—1061no—
324C23—1061no—
325C23—2121no—
326C23—2121no—
327C23—2122no—
328C23—2122no—
329C23—2128no—
330C23—2122no—
331C23—2128no—
332C23—2122no—
333C23C16×D5312yescomplemented
334C23C2×C8×D5311yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—531no—
343C2×C4—532no—
344C2×C4—532no—
345C2×C4—531no—
346C2×C4—1062no—
347C2×C4—1062no—
348C2×C4—1062no—
349C2×C4—1061no—
350C2×C4—1061no—
351C2×C4—1061no—
352C2×C4—2122no—
353C2×C4—2122no—
354C2×C4—2122no—
355C2×C4—2122no—
356C2×C4—2122no—
357C2×C4—2122no—
358C2×C4—2122no—
359C2×C4—2121no—
360C2×C4—2121no—
361C2×C4—2121no—
362C2×C4C22⋊C4×D5311yescharacteristic
363C2×C4M16×D5311yescharacteristic
364C8—22no—
365C8—41no—
366C8—1062no—
367C8—2121no—
368C22—21no—
369C22—21no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—532no—
376C22—532no—
377C22—532no—
378C22—532no—
379C22—1064no—
380C22—1064no—
381C22—1061no—
382C22—1061no—
383C22—1062no—
384C22—2122no—
385C22—2122no—
386C22—2128no—
387C22—2128no—
388C22—2121no—
389C22—2121no—
390C22C22⋊C8×D5311yescharacteristic
391C22C2×C16×D5311yescharacteristic
392C22M32×D5311yescharacteristic
393C4—21no—
394C4—41no—
395C4—532no—
396C4—1061no—
397C4—2121no—
398C4#99×D5311yescharacteristic
399C4#100×D5311yescharacteristic
400C2—21no—
401C2—21no—
402C2—42no—
403C2—534no—
404C2—1062no—
405C2—2122no—
406C2#323×D5311yescharacteristic
407C2C22⋊C16×D5311yescharacteristic
408C2#349×D5311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D53
commutatorC22×C53C22×C16
FrattiniC22×C8C22×D53
FittingC53×#1314C2
socleC22×C53C2×C22⋊C8
prime radicalC24×D53C8
cosocleC22×C8×C53C23
hypercenter#1314D53
hypocenterC53C2×#1314
LCSG ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D53C2semidirect
3. #20272639C2semidirect
4. #20272638C2semidirect
5. C53×#1314C2semidirect
15. C22⋊#11719908C22semidirect
18. C53×C22⋊C16C22semidirect
55. C23×D53C16semidirect
109. C23×C53C2×C16semidirect
128. C22×D53C2×C16semidirect
200. #1314D53direct (N × H)
209. D53#1314direct (N × H)
222. C22⋊C16C2×D53semidirect
223. C53C2×#1314semidirect
333. C23C16×D53semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D532
C22⋊C16×D532
#202726392
#202726382
C53×#13142
C2×#131453