Finite Group Databasebeta

← C53×#8154 #27215666

Subgroups — C53×#8154 #27215666

Order 13568.

602 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#387C211yesmaximal, characteristic
2C53×#1749C211yesmaximal, characteristic
3C4×C22⋊C8×C53C211yesmaximal, characteristic
4C2×C53×#324C212yesmaximal
5C53×#1280C212yesmaximal
6C22×C4⋊C4×C53C411yescharacteristic
7C22×C4⋊C4×C53C2211yescharacteristic
8C22×C42×C53C2211yescharacteristic
9C2×C22⋊C8×C53C2212yes—
10C2×C22⋊C8×C53C2212yes—
11C2×#97×C53—21no—
12C2×C4×C8×C53—21no—
13C53×#387—21no—
14C53×#387—21no—
15C53×#387—21no—
16C53×#387—21no—
17C2×#95×C53C411yescharacteristic
18C2×#95×C53C411yescharacteristic
19C2×#95×C53C411yescharacteristic
20C2×#95×C53C2211yescharacteristic
21C53×#336—21no—
22C53×#336—21no—
23C53×#324C418yescomplemented
24C23×C4×C53C2×C411yescharacteristic
25C23×C4×C53C2×C411yescharacteristic
26C23×C4×C53C2×C411yescharacteristic
27C23×C4×C53C2×C411yescharacteristic
28C23×C4×C53C2×C411yescharacteristic
29C23×C4×C53C2×C411yescharacteristic
30C23×C4×C53C2311yescharacteristic
31C22×C8×C53—22no—
32C22×C8×C53—22no—
33C2×C4⋊C4×C53—21no—
34C2×C4⋊C4×C53—21no—
35C2×C4⋊C4×C53—21no—
36C2×C4⋊C4×C53—21no—
37C2×C4⋊C4×C53—22no—
38C2×C4⋊C4×C53—42no—
39C2×C4⋊C4×C53C2×C414yes—
40C2×C42×C53—42no—
41C2×C42×C53D411yescharacteristic
42C2×C42×C53D411yescharacteristic
43C2×C42×C53D411yescharacteristic
44C2×C42×C53D411yescharacteristic
45C22⋊C8×C53—22no—
46C22⋊C8×C53—22no—
47C22⋊C8×C53C2×C414yes—
48C22⋊C8×C53C2×C414yes—
49#97×C53—42no—
50C4×C8×C53—42no—
51#95×C53—21no—
52#95×C53—21no—
53#95×C53—21no—
54#95×C53—21no—
55#95×C53—21no—
56#95×C53—21no—
57#95×C53—21no—
58#95×C53—21no—
59C24×C53C22×C411yescharacteristic
60C22×C4×C53—21no—
61C22×C4×C53—21no—
62C22×C4×C53—21no—
63C22×C4×C53—21no—
64C22×C4×C53—22no—
65C22×C4×C53—22no—
66C22×C4×C53—22no—
67C22×C4×C53—22no—
68C22×C4×C53—22no—
69C22×C4×C53—22no—
70C22×C4×C53—21no—
71C22×C4×C53—21no—
72C22×C4×C53—22no—
73C22×C4×C53—22no—
74C22×C4×C53—41no—
75C22×C4×C53—41no—
76C22×C4×C53—41no—
77C22×C4×C53—41no—
78C22×C4×C53—41no—
79C22×C4×C53—41no—
80C22×C4×C53—41no—
81C22×C4×C53—41no—
82C22×C4×C53—41no—
83C22×C4×C53—41no—
84C22×C4×C53C4212yes—
85C22×C4×C53C4212yes—
86C22×C4×C53C22⋊C411yescharacteristic
87C22×C4×C53C22⋊C411yescharacteristic
88C22×C4×C53C22⋊C411yescharacteristic
89C22×C4×C53C22⋊C411yescharacteristic
90C22×C4×C53C22×C412yes—
91C22×C4×C53C2×D411yescharacteristic
92C22×C4×C53C2×D411yescharacteristic
93C22×C4×C53#4112yes—
94C2×C8×C53—24no—
95C2×C8×C53—24no—
96C2×C8×C53—42no—
97C2×C8×C53—42no—
98C2×C8×C53—42no—
99C2×C8×C53—42no—
100C4⋊C4×C53—24no—
101C4⋊C4×C53—24no—
102C4⋊C4×C53—42no—
103C4⋊C4×C53—42no—
104C42×C53—22no—
105C42×C53—22no—
106C42×C53—41no—
107C42×C53—41no—
108C23×C53—21no—
109C23×C53—21no—
110C23×C53—21no—
111C23×C53—21no—
112C23×C53C2×C4211yescharacteristic
113C23×C53C2×C22⋊C411yescharacteristic
114C23×C53#11711yescharacteristic
115C23×C53#13112yes—
116C23×C53#13112yes—
117C2×C4×C53—21no—
118C2×C4×C53—21no—
119C2×C4×C53—21no—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—22no—
126C2×C4×C53—22no—
127C2×C4×C53—24no—
128C2×C4×C53—21no—
129C2×C4×C53—21no—
130C2×C4×C53—21no—
131C2×C4×C53—21no—
132C2×C4×C53—21no—
133C2×C4×C53—21no—
134C2×C4×C53—42no—
135C2×C4×C53—42no—
136C2×C4×C53—44no—
137C2×C4×C53—44no—
138C2×C4×C53—42no—
139C2×C4×C53—41no—
140C2×C4×C53—41no—
141C2×C4×C53—41no—
142C2×C4×C53—41no—
143C2×C4×C53—42no—
144C2×C4×C53—42no—
145C2×C4×C53—41no—
146C2×C4×C53—41no—
147C2×C4×C53—41no—
148C2×C4×C53—41no—
149C2×C4×C53—41no—
150C2×C4×C53—41no—
151C2×C4×C53—82no—
152C2×C4×C53—82no—
153C2×C4×C53#9912yes—
154C2×C4×C53#10112yes—
155C2×C4×C53C4×D412yes—
156C2×C4×C53C4×D412yes—
157C8×C53—44no—
158C8×C53—44no—
159#8154C5311yesmaximal, characteristic, direct product factor, Sylow
160C22×C53—22no—
161C22×C53—22no—
162C22×C53—22no—
163C22×C53—22no—
164C22×C53—21no—
165C22×C53—21no—
166C22×C53—21no—
167C22×C53—21no—
168C22×C53C4×C22⋊C411yescharacteristic
169C22×C53#40512yes—
170C22×C53#40811yescharacteristic
171C22×C53#40811yescharacteristic
172C22×C53C2×#9911yescharacteristic
173C22×C53#41011yescharacteristic
174C22×C53C2×#10111yescharacteristic
175C22×C53#41311yescharacteristic
176C22×C53#43312yes—
177C4×C53—22no—
178C4×C53—22no—
179C4×C53—22no—
180C4×C53—22no—
181C4×C53—41no—
182C4×C53—41no—
183C4×C53—42no—
184C4×C53—42no—
185C4×C53—81no—
186C4×C53—81no—
187C2×#387C2×C5311yescharacteristic
188#1749C2×C5311yescharacteristic
189C4×C22⋊C8C2×C5311yescharacteristic
190C2×#324C2×C5312yes—
191#1280C2×C5312yes—
192C2×C53—22no—
193C2×C53—22no—
194C2×C53#146811yescharacteristic
195C2×C53#147011yescharacteristic
196C2×C53#147211yescharacteristic
197C2×C53#147311yescharacteristic
198C2×C53#175011yescharacteristic
199C2×C53C4×#9911yescharacteristic
200C2×C53C4×#10111yescharacteristic
201C22×C4⋊C4C4×C5311yescharacteristic
202C22×C4⋊C4C22×C5311yescharacteristic
203C22×C42C22×C5311yescharacteristic
204C2×C22⋊C8C22×C5312yes—
205C2×C22⋊C8C22×C5312yes—
206C2×#97—21no—
207C2×C4×C8—21no—
208#387—21no—
209#387—21no—
210#387—21no—
211#387—21no—
212C2×#95C4×C5311yescharacteristic
213C2×#95C4×C5311yescharacteristic
214C2×#95C4×C5311yescharacteristic
215C2×#95C22×C5311yescharacteristic
216#336—21no—
217#336—21no—
218#324C4×C5318yescomplemented
219C53#815411yescharacteristic, direct product factor, Sylow
220C23×C4C2×C4×C5311yescharacteristic
221C23×C4C2×C4×C5311yescharacteristic
222C23×C4C2×C4×C5311yescharacteristic
223C23×C4C2×C4×C5311yescharacteristic
224C23×C4C2×C4×C5311yescharacteristic
225C23×C4C2×C4×C5311yescharacteristic
226C23×C4C23×C5311yescharacteristic
227C22×C8—22no—
228C22×C8—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4C2×C4×C5314yes—
236C2×C42—42no—
237C2×C42D4×C5311yescharacteristic
238C2×C42D4×C5311yescharacteristic
239C2×C42D4×C5311yescharacteristic
240C2×C42D4×C5311yescharacteristic
241C22⋊C8—22no—
242C22⋊C8—22no—
243C22⋊C8C2×C4×C5314yes—
244C22⋊C8C2×C4×C5314yes—
245#97—42no—
246C4×C8—42no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24C22×C4×C5311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C42×C5312yes—
281C22×C4C42×C5312yes—
282C22×C4C22⋊C4×C5311yescharacteristic
283C22×C4C22⋊C4×C5311yescharacteristic
284C22×C4C22⋊C4×C5311yescharacteristic
285C22×C4C22⋊C4×C5311yescharacteristic
286C22×C4C22×C4×C5312yes—
287C22×C4C2×D4×C5311yescharacteristic
288C22×C4C2×D4×C5311yescharacteristic
289C22×C4#41×C5312yes—
290C2×C8—24no—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C2×C42×C5311yescharacteristic
309C23C2×C22⋊C4×C5311yescharacteristic
310C23#117×C5311yescharacteristic
311C23#131×C5312yes—
312C23#131×C5312yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4#99×C5312yes—
350C2×C4#101×C5312yes—
351C2×C4C4×D4×C5312yes—
352C2×C4C4×D4×C5312yes—
353C8—44no—
354C8—44no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22C4×C22⋊C4×C5311yescharacteristic
364C22C53×#40512yes—
365C22C53×#40811yescharacteristic
366C22C53×#40811yescharacteristic
367C22C2×#99×C5311yescharacteristic
368C22C53×#41011yescharacteristic
369C22C2×#101×C5311yescharacteristic
370C22C53×#41311yescharacteristic
371C22C53×#43312yes—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—42no—
379C4—42no—
380C4—81no—
381C4—81no—
382C2—22no—
383C2—22no—
384C2C53×#146811yescharacteristic
385C2C53×#147011yescharacteristic
386C2C53×#147211yescharacteristic
387C2C53×#147311yescharacteristic
388C2C53×#175011yescharacteristic
389C2C4×#99×C5311yescharacteristic
390C2C4×#101×C5311yescharacteristic
subgroupG/H
center, socleC23×C53C2×C22⋊C4
commutatorC23C2×C42×C53
Frattini, cosocleC23×C4C23×C53
prime radicalC24×C53C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
23. C53×#324C4semidirect
159. #8154C53direct (N × H)
218. #324C4×C53semidirect
219. C53#8154direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C53×#3872
C53×#17492
C4×C22⋊C8×C532
C2×C53×#3242
C53×#12802
#815453