Finite Group Databasebeta

← C53×#9650 #27217162

Subgroups — C53×#9650 #27217162

Order 13568.

656 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#389C211yesmaximal, characteristic
2C53×#1797C211yesmaximal, characteristic
3C4×C22⋊C8×C53C211yesmaximal, characteristic
4C2×C53×#324C214yesmaximal
5C22×C4⋊C4×C53C411yescharacteristic
6C22×C4⋊C4×C53C411yescharacteristic
7C22×C4⋊C4×C53C2212yes—
8C22×C42×C53C2211yescharacteristic
9C2×C4⋊C8×C53—21no—
10C2×C22⋊C8×C53C2212yes—
11C2×C22⋊C8×C53C2212yes—
12C2×C4×C8×C53—21no—
13C53×#389—21no—
14C53×#389—21no—
15C53×#389—21no—
16C53×#389—21no—
17C2×#95×C53C412yes—
18C53×#336—21no—
19C53×#336—21no—
20C53×#324—28no—
21C23×C4×C53C2×C412yes—
22C23×C4×C53C2×C411yescharacteristic
23C23×C4×C53C2×C411yescharacteristic
24C23×C4×C53C2×C412yes—
25C23×C4×C53C2311yescharacteristic
26C22×C8×C53—22no—
27C22×C8×C53—22no—
28C2×C4⋊C4×C53—21no—
29C2×C4⋊C4×C53—21no—
30C2×C4⋊C4×C53—21no—
31C2×C4⋊C4×C53—21no—
32C2×C4⋊C4×C53—22no—
33C2×C4⋊C4×C53—24no—
34C2×C4⋊C4×C53—22no—
35C2×C4⋊C4×C53—22no—
36C2×C4⋊C4×C53—24no—
37C2×C4⋊C4×C53—42no—
38C2×C4⋊C4×C53C814yescomplemented
39C2×C42×C53—42no—
40C2×C42×C53D411yescharacteristic
41C2×C42×C53D411yescharacteristic
42C2×C42×C53D411yescharacteristic
43C2×C42×C53D411yescharacteristic
44C4⋊C8×C53—42no—
45C22⋊C8×C53—24no—
46C22⋊C8×C53—22no—
47C22⋊C8×C53D414yes—
48C4×C8×C53—42no—
49#95×C53—22no—
50#95×C53—22no—
51C24×C53C22×C411yescharacteristic
52C22×C4×C53—22no—
53C22×C4×C53—22no—
54C22×C4×C53—22no—
55C22×C4×C53—24no—
56C22×C4×C53—22no—
57C22×C4×C53—22no—
58C22×C4×C53—24no—
59C22×C4×C53—22no—
60C22×C4×C53—22no—
61C22×C4×C53—24no—
62C22×C4×C53—41no—
63C22×C4×C53—41no—
64C22×C4×C53—41no—
65C22×C4×C53—42no—
66C22×C4×C53—42no—
67C22×C4×C53C22⋊C411yescharacteristic
68C22×C4×C53C22⋊C411yescharacteristic
69C22×C4×C53C22⋊C411yescharacteristic
70C22×C4×C53C22⋊C411yescharacteristic
71C22×C4×C53C2×C814yes—
72C22×C4×C53C2×C812yes—
73C22×C4×C53M1612yes—
74C22×C4×C53C2×D411yescharacteristic
75C22×C4×C53C2×D411yescharacteristic
76C22×C4×C53C2×D412yes—
77C22×C4×C53#4112yes—
78C2×C8×C53—24no—
79C2×C8×C53—42no—
80C2×C8×C53—42no—
81C2×C8×C53—42no—
82C2×C8×C53—42no—
83C2×C8×C53—42no—
84C4⋊C4×C53—24no—
85C4⋊C4×C53—24no—
86C4⋊C4×C53—42no—
87C4⋊C4×C53—42no—
88C4⋊C4×C53—44no—
89C4⋊C4×C53—42no—
90C4⋊C4×C53—42no—
91C42×C53—22no—
92C42×C53—22no—
93C42×C53—41no—
94C42×C53—41no—
95C23×C53—21no—
96C23×C53—21no—
97C23×C53—21no—
98C23×C53—21no—
99C23×C53C2×C22⋊C411yescharacteristic
100C23×C53C4×D412yes—
101C23×C53C22×C811yescharacteristic
102C23×C53C2×M1611yescharacteristic
103C23×C53#13112yes—
104C2×C4×C53—21no—
105C2×C4×C53—21no—
106C2×C4×C53—21no—
107C2×C4×C53—21no—
108C2×C4×C53—21no—
109C2×C4×C53—21no—
110C2×C4×C53—21no—
111C2×C4×C53—21no—
112C2×C4×C53—24no—
113C2×C4×C53—24no—
114C2×C4×C53—24no—
115C2×C4×C53—21no—
116C2×C4×C53—21no—
117C2×C4×C53—21no—
118C2×C4×C53—28no—
119C2×C4×C53—42no—
120C2×C4×C53—42no—
121C2×C4×C53—44no—
122C2×C4×C53—42no—
123C2×C4×C53—42no—
124C2×C4×C53—44no—
125C2×C4×C53—42no—
126C2×C4×C53—42no—
127C2×C4×C53—42no—
128C2×C4×C53—84no—
129C2×C4×C53C22⋊C812yes—
130C2×C4×C53C22⋊C812yes—
131C2×C4×C53#9912yes—
132C2×C4×C53#10112yes—
133C2×C4×C53#10112yes—
134C2×C4×C53#12112yes—
135C2×C4×C53#12411yescharacteristic
136C2×C4×C53#12711yescharacteristic
137C8×C53—44no—
138C8×C53—82no—
139#9650C5311yesmaximal, characteristic, direct product factor, Sylow
140C22×C53—22no—
141C22×C53—22no—
142C22×C53—21no—
143C22×C53—21no—
144C22×C53—21no—
145C22×C53—21no—
146C22×C53—22no—
147C22×C53—22no—
148C22×C53#39011yescharacteristic
149C22×C53C2×C22⋊C811yescharacteristic
150C22×C53#40811yescharacteristic
151C22×C53C2×#9911yescharacteristic
152C22×C53#41011yescharacteristic
153C22×C53C2×#10111yescharacteristic
154C22×C53C2×#10111yescharacteristic
155C22×C53C8×D412yes—
156C22×C53#43612yes—
157C4×C53—22no—
158C4×C53—21no—
159C4×C53—21no—
160C4×C53—22no—
161C4×C53—22no—
162C4×C53—44no—
163C4×C53—41no—
164C4×C53—82no—
165C4×C53#32414yescomplemented
166C2×#389C2×C5311yescharacteristic
167#1797C2×C5311yescharacteristic
168C4×C22⋊C8C2×C5311yescharacteristic
169C2×#324C2×C5314yes—
170C2×C53—22no—
171C2×C53—22no—
172C2×C53C2×#32411yescharacteristic
173C2×C53#146111yescharacteristic
174C2×C53#147011yescharacteristic
175C2×C53#147211yescharacteristic
176C2×C53#195411yescharacteristic
177C2×C53#196411yescharacteristic
178C2×C53#196611yescharacteristic
179C22×C4⋊C4C4×C5311yescharacteristic
180C22×C4⋊C4C4×C5311yescharacteristic
181C22×C4⋊C4C22×C5312yes—
182C22×C42C22×C5311yescharacteristic
183C2×C4⋊C8—21no—
184C2×C22⋊C8C22×C5312yes—
185C2×C22⋊C8C22×C5312yes—
186C2×C4×C8—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191C2×#95C4×C5312yes—
192#336—21no—
193#336—21no—
194#324—28no—
195C53#965011yescharacteristic, direct product factor, Sylow
196C23×C4C2×C4×C5312yes—
197C23×C4C2×C4×C5311yescharacteristic
198C23×C4C2×C4×C5311yescharacteristic
199C23×C4C2×C4×C5312yes—
200C23×C4C23×C5311yescharacteristic
201C22×C8—22no—
202C22×C8—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—24no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—42no—
213C2×C4⋊C4C8×C5314yescomplemented
214C2×C42—42no—
215C2×C42D4×C5311yescharacteristic
216C2×C42D4×C5311yescharacteristic
217C2×C42D4×C5311yescharacteristic
218C2×C42D4×C5311yescharacteristic
219C4⋊C8—42no—
220C22⋊C8—22no—
221C22⋊C8—24no—
222C22⋊C8D4×C5314yes—
223C4×C8—42no—
224#95—22no—
225#95—22no—
226C24C22×C4×C5311yescharacteristic
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C22⋊C4×C5311yescharacteristic
243C22×C4C22⋊C4×C5311yescharacteristic
244C22×C4C22⋊C4×C5311yescharacteristic
245C22×C4C22⋊C4×C5311yescharacteristic
246C22×C4C2×C8×C5314yes—
247C22×C4C2×C8×C5312yes—
248C22×C4M16×C5312yes—
249C22×C4C2×D4×C5311yescharacteristic
250C22×C4C2×D4×C5311yescharacteristic
251C22×C4C2×D4×C5312yes—
252C22×C4#41×C5312yes—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—44no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C42—22no—
267C42—22no—
268C42—41no—
269C42—41no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23C2×C22⋊C4×C5311yescharacteristic
275C23C4×D4×C5312yes—
276C23C22×C8×C5311yescharacteristic
277C23C2×M16×C5311yescharacteristic
278C23#131×C5312yes—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—28no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—84no—
304C2×C4C22⋊C8×C5312yes—
305C2×C4C22⋊C8×C5312yes—
306C2×C4#99×C5312yes—
307C2×C4#101×C5312yes—
308C2×C4#101×C5312yes—
309C2×C4#121×C5312yes—
310C2×C4#124×C5311yescharacteristic
311C2×C4#127×C5311yescharacteristic
312C8—44no—
313C8—82no—
314C22—22no—
315C22—22no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—22no—
322C22C53×#39011yescharacteristic
323C22C2×C22⋊C8×C5311yescharacteristic
324C22C53×#40811yescharacteristic
325C22C2×#99×C5311yescharacteristic
326C22C53×#41011yescharacteristic
327C22C2×#101×C5311yescharacteristic
328C22C2×#101×C5311yescharacteristic
329C22C8×D4×C5312yes—
330C22C53×#43612yes—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—44no—
337C4—41no—
338C4—82no—
339C4C53×#32414yescomplemented
340C2—22no—
341C2—22no—
342C2C2×C53×#32411yescharacteristic
343C2C53×#146111yescharacteristic
344C2C53×#147011yescharacteristic
345C2C53×#147211yescharacteristic
346C2C53×#195411yescharacteristic
347C2C53×#196411yescharacteristic
348C2C53×#196611yescharacteristic
subgroupG/H
center, socleC23×C53C2×C22⋊C4
commutatorC23C22×C8×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
38. C2×C4⋊C4×C53C8semidirect
139. #9650C53direct (N × H)
165. C4×C53#324semidirect
195. C53#9650direct (N × H)
213. C2×C4⋊C4C8×C53semidirect
339. C4C53×#324semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3892
C53×#17972
C4×C22⋊C8×C532
C2×C53×#3242
#965053