Finite Group Databasebeta

← C53×#9030 #27216542

Subgroups — C53×#9030 #27216542

Order 13568.

484 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#2983C211yesmaximal, characteristic
2C53×#2399C211yesmaximal, characteristic
3C4×#101×C53C211yesmaximal, characteristic
4C53×#1491C212yesmaximal
5C53×#1300C212yesmaximal
6C2×C4×Q8×C53C2211yescharacteristic
7C2×C4×Q8×C53C2211yescharacteristic
8C53×#446—24no—
9C53×#432—21no—
10C53×#432C2212yes—
11C53×#431—21no—
12C2×#101×C53—21no—
13C4×M16×C53C2212yes—
14C53×#398—21no—
15C53×#398C411yescharacteristic
16C53×#398C411yescharacteristic
17C53×#395—21no—
18C53×#395C411yescharacteristic
19C53×#395C411yescharacteristic
20C4×C4⋊C4×C53—21no—
21C4×C4⋊C4×C53—21no—
22C53×#376C2211yescharacteristic
23C53×#343—21no—
24C53×Q8⋊C8—24no—
25C22×Q8×C53C2×C411yescharacteristic
26C22×Q8×C53D411yescharacteristic
27C2×M16×C53—22no—
28C4×Q8×C53—22no—
29C4×Q8×C53—22no—
30C4×Q8×C53—22no—
31C4×Q8×C53—22no—
32C2×C4⋊C4×C53—21no—
33C2×C4⋊C4×C53—21no—
34C2×C4⋊C4×C53—21no—
35C2×C4⋊C4×C53—21no—
36C2×C4⋊C4×C53—21no—
37C2×C4⋊C4×C53C2×C411yescharacteristic
38C2×C4⋊C4×C53C2×C411yescharacteristic
39C2×C4⋊C4×C53C2×C411yescharacteristic
40C2×C4⋊C4×C53D411yescharacteristic
41C2×C42×C53—21no—
42C2×C42×C53—21no—
43C2×C42×C53D411yescharacteristic
44C2×C42×C53D411yescharacteristic
45C2×C42×C53C2311yescharacteristic
46C4⋊C8×C53—22no—
47C4⋊C8×C53—22no—
48C4⋊C8×C53D414yes—
49#101×C53—24no—
50C22⋊C8×C53—22no—
51#97×C53—22no—
52#97×C53—22no—
53#97×C53—22no—
54C4×C8×C53—22no—
55C4×C8×C53—22no—
56#95×C53—21no—
57#95×C53—21no—
58#95×C53—21no—
59#95×C53—21no—
60#95×C53—21no—
61#95×C53C2×C411yescharacteristic
62#95×C53C2×C411yescharacteristic
63C2×Q8×C53—22no—
64C2×Q8×C53—22no—
65C2×Q8×C53—22no—
66C2×Q8×C53—41no—
67C2×Q8×C53—42no—
68C22×C4×C53—21no—
69C22×C4×C53—21no—
70C22×C4×C53—21no—
71C22×C4×C53—21no—
72C22×C4×C53C22⋊C411yescharacteristic
73C22×C4×C53C22⋊C411yescharacteristic
74C22×C4×C53C22⋊C411yescharacteristic
75C22×C4×C53C22⋊C411yescharacteristic
76C22×C4×C53C22×C411yescharacteristic
77C22×C4×C53C2×D411yescharacteristic
78C22×C4×C53C2×D411yescharacteristic
79M16×C53—24no—
80M16×C53—42no—
81C2×C8×C53—24no—
82C2×C8×C53—42no—
83C4⋊C4×C53—22no—
84C4⋊C4×C53—22no—
85C4⋊C4×C53—22no—
86C4⋊C4×C53—22no—
87C4⋊C4×C53—42no—
88C4⋊C4×C53—42no—
89C4⋊C4×C53—42no—
90C4⋊C4×C53—42no—
91C4⋊C4×C53—42no—
92C42×C53—24no—
93C42×C53—21no—
94C42×C53—21no—
95C42×C53—21no—
96C42×C53—21no—
97C42×C53—41no—
98C42×C53—41no—
99C42×C53C2×D412yes—
100C42×C53#4112yes—
101C23×C53C2×C22⋊C411yescharacteristic
102Q8×C53—24no—
103Q8×C53—44no—
104Q8×C53—42no—
105C2×C4×C53—21no—
106C2×C4×C53—21no—
107C2×C4×C53—21no—
108C2×C4×C53—21no—
109C2×C4×C53—22no—
110C2×C4×C53—22no—
111C2×C4×C53—22no—
112C2×C4×C53—22no—
113C2×C4×C53—21no—
114C2×C4×C53—21no—
115C2×C4×C53—21no—
116C2×C4×C53—21no—
117C2×C4×C53—21no—
118C2×C4×C53—41no—
119C2×C4×C53—41no—
120C2×C4×C53—41no—
121C2×C4×C53—41no—
122C2×C4×C53—41no—
123C2×C4×C53—41no—
124C2×C4×C53—41no—
125C2×C4×C53—41no—
126C2×C4×C53—41no—
127C2×C4×C53—41no—
128C2×C4×C53—41no—
129C2×C4×C53—41no—
130C2×C4×C53#10412yes—
131C2×C4×C53C4×D412yes—
132C2×C4×C53#12011yescharacteristic
133C2×C4×C53#12112yes—
134C2×C4×C53#12311yescharacteristic
135C8×C53—44no—
136C8×C53—44no—
137#9030C5311yesmaximal, characteristic, direct product factor, Sylow
138C22×C53—21no—
139C22×C53—21no—
140C22×C53#38611yescharacteristic
141C22×C53C2×#10411yescharacteristic
142C22×C53#42111yescharacteristic
143C4×C53—22no—
144C4×C53—22no—
145C4×C53—21no—
146C4×C53—22no—
147C4×C53—42no—
148C4×C53—42no—
149C4×C53—41no—
150C4×C53—41no—
151C4×C53—41no—
152C4×C53—42no—
153C4×C53—81no—
154C4×C53#45612yes—
155#2983C2×C5311yescharacteristic
156#2399C2×C5311yescharacteristic
157C4×#101C2×C5311yescharacteristic
158#1491C2×C5312yes—
159#1300C2×C5312yes—
160C2×C53—21no—
161C2×C53—21no—
162C2×C53#187111yescharacteristic
163C2×C53#188611yescharacteristic
164C2×C53#189111yescharacteristic
165C2×C4×Q8C22×C5311yescharacteristic
166C2×C4×Q8C22×C5311yescharacteristic
167#446—24no—
168#432—21no—
169#432C22×C5312yes—
170#431—21no—
171C2×#101—21no—
172C4×M16C22×C5312yes—
173#398—21no—
174#398C4×C5311yescharacteristic
175#398C4×C5311yescharacteristic
176#395—21no—
177#395C4×C5311yescharacteristic
178#395C4×C5311yescharacteristic
179C4×C4⋊C4—21no—
180C4×C4⋊C4—21no—
181#376C22×C5311yescharacteristic
182#343—21no—
183Q8⋊C8—24no—
184C53#903011yescharacteristic, direct product factor, Sylow
185C22×Q8C2×C4×C5311yescharacteristic
186C22×Q8D4×C5311yescharacteristic
187C2×M16—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C5311yescharacteristic
198C2×C4⋊C4C2×C4×C5311yescharacteristic
199C2×C4⋊C4C2×C4×C5311yescharacteristic
200C2×C4⋊C4D4×C5311yescharacteristic
201C2×C42—21no—
202C2×C42—21no—
203C2×C42D4×C5311yescharacteristic
204C2×C42D4×C5311yescharacteristic
205C2×C42C23×C5311yescharacteristic
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8D4×C5314yes—
209#101—24no—
210C22⋊C8—22no—
211#97—22no—
212#97—22no—
213#97—22no—
214C4×C8—22no—
215C4×C8—22no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C2×C4×C5311yescharacteristic
222#95C2×C4×C5311yescharacteristic
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—42no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22⋊C4×C5311yescharacteristic
233C22×C4C22⋊C4×C5311yescharacteristic
234C22×C4C22⋊C4×C5311yescharacteristic
235C22×C4C22⋊C4×C5311yescharacteristic
236C22×C4C22×C4×C5311yescharacteristic
237C22×C4C2×D4×C5311yescharacteristic
238C22×C4C2×D4×C5311yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—24no—
242C2×C8—42no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C42—24no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—41no—
258C42—41no—
259C42C2×D4×C5312yes—
260C42#41×C5312yes—
261C23C2×C22⋊C4×C5311yescharacteristic
262Q8—24no—
263Q8—44no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4#104×C5312yes—
291C2×C4C4×D4×C5312yes—
292C2×C4#120×C5311yescharacteristic
293C2×C4#121×C5312yes—
294C2×C4#123×C5311yescharacteristic
295C8—44no—
296C8—44no—
297C22—21no—
298C22—21no—
299C22C53×#38611yescharacteristic
300C22C2×#104×C5311yescharacteristic
301C22C53×#42111yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4C53×#45612yes—
314C2—21no—
315C2—21no—
316C2C53×#187111yescharacteristic
317C2C53×#188611yescharacteristic
318C2C53×#189111yescharacteristic
subgroupG/H
centerC2×C4×C53#120
commutatorC22×C4C22×C4×C53
Frattini, cosocleC2×C42C23×C53
socleC22×C53#386
prime radicalC23×C53C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
137. #9030C53direct (N × H)
184. C53#9030direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#29832
C53×#23992
C4×#101×C532
C53×#14912
C53×#13002
#903053