Finite Group Databasebeta

← C53×#9883 #27217395

Subgroups — C53×#9883 #27217395

Order 13568.

600 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#389C211yesmaximal, characteristic
2C53×#1797C211yesmaximal, characteristic
3C53×#1749C211yesmaximal, characteristic
4C53×#1280C214yesmaximal
5C22×C4⋊C4×C53C411yescharacteristic
6C22×C4⋊C4×C53C411yescharacteristic
7C22×C4⋊C4×C53C412yes—
8C22×C42×C53C2211yescharacteristic
9C2×C4⋊C8×C53—21no—
10C2×C22⋊C8×C53C2212yes—
11C2×C22⋊C8×C53C2212yes—
12C2×#97×C53—21no—
13C53×#389—21no—
14C53×#389—21no—
15C53×#389—21no—
16C53×#389—21no—
17C2×#95×C53C2212yes—
18C53×#336—21no—
19C53×#336—21no—
20C23×C4×C53C2×C411yescharacteristic
21C23×C4×C53C2×C411yescharacteristic
22C23×C4×C53C2×C412yes—
23C23×C4×C53C2×C412yes—
24C23×C4×C53C2311yescharacteristic
25C22×C8×C53—22no—
26C22×C8×C53—22no—
27C2×C4⋊C4×C53—21no—
28C2×C4⋊C4×C53—21no—
29C2×C4⋊C4×C53—22no—
30C2×C4⋊C4×C53—22no—
31C2×C4⋊C4×C53—21no—
32C2×C4⋊C4×C53—21no—
33C2×C4⋊C4×C53—24no—
34C2×C4⋊C4×C53—42no—
35C2×C4⋊C4×C53—44no—
36C2×C42×C53—42no—
37C2×C42×C53D411yescharacteristic
38C2×C42×C53D411yescharacteristic
39C2×C42×C53D411yescharacteristic
40C2×C42×C53D411yescharacteristic
41C4⋊C8×C53—42no—
42C22⋊C8×C53—22no—
43C22⋊C8×C53—24no—
44C22⋊C8×C53Q814yes—
45#97×C53—42no—
46#95×C53—22no—
47#95×C53—22no—
48C24×C53C22×C411yescharacteristic
49C22×C4×C53—22no—
50C22×C4×C53—22no—
51C22×C4×C53—22no—
52C22×C4×C53—22no—
53C22×C4×C53—22no—
54C22×C4×C53—22no—
55C22×C4×C53—22no—
56C22×C4×C53—22no—
57C22×C4×C53—24no—
58C22×C4×C53—41no—
59C22×C4×C53—41no—
60C22×C4×C53—41no—
61C22×C4×C53—42no—
62C22×C4×C53—42no—
63C22×C4×C53—42no—
64C22×C4×C53—42no—
65C22×C4×C53C22⋊C411yescharacteristic
66C22×C4×C53C22⋊C411yescharacteristic
67C22×C4×C53C22⋊C411yescharacteristic
68C22×C4×C53C22⋊C411yescharacteristic
69C22×C4×C53M1614yes—
70C22×C4×C53C2×D411yescharacteristic
71C22×C4×C53C2×D411yescharacteristic
72C22×C4×C53C2×Q812yes—
73C22×C4×C53#4112yes—
74C2×C8×C53—24no—
75C2×C8×C53—42no—
76C2×C8×C53—42no—
77C2×C8×C53—42no—
78C2×C8×C53—42no—
79C2×C8×C53—42no—
80C4⋊C4×C53—24no—
81C4⋊C4×C53—24no—
82C4⋊C4×C53—42no—
83C4⋊C4×C53—44no—
84C4⋊C4×C53—42no—
85C4⋊C4×C53—44no—
86C42×C53—22no—
87C42×C53—22no—
88C42×C53—41no—
89C42×C53—41no—
90C23×C53—21no—
91C23×C53—21no—
92C23×C53—21no—
93C23×C53—21no—
94C23×C53C2×C22⋊C411yescharacteristic
95C23×C53C4×Q812yes—
96C23×C53C2×M1612yes—
97C23×C53#13112yes—
98C2×C4×C53—28no—
99C2×C4×C53—21no—
100C2×C4×C53—21no—
101C2×C4×C53—21no—
102C2×C4×C53—21no—
103C2×C4×C53—21no—
104C2×C4×C53—21no—
105C2×C4×C53—21no—
106C2×C4×C53—21no—
107C2×C4×C53—21no—
108C2×C4×C53—21no—
109C2×C4×C53—24no—
110C2×C4×C53—21no—
111C2×C4×C53—21no—
112C2×C4×C53—21no—
113C2×C4×C53—42no—
114C2×C4×C53—42no—
115C2×C4×C53—44no—
116C2×C4×C53—44no—
117C2×C4×C53—42no—
118C2×C4×C53—42no—
119C2×C4×C53—44no—
120C2×C4×C53—42no—
121C2×C4×C53—42no—
122C2×C4×C53—42no—
123C2×C4×C53—84no—
124C2×C4×C53#9912yes—
125C2×C4×C53#10012yes—
126C2×C4×C53#10112yes—
127C2×C4×C53C22⋊Q812yes—
128C2×C4×C53#12411yescharacteristic
129C2×C4×C53C4⋊Q811yescharacteristic
130C8×C53—44no—
131C8×C53—82no—
132#9883C5311yesmaximal, characteristic, direct product factor, Sylow
133C22×C53—22no—
134C22×C53—22no—
135C22×C53—22no—
136C22×C53—22no—
137C22×C53—22no—
138C22×C53—22no—
139C22×C53#39111yescharacteristic
140C22×C53#40711yescharacteristic
141C22×C53#40811yescharacteristic
142C22×C53C2×#9911yescharacteristic
143C22×C53#41011yescharacteristic
144C22×C53C2×#10011yescharacteristic
145C22×C53C2×#10111yescharacteristic
146C22×C53#44614yes—
147C4×C53—22no—
148C4×C53—22no—
149C4×C53—22no—
150C4×C53—22no—
151C4×C53—21no—
152C4×C53—21no—
153C4×C53—44no—
154C4×C53—41no—
155C4×C53—82no—
156C2×#389C2×C5311yescharacteristic
157#1797C2×C5311yescharacteristic
158#1749C2×C5311yescharacteristic
159#1280C2×C5314yes—
160C2×C53—24no—
161C2×C53#146311yescharacteristic
162C2×C53#146611yescharacteristic
163C2×C53#147011yescharacteristic
164C2×C53#147111yescharacteristic
165C2×C53#198511yescharacteristic
166C2×C53#199611yescharacteristic
167C2×C53#199711yescharacteristic
168C22×C4⋊C4C4×C5311yescharacteristic
169C22×C4⋊C4C4×C5311yescharacteristic
170C22×C4⋊C4C4×C5312yes—
171C22×C42C22×C5311yescharacteristic
172C2×C4⋊C8—21no—
173C2×C22⋊C8C22×C5312yes—
174C2×C22⋊C8C22×C5312yes—
175C2×#97—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180C2×#95C22×C5312yes—
181#336—21no—
182#336—21no—
183C53#988311yescharacteristic, direct product factor, Sylow
184C23×C4C2×C4×C5311yescharacteristic
185C23×C4C2×C4×C5311yescharacteristic
186C23×C4C2×C4×C5312yes—
187C23×C4C2×C4×C5312yes—
188C23×C4C23×C5311yescharacteristic
189C22×C8—22no—
190C22×C8—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—44no—
200C2×C42—42no—
201C2×C42D4×C5311yescharacteristic
202C2×C42D4×C5311yescharacteristic
203C2×C42D4×C5311yescharacteristic
204C2×C42D4×C5311yescharacteristic
205C4⋊C8—42no—
206C22⋊C8—22no—
207C22⋊C8—24no—
208C22⋊C8Q8×C5314yes—
209#97—42no—
210#95—22no—
211#95—22no—
212C24C22×C4×C5311yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4C22⋊C4×C5311yescharacteristic
230C22×C4C22⋊C4×C5311yescharacteristic
231C22×C4C22⋊C4×C5311yescharacteristic
232C22×C4C22⋊C4×C5311yescharacteristic
233C22×C4M16×C5314yes—
234C22×C4C2×D4×C5311yescharacteristic
235C22×C4C2×D4×C5311yescharacteristic
236C22×C4C2×Q8×C5312yes—
237C22×C4#41×C5312yes—
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23C2×C22⋊C4×C5311yescharacteristic
259C23C4×Q8×C5312yes—
260C23C2×M16×C5312yes—
261C23#131×C5312yes—
262C2×C4—28no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—24no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—84no—
288C2×C4#99×C5312yes—
289C2×C4#100×C5312yes—
290C2×C4#101×C5312yes—
291C2×C4C22⋊Q8×C5312yes—
292C2×C4#124×C5311yescharacteristic
293C2×C4C4⋊Q8×C5311yescharacteristic
294C8—44no—
295C8—82no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22C53×#39111yescharacteristic
303C22C53×#40711yescharacteristic
304C22C53×#40811yescharacteristic
305C22C2×#99×C5311yescharacteristic
306C22C53×#41011yescharacteristic
307C22C2×#100×C5311yescharacteristic
308C22C2×#101×C5311yescharacteristic
309C22C53×#44614yes—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—41no—
318C4—82no—
319C2—24no—
320C2C53×#146311yescharacteristic
321C2C53×#146611yescharacteristic
322C2C53×#147011yescharacteristic
323C2C53×#147111yescharacteristic
324C2C53×#198511yescharacteristic
325C2C53×#199611yescharacteristic
326C2C53×#199711yescharacteristic
subgroupG/H
center, socleC23×C53C2×C22⋊C4
commutatorC24C22×C4×C53
Frattini, cosocleC23×C4C23×C53
prime radicalC24×C53C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
132. #9883C53direct (N × H)
183. C53#9883direct (N × H)

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
C53×#17492
C53×#12802
#988353