Finite Group Databasebeta

← C53×#10182 #27217694

Subgroups — C53×#10182 #27217694

Order 13568.

508 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3209C211yesmaximal, characteristic, complemented
2C53×#3077C211yesmaximal, characteristic
3C2×C53×#476C211yesmaximal, characteristic
4C53×#1549C211yesmaximal, characteristic, complemented
5C53×#1481C211yesmaximal, characteristic, complemented
6C53×#1460C211yesmaximal, characteristic
7C53×#1301C211yesmaximal, characteristic, complemented
8C53×#533C2211yescharacteristic
9C2×C4⋊Q8×C53C2211yescharacteristic
10C2×C4×D4×C53C2211yescharacteristic
11C53×#494—21no—
12C53×#487—21no—
13C53×#478—22no—
14C53×#476—22no—
15C53×#476—21no—
16C53×#476—22no—
17C53×#474—21no—
18C53×#462—22no—
19C53×#451—22no—
20C53×#431C2211yescharacteristic
21C53×#431C2211yescharacteristic
22C53×#428—21no—
23C2×#106×C53—21no—
24C53×#423C2211yescharacteristic
25C2×C4⋊C8×C53C2211yescharacteristic
26C53×#418—21no—
27C2×#102×C53—21no—
28C53×#332—22no—
29C53×Q8⋊C8—22no—
30C53×#323—22no—
31C22×Q8×C53—21no—
32C22×D4×C53D411yescharacteristic
33C23×C4×C53—21no—
34C2×Q16×C53—24no—
35C2×M16×C53—21no—
36C22×C8×C53—21no—
37C4⋊Q8×C53—21no—
38C4⋊Q8×C53—21no—
39C4⋊Q8×C53—21no—
40C4⋊Q8×C53D411yescharacteristic
41C4⋊Q8×C53D411yescharacteristic
42C4⋊Q8×C53D412yes—
43#125×C53—21no—
44C22⋊Q8×C53—21no—
45C22⋊Q8×C53—21no—
46C4×Q8×C53—21no—
47C4×Q8×C53—21no—
48C4×D4×C53—21no—
49C4×D4×C53—21no—
50C4×D4×C53—21no—
51C4×D4×C53—21no—
52#117×C53—21no—
53C2×C4⋊C4×C53—21no—
54C2×C4⋊C4×C53—21no—
55C2×C4⋊C4×C53D411yescharacteristic
56C2×C22⋊C4×C53—21no—
57C2×C42×C53C2311yescharacteristic
58#107×C53—22no—
59#106×C53—24no—
60#106×C53—22no—
61C4⋊C8×C53—21no—
62C4⋊C8×C53—21no—
63C4⋊C8×C53—21no—
64C4⋊C8×C53—21no—
65C4⋊C8×C53D412yes—
66C4⋊C8×C53D412yes—
67#103×C53—24no—
68#102×C53—24no—
69#102×C53—22no—
70#102×C53—22no—
71C22⋊C8×C53—21no—
72C22⋊C8×C53D412yes—
73C4×C8×C53—21no—
74C4×C8×C53—21no—
75C24×C53—21no—
76C2×Q8×C53—22no—
77C2×Q8×C53—21no—
78C2×Q8×C53—21no—
79C2×Q8×C53—41no—
80C2×Q8×C53—82no—
81C2×D4×C53—21no—
82C2×D4×C53—21no—
83C2×D4×C53—21no—
84C2×D4×C53—21no—
85C2×D4×C53—21no—
86C2×D4×C53Q1612yescomplemented
87C22×C4×C53—21no—
88C22×C4×C53—41no—
89C22×C4×C53—41no—
90C22×C4×C53—41no—
91C22×C4×C53—82no—
92C22×C4×C53C2×D411yescharacteristic
93C22×C4×C53C2×D411yescharacteristic
94C22×C4×C53#4111yescharacteristic
95Q16×C53—84no—
96M16×C53—41no—
97M16×C53—41no—
98C2×C8×C53—22no—
99C2×C8×C53—22no—
100C2×C8×C53—22no—
101C2×C8×C53—41no—
102C2×C8×C53—41no—
103C2×C8×C53—41no—
104C4⋊C4×C53—22no—
105C4⋊C4×C53—21no—
106C4⋊C4×C53—21no—
107C4⋊C4×C53—21no—
108C4⋊C4×C53—21no—
109C4⋊C4×C53—21no—
110C4⋊C4×C53—22no—
111C4⋊C4×C53—21no—
112C4⋊C4×C53—41no—
113C4⋊C4×C53—41no—
114C4⋊C4×C53—41no—
115C4⋊C4×C53—41no—
116C22⋊C4×C53—41no—
117C22⋊C4×C53—41no—
118C22⋊C4×C53—41no—
119C42×C53—41no—
120C42×C53C2×D411yescharacteristic
121C42×C53C2×D411yescharacteristic
122C42×C53C2×D411yescharacteristic
123C42×C53C2×D411yescharacteristic
124C23×C53—22no—
125C23×C53—41no—
126C23×C53—41no—
127C23×C53—81no—
128C23×C53—81no—
129C23×C53#12111yescharacteristic
130Q8×C53—44no—
131Q8×C53—42no—
132Q8×C53—42no—
133Q8×C53—82no—
134D4×C53—22no—
135D4×C53—22no—
136D4×C53—41no—
137D4×C53—41no—
138C2×C4×C53—22no—
139C2×C4×C53—41no—
140C2×C4×C53—41no—
141C2×C4×C53—42no—
142C2×C4×C53—41no—
143C2×C4×C53—41no—
144C2×C4×C53—82no—
145C2×C4×C53—82no—
146C2×C4×C53—82no—
147C2×C4×C53—81no—
148C2×C4×C53#12011yescharacteristic
149C2×C4×C53#12011yescharacteristic
150C2×C4×C53#12011yescharacteristic
151C2×C4×C53#12111yescharacteristic
152C2×C4×C53#12111yescharacteristic
153C2×C4×C53#12711yescharacteristic
154C2×C4×C53C2×Q1611yescharacteristic
155C2×C4×C53#13511yescharacteristic
156C2×C4×C53#13711yescharacteristic
157C2×C4×C53#13711yescharacteristic
158C8×C53—42no—
159C8×C53—42no—
160C8×C53—42no—
161C8×C53—81no—
162#10182C5311yesmaximal, characteristic, direct product factor, Sylow
163C22×C53—21no—
164C22×C53—21no—
165C22×C53—42no—
166C22×C53—82no—
167C22×C53—82no—
168C22×C53—81no—
169C22×C53—81no—
170C22×C53#39211yescharacteristic
171C22×C53#46711yescharacteristic
172C22×C53#47011yescharacteristic
173C4×C53—21no—
174C4×C53—21no—
175C4×C53—21no—
176C4×C53—82no—
177C4×C53—81no—
178C4×C53—81no—
179C4×C53—81no—
180C4×C53#45111yescharacteristic
181C4×C53#45111yescharacteristic
182C4×C53#45211yescharacteristic
183C4×C53#45211yescharacteristic
184C4×C53#47112yes—
185#3209C2×C5311yescharacteristic, complemented
186#3077C2×C5311yescharacteristic
187C2×#476C2×C5311yescharacteristic
188#1549C2×C5311yescharacteristic, complemented
189#1481C2×C5311yescharacteristic, complemented
190#1460C2×C5311yescharacteristic
191#1301C2×C5311yescharacteristic, complemented
192C2×C53—21no—
193C2×C53—21no—
194C2×C53—82no—
195C2×C53#200111yescharacteristic
196C2×C53#200811yescharacteristic
197C2×C53#201911yescharacteristic
198#533C22×C5311yescharacteristic
199C2×C4⋊Q8C22×C5311yescharacteristic
200C2×C4×D4C22×C5311yescharacteristic
201#494—21no—
202#487—21no—
203#478—22no—
204#476—21no—
205#476—22no—
206#476—22no—
207#474—21no—
208#462—22no—
209#451—22no—
210#431C22×C5311yescharacteristic
211#431C22×C5311yescharacteristic
212#428—21no—
213C2×#106—21no—
214#423C22×C5311yescharacteristic
215C2×C4⋊C8C22×C5311yescharacteristic
216#418—21no—
217C2×#102—21no—
218#332—22no—
219Q8⋊C8—22no—
220#323—22no—
221C53#1018211yescharacteristic, direct product factor, Sylow
222C22×Q8—21no—
223C22×D4D4×C5311yescharacteristic
224C23×C4—21no—
225C2×Q16—24no—
226C2×M16—21no—
227C22×C8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8D4×C5312yes—
232C4⋊Q8D4×C5311yescharacteristic
233C4⋊Q8D4×C5311yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C5311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C42C23×C5311yescharacteristic
249#107—22no—
250#106—24no—
251#106—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8D4×C5312yes—
257C4⋊C8D4×C5312yes—
258#103—24no—
259#102—24no—
260#102—22no—
261#102—22no—
262C22⋊C8—21no—
263C22⋊C8D4×C5312yes—
264C4×C8—21no—
265C4×C8—21no—
266C24—21no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—82no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4Q16×C5312yescomplemented
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—82no—
283C22×C4C2×D4×C5311yescharacteristic
284C22×C4C2×D4×C5311yescharacteristic
285C22×C4#41×C5311yescharacteristic
286Q16—84no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—41no—
311C42C2×D4×C5311yescharacteristic
312C42C2×D4×C5311yescharacteristic
313C42C2×D4×C5311yescharacteristic
314C42C2×D4×C5311yescharacteristic
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23#121×C5311yescharacteristic
321Q8—42no—
322Q8—44no—
323Q8—42no—
324Q8—82no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4#120×C5311yescharacteristic
340C2×C4#120×C5311yescharacteristic
341C2×C4#120×C5311yescharacteristic
342C2×C4#121×C5311yescharacteristic
343C2×C4#121×C5311yescharacteristic
344C2×C4#127×C5311yescharacteristic
345C2×C4C2×Q16×C5311yescharacteristic
346C2×C4#135×C5311yescharacteristic
347C2×C4#137×C5311yescharacteristic
348C2×C4#137×C5311yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22C53×#39211yescharacteristic
361C22C53×#46711yescharacteristic
362C22C53×#47011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4C53×#45111yescharacteristic
371C4C53×#45111yescharacteristic
372C4C53×#45211yescharacteristic
373C4C53×#45211yescharacteristic
374C4C53×#47112yes—
375C2—21no—
376C2—21no—
377C2—82no—
378C2C53×#200111yescharacteristic
379C2C53×#200811yescharacteristic
380C2C53×#201911yescharacteristic
subgroupG/H
center, socleC22×C53#392
commutator, Frattini, cosocleC2×C42C23×C53
prime radicalC22×D4×C53D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3209C2semidirect
4. C53×#1549C2semidirect
5. C53×#1481C2semidirect
7. C53×#1301C2semidirect
86. C2×D4×C53Q16semidirect
162. #10182C53direct (N × H)
185. #3209C2×C53semidirect
188. #1549C2×C53semidirect
189. #1481C2×C53semidirect
191. #1301C2×C53semidirect
221. C53#10182direct (N × H)
277. C2×D4Q16×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#32092
C53×#30772
C2×C53×#4762
C53×#15492
C53×#14812
C53×#14602
C53×#13012
#1018253