Finite Group Databasebeta

← C5×#10193 #11932913

Subgroups — C5×#10193 #11932913

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3246C211yesmaximal, characteristic, complemented
2C5×#3205C211yesmaximal, characteristic
3C5×#3138C211yesmaximal, characteristic, complemented
4C5×#1982C211yesmaximal, characteristic, complemented
5C5×#1980C211yesmaximal, characteristic, complemented
6C5×#1503C211yesmaximal, characteristic, complemented
7C5×#1283C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C2×C5×#127C2211yescharacteristic
11C5×#493—21no—
12C5×#490—22no—
13C5×#486—21no—
14C5×#486—21no—
15C5×#486—21no—
16C5×#476—21no—
17C5×#475—21no—
18C5×#465—22no—
19C5×#461—21no—
20C5×#460—21no—
21C5×#459—22no—
22C5×#447—22no—
23C5×#431C2211yescharacteristic
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×#104—22no—
26C5×#418—22no—
27C2×C5×#102—22no—
28C4×C5×M16C2211yescharacteristic
29C4×C5×C4⋊C4C2211yescharacteristic
30C5×#328—22no—
31#10193C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C2×C5×SD16—22no—
37C2×C5×D8—24no—
38C2×C5×M16D412yes—
39C22×C5×C8D412yes—
40C5×C4⋊Q8D411yescharacteristic
41C5×C4⋊Q8D411yescharacteristic
42C5×C4⋊Q8D411yescharacteristic
43C5×#127—21no—
44C5×#127—21no—
45C5×#127—21no—
46C5×#127D412yes—
47C5×#127D411yescharacteristic
48C5×#125—21no—
49C5×#124—21no—
50C5×C22⋊Q8—21no—
51C5×C22⋊Q8—21no—
52C5×#121—21no—
53C5×#121—21no—
54C4×C5×Q8—21no—
55C4×C5×Q8—21no—
56C4×C5×D4—21no—
57C4×C5×D4—21no—
58C5×#117—21no—
59C2×C5×C4⋊C4—21no—
60C2×C42×C5—21no—
61C2×C42×C5C2311yescharacteristic
62C5×#106—22no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×#104—44no—
67C5×#103—22no—
68C5×#102—24no—
69C5×#102—24no—
70C5×#102—24no—
71C5×#102—22no—
72C5×#102—44no—
73C5×C22⋊C8D412yes—
74C5×#97—21no—
75C4×C5×C8—21no—
76C4×C5×C8—21no—
77C5×#95—21no—
78#3246C2×C511yescharacteristic, complemented
79#3205C2×C511yescharacteristic
80#3138C2×C511yescharacteristic, complemented
81#1982C2×C511yescharacteristic, complemented
82#1980C2×C511yescharacteristic, complemented
83#1503C2×C511yescharacteristic, complemented
84#1283C2×C511yescharacteristic, complemented
85C24×C5—41no—
86C5×#41—42no—
87C5×#41—42no—
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×Q8—21no—
91C2×C5×D4—21no—
92C2×C5×D4—21no—
93C2×C5×D4—22no—
94C2×C5×D4—22no—
95C2×C5×D4—21no—
96C2×C5×D4—22no—
97C2×C5×D4—42no—
98C2×C5×D4—42no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—42no—
104C2×C5×D4—42no—
105C2×C5×D4—82no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C5×SD16—82no—
112C5×D8—84no—
113C5×M16—22no—
114C5×M16—22no—
115C2×C5×C8—22no—
116C2×C5×C8—22no—
117C2×C5×C8—22no—
118C2×C5×C8—42no—
119C5×C4⋊C4—22no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—41no—
127C5×C4⋊C4—41no—
128C5×C4⋊C4—41no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—41no—
132C42×C5—41no—
133C42×C5—42no—
134C42×C5C2×D411yescharacteristic
135C42×C5C2×D411yescharacteristic
136C42×C5C2×D411yescharacteristic
137C42×C5#4111yescharacteristic
138#533C22×C511yescharacteristic
139#532C22×C511yescharacteristic
140C2×#127C22×C511yescharacteristic
141#493—21no—
142#490—22no—
143#486—21no—
144#486—21no—
145#486—21no—
146#476—21no—
147#475—21no—
148#465—22no—
149#461—21no—
150#460—21no—
151#459—22no—
152#447—22no—
153#431C22×C511yescharacteristic
154C2×C4⋊C8C22×C511yescharacteristic
155C2×#104—22no—
156#418—22no—
157C2×#102—22no—
158C4×M16C22×C511yescharacteristic
159C4×C4⋊C4C22×C511yescharacteristic
160#328—22no—
161C23×C5—41no—
162C23×C5—42no—
163C23×C5—82no—
164C23×C5—82no—
165C23×C5—81no—
166C23×C5—81no—
167C23×C5#12711yescharacteristic
168C5×Q8—41no—
169C5×Q8—41no—
170C5×Q8—42no—
171C5×Q8—81no—
172C5×D4—42no—
173C5×D4—44no—
174C5×D4—44no—
175C5×D4—44no—
176C5×D4—41no—
177C5×D4—41no—
178C5×D4—42no—
179C5×D4—82no—
180C5×D4—81no—
181C5×D4—81no—
182C5×D4—81no—
183C5×D4—81no—
184C5×D4—82no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—41no—
188C2×C4×C5—42no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5—82no—
195C2×C4×C5#12011yescharacteristic
196C2×C4×C5#12011yescharacteristic
197C2×C4×C5#12011yescharacteristic
198C2×C4×C5#12111yescharacteristic
199C2×C4×C5#12111yescharacteristic
200C2×C4×C5#12111yescharacteristic
201C2×C4×C5#13512yes—
202C2×C4×C5AGL(1,ℤ/8)12yes—
203C5×C8—42no—
204C5×C8—42no—
205C5×C8—42no—
206C2×#41—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C2×SD16—22no—
211C2×D8—24no—
212C2×M16C5×D412yes—
213C22×C8C5×D412yes—
214C4⋊Q8C5×D411yescharacteristic
215C4⋊Q8C5×D411yescharacteristic
216C4⋊Q8C5×D411yescharacteristic
217#127—21no—
218#127—21no—
219#127—21no—
220#127C5×D412yes—
221#127C5×D411yescharacteristic
222#125—21no—
223#124—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226#121—21no—
227#121—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—21no—
231C4×D4—21no—
232#117—21no—
233C2×C4⋊C4—21no—
234C2×C42—21no—
235C2×C42C23×C511yescharacteristic
236#106—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240#104—44no—
241#103—22no—
242#102—24no—
243#102—24no—
244#102—24no—
245#102—22no—
246#102—44no—
247C22⋊C8C5×D412yes—
248#97—21no—
249C4×C8—21no—
250C4×C8—21no—
251#95—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—82no—
255C22×C5—81no—
256C22×C5—82no—
257C22×C5—81no—
258C22×C5—81no—
259C22×C5—82no—
260C22×C5—162no—
261C22×C5—162no—
262C22×C5#39211yescharacteristic
263C22×C5#49511yescharacteristic
264C22×C5#49611yescharacteristic
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—82no—
269C4×C5—81no—
270C4×C5—81no—
271C4×C5—81no—
272C4×C5#44912yes—
273C4×C5#45311yescharacteristic
274C4×C5#45411yescharacteristic
275C4×C5#46312yes—
276C24—41no—
277#41—42no—
278#41—42no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—82no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4C2×C5×D411yescharacteristic
300C22×C4C2×C5×D411yescharacteristic
301C22×C4C2×C5×D411yescharacteristic
302SD16—82no—
303D8—84no—
304M16—22no—
305M16—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—42no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—41no—
324C42—42no—
325C42C2×C5×D411yescharacteristic
326C42C2×C5×D411yescharacteristic
327C42C2×C5×D411yescharacteristic
328C42C5×#4111yescharacteristic
329C2×C5—21no—
330C2×C5—21no—
331C2×C5—161no—
332C2×C5—162no—
333C2×C5#200611yescharacteristic
334C2×C5#200811yescharacteristic
335C2×C5#201211yescharacteristic
336C23—41no—
337C23—42no—
338C23—82no—
339C23—82no—
340C23—81no—
341C23—81no—
342C23C5×#12711yescharacteristic
343Q8—41no—
344Q8—41no—
345Q8—42no—
346Q8—81no—
347D4—42no—
348D4—44no—
349D4—44no—
350D4—44no—
351D4—41no—
352D4—41no—
353D4—42no—
354D4—82no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—82no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—82no—
370C2×C4C5×#12011yescharacteristic
371C2×C4C5×#12011yescharacteristic
372C2×C4C5×#12011yescharacteristic
373C2×C4C5×#12111yescharacteristic
374C2×C4C5×#12111yescharacteristic
375C2×C4C5×#12111yescharacteristic
376C2×C4C5×#13512yes—
377C2×C4C5×AGL(1,ℤ/8)12yes—
378C8—42no—
379C8—42no—
380C8—42no—
381C5#1019311yescharacteristic, direct product factor, Sylow
382C22—21no—
383C22—21no—
384C22—81no—
385C22—82no—
386C22—82no—
387C22—81no—
388C22—82no—
389C22—81no—
390C22—162no—
391C22—162no—
392C22C5×#39211yescharacteristic
393C22C5×#49511yescharacteristic
394C22C5×#49611yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C5×#44912yes—
403C4C5×#45311yescharacteristic
404C4C5×#45411yescharacteristic
405C4C5×#46312yes—
406C2—21no—
407C2—21no—
408C2—162no—
409C2—161no—
410C2C5×#200611yescharacteristic
411C2C5×#200811yescharacteristic
412C2C5×#201211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3205C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3246C2semidirect
3. C5×#3138C2semidirect
4. C5×#1982C2semidirect
5. C5×#1980C2semidirect
6. C5×#1503C2semidirect
7. C5×#1283C2semidirect
31. #10193C5direct (N × H)
78. #3246C2×C5semidirect
80. #3138C2×C5semidirect
81. #1982C2×C5semidirect
82. #1980C2×C5semidirect
83. #1503C2×C5semidirect
84. #1283C2×C5semidirect
381. C5#10193direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32462
C5×#32052
C5×#31382
C5×#19822
C5×#19802
C5×#15032
C5×#12832
#101935