Finite Group Databasebeta

← C5×#71920 #14290006

Subgroups — C5×#71920 #14290006

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, characteristic
2C5×#5070C211yesmaximal, characteristic, complemented
3C5×#5031C211yesmaximal, characteristic, complemented
4C5×#5007C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6C5×#4535C211yesmaximal, characteristic, complemented
7C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C5×#1641—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#127—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C5×#121—22no—
13C3×C5×#121—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×C5×#216—21no—
18C5×#869C2211yescharacteristic
19C5×#832—21no—
20C5×#832—22no—
21C5×#810—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71920C511yesmaximal, characteristic, direct product factor, Hall
27C5×#550D311yescharacteristic
28C5×#486—31no—
29C5×#474—31no—
30C5×#462—31no—
31C5×#331—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C2×C3×C5×D4D412yes—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—21no—
45C2×C5×Dic6—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53C5×#216—42no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8—21no—
59C3×#550C2×C511yescharacteristic
60#5070C2×C511yescharacteristic, complemented
61#5031C2×C511yescharacteristic, complemented
62#5007C2×C511yescharacteristic, complemented
63#4544C2×C511yescharacteristic, complemented
64#4535C2×C511yescharacteristic, complemented
65D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
66C2×C5×#41—21no—
67C2×C5×Q16—61no—
68C5×C4⋊Q8—31no—
69C5×#127—21no—
70C5×#127C2×D311yescharacteristic
71C5×#121—22no—
72C5×#121—21no—
73C4×C5×Q8C2×D311yescharacteristic
74C4×C5×D4—21no—
75C4×C5×D4C2×D311yescharacteristic
76C5×#107—61no—
77C5×C4⋊C8—31no—
78C5×C4⋊C8—31no—
79C5×#103—61no—
80C5×#102—61no—
81C5×#102—62no—
82C4×C5×C8—31no—
83#1641—31noSylow
84C23×C3×C5—21no—
85C23×C3×C5—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8D812yes—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—44no—
91C3×C5×D4—42no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—82no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—44no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C5×Dic3—41no—
107C5×Dic6—41no—
108C5×Dic6—41no—
109C5×C3⋊C8—41no—
110C5×C3⋊C8—41no—
111C5×C3⋊C8—41no—
112C2×C3×#41—21no—
113C3×#127—21no—
114C3×#127C22×C511yescharacteristic
115C3×#121—22no—
116C3×#121—21no—
117C3×C4×Q8C22×C511yescharacteristic
118C3×C4×D4—21no—
119C3×C4×D4C22×C511yescharacteristic
120C2×#216—21no—
121#869C22×C511yescharacteristic
122#832—21no—
123#832—22no—
124#810—21no—
125#807—21no—
126C4⋊(C3⋊C8)C22×C511yescharacteristic
127C4⋊(C3⋊C8)C22×C511yescharacteristic
128C4×C3⋊C8C22×C511yescharacteristic
129C5×#41—42no—
130C5×#41—42no—
131C2×C5×Q8—61no—
132C2×C5×Q8#6711yescharacteristic
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4#6711yescharacteristic
138C2×C5×D4#6712yes—
139C22×C4×C5—22no—
140C22×C4×C5—21no—
141C5×Q16—122no—
142C2×C5×C8—61no—
143C2×C5×C8—61no—
144C2×C5×C8—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4#6711yescharacteristic
149C5×C4⋊C4#6711yescharacteristic
150C5×C22⋊C4—22no—
151C5×C22⋊C4—21no—
152C42×C5—21no—
153C42×C5C22×D311yescharacteristic
154#550C5×D311yescharacteristic
155#486—31no—
156#474—31no—
157#462—31no—
158#331—31no—
159Q8⋊C8—31no—
160D4⋊C8—31no—
161C22×C3×C5—42no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5—42no—
165C22×C3×C5—42no—
166C22×C3×C5—41no—
167C22×C3×C5#12011yescharacteristic
168C3×C4×C5—22no—
169C3×C4×C5—21no—
170C3×C4×C5—41no—
171C3×C4×C5—41no—
172C3×C4×C5C2×D811yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5#13711yescharacteristic
176C5×Dic3—81no—
177C3×#41—42no—
178C3×#41—42no—
179C2×C3×Q8C5×D411yescharacteristic
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4C5×D411yescharacteristic
185C2×C3×D4C5×D412yes—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C2×Dic6—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4C5×D411yescharacteristic
191C3×C4⋊C4C5×D411yescharacteristic
192C3×C22⋊C4—22no—
193C3×C22⋊C4—21no—
194C3×C42—21no—
195C3×C42C23×C511yescharacteristic
196#216—42no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C23×C5—21no—
203C23×C5—22no—
204C5×Q8—21no—
205C5×Q8—121no—
206C5×Q8—121no—
207C5×Q8#21312yes—
208C5×D4—21no—
209C5×D4—21no—
210C5×D4—42no—
211C5×D4—44no—
212C5×D4—41no—
213C5×D4—41no—
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—82no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—44no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—121no—
224C2×C4×C5C2×#6711yescharacteristic
225C2×C4×C5C2×#6711yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C5×C8—121no—
228C5×C8—121no—
229C5×C8—121no—
230C2×#41—21no—
231C2×Q16—61no—
232C4⋊Q8—31no—
233#127—21no—
234#127C2×C5×D311yescharacteristic
235#121—22no—
236#121—21no—
237C4×Q8C2×C5×D311yescharacteristic
238C4×D4—21no—
239C4×D4C2×C5×D311yescharacteristic
240#107—61no—
241C4⋊C8—31no—
242C4⋊C8—31no—
243#103—61no—
244#102—61no—
245#102—62no—
246C4×C8—31no—
247C2×C3×C5—81no—
248C2×C3×C5—82no—
249C2×C3×C5#44711yescharacteristic
250C2×C3×C5#45211yescharacteristic
251C2×C3×C5#45511yescharacteristic
252C23×C3—21no—
253C23×C3—22no—
254C3×Q8—21no—
255C3×Q8C5×D812yes—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—42no—
259C3×D4—44no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—82no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—44no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4C2×C5×D411yescharacteristic
272C2×C3×C4C2×C5×D411yescharacteristic
273C2×C3×C4C2×C5×D411yescharacteristic
274C2×Dic3—41no—
275Dic6—41no—
276Dic6—41no—
277C3⋊C8—41no—
278C3⋊C8—41no—
279C3⋊C8—41no—
280C22×C5—42no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—42no—
284C22×C5—42no—
285C22×C5—41no—
286C22×C5#95311yescharacteristic
287C4×C5—22no—
288C4×C5—21no—
289C4×C5—41no—
290C4×C5—41no—
291C4×C5—241no—
292C4×C5C2×#21311yescharacteristic
293C4×C5#93211yescharacteristic
294C4×C5#95011yescharacteristic
295C4×C5#95111yescharacteristic
296#41—42no—
297#41—42no—
298C2×Q8—61no—
299C2×Q8C5×#6711yescharacteristic
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C5×#6711yescharacteristic
305C2×D4C5×#6712yes—
306C22×C4—22no—
307C22×C4—21no—
308Q16—122no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—61no—
312C4⋊C4—21no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4C5×#6711yescharacteristic
316C4⋊C4C5×#6711yescharacteristic
317C22⋊C4—22no—
318C22⋊C4—21no—
319C42—21no—
320C42C22×C5×D311yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—42no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—41no—
328C22×C3C5×#12011yescharacteristic
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4C2×C5×D811yescharacteristic
334C3×C4C5×#13511yescharacteristic
335C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
336C3×C4C5×#13711yescharacteristic
337Dic3—81no—
338C2×C5—81no—
339C2×C5—82no—
340C2×C5#521711yescharacteristic
341C2×C5#523911yescharacteristic
342C2×C5#524211yescharacteristic
343C23—21no—
344C23—22no—
345Q8—21no—
346Q8—121no—
347Q8—121no—
348Q8C5×#21312yes—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—44no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—82no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—121no—
365C2×C4C2×C5×#6711yescharacteristic
366C2×C4C2×C5×#6711yescharacteristic
367C2×C4C2×C5×#6711yescharacteristic
368C8—121no—
369C8—121no—
370C8—121no—
371C2×C3—81no—
372C2×C3—82no—
373C2×C3C5×#44711yescharacteristic
374C2×C3C5×#45211yescharacteristic
375C2×C3C5×#45511yescharacteristic
376C5#7192011yescharacteristic, direct product factor, Sylow
377C22—42no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22C5×#95311yescharacteristic
384C4—22no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—241no—
389C4C2×C5×#21311yescharacteristic
390C4C5×#93211yescharacteristic
391C4C5×#95011yescharacteristic
392C4C5×#95111yescharacteristic
393C3C5×#164111yescharacteristic, complemented, Sylow
394C2—81no—
395C2—82no—
396C2C5×#521711yescharacteristic
397C2C5×#523911yescharacteristic
398C2C5×#524211yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
Fitting, prime radicalC3×C5×#550C2
socleC22×C3×C5#120
hypercenterC5×#550D3
hypocenterC3C5×#1641
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#550

Complements

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

NH ≅ G/Ntype
2. C5×#5070C2semidirect
3. C5×#5031C2semidirect
4. C5×#5007C2semidirect
5. C5×#4544C2semidirect
6. C5×#4535C2semidirect
7. C5×D4⋊(C3⋊C8)C2semidirect
26. #71920C5direct (N × H)
60. #5070C2×C5semidirect
61. #5031C2×C5semidirect
62. #5007C2×C5semidirect
63. #4544C2×C5semidirect
64. #4535C2×C5semidirect
65. D4⋊(C3⋊C8)C2×C5semidirect
321. C3×C5#1641semidirect
376. C5#71920direct (N × H)
393. C3C5×#1641semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5502
C5×#50702
C5×#50312
C5×#50072
C5×#45442
C5×#45352
C5×D4⋊(C3⋊C8)2
C5×#16413
#719205