Finite Group Databasebeta

← C5×#69562 #14299784

Subgroups — C5×#69562 #14299784

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5504C211yesmaximal, characteristic
2C3×C5×#382C211yesmaximal, characteristic, complemented
3C5×#4966C211yesmaximal, characteristic
4C5×#4964C211yesmaximal, characteristic, complemented
5C2×C5×#805C211yesmaximal, characteristic
6C5×#4530C211yesmaximal, characteristic, complemented
7C5×#4523C211yesmaximal, characteristic, complemented
8C5×#1860—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C4×C5×#67—22no—
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C5×#893—21no—
18C5×#892—21no—
19C5×D3×C4⋊C4—21no—
20C5×#887—21no—
21C3×C5×#95—22no—
22C5×#810—21no—
23C5×#809—21no—
24C5×#808—21no—
25C5×#807—21no—
26C5×#805C414yescomplemented
27#69562C511yesmaximal, characteristic, direct product factor, Hall
28C5×#520—31no—
29C5×#428—31no—
30C2×C5×#104—31no—
31C5×#417—31no—
32C5×#382D311yescharacteristic, complemented
33C5×#343—31no—
34C5×#339—31no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C2×C5×#67—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235C2×C412yes—
43C5×#235Q812yes—
44C2×C5×D12D411yescharacteristic
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3—22no—
47C2×C5×Dic6D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C42×C5—21no—
53C3×C42×C5C2×C412yescomplemented
54C5×#217—21no—
55C5×(C2×D3)⋊C4—22no—
56C5×C4⋊Dic3D411yescharacteristic
57C5×C4⋊Dic3D411yescharacteristic
58C5×Dic3⋊C4—22no—
59C4×C5×Dic3—22no—
60C4×C5×Dic3—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208—21no—
64C5×#208C2×C412yescomplemented
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67#5504C2×C511yescharacteristic
68C3×#382C2×C511yescharacteristic, complemented
69#4966C2×C511yescharacteristic
70#4964C2×C511yescharacteristic, complemented
71C2×#805C2×C511yescharacteristic
72#4530C2×C511yescharacteristic, complemented
73#4523C2×C511yescharacteristic, complemented
74C2×C5×#41—31no—
75C2×C5×M16—31no—
76C2×C5×M16—31no—
77C4×C5×Q8—61no—
78C4×C5×D4—61no—
79C4×C5×D4—62no—
80C5×#117—31no—
81C5×#117—61no—
82C2×C5×C4⋊C4—61no—
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×C42×C5C2×D311yescharacteristic
86C5×#107—61no—
87C5×#106—61no—
88C5×#104—34no—
89C5×#103—61no—
90C5×#102—61no—
91C5×#95—22no—
92#1860—31noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×C5×D3—21no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C5×#67—22no—
109C5×#67—22no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C5×D12—21no—
114C5×D12C4⋊C412yes—
115C4×C5×D3—22no—
116C4×C5×D3—22no—
117C4×C5×D3—82no—
118C5×Dic6—21no—
119C5×Dic6C4⋊C412yes—
120C5×C3⋊C8—22no—
121C5×C3⋊C8—41no—
122C2×#235C22×C511yescharacteristic
123C2×C3×C4⋊C4C22×C511yescharacteristic
124C2×C3×C4⋊C4C22×C511yescharacteristic
125C2×C3×C42C22×C511yescharacteristic
126C4×#67—22no—
127#926C22×C511yescharacteristic
128C2×#208C22×C511yescharacteristic
129C2×#208C22×C511yescharacteristic
130#893—21no—
131#892—21no—
132D3×C4⋊C4—21no—
133#887—21no—
134C3×#95—22no—
135#810—21no—
136#809—21no—
137#808—21no—
138#807—21no—
139#805C4×C514yescomplemented
140C5×#41—32no—
141C5×#41—32no—
142C5×#41—61no—
143C5×#41—61no—
144C2×C5×Q8—31no—
145C2×C5×D4—31no—
146C2×C5×D4—61no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—62no—
150C22×C4×C5—61no—
151C22×C4×C5#6712yes—
152C22×C4×C5C22×D311yescharacteristic
153C5×M16—32no—
154C5×M16—61no—
155C5×M16—61no—
156C5×M16—61no—
157C2×C5×C8—61no—
158C2×C5×C8—61no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—31no—
164C5×C4⋊C4—31no—
165C5×C4⋊C4—62no—
166C5×C22⋊C4—62no—
167C5×C22⋊C4—61no—
168C42×C5—21no—
169C42×C5—62no—
170C42×C5—61no—
171C42×C5C4×D312yescomplemented
172#520—31no—
173#428—31no—
174C2×#104—31no—
175#417—31no—
176#382C5×D311yescharacteristic, complemented
177#343—31no—
178#339—31no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5C4×D411yescharacteristic
182C22×C3×C5#12011yescharacteristic
183C22×C3×C5C22⋊Q811yescharacteristic
184C2×C5×D3—22no—
185C2×C5×D3—41no—
186C2×C5×D3—41no—
187C3×C4×C5—42no—
188C3×C4×C5—42no—
189C3×C4×C5—81no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5#12311yescharacteristic
194C5×Dic3—22no—
195C5×Dic3—41no—
196C5×Dic3—41no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4C5×D412yes—
200C22×C3×C4C23×C511yescharacteristic
201C2×#67—21no—
202#235—21no—
203#235—21no—
204#235C2×C4×C512yes—
205#235C5×Q812yes—
206C2×D12C5×D411yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—22no—
209C2×Dic6C5×D411yescharacteristic
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C42—21no—
215C3×C42C2×C4×C512yescomplemented
216#217—21no—
217(C2×D3)⋊C4—22no—
218C4⋊Dic3C5×D411yescharacteristic
219C4⋊Dic3C5×D411yescharacteristic
220Dic3⋊C4—22no—
221C4×Dic3—22no—
222C4×Dic3—21no—
223#208—21no—
224#208—21no—
225#208—21no—
226#208C2×C4×C512yescomplemented
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C23×C5—61no—
230C23×C5C2×#6711yescharacteristic
231C5×Q8—32no—
232C5×Q8—61no—
233C5×D4—32no—
234C5×D4—62no—
235C5×D4—62no—
236C5×D4—61no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—41no—
244C2×C4×C5—61no—
245C2×C4×C5—62no—
246C2×C4×C5—62no—
247C2×C4×C5—61no—
248C2×C4×C5—61no—
249C2×C4×C5—242no—
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×Q811yescharacteristic
255C2×C4×C5#23911yescharacteristic
256C5×C8—62no—
257C5×C8—121no—
258C2×#41—31no—
259C2×M16—31no—
260C2×M16—31no—
261C4×Q8—61no—
262C4×D4—61no—
263C4×D4—62no—
264#117—31no—
265#117—61no—
266C2×C4⋊C4—61no—
267C2×C4⋊C4C2×C5×D311yescharacteristic
268C2×C4⋊C4C2×C5×D311yescharacteristic
269C2×C42C2×C5×D311yescharacteristic
270#107—61no—
271#106—61no—
272#104—34no—
273#103—61no—
274#102—61no—
275#95—22no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#45411yescharacteristic
280C2×C3×C5#45511yescharacteristic
281C5×D3—42no—
282C23×C3C2×C5×D411yescharacteristic
283C22×D3—21no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4C22×C4×C511yescharacteristic
292C2×C3×C4C2×C5×D411yescharacteristic
293C2×C3×C4C2×C5×D411yescharacteristic
294C2×C3×C4C2×C5×Q811yescharacteristic
295C2×C3×C4C5×#4111yescharacteristic
296C2×C3×C4C5×#4111yescharacteristic
297#67—22no—
298#67—22no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302D12—21no—
303D12C5×C4⋊C412yes—
304C4×D3—22no—
305C4×D3—22no—
306C4×D3—82no—
307Dic6—21no—
308Dic6C5×C4⋊C412yes—
309C3⋊C8—22no—
310C3⋊C8—41no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—62no—
314C22×C5—121no—
315C22×C5—121no—
316C22×C5C4×#6711yescharacteristic
317C22×C5#93711yescharacteristic
318C22×C5#94611yescharacteristic
319C4×C5—42no—
320C4×C5—42no—
321C4×C5—62no—
322C4×C5—81no—
323C4×C5—121no—
324C4×C5—121no—
325C4×C5D3×C4⋊C411yescharacteristic
326C4×C5#89311yescharacteristic
327C4×C5#89411yescharacteristic
328C4×C5#89611yescharacteristic
329#41—32no—
330#41—32no—
331#41—61no—
332#41—61no—
333C2×Q8—31no—
334C2×D4—31no—
335C2×D4—61no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—62no—
339C22×C4—61no—
340C22×C4C5×#6712yes—
341C22×C4C22×C5×D311yescharacteristic
342M16—32no—
343M16—61no—
344M16—61no—
345M16—61no—
346C2×C8—61no—
347C2×C8—61no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—31no—
353C4⋊C4—31no—
354C4⋊C4—62no—
355C22⋊C4—62no—
356C22⋊C4—61no—
357C42—21no—
358C42—62no—
359C42—61no—
360C42C4×C5×D312yescomplemented
361C3×C5#186011yescharacteristic, complemented, Hall
362C22×C3—21no—
363C22×C3—21no—
364C22×C3C4×C5×D411yescharacteristic
365C22×C3C5×#12011yescharacteristic
366C22×C3C5×C22⋊Q811yescharacteristic
367C2×D3—22no—
368C2×D3—41no—
369C2×D3—41no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—81no—
373C3×C4C2×C5×C4⋊C411yescharacteristic
374C3×C4C4×C5×D411yescharacteristic
375C3×C4C5×C22⋊Q811yescharacteristic
376C3×C4C5×#12311yescharacteristic
377Dic3—22no—
378Dic3—41no—
379Dic3—41no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—122no—
383C2×C5#498911yescharacteristic
384C2×C5#506111yescharacteristic
385C2×C5#506211yescharacteristic
386C23—61no—
387C23C2×C5×#6711yescharacteristic
388Q8—32no—
389Q8—61no—
390D4—32no—
391D4—62no—
392D4—62no—
393D4—61no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—61no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—242no—
407C2×C4C2×C4×C5×D311yescharacteristic
408C2×C4C5×#23511yescharacteristic
409C2×C4C5×D3×D411yescharacteristic
410C2×C4C5×D3×D411yescharacteristic
411C2×C4C5×D3×Q811yescharacteristic
412C2×C4C5×#23911yescharacteristic
413C8—62no—
414C8—121no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3C5×#38511yescharacteristic
418C2×C3C5×#45411yescharacteristic
419C2×C3C5×#45511yescharacteristic
420D3—42no—
421C5#6956211yescharacteristic, direct product factor, Sylow
422C22—21no—
423C22—21no—
424C22—62no—
425C22—121no—
426C22—121no—
427C22C4×C5×#6711yescharacteristic
428C22C5×#93711yescharacteristic
429C22C5×#94611yescharacteristic
430C4—42no—
431C4—42no—
432C4—62no—
433C4—81no—
434C4—121no—
435C4—121no—
436C4C5×D3×C4⋊C411yescharacteristic
437C4C5×#89311yescharacteristic
438C4C5×#89411yescharacteristic
439C4C5×#89611yescharacteristic
440C3C5×#186011yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—122no—
444C2C5×#498911yescharacteristic
445C2C5×#506111yescharacteristic
446C2C5×#506211yescharacteristic
subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#382C2
socleC22×C3×C5#120
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#382D3
hypocenterC3C5×#1860
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#382

Complements

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

NH ≅ G/Ntype
2. C3×C5×#382C2semidirect
4. C5×#4964C2semidirect
6. C5×#4530C2semidirect
7. C5×#4523C2semidirect
26. C5×#805C4semidirect
27. #69562C5direct (N × H)
32. C5×#382D3semidirect
53. C3×C42×C5C2×C4semidirect
64. C5×#208C2×C4semidirect
68. C3×#382C2×C5semidirect
70. #4964C2×C5semidirect
72. #4530C2×C5semidirect
73. #4523C2×C5semidirect
139. #805C4×C5semidirect
171. C42×C5C4×D3semidirect
176. #382C5×D3semidirect
215. C3×C42C2×C4×C5semidirect
226. #208C2×C4×C5semidirect
360. C42C4×C5×D3semidirect
361. C3×C5#1860semidirect
421. C5#69562direct (N × H)
440. C3C5×#1860semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
C3×C5×#3822
C5×#49662
C5×#49642
C2×C5×#8052
C5×#45302
C5×#45232
C5×#18603
#695625