Finite Group Databasebeta

← C5×#70313 #14308902

Subgroups — C5×#70313 #14308902

Order 1920.

564 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5519C211yesmaximal, characteristic, complemented
2C3×C5×#418C211yesmaximal, characteristic
3C5×#5221C211yesmaximal, characteristic
4C5×#5215C211yesmaximal, characteristic
5C5×#4555C211yesmaximal, characteristic, complemented
6C5×#4554C211yesmaximal, characteristic, complemented
7C5×#4532C211yesmaximal, characteristic, complemented
8C5×#2027—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C5×#217—22no—
13C5×#926C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C5×#890—21no—
18C5×#888—21no—
19C5×#878—22no—
20C5×#870—21no—
21C5×#869—21no—
22C3×C5×#102—21no—
23C3×C5×#102—21no—
24C5×#832—21no—
25C5×#832—21no—
26#70313C511yesmaximal, characteristic, direct product factor, Hall
27C5×#544—31no—
28C5×#418—31no—
29C5×#418D311yescharacteristic
30C5×#390—31no—
31C5×#343—31no—
32C5×#339—31no—
33C5×#339—31no—
34C24×C3×C5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4Q812yescomplemented
41C22×C3×C4×C5C2311yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3D412yes—
44C2×C5×Dic6—22no—
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C5×#217—21no—
53C5×#217—44no—
54C5×C4⋊Dic3—22no—
55C5×C4⋊Dic3—21no—
56C5×C4⋊Dic3—21no—
57C5×C4⋊Dic3D411yescharacteristic
58C5×C4⋊Dic3D411yescharacteristic
59C5×Dic3⋊C4—22no—
60C5×Dic3⋊C4—22no—
61C4×C5×Dic3—21no—
62C4×C5×Dic3—21no—
63C4×C5×Dic3—21no—
64C5×#208—21no—
65C5×#208—21no—
66C2×C5×C3⋊C8—21no—
67#5519C2×C511yescharacteristic, complemented
68C3×#418C2×C511yescharacteristic
69#5221C2×C511yescharacteristic
70#5215C2×C511yescharacteristic
71#4555C2×C511yescharacteristic, complemented
72#4554C2×C511yescharacteristic, complemented
73#4532C2×C511yescharacteristic, complemented
74C22×C5×D4C2×D311yescharacteristic
75C2×C5×M16—31no—
76C2×C5×M16C2×D311yescharacteristic
77C5×C4⋊Q8—61no—
78C5×C4⋊Q8—61no—
79C5×#125—61no—
80C5×#125—61no—
81C5×C22⋊Q8—62no—
82C5×#117—31no—
83C5×#117C2×D311yescharacteristic
84C2×C5×C4⋊C4—31no—
85C2×C5×C22⋊C4—62no—
86C2×C42×C5—31no—
87C5×#102—21no—
88C5×#102—21no—
89C5×#102—61no—
90C5×#102—61no—
91#2027—31noSylow
92C23×C3×C5—22no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5C2×D411yescharacteristic
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C5×Dic3—22no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—42no—
117C5×Dic6—82no—
118C3×C5×C8—41no—
119C5×C3⋊C8—41no—
120C22×C3×D4C22×C511yescharacteristic
121C2×C3×M16C22×C511yescharacteristic
122C3×#117C22×C511yescharacteristic
123C2×#217—22no—
124#926C22×C511yescharacteristic
125C2×C4⋊Dic3C22×C511yescharacteristic
126C2×C4×Dic3C22×C511yescharacteristic
127C2×#208C22×C511yescharacteristic
128#890—21no—
129#888—21no—
130#878—22no—
131#870—21no—
132#869—21no—
133C3×#102—21no—
134C3×#102—21no—
135#832—21no—
136#832—21no—
137C24×C5—21no—
138C2×C5×Q8—62no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4Dic612yescomplemented
145C22×C4×C5—32no—
146C22×C4×C5—61no—
147C22×C4×C5C22×D311yescharacteristic
148C5×M16—21no—
149C5×M16—21no—
150C5×M16—61no—
151C5×M16—61no—
152C2×C5×C8—21no—
153C2×C5×C8—61no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—31no—
156C5×C4⋊C4—62no—
157C5×C4⋊C4—62no—
158C5×C4⋊C4—62no—
159C5×C4⋊C4—61no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4#6711yescharacteristic
162C5×C4⋊C4#6711yescharacteristic
163C5×C22⋊C4—21no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—124no—
166C42×C5—21no—
167C42×C5—61no—
168C42×C5—61no—
169C42×C5—61no—
170#544—31no—
171#418—31no—
172#418C5×D311yescharacteristic
173#390—31no—
174#343—31no—
175#339—31no—
176#339—31no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—44no—
180C22×C3×C5—42no—
181C22×C3×C5—82no—
182C22×C3×C5—81no—
183C22×C3×C5—81no—
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C22×C3×C5#12411yescharacteristic
187C3×C4×C5—41no—
188C3×C4×C5—41no—
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5#12411yescharacteristic
192C3×C4×C5#12411yescharacteristic
193C5×Dic3—42no—
194C5×Dic3—41no—
195C5×Dic3—42no—
196C5×Dic3—41no—
197C24×C3—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4C5×Q812yescomplemented
204C22×C3×C4C23×C511yescharacteristic
205C22×Dic3—21no—
206C22×Dic3C5×D412yes—
207C2×Dic6—22no—
208C3×M16—21no—
209C3×M16—21no—
210C2×C3×C8—21no—
211C3×C4⋊C4C5×D411yescharacteristic
212C3×C4⋊C4C5×D411yescharacteristic
213C3×C22⋊C4—21no—
214C3×C42—21no—
215#217—21no—
216#217—44no—
217C4⋊Dic3—22no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3C5×D411yescharacteristic
221C4⋊Dic3C5×D411yescharacteristic
222Dic3⋊C4—22no—
223Dic3⋊C4—22no—
224C4×Dic3—21no—
225C4×Dic3—21no—
226C4×Dic3—21no—
227#208—21no—
228#208—21no—
229C2×C3⋊C8—21no—
230C23×C5—22no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—41no—
234C23×C5—41no—
235C23×C5D3×D411yescharacteristic
236C5×Q8—242no—
237C5×D4—22no—
238C5×D4—22no—
239C5×D4—41no—
240C5×D4—41no—
241C2×C4×C5—21no—
242C2×C4×C5—21no—
243C2×C4×C5—62no—
244C2×C4×C5—61no—
245C2×C4×C5—61no—
246C2×C4×C5—62no—
247C2×C4×C5—121no—
248C2×C4×C5—121no—
249C2×C4×C5—122no—
250C2×C4×C5C2×Dic611yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23711yescharacteristic
254C2×C4×C5#23711yescharacteristic
255C2×C4×C5C2×#6711yescharacteristic
256C5×C8—41no—
257C5×C8—121no—
258C22×D4C2×C5×D311yescharacteristic
259C2×M16—31no—
260C2×M16C2×C5×D311yescharacteristic
261C4⋊Q8—61no—
262C4⋊Q8—61no—
263#125—61no—
264#125—61no—
265C22⋊Q8—62no—
266#117—31no—
267#117C2×C5×D311yescharacteristic
268C2×C4⋊C4—31no—
269C2×C22⋊C4—62no—
270C2×C42—31no—
271#102—21no—
272#102—21no—
273#102—61no—
274#102—61no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5—82no—
278C2×C3×C5#39311yescharacteristic
279C2×C3×C5#45311yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C23×C3—22no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3C2×C5×D411yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4C2×C5×D411yescharacteristic
294C2×C3×C4C2×C5×D411yescharacteristic
295C2×C3×C4C2×C5×Q811yescharacteristic
296C2×C3×C4C5×#4111yescharacteristic
297C2×C3×C4C5×#4111yescharacteristic
298C2×C3×C4C5×#4111yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—22no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—42no—
306Dic6—82no—
307C3×C8—41no—
308C3⋊C8—41no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—44no—
312C22×C5—42no—
313C22×C5—82no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5#87811yescharacteristic
317C22×C5#88511yescharacteristic
318C22×C5#93711yescharacteristic
319C4×C5—41no—
320C4×C5—41no—
321C4×C5—122no—
322C4×C5—122no—
323C4×C5—121no—
324C4×C5—121no—
325C4×C5#87811yescharacteristic
326C4×C5#88511yescharacteristic
327C4×C5#92411yescharacteristic
328C4×C5#93611yescharacteristic
329C24—21no—
330C2×Q8—62no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4C5×Dic612yescomplemented
337C22×C4—32no—
338C22×C4—61no—
339C22×C4C22×C5×D311yescharacteristic
340M16—21no—
341M16—21no—
342M16—61no—
343M16—61no—
344C2×C8—21no—
345C2×C8—61no—
346C4⋊C4—31no—
347C4⋊C4—31no—
348C4⋊C4—62no—
349C4⋊C4—62no—
350C4⋊C4—62no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4C5×#6711yescharacteristic
354C4⋊C4C5×#6711yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—61no—
357C22⋊C4—124no—
358C42—21no—
359C42—61no—
360C42—61no—
361C42—61no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—44no—
366C22×C3—42no—
367C22×C3—82no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3C5×#12011yescharacteristic
371C22×C3C5×C22⋊Q811yescharacteristic
372C22×C3C5×#12411yescharacteristic
373C3×C4—41no—
374C3×C4—41no—
375C3×C4C5×C22⋊Q811yescharacteristic
376C3×C4C5×C22⋊Q811yescharacteristic
377C3×C4C5×#12411yescharacteristic
378C3×C4C5×#12411yescharacteristic
379Dic3—42no—
380Dic3—41no—
381Dic3—42no—
382Dic3—41no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5—82no—
386C2×C5#494711yescharacteristic
387C2×C5#519811yescharacteristic
388C2×C5#520111yescharacteristic
389C23—22no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23C5×D3×D411yescharacteristic
395Q8—242no—
396D4—22no—
397D4—22no—
398D4—41no—
399D4—41no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—62no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—62no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—122no—
409C2×C4C2×C5×Dic611yescharacteristic
410C2×C4C5×#23511yescharacteristic
411C2×C4C5×D3×D411yescharacteristic
412C2×C4C5×#23711yescharacteristic
413C2×C4C5×#23711yescharacteristic
414C2×C4C2×C5×#6711yescharacteristic
415C8—41no—
416C8—121no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—82no—
420C2×C3C5×#39311yescharacteristic
421C2×C3C5×#45311yescharacteristic
422C2×C3C5×#45411yescharacteristic
423C5#7031311yescharacteristic, direct product factor, Sylow
424C22—21no—
425C22—21no—
426C22—44no—
427C22—42no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22C5×#87811yescharacteristic
432C22C5×#88511yescharacteristic
433C22C5×#93711yescharacteristic
434C4—41no—
435C4—41no—
436C4—122no—
437C4—122no—
438C4—121no—
439C4—121no—
440C4C5×#87811yescharacteristic
441C4C5×#88511yescharacteristic
442C4C5×#92411yescharacteristic
443C4C5×#93611yescharacteristic
444C3C5×#202711yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—82no—
448C2C5×#494711yescharacteristic
449C2C5×#519811yescharacteristic
450C2C5×#520111yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#418C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
hypercenterC5×#418D3
hypocenterC3C5×#2027
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#418

Complements

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

NH ≅ G/Ntype
1. C5×#5519C2semidirect
5. C5×#4555C2semidirect
6. C5×#4554C2semidirect
7. C5×#4532C2semidirect
26. #70313C5direct (N × H)
40. C2×C3×C5×D4Q8semidirect
67. #5519C2×C5semidirect
71. #4555C2×C5semidirect
72. #4554C2×C5semidirect
73. #4532C2×C5semidirect
144. C2×C5×D4Dic6semidirect
203. C2×C3×D4C5×Q8semidirect
336. C2×D4C5×Dic6semidirect
362. C3×C5#2027semidirect
423. C5#70313direct (N × H)
444. C3C5×#2027semidirect

Maximal subgroups

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

subgroupindex
C5×#55192
C3×C5×#4182
C5×#52212
C5×#52152
C5×#45552
C5×#45542
C5×#45322
C5×#20273
#703135