Finite Group Databasebeta

← C5×#71947 #14316817

Subgroups — C5×#71947 #14316817

Order 1920.

520 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#560C211yesmaximal, characteristic, complemented
2C5×#5077C211yesmaximal, characteristic, complemented
3C5×#5053C211yesmaximal, characteristic, complemented
4C5×#5032C211yesmaximal, characteristic, complemented
5C5×#4545C211yesmaximal, characteristic, complemented
6C5×#4539C211yesmaximal, characteristic, complemented
7C5×#4536C211yesmaximal, characteristic, complemented
8C5×#2200—31nomaximal, Hall
9C5×#1004C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C3×C5×#126—21no—
12C3×C5×#123—21no—
13C3×C5×#123C2211yescharacteristic
14C3×C5×#121—21no—
15C3×C5×#121—21no—
16C3×C5×#121—21no—
17C3×C5×#120—21no—
18C3×C5×#120C2211yescharacteristic
19C5×#953—21no—
20C5×#932—21no—
21C5×#929—21no—
22C5×#834C2211yescharacteristic
23C5×#834C2211yescharacteristic
24C5×#833C2211yescharacteristic
25C5×#806—21no—
26C5×#806—21no—
27C5×#805—21no—
28#71947C511yesmaximal, characteristic, direct product factor, Hall
29C5×#560D311yescharacteristic, complemented
30C5×#458—31no—
31C5×B(4,𝔽2)—31no—
32C5×#453—31no—
33C5×#353—31no—
34C5×#352—31no—
35C5×AΣL(1,𝔽16)—31no—
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4D411yescharacteristic, complemented
43C2×C3×C5×D4C2311yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5D411yescharacteristic, complemented
46C2×C5×#67—21no—
47C2×C5×#67—21no—
48C2×C5×#67—41no—
49C5×#237—41no—
50C5×D3×D4—41no—
51C5×#235—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4D411yescharacteristic
61C3×C5×C22⋊C4D411yescharacteristic, complemented
62C3×C42×C5D411yescharacteristic, complemented
63C5×#217—21no—
64C5×#217—21no—
65C5×#217—41no—
66C5×#214—41no—
67C5×#213—41no—
68C5×(C2×D3)⋊C4—41no—
69C5×Dic3⋊C4—41no—
70C5×#208—21no—
71C3×#560C2×C511yescharacteristic, complemented
72#5077C2×C511yescharacteristic, complemented
73#5053C2×C511yescharacteristic, complemented
74#5032C2×C511yescharacteristic, complemented
75#4545C2×C511yescharacteristic, complemented
76#4539C2×C511yescharacteristic, complemented
77#4536C2×C511yescharacteristic, complemented
78C5×H(5,𝔽2)—31no—
79C5×AGL(1,ℤ/8)—61no—
80C5×#127C2×D311yescharacteristic
81C5×#126—21no—
82C5×#123—21no—
83C5×#123—61no—
84C5×#123C2×D311yescharacteristic
85C5×#121—21no—
86C5×#121—21no—
87C5×#121—21no—
88C5×#120—21no—
89C5×#120—61no—
90C5×#120C2×D311yescharacteristic
91C5×#104—61no—
92C5×#100—31no—
93C5×#99—31no—
94C5×#99—31no—
95C5×#99—61no—
96C5×#99—61no—
97#2200—31noSylow
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5—41no—
101C23×C3×C5—81no—
102C23×C3×C5C2×D411yescharacteristic
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3—21no—
105C22×C5×D3—21no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C3×C5×D4—81no—
109C3×C5×D4—81no—
110C3×C5×D4—81no—
111C3×C5×D4—81no—
112C3×C5×D4—81no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—81no—
119C2×C3×C4×C5C2×D411yescharacteristic
120C5×#67—41no—
121C5×#67—41no—
122C5×#67—41no—
123C5×#67—82no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—41no—
127C2×C5×Dic3—41no—
128C5×D12—21no—
129C4×C5×D3—41no—
130C5×Dic6—21no—
131C5×C3⋊C8—41no—
132#1004C22×C511yescharacteristic
133C3×#127C22×C511yescharacteristic
134C3×#126—21no—
135C3×#123—21no—
136C3×#123C22×C511yescharacteristic
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#120—21no—
141C3×#120C22×C511yescharacteristic
142#953—21no—
143#932—21no—
144#929—21no—
145#834C22×C511yescharacteristic
146#834C22×C511yescharacteristic
147#833C22×C511yescharacteristic
148#806—21no—
149#806—21no—
150#805—21no—
151C24×C5#6711yescharacteristic
152C5×#41—61no—
153C5×#41—121no—
154C2×C5×D4—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—61no—
160C2×C5×D4—61no—
161C2×C5×D4—121no—
162C2×C5×D4—121no—
163C2×C5×D4#6711yescharacteristic, complemented
164C2×C5×D4C22×D311yescharacteristic
165C22×C4×C5—21no—
166C22×C4×C5#6711yescharacteristic, complemented
167C5×SD16—121no—
168C5×D8—121no—
169C5×M16—61no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—121no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—21no—
177C5×C22⋊C4—21no—
178C5×C22⋊C4—21no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181C5×C22⋊C4—121no—
182C5×C22⋊C4—121no—
183C5×C22⋊C4#6711yescharacteristic
184C5×C22⋊C4#6711yescharacteristic, complemented
185C42×C5#6711yescharacteristic, complemented
186#560C5×D311yescharacteristic, complemented
187#458—31no—
188B(4,𝔽2)—31no—
189#453—31no—
190#353—31no—
191#352—31no—
192AΣL(1,𝔽16)—31no—
193C22×C3×C5—21no—
194C22×C3×C5—21no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—42no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5—81no—
205C22×C3×C5#12011yescharacteristic
206C2×C5×D3—41no—
207C2×C5×D3—81no—
208C2×C5×D3—81no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—41no—
212C3×C4×C5—41no—
213C3×C4×C5—41no—
214C5×Dic3—41no—
215C5×Dic3—81no—
216C5×Dic3—81no—
217C24×C3C5×D411yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4C5×D411yescharacteristic, complemented
224C2×C3×D4C23×C511yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4C5×D411yescharacteristic, complemented
227C2×#67—21no—
228C2×#67—21no—
229C2×#67—41no—
230#237—41no—
231D3×D4—41no—
232#235—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4C5×D411yescharacteristic
242C3×C22⋊C4C5×D411yescharacteristic, complemented
243C3×C42C5×D411yescharacteristic, complemented
244#217—21no—
245#217—21no—
246#217—41no—
247#214—41no—
248#213—41no—
249(C2×D3)⋊C4—41no—
250Dic3⋊C4—41no—
251#208—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—41no—
255C23×C5—61no—
256C23×C5—61no—
257C23×C5—81no—
258C23×C5C2×#6711yescharacteristic
259C23×C5C2×#6711yescharacteristic
260C5×Q8—61no—
261C5×D4—41no—
262C5×D4—41no—
263C5×D4—61no—
264C5×D4—81no—
265C5×D4—81no—
266C5×D4—81no—
267C5×D4—81no—
268C5×D4—81no—
269C5×D4—121no—
270C5×D4—121no—
271C5×D4—121no—
272C5×D4—242no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—41no—
278C2×C4×C5—61no—
279C2×C4×C5—61no—
280C2×C4×C5—81no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5C2×#6711yescharacteristic
285C5×C8—121no—
286H(5,𝔽2)—31no—
287AGL(1,ℤ/8)—61no—
288#127C2×C5×D311yescharacteristic
289#126—21no—
290#123—21no—
291#123—61no—
292#123C2×C5×D311yescharacteristic
293#121—21no—
294#121—21no—
295#121—21no—
296#120—21no—
297#120—61no—
298#120C2×C5×D311yescharacteristic
299#104—61no—
300#100—31no—
301#99—31no—
302#99—31no—
303#99—61no—
304#99—61no—
305C2×C3×C5—21no—
306C2×C3×C5—41no—
307C2×C3×C5—41no—
308C2×C3×C5—81no—
309C2×C3×C5—81no—
310C2×C3×C5B(4,𝔽2)11yescharacteristic
311C5×D3—81no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—41no—
315C23×C3—81no—
316C23×C3C2×C5×D411yescharacteristic
317C23×C3C2×C5×D411yescharacteristic
318C22×D3—21no—
319C22×D3—21no—
320C3×D4—41no—
321C3×D4—41no—
322C3×D4—81no—
323C3×D4—81no—
324C3×D4—81no—
325C3×D4—81no—
326C3×D4—81no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—41no—
332C2×C3×C4—81no—
333C2×C3×C4C2×C5×D411yescharacteristic
334#67—41no—
335#67—41no—
336#67—41no—
337#67—82no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342D12—21no—
343C4×D3—41no—
344Dic6—21no—
345C3⋊C8—41no—
346C22×C5—21no—
347C22×C5—21no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5—41no—
352C22×C5—41no—
353C22×C5—41no—
354C22×C5—42no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—81no—
358C22×C5—121no—
359C22×C5—241no—
360C22×C5—241no—
361C22×C5#95311yescharacteristic
362C4×C5—21no—
363C4×C5—41no—
364C4×C5—41no—
365C4×C5—41no—
366C4×C5—41no—
367C4×C5—121no—
368C4×C5—241no—
369C4×C5—241no—
370C24C5×#6711yescharacteristic
371#41—61no—
372#41—121no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4—121no—
381C2×D4—121no—
382C2×D4C5×#6711yescharacteristic, complemented
383C2×D4C22×C5×D311yescharacteristic
384C22×C4—21no—
385C22×C4C5×#6711yescharacteristic, complemented
386SD16—121no—
387D8—121no—
388M16—61no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—121no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—61no—
399C22⋊C4—61no—
400C22⋊C4—121no—
401C22⋊C4—121no—
402C22⋊C4C5×#6711yescharacteristic
403C22⋊C4C5×#6711yescharacteristic, complemented
404C42C5×#6711yescharacteristic, complemented
405C3×C5#220011yescharacteristic, complemented, Hall
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—81no—
418C22×C3C5×#12011yescharacteristic
419C2×D3—41no—
420C2×D3—81no—
421C2×D3—81no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—41no—
427Dic3—41no—
428Dic3—81no—
429Dic3—81no—
430C2×C5—21no—
431C2×C5—41no—
432C2×C5—41no—
433C2×C5—81no—
434C2×C5—81no—
435C2×C5—241no—
436C2×C5#524411yescharacteristic
437C23—21no—
438C23—21no—
439C23—41no—
440C23—61no—
441C23—61no—
442C23—81no—
443C23C2×C5×#6711yescharacteristic
444C23C2×C5×#6711yescharacteristic
445Q8—61no—
446D4—41no—
447D4—41no—
448D4—61no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—81no—
454D4—121no—
455D4—121no—
456D4—121no—
457D4—242no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—81no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4C2×C5×#6711yescharacteristic
470C8—121no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—81no—
475C2×C3—81no—
476C2×C3C5×B(4,𝔽2)11yescharacteristic
477D3—81no—
478C5#7194711yescharacteristic, direct product factor, Sylow
479C22—21no—
480C22—21no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22—81no—
491C22—121no—
492C22—241no—
493C22—241no—
494C22C5×#95311yescharacteristic
495C4—21no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—121no—
501C4—241no—
502C4—241no—
503C3C5×#220011yescharacteristic, complemented, Sylow
504C2—21no—
505C2—41no—
506C2—41no—
507C2—81no—
508C2—81no—
509C2—241no—
510C2C5×#524411yescharacteristic
subgroupG/H
centerC2×C5#5244
commutator, cosocleC2×C3×D4C23×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×#560C2
socleC2×C3×C5B(4,𝔽2)
hypercenterC5×#560D3
hypocenterC3C5×#2200
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C5×D4 ◁ C5×#560

Complements

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

NH ≅ G/Ntype
1. C3×C5×#560C2semidirect
2. C5×#5077C2semidirect
3. C5×#5053C2semidirect
4. C5×#5032C2semidirect
5. C5×#4545C2semidirect
6. C5×#4539C2semidirect
7. C5×#4536C2semidirect
28. #71947C5direct (N × H)
29. C5×#560D3semidirect
42. C2×C3×C5×D4D4semidirect
45. C22×C3×C4×C5D4semidirect
61. C3×C5×C22⋊C4D4semidirect
62. C3×C42×C5D4semidirect
71. C3×#560C2×C5semidirect
72. #5077C2×C5semidirect
73. #5053C2×C5semidirect
74. #5032C2×C5semidirect
75. #4545C2×C5semidirect
76. #4539C2×C5semidirect
77. #4536C2×C5semidirect
163. C2×C5×D4#67semidirect
166. C22×C4×C5#67semidirect
184. C5×C22⋊C4#67semidirect
185. C42×C5#67semidirect
186. #560C5×D3semidirect
223. C2×C3×D4C5×D4semidirect
226. C22×C3×C4C5×D4semidirect
242. C3×C22⋊C4C5×D4semidirect
243. C3×C42C5×D4semidirect
382. C2×D4C5×#67semidirect
385. C22×C4C5×#67semidirect
403. C22⋊C4C5×#67semidirect
404. C42C5×#67semidirect
405. C3×C5#2200semidirect
478. C5#71947direct (N × H)
503. C3C5×#2200semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5602
C5×#50772
C5×#50532
C5×#50322
C5×#45452
C5×#45392
C5×#45362
C5×#22003
#719475