Finite Group Databasebeta

← C5×#69133 #14316823

Subgroups — C5×#69133 #14316823

Order 1920.

520 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C5×#5595C211yesmaximal, characteristic, complemented
2C5×#5032C211yesmaximal, characteristic, complemented
3C5×#4747C211yesmaximal, characteristic, complemented
4C5×#4742C211yesmaximal, characteristic, complemented
5C3×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
6C5×#4476C211yesmaximal, characteristic, complemented
7C5×#4474C211yesmaximal, characteristic, complemented
8C5×#2200—31nomaximal, Hall
9C5×#1004C2211yescharacteristic
10C3×C5×#120C2211yescharacteristic
11C5×#953—21no—
12C5×#953—21no—
13C5×#940C2211yescharacteristic
14C5×#939—21no—
15C5×#938—21no—
16C5×#935C2211yescharacteristic
17C5×#908—21no—
18C5×#886—21no—
19C5×#884—21no—
20C5×#883—21no—
21C5×#879—21no—
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#825—21no—
26C5×#806—21no—
27C5×#806—21no—
28#69133C511yesmaximal, characteristic, direct product factor, Hall
29C5×#560—31no—
30C5×#458—31no—
31C5×B(4,𝔽2)—31no—
32C5×#453—31no—
33C5×#353—31no—
34C5×#352—31no—
35C5×AΣL(1,𝔽16)D311yescharacteristic, complemented
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2311yescharacteristic
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C2×C5×#67—41no—
46C22×C5×Dic3D411yescharacteristic, complemented
47C5×#237—41no—
48C5×D3×D4—41no—
49C5×#235—21no—
50C2×C5×D12D411yescharacteristic, complemented
51C2×C4×C5×D3—21no—
52C3×C5×M16—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4D411yescharacteristic
56C5×#217—21no—
57C5×#217—21no—
58C5×#217—21no—
59C5×#217—21no—
60C5×#217—41no—
61C5×#217D411yescharacteristic, complemented
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—41no—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3—41no—
66C5×Dic3⋊C4—21no—
67C5×Dic3⋊C4—21no—
68C4×C5×Dic3D411yescharacteristic, complemented
69C5×D24—41no—
70C5×#204—41no—
71#5595C2×C511yescharacteristic, complemented
72#5032C2×C511yescharacteristic, complemented
73#4747C2×C511yescharacteristic, complemented
74#4742C2×C511yescharacteristic, complemented
75C3×AΣL(1,𝔽16)C2×C511yescharacteristic, complemented
76#4476C2×C511yescharacteristic, complemented
77#4474C2×C511yescharacteristic, complemented
78C5×H(5,𝔽2)—31no—
79C5×AGL(1,ℤ/8)—61no—
80C5×#127—31no—
81C5×#126—61no—
82C5×#123—31no—
83C5×#123—61no—
84C5×#123—61no—
85C5×#121—61no—
86C5×#121—61no—
87C5×#121—61no—
88C5×#120—61no—
89C5×#120—61no—
90C5×#120C2×D311yescharacteristic
91C5×#104—61no—
92C5×#100C2×D311yescharacteristic
93C5×#99—31no—
94C5×#99—61no—
95C5×#99—61no—
96C5×#99C2×D311yescharacteristic
97#2200—31noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—81no—
101C23×C3×C5C2×D411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—21no—
106C3×C5×D4—41no—
107C3×C5×D4—81no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C5×#67—41no—
112C5×#67—41no—
113C5×#67—41no—
114C5×#67—81no—
115C5×#67—81no—
116C5×#67—81no—
117C5×#67—81no—
118C5×#67—82no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C5×D12—21no—
127C5×D12—41no—
128C4×C5×D3—41no—
129C4×C5×D3—81no—
130C5×Dic6—21no—
131C3×C5×C8—41no—
132#1004C22×C511yescharacteristic
133C3×#120C22×C511yescharacteristic
134#953—21no—
135#953—21no—
136#940C22×C511yescharacteristic
137#939—21no—
138#938—21no—
139#935C22×C511yescharacteristic
140#908—21no—
141#886—21no—
142#884—21no—
143#883—21no—
144#879—21no—
145C3×#100C22×C511yescharacteristic
146C3×#99C22×C511yescharacteristic
147#834C22×C511yescharacteristic
148#825—21no—
149#806—21no—
150#806—21no—
151C24×C5D1211yescharacteristic
152C5×#41—61no—
153C5×#41—121no—
154C2×C5×D4—21no—
155C2×C5×D4—31no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C2×C5×D4—61no—
159C2×C5×D4—61no—
160C2×C5×D4—61no—
161C2×C5×D4—61no—
162C2×C5×D4—121no—
163C2×C5×D4—121no—
164C2×C5×D4C22×D311yescharacteristic
165C22×C4×C5—31no—
166C22×C4×C5—61no—
167C5×SD16—121no—
168C5×D8—121no—
169C5×M16—21no—
170C5×C4⋊C4—61no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4—61no—
173C5×C4⋊C4—121no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—31no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181C5×C22⋊C4—61no—
182C5×C22⋊C4—121no—
183C5×C22⋊C4—121no—
184C5×C22⋊C4D1211yescharacteristic
185C42×C5—31no—
186#560—31no—
187#458—31no—
188B(4,𝔽2)—31no—
189#453—31no—
190#353—31no—
191#352—31no—
192AΣL(1,𝔽16)C5×D311yescharacteristic, complemented
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—42no—
200C22×C3×C5—41no—
201C22×C3×C5—81no—
202C22×C3×C5#12011yescharacteristic
203C2×C5×D3—41no—
204C2×C5×D3—41no—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—81no—
208C2×C5×D3—81no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—81no—
212C5×Dic3—41no—
213C5×Dic3—41no—
214C5×Dic3—41no—
215C5×Dic3—41no—
216C5×Dic3—81no—
217C24×C3C5×D411yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4C23×C511yescharacteristic
220C2×#67—21no—
221C2×#67—21no—
222C2×#67—21no—
223C2×#67—21no—
224C2×#67—21no—
225C2×#67—21no—
226C2×#67—41no—
227C22×Dic3C5×D411yescharacteristic, complemented
228#237—41no—
229D3×D4—41no—
230#235—21no—
231C2×D12C5×D411yescharacteristic, complemented
232C2×C4×D3—21no—
233C3×M16—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4C5×D411yescharacteristic
237#217—21no—
238#217—21no—
239#217—21no—
240#217—21no—
241#217—41no—
242#217C5×D411yescharacteristic, complemented
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—41no—
245C4⋊Dic3—21no—
246C4⋊Dic3—41no—
247Dic3⋊C4—21no—
248Dic3⋊C4—21no—
249C4×Dic3C5×D411yescharacteristic, complemented
250D24—41no—
251#204—41no—
252C23×C5—21no—
253C23×C5—41no—
254C23×C5—61no—
255C23×C5—61no—
256C23×C5—61no—
257C23×C5—81no—
258C23×C5C2×D1211yescharacteristic
259C23×C5D3×D411yescharacteristic
260C5×Q8—61no—
261C5×D4—41no—
262C5×D4—61no—
263C5×D4—81no—
264C5×D4—121no—
265C5×D4—121no—
266C5×D4—121no—
267C5×D4—121no—
268C5×D4—241no—
269C5×D4—241no—
270C5×D4—241no—
271C5×D4—241no—
272C5×D4—242no—
273C2×C4×C5—21no—
274C2×C4×C5—41no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5—61no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5—241no—
284C2×C4×C5D3×D411yescharacteristic
285C5×C8—41no—
286H(5,𝔽2)—31no—
287AGL(1,ℤ/8)—61no—
288#127—31no—
289#126—61no—
290#123—31no—
291#123—61no—
292#123—61no—
293#121—61no—
294#121—61no—
295#121—61no—
296#120—61no—
297#120—61no—
298#120C2×C5×D311yescharacteristic
299#104—61no—
300#100C2×C5×D311yescharacteristic
301#99—31no—
302#99—61no—
303#99—61no—
304#99C2×C5×D311yescharacteristic
305C2×C3×C5—21no—
306C2×C3×C5—41no—
307C2×C3×C5—41no—
308C2×C3×C5—81no—
309C2×C3×C5B(4,𝔽2)11yescharacteristic
310C5×D3—81no—
311C5×D3—81no—
312C23×C3—21no—
313C23×C3—41no—
314C23×C3—81no—
315C23×C3C2×C5×D411yescharacteristic
316C23×C3C2×C5×D411yescharacteristic
317C22×D3—21no—
318C22×D3—21no—
319C22×D3—21no—
320C3×D4—41no—
321C3×D4—81no—
322C2×C3×C4—21no—
323C2×C3×C4—41no—
324C2×C3×C4C2×C5×D411yescharacteristic
325#67—41no—
326#67—41no—
327#67—41no—
328#67—81no—
329#67—81no—
330#67—81no—
331#67—81no—
332#67—82no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340D12—21no—
341D12—41no—
342C4×D3—41no—
343C4×D3—81no—
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—42no—
353C22×C5—41no—
354C22×C5—81no—
355C22×C5—121no—
356C22×C5—121no—
357C22×C5—121no—
358C22×C5—121no—
359C22×C5—241no—
360C22×C5—241no—
361C22×C5#88211yescharacteristic
362C4×C5—21no—
363C4×C5—41no—
364C4×C5—81no—
365C4×C5—121no—
366C4×C5—121no—
367C4×C5—121no—
368C4×C5—121no—
369C4×C5—241no—
370C24C5×D1211yescharacteristic
371#41—61no—
372#41—121no—
373C2×D4—21no—
374C2×D4—31no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4—61no—
381C2×D4—121no—
382C2×D4—121no—
383C2×D4C22×C5×D311yescharacteristic
384C22×C4—31no—
385C22×C4—61no—
386SD16—121no—
387D8—121no—
388M16—21no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—121no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—31no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—61no—
399C22⋊C4—61no—
400C22⋊C4—61no—
401C22⋊C4—121no—
402C22⋊C4—121no—
403C22⋊C4C5×D1211yescharacteristic
404C42—31no—
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—42no—
413C22×C3—41no—
414C22×C3—81no—
415C22×C3C5×#12011yescharacteristic
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—81no—
421C2×D3—81no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—81no—
425Dic3—41no—
426Dic3—41no—
427Dic3—41no—
428Dic3—41no—
429Dic3—81no—
430C2×C5—21no—
431C2×C5—41no—
432C2×C5—41no—
433C2×C5—81no—
434C2×C5—241no—
435C2×C5—241no—
436C2×C5#474111yescharacteristic
437C23—21no—
438C23—41no—
439C23—61no—
440C23—61no—
441C23—61no—
442C23—81no—
443C23C2×C5×D1211yescharacteristic
444C23C5×D3×D411yescharacteristic
445Q8—61no—
446D4—41no—
447D4—61no—
448D4—81no—
449D4—121no—
450D4—121no—
451D4—121no—
452D4—121no—
453D4—241no—
454D4—241no—
455D4—241no—
456D4—241no—
457D4—242no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—241no—
469C2×C4C5×D3×D411yescharacteristic
470C8—41no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—81no—
475C2×C3C5×B(4,𝔽2)11yescharacteristic
476D3—81no—
477D3—81no—
478C5#6913311yescharacteristic, direct product factor, Sylow
479C22—21no—
480C22—21no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—81no—
488C22—121no—
489C22—121no—
490C22—121no—
491C22—121no—
492C22—241no—
493C22—241no—
494C22C5×#88211yescharacteristic
495C4—21no—
496C4—41no—
497C4—81no—
498C4—121no—
499C4—121no—
500C4—121no—
501C4—121no—
502C4—241no—
503C3C5×#220011yescharacteristic, complemented, Sylow
504C2—21no—
505C2—41no—
506C2—41no—
507C2—81no—
508C2—241no—
509C2—241no—
510C2C5×#474111yescharacteristic
subgroupG/H
centerC2×C5#4741
commutator, cosocleC2×C3×D4C23×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×AΣL(1,𝔽16)C2
socleC2×C3×C5B(4,𝔽2)
hypercenterC5×AΣL(1,𝔽16)D3
hypocenterC3C5×#2200
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C5×D4 ◁ C5×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
1. C5×#5595C2semidirect
2. C5×#5032C2semidirect
3. C5×#4747C2semidirect
4. C5×#4742C2semidirect
5. C3×C5×AΣL(1,𝔽16)C2semidirect
6. C5×#4476C2semidirect
7. C5×#4474C2semidirect
28. #69133C5direct (N × H)
35. C5×AΣL(1,𝔽16)D3semidirect
46. C22×C5×Dic3D4semidirect
50. C2×C5×D12D4semidirect
61. C5×#217D4semidirect
68. C4×C5×Dic3D4semidirect
71. #5595C2×C5semidirect
72. #5032C2×C5semidirect
73. #4747C2×C5semidirect
74. #4742C2×C5semidirect
75. C3×AΣL(1,𝔽16)C2×C5semidirect
76. #4476C2×C5semidirect
77. #4474C2×C5semidirect
192. AΣL(1,𝔽16)C5×D3semidirect
227. C22×Dic3C5×D4semidirect
231. C2×D12C5×D4semidirect
242. #217C5×D4semidirect
249. C4×Dic3C5×D4semidirect
405. C3×C5#2200semidirect
478. C5#69133direct (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
C5×#55952
C5×#50322
C5×#47472
C5×#47422
C3×C5×AΣL(1,𝔽16)2
C5×#44762
C5×#44742
C5×#22003
#691335