Finite Group Databasebeta

← C2×C5×#5834 #14482969

Subgroups — C2×C5×#5834 #14482969

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C22×C5×#239C211yesmaximal, characteristic, complemented
3C5×#5834C2116yesmaximal, direct product factor
4C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
5C2×C5×#940C213yesmaximal, complemented
6C2×C5×#938C213yesmaximal, complemented
7C2×C5×#930C213yesmaximal, complemented
8C2×C4×C5×#67C213yesmaximal, complemented
9C2×C5×#550—31nomaximal, Hall
10C2×C3×C5×#41—28no—
11C2×C3×C5×#41C2218yescomplemented
12C22×C3×C5×Q8C2211yescharacteristic
13C22×C3×C5×D4C2213yes—
14C23×C3×C4×C5C2213yes—
15C22×C5×#67C2213yes—
16C22×C5×#67C2216yes—
17C2×C5×#239—28no—
18C2×C5×#239C2218yescomplemented
19C22×C5×D12C2213yes—
20C22×C4×C5×D3C2213yes—
21C2×C5×#217C2213yes—
22C5×Q8×Dic3C2218yescomplemented
23C5×#940C22124yescomplemented
24C5×#938C22124yescomplemented
25C5×#930C22124yescomplemented
26C4×C5×#67C22124yescomplemented
27C2×C5×(C2×D3)⋊C4C2213yes—
28C2×C5×C4⋊Dic3C2213yes—
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2213yes—
31C2×#5834C511yesmaximal, characteristic, direct product factor, Hall
32C22×C5×#41—31no—
33C22×C5×#41D311yescharacteristic, complemented
34C5×#550—316no—
35C2×C5×#127—33no—
36C2×C5×#121—33no—
37C2×C5×#121—33no—
38C2×C4×C5×Q8—31no—
39C2×C4×C5×D4—33no—
40C24×C3×C5C2313yes—
41C23×C5×D3C2313yes—
42C3×C5×#41—232no—
43C2×C3×C5×Q8D418yescomplemented
44C2×C3×C5×Q8C2314yes—
45C2×C3×C5×D4—212no—
46C2×C3×C5×D4C23112yes—
47C22×C3×C4×C5—212no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×C4×C5C23112yes—
50C22×C3×C4×C5C2313yes—
51C2×C5×#67—212no—
52C2×C5×#67—412no—
53C2×C5×#67C23112yes—
54C2×C5×#67C23124yes—
55C22×C5×Dic3C2313yes—
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2311yescharacteristic
58C5×#239—232no—
59C2×C5×D12—212no—
60C2×C5×D12C23112yes—
61C2×C4×C5×D3—212no—
62C2×C4×C5×D3C23112yes—
63C5×#217C23112yes—
64C5×(C2×D3)⋊C4C23112yes—
65C5×C4⋊Dic3C23112yes—
66C5×Dic3⋊C4C2314yes—
67C4×C5×Dic3C23112yes—
68C22×C3×#41C2×C511yescharacteristic, complemented
69C22×#239C2×C511yescharacteristic, complemented
70#5834C2×C5116yesdirect product factor
71C2×Q8×Dic3C2×C511yescharacteristic, complemented
72C2×#940C2×C513yescomplemented
73C2×#938C2×C513yescomplemented
74C2×#930C2×C513yescomplemented
75C2×C4×#67C2×C513yescomplemented
76C2×C5×#41—28no—
77C2×C5×#41—38no—
78C2×C5×#41—68no—
79C2×C5×#41C2×D318yescomplemented
80C22×C5×Q8C2×D311yescharacteristic
81C22×C5×D4—33no—
82C22×C5×D4—36no—
83C22×C5×D4—33no—
84C22×C5×D4C2×D313yes—
85C23×C4×C5—33no—
86C23×C4×C5C2×D313yes—
87C5×#127—324no—
88C5×#121—324no—
89C5×#121—324no—
90C4×C5×Q8—38no—
91C4×C5×D4—324no—
92C2×C5×C4⋊C4—31no—
93C2×C5×C4⋊C4—33no—
94C2×C5×C22⋊C4—33no—
95C2×C5×C22⋊C4—33no—
96C2×C42×C5—33no—
97C2×#550—31noSylow
98C23×C3×C5—26no—
99C23×C3×C5—26no—
100C23×C3×C5—26no—
101C23×C3×C5C2416yes—
102C23×C3×C5C2411yescharacteristic
103C22×C5×D3—26no—
104C22×C5×D3—26no—
105C22×C5×D3—26no—
106C22×C5×D3C2416yes—
107C3×C5×Q8C2×D4116yescomplemented
108C3×C5×D4—224no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—224no—
111C2×C3×C4×C5C2×D4112yes—
112C2×C3×C4×C5C2412yes—
113C2×C3×C4×C5C2416yes—
114C5×#67—224no—
115C5×#67—424no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—26no—
118C2×C5×Dic3#4114yescomplemented
119C2×C5×Dic3C2416yes—
120C2×C5×Dic3C2412yes—
121C2×C5×Dic3C2412yes—
122C5×D12—224no—
123C4×C5×D3—224no—
124C2×C3×#41—28no—
125C2×C3×#41C22×C518yescomplemented
126C22×C3×Q8C22×C511yescharacteristic
127C22×C3×D4C22×C513yes—
128C23×C3×C4C22×C513yes—
129C22×#67C22×C513yes—
130C22×#67C22×C516yes—
131C2×#239—28no—
132C2×#239C22×C518yescomplemented
133C22×D12C22×C513yes—
134C22×C4×D3C22×C513yes—
135C2×#217C22×C513yes—
136Q8×Dic3C22×C518yescomplemented
137#940C22×C5124yescomplemented
138#938C22×C5124yescomplemented
139#930C22×C5124yescomplemented
140C4×#67C22×C5124yescomplemented
141C2×(C2×D3)⋊C4C22×C513yes—
142C2×C4⋊Dic3C22×C513yes—
143C2×Dic3⋊C4C22×C511yescharacteristic
144C2×C4×Dic3C22×C513yes—
145C24×C5—33no—
146C24×C5C22×D313yes—
147C5×#41—232no—
148C5×#41—632no—
149C2×C5×Q8#6718yescomplemented
150C2×C5×Q8C22×D314yes—
151C2×C5×D4—212no—
152C2×C5×D4—312no—
153C2×C5×D4—324no—
154C2×C5×D4—312no—
155C2×C5×D4—612no—
156C2×C5×D4—612no—
157C2×C5×D4—1212no—
158C2×C5×D4C22×D3112yes—
159C22×C4×C5—212no—
160C22×C4×C5—31no—
161C22×C4×C5—33no—
162C22×C4×C5—31no—
163C22×C4×C5—312no—
164C22×C4×C5—612no—
165C22×C4×C5C22×D3112yes—
166C22×C4×C5C22×D311yescharacteristic
167C22×C4×C5C22×D313yes—
168C5×C4⋊C4—34no—
169C5×C4⋊C4—312no—
170C5×C22⋊C4—312no—
171C5×C22⋊C4—312no—
172C42×C5—312no—
173C22×#41—31no—
174C22×#41C5×D311yescharacteristic, complemented
175#550—316no—
176C2×#127—33no—
177C2×#121—33no—
178C2×#121—33no—
179C2×C4×Q8—31no—
180C2×C4×D4—33no—
181C22×C3×C5—26no—
182C22×C3×C5—26no—
183C22×C3×C5—26no—
184C22×C3×C5—412no—
185C22×C3×C5C22×D412yes—
186C22×C3×C5C2×#4112yes—
187C22×C3×C5H(5,𝔽2)12yes—
188C22×C3×C5C2511yescharacteristic
189C2×C5×D3—26no—
190C2×C5×D3—26no—
191C2×C5×D3—26no—
192C2×C5×D3—412no—
193C3×C4×C5—22no—
194C3×C4×C5C22×D4112yes—
195C5×Dic3—22no—
196C5×Dic3—26no—
197C5×Dic3C2×#4114yescomplemented
198C24×C3C23×C513yes—
199C23×D3C23×C513yes—
200C3×#41—232no—
201C2×C3×Q8C5×D418yescomplemented
202C2×C3×Q8C23×C514yes—
203C2×C3×D4—212no—
204C2×C3×D4C23×C5112yes—
205C22×C3×C4—212no—
206C22×C3×C4C23×C511yescharacteristic
207C22×C3×C4C23×C5112yes—
208C22×C3×C4C23×C513yes—
209C2×#67—212no—
210C2×#67—412no—
211C2×#67C23×C5112yes—
212C2×#67C23×C5124yes—
213C22×Dic3C23×C513yes—
214C22×Dic3C23×C511yescharacteristic
215C22×Dic3C23×C511yescharacteristic
216#239—232no—
217C2×D12—212no—
218C2×D12C23×C5112yes—
219C2×C4×D3—212no—
220C2×C4×D3C23×C5112yes—
221#217C23×C5112yes—
222(C2×D3)⋊C4C23×C5112yes—
223C4⋊Dic3C23×C5112yes—
224Dic3⋊C4C23×C514yes—
225C4×Dic3C23×C5112yes—
226C23×C5—26no—
227C23×C5—26no—
228C23×C5—26no—
229C23×C5—36no—
230C23×C5—66no—
231C23×C5—66no—
232C23×C5—66no—
233C23×C5C23×D316yes—
234C23×C5C23×D311yescharacteristic
235C5×Q8C2×#67116yescomplemented
236C5×D4—224no—
237C5×D4—624no—
238C5×D4—624no—
239C5×D4—1224no—
240C2×C4×C5—22no—
241C2×C4×C5—224no—
242C2×C4×C5—34no—
243C2×C4×C5—32no—
244C2×C4×C5—36no—
245C2×C4×C5—32no—
246C2×C4×C5—66no—
247C2×C4×C5—62no—
248C2×C4×C5—624no—
249C2×C4×C5C2×#67112yes—
250C2×C4×C5C23×D312yes—
251C2×C4×C5C23×D316yes—
252C2×#41—28no—
253C2×#41—38no—
254C2×#41—68no—
255C2×#41C2×C5×D318yescomplemented
256C22×Q8C2×C5×D311yescharacteristic
257C22×D4—33no—
258C22×D4—36no—
259C22×D4—33no—
260C22×D4C2×C5×D313yes—
261C23×C4—33no—
262C23×C4C2×C5×D313yes—
263#127—324no—
264#121—324no—
265#121—324no—
266C4×Q8—38no—
267C4×D4—324no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—33no—
270C2×C22⋊C4—33no—
271C2×C22⋊C4—33no—
272C2×C42—33no—
273C2×C3×C5—46no—
274C2×C3×C5#55014yescomplemented
275C2×C3×C5C23×D411yescharacteristic
276C2×C3×C5C22×#4111yescharacteristic
277C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
278C5×D3—46no—
279C23×C3—26no—
280C23×C3—26no—
281C23×C3—26no—
282C23×C3C24×C516yes—
283C23×C3C24×C511yescharacteristic
284C22×D3—26no—
285C22×D3—26no—
286C22×D3—26no—
287C22×D3C24×C516yes—
288C3×Q8C2×C5×D4116yescomplemented
289C3×D4—224no—
290C2×C3×C4—22no—
291C2×C3×C4—224no—
292C2×C3×C4C2×C5×D4112yes—
293C2×C3×C4C24×C512yes—
294C2×C3×C4C24×C516yes—
295#67—224no—
296#67—424no—
297C2×Dic3—22no—
298C2×Dic3—26no—
299C2×Dic3C5×#4114yescomplemented
300C2×Dic3C24×C516yes—
301C2×Dic3C24×C512yes—
302C2×Dic3C24×C512yes—
303D12—224no—
304C4×D3—224no—
305C22×C5—26no—
306C22×C5—26no—
307C22×C5—26no—
308C22×C5—412no—
309C22×C5—66no—
310C22×C5—66no—
311C22×C5—66no—
312C22×C5—1212no—
313C22×C5D3×#4112yes—
314C22×C5#100912yes—
315C22×C5C22×#6712yes—
316C22×C5C24×D311yescharacteristic
317C4×C5—22no—
318C4×C5—34no—
319C4×C5—66no—
320C4×C5—62no—
321C4×C5C22×#67112yes—
322C24—33no—
323C24C22×C5×D313yes—
324#41—232no—
325#41—632no—
326C2×Q8C5×#6718yescomplemented
327C2×Q8C22×C5×D314yes—
328C2×D4—212no—
329C2×D4—312no—
330C2×D4—324no—
331C2×D4—312no—
332C2×D4—612no—
333C2×D4—612no—
334C2×D4—1212no—
335C2×D4C22×C5×D3112yes—
336C22×C4—212no—
337C22×C4—31no—
338C22×C4—33no—
339C22×C4—31no—
340C22×C4—312no—
341C22×C4—612no—
342C22×C4C22×C5×D311yescharacteristic
343C22×C4C22×C5×D3112yes—
344C22×C4C22×C5×D313yes—
345C4⋊C4—34no—
346C4⋊C4—312no—
347C22⋊C4—312no—
348C22⋊C4—312no—
349C42—312no—
350C3×C5C2×#55011yescharacteristic, complemented, Hall
351C22×C3—26no—
352C22×C3—26no—
353C22×C3—26no—
354C22×C3—412no—
355C22×C3C22×C5×D412yes—
356C22×C3C2×C5×#4112yes—
357C22×C3C5×H(5,𝔽2)12yes—
358C22×C3C25×C511yescharacteristic
359C2×D3—26no—
360C2×D3—26no—
361C2×D3—26no—
362C2×D3—412no—
363C3×C4—22no—
364C3×C4C22×C5×D4112yes—
365Dic3—22no—
366Dic3—26no—
367Dic3C2×C5×#4114yescomplemented
368C2×C5—46no—
369C2×C5—126no—
370C2×C5#583414yesdirect product factor
371C2×C5C2×D3×#4111yescharacteristic
372C2×C5C2×#100911yescharacteristic
373C2×C5C23×#6711yescharacteristic
374C23—26no—
375C23—26no—
376C23—26no—
377C23—36no—
378C23—66no—
379C23—66no—
380C23—66no—
381C23C23×C5×D316yes—
382C23C23×C5×D311yescharacteristic
383Q8C2×C5×#67116yescomplemented
384D4—224no—
385D4—624no—
386D4—624no—
387D4—1224no—
388C2×C4—22no—
389C2×C4—224no—
390C2×C4—34no—
391C2×C4—32no—
392C2×C4—36no—
393C2×C4—32no—
394C2×C4—66no—
395C2×C4—62no—
396C2×C4—624no—
397C2×C4C2×C5×#67112yes—
398C2×C4C23×C5×D312yes—
399C2×C4C23×C5×D316yes—
400C2×C3—46no—
401C2×C3C5×#55014yescomplemented
402C2×C3C23×C5×D411yescharacteristic
403C2×C3C22×C5×#4111yescharacteristic
404C2×C3C2×C5×H(5,𝔽2)11yescharacteristic
405D3—46no—
406C5C2×#583411yescharacteristic, direct product factor, Sylow
407C22—26no—
408C22—26no—
409C22—26no—
410C22—412no—
411C22—66no—
412C22—66no—
413C22—66no—
414C22—1212no—
415C22C5×D3×#4112yes—
416C22C5×#100912yes—
417C22C22×C5×#6712yes—
418C22C24×C5×D311yescharacteristic
419C4—22no—
420C4—34no—
421C4—66no—
422C4—62no—
423C4C22×C5×#67112yes—
424C3C2×C5×#55011yescharacteristic, complemented, Sylow
425C2—46no—
426C2—126no—
427C2C5×#583414yesdirect product factor
428C2C2×C5×D3×#4111yescharacteristic
429C2C2×C5×#100911yescharacteristic
430C2C23×C5×#6711yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC22×C3×C5×#41C2
socleC23×C3×C5C24
hypercenterC22×C5×#41D3
hypocenterC3C2×C5×#550
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C5×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C22×C5×#239C2semidirect
3. C5×#5834C2direct (N × H)
4. C2×C5×Q8×Dic3C2semidirect
5. C2×C5×#940C2semidirect
6. C2×C5×#938C2semidirect
7. C2×C5×#930C2semidirect
8. C2×C4×C5×#67C2semidirect
11. C2×C3×C5×#41C22semidirect
18. C2×C5×#239C22semidirect
22. C5×Q8×Dic3C22semidirect
23. C5×#940C22semidirect
24. C5×#938C22semidirect
25. C5×#930C22semidirect
26. C4×C5×#67C22semidirect
31. C2×#5834C5direct (N × H)
33. C22×C5×#41D3semidirect
43. C2×C3×C5×Q8D4semidirect
68. C22×C3×#41C2×C5semidirect
69. C22×#239C2×C5semidirect
70. #5834C2×C5direct (N × H)
71. C2×Q8×Dic3C2×C5semidirect
72. C2×#940C2×C5semidirect
73. C2×#938C2×C5semidirect
74. C2×#930C2×C5semidirect
75. C2×C4×#67C2×C5semidirect
79. C2×C5×#41C2×D3semidirect
107. C3×C5×Q8C2×D4semidirect
118. C2×C5×Dic3#41semidirect
125. C2×C3×#41C22×C5semidirect
132. C2×#239C22×C5semidirect
136. Q8×Dic3C22×C5semidirect
137. #940C22×C5semidirect
138. #938C22×C5semidirect
139. #930C22×C5semidirect
140. C4×#67C22×C5semidirect
149. C2×C5×Q8#67semidirect
174. C22×#41C5×D3semidirect
197. C5×Dic3C2×#41semidirect
201. C2×C3×Q8C5×D4semidirect
235. C5×Q8C2×#67semidirect
255. C2×#41C2×C5×D3semidirect
274. C2×C3×C5#550semidirect
288. C3×Q8C2×C5×D4semidirect
299. C2×Dic3C5×#41semidirect
326. C2×Q8C5×#67semidirect
350. C3×C5C2×#550semidirect
367. Dic3C2×C5×#41semidirect
370. C2×C5#5834direct (N × H)
383. Q8C2×C5×#67semidirect
401. C2×C3C5×#550semidirect
406. C5C2×#5834direct (N × H)
424. C3C2×C5×#550semidirect
427. C2C5×#5834direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C22×C5×#2392
C5×#58342
C2×C5×Q8×Dic32
C2×C5×#9402
C2×C5×#9382
C2×C5×#9302
C2×C4×C5×#672
C2×C5×#5503
C2×#58345