Finite Group Databasebeta

← C5×#71104 #14292360

Subgroups — C5×#71104 #14292360

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#474C211yesmaximal, characteristic, complemented
2C5×#5085C211yesmaximal, characteristic, complemented
3C5×#5015C211yesmaximal, characteristic
4C5×#5012C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4479C211yesmaximal, characteristic, complemented
8C5×#1685—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C2×C5×#215—21no—
12C2×C5×#215—21no—
13C2×C5×#213—21no—
14C2×C5×#208—21no—
15C5×#874C2211yescharacteristic
16C3×C5×#107—21no—
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×C5×#102—21no—
19C5×#830—21no—
20C5×#809—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#71104C511yesmaximal, characteristic, direct product factor, Hall
25C5×#492—31no—
26C5×#474D311yescharacteristic, complemented
27C5×#459—31no—
28C5×#436—31no—
29C5×#335—31no—
30C5×#332—31no—
31C5×#331—31no—
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4D411yescharacteristic
34C22×C3×C4×C5—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C5×#215—42no—
45C5×#215—42no—
46C5×#213—42no—
47C5×#208—42no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8D411yescharacteristic
51C2×C5×C3⋊C8D411yescharacteristic
52C3×#474C2×C511yescharacteristic, complemented
53#5085C2×C511yescharacteristic, complemented
54#5015C2×C511yescharacteristic
55#5012C2×C511yescharacteristic, complemented
56#4547C2×C511yescharacteristic, complemented
57#4485C2×C511yescharacteristic, complemented
58#4479C2×C511yescharacteristic, complemented
59C2×C5×SD16—61no—
60C2×C5×SD16—61no—
61C2×C5×D8—61no—
62C2×C5×M16—61no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C5×#127—31no—
65C4×C5×D4C2×D311yescharacteristic
66C5×#107—21no—
67C5×C4⋊C8—31no—
68C5×C4⋊C8—31no—
69C5×C4⋊C8C2×D311yescharacteristic
70C5×#102—21no—
71C5×#102—61no—
72C5×C22⋊C8—61no—
73C4×C5×C8—31no—
74#1685—31noSylow
75C23×C3×C5—21no—
76C22×C5×D3—41no—
77C3×C5×Q8—41no—
78C3×C5×Q8—41no—
79C3×C5×D4—21no—
80C3×C5×D4—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C5×D12—41no—
89C5×D12—41no—
90C5×D12—41no—
91C5×D12—41no—
92C5×D12—81no—
93C3×C5×C8—41no—
94C5×C3⋊C8—21no—
95C5×C3⋊C8—41no—
96C5×C3⋊C8—41no—
97C5×C3⋊C8D812yescomplemented
98C3×C4⋊Q8C22×C511yescharacteristic
99C3×C4×D4C22×C511yescharacteristic
100C2×#215—21no—
101C2×#215—21no—
102C2×#213—21no—
103C2×#208—21no—
104#874C22×C511yescharacteristic
105C3×#107—21no—
106C3×C4⋊C8C22×C511yescharacteristic
107C3×#102—21no—
108#830—21no—
109#809—21no—
110C4⋊(C3⋊C8)C22×C511yescharacteristic
111C4⋊(C3⋊C8)C22×C511yescharacteristic
112C4×C3⋊C8C22×C511yescharacteristic
113C2×C5×Q8—21no—
114C2×C5×D4—61no—
115C2×C5×D4—61no—
116C2×C5×D4—61no—
117C2×C5×D4#6711yescharacteristic
118C22×C4×C5—21no—
119C5×SD16—122no—
120C5×SD16—122no—
121C5×D8—122no—
122C5×M16—122no—
123C2×C5×C8—21no—
124C2×C5×C8—31no—
125C2×C5×C8—31no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4#6711yescharacteristic
131C5×C22⋊C4—21no—
132C42×C5C22×D311yescharacteristic
133#492—31no—
134#474C5×D311yescharacteristic, complemented
135#459—31no—
136#436—31no—
137#335—31no—
138#332—31no—
139#331—31no—
140C22×C3×C5—41no—
141C22×C3×C5—41no—
142C22×C3×C5—41no—
143C22×C3×C5#12111yescharacteristic
144C2×C5×D3—81no—
145C2×C5×D3—81no—
146C2×C5×D3—81no—
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×C4×C5—81no—
150C3×C4×C5C2×D811yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C3×C4×C5#13711yescharacteristic
154C2×C3×Q8—21no—
155C2×C3×D4C5×D411yescharacteristic
156C22×C3×C4—21no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—21no—
160C2×C3×C8—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4C5×D411yescharacteristic
164C3×C22⋊C4—21no—
165C3×C42C23×C511yescharacteristic
166#215—42no—
167#215—42no—
168#213—42no—
169#208—42no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8C5×D411yescharacteristic
173C2×C3⋊C8C5×D411yescharacteristic
174C23×C5—21no—
175C23×C5—121no—
176C5×Q8—41no—
177C5×Q8—41no—
178C5×D4—21no—
179C5×D4—21no—
180C5×D4—121no—
181C5×D4—121no—
182C5×D4—121no—
183C5×D4—121no—
184C5×D4—241no—
185C2×C4×C5—21no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5#23711yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C5×C8—32no—
193C5×C8—41no—
194C5×C8—61no—
195C5×C8—121no—
196C5×C8—121no—
197C2×SD16—61no—
198C2×SD16—61no—
199C2×D8—61no—
200C2×M16—61no—
201C4⋊Q8C2×C5×D311yescharacteristic
202#127—31no—
203C4×D4C2×C5×D311yescharacteristic
204#107—21no—
205C4⋊C8—31no—
206C4⋊C8—31no—
207C4⋊C8C2×C5×D311yescharacteristic
208#102—21no—
209#102—61no—
210C22⋊C8—61no—
211C4×C8—31no—
212C2×C3×C5—81no—
213C2×C3×C5#45911yescharacteristic
214C2×C3×C5#46811yescharacteristic
215C2×C3×C5#47111yescharacteristic
216C5×D3—161no—
217C23×C3—21no—
218C22×D3—41no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×D4—21no—
222C3×D4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4C2×C5×D411yescharacteristic
228C2×C3×C4C2×C5×D411yescharacteristic
229C2×C3×C4C5×#4111yescharacteristic
230D12—41no—
231D12—41no—
232D12—41no—
233D12—41no—
234D12—81no—
235C3×C8—41no—
236C3⋊C8—21no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8C5×D812yescomplemented
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—241no—
244C22×C5—241no—
245C22×C5—241no—
246C22×C5#93911yescharacteristic
247C4×C5—21no—
248C4×C5—41no—
249C4×C5—81no—
250C4×C5D3×D811yescharacteristic
251C4×C5#91111yescharacteristic
252C4×C5#94211yescharacteristic
253C4×C5#94911yescharacteristic
254C2×Q8—21no—
255C2×D4—61no—
256C2×D4—61no—
257C2×D4—61no—
258C2×D4C5×#6711yescharacteristic
259C22×C4—21no—
260SD16—122no—
261SD16—122no—
262D8—122no—
263M16—122no—
264C2×C8—21no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—61no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4C5×#6711yescharacteristic
272C22⋊C4—21no—
273C42C22×C5×D311yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3C5×#12111yescharacteristic
279C2×D3—81no—
280C2×D3—81no—
281C2×D3—81no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—81no—
285C3×C4C2×C5×D811yescharacteristic
286C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
287C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
288C3×C4C5×#13711yescharacteristic
289C2×C5—81no—
290C2×C5—481no—
291C2×C5#504911yescharacteristic
292C2×C5#515011yescharacteristic
293C2×C5#520311yescharacteristic
294C23—21no—
295C23—121no—
296Q8—41no—
297Q8—41no—
298D4—21no—
299D4—21no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—121no—
304D4—241no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4C5×D3×D411yescharacteristic
310C2×C4C5×#23711yescharacteristic
311C2×C4C2×C5×#6711yescharacteristic
312C8—32no—
313C8—41no—
314C8—61no—
315C8—121no—
316C8—121no—
317C2×C3—81no—
318C2×C3C5×#45911yescharacteristic
319C2×C3C5×#46811yescharacteristic
320C2×C3C5×#47111yescharacteristic
321D3—161no—
322C5#7110411yescharacteristic, direct product factor, Sylow
323C22—41no—
324C22—41no—
325C22—41no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22C5×#93911yescharacteristic
330C4—21no—
331C4—41no—
332C4—81no—
333C4C5×D3×D811yescharacteristic
334C4C5×#91111yescharacteristic
335C4C5×#94211yescharacteristic
336C4C5×#94911yescharacteristic
337C3C5×#168511yescharacteristic, complemented, Sylow
338C2—81no—
339C2—481no—
340C2C5×#504911yescharacteristic
341C2C5×#515011yescharacteristic
342C2C5×#520311yescharacteristic
subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#474C2
socleC22×C3×C5#121
prime radicalC5×#5015C2
hypercenterC5×#474D3
hypocenterC3C5×#1685
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#474

Complements

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

NH ≅ G/Ntype
1. C3×C5×#474C2semidirect
2. C5×#5085C2semidirect
4. C5×#5012C2semidirect
5. C5×#4547C2semidirect
6. C5×#4485C2semidirect
7. C5×#4479C2semidirect
24. #71104C5direct (N × H)
26. C5×#474D3semidirect
52. C3×#474C2×C5semidirect
53. #5085C2×C5semidirect
55. #5012C2×C5semidirect
56. #4547C2×C5semidirect
57. #4485C2×C5semidirect
58. #4479C2×C5semidirect
97. C5×C3⋊C8D8semidirect
134. #474C5×D3semidirect
239. C3⋊C8C5×D8semidirect
274. C3×C5#1685semidirect
322. C5#71104direct (N × H)
337. C3C5×#1685semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4742
C5×#50852
C5×#50152
C5×#50122
C5×#45472
C5×#44852
C5×#44792
C5×#16853
#711045