Finite Group Databasebeta

← C5×#71008 #14292348

Subgroups — C5×#71008 #14292348

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×#459C211yesmaximal, characteristic
2C5×#5076C211yesmaximal, characteristic, complemented
3C5×#5012C211yesmaximal, characteristic, complemented
4C5×#5007C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6C5×#4486C211yesmaximal, characteristic, complemented
7C5×#4479C211yesmaximal, characteristic, complemented
8C5×#1685—31nomaximal, Hall
9C2×C3×C5×D8—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C2×C5×#214—21no—
13C2×C5×#214—21no—
14C2×C5×#208—21no—
15C5×#869C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×#102—21no—
18C5×#832—21no—
19C5×#830—21no—
20C5×#807—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#71008C511yesmaximal, characteristic, direct product factor, Hall
25C5×#492—31no—
26C5×#474—31no—
27C5×#459D311yescharacteristic
28C5×#436—31no—
29C5×#335—31no—
30C5×#332—31no—
31C5×#331—31no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C5×Dic6—21no—
38C3×C5×D8—42no—
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C5×#214—42no—
44C5×#214—42no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C5×#208—42no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8D411yescharacteristic
51C2×C5×C3⋊C8D411yescharacteristic
52C3×#459C2×C511yescharacteristic
53#5076C2×C511yescharacteristic, complemented
54#5012C2×C511yescharacteristic, complemented
55#5007C2×C511yescharacteristic, complemented
56#4544C2×C511yescharacteristic, complemented
57#4486C2×C511yescharacteristic, complemented
58#4479C2×C511yescharacteristic, complemented
59C2×C5×SD16—61no—
60C2×C5×SD16—61no—
61C2×C5×D8—21no—
62C2×C5×M16—61no—
63C5×C4⋊Q8—31no—
64C5×#127C2×D311yescharacteristic
65C4×C5×D4C2×D311yescharacteristic
66C5×#107—61no—
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—
76C23×C3×C5—41no—
77C3×C5×D4—21no—
78C3×C5×D4—21no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C5×Dic3—41no—
91C5×Dic6—41no—
92C5×Dic6—41no—
93C3×C5×C8—41no—
94C5×C3⋊C8—21no—
95C5×C3⋊C8—41no—
96C5×C3⋊C8—41no—
97C5×C3⋊C8D812yescomplemented
98C2×C3×D8—21no—
99C3×#127C22×C511yescharacteristic
100C3×C4×D4C22×C511yescharacteristic
101C2×#214—21no—
102C2×#214—21no—
103C2×#208—21no—
104#869C22×C511yescharacteristic
105C3×C4⋊C8C22×C511yescharacteristic
106C3×#102—21no—
107#832—21no—
108#830—21no—
109#807—21no—
110C4⋊(C3⋊C8)C22×C511yescharacteristic
111C4⋊(C3⋊C8)C22×C511yescharacteristic
112C4×C3⋊C8C22×C511yescharacteristic
113C2×C5×Q8—61no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×C5×D4#6711yescharacteristic
118C22×C4×C5—21no—
119C5×SD16—122no—
120C5×SD16—122no—
121C5×D8—42no—
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—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4#6711yescharacteristic
131C5×C22⋊C4—21no—
132C42×C5C22×D311yescharacteristic
133#492—31no—
134#474—31no—
135#459C5×D311yescharacteristic
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—81no—
144C22×C3×C5—81no—
145C22×C3×C5—81no—
146C22×C3×C5#12111yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C5×Dic3—81no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4C5×D411yescharacteristic
158C22×C3×C4—21no—
159C2×Dic6—21no—
160C3×D8—42no—
161C2×C3×C8—21no—
162C3×C4⋊C4C5×D411yescharacteristic
163C3×C22⋊C4—21no—
164C3×C42C23×C511yescharacteristic
165#214—42no—
166#214—42no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169#208—42no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8C5×D411yescharacteristic
173C2×C3⋊C8C5×D411yescharacteristic
174C23×C5—21no—
175C23×C5—41no—
176C5×Q8—121no—
177C5×Q8—121no—
178C5×D4—21no—
179C5×D4—21no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—41no—
183C5×D4—41no—
184C5×D4—81no—
185C2×C4×C5—21no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—121no—
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—21no—
200C2×M16—61no—
201C4⋊Q8—31no—
202#127C2×C5×D311yescharacteristic
203C4×D4C2×C5×D311yescharacteristic
204#107—61no—
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—161no—
214C2×C3×C5#45911yescharacteristic
215C2×C3×C5#46811yescharacteristic
216C2×C3×C5#47111yescharacteristic
217C23×C3—21no—
218C23×C3—41no—
219C3×D4—21no—
220C3×D4—21no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—81no—
226C2×C3×C4—21no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4C2×C5×D411yescharacteristic
230C2×C3×C4C2×C5×D411yescharacteristic
231C2×C3×C4C5×#4111yescharacteristic
232C2×Dic3—41no—
233Dic6—41no—
234Dic6—41no—
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—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5#93911yescharacteristic
247C4×C5—21no—
248C4×C5—41no—
249C4×C5—241no—
250C4×C5D3×D811yescharacteristic
251C4×C5#91111yescharacteristic
252C4×C5#93211yescharacteristic
253C4×C5#95111yescharacteristic
254C2×Q8—61no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4C5×#6711yescharacteristic
259C22×C4—21no—
260SD16—122no—
261SD16—122no—
262D8—42no—
263M16—122no—
264C2×C8—21no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—61no—
269C4⋊C4—61no—
270C4⋊C4—61no—
271C4⋊C4C5×#6711yescharacteristic
272C22⋊C4—21no—
273C42C22×C5×D311yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3C5×#12111yescharacteristic
282C3×C4—21no—
283C3×C4—41no—
284C3×C4C2×C5×D811yescharacteristic
285C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
286C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
287C3×C4C5×#13711yescharacteristic
288Dic3—81no—
289C2×C5—81no—
290C2×C5—161no—
291C2×C5#504211yescharacteristic
292C2×C5#515011yescharacteristic
293C2×C5#520011yescharacteristic
294C23—21no—
295C23—41no—
296Q8—121no—
297Q8—121no—
298D4—21no—
299D4—21no—
300D4—41no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—81no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—121no—
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×C3—161no—
319C2×C3C5×#45911yescharacteristic
320C2×C3C5×#46811yescharacteristic
321C2×C3C5×#47111yescharacteristic
322C5#7100811yescharacteristic, direct product factor, Sylow
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C5×#93911yescharacteristic
330C4—21no—
331C4—41no—
332C4—241no—
333C4C5×D3×D811yescharacteristic
334C4C5×#91111yescharacteristic
335C4C5×#93211yescharacteristic
336C4C5×#95111yescharacteristic
337C3C5×#168511yescharacteristic, complemented, Sylow
338C2—81no—
339C2—161no—
340C2C5×#504211yescharacteristic
341C2C5×#515011yescharacteristic
342C2C5×#520011yescharacteristic
subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
Fitting, prime radicalC3×C5×#459C2
socleC22×C3×C5#121
hypercenterC5×#459D3
hypocenterC3C5×#1685
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#459

Complements

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

NH ≅ G/Ntype
2. C5×#5076C2semidirect
3. C5×#5012C2semidirect
4. C5×#5007C2semidirect
5. C5×#4544C2semidirect
6. C5×#4486C2semidirect
7. C5×#4479C2semidirect
24. #71008C5direct (N × H)
53. #5076C2×C5semidirect
54. #5012C2×C5semidirect
55. #5007C2×C5semidirect
56. #4544C2×C5semidirect
57. #4486C2×C5semidirect
58. #4479C2×C5semidirect
97. C5×C3⋊C8D8semidirect
239. C3⋊C8C5×D8semidirect
274. C3×C5#1685semidirect
322. C5#71008direct (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×#4592
C5×#50762
C5×#50122
C5×#50072
C5×#45442
C5×#44862
C5×#44792
C5×#16853
#710085