Finite Group Databasebeta

← C5×#68397 #14292099

Subgroups — C5×#68397 #14292099

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5072C211yesmaximal, characteristic
2C5×#5070C211yesmaximal, characteristic, complemented
3C5×#4841C211yesmaximal, characteristic, complemented
4C5×#4834C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6C5×#4486C211yesmaximal, characteristic, complemented
7C5×#4479C211yesmaximal, characteristic, complemented
8C5×#1681—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×C5×#213—21no—
11C2×C5×#204—21no—
12C2×C5×D3×C8—21no—
13C4×C5×D12C2211yescharacteristic
14C5×#869C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C5×#832—21no—
18C5×#832—21no—
19C5×#832—21no—
20C5×(C2×D3)⋊C8—21no—
21C5×#816—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#68397C511yesmaximal, characteristic, direct product factor, Hall
25C5×#486—31no—
26C5×#461—31no—
27C5×#459—31no—
28C5×C8×D4—31no—
29C5×#335—31no—
30C5×#332—31no—
31C5×#331D311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C5×#213—42no—
42C5×(C2×D3)⋊C4—21no—
43C5×C4⋊Dic3—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C2×C5×C3⋊C8—21no—
47C2×C5×C3⋊C8D411yescharacteristic
48C2×C5×C3⋊C8D411yescharacteristic
49C5×#204—42no—
50C5×D3×C8—42no—
51#5072C2×C511yescharacteristic
52#5070C2×C511yescharacteristic, complemented
53#4841C2×C511yescharacteristic, complemented
54#4834C2×C511yescharacteristic, complemented
55C3×#331C2×C511yescharacteristic, complemented
56#4486C2×C511yescharacteristic, complemented
57#4479C2×C511yescharacteristic, complemented
58C2×C5×SD16—61no—
59C2×C5×D8—61no—
60C22×C5×C8—61no—
61C5×C4⋊Q8—31no—
62C5×#127C2×D311yescharacteristic
63C4×C5×D4—31no—
64C5×C4⋊C8—31no—
65C5×C4⋊C8C2×D311yescharacteristic
66C5×C4⋊C8C2×D311yescharacteristic
67C5×#103—61no—
68C5×#102—61no—
69C5×#102—61no—
70C5×#102—61no—
71C5×C22⋊C8—61no—
72C4×C5×C8—31no—
73#1681—31noSylow
74C23×C3×C5—41no—
75C22×C5×D3—21no—
76C3×C5×D4—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—81no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×C5×Dic3—21no—
85C2×C5×Dic3—41no—
86C5×D12—21no—
87C5×D12D812yes—
88C4×C5×D3—41no—
89C4×C5×D3—41no—
90C5×Dic6—41no—
91C5×Dic6—41no—
92C3×C5×C8—41no—
93C3×C5×C8—41no—
94C5×C3⋊C8—21no—
95C5×C3⋊C8—21no—
96C5×C3⋊C8—41no—
97C3×#127C22×C511yescharacteristic
98C2×#213—21no—
99C2×#204—21no—
100C2×D3×C8—21no—
101C4×D12C22×C511yescharacteristic
102#869C22×C511yescharacteristic
103C3×C4⋊C8C22×C511yescharacteristic
104C3×C4⋊C8C22×C511yescharacteristic
105#832—21no—
106#832—21no—
107#832—21no—
108(C2×D3)⋊C8—21no—
109#816—21no—
110C4⋊(C3⋊C8)C22×C511yescharacteristic
111C4×C3⋊C8C22×C511yescharacteristic
112C2×C5×Q8—61no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—31no—
117C22×C4×C5—61no—
118C5×SD16—122no—
119C5×D8—122no—
120C2×C5×C8—21no—
121C2×C5×C8—21no—
122C2×C5×C8—31no—
123C2×C5×C8—31no—
124C2×C5×C8—61no—
125C2×C5×C8—122no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C22⋊C4—61no—
130C42×C5C22×D311yescharacteristic
131#486—31no—
132#461—31no—
133#459—31no—
134C8×D4—31no—
135#335—31no—
136#332—31no—
137#331C5×D311yescharacteristic, complemented
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12111yescharacteristic
142C2×C5×D3—22no—
143C2×C5×D3—41no—
144C2×C5×D3—41no—
145C3×C4×C5—21no—
146C3×C4×C5C2×D811yescharacteristic
147C3×C4×C5#13511yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C5×Dic3—41no—
151C5×Dic3—81no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×D12C5×D411yescharacteristic
156C2×C4×D3—21no—
157C2×Dic6—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C3×C42C23×C511yescharacteristic
161#213—42no—
162(C2×D3)⋊C4—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3C5×D411yescharacteristic
166C2×C3⋊C8—21no—
167C2×C3⋊C8C5×D411yescharacteristic
168C2×C3⋊C8C5×D411yescharacteristic
169#204—42no—
170D3×C8—42no—
171C23×C5—41no—
172C23×C5—61no—
173C5×Q8—121no—
174C5×Q8—121no—
175C5×D4—32no—
176C5×D4—41no—
177C5×D4—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—61no—
181C5×D4—81no—
182C2×C4×C5—61no—
183C2×C4×C5—121no—
184C2×C4×C5—121no—
185C2×C4×C5—121no—
186C2×C4×C5#23511yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C5×C8—41no—
190C5×C8—41no—
191C5×C8—61no—
192C5×C8—61no—
193C5×C8—121no—
194C2×SD16—61no—
195C2×D8—61no—
196C22×C8—61no—
197C4⋊Q8—31no—
198#127C2×C5×D311yescharacteristic
199C4×D4—31no—
200C4⋊C8—31no—
201C4⋊C8C2×C5×D311yescharacteristic
202C4⋊C8C2×C5×D311yescharacteristic
203#103—61no—
204#102—61no—
205#102—61no—
206#102—61no—
207C22⋊C8—61no—
208C4×C8—31no—
209C2×C3×C5—161no—
210C2×C3×C5#46311yescharacteristic
211C2×C3×C5#46611yescharacteristic
212C2×C3×C5#47111yescharacteristic
213C5×D3—42no—
214C23×C3—41no—
215C22×D3—21no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—81no—
221C2×C3×C4C2×C5×D411yescharacteristic
222C2×C3×C4C2×C5×D411yescharacteristic
223C2×C3×C4C5×#4111yescharacteristic
224C2×Dic3—21no—
225C2×Dic3—41no—
226D12—21no—
227D12C5×D812yes—
228C4×D3—41no—
229C4×D3—41no—
230Dic6—41no—
231Dic6—41no—
232C3×C8—41no—
233C3×C8—41no—
234C3⋊C8—21no—
235C3⋊C8—21no—
236C3⋊C8—41no—
237C22×C5—62no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5—81no—
241C22×C5—121no—
242C22×C5—121no—
243C22×C5#88411yescharacteristic
244C4×C5—21no—
245C4×C5—121no—
246C4×C5—241no—
247C4×C5D3×D811yescharacteristic
248C4×C5#91111yescharacteristic
249C4×C5#91611yescharacteristic
250C4×C5#91611yescharacteristic
251C2×Q8—61no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—31no—
256C22×C4—61no—
257SD16—122no—
258D8—122no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—61no—
264C2×C8—122no—
265C4⋊C4—31no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C22⋊C4—61no—
269C42C22×C5×D311yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3C5×#12111yescharacteristic
275C2×D3—22no—
276C2×D3—41no—
277C2×D3—41no—
278C3×C4—21no—
279C3×C4C2×C5×D811yescharacteristic
280C3×C4C5×#13511yescharacteristic
281C3×C4C5×#13511yescharacteristic
282C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
283Dic3—41no—
284Dic3—81no—
285C2×C5—122no—
286C2×C5—161no—
287C2×C5#474811yescharacteristic
288C2×C5#477511yescharacteristic
289C2×C5#478711yescharacteristic
290C23—41no—
291C23—61no—
292Q8—121no—
293Q8—121no—
294D4—32no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—41no—
299D4—61no—
300D4—81no—
301C2×C4—61no—
302C2×C4—121no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4C5×#23511yescharacteristic
306C2×C4C5×D3×D411yescharacteristic
307C2×C4C5×D3×D411yescharacteristic
308C8—41no—
309C8—41no—
310C8—61no—
311C8—61no—
312C8—121no—
313C2×C3—161no—
314C2×C3C5×#46311yescharacteristic
315C2×C3C5×#46611yescharacteristic
316C2×C3C5×#47111yescharacteristic
317D3—42no—
318C5#6839711yescharacteristic, direct product factor, Sylow
319C22—62no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—121no—
324C22—121no—
325C22C5×#88411yescharacteristic
326C4—21no—
327C4—121no—
328C4—241no—
329C4C5×D3×D811yescharacteristic
330C4C5×#91111yescharacteristic
331C4C5×#91611yescharacteristic
332C4C5×#91611yescharacteristic
333C3C5×#168111yescharacteristic, complemented, Sylow
334C2—122no—
335C2—161no—
336C2C5×#474811yescharacteristic
337C2C5×#477511yescharacteristic
338C2C5×#478711yescharacteristic
subgroupG/H
centerC22×C5#884
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#331C2
socleC22×C3×C5#121
prime radicalC5×#5072C2
hypercenterC5×#331D3
hypocenterC3C5×#1681
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#331

Complements

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

NH ≅ G/Ntype
2. C5×#5070C2semidirect
3. C5×#4841C2semidirect
4. C5×#4834C2semidirect
5. C3×C5×#331C2semidirect
6. C5×#4486C2semidirect
7. C5×#4479C2semidirect
24. #68397C5direct (N × H)
31. C5×#331D3semidirect
52. #5070C2×C5semidirect
53. #4841C2×C5semidirect
54. #4834C2×C5semidirect
55. C3×#331C2×C5semidirect
56. #4486C2×C5semidirect
57. #4479C2×C5semidirect
137. #331C5×D3semidirect
270. C3×C5#1681semidirect
318. C5#68397direct (N × H)
333. C3C5×#1681semidirect

Maximal subgroups

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

subgroupindex
C5×#50722
C5×#50702
C5×#48412
C5×#48342
C3×C5×#3312
C5×#44862
C5×#44792
C5×#16813
#683975