Finite Group Databasebeta

← C5×#68203 #14289592

Subgroups — C5×#68203 #14289592

Order 1920.

436 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5563C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic, complemented
3C5×#4842C211yesmaximal, characteristic, complemented
4C5×#4699C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C5×#4481C211yesmaximal, characteristic, complemented
7C5×#4459C211yesmaximal, characteristic, complemented
8C5×#1634—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#938—21no—
11C5×#930—21no—
12C5×#926—21no—
13C2×C5×Dic12—22no—
14C5×#892—21no—
15C5×#885—22no—
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C5×#832—21no—
22C5×#821—21no—
23C5×#817—21no—
24C5×#808—21no—
25C5×C4⋊(C3⋊C8)C2211yescharacteristic
26#68203C511yesmaximal, characteristic, direct product factor, Hall
27C5×#555—31no—
28C5×#494—31no—
29C5×#476—31no—
30C5×#476—31no—
31C5×#333—31no—
32C5×D4⋊C8—31no—
33C5×D4⋊C8D311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×#67—22no—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6—21no—
40C2×C5×Dic6D412yes—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C5×#217—22no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C4×C5×Dic3—22no—
55C2×C5×C3⋊C8—21no—
56C5×Dic12—44no—
57#5563C2×C511yescharacteristic
58#5008C2×C511yescharacteristic, complemented
59#4842C2×C511yescharacteristic, complemented
60#4699C2×C511yescharacteristic, complemented
61C3×D4⋊C8C2×C511yescharacteristic, complemented
62#4481C2×C511yescharacteristic, complemented
63#4459C2×C511yescharacteristic, complemented
64C2×C5×Q16—62no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8—31no—
67C5×#124—62no—
68C5×#121—61no—
69C5×#121—61no—
70C4×C5×D4—31no—
71C4×C5×D4C2×D311yescharacteristic
72C5×#117—61no—
73C5×#117—61no—
74C5×#106—61no—
75C5×#106—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#102—61no—
79C5×#102—61no—
80C4×C5×C8C2×D311yescharacteristic
81#1634—31noSylow
82C23×C3×C5—21no—
83C22×C5×D3—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C5×#67—82no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—22no—
95C2×C5×Dic3—41no—
96C5×D12—21no—
97C5×D12—21no—
98C4×C5×D3—41no—
99C4×C5×D3—41no—
100C5×Dic6—42no—
101C5×Dic6—42no—
102C3×C5×C8—22no—
103C3×C5×C8—41no—
104C5×C3⋊C8—41no—
105C3×C4×D4C22×C511yescharacteristic
106#938—21no—
107#930—21no—
108#926—21no—
109C2×Dic12—22no—
110#892—21no—
111#885—22no—
112C4×D12C22×C511yescharacteristic
113#869C22×C511yescharacteristic
114#869C22×C511yescharacteristic
115C3×C4⋊C8C22×C511yescharacteristic
116C3×C4×C8C22×C511yescharacteristic
117#832—21no—
118#821—21no—
119#817—21no—
120#808—21no—
121C4⋊(C3⋊C8)C22×C511yescharacteristic
122C2×C5×Q8—32no—
123C2×C5×Q8—61no—
124C2×C5×D4—31no—
125C2×C5×D4—62no—
126C2×C5×D4D1211yescharacteristic
127C22×C4×C5—21no—
128C22×C4×C5—61no—
129C5×Q16—124no—
130C2×C5×C8—21no—
131C2×C5×C8—21no—
132C2×C5×C8—61no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4D1211yescharacteristic
139C5×C22⋊C4—21no—
140C5×C22⋊C4—62no—
141C5×C22⋊C4—62no—
142C5×C22⋊C4—61no—
143C42×C5—62no—
144C42×C5C22×D311yescharacteristic
145#555—31no—
146#494—31no—
147#476—31no—
148#476—31no—
149#333—31no—
150D4⋊C8—31no—
151D4⋊C8C5×D311yescharacteristic, complemented
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C5×Dic3—41no—
166C5×Dic3—42no—
167C5×Dic3—81no—
168C2×C3×D4C5×D411yescharacteristic
169C22×C3×C4—21no—
170C2×#67—22no—
171C2×D12C5×D411yescharacteristic
172C2×C4×D3—21no—
173C2×Dic6—21no—
174C2×Dic6C5×D412yes—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C3×C4⋊C4C5×D411yescharacteristic
178C3×C22⋊C4—21no—
179C3×C42C23×C511yescharacteristic
180#217—22no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3C5×D411yescharacteristic
188C4×Dic3—22no—
189C2×C3⋊C8—21no—
190Dic12—44no—
191C23×C5—21no—
192C23×C5—61no—
193C5×Q8—122no—
194C5×Q8—122no—
195C5×D4—21no—
196C5×D4—21no—
197C5×D4—61no—
198C5×D4—61no—
199C5×D4—242no—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—61no—
204C2×C4×C5—62no—
205C2×C4×C5—121no—
206C2×C4×C5—121no—
207C2×C4×C5—121no—
208C2×C4×C5C2×D1211yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C5×C8—22no—
212C5×C8—41no—
213C5×C8—121no—
214C2×Q16—62no—
215C4⋊Q8—31no—
216C4⋊Q8—31no—
217#124—62no—
218#121—61no—
219#121—61no—
220C4×D4—31no—
221C4×D4C2×C5×D311yescharacteristic
222#117—61no—
223#117—61no—
224#106—61no—
225#106—61no—
226C4⋊C8—31no—
227C4⋊C8C2×C5×D311yescharacteristic
228#102—61no—
229#102—61no—
230C4×C8C2×C5×D311yescharacteristic
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C5×D3—81no—
236C23×C3—21no—
237C22×D3—21no—
238C3×D4—21no—
239C3×D4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4C2×C5×D411yescharacteristic
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×C3×C4C2×C5×D411yescharacteristic
246#67—82no—
247C2×Dic3—21no—
248C2×Dic3—22no—
249C2×Dic3—41no—
250D12—21no—
251D12—21no—
252C4×D3—41no—
253C4×D3—41no—
254Dic6—42no—
255Dic6—42no—
256C3×C8—22no—
257C3×C8—41no—
258C3⋊C8—41no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5#88211yescharacteristic
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—121no—
269C4×C5—122no—
270C4×C5—241no—
271C4×C5#90411yescharacteristic
272C4×C5#90911yescharacteristic
273C4×C5#91211yescharacteristic
274C4×C5#91511yescharacteristic
275C2×Q8—32no—
276C2×Q8—61no—
277C2×D4—31no—
278C2×D4—62no—
279C2×D4C5×D1211yescharacteristic
280C22×C4—21no—
281C22×C4—61no—
282Q16—124no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—61no—
286C4⋊C4—31no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4C5×D1211yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—61no—
296C42—62no—
297C42C22×C5×D311yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3C5×#12011yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4C5×#13511yescharacteristic
309C3×C4C5×#13511yescharacteristic
310C3×C4C5×#13711yescharacteristic
311C3×C4C5×#13711yescharacteristic
312Dic3—41no—
313Dic3—42no—
314Dic3—81no—
315C2×C5—81no—
316C2×C5—241no—
317C2×C5#473311yescharacteristic
318C2×C5#478311yescharacteristic
319C2×C5#482211yescharacteristic
320C23—21no—
321C23—61no—
322Q8—122no—
323Q8—122no—
324D4—21no—
325D4—21no—
326D4—61no—
327D4—61no—
328D4—242no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—61no—
333C2×C4—62no—
334C2×C4—121no—
335C2×C4—121no—
336C2×C4—121no—
337C2×C4C2×C5×D1211yescharacteristic
338C2×C4C5×D3×D411yescharacteristic
339C2×C4C5×D3×D411yescharacteristic
340C8—22no—
341C8—41no—
342C8—121no—
343C2×C3—81no—
344C2×C3C5×#45211yescharacteristic
345C2×C3C5×#45211yescharacteristic
346C2×C3C5×#45311yescharacteristic
347D3—81no—
348C5#6820311yescharacteristic, direct product factor, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22C5×#88211yescharacteristic
356C4—21no—
357C4—41no—
358C4—121no—
359C4—122no—
360C4—241no—
361C4C5×#90411yescharacteristic
362C4C5×#90911yescharacteristic
363C4C5×#91211yescharacteristic
364C4C5×#91511yescharacteristic
365C3C5×#163411yescharacteristic, complemented, Sylow
366C2—81no—
367C2—241no—
368C2C5×#473311yescharacteristic
369C2C5×#478311yescharacteristic
370C2C5×#482211yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC5×#5563C2
hypercenterC5×D4⋊C8D3
hypocenterC3C5×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#5008C2semidirect
3. C5×#4842C2semidirect
4. C5×#4699C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#4481C2semidirect
7. C5×#4459C2semidirect
26. #68203C5direct (N × H)
33. C5×D4⋊C8D3semidirect
58. #5008C2×C5semidirect
59. #4842C2×C5semidirect
60. #4699C2×C5semidirect
61. C3×D4⋊C8C2×C5semidirect
62. #4481C2×C5semidirect
63. #4459C2×C5semidirect
151. D4⋊C8C5×D3semidirect
298. C3×C5#1634semidirect
348. C5#68203direct (N × H)
365. C3C5×#1634semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
C5×#50082
C5×#48422
C5×#46992
C3×C5×D4⋊C82
C5×#44812
C5×#44592
C5×#16343
#682035