Finite Group Databasebeta

← C5×#71932 #14289817

Subgroups — C5×#71932 #14289817

Order 1920.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#556C211yesmaximal, characteristic
2C5×#5093C211yesmaximal, characteristic, complemented
3C5×#5021C211yesmaximal, characteristic, complemented
4C5×#5008C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic, complemented
6C5×#4535C211yesmaximal, characteristic, complemented
7C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic
8C5×#1638—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#126—22no—
11C3×C5×#124—21no—
12C3×C5×C22⋊Q8—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C5×#869C2211yescharacteristic
18C5×#835—21no—
19C5×#832—21no—
20C5×#810—22no—
21C5×#808—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71932C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556D311yescharacteristic
28C5×#487—31no—
29C5×#477—31no—
30C5×#476—31no—
31C5×#332—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C5×Dic6—21no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D412yes—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—22no—
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C3×#556C2×C511yescharacteristic
57#5093C2×C511yescharacteristic, complemented
58#5021C2×C511yescharacteristic, complemented
59#5008C2×C511yescharacteristic
60#4547C2×C511yescharacteristic, complemented
61#4535C2×C511yescharacteristic, complemented
62D4⋊(C3⋊C8)C2×C511yescharacteristic
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C5×#126—22no—
66C5×#124—21no—
67C5×C22⋊Q8—21no—
68C4×C5×Q8—21no—
69C4×C5×Q8C2×D311yescharacteristic
70C4×C5×D4C2×D311yescharacteristic
71C5×#117—21no—
72C5×#107—61no—
73C5×#106—61no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77C5×#103—62no—
78C5×#102—61no—
79C4×C5×C8—31no—
80#1638—31noSylow
81C23×C3×C5—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C5×Dic3—41no—
98C5×Dic6—42no—
99C5×C3⋊C8—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8C22×C511yescharacteristic
103C3×#126—22no—
104C3×#124—21no—
105C3×C22⋊Q8—21no—
106C3×C4×Q8—21no—
107C3×C4×Q8C22×C511yescharacteristic
108C3×C4×D4C22×C511yescharacteristic
109C3×#117—21no—
110#869C22×C511yescharacteristic
111#835—21no—
112#832—21no—
113#810—22no—
114#808—21no—
115#807—21no—
116C4⋊(C3⋊C8)C22×C511yescharacteristic
117C4⋊(C3⋊C8)C22×C511yescharacteristic
118C4×C3⋊C8C22×C511yescharacteristic
119C2×C5×Q8—21no—
120C2×C5×Q8—61no—
121C2×C5×Q8#6711yescharacteristic
122C2×C5×D4#6711yescharacteristic
123C22×C4×C5—21no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C2×C5×C8—61no—
127C5×C4⋊C4—22no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C4⋊C4#6711yescharacteristic
134C5×C4⋊C4#6712yes—
135C5×C22⋊C4—22no—
136C5×C22⋊C4—22no—
137C5×C22⋊C4—21no—
138C42×C5—22no—
139C42×C5—21no—
140C42×C5C22×D311yescharacteristic
141#556C5×D311yescharacteristic
142#487—31no—
143#477—31no—
144#476—31no—
145#332—31no—
146Q8⋊C8—31no—
147D4⋊C8—31no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—41no—
155C3×C4×C5—42no—
156C3×C4×C5—41no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C5×Dic3—81no—
162C2×C3×Q8—21no—
163C2×C3×Q8C5×D411yescharacteristic
164C2×C3×D4C5×D411yescharacteristic
165C22×C3×C4—21no—
166C2×Dic6—21no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4C5×D411yescharacteristic
171C3×C4⋊C4C5×D411yescharacteristic
172C3×C4⋊C4C5×D412yes—
173C3×C22⋊C4—22no—
174C3×C22⋊C4—22no—
175C3×C22⋊C4—21no—
176C3×C42—22no—
177C3×C42—21no—
178C3×C42C23×C511yescharacteristic
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C23×C5—21no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—41no—
188C5×Q8—41no—
189C5×Q8—122no—
190C5×D4—21no—
191C5×D4—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—22no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—121no—
199C2×C4×C5C2×#6711yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C5×C8—121no—
203C5×C8—121no—
204C5×C8—121no—
205C4⋊Q8—31no—
206C4⋊Q8C2×C5×D311yescharacteristic
207#126—22no—
208#124—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8C2×C5×D311yescharacteristic
212C4×D4C2×C5×D311yescharacteristic
213#117—21no—
214#107—61no—
215#106—61no—
216C4⋊C8—31no—
217C4⋊C8—31no—
218#103—61no—
219#103—62no—
220#102—61no—
221C4×C8—31no—
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×D4—21no—
232C3×D4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4C2×C5×D411yescharacteristic
240C2×C3×C4C2×C5×D411yescharacteristic
241C2×C3×C4C2×C5×D411yescharacteristic
242C2×Dic3—41no—
243Dic6—42no—
244C3⋊C8—41no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5#95311yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—42no—
255C4×C5—41no—
256C4×C5—241no—
257C4×C5#95011yescharacteristic
258C4×C5#95011yescharacteristic
259C4×C5#95111yescharacteristic
260C4×C5#95111yescharacteristic
261C2×Q8—21no—
262C2×Q8—61no—
263C2×Q8C5×#6711yescharacteristic
264C2×D4C5×#6711yescharacteristic
265C22×C4—21no—
266C2×C8—61no—
267C2×C8—61no—
268C2×C8—61no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4C5×#6712yes—
275C4⋊C4C5×#6711yescharacteristic
276C4⋊C4C5×#6711yescharacteristic
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—21no—
280C42—22no—
281C42—21no—
282C42C22×C5×D311yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3C5×#12011yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4C5×#13511yescharacteristic
294C3×C4C5×#13511yescharacteristic
295C3×C4C5×#13711yescharacteristic
296C3×C4C5×#13711yescharacteristic
297Dic3—81no—
298C2×C5—81no—
299C2×C5#523911yescharacteristic
300C2×C5#523911yescharacteristic
301C2×C5#524511yescharacteristic
302C23—21no—
303Q8—21no—
304Q8—21no—
305Q8—41no—
306Q8—41no—
307Q8—122no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—121no—
317C2×C4C2×C5×#6711yescharacteristic
318C2×C4C2×C5×#6711yescharacteristic
319C2×C4C2×C5×#6711yescharacteristic
320C8—121no—
321C8—121no—
322C8—121no—
323C2×C3—81no—
324C2×C3C5×#45211yescharacteristic
325C2×C3C5×#45211yescharacteristic
326C2×C3C5×#45411yescharacteristic
327C5#7193211yescharacteristic, direct product factor, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22C5×#95311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—241no—
338C4C5×#95011yescharacteristic
339C4C5×#95011yescharacteristic
340C4C5×#95111yescharacteristic
341C4C5×#95111yescharacteristic
342C3C5×#163811yescharacteristic, complemented, Sylow
343C2—81no—
344C2C5×#523911yescharacteristic
345C2C5×#523911yescharacteristic
346C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#556C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×#556D3
hypocenterC3C5×#1638
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#556

Complements

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

NH ≅ G/Ntype
2. C5×#5093C2semidirect
3. C5×#5021C2semidirect
5. C5×#4547C2semidirect
6. C5×#4535C2semidirect
26. #71932C5direct (N × H)
57. #5093C2×C5semidirect
58. #5021C2×C5semidirect
60. #4547C2×C5semidirect
61. #4535C2×C5semidirect
283. C3×C5#1638semidirect
327. C5#71932direct (N × H)
342. C3C5×#1638semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5562
C5×#50932
C5×#50212
C5×#50082
C5×#45472
C5×#45352
C5×D4⋊(C3⋊C8)2
C5×#16383
#719325