Finite Group Databasebeta

← C5×#69109 #14316109

Subgroups — C5×#69109 #14316109

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#904C211yesmaximal, characteristic, complemented
2C5×#5115C211yesmaximal, characteristic, complemented
3C2×C5×#800C211yesmaximal, characteristic, complemented
4C2×C5×D48C211yesmaximal, characteristic, complemented
5C3×C5×C22⋊C16C211yesmaximal, characteristic, complemented
6C5×#4509C211yesmaximal, characteristic, complemented
7C5×#4503C211yesmaximal, characteristic, complemented
8C5×#2186—31nomaximal, Hall
9C2×C5×#235—21no—
10C22×C3×C5×C8C2211yescharacteristic
11C5×#930—21no—
12C2×C5×Dic12C2211yescharacteristic
13C5×#904—22no—
14C5×#904—22no—
15C2×C5×D24C2211yescharacteristic
16C2×C5×D24C2211yescharacteristic
17C2×C5×#204—21no—
18C2×C3×C5×C16C2211yescharacteristic
19C2×C3×C5×C16C2211yescharacteristic
20C5×#821—21no—
21C5×#818C2211yescharacteristic
22C5×#800—22no—
23C5×D48—22no—
24#69109C511yesmaximal, characteristic, direct product factor, Hall
25C2×C5×#135—31no—
26C2×C5×SD32—31no—
27C2×C5×D16—31no—
28C5×#466—31no—
29C5×#358—31no—
30C5×#357—31no—
31C5×C22⋊C16D311yescharacteristic, complemented
32C22×C3×C4×C5D411yescharacteristic
33C2×C5×#67—41no—
34C2×C5×#67—41no—
35C5×#235—24no—
36C5×#235—42no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C4×C5×D3—41no—
40C2×C5×Dic6—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8D411yescharacteristic
44C2×C3×C5×C8C2311yescharacteristic
45C5×(C2×D3)⋊C4—41no—
46C5×C4⋊Dic3—21no—
47C5×Dic12—21no—
48C5×Dic12D412yescomplemented
49C5×D24—21no—
50C5×D24—21no—
51C5×D24—21no—
52C5×D24D412yescomplemented
53C5×#204—24no—
54C3×C5×C16—21no—
55C3×C5×C16—21no—
56C2×#904C2×C511yescharacteristic, complemented
57#5115C2×C511yescharacteristic, complemented
58C2×#800C2×C511yescharacteristic, complemented
59C2×D48C2×C511yescharacteristic, complemented
60C3×C22⋊C16C2×C511yescharacteristic, complemented
61#4509C2×C511yescharacteristic, complemented
62#4503C2×C511yescharacteristic, complemented
63C2×C5×#41—61no—
64C5×#135—62no—
65C5×#135—62no—
66C2×C5×Q16—31no—
67C2×C5×SD16—61no—
68C2×C5×D8—31no—
69C2×C5×D8—31no—
70C22×C5×C8C2×D311yescharacteristic
71C5×#121—61no—
72C5×SD32—62no—
73C5×D16—62no—
74C2×C5×C16C2×D311yescharacteristic
75C2×C5×C16C2×D311yescharacteristic
76C5×#107—31no—
77C5×#102—61no—
78#2186—31noSylow
79C23×C3×C5D811yescharacteristic
80C22×C5×D3—41no—
81C22×C5×D3—41no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5D811yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C5×#67—44no—
87C5×#67—82no—
88C2×C5×Dic3—41no—
89C2×C5×Dic3—41no—
90C5×D12—22no—
91C5×D12—41no—
92C5×D12—41no—
93C5×D12—41no—
94C4×C5×D3—44no—
95C5×Dic6—22no—
96C5×Dic6—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×#235—21no—
101C22×C3×C8C22×C511yescharacteristic
102#930—21no—
103C2×Dic12C22×C511yescharacteristic
104#904—22no—
105#904—22no—
106C2×D24C22×C511yescharacteristic
107C2×D24C22×C511yescharacteristic
108C2×#204—21no—
109C2×C3×C16C22×C511yescharacteristic
110C2×C3×C16C22×C511yescharacteristic
111#821—21no—
112#818C22×C511yescharacteristic
113#800—22no—
114D48—22no—
115C5×#41—64no—
116C5×#41—122no—
117C2×C5×Q8—61no—
118C2×C5×D4—61no—
119C2×C5×D4—61no—
120C2×C5×D4—121no—
121C2×C5×D4—121no—
122C22×C4×C5—121no—
123C22×C4×C5D1211yescharacteristic
124C5×Q16—32no—
125C5×Q16—61no—
126C5×SD16—64no—
127C5×D8—32no—
128C5×D8—61no—
129C5×D8—61no—
130C5×D8—61no—
131C2×C5×C8—21no—
132C2×C5×C8—21no—
133C2×C5×C8D1211yescharacteristic
134C2×C5×C8C22×D311yescharacteristic
135C5×C4⋊C4—61no—
136C5×C22⋊C4—121no—
137C5×C16—21no—
138C5×C16—21no—
139C2×#135—31no—
140C2×SD32—31no—
141C2×D16—31no—
142#466—31no—
143#358—31no—
144#357—31no—
145C22⋊C16C5×D311yescharacteristic, complemented
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5C2×D811yescharacteristic
150C2×C5×D3—42no—
151C2×C5×D3—81no—
152C2×C5×D3—81no—
153C2×C5×D3—81no—
154C2×C5×D3—81no—
155C2×C5×D3—81no—
156C3×C4×C5—21no—
157C3×C4×C5#12011yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C5×Dic3—42no—
160C5×Dic3—81no—
161C22×C3×C4C5×D411yescharacteristic
162C2×#67—41no—
163C2×#67—41no—
164#235—24no—
165#235—42no—
166C2×D12—21no—
167C2×D12—21no—
168C2×C4×D3—41no—
169C2×Dic6—21no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8C5×D411yescharacteristic
173C2×C3×C8C23×C511yescharacteristic
174(C2×D3)⋊C4—41no—
175C4⋊Dic3—21no—
176Dic12—21no—
177Dic12C5×D412yescomplemented
178D24—21no—
179D24—21no—
180D24—21no—
181D24C5×D412yescomplemented
182#204—24no—
183C3×C16—21no—
184C3×C16—21no—
185C23×C5—121no—
186C23×C5—121no—
187C23×C5D2411yescharacteristic
188C5×Q8—62no—
189C5×Q8—121no—
190C5×D4—62no—
191C5×D4—124no—
192C5×D4—121no—
193C5×D4—121no—
194C5×D4—121no—
195C5×D4—242no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—124no—
199C2×C4×C5—121no—
200C2×C4×C5—121no—
201C2×C4×C5D2411yescharacteristic
202C2×C4×C5C2×D1211yescharacteristic
203C5×C8—21no—
204C5×C8D3×D411yescharacteristic
205C5×C8D3×D411yescharacteristic
206C2×#41—61no—
207#135—62no—
208#135—62no—
209C2×Q16—31no—
210C2×SD16—61no—
211C2×D8—31no—
212C2×D8—31no—
213C22×C8C2×C5×D311yescharacteristic
214#121—61no—
215SD32—62no—
216D16—62no—
217C2×C16C2×C5×D311yescharacteristic
218C2×C16C2×C5×D311yescharacteristic
219#107—31no—
220#102—61no—
221C2×C3×C5—41no—
222C2×C3×C5#44711yescharacteristic
223C2×C3×C5#50811yescharacteristic
224C2×C3×C5#50911yescharacteristic
225C5×D3—82no—
226C5×D3—161no—
227C23×C3C5×D811yescharacteristic
228C22×D3—41no—
229C22×D3—41no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4C5×D811yescharacteristic
233C2×C3×C4C2×C5×D411yescharacteristic
234#67—44no—
235#67—82no—
236C2×Dic3—41no—
237C2×Dic3—41no—
238D12—22no—
239D12—41no—
240D12—41no—
241D12—41no—
242C4×D3—44no—
243Dic6—22no—
244Dic6—41no—
245C3×C8—21no—
246C3×C8C2×C5×D411yescharacteristic
247C3×C8C2×C5×D411yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—122no—
252C22×C5—241no—
253C22×C5—241no—
254C22×C5—241no—
255C22×C5—241no—
256C22×C5—241no—
257C22×C5C2×D2411yescharacteristic
258C4×C5—21no—
259C4×C5—122no—
260C4×C5—241no—
261C4×C5#88211yescharacteristic
262C4×C5#90811yescharacteristic
263#41—64no—
264#41—122no—
265C2×Q8—61no—
266C2×D4—61no—
267C2×D4—61no—
268C2×D4—121no—
269C2×D4—121no—
270C22×C4—121no—
271C22×C4C5×D1211yescharacteristic
272Q16—32no—
273Q16—61no—
274SD16—64no—
275D8—32no—
276D8—61no—
277D8—61no—
278D8—61no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8C5×D1211yescharacteristic
282C2×C8C22×C5×D311yescharacteristic
283C4⋊C4—61no—
284C22⋊C4—121no—
285C16—21no—
286C16—21no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3C2×C5×D811yescharacteristic
292C2×D3—42no—
293C2×D3—81no—
294C2×D3—81no—
295C2×D3—81no—
296C2×D3—81no—
297C2×D3—81no—
298C3×C4—21no—
299C3×C4C5×#12011yescharacteristic
300C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
301Dic3—42no—
302Dic3—81no—
303C2×C5—41no—
304C2×C5—242no—
305C2×C5—481no—
306C2×C5#473211yescharacteristic
307C2×C5#490411yescharacteristic
308C2×C5#490811yescharacteristic
309C23—121no—
310C23—121no—
311C23C5×D2411yescharacteristic
312Q8—62no—
313Q8—121no—
314D4—62no—
315D4—124no—
316D4—121no—
317D4—121no—
318D4—121no—
319D4—242no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—124no—
323C2×C4—121no—
324C2×C4—121no—
325C2×C4C5×D2411yescharacteristic
326C2×C4C2×C5×D1211yescharacteristic
327C8—21no—
328C8C5×D3×D411yescharacteristic
329C8C5×D3×D411yescharacteristic
330C2×C3—41no—
331C2×C3C5×#44711yescharacteristic
332C2×C3C5×#50811yescharacteristic
333C2×C3C5×#50911yescharacteristic
334D3—82no—
335D3—161no—
336C5#6910911yescharacteristic, direct product factor, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—122no—
341C22—241no—
342C22—241no—
343C22—241no—
344C22—241no—
345C22—241no—
346C22C2×C5×D2411yescharacteristic
347C4—21no—
348C4—122no—
349C4—241no—
350C4C5×#88211yescharacteristic
351C4C5×#90811yescharacteristic
352C3C5×#218611yescharacteristic, complemented, Sylow
353C2—41no—
354C2—242no—
355C2—481no—
356C2C5×#473211yescharacteristic
357C2C5×#490411yescharacteristic
358C2C5×#490811yescharacteristic
subgroupG/H
centerC22×C5C2×D24
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×C22⋊C16C2
socleC22×C3×C5C2×D8
hypercenterC5×C22⋊C16D3
hypocenterC3C5×#2186
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C5×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×C5×#904C2semidirect
2. C5×#5115C2semidirect
3. C2×C5×#800C2semidirect
4. C2×C5×D48C2semidirect
5. C3×C5×C22⋊C16C2semidirect
6. C5×#4509C2semidirect
7. C5×#4503C2semidirect
24. #69109C5direct (N × H)
31. C5×C22⋊C16D3semidirect
48. C5×Dic12D4semidirect
52. C5×D24D4semidirect
56. C2×#904C2×C5semidirect
57. #5115C2×C5semidirect
58. C2×#800C2×C5semidirect
59. C2×D48C2×C5semidirect
60. C3×C22⋊C16C2×C5semidirect
61. #4509C2×C5semidirect
62. #4503C2×C5semidirect
145. C22⋊C16C5×D3semidirect
177. Dic12C5×D4semidirect
181. D24C5×D4semidirect
287. C3×C5#2186semidirect
336. C5#69109direct (N × H)
352. C3C5×#2186semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9042
C5×#51152
C2×C5×#8002
C2×C5×D482
C3×C5×C22⋊C162
C5×#45092
C5×#45032
C5×#21863
#691095