Finite Group Databasebeta

← C5×#73053 #14510777

Subgroups — C5×#73053 #14510777

Order 1920.

434 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C4⋊S4C211yesmaximal, characteristic
2C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C5×A4⋊C8C211yesmaximal, characteristic, complemented
4C5×#1874—31nomaximal, Hall
5C22×C5×S4—21no—
6C2×C4×C5×A4—21no—
7C2×C4×C5×A4C2211yescharacteristic
8C5×C4⋊S4—21no—
9C5×C4⋊S4C412yescomplemented
10C5×A4⋊C8—21no—
11C5×#809—41nomaximal
12#73053C511yesmaximal, characteristic, direct product factor, Hall
13C2×C5×#121—31no—
14C22×C5×C4⋊C4D311yescharacteristic, complemented
15C2×C5×#102—31no—
16C2×C5×#102—31no—
17C2×C5×C22⋊C8—31no—
18C5×#340—31no—
19C5×#340—31no—
20C22×C5×A4D411yescharacteristic
21C2×C5×S4—22no—
22C2×C5×S4—41no—
23C2×C5×S4—41no—
24C2×C5×D12—41no—
25C4×C5×A4—41no—
26C4×C5×A4C2×C411yescharacteristic
27C4×C5×A4D411yescharacteristic
28C3×C5×C4⋊C4—41no—
29C2×C5×C3⋊C8—41no—
30C2×C4⋊S4C2×C511yescharacteristic
31A4×C4⋊C4C2×C511yescharacteristic, complemented
32C2×A4⋊C8C2×C511yescharacteristic, complemented
33C22×C5×D4—31no—
34C22×C5×D4—61no—
35C23×C4×C5—21no—
36C23×C4×C5C2×D311yescharacteristic
37C22×C5×C8—31no—
38C22×C5×C8—31no—
39C5×#121—32no—
40C5×#121—32no—
41C5×#121—61no—
42C5×#121—61no—
43C2×C5×C4⋊C4—31no—
44C2×C5×C4⋊C4—31no—
45C2×C5×C4⋊C4—31no—
46C2×C5×C4⋊C4—61no—
47C2×C5×C22⋊C4—61no—
48C5×#102—62no—
49C5×#102—61no—
50C5×#102—61no—
51C5×C22⋊C8—61no—
52C5×C22⋊C8—61no—
53#1874—31noSylow
54C22×C5×D3—81no—
55C2×C5×A4C22⋊C411yescharacteristic
56C2×C5×A4D811yescharacteristic
57C2×C5×A4SD1611yescharacteristic
58C5×S4—42no—
59C2×C3×C4×C5—41no—
60C2×C3×C4×C5—81no—
61C5×D12—42no—
62C5×D12—81no—
63C5×C3⋊C8—81no—
64C22×S4—21no—
65C2×C4×A4—21no—
66C2×C4×A4C22×C511yescharacteristic
67C4⋊S4—21no—
68C4⋊S4C4×C512yescomplemented
69A4⋊C8—21no—
70#809—41no—
71C24×C5—61no—
72C24×C5#6711yescharacteristic
73C2×C5×D4—32no—
74C2×C5×D4—61no—
75C2×C5×D4—61no—
76C2×C5×D4—61no—
77C2×C5×D4—61no—
78C2×C5×D4—62no—
79C2×C5×D4—62no—
80C2×C5×D4—61no—
81C2×C5×D4—121no—
82C2×C5×D4—121no—
83C2×C5×D4—121no—
84C2×C5×D4—121no—
85C22×C4×C5—31no—
86C22×C4×C5—31no—
87C22×C4×C5—31no—
88C22×C4×C5—31no—
89C22×C4×C5—41no—
90C22×C4×C5—61no—
91C22×C4×C5—61no—
92C22×C4×C5—61no—
93C22×C4×C5—121no—
94C22×C4×C5C4×D311yescharacteristic
95C22×C4×C5D1211yescharacteristic
96C2×C5×C8—61no—
97C2×C5×C8—61no—
98C2×C5×C8—61no—
99C2×C5×C8—61no—
100C2×C5×C8—61no—
101C2×C5×C8—61no—
102C5×C4⋊C4—32no—
103C5×C4⋊C4—32no—
104C5×C4⋊C4—31no—
105C5×C4⋊C4—61no—
106C5×C4⋊C4—61no—
107C5×C4⋊C4S411yescharacteristic, complemented
108C5×C22⋊C4—62no—
109C5×C22⋊C4—62no—
110C2×#121—31no—
111C22×C4⋊C4C5×D311yescharacteristic, complemented
112C2×#102—31no—
113C2×#102—31no—
114C2×C22⋊C8—31no—
115#340—31no—
116#340—31no—
117C22×C3×C5—41no—
118C2×C5×D3—82no—
119C2×C5×D3—161no—
120C2×C5×D3—161no—
121C5×A4#10211yescharacteristic, complemented
122C3×C4×C5—41no—
123C3×C4×C5—41no—
124C3×C4×C5—161no—
125C22×A4C5×D411yescharacteristic
126C2×S4—22no—
127C2×S4—41no—
128C2×S4—41no—
129C2×D12—41no—
130C4×A4—41no—
131C4×A4C2×C4×C511yescharacteristic
132C4×A4C5×D411yescharacteristic
133C3×C4⋊C4—41no—
134C2×C3⋊C8—41no—
135C23×C5—31no—
136C23×C5—31no—
137C23×C5—31no—
138C23×C5—31no—
139C23×C5—62no—
140C23×C5—121no—
141C23×C5—121no—
142C23×C5—121no—
143C23×C5—121no—
144C23×C5—121no—
145C23×C5—121no—
146C23×C5(C2×D3)⋊C411yescharacteristic
147C23×C5#21311yescharacteristic
148C23×C5#21511yescharacteristic
149C5×D4—62no—
150C5×D4—62no—
151C5×D4—121no—
152C5×D4—122no—
153C5×D4—122no—
154C5×D4—122no—
155C5×D4—122no—
156C5×D4—121no—
157C2×C4×C5—21no—
158C2×C4×C5—31no—
159C2×C4×C5—31no—
160C2×C4×C5—31no—
161C2×C4×C5—31no—
162C2×C4×C5—31no—
163C2×C4×C5—31no—
164C2×C4×C5—31no—
165C2×C4×C5—61no—
166C2×C4×C5—62no—
167C2×C4×C5—61no—
168C2×C4×C5—121no—
169C2×C4×C5—121no—
170C2×C4×C5—121no—
171C2×C4×C5—121no—
172C2×C4×C5—121no—
173C2×C4×C5—121no—
174C2×C4×C5C2×S411yescharacteristic
175C5×C8—121no—
176C5×C8—121no—
177C22×D4—31no—
178C22×D4—61no—
179C23×C4—21no—
180C23×C4C2×C5×D311yescharacteristic
181C22×C8—31no—
182C22×C8—31no—
183#121—32no—
184#121—32no—
185#121—61no—
186#121—61no—
187C2×C4⋊C4—31no—
188C2×C4⋊C4—31no—
189C2×C4⋊C4—31no—
190C2×C4⋊C4—61no—
191C2×C22⋊C4—61no—
192#102—62no—
193#102—61no—
194#102—61no—
195C22⋊C8—61no—
196C22⋊C8—61no—
197C2×C3×C5—41no—
198C2×C3×C5—41no—
199C2×C3×C5—41no—
200C5×D3—162no—
201C22×D3—81no—
202C2×A4C5×C22⋊C411yescharacteristic
203C2×A4C5×D811yescharacteristic
204C2×A4C5×SD1611yescharacteristic
205S4—42no—
206C2×C3×C4—41no—
207C2×C3×C4—81no—
208D12—42no—
209D12—81no—
210C3⋊C8—81no—
211C22×C5—31no—
212C22×C5—31no—
213C22×C5—31no—
214C22×C5—31no—
215C22×C5—31no—
216C22×C5—31no—
217C22×C5—31no—
218C22×C5—31no—
219C22×C5—31no—
220C22×C5—61no—
221C22×C5—122no—
222C22×C5—122no—
223C22×C5—122no—
224C22×C5—241no—
225C22×C5—241no—
226C22×C5—241no—
227C22×C5—241no—
228C22×C5#80911yescharacteristic, complemented
229C22×C5GL(2,ℤ/4)11yescharacteristic
230C4×C5—31no—
231C4×C5—31no—
232C4×C5—41no—
233C4×C5—122no—
234C4×C5—121no—
235C4×C5C4×S411yescharacteristic
236C4×C5C4⋊S411yescharacteristic
237C24—61no—
238C24C5×#6711yescharacteristic
239C2×D4—32no—
240C2×D4—61no—
241C2×D4—61no—
242C2×D4—61no—
243C2×D4—61no—
244C2×D4—62no—
245C2×D4—62no—
246C2×D4—61no—
247C2×D4—121no—
248C2×D4—121no—
249C2×D4—121no—
250C2×D4—121no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—41no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4—61no—
259C22×C4—121no—
260C22×C4C4×C5×D311yescharacteristic
261C22×C4C5×D1211yescharacteristic
262C2×C8—61no—
263C2×C8—61no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—61no—
267C2×C8—61no—
268C4⋊C4—32no—
269C4⋊C4—32no—
270C4⋊C4—31no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4C5×S411yescharacteristic, complemented
274C22⋊C4—62no—
275C22⋊C4—62no—
276C3×C5—41noHall
277C22×C3—41no—
278C2×D3—82no—
279C2×D3—161no—
280C2×D3—161no—
281A4C5×#10211yescharacteristic, complemented
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—161no—
285C2×C5—31no—
286C2×C5—31no—
287C2×C5—31no—
288C2×C5—31no—
289C2×C5—242no—
290C2×C5(C2×S4)⋊C411yescharacteristic
291C2×C5#541511yescharacteristic
292C2×C5#541711yescharacteristic
293C23—31no—
294C23—31no—
295C23—31no—
296C23—31no—
297C23—62no—
298C23—121no—
299C23—121no—
300C23—121no—
301C23—121no—
302C23—121no—
303C23—121no—
304C23C5×(C2×D3)⋊C411yescharacteristic
305C23C5×#21311yescharacteristic
306C23C5×#21511yescharacteristic
307D4—62no—
308D4—62no—
309D4—121no—
310D4—122no—
311D4—122no—
312D4—122no—
313D4—122no—
314D4—121no—
315C2×C4—21no—
316C2×C4—31no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—61no—
324C2×C4—62no—
325C2×C4—61no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4—121no—
331C2×C4—121no—
332C2×C4C2×C5×S411yescharacteristic
333C8—121no—
334C8—121no—
335C2×C3—41no—
336C2×C3—41no—
337C2×C3—41no—
338D3—162no—
339C5#7305311yescharacteristic, direct product factor, Sylow
340C22—31no—
341C22—31no—
342C22—31no—
343C22—31no—
344C22—31no—
345C22—31no—
346C22—31no—
347C22—31no—
348C22—31no—
349C22—61no—
350C22—122no—
351C22—122no—
352C22—122no—
353C22—241no—
354C22—241no—
355C22—241no—
356C22—241no—
357C22C5×#80911yescharacteristic, complemented
358C22C5×GL(2,ℤ/4)11yescharacteristic
359C4—31no—
360C4—31no—
361C4—41no—
362C4—122no—
363C4—121no—
364C4C4×C5×S411yescharacteristic
365C4C5×C4⋊S411yescharacteristic
366C3—41noSylow
367C2—31no—
368C2—31no—
369C2—31no—
370C2—31no—
371C2—242no—
372C2C5×(C2×S4)⋊C411yescharacteristic
373C2C5×#541511yescharacteristic
374C2C5×#541711yescharacteristic
subgroupG/H
centerC22×C5GL(2,ℤ/4)
commutatorC4×A4C2×C4×C5
FrattiniC2×C4C2×C5×S4
FittingC22×C5×C4⋊C4D3
socleC24×C5#67
prime radicalC2×C5×C4⋊S4C2
cosocleC2×C4×A4C22×C5
hypercenterC5×C4⋊C4S4
hypocenterA4C5×#102
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×A4×C4⋊C4C2semidirect
3. C2×C5×A4⋊C8C2semidirect
9. C5×C4⋊S4C4semidirect
12. #73053C5direct (N × H)
14. C22×C5×C4⋊C4D3semidirect
31. A4×C4⋊C4C2×C5semidirect
32. C2×A4⋊C8C2×C5semidirect
68. C4⋊S4C4×C5semidirect
107. C5×C4⋊C4S4semidirect
111. C22×C4⋊C4C5×D3semidirect
121. C5×A4#102semidirect
228. C22×C5#809semidirect
273. C4⋊C4C5×S4semidirect
281. A4C5×#102semidirect
339. C5#73053direct (N × H)
357. C22C5×#809semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C4⋊S42
C5×A4×C4⋊C42
C2×C5×A4⋊C82
C5×#18743
C5×#8094
#730535