Finite Group Databasebeta

← C5×#85442 #14511180

Subgroups — C5×#85442 #14511180

Order 1920.

540 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5912C211yesmaximal, characteristic
2C5×A4×M16C211yesmaximal, characteristic, complemented
3C2×C5×A4⋊C8C211yesmaximal, characteristic, complemented
4C5×#5400C212yesmaximal, complemented
5C5×C8×S4C212yesmaximal, complemented
6C5×#2933—31nomaximal, Hall
7C2×C4×C5×A4C2211yescharacteristic
8C5×GL(2,ℤ/4)C412yes—
9C5×C4⋊S4C411yescharacteristic
10C4×C5×S4C2212yes—
11C5×A4⋊Q8C411yescharacteristic
12C5×#907—41nomaximal
13C5×C8×A4C2212yes—
14C5×A4⋊C8C2211yescharacteristic
15C5×A4⋊C8C2211yescharacteristic
16#85442C511yesmaximal, characteristic, direct product factor, Hall
17C2×C5×#131—31no—
18C22×C5×M16D311yescharacteristic, complemented
19C5×#525—31no—
20C5×#436—32no—
21C5×#435—32no—
22C5×#435—32no—
23C5×C8×D4—32no—
24C5×#424—31no—
25C5×#408—31no—
26C2×C5×C22⋊C8—31no—
27C5×#405—31no—
28C22×C5×A4C2×C411yescharacteristic
29C2×C5×S4C2×C412yes—
30C5×#235—41no—
31C4×C5×A4C2×C411yescharacteristic
32C4×C5×A4C2311yescharacteristic
33C5×SL(2,ℤ/4)C2×C412yes—
34C3×C5×M16—41no—
35C2×C5×C3⋊C8—41no—
36C5×ΓL(1,𝔽25)—42no—
37C5×D3×C8—42no—
38#5912C2×C511yescharacteristic
39A4×M16C2×C511yescharacteristic, complemented
40C2×A4⋊C8C2×C511yescharacteristic, complemented
41#5400C2×C512yescomplemented
42C8×S4C2×C512yescomplemented
43C2×C5×#41—31no—
44C23×C4×C5C2×D311yescharacteristic
45C5×#131—61no—
46C5×#131—62no—
47C5×#131—61no—
48C2×C5×M16—31no—
49C2×C5×M16—31no—
50C2×C5×M16—32no—
51C2×C5×M16—32no—
52C22×C5×C8—31no—
53C22×C5×C8—31no—
54C22×C5×C8—32no—
55C22×C5×C8C2×D312yes—
56C5×#123—32no—
57C5×C22⋊Q8—31no—
58C5×C22⋊Q8—31no—
59C5×#121—31no—
60C5×#121—31no—
61C5×#120—32no—
62C4×C5×D4—32no—
63C4×C5×D4—32no—
64C5×#117—31no—
65C5×C4⋊C8—32no—
66C5×C4⋊C8—32no—
67C5×C22⋊C8—31no—
68C5×C22⋊C8—31no—
69C5×C22⋊C8—32no—
70C5×C22⋊C8—32no—
71C5×C22⋊C8—31no—
72C5×C22⋊C8—31no—
73C5×#97—32no—
74C4×C5×C8—32no—
75#2933—31noSylow
76C2×C5×A4—21no—
77C2×C5×A4C22×C411yescharacteristic
78C5×S4—22no—
79C2×C3×C4×C5—41no—
80C5×#67—42no—
81C5×D12—41no—
82C4×C5×D3—42no—
83C5×Dic6—41no—
84C3×C5×C8—42no—
85C5×C3⋊C8—41no—
86C5×C3⋊C8—41no—
87C2×C4×A4C22×C511yescharacteristic
88GL(2,ℤ/4)C4×C512yes—
89C4⋊S4C4×C511yescharacteristic
90C4×S4C22×C512yes—
91A4⋊Q8C4×C511yescharacteristic
92#907—41no—
93C8×A4C22×C512yes—
94A4⋊C8C22×C511yescharacteristic
95A4⋊C8C22×C511yescharacteristic
96C24×C5C4×D311yescharacteristic
97C5×#41—61no—
98C5×#41—61no—
99C5×#41—61no—
100C5×#41—61no—
101C2×C5×Q8—31no—
102C2×C5×D4—32no—
103C2×C5×D4—31no—
104C2×C5×D4—32no—
105C2×C5×D4—32no—
106C22×C4×C5—31no—
107C22×C4×C5—31no—
108C22×C4×C5—31no—
109C22×C4×C5—31no—
110C22×C4×C5—32no—
111C22×C4×C5C4×D311yescharacteristic
112C22×C4×C5C22×D311yescharacteristic
113C5×M16—31no—
114C5×M16—32no—
115C5×M16—61no—
116C5×M16—62no—
117C5×M16—62no—
118C5×M16S411yescharacteristic, complemented
119C2×C5×C8—32no—
120C2×C5×C8—32no—
121C2×C5×C8—31no—
122C2×C5×C8—31no—
123C2×C5×C8—31no—
124C2×C5×C8—31no—
125C2×C5×C8—62no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C2×C5×C8—62no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—32no—
134C5×C4⋊C4—32no—
135C5×C22⋊C4—32no—
136C5×C22⋊C4—32no—
137C5×C22⋊C4—32no—
138C5×C22⋊C4—32no—
139C5×C22⋊C4—32no—
140C42×C5—32no—
141C2×#131—31no—
142C22×M16C5×D311yescharacteristic, complemented
143#525—31no—
144#436—32no—
145#435—32no—
146#435—32no—
147C8×D4—32no—
148#424—31no—
149#408—31no—
150C2×C22⋊C8—31no—
151#405—31no—
152C22×C3×C5—41no—
153C2×C5×D3—42no—
154C5×A4#13111yescharacteristic, complemented
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C5×Dic3—42no—
158C22×A4C2×C4×C511yescharacteristic
159C2×S4C2×C4×C512yes—
160#235—41no—
161C4×A4C2×C4×C511yescharacteristic
162C4×A4C23×C511yescharacteristic
163SL(2,ℤ/4)C2×C4×C512yes—
164C3×M16—41no—
165C2×C3⋊C8—41no—
166ΓL(1,𝔽25)—42no—
167D3×C8—42no—
168C23×C5—21no—
169C23×C5—31no—
170C23×C5—31no—
171C23×C5—32no—
172C23×C5—61no—
173C23×C5C2×C4×D311yescharacteristic
174C5×Q8—61no—
175C5×Q8—61no—
176C5×D4—61no—
177C5×D4—62no—
178C5×D4—62no—
179C5×D4—62no—
180C5×D4—62no—
181C5×D4—61no—
182C5×D4—122no—
183C2×C4×C5—31no—
184C2×C4×C5—31no—
185C2×C4×C5—31no—
186C2×C4×C5—31no—
187C2×C4×C5—31no—
188C2×C4×C5—31no—
189C2×C4×C5—31no—
190C2×C4×C5—32no—
191C2×C4×C5—32no—
192C2×C4×C5—32no—
193C2×C4×C5—61no—
194C2×C4×C5—62no—
195C2×C4×C5—62no—
196C2×C4×C5C2×S411yescharacteristic
197C5×C8—32no—
198C5×C8—61no—
199C5×C8—61no—
200C5×C8—61no—
201C5×C8—61no—
202C5×C8C2×S412yes—
203C2×#41—31no—
204C23×C4C2×C5×D311yescharacteristic
205#131—61no—
206#131—62no—
207#131—61no—
208C2×M16—31no—
209C2×M16—31no—
210C2×M16—32no—
211C2×M16—32no—
212C22×C8—31no—
213C22×C8—32no—
214C22×C8—31no—
215C22×C8C2×C5×D312yes—
216#123—32no—
217C22⋊Q8—31no—
218C22⋊Q8—31no—
219#121—31no—
220#121—31no—
221#120—32no—
222C4×D4—32no—
223C4×D4—32no—
224#117—31no—
225C4⋊C8—32no—
226C4⋊C8—32no—
227C22⋊C8—31no—
228C22⋊C8—31no—
229C22⋊C8—32no—
230C22⋊C8—32no—
231C22⋊C8—31no—
232C22⋊C8—31no—
233#97—32no—
234C4×C8—32no—
235C2×C3×C5—41no—
236C2×C3×C5—81no—
237C5×D3—82no—
238C2×A4—21no—
239C2×A4C22×C4×C511yescharacteristic
240S4—22no—
241C2×C3×C4—41no—
242#67—42no—
243D12—41no—
244C4×D3—42no—
245Dic6—41no—
246C3×C8—42no—
247C3⋊C8—41no—
248C3⋊C8—41no—
249C22×C5—31no—
250C22×C5—31no—
251C22×C5—31no—
252C22×C5—61no—
253C22×C5—61no—
254C22×C5—61no—
255C22×C5—61no—
256C22×C5—62no—
257C22×C5—62no—
258C22×C5—62no—
259C22×C5#90711yescharacteristic, complemented
260C22×C5C4×S411yescharacteristic
261C4×C5—31no—
262C4×C5—31no—
263C4×C5—62no—
264C4×C5—62no—
265C4×C5—62no—
266C4×C5C4×S411yescharacteristic
267C4×C5C22×S411yescharacteristic
268C24C4×C5×D311yescharacteristic
269#41—61no—
270#41—61no—
271#41—61no—
272#41—61no—
273C2×Q8—31no—
274C2×D4—32no—
275C2×D4—31no—
276C2×D4—32no—
277C2×D4—32no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—32no—
283C22×C4C4×C5×D311yescharacteristic
284C22×C4C22×C5×D311yescharacteristic
285M16—31no—
286M16—32no—
287M16—61no—
288M16—62no—
289M16—62no—
290M16C5×S411yescharacteristic, complemented
291C2×C8—32no—
292C2×C8—32no—
293C2×C8—31no—
294C2×C8—31no—
295C2×C8—31no—
296C2×C8—31no—
297C2×C8—62no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—62no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—32no—
306C4⋊C4—32no—
307C22⋊C4—32no—
308C22⋊C4—32no—
309C22⋊C4—32no—
310C22⋊C4—32no—
311C22⋊C4—32no—
312C42—32no—
313C3×C5—41noHall
314C22×C3—41no—
315C2×D3—42no—
316A4C5×#13111yescharacteristic, complemented
317C3×C4—41no—
318C3×C4—41no—
319Dic3—42no—
320C2×C5—21no—
321C2×C5—31no—
322C2×C5—31no—
323C2×C5—61no—
324C2×C5—122no—
325C2×C5C2×C4×S411yescharacteristic
326C23—21no—
327C23—31no—
328C23—31no—
329C23—32no—
330C23—61no—
331C23C2×C4×C5×D311yescharacteristic
332Q8—61no—
333Q8—61no—
334D4—61no—
335D4—62no—
336D4—62no—
337D4—62no—
338D4—62no—
339D4—61no—
340D4—122no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—32no—
349C2×C4—32no—
350C2×C4—32no—
351C2×C4—61no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4C2×C5×S411yescharacteristic
355C8—32no—
356C8—61no—
357C8—61no—
358C8—61no—
359C8—61no—
360C8C2×C5×S412yes—
361C2×C3—41no—
362C2×C3—81no—
363D3—82no—
364C5#8544211yescharacteristic, direct product factor, Sylow
365C22—31no—
366C22—31no—
367C22—31no—
368C22—61no—
369C22—61no—
370C22—61no—
371C22—61no—
372C22—62no—
373C22—62no—
374C22—62no—
375C22C5×#90711yescharacteristic, complemented
376C22C4×C5×S411yescharacteristic
377C4—31no—
378C4—31no—
379C4—62no—
380C4—62no—
381C4—62no—
382C4C4×C5×S411yescharacteristic
383C4C22×C5×S411yescharacteristic
384C3—41noSylow
385C2—21no—
386C2—31no—
387C2—31no—
388C2—61no—
389C2—122no—
390C2C2×C4×C5×S411yescharacteristic
subgroupG/H
centerC4×C5C22×S4
commutatorC2×A4C22×C4×C5
FrattiniC4C22×C5×S4
FittingC22×C5×M16D3
socleC23×C5C2×C4×D3
prime radicalC5×#5912C2
cosocleC4×A4C23×C5
hypercenterC5×M16S4
hypocenterA4C5×#131
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C4×C5 ◁ C5×M16

Complements

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

NH ≅ G/Ntype
2. C5×A4×M16C2semidirect
3. C2×C5×A4⋊C8C2semidirect
4. C5×#5400C2semidirect
5. C5×C8×S4C2semidirect
16. #85442C5direct (N × H)
18. C22×C5×M16D3semidirect
39. A4×M16C2×C5semidirect
40. C2×A4⋊C8C2×C5semidirect
41. #5400C2×C5semidirect
42. C8×S4C2×C5semidirect
118. C5×M16S4semidirect
142. C22×M16C5×D3semidirect
154. C5×A4#131semidirect
259. C22×C5#907semidirect
290. M16C5×S4semidirect
316. A4C5×#131semidirect
364. C5#85442direct (N × H)
375. C22C5×#907semidirect

Maximal subgroups

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

subgroupindex
C5×#59122
C5×A4×M162
C2×C5×A4⋊C82
C5×#54002
C5×C8×S42
C5×#29333
C5×#9074
#854425