Finite Group Databasebeta

← C5×#85444 #14511182

Subgroups — C5×#85444 #14511182

Order 1920.

530 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 76 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
2C2×C5×A4⋊Q8C211yesmaximal, characteristic, complemented
3C5×A4×M16C211yesmaximal, characteristic, complemented
4C5×#5401C212yesmaximal, complemented
5C5×#5398C212yesmaximal, complemented
6C5×#3056—31nomaximal, Hall
7C2×C4×C5×A4C2211yescharacteristic
8C5×GL(2,ℤ/4)—21no—
9C2×C5×SL(2,ℤ/4)—21no—
10C5×C4⋊S4C2211yescharacteristic
11C4×C5×S4—21no—
12C5×A4⋊Q8—21no—
13C5×A4⋊Q8C2212yes—
14C5×A4⋊Q8C2211yescharacteristic
15C5×#909—41nomaximal
16C5×C8×A4C2212yes—
17#85444C511yesmaximal, characteristic, direct product factor, Hall
18C2×C5×#137—31no—
19C22×C5×M16D311yescharacteristic, complemented
20C5×#525—31no—
21C2×C5×C22⋊Q8—31no—
22C5×#470—32no—
23C5×#468—32no—
24C5×#467—32no—
25C5×#465—32no—
26C5×#428—31no—
27C5×#419—31no—
28C5×#417—31no—
29C22×C5×A4D411yescharacteristic
30C2×C5×S4—21no—
31C5×#235—41no—
32C2×C5×Dic6—41no—
33C4×C5×A4D411yescharacteristic
34C4×C5×A4C2311yescharacteristic
35C5×SL(2,ℤ/4)—22no—
36C5×SL(2,ℤ/4)—21no—
37C3×C5×M16—41no—
38C5×Dic12—42no—
39C5×#204—42no—
40#5912C2×C511yescharacteristic
41C2×A4⋊Q8C2×C511yescharacteristic, complemented
42A4×M16C2×C511yescharacteristic, complemented
43#5401C2×C512yescomplemented
44#5398C2×C512yescomplemented
45C2×C5×#41—31no—
46C22×C5×Q8—31no—
47C23×C4×C5C2×D311yescharacteristic
48C5×#137—61no—
49C5×#137—62no—
50C5×#137—61no—
51C2×C5×Q16—32no—
52C2×C5×SD16—32no—
53C2×C5×M16—31no—
54C2×C5×M16—31no—
55C2×C5×M16—32no—
56C22×C5×C8C2×D312yes—
57C5×#123—61no—
58C5×C22⋊Q8—32no—
59C5×C22⋊Q8—31no—
60C5×C22⋊Q8—32no—
61C5×C22⋊Q8—31no—
62C5×C22⋊Q8—61no—
63C5×C22⋊Q8—61no—
64C5×#121—31no—
65C5×#121—31no—
66C5×#120—61no—
67C4×C5×D4—61no—
68C4×C5×D4—61no—
69C5×#117—31no—
70C2×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4—61no—
72C2×C5×C22⋊C4—61no—
73C5×#107—32no—
74C5×#106—32no—
75C5×#103—32no—
76C5×#103—32no—
77C5×#103—32no—
78C5×#102—32no—
79#3056—31noSylow
80C2×C5×A4—21no—
81C2×C5×A4C2×D411yescharacteristic
82C5×S4—41no—
83C2×C3×C4×C5—41no—
84C5×#67—81no—
85C2×C5×Dic3—81no—
86C5×D12—41no—
87C4×C5×D3—81no—
88C5×Dic6—42no—
89C5×Dic6—41no—
90C5×Dic6—81no—
91C3×C5×C8—42no—
92C2×C4×A4C22×C511yescharacteristic
93GL(2,ℤ/4)—21no—
94C2×SL(2,ℤ/4)—21no—
95C4⋊S4C22×C511yescharacteristic
96C4×S4—21no—
97A4⋊Q8—21no—
98A4⋊Q8C22×C512yes—
99A4⋊Q8C22×C511yescharacteristic
100#909—41no—
101C8×A4C22×C512yes—
102C24×C5D1211yescharacteristic
103C5×#41—61no—
104C5×#41—61no—
105C5×#41—61no—
106C5×#41—61no—
107C2×C5×Q8—32no—
108C2×C5×Q8—31no—
109C2×C5×Q8—61no—
110C2×C5×Q8—61no—
111C2×C5×Q8—61no—
112C2×C5×Q8—61no—
113C2×C5×Q8—61no—
114C2×C5×D4—31no—
115C2×C5×D4—61no—
116C2×C5×D4—61no—
117C2×C5×D4—61no—
118C22×C4×C5—31no—
119C22×C4×C5—31no—
120C22×C4×C5—31no—
121C22×C4×C5—31no—
122C22×C4×C5—61no—
123C22×C4×C5—61no—
124C22×C4×C5—61no—
125C22×C4×C5D1211yescharacteristic
126C22×C4×C5C22×D311yescharacteristic
127C5×Q16—62no—
128C5×Q16—62no—
129C5×SD16—62no—
130C5×SD16—62no—
131C5×M16—31no—
132C5×M16—32no—
133C5×M16—61no—
134C5×M16S411yescharacteristic, complemented
135C2×C5×C8—32no—
136C2×C5×C8—32no—
137C5×C4⋊C4—32no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—62no—
142C5×C4⋊C4—62no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4—61no—
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—62no—
148C5×C22⋊C4—61no—
149C5×C22⋊C4—61no—
150C5×C22⋊C4—62no—
151C5×C22⋊C4—61no—
152C42×C5—61no—
153C2×#137—31no—
154C22×M16C5×D311yescharacteristic, complemented
155#525—31no—
156C2×C22⋊Q8—31no—
157#470—32no—
158#468—32no—
159#467—32no—
160#465—32no—
161#428—31no—
162#419—31no—
163#417—31no—
164C22×C3×C5—41no—
165C2×C5×D3—81no—
166C5×A4#13711yescharacteristic, complemented
167C3×C4×C5—41no—
168C3×C4×C5—41no—
169C5×Dic3—82no—
170C5×Dic3—81no—
171C22×A4C5×D411yescharacteristic
172C2×S4—21no—
173#235—41no—
174C2×Dic6—41no—
175C4×A4C5×D411yescharacteristic
176C4×A4C23×C511yescharacteristic
177SL(2,ℤ/4)—22no—
178SL(2,ℤ/4)—21no—
179C3×M16—41no—
180Dic12—42no—
181#204—42no—
182C23×C5—21no—
183C23×C5—31no—
184C23×C5—31no—
185C23×C5—61no—
186C23×C5—61no—
187C23×C5C2×D1211yescharacteristic
188C5×Q8—62no—
189C5×Q8—61no—
190C5×Q8—62no—
191C5×Q8—61no—
192C5×Q8—121no—
193C5×Q8—121no—
194C5×D4—61no—
195C5×D4—61no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—122no—
199C5×D4—121no—
200C5×D4—121no—
201C2×C4×C5—31no—
202C2×C4×C5—31no—
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5—31no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5—61no—
211C2×C4×C5—62no—
212C2×C4×C5—61no—
213C2×C4×C5—62no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5—122no—
217C2×C4×C5—121no—
218C2×C4×C5—121no—
219C2×C4×C5C2×S411yescharacteristic
220C5×C8—32no—
221C5×C8C2×S412yes—
222C2×#41—31no—
223C22×Q8—31no—
224C23×C4C2×C5×D311yescharacteristic
225#137—61no—
226#137—62no—
227#137—61no—
228C2×Q16—32no—
229C2×SD16—32no—
230C2×M16—31no—
231C2×M16—31no—
232C2×M16—32no—
233C22×C8C2×C5×D312yes—
234#123—61no—
235C22⋊Q8—32no—
236C22⋊Q8—31no—
237C22⋊Q8—32no—
238C22⋊Q8—31no—
239C22⋊Q8—61no—
240C22⋊Q8—61no—
241#121—31no—
242#121—31no—
243#120—61no—
244C4×D4—61no—
245C4×D4—61no—
246#117—31no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—61no—
249C2×C22⋊C4—61no—
250#107—32no—
251#106—32no—
252#103—32no—
253#103—32no—
254#103—32no—
255#102—32no—
256C2×C3×C5—41no—
257C2×C3×C5—81no—
258C5×D3—161no—
259C2×A4—21no—
260C2×A4C2×C5×D411yescharacteristic
261S4—41no—
262C2×C3×C4—41no—
263#67—81no—
264C2×Dic3—81no—
265D12—41no—
266C4×D3—81no—
267Dic6—42no—
268Dic6—41no—
269Dic6—81no—
270C3×C8—42no—
271C22×C5—31no—
272C22×C5—31no—
273C22×C5—31no—
274C22×C5—61no—
275C22×C5—61no—
276C22×C5—61no—
277C22×C5—61no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5—121no—
281C22×C5#90911yescharacteristic, complemented
282C22×C5C4⋊S411yescharacteristic
283C4×C5—31no—
284C4×C5—31no—
285C4×C5—122no—
286C4×C5—121no—
287C4×C5—121no—
288C4×C5—121no—
289C4×C5—122no—
290C4×C5C4⋊S411yescharacteristic
291C4×C5C22×S411yescharacteristic
292C24C5×D1211yescharacteristic
293#41—61no—
294#41—61no—
295#41—61no—
296#41—61no—
297C2×Q8—32no—
298C2×Q8—31no—
299C2×Q8—61no—
300C2×Q8—61no—
301C2×Q8—61no—
302C2×Q8—61no—
303C2×Q8—61no—
304C2×D4—31no—
305C2×D4—61no—
306C2×D4—61no—
307C2×D4—61no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—61no—
313C22×C4—61no—
314C22×C4—61no—
315C22×C4C5×D1211yescharacteristic
316C22×C4C22×C5×D311yescharacteristic
317Q16—62no—
318Q16—62no—
319SD16—62no—
320SD16—62no—
321M16—31no—
322M16—32no—
323M16—61no—
324M16C5×S411yescharacteristic, complemented
325C2×C8—32no—
326C2×C8—32no—
327C4⋊C4—32no—
328C4⋊C4—31no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—62no—
332C4⋊C4—62no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C22⋊C4—62no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—62no—
341C22⋊C4—61no—
342C42—61no—
343C3×C5—41noHall
344C22×C3—41no—
345C2×D3—81no—
346A4C5×#13711yescharacteristic, complemented
347C3×C4—41no—
348C3×C4—41no—
349Dic3—82no—
350Dic3—81no—
351C2×C5—21no—
352C2×C5—31no—
353C2×C5—31no—
354C2×C5—61no—
355C2×C5—241no—
356C2×C5C2×C4⋊S411yescharacteristic
357C23—21no—
358C23—31no—
359C23—31no—
360C23—61no—
361C23—61no—
362C23C2×C5×D1211yescharacteristic
363Q8—62no—
364Q8—61no—
365Q8—62no—
366Q8—61no—
367Q8—121no—
368Q8—121no—
369D4—61no—
370D4—61no—
371D4—121no—
372D4—121no—
373D4—122no—
374D4—121no—
375D4—121no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—62no—
387C2×C4—61no—
388C2×C4—62no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—122no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4C2×C5×S411yescharacteristic
395C8—32no—
396C8C2×C5×S412yes—
397C2×C3—41no—
398C2×C3—81no—
399D3—161no—
400C5#8544411yescharacteristic, direct product factor, Sylow
401C22—31no—
402C22—31no—
403C22—31no—
404C22—61no—
405C22—61no—
406C22—61no—
407C22—61no—
408C22—121no—
409C22—121no—
410C22—121no—
411C22C5×#90911yescharacteristic, complemented
412C22C5×C4⋊S411yescharacteristic
413C4—31no—
414C4—31no—
415C4—122no—
416C4—121no—
417C4—121no—
418C4—121no—
419C4—122no—
420C4C5×C4⋊S411yescharacteristic
421C4C22×C5×S411yescharacteristic
422C3—41noSylow
423C2—21no—
424C2—31no—
425C2—31no—
426C2—61no—
427C2—241no—
428C2C2×C5×C4⋊S411yescharacteristic
subgroupG/H
centerC2×C5C2×C4⋊S4
commutator, cosocleC4×A4C23×C5
FrattiniC4C22×C5×S4
FittingC22×C5×M16D3
socleC23×C5C2×D12
prime radicalC5×#5912C2
hypercenterC5×M16S4
hypocenterA4C5×#137
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×M16

Complements

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

NH ≅ G/Ntype
2. C2×C5×A4⋊Q8C2semidirect
3. C5×A4×M16C2semidirect
4. C5×#5401C2semidirect
5. C5×#5398C2semidirect
17. #85444C5direct (N × H)
19. C22×C5×M16D3semidirect
41. C2×A4⋊Q8C2×C5semidirect
42. A4×M16C2×C5semidirect
43. #5401C2×C5semidirect
44. #5398C2×C5semidirect
134. C5×M16S4semidirect
154. C22×M16C5×D3semidirect
166. C5×A4#137semidirect
281. C22×C5#909semidirect
324. M16C5×S4semidirect
346. A4C5×#137semidirect
400. C5#85444direct (N × H)
411. C22C5×#909semidirect

Maximal subgroups

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

subgroupindex
C5×#59122
C2×C5×A4⋊Q82
C5×A4×M162
C5×#54012
C5×#53982
C5×#30563
C5×#9094
#854445