Finite Group Databasebeta

← C5×A4×#103 #14510960

Subgroups — C5×A4×#103 #14510960

Order 1920.

412 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 84 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×Q8×A4C211yesmaximal, characteristic
2C2×C5×C8×A4C211yesmaximal, characteristic
3C5×A4×C4⋊C4C211yesmaximal, characteristic
4C22×C5×#103C311yesmaximal, characteristic, complemented, Hall
5C5×Q8×A4—21no—
6C5×Q8×A4C412yescomplemented
7C2×C4×C5×A4—21no—
8C2×C4×C5×A4—21no—
9C2×C4×C5×A4C2211yescharacteristic
10C5×C8×A4—21no—
11C3×C5×#103—41nomaximal
12A4×#103C511yesmaximal, characteristic, direct product factor, Hall
13C23×C5×Q8C2×C311yescharacteristic
14C23×C5×C8C2×C311yescharacteristic
15C22×C5×C4⋊C4C2×C311yescharacteristic
16C2×C5×#103—31no—
17C2×C5×#103—31no—
18C2×C5×#103—31no—
19C2×C5×#103—31no—
20C22×C5×A4D411yescharacteristic
21C2×C3×C5×Q8—41no—
22C4×C5×A4—22no—
23C4×C5×A4—41no—
24C4×C5×A4C2×C411yescharacteristic
25C4×C5×A4D411yescharacteristic
26C2×C3×C5×C8—41no—
27C3×C5×C4⋊C4—41no—
28C2×Q8×A4C2×C511yescharacteristic
29C2×C8×A4C2×C511yescharacteristic
30A4×C4⋊C4C2×C511yescharacteristic
31C22×C5×Q8—21no—
32C22×C5×Q8—31no—
33C22×C5×Q8—32no—
34C22×C5×Q8—31no—
35C22×C5×Q8—61no—
36C22×C5×Q8—61no—
37C22×C5×Q8C3×C412yescomplemented
38C23×C4×C5—21no—
39C23×C4×C5—21no—
40C23×C4×C5C22×C311yescharacteristic
41C22×C5×C8—21no—
42C22×C5×C8—31no—
43C22×C5×C8—31no—
44C22×C5×C8—61no—
45C2×C5×C4⋊C4—31no—
46C2×C5×C4⋊C4—31no—
47C2×C5×C4⋊C4—61no—
48C5×#103—32no—
49C5×#103—31no—
50C5×#103—31no—
51C5×#103—31no—
52C5×#103A411yescharacteristic, direct product factor
53C22×#103C3×C511yescharacteristic, complemented, Sylow
54C2×C5×A4C22⋊C411yescharacteristic
55C2×C5×A4SD1611yescharacteristic
56C2×C5×A4Q1611yescharacteristic
57C3×C5×Q8—42no—
58C3×C5×Q8—81no—
59C2×C3×C4×C5—41no—
60C2×C3×C4×C5—81no—
61C2×C3×C4×C5—81no—
62C3×C5×C8—81no—
63Q8×A4—21no—
64Q8×A4C4×C512yescomplemented
65C2×C4×A4—21no—
66C2×C4×A4—21no—
67C2×C4×A4C22×C511yescharacteristic
68C8×A4—21no—
69C3×#103—41no—
70C24×C5C3×D411yescharacteristic
71C2×C5×Q8—32no—
72C2×C5×Q8—32no—
73C2×C5×Q8—32no—
74C2×C5×Q8—32no—
75C2×C5×Q8—31no—
76C2×C5×Q8—61no—
77C2×C5×Q8—61no—
78C2×C5×Q8—61no—
79C2×C5×Q8—62no—
80C2×C5×Q8—61no—
81C2×C5×Q8—62no—
82C2×C5×Q8—61no—
83C2×C5×Q8—64no—
84C2×C5×Q8—61no—
85C2×C5×Q8C2×A411yescharacteristic
86C22×C4×C5—22no—
87C22×C4×C5—31no—
88C22×C4×C5—31no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—41no—
92C22×C4×C5—61no—
93C22×C4×C5—61no—
94C22×C4×C5—62no—
95C22×C4×C5—61no—
96C22×C4×C5—61no—
97C22×C4×C5—121no—
98C22×C4×C5C2×C3×C411yescharacteristic
99C22×C4×C5C3×D411yescharacteristic
100C2×C5×C8—31no—
101C2×C5×C8—61no—
102C2×C5×C8—61no—
103C2×C5×C8—61no—
104C2×C5×C8—61no—
105C2×C5×C8C2×A411yescharacteristic
106C5×C4⋊C4—31no—
107C5×C4⋊C4—61no—
108C5×C4⋊C4—61no—
109C5×C4⋊C4C2×A411yescharacteristic
110C23×Q8C2×C3×C511yescharacteristic
111C23×C8C2×C3×C511yescharacteristic
112C22×C4⋊C4C2×C3×C511yescharacteristic
113C2×#103—31no—
114C2×#103—31no—
115C2×#103—31no—
116C2×#103—31no—
117C22×C3×C5—41no—
118C5×A4#10311yescharacteristic, direct product factor
119C3×C4×C5—41no—
120C3×C4×C5—41no—
121C3×C4×C5—82no—
122C3×C4×C5—161no—
123C22×A4C5×D411yescharacteristic
124C2×C3×Q8—41no—
125C4×A4—22no—
126C4×A4—41no—
127C4×A4C2×C4×C511yescharacteristic
128C4×A4C5×D411yescharacteristic
129C2×C3×C8—41no—
130C3×C4⋊C4—41no—
131C23×C5—31no—
132C23×C5—31no—
133C23×C5—31no—
134C23×C5—31no—
135C23×C5C3×C22⋊C411yescharacteristic
136C23×C5C3×SD1611yescharacteristic
137C23×C5C3×Q1611yescharacteristic
138C5×Q8—21no—
139C5×Q8—32no—
140C5×Q8—62no—
141C5×Q8—62no—
142C5×Q8—62no—
143C5×Q8—62no—
144C5×Q8—61no—
145C5×Q8C4×A412yescomplemented
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—32no—
149C2×C4×C5—31no—
150C2×C4×C5—31no—
151C2×C4×C5—31no—
152C2×C4×C5—31no—
153C2×C4×C5—31no—
154C2×C4×C5—31no—
155C2×C4×C5—31no—
156C2×C4×C5—62no—
157C2×C4×C5—62no—
158C2×C4×C5—62no—
159C2×C4×C5—61no—
160C2×C4×C5—62no—
161C2×C4×C5—61no—
162C2×C4×C5—121no—
163C2×C4×C5—121no—
164C2×C4×C5—121no—
165C2×C4×C5—121no—
166C2×C4×C5C22×A411yescharacteristic
167C5×C8—21no—
168C5×C8—61no—
169C22×Q8—21no—
170C22×Q8—32no—
171C22×Q8—31no—
172C22×Q8—31no—
173C22×Q8—61no—
174C22×Q8—61no—
175C22×Q8C3×C4×C512yescomplemented
176C23×C4—21no—
177C23×C4—21no—
178C23×C4C22×C3×C511yescharacteristic
179C22×C8—21no—
180C22×C8—31no—
181C22×C8—31no—
182C22×C8—61no—
183C2×C4⋊C4—31no—
184C2×C4⋊C4—31no—
185C2×C4⋊C4—61no—
186#103—32no—
187#103—31no—
188#103—31no—
189#103—31no—
190#103C5×A411yescharacteristic, direct product factor
191C2×C3×C5—41no—
192C2×C3×C5—41no—
193C2×C3×C5—41no—
194C2×A4C5×C22⋊C411yescharacteristic
195C2×A4C5×SD1611yescharacteristic
196C2×A4C5×Q1611yescharacteristic
197C3×Q8—42no—
198C3×Q8—81no—
199C2×C3×C4—41no—
200C2×C3×C4—81no—
201C2×C3×C4—81no—
202C3×C8—81no—
203C22×C5—31no—
204C22×C5—31no—
205C22×C5—31no—
206C22×C5—32no—
207C22×C5—31no—
208C22×C5—31no—
209C22×C5—31no—
210C22×C5—31no—
211C22×C5—31no—
212C22×C5—31no—
213C22×C5C3×#10311yescharacteristic, complemented
214C22×C5D4×A411yescharacteristic
215C4×C5—22no—
216C4×C5—31no—
217C4×C5—31no—
218C4×C5—41no—
219C4×C5—62no—
220C4×C5—121no—
221C4×C5C2×C4×A411yescharacteristic
222C4×C5D4×A411yescharacteristic
223C24C3×C5×D411yescharacteristic
224C2×Q8—32no—
225C2×Q8—32no—
226C2×Q8—32no—
227C2×Q8—32no—
228C2×Q8—31no—
229C2×Q8—61no—
230C2×Q8—61no—
231C2×Q8—61no—
232C2×Q8—62no—
233C2×Q8—61no—
234C2×Q8—62no—
235C2×Q8—61no—
236C2×Q8—64no—
237C2×Q8—61no—
238C2×Q8C2×C5×A411yescharacteristic
239C22×C4—22no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—41no—
245C22×C4—61no—
246C22×C4—61no—
247C22×C4—62no—
248C22×C4—61no—
249C22×C4—61no—
250C22×C4—121no—
251C22×C4C2×C3×C4×C511yescharacteristic
252C22×C4C3×C5×D411yescharacteristic
253C2×C8—31no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—61no—
257C2×C8—61no—
258C2×C8C2×C5×A411yescharacteristic
259C4⋊C4—31no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4C2×C5×A411yescharacteristic
263C3×C5—41noHall
264C22×C3—41no—
265A4C5×#10311yescharacteristic, direct product factor
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—82no—
269C3×C4—161no—
270C2×C5—31no—
271C2×C5—31no—
272C2×C5—31no—
273C2×C5—31no—
274C2×C5A4×C22⋊C411yescharacteristic
275C2×C5A4×SD1611yescharacteristic
276C2×C5A4×Q1611yescharacteristic
277C23—31no—
278C23—31no—
279C23—31no—
280C23—31no—
281C23C3×C5×C22⋊C411yescharacteristic
282C23C3×C5×SD1611yescharacteristic
283C23C3×C5×Q1611yescharacteristic
284Q8—21no—
285Q8—32no—
286Q8—62no—
287Q8—62no—
288Q8—62no—
289Q8—62no—
290Q8—61no—
291Q8C4×C5×A412yescomplemented
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—32no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—31no—
299C2×C4—31no—
300C2×C4—31no—
301C2×C4—31no—
302C2×C4—62no—
303C2×C4—62no—
304C2×C4—62no—
305C2×C4—61no—
306C2×C4—62no—
307C2×C4—61no—
308C2×C4—121no—
309C2×C4—121no—
310C2×C4—121no—
311C2×C4—121no—
312C2×C4C22×C5×A411yescharacteristic
313C8—21no—
314C8—61no—
315C2×C3—41no—
316C2×C3—41no—
317C2×C3—41no—
318C5A4×#10311yescharacteristic, direct product factor, Sylow
319C22—31no—
320C22—31no—
321C22—31no—
322C22—32no—
323C22—31no—
324C22—31no—
325C22—31no—
326C22—31no—
327C22—31no—
328C22—31no—
329C22C3×C5×#10311yescharacteristic, complemented
330C22C5×D4×A411yescharacteristic
331C4—22no—
332C4—31no—
333C4—31no—
334C4—41no—
335C4—62no—
336C4—121no—
337C4C2×C4×C5×A411yescharacteristic
338C4C5×D4×A411yescharacteristic
339C3—41noSylow
340C2—31no—
341C2—31no—
342C2—31no—
343C2—31no—
344C2C5×A4×C22⋊C411yescharacteristic
345C2C5×A4×SD1611yescharacteristic
346C2C5×A4×Q1611yescharacteristic
subgroupG/H
centerC22×C5D4×A4
commutatorC22×C4C2×C3×C4×C5
FrattiniC2×C4C22×C5×A4
FittingC22×C5×#103C3
socleC24×C5C3×D4
prime radicalC22×C5×A4D4
cosocleC23×C4C22×C3×C5
hypercenterC5×#103A4
hypocenterC22C3×C5×#103
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×#103

Complements

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

NH ≅ G/Ntype
4. C22×C5×#103C3semidirect
6. C5×Q8×A4C4semidirect
12. A4×#103C5direct (N × H)
37. C22×C5×Q8C3×C4semidirect
52. C5×#103A4direct (N × H)
53. C22×#103C3×C5semidirect
64. Q8×A4C4×C5semidirect
118. C5×A4#103direct (N × H)
145. C5×Q8C4×A4semidirect
175. C22×Q8C3×C4×C5semidirect
190. #103C5×A4direct (N × H)
213. C22×C5C3×#103semidirect
265. A4C5×#103direct (N × H)
291. Q8C4×C5×A4semidirect
318. C5A4×#103direct (N × H)
329. C22C3×C5×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q8×A42
C2×C5×C8×A42
C5×A4×C4⋊C42
C22×C5×#1033
C3×C5×#1034
A4×#1035