Finite Group Databasebeta

← #14284757

Subgroups — #14284757

Order 1920.

404 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5728C211yesmaximal, characteristic
2#11746853C211yesmaximal, characteristic
3#11746853C211yesmaximal, characteristic
4#11746368C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745858C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10602622—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C5×#946—21no—
11C5×Q8×Dic3—21no—
12C5×#897—21no—
13C5×#892C412yes—
14C5×#890C412yes—
15C5×#887—21no—
16C42×C5×D3C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22(C2×D3)⋊#168—21no—
23(C2×D3)⋊#168—21no—
24Dic3×#168—21no—
25Dic3×#168—21no—
26#68419—51nomaximal, Hall
27C5×#533—31no—
28#65214—31no—
29#65214—31no—
30#64767—31no—
31#64767—31no—
32#64767—31no—
33#64767D311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C4×C5×D3C2×C411yescharacteristic
36C2×C4×C5×D3D411yescharacteristic
37C2×C4×C5×D3D411yescharacteristic
38C2×C5×Dic6—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4C2×C412yes—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×(C2×D3)⋊C4—22no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—22no—
47C5×C4⋊Dic3C2×C412yes—
48C5×Dic3⋊C4—22no—
49C4×C5×Dic3—22no—
50C4×C5×Dic3C2×C411yescharacteristic
51C4×C5×Dic3D411yescharacteristic
52C4×C5×Dic3D411yescharacteristic
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55#5728D511yescharacteristic
56#4833—51no—
57#4833—51no—
58C3×#332—51no—
59#4547—51no—
60#4486—51no—
61#4482—51no—
62C5×C4⋊Q8—31no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C5×#125—32no—
65C5×C22⋊Q8—61no—
66C5×C22⋊Q8—61no—
67C4×C5×Q8—61no—
68C4×C5×Q8—61no—
69C5×#117—32no—
70C2×C42×C5—31no—
71C22⋊#168—61no—
72C22⋊#168—61no—
73C4⋊#168—31no—
74C4⋊#168—31no—
75C4⋊#168C2×D311yescharacteristic
76C4⋊#168C2×D311yescharacteristic
77C4×#168—61no—
78C4×#168—61no—
79#1544—151noSylow
80C22×C5×D3C22⋊C411yescharacteristic
81C3×C5×Q8—41no—
82C3×C5×Q8—41no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C5×Dic3—22no—
88C2×C5×Dic3C22⋊C411yescharacteristic
89C2×C5×Dic3C22⋊C411yescharacteristic
90C2×C5×Dic3C22⋊C411yescharacteristic
91C4×C5×D3—21no—
92C4×C5×D3—21no—
93C4×C5×D3—21no—
94C4×C5×D3—21no—
95C4×C5×D3—22no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C3⋊#168—41no—
99C3⋊#168—41no—
100C3×#168—41no—
101C3×#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103#946—21no—
104Q8×Dic3—21no—
105#897—21no—
106#892Dic512yes—
107#890Dic512yes—
108#887—21no—
109C42×D3C2×D511yescharacteristic
110#869C2×D511yescharacteristic
111C3×C4⋊C8—51no—
112C3×C4⋊C8—51no—
113(C2×D3)⋊C8—101no—
114(C2×D3)⋊C8—101no—
115C8×Dic3—101no—
116C8×Dic3—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8—61no—
121C22×C4×C5—31no—
122C22×C4×C5—31no—
123C22×C4×C5—31no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—32no—
126C5×C4⋊C4—62no—
127C5×C4⋊C4—62no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4C4×D312yes—
130C5×C22⋊C4—62no—
131C42×C5—31no—
132C42×C5—31no—
133C42×C5—31no—
134C42×C5—62no—
135C42×C5C22×D311yescharacteristic
136C2×#168—21no—
137C2×#168—21no—
138C2×#168—61no—
139C2×#168—61no—
140#533—31no—
141#431—151no—
142#431—151no—
143#332—51no—
144#332—151no—
145#332—151no—
146#332—151no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C2×C5×D3—21no—
149C2×C5×D3—21no—
150C2×C5×D3—21no—
151C3×C4×C5—21no—
152C3×C4×C5—42no—
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C5×Dic3—21no—
158C5×Dic3—21no—
159C5×Dic3—42no—
160C5×Dic3#10112yes—
161C2×C3×Q8—21no—
162C2×C4×D3C2×Dic511yescharacteristic
163C2×C4×D3C22⋊D511yescharacteristic
164C2×C4×D3C22⋊D511yescharacteristic
165C2×Dic6—21no—
166C2×C3×C8—101no—
167C2×C3×C8—101no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4C2×Dic512yes—
170C3×C42C22×D511yescharacteristic
171(C2×D3)⋊C4—22no—
172C4⋊Dic3—21no—
173C4⋊Dic3—22no—
174C4⋊Dic3C2×Dic512yes—
175Dic3⋊C4—22no—
176C4×Dic3—22no—
177C4×Dic3C2×Dic511yescharacteristic
178C4×Dic3C22⋊D511yescharacteristic
179C4×Dic3C22⋊D511yescharacteristic
180C2×C3⋊C8—101no—
181C2×C3⋊C8—101no—
182C23×C5—31no—
183C5×Q8—41no—
184C5×Q8—41no—
185C5×Q8—121no—
186C5×Q8—121no—
187C2×C4×C5—22no—
188C2×C4×C5—31no—
189C2×C4×C5—31no—
190C2×C4×C5—31no—
191C2×C4×C5—62no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5—61no—
196C2×C4×C5—62no—
197C2×C4×C5C2×C4×D311yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200#168—41no—
201#168—41no—
202#168—121no—
203#168—121no—
204C4⋊Q8—31no—
205C4⋊Q8D3×D511yescharacteristic
206#125—32no—
207C22⋊Q8—61no—
208C22⋊Q8—61no—
209C4×Q8—61no—
210C4×Q8—61no—
211#117—32no—
212C2×C42—31no—
213C4⋊C8—51no—
214C4⋊C8—51no—
215C4⋊C8—151no—
216C4⋊C8—151no—
217C22⋊C8—301no—
218C22⋊C8—301no—
219C4×C8—301no—
220C4×C8—301no—
221C2×C3×C5C2×#10111yescharacteristic
222C2×C3×C5#41611yescharacteristic
223C2×C3×C5#41611yescharacteristic
224C5×D3—41no—
225C22×D3C22⋊Dic511yescharacteristic
226C3×Q8—41no—
227C3×Q8—41no—
228C2×C3×C4—22no—
229C2×C3×C4C22×Dic511yescharacteristic
230C2×C3×C4C2×C22⋊D511yescharacteristic
231C2×C3×C4C2×C22⋊D511yescharacteristic
232C2×Dic3—22no—
233C2×Dic3C22⋊Dic511yescharacteristic
234C2×Dic3C22⋊Dic511yescharacteristic
235C2×Dic3C22⋊Dic511yescharacteristic
236C4×D3—21no—
237C4×D3—21no—
238C4×D3—21no—
239C4×D3—21no—
240C4×D3—22no—
241Dic6—41no—
242Dic6—41no—
243C3×C8—201no—
244C3×C8—201no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5—61no—
248C22×C5—61no—
249C22×C5—61no—
250C22×C5D3×C22⋊C411yescharacteristic
251C4×C5—21no—
252C4×C5—32no—
253C4×C5—42no—
254C4×C5—61no—
255C4×C5—61no—
256C4×C5—122no—
257C4×C5#91211yescharacteristic
258C4×C5#91611yescharacteristic
259C4×C5#91611yescharacteristic
260C4×C5#91911yescharacteristic
261C2×Q8—21no—
262C2×Q8—61no—
263C22×C4—31no—
264C22×C4—31no—
265C22×C4—31no—
266C2×C8—101no—
267C2×C8—101no—
268C2×C8—301no—
269C2×C8—301no—
270C4⋊C4—21no—
271C4⋊C4—32no—
272C4⋊C4—62no—
273C4⋊C4—62no—
274C4⋊C4—61no—
275C4⋊C4D3×Dic512yes—
276C22⋊C4—62no—
277C42—31no—
278C42—31no—
279C42—31no—
280C42—62no—
281C42C2×D3×D511yescharacteristic
282C3×C5#154411yescharacteristic, complemented, Hall
283C22×C3C2×C22⋊Dic511yescharacteristic
284C2×D3—21no—
285C2×D3—21no—
286C2×D3—21no—
287C3×C4—21no—
288C3×C4—42no—
289C3×C4#409611yescharacteristic
290C3×C4#409611yescharacteristic
291C3×C4#409611yescharacteristic
292C3×C4#409611yescharacteristic
293Dic3—21no—
294Dic3—21no—
295Dic3—42no—
296Dic3#396812yes—
297C2×C5—121no—
298C2×C5D3×#10111yescharacteristic
299C2×C5#477211yescharacteristic
300C2×C5#480411yescharacteristic
301C23—31no—
302Q8—41no—
303Q8—41no—
304Q8—121no—
305Q8—121no—
306C2×C4—22no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—62no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—62no—
316C2×C4C2×D3×Dic511yescharacteristic
317C2×C4D3×C22⋊D511yescharacteristic
318C2×C4D3×C22⋊D511yescharacteristic
319C8—201no—
320C8—201no—
321C8—601no—
322C8—601no—
323C2×C3C2×#396811yescharacteristic
324C2×C3#6552211yescharacteristic
325C2×C3#6552211yescharacteristic
326D3—41no—
327C5#6841911yescharacteristic, complemented, Sylow
328C22—61no—
329C22—61no—
330C22—61no—
331C22D3×C22⋊Dic511yescharacteristic
332C4—21no—
333C4—32no—
334C4—42no—
335C4—61no—
336C4—61no—
337C4—122no—
338C4#9149311yescharacteristic
339C4#9149511yescharacteristic
340C4#9151711yescharacteristic
341C4#9151911yescharacteristic
342C3#1060262211yescharacteristic, complemented, Sylow
343C2—121no—
344C2#1174896511yescharacteristic
345C2#1174921111yescharacteristic
346C2D3×#396811yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1544
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746368C2semidirect
5. C3×#64767C2semidirect
6. #11745858C2semidirect
7. #11745857C2semidirect
33. #64767D3semidirect
282. C3×C5#1544semidirect
327. C5#68419semidirect
342. C3#10602622semidirect

Maximal subgroups

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

subgroupindex
C5×#57282
#117468532
#117463682
C3×#647672
#117458582
#117458572
#106026223
#684195