Finite Group Databasebeta

← #14281289

Subgroups — #14281289

Order 1920.

408 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 109 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×C3×#4035C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic
3#11752407C211yesmaximal, characteristic
4#11746785C212yesmaximal
5#11746784C212yesmaximal
6#10604297—31nomaximal, Hall
7C2×C3×C5×C4⋊C4C411yescharacteristic
8C2×C3×C4⋊Dic5C2211yescharacteristic
9C2×C3×#683C411yescharacteristic
10C2×C3×#683C411yescharacteristic
11C2×C3×#683C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4035—21no—
15C3×#4035—21no—
16C3×#4035—21no—
17C3×#4035—21no—
18#91241C2212yes—
19#91241C2212yes—
20#91233—21no—
21#91231—21no—
22C4⋊(C3⋊#170)—21no—
23C4×C3⋊#170—21no—
24#71737—51nomaximal, Hall
25C2×#4035D311yescharacteristic
26#65757—31no—
27#65748—31no—
28#64914—32no—
29#64913—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×Dic5C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2311yescharacteristic
37C2×C3⋊#170—22no—
38C2×C3⋊#170—22no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C4⋊Dic5—21no—
42C3×C4⋊Dic5—21no—
43C3×#683—21no—
44C3×#683—21no—
45C3×#683—21no—
46C3×#683—21no—
47C3×#683—21no—
48C3×#683—21no—
49C3×#683—21no—
50C3×#683—21no—
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#125—51no—
56#4926—51no—
57#4925—51no—
58#4528—52no—
59#4528—52no—
60C2×C5×C4⋊C4Dic311yescharacteristic
61C2×C4⋊Dic5C2×D311yescharacteristic
62C2×#683Dic311yescharacteristic
63C2×#683Dic311yescharacteristic
64C2×#683Dic311yescharacteristic
65C2×#683C2×D311yescharacteristic
66C2×C4×Dic5C2×D311yescharacteristic
67#4035—21no—
68#4035—21no—
69#4035—21no—
70#4035—21no—
71C22⋊#170—32no—
72C22⋊#170—32no—
73#4004—61no—
74#4002—61no—
75C4⋊#170—61no—
76C4×#170—61no—
77#1470—151noSylow
78C23×C3×C5C22×C411yescharacteristic
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×Dic5—22no—
87C2×C3×Dic5—21no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—41no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C3⋊#170—42no—
97C3⋊#170—42no—
98C3×#125—101no—
99C3×#125—101no—
100C3×#125—101no—
101C3×#125—101no—
102C2×C3×C4⋊C4—51no—
103C2×C3×C4⋊C4—51no—
104C2×C3×C4⋊C4—51no—
105C2×C3×C4⋊C4—51no—
106C2×C3×C4⋊C4—51no—
107C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
108C2×C3×C42—51no—
109#830—52no—
110#830—52no—
111C4⋊(C3⋊C8)—101no—
112C4⋊(C3⋊C8)—101no—
113#803—101no—
114C4×C3⋊C8—101no—
115C22×C4×C5C2×Dic311yescharacteristic
116C22×C4×C5C2×Dic311yescharacteristic
117C22×C4×C5C2×Dic311yescharacteristic
118C22×Dic5C2×Dic311yescharacteristic
119C22×Dic5C2×Dic311yescharacteristic
120C22×Dic5C2×Dic311yescharacteristic
121C22×Dic5C22×D311yescharacteristic
122C2×#170—62no—
123C2×#170—62no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C4⋊Dic5—21no—
127C4⋊Dic5—21no—
128#683—21no—
129#683—21no—
130#683—21no—
131#683—21no—
132#683—21no—
133#683—21no—
134#683—21no—
135#683—21no—
136C4×Dic5#6711yescharacteristic
137C4×Dic5#6711yescharacteristic
138C4×Dic5#6711yescharacteristic
139C4×Dic5#6711yescharacteristic
140C2×#125—51no—
141#432—151no—
142#431—151no—
143#324—152no—
144#324—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C22×C3×C5#13112yes—
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151C3×C4×C5—41no—
152C3×C4×C5—41no—
153C3×Dic5—21no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C3×Dic5—41no—
157C3×Dic5—41no—
158C3×Dic5#10112yes—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
164C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
165C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—101no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C42—51no—
179C3×C42—51no—
180C3×C42—51no—
181C3×C42—51no—
182C2×C3⋊C8—102no—
183C2×C3⋊C8—102no—
184C23×C5C22×Dic311yescharacteristic
185C2×C4×C5—22no—
186C2×C4×C5—22no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—41no—
190C2×C4×C5#21711yescharacteristic
191C2×C4×C5#21711yescharacteristic
192C2×Dic5—22no—
193C2×Dic5—22no—
194C2×Dic5—21no—
195C2×Dic5—21no—
196C2×Dic5—41no—
197C2×Dic5—41no—
198C2×Dic5#21711yescharacteristic
199C2×Dic5#21711yescharacteristic
200C2×Dic5C2×#6711yescharacteristic
201C2×Dic5C2×#6711yescharacteristic
202#170—122no—
203#170—122no—
204#125—101no—
205#125—101no—
206#125—101no—
207#125—101no—
208C2×C4⋊C4—51no—
209C2×C4⋊C4—51no—
210C2×C4⋊C4—51no—
211C2×C4⋊C4—51no—
212C2×C4⋊C4—51no—
213C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
214C2×C42—51no—
215C4⋊C8—301no—
216C4⋊C8—301no—
217C22⋊C8—152no—
218C22⋊C8—152no—
219#97—301no—
220C4×C8—301no—
221C2×C3×C5—22no—
222C2×C3×C5#40811yescharacteristic
223C2×C3×C5#41011yescharacteristic
224C2×C3×C5C2×#10111yescharacteristic
225C23×C3C22×AGL(1,𝔽5)11yescharacteristic
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—41no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—102no—
236C2×C3×C4—102no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—201no—
240C2×C3×C4—201no—
241C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
242C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
243C3⋊C8—202no—
244C3⋊C8—202no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5#94812yes—
248C22×C5C2×#21711yescharacteristic
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—41no—
252C4×C5—41no—
253Dic5—21no—
254Dic5—21no—
255Dic5—21no—
256Dic5—41no—
257Dic5—41no—
258Dic5#83612yes—
259C22×C4—51no—
260C22×C4—51no—
261C22×C4—51no—
262C22×C4—51no—
263C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
264C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
265C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
266C2×C8—302no—
267C2×C8—302no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C42—51no—
281C42—51no—
282C42—51no—
283C42—51no—
284C3×C5#147011yescharacteristic, complemented, Hall
285C22×C3—21no—
286C22×C3—21no—
287C22×C3#413112yes—
288C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—52no—
294C3×C4—101no—
295C3×C4—101no—
296C3×C4—101no—
297C3×C4—201no—
298C3×C4—201no—
299C2×C5—22no—
300C2×C5C2×#83611yescharacteristic
301C2×C5#523411yescharacteristic
302C2×C5#524011yescharacteristic
303C23C22×ΓL(1,𝔽16)11yescharacteristic
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—51no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—51no—
313C2×C4—102no—
314C2×C4—102no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—201no—
318C2×C4—201no—
319C2×C4#676311yescharacteristic
320C2×C4#676311yescharacteristic
321C8—602no—
322C8—602no—
323C2×C3—22no—
324C2×C3#6574511yescharacteristic
325C2×C3#6577511yescharacteristic
326C2×C3D5⋊#10111yescharacteristic
327C5#7173711yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22#9199012yes—
331C22C2×#676311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—52no—
337C4—101no—
338C4—101no—
339C4—101no—
340C4—201no—
341C4—201no—
342C3#1060429711yescharacteristic, complemented, Sylow
343C2—22no—
344C2#1175240411yescharacteristic
345C2#1175243411yescharacteristic
346C2D5⋊#83611yescharacteristic
subgroupG/H
centerC22C2×#6763
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1470
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
284. C3×C5#1470semidirect
327. C5#71737semidirect
342. C3#10604297semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40352
#117524162
#117524072
#117467852
#117467842
#106042973
#717375