Finite Group Databasebeta

← #14282313

Subgroups — #14282313

Order 1920.

632 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 114 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×Dic5×D12C211yesmaximal, characteristic
2#11752418C211yesmaximal, characteristic, complemented
3C3×C4×#704C211yesmaximal, characteristic, complemented
4#11746489C214yesmaximal, complemented
5#10604924—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic
7C22×D3×Dic5—21no—
8C2×C3×#704—21no—
9C2×C4⋊Dic15C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×(C2×D3)⋊Dic5—21no—
12Dic5×D12—21no—
13Dic5×D12—21no—
14Dic5×D12C412yes—
15Dic5×D12C2212yes—
16#91241—21no—
17#91231—21no—
18C4⋊(C3⋊#170)C2212yescomplemented
19C3×#4002—21no—
20C3×C4×#170C2212yescomplemented
21#69855—51nomaximal, Hall
22C2×D4×Dic5—31no—
23#65759—31no—
24C4×#704D311yescharacteristic, complemented
25D4⋊#170—34no—
26C23×C5×D3—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15—21no—
29C2×C5×D12—21no—
30C2×C5×D12—24no—
31C2×C5×D12C2×C412yes—
32C22×C3×Dic5D411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C2×D3×Dic5—22no—
35C2×D3×Dic5—22no—
36C2×D3×Dic5—44no—
37C2×C3⋊#170—22no—
38C3×#704—24no—
39C2×C3×#170—22no—
40C4⋊Dic15—21no—
41C4⋊Dic15C2×C412yes—
42C3×C4×Dic5C2×C411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46(C2×D3)⋊Dic5—22no—
47(C2×D3)⋊Dic5—22no—
48C2×C4×D12—51no—
49C3×C4×M16—51no—
50#4926—51no—
51#4459—54no—
52C22×C5×D4—31no—
53C23×Dic5—61no—
54C2×#704—21no—
55C2×C22⋊Dic5—61no—
56D4×Dic5—32no—
57D4×Dic5—32no—
58D4×Dic5—61no—
59D4×Dic5—61no—
60C2×C4⋊Dic5—31no—
61C2×C4×Dic5C2×D311yescharacteristic
62C22⋊#170—61no—
63#4002—21no—
64#4002—61no—
65C4⋊#170—32no—
66C4×#170C2×D312yescomplemented
67#1490—151noSylow
68C23×C3×C5C22⋊C411yescharacteristic
69C22×C5×D3—24no—
70C22×C5×D3—22no—
71C22×C5×D3—42no—
72C22×C5×D3—42no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5C22⋊C411yescharacteristic
75C2×C3×C4×C5C22×C411yescharacteristic
76C2×Dic15—22no—
77C2×Dic15—42no—
78C5×D12—24no—
79C5×D12—22no—
80C5×D12M1614yescomplemented
81C2×C3×Dic5—22no—
82C2×C3×Dic5—22no—
83C2×C3×Dic5C22⋊C411yescharacteristic
84C2×C3×Dic5C22⋊C411yescharacteristic
85C2×C3×Dic5C2×D411yescharacteristic
86C2×C3×Dic5C2×D411yescharacteristic
87D3×Dic5—44no—
88D3×Dic5—44no—
89C3⋊#170—42no—
90C3×#170—24no—
91C22×D12AGL(1,𝔽5)11yescharacteristic
92C22×C4×D3—101no—
93C2×C3×M16—101no—
94C2×C3×C42—51no—
95C2×(C2×D3)⋊C4—101no—
96C2×C4⋊Dic3—51no—
97C4×D12—52no—
98C4×D12—52no—
99C4×D12—101no—
100C4×D12—101no—
101C3×#97—101no—
102C3×C4×C8—52no—
103#830—101no—
104C4⋊(C3⋊C8)—52no—
105#803—101no—
106C24×C5—61no—
107C2×C5×D4—32no—
108C2×C5×D4—64no—
109C2×C5×D4—61no—
110C22×C4×C5C4×D311yescharacteristic
111C22×Dic5—61no—
112C22×Dic5—62no—
113C22×Dic5—62no—
114C22×Dic5—124no—
115C22×Dic5D1211yescharacteristic
116C22×Dic5#6711yescharacteristic
117#704—24no—
118C2×#170—22no—
119C2×#170—62no—
120C22⋊Dic5—62no—
121C22⋊Dic5—62no—
122C4⋊Dic5—32no—
123C4⋊Dic5—61no—
124C4×Dic5C4×D311yescharacteristic
125C4×Dic5D1211yescharacteristic
126C4×Dic5#6711yescharacteristic
127C4×Dic5C22×D311yescharacteristic
128C2×C4×D4—151no—
129#432—151no—
130C4×M16—51no—
131D4⋊C8—154no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5#10412yes—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C2×C5×D3—24no—
137C2×C5×D3—48no—
138C2×C5×D3—42no—
139C2×C5×D3—42no—
140C3×C4×C5—21no—
141C3×C4×C5C2×M1612yes—
142Dic15—42no—
143C3×Dic5—21no—
144C3×Dic5—21no—
145C3×Dic5—21no—
146C3×Dic5AGL(1,ℤ/8)12yes—
147C23×D3—21no—
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
151C22×Dic3—101no—
152C2×D12—21no—
153C2×D12—24no—
154C2×D12C2×AGL(1,𝔽5)12yes—
155C2×C4×D3—102no—
156C2×C4×D3—102no—
157C2×C4×D3—204no—
158C3×M16—104no—
159C2×C3×C8—102no—
160C3×C42—51no—
161C3×C42—51no—
162C3×C42—51no—
163C3×C42—51no—
164(C2×D3)⋊C4—102no—
165(C2×D3)⋊C4—102no—
166C4⋊Dic3—52no—
167C4⋊Dic3—101no—
168C2×C3⋊C8—102no—
169C23×C5—64no—
170C23×C5—62no—
171C23×C5—122no—
172C23×C5—122no—
173C23×C5(C2×D3)⋊C411yescharacteristic
174C5×D4—34no—
175C5×D4—64no—
176C5×D4—62no—
177C2×C4×C5—22no—
178C2×C4×C5(C2×D3)⋊C411yescharacteristic
179C2×C4×C5C2×C4×D311yescharacteristic
180C2×Dic5—22no—
181C2×Dic5—22no—
182C2×Dic5—62no—
183C2×Dic5—124no—
184C2×Dic5—122no—
185C2×Dic5—124no—
186C2×Dic5(C2×D3)⋊C411yescharacteristic
187C2×Dic5(C2×D3)⋊C411yescharacteristic
188C2×Dic5C2×D1211yescharacteristic
189C2×Dic5C2×#6711yescharacteristic
190#170—24no—
191#170—122no—
192C22×D4—31no—
193C23×C4—301no—
194C2×M16—101no—
195C4×D4—152no—
196C4×D4—152no—
197C4×D4—301no—
198C4×D4—301no—
199C2×C4⋊C4—151no—
200C2×C22⋊C4—301no—
201C2×C42—51no—
202C4⋊C8—152no—
203C22⋊C8—301no—
204#97—101no—
205#97—301no—
206C4×C8—52no—
207C2×C3×C5—22no—
208C2×C3×C5#40711yescharacteristic
209C2×C3×C5#41811yescharacteristic
210C2×C3×C5C2×#10411yescharacteristic
211C5×D3—44no—
212C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
213C22×D3—24no—
214C22×D3—22no—
215C22×D3—42no—
216C22×D3—42no—
217C2×C3×C4—22no—
218C2×C3×C4—51no—
219C2×C3×C4—51no—
220C2×C3×C4—51no—
221C2×C3×C4—51no—
222C2×C3×C4—102no—
223C2×C3×C4—102no—
224C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
225C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
226C2×Dic3—102no—
227C2×Dic3—202no—
228D12—24no—
229D12—22no—
230D12#70414yescomplemented
231C4×D3—204no—
232C4×D3—204no—
233C3×C8—104no—
234C3⋊C8—202no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—64no—
238C22×C5—128no—
239C22×C5—122no—
240C22×C5—122no—
241C22×C5#80512yes—
242C22×C5C2×(C2×D3)⋊C411yescharacteristic
243C4×C5—21no—
244C4×C5D3×M1612yes—
245Dic5—21no—
246Dic5—21no—
247Dic5—21no—
248Dic5—122no—
249Dic5#90812yes—
250C24—61no—
251C2×D4—32no—
252C2×D4—64no—
253C2×D4—61no—
254C22×C4—51no—
255C22×C4—51no—
256C22×C4—302no—
257C22×C4—302no—
258C22×C4—301no—
259C22×C4—604no—
260C22×C4D3×AGL(1,𝔽5)11yescharacteristic
261M16—104no—
262C2×C8—102no—
263C2×C8—302no—
264C4⋊C4—152no—
265C4⋊C4—301no—
266C22⋊C4—302no—
267C22⋊C4—302no—
268C42—51no—
269C42—51no—
270C42—51no—
271C42—51no—
272C3×C5#149011yescharacteristic, complemented, Hall
273C22×C3—21no—
274C22×C3—21no—
275C22×C3#400812yes—
276C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
277C2×D3—24no—
278C2×D3—48no—
279C2×D3—42no—
280C2×D3—42no—
281C3×C4—21no—
282C3×C4—52no—
283C3×C4—101no—
284C3×C4—101no—
285C3×C4—101no—
286C3×C4C2×#70412yes—
287Dic3—202no—
288C2×C5—22no—
289C2×C5—124no—
290C2×C5C2×#80511yescharacteristic
291C2×C5#512611yescharacteristic
292C2×C5#513111yescharacteristic
293C23—64no—
294C23—62no—
295C23—122no—
296C23—122no—
297C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
298D4—34no—
299D4—64no—
300D4—62no—
301C2×C4—22no—
302C2×C4—51no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—102no—
307C2×C4—102no—
308C2×C4—302no—
309C2×C4—604no—
310C2×C4—604no—
311C2×C4—602no—
312C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
313C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
314C8—104no—
315C8—602no—
316C2×C3—22no—
317C2×C3#6576711yescharacteristic
318C2×C3C2×#400811yescharacteristic
319C2×C3#6579811yescharacteristic
320D3—44no—
321C5#6985511yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—64no—
325C22—128no—
326C22—122no—
327C22—122no—
328C22#9115612yes—
329C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
330C4—21no—
331C4—52no—
332C4—101no—
333C4—101no—
334C4—101no—
335C4—602no—
336C4D3×#70412yes—
337C3#1060492411yescharacteristic, complemented, Sylow
338C2—22no—
339C2—124no—
340C2#1175170711yescharacteristic
341C2C2×#9115611yescharacteristic
342C2#1175200011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D12C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1490
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752418C2semidirect
3. C3×C4×#704C2semidirect
4. #11746489C2semidirect
18. C4⋊(C3⋊#170)C22semidirect
20. C3×C4×#170C22semidirect
24. C4×#704D3semidirect
66. C4×#170C2×D3semidirect
80. C5×D12M16semidirect
230. D12#704semidirect
272. C3×C5#1490semidirect
321. C5#69855semidirect
337. C3#10604924semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×D122
#117524182
C3×C4×#7042
#117464892
#106049243
#698555