Finite Group Databasebeta

← #14312818

Subgroups — #14312818

Order 1920.

544 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 124 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×D3×C8×D5C211yesmaximal, characteristic
2C2×#91164C212yesmaximal, complemented
3#11746758C211yesmaximal, characteristic, complemented
4C3×#64887C211yesmaximal, characteristic, complemented
5(C2×D3)⋊#674C212yesmaximal, complemented
6D5⋊(C22⋊C16)—31nomaximal, Hall
7C2×C4×D3×D5C411yescharacteristic
8C2×C8×D15C411yescharacteristic
9C2×C5×D3×C8C411yescharacteristic
10C2×C3×C8×D5C2211yescharacteristic
11C2×#6648C2211yescharacteristic
12C2×D3×#168C2211yescharacteristic
13C2×D5×C3⋊C8C411yescharacteristic
14D3×C8×D5—24no—
15C2×C3⋊#674C2212yescomplemented
16C2×C3×#674C2212yescomplemented
17#91164—24no—
18D3×C22⋊C16—51nomaximal, Hall
19C22×C8×D5—31no—
20C2×D5⋊C16—32no—
21C22⋊#674—32no—
22#64887—31no—
23#64887D311yescharacteristic, complemented
24C22×D3×D5C811yescharacteristic
25C2×C4×D15C2×C411yescharacteristic
26C2×C4×C5×D3C2×C411yescharacteristic
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×#1200C811yescharacteristic
29C2×D3×Dic5C811yescharacteristic
30C2×D5×Dic3C811yescharacteristic
31C4×D3×D5—22no—
32C4×D3×D5—22no—
33C2×C3×C5×C8C2×C411yescharacteristic
34C2×C3⋊#168C2×C411yescharacteristic
35C8×D15—22no—
36C2×C5×C3⋊C8C2×C411yescharacteristic
37C5×D3×C8—22no—
38C2×C3×#168C2311yescharacteristic
39C3×C8×D5—22no—
40#6648D414yes—
41D3×#168—22no—
42D5×C3⋊C8—22no—
43C3⋊#674—22no—
44C3×#674—22no—
45C22×D3×C8—51no—
46C2×D3×C16—52no—
47C3×C22⋊C16—51no—
48#4549—51no—
49(C2×D3)⋊C16—52no—
50C22×C4×D5—31no—
51C22×C5×C8—31no—
52C22×#168—31no—
53C2×C8×D5—31no—
54C2×C8×D5—31no—
55C2×C8×D5—31no—
56C2×C8×D5—64no—
57C2×C8×D5C2×D311yescharacteristic
58C2×#674—32no—
59C2×#674C2×D312yescomplemented
60D5⋊C16—64no—
61C2×C22⋊C16—151noSylow
62C22×D15C2×C811yescharacteristic
63C22×C5×D3C2×C811yescharacteristic
64C22×C3×D5C2×C811yescharacteristic
65C2×D3×D5—22no—
66C2×D3×D5—22no—
67C2×D3×D5C1614yescomplemented
68C2×C3×C4×C5C22×C411yescharacteristic
69C2×Dic15C2×C811yescharacteristic
70C4×D15C22⋊C412yes—
71C4×D15M1612yes—
72C2×C5×Dic3C2×C811yescharacteristic
73C4×C5×D3—21no—
74C4×C5×D3—21no—
75C2×C3×Dic5C2×C811yescharacteristic
76C3×C4×D5—21no—
77C3×C4×D5—21no—
78#1200—22no—
79D3×Dic5—22no—
80D5×Dic3—22no—
81C3×C5×C8—21no—
82C3⋊#168—21no—
83C3×#168C2×D412yes—
84C5×C3⋊C8C22⋊C412yes—
85C22×C4×D3—51no—
86C22×C3×C8—51no—
87C22×C3⋊C8—51no—
88C2×D3×C8—51no—
89C2×D3×C8—51no—
90C2×D3×C8—51no—
91C2×D3×C8—104no—
92C2×D3×C8AGL(1,𝔽5)11yescharacteristic
93C2×C3×C16—52no—
94C2×C3⋊C16—52no—
95D3×C16—104no—
96C23×D5—31no—
97C22×C4×C5—31no—
98C22×Dic5—31no—
99C2×C4×D5—31no—
100C2×C4×D5—31no—
101C2×C4×D5—31no—
102C2×C4×D5—62no—
103C2×C4×D5—62no—
104C2×C4×D5C4×D311yescharacteristic
105C2×C5×C8—31no—
106C2×C5×C8—62no—
107C2×C5×C8C4×D311yescharacteristic
108C2×#168—31no—
109C2×#168—62no—
110C2×#168C22×D311yescharacteristic
111C8×D5—22no—
112C8×D5—34no—
113C8×D5—62no—
114C8×D5—62no—
115#674—22no—
116#674—62no—
117C23×C8—151no—
118C22×C16—152no—
119C22⋊C16—51no—
120C22⋊C16—152no—
121C22⋊C16—151no—
122C22×C3×C5C22×C811yescharacteristic
123C2×D15C22⋊C812yes—
124C2×D15C2×C1612yes—
125C2×D15M3212yes—
126C2×C5×D3—21no—
127C2×C5×D3—21no—
128C2×C5×D3C2×C1612yescomplemented
129C2×C3×D5—21no—
130C2×C3×D5—21no—
131C2×C3×D5C2×C1612yescomplemented
132D3×D5—28no—
133C3×C4×C5C2×C22⋊C411yescharacteristic
134C3×C4×C5C2×M1611yescharacteristic
135Dic15C22⋊C812yes—
136C3×Dic5—21no—
137C5×Dic3—21no—
138C23×D3—51no—
139C22×C3×C4—51no—
140C22×Dic3—51no—
141C2×C4×D3—51no—
142C2×C4×D3—51no—
143C2×C4×D3—51no—
144C2×C4×D3—102no—
145C2×C4×D3—102no—
146C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
147C2×C3×C8—51no—
148C2×C3×C8—102no—
149C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
150C2×C3⋊C8—51no—
151C2×C3⋊C8—102no—
152C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
153D3×C8—22no—
154D3×C8—54no—
155D3×C8—102no—
156D3×C8—102no—
157C3×C16—102no—
158C3⋊C16—102no—
159C23×C5—31no—
160C22×D5—31no—
161C22×D5—34no—
162C22×D5—62no—
163C22×D5—62no—
164C22×D5D3×C811yescharacteristic
165C2×C4×C5—31no—
166C2×C4×C5—61no—
167C2×C4×C5—61no—
168C2×C4×C5C2×C4×D311yescharacteristic
169C2×Dic5—31no—
170C2×Dic5—62no—
171C2×Dic5D3×C811yescharacteristic
172C4×D5—21no—
173C4×D5—21no—
174C4×D5—32no—
175C4×D5—32no—
176C4×D5—62no—
177C4×D5—62no—
178C5×C8—21no—
179C5×C8—32no—
180#168—61no—
181#168D3×D412yes—
182C23×C4—151no—
183C22×C8—31no—
184C22×C8—51no—
185C22×C8—151no—
186C22×C8—151no—
187C22×C8—151no—
188C22×C8—151no—
189C22×C8—304no—
190C2×C16—52no—
191C2×C16—152no—
192C2×C16—304no—
193C2×C3×C5C2×C22⋊C811yescharacteristic
194C2×C3×C5C22×C1611yescharacteristic
195C2×C3×C5C2×M3211yescharacteristic
196D15C22⋊C1614yescomplemented
197C3×D5—22no—
198C5×D3—22no—
199C23×C3—51no—
200C22×D3—51no—
201C22×D3—54no—
202C22×D3—102no—
203C22×D3—102no—
204C22×D3D5⋊C811yescharacteristic
205C2×C3×C4—51no—
206C2×C3×C4—101no—
207C2×C3×C4—101no—
208C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
209C2×Dic3—51no—
210C2×Dic3—102no—
211C2×Dic3D5⋊C811yescharacteristic
212C4×D3—21no—
213C4×D3—21no—
214C4×D3—52no—
215C4×D3—52no—
216C4×D3—102no—
217C4×D3—102no—
218C3×C8—21no—
219C3×C8—52no—
220C3⋊C8—101no—
221C3⋊C8C22⋊AGL(1,𝔽5)12yes—
222C22×C5—32no—
223C22×C5—61no—
224C22×C5—61no—
225C22×C5C2×D3×C811yescharacteristic
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—32no—
229C2×D5—32no—
230C2×D5—32no—
231C2×D5—68no—
232C2×D5D3×C1612yescomplemented
233C4×C5—61no—
234C4×C5D3×C22⋊C411yescharacteristic
235C4×C5D3×M1611yescharacteristic
236Dic5—21no—
237Dic5—32no—
238C24—151no—
239C22×C4—31no—
240C22×C4—51no—
241C22×C4—151no—
242C22×C4—151no—
243C22×C4—151no—
244C22×C4—151no—
245C22×C4—302no—
246C22×C4—302no—
247C2×C8—31no—
248C2×C8—51no—
249C2×C8—62no—
250C2×C8—102no—
251C2×C8—154no—
252C2×C8—151no—
253C2×C8—302no—
254C2×C8—302no—
255C2×C8—302no—
256C2×C8D3×AGL(1,𝔽5)11yescharacteristic
257C16—102no—
258C16—302no—
259C3×C5C2×C22⋊C1611yescharacteristic, complemented, Hall
260C22×C3—52no—
261C22×C3—101no—
262C22×C3—101no—
263C22×C3C2×D5⋊C811yescharacteristic
264C2×D3—21no—
265C2×D3—21no—
266C2×D3—52no—
267C2×D3—52no—
268C2×D3—52no—
269C2×D3—108no—
270C2×D3D5⋊C1612yescomplemented
271C3×C4—101no—
272C3×C4D5⋊M1611yescharacteristic
273C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
274Dic3—21no—
275Dic3—52no—
276C2×C5—62no—
277C2×C5D3×C22⋊C811yescharacteristic
278C2×C5C2×D3×C1611yescharacteristic
279C2×C5D3×M3211yescharacteristic
280D5—22no—
281D5—34no—
282C23—31no—
283C23—51no—
284C23—154no—
285C23—151no—
286C23—302no—
287C23—302no—
288C2×C4—31no—
289C2×C4—51no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—151no—
295C2×C4—152no—
296C2×C4—152no—
297C2×C4—302no—
298C2×C4—302no—
299C2×C4—302no—
300C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
301C8—21no—
302C8—32no—
303C8—52no—
304C8—301no—
305C2×C3—102no—
306C2×C3C2×D5⋊C1611yescharacteristic
307C2×C3D5⋊M3211yescharacteristic
308C2×C3D5⋊(C22⋊C8)11yescharacteristic
309D3—22no—
310D3—54no—
311C5D3×C22⋊C1611yescharacteristic, complemented, Sylow
312C22—32no—
313C22—52no—
314C22—61no—
315C22—61no—
316C22—101no—
317C22—101no—
318C22—152no—
319C22—152no—
320C22—152no—
321C22—308no—
322C22D3×D5⋊C811yescharacteristic
323C4—61no—
324C4—101no—
325C4—152no—
326C4#9191511yescharacteristic
327C4D3×C22⋊AGL(1,𝔽5)11yescharacteristic
328C3D5⋊(C22⋊C16)11yescharacteristic, complemented, Sylow
329C2—62no—
330C2—102no—
331C2—154no—
332C2D3×D5⋊C1611yescharacteristic
333C2#1175164611yescharacteristic
334C2#1175188311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C16
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C22×C8
prime radicalC22×D3×D5C8
cosocleC2×C3×#168C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C22⋊C16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#91164C2semidirect
3. #11746758C2semidirect
4. C3×#64887C2semidirect
5. (C2×D3)⋊#674C2semidirect
15. C2×C3⋊#674C22semidirect
16. C2×C3×#674C22semidirect
23. #64887D3semidirect
59. C2×#674C2×D3semidirect
67. C2×D3×D5C16semidirect
128. C2×C5×D3C2×C16semidirect
131. C2×C3×D5C2×C16semidirect
196. D15C22⋊C16semidirect
232. C2×D5D3×C16semidirect
259. C3×C5C2×C22⋊C16semidirect
270. C2×D3D5⋊C16semidirect
311. C5D3×C22⋊C16semidirect
328. C3D5⋊(C22⋊C16)semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C8×D52
C2×#911642
#117467582
C3×#648872
(C2×D3)⋊#6742
D5⋊(C22⋊C16)3
D3×C22⋊C165