Finite Group Databasebeta

← #14286567

Subgroups — #14286567

Order 1920.

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

normal subgroups only

This group has 364 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
1#11752433C211yesmaximal, characteristic, complemented
2#11751904C211yesmaximal, characteristic, complemented
3#11748975C211yesmaximal, characteristic
4C3×D4⋊#170C211yesmaximal, characteristic, complemented
5#11746514C211yesmaximal, characteristic, complemented
6#11746491C211yesmaximal, characteristic, complemented
7#11746487C211yesmaximal, characteristic, complemented
8#10603940—31nomaximal, Hall
9C2×#6762—21no—
10C2×#6738—21no—
11C2×#6715C411yescharacteristic
12C3×D4×Dic5C2211yescharacteristic
13#91418C2211yescharacteristic
14#91241—21no—
15C4⋊(C3⋊#170)C2211yescharacteristic
16C4×C3⋊#170C2211yescharacteristic
17C3×C4⋊#170C2211yescharacteristic
18C3×C4×#170C2211yescharacteristic
19#91171—21no—
20C5×#832C411yescharacteristic
21#90989C411yescharacteristic
22#90968C411yescharacteristic
23Dic5×C3⋊C8C2211yescharacteristic
24#68153—51nomaximal, Hall
25#65774—31no—
26#65702—31no—
27#65045—31no—
28D4⋊#170D311yescharacteristic, complemented
29#64882—31no—
30#170⋊C8—31no—
31#64871—31no—
32C2×C3×C5×D4C2×C411yescharacteristic
33C2×D60C2×C411yescharacteristic
34C22×C3×Dic5—21no—
35C2×#1200—21no—
36#6762—42no—
37C2×C3⋊#170—21no—
38C2×C3⋊#170D411yescharacteristic
39C2×C3⋊#170D411yescharacteristic
40C2×C3×#170—21no—
41C2×C3×#170—21no—
42#6738—42no—
43#6715—22no—
44C2×C3⋊#168C2×C411yescharacteristic
45C5×C4⋊Dic3C2×C411yescharacteristic
46C2×C5×C3⋊C8C2×C411yescharacteristic
47C3×C22⋊Dic5—21no—
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50#6667—21no—
51C4×#213—51no—
52#5012—51no—
53#4834—51no—
54C3×D4⋊C8—51no—
55#4479—51no—
56#4459—51no—
57#4454—51no—
58C2×#704—61no—
59C2×D5⋊C8—61no—
60D4×Dic5C2×D311yescharacteristic
61C2×#686—31no—
62#4039—31no—
63C22⋊#170—61no—
64#4003—61no—
65C4⋊#170—31no—
66C4⋊#170C2×D311yescharacteristic
67C4×#170—31no—
68C4×#170C2×D311yescharacteristic
69C5×#102—31no—
70#3953—31no—
71C8×Dic5—31no—
72#3939—31no—
73#1581—151noSylow
74C23×C3×C5—21no—
75C22×D15—21no—
76C3×C5×D4—21no—
77C3×C5×D4—21no—
78C2×C3×C4×C5C22×C411yescharacteristic
79D60—21no—
80D60M1612yescomplemented
81C2×C5×Dic3—21no—
82C2×C3×Dic5—21no—
83C2×C3×Dic5—41no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5C2×D411yescharacteristic
86C2×C3×Dic5#4111yescharacteristic
87#1200—41no—
88#1200—41no—
89C3⋊#170—21no—
90C3⋊#170—41no—
91C3⋊#170D812yescomplemented
92C3×#170—41no—
93C3×#170—41no—
94C3⋊#168—21no—
95C5×C3⋊C8—21no—
96C3×C4×D4—51no—
97C2×#213—51no—
98C2×#208—101no—
99C2×D3×C8—101no—
100C4×D12—51no—
101C3×C4⋊C8—51no—
102C3×C4×C8—51no—
103#832AGL(1,𝔽5)11yescharacteristic
104#830—101no—
105(C2×D3)⋊C8—101no—
106#809—51no—
107#807—51no—
108C4⋊(C3⋊C8)—51no—
109C4×C3⋊C8—51no—
110C4×C3⋊C8—51no—
111C2×C5×D4C4×D311yescharacteristic
112C22×Dic5—21no—
113C2×D20—31no—
114C2×C4×D5—61no—
115#704—122no—
116C2×#170—21no—
117C2×#170—21no—
118C2×#170—31no—
119C2×#170—31no—
120C2×#170—61no—
121D5⋊C8—122no—
122C2×C5×C8—31no—
123C5×C4⋊C4—31no—
124C22⋊Dic5—21no—
125#686—62no—
126#685—61no—
127C4⋊Dic5C4×D311yescharacteristic
128C4×Dic5C22×D311yescharacteristic
129C2×#168—31no—
130C4×D8—151no—
131#436—151no—
132C8×D4—151no—
133#335—151no—
134D4⋊C8—51no—
135D4⋊C8—151no—
136#322—151no—
137C22×C3×C5—41no—
138C22×C3×C5—41no—
139C22×C3×C5—41no—
140C22×C3×C5C4×D411yescharacteristic
141C2×D15—22no—
142C2×D15—41no—
143C2×D15—41no—
144C3×C4×C5C2×M1611yescharacteristic
145C3×C4×C5#13111yescharacteristic
146C3×Dic5—21no—
147C3×Dic5—41no—
148C3×Dic5C2×D811yescharacteristic
149C3×Dic5#13511yescharacteristic
150C5×Dic3—41no—
151C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
152C22×C3×C4—101no—
153C2×D12—51no—
154C2×C4×D3—101no—
155C2×C3×C8—101no—
156C2×C3×C8—101no—
157C3×C4⋊C4—51no—
158C3×C22⋊C4—101no—
159C3×C42—51no—
160#213—102no—
161(C2×D3)⋊C4—101no—
162C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
163#208—202no—
164C2×C3⋊C8—51no—
165C2×C3⋊C8—51no—
166C2×C3⋊C8—51no—
167C2×C3⋊C8—101no—
168C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
169D3×C8—202no—
170C23×C5—21no—
171C22×D5—61no—
172C5×D4—21no—
173C5×D4—21no—
174C2×C4×C5—61no—
175C2×C4×C5C2×C4×D311yescharacteristic
176C2×Dic5—21no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5D3×D411yescharacteristic
180C2×Dic5#23711yescharacteristic
181D20—32no—
182D20—61no—
183C4×D5—121no—
184C4×D5—121no—
185#170—32no—
186#170—41no—
187#170—41no—
188#170—61no—
189#170—121no—
190C5×C8—61no—
191#168—61no—
192C2×D8—151no—
193C2×M16—301no—
194C22×C8—301no—
195C4×D4—51no—
196C4×D4—151no—
197#107—151no—
198C4⋊C8—51no—
199C4⋊C8—151no—
200#102—31no—
201#102—151no—
202C22⋊C8—301no—
203C22⋊C8—301no—
204C4×C8—51no—
205C4×C8—151no—
206C4×C8—151no—
207C2×C3×C5—81no—
208C2×C3×C5#43511yescharacteristic
209C2×C3×C5C4×D811yescharacteristic
210C2×C3×C5#44411yescharacteristic
211D15—42no—
212C23×C3—21no—
213C22×D3—101no—
214C3×D4—21no—
215C3×D4—21no—
216C2×C3×C4—51no—
217C2×C3×C4—51no—
218C2×C3×C4—101no—
219C2×C3×C4—201no—
220C2×C3×C4—201no—
221C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
222C2×Dic3—21no—
223D12—52no—
224D12—101no—
225C4×D3—201no—
226C4×D3—201no—
227C3×C8—201no—
228C3×C8—201no—
229C3⋊C8—21no—
230C3⋊C8—52no—
231C3⋊C8—101no—
232C3⋊C8—101no—
233C3⋊C8—201no—
234C22×C5—41no—
235C22×C5—41no—
236C22×C5—41no—
237C22×C5#67⋊C411yescharacteristic
238C2×D5—62no—
239C2×D5—121no—
240C2×D5—121no—
241C4×C5—121no—
242C4×C5#90111yescharacteristic
243C4×C5D3×M1611yescharacteristic
244Dic5—21no—
245Dic5—41no—
246Dic5D3×D811yescharacteristic
247Dic5#91611yescharacteristic
248C2×D4—151no—
249C2×D4D3×AGL(1,𝔽5)11yescharacteristic
250C22×C4—101no—
251C22×C4—301no—
252D8—302no—
253M16—602no—
254C2×C8—31no—
255C2×C8—101no—
256C2×C8—101no—
257C2×C8—151no—
258C2×C8—151no—
259C2×C8—151no—
260C2×C8—301no—
261C2×C8—602no—
262C4⋊C4—31no—
263C4⋊C4—51no—
264C22⋊C4—101no—
265C22⋊C4—301no—
266C42—51no—
267C3×C5#158111yescharacteristic, complemented, Hall
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3D4×AGL(1,𝔽5)11yescharacteristic
272C2×D3—102no—
273C2×D3—201no—
274C2×D3—201no—
275C3×C4—51no—
276C3×C4—51no—
277C3×C4—101no—
278C3×C4—201no—
279C3×C4D5⋊M1611yescharacteristic
280C3×C4#413111yescharacteristic
281Dic3—41no—
282C2×C5—81no—
283C2×C5#472811yescharacteristic
284C2×C5#475611yescharacteristic
285C2×C5#482311yescharacteristic
286D5—122no—
287C23—21no—
288C23—301no—
289D4—21no—
290D4—21no—
291D4—152no—
292D4—301no—
293C2×C4—51no—
294C2×C4—51no—
295C2×C4—61no—
296C2×C4—101no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—601no—
300C2×C4—601no—
301C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
302C8—61no—
303C8—152no—
304C8—201no—
305C8—201no—
306C8—301no—
307C8—301no—
308C8—601no—
309C2×C3—81no—
310C2×C3#6569411yescharacteristic
311C2×C3D8×AGL(1,𝔽5)11yescharacteristic
312C2×C3#6573711yescharacteristic
313D3—202no—
314C5#6815311yescharacteristic, complemented, Sylow
315C22—41no—
316C22—41no—
317C22—41no—
318C22—302no—
319C22—601no—
320C22—601no—
321C22#67⋊AGL(1,𝔽5)11yescharacteristic
322C4—51no—
323C4—51no—
324C4—101no—
325C4—121no—
326C4—201no—
327C4#9192711yescharacteristic
328C4#9193111yescharacteristic
329C3#1060394011yescharacteristic, complemented, Sylow
330C2—81no—
331C2—602no—
332C2#1175194111yescharacteristic
333C2#1175195811yescharacteristic
334C2#1175204111yescharacteristic
subgroupG/H
centerC22#67⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×#6715C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1581
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11752433C2semidirect
2. #11751904C2semidirect
4. C3×D4⋊#170C2semidirect
5. #11746514C2semidirect
6. #11746491C2semidirect
7. #11746487C2semidirect
28. D4⋊#170D3semidirect
80. D60M16semidirect
91. C3⋊#170D8semidirect
267. C3×C5#1581semidirect
314. C5#68153semidirect
329. C3#10603940semidirect

Maximal subgroups

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

subgroupindex
#117524332
#117519042
#117489752
C3×D4⋊#1702
#117465142
#117464912
#117464872
#106039403
#681535