Finite Group Databasebeta

← #14285116

Subgroups — #14285116

Order 1920.

416 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 98 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#11752498C211yesmaximal, characteristic
2D5⋊(C4⋊(C3⋊C8))C211yesmaximal, characteristic
3C3×#65684C211yesmaximal, characteristic
4#11746510C212yesmaximal, complemented
5#11746509C212yesmaximal, complemented
6#10604585—31nomaximal, Hall
7C2×D5⋊(C3⋊C8)—21no—
8#91759C411yescharacteristic
9C5×#870C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91468C2211yescharacteristic
12#91468C2211yescharacteristic
13#91358C411yescharacteristic
14#91358C411yescharacteristic
15#91349—21no—
16#91349—21no—
17#91323—21no—
18#91323—21no—
19#91233C2212yes—
20C4⋊(C3⋊#170)—21no—
21C3×#4004C2212yes—
22C3×#4003—21no—
23C3×#4002—21no—
24#70820—51nomaximal, Hall
25#66022—31no—
26#65684D311yescharacteristic
27D5⋊(C4⋊C8)—31no—
28#64873—32no—
29#64873—32no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×#1204—21no—
34C2×#1204—21no—
35C2×C3⋊#170—22no—
36D5⋊(C3⋊C8)—42no—
37C2×C3×#170—22no—
38C3×C42×C5C2×C411yescharacteristic
39C4⋊Dic15C2×C411yescharacteristic
40C4⋊Dic15C2×C411yescharacteristic
41#6712—21no—
42#6712—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×Dic3⋊C4—21no—
46C5×Dic3⋊C4—21no—
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50#6668—21no—
51#6668—21no—
52#6665—21no—
53#6665—21no—
54Dic3×Dic5—21no—
55Dic3×Dic5—21no—
56#5470—51no—
57C3×#432—51no—
58C2×C4⋊(C3⋊C8)—51no—
59#4486—52no—
60#4482—52no—
61C2×D5⋊C8—61no—
62C5×#125—31no—
63#4042—61no—
64#4042—61no—
65#4038—31no—
66#4038—31no—
67#4034—31no—
68#4034—31no—
69#4033—61no—
70#4033—61no—
71C42×D5C2×D311yescharacteristic
72#4016—31no—
73#4004—32no—
74#4004C2×D312yes—
75#4003—21no—
76#4002—21no—
77C4⋊#170—61no—
78#1552—151noSylow
79C22×C3×D5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85C2×C5×Dic3—21no—
86C2×C5×Dic3—21no—
87C2×C3×Dic5C22⋊C411yescharacteristic
88C2×C3×Dic5C2×D411yescharacteristic
89C2×C3×Dic5C2×D411yescharacteristic
90C3×C4×D5—22no—
91C3×C4×D5—22no—
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94#1204—42no—
95#1204—41no—
96#1204—41no—
97C3⋊#170—42no—
98C3×#170—42no—
99C2×C3×C42—51no—
100#926—51no—
101#926—51no—
102#924—101no—
103#924—101no—
104C22×C3⋊C8—101no—
105#870—51no—
106#870AGL(1,𝔽5)11yescharacteristic
107#869—51no—
108#869—51no—
109C4×Dic6—101no—
110C4×Dic6—101no—
111C3×C4⋊C8—52no—
112C3×C22⋊C8—101no—
113C3×#97—101no—
114C4⋊(C3⋊C8)—52no—
115C4⋊(C3⋊C8)—101no—
116C2×C4×D5C4×D311yescharacteristic
117C2×C4×D5D1211yescharacteristic
118C2×C4×D5#6711yescharacteristic
119C2×Dic10—61no—
120C2×Dic10—61no—
121C2×#170—22no—
122C2×#170—62no—
123D5⋊C8—122no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C42×C5C4×D311yescharacteristic
129#685—61no—
130#685—61no—
131C4⋊Dic5—31no—
132C4⋊Dic5—31no—
133#683—61no—
134#683—61no—
135#683—61no—
136#683—61no—
137C4×Dic5—61no—
138C4×Dic5—61no—
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142#533—151no—
143#432—51no—
144C2×C4⋊C8—151no—
145#332—152no—
146#332—152no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C2×C3×D5—21no—
149C2×C3×D5—21no—
150C2×C3×D5#10112yes—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154Dic15—41no—
155Dic15—41no—
156C3×Dic5—21no—
157C3×Dic5#13512yes—
158C3×Dic5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5#13711yescharacteristic
160C5×Dic3—41no—
161C5×Dic3—41no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C2×Dic6—101no—
166C2×Dic6—101no—
167C2×C3×C8—102no—
168C3×C42—51no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42C2×AGL(1,𝔽5)11yescharacteristic
172#217—101no—
173#217—101no—
174C4⋊Dic3—51no—
175C4⋊Dic3—51no—
176C4⋊Dic3—101no—
177C4⋊Dic3—101no—
178C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
179C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—21no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C4×Dic3—101no—
186C2×C3⋊C8—102no—
187C2×C3⋊C8—202no—
188C22×D5(C2×D3)⋊C411yescharacteristic
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×Dic5—61no—
195C2×Dic5—61no—
196C2×Dic5(C2×D3)⋊C411yescharacteristic
197C2×Dic5C2×D1211yescharacteristic
198C2×Dic5C2×#6711yescharacteristic
199C4×D5—22no—
200C4×D5—21no—
201C4×D5—21no—
202C4×D5—22no—
203Dic10—121no—
204Dic10—121no—
205Dic10—122no—
206#170—42no—
207#170—122no—
208C22×C8—301no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—31no—
212#125—151no—
213C22⋊Q8—301no—
214C22⋊Q8—301no—
215C4×Q8—301no—
216C4×Q8—301no—
217#117—151no—
218#117—151no—
219C2×C42—51no—
220C4⋊C8—52no—
221C4⋊C8—152no—
222C4⋊C8—301no—
223C22⋊C8—101no—
224#97—101no—
225C2×C3×C5C2×#10111yescharacteristic
226C2×C3×C5#41611yescharacteristic
227C2×C3×C5#41711yescharacteristic
228C3×D5—22no—
229C23×C3—51no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—102no—
236C2×C3×C4—102no—
237C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
238C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
239C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—101no—
243C2×Dic3—101no—
244Dic6—201no—
245Dic6—201no—
246Dic6—202no—
247C3×C8—202no—
248C3⋊C8—202no—
249C22×C5C2×(C2×D3)⋊C411yescharacteristic
250C2×D5—21no—
251C2×D5—21no—
252C2×D5#82412yes—
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—21no—
256C4×C5—121no—
257C4×C5—121no—
258Dic5—21no—
259Dic5—121no—
260Dic5—121no—
261Dic5#90811yescharacteristic
262Dic5#90911yescharacteristic
263Dic5#95012yes—
264C2×Q8—301no—
265C2×Q8—301no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C2×C8—102no—
270C2×C8—302no—
271C2×C8—602no—
272C4⋊C4—31no—
273C4⋊C4—31no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—151no—
277C4⋊C4—151no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C22⋊C4—301no—
283C22⋊C4—301no—
284C42—51no—
285C42—51no—
286C42—51no—
287C42—301no—
288C42—301no—
289C42D3×AGL(1,𝔽5)11yescharacteristic
290C3×C5#155211yescharacteristic, complemented, Hall
291C22×C3—52no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—51no—
299C3×C4—51no—
300C3×C4—52no—
301C3×C4—101no—
302Dic3—41no—
303Dic3—41no—
304Dic3—201no—
305Dic3—201no—
306C2×C5#500211yescharacteristic
307C2×C5#513311yescharacteristic
308C2×C5C2×#82411yescharacteristic
309D5—22no—
310C23—51no—
311Q8—602no—
312Q8—601no—
313Q8—601no—
314C2×C4—51no—
315C2×C4—51no—
316C2×C4—51no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—101no—
320C2×C4—102no—
321C2×C4—101no—
322C2×C4—102no—
323C2×C4—301no—
324C2×C4—301no—
325C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
326C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
327C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
328C8—202no—
329C8—602no—
330C2×C3—102no—
331C2×C3D5⋊#10111yescharacteristic
332C2×C3#6579311yescharacteristic
333C2×C3#6579411yescharacteristic
334C5#7082011yescharacteristic, complemented, Sylow
335C22—52no—
336C22—101no—
337C22—101no—
338C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—52no—
343C4—51no—
344C4—51no—
345C4—101no—
346C4—121no—
347C4—121no—
348C4—601no—
349C4—601no—
350C3#1060458511yescharacteristic, complemented, Sylow
351C2—102no—
352C2#1175170311yescharacteristic
353C2#1175170811yescharacteristic
354C2D5⋊#82411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1552
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746510C2semidirect
5. #11746509C2semidirect
290. C3×C5#1552semidirect
334. C5#70820semidirect
350. C3#10604585semidirect

Maximal subgroups

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

subgroupindex
#117524982
D5⋊(C4⋊(C3⋊C8))2
C3×#656842
#117465102
#117465092
#106045853
#708205