Finite Group Databasebeta

← #14283961

Subgroups — #14283961

Order 1920.

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

normal subgroups only

This group has 468 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#11752682C211yesmaximal, characteristic
2#11752335C211yesmaximal, characteristic, complemented
3C3×C4×#700C211yesmaximal, characteristic, complemented
4#11746506C212yesmaximal, complemented
5#11746504C212yesmaximal, complemented
6#10604396—31nomaximal, Hall
7C2×D5⋊(C3⋊C8)—21no—
8C2×C3×#700—21no—
9C4×Dic30C411yescharacteristic
10C4×C5×D12C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91449C411yescharacteristic
13#91447—21no—
14C4×#1201—21no—
15#91388C2211yescharacteristic
16#91373C2211yescharacteristic
17#91372—21no—
18#91371—21no—
19#91360C411yescharacteristic
20#91231—21no—
21#91231C2212yes—
22C3×#4002C2212yes—
23C3×C4×#170—21no—
24#69858—51nomaximal, Hall
25#65891—31no—
26C4×#700D311yescharacteristic, complemented
27#65676—31no—
28#64921—32no—
29#64870—32no—
30C2×Dic30C2×C411yescharacteristic
31C2×C5×D12C2×C411yescharacteristic
32C2×C4×C5×D3—21no—
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×#1201—21no—
37C2×C3⋊#170—22no—
38D5⋊(C3⋊C8)—24no—
39C2×C3×#170—22no—
40C3×#700—24no—
41C3×C42×C5C2×C411yescharacteristic
42C4⋊Dic15C2×C411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C5×(C2×D3)⋊C4—21no—
46C5×C4⋊Dic3C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51Dic3⋊Dic5—21no—
52#6669—21no—
53(C2×D3)⋊Dic5—21no—
54(C2×D3)⋊Dic5—21no—
55(C2×D3)⋊Dic5—21no—
56#6665—21no—
57#5479—51no—
58C3×C4×M16—51no—
59C2×#803—51no—
60#4465—52no—
61#4464—52no—
62C2×#700—21no—
63C2×D5⋊C8—61no—
64C4×C5×D4—31no—
65#4084—31no—
66#4082—31no—
67C4×C22⋊D5—61no—
68#4072—61no—
69#4043—31no—
70#4036—31no—
71#4029—61no—
72#4025—61no—
73C42×D5C2×D311yescharacteristic
74C4×Dic10—31no—
75#4002—32no—
76#4002—61no—
77#4002C2×D312yes—
78C4×#170—21no—
79#1524—151noSylow
80C22×C5×D3—21no—
81C22×C3×D5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87Dic30—41no—
88C2×C5×Dic3—21no—
89C5×D12—41no—
90C4×C5×D3—42no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C3×C4×D5—22no—
95C3×C4×D5—22no—
96C3×C4×D5—41no—
97#1201—42no—
98C3⋊#170—24no—
99C3×#170—24no—
100C2×C3×M16—101no—
101C2×C3×C42—51no—
102#930—51no—
103#929—101no—
104C4×#67—101no—
105#924—51no—
106C22×C3⋊C8—101no—
107#876—101no—
108#875—51no—
109C4×D12AGL(1,𝔽5)11yescharacteristic
110#872—101no—
111#870—51no—
112C4×Dic6—51no—
113C3×#97—52no—
114C3×C4×C8—101no—
115#803—52no—
116#803—101no—
117C2×C5×D4—31no—
118C22×C4×C5—61no—
119C2×C22⋊D5—61no—
120C2×C4×D5C4×D311yescharacteristic
121C2×C4×D5D1211yescharacteristic
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—31no—
124C2×#170—22no—
125C2×#170—62no—
126#700—24no—
127D5⋊C8—64no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—61no—
130C42×C5C4×D311yescharacteristic
131C22⋊Dic5—61no—
132C22⋊Dic5—61no—
133C22⋊Dic5—61no—
134#685—61no—
135C4⋊Dic5—31no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138#683—61no—
139#683—61no—
140C4×Dic5—61no—
141C4×Dic5D1211yescharacteristic
142C4×Dic5#6711yescharacteristic
143C4×Dic5C22×D311yescharacteristic
144#529—151no—
145C4×M16—51no—
146C2×#97—151no—
147#330—152no—
148#329—152no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C2×C5×D3—41no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5#10412yes—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5#10412yes—
159Dic15—41no—
160Dic15—41no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C5×Dic3—41no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C2×#67—101no—
169C2×D12C2×AGL(1,𝔽5)11yescharacteristic
170C2×C4×D3—21no—
171C2×Dic6—51no—
172C3×M16—104no—
173C2×C3×C8—102no—
174C3×C42—51no—
175C3×C42—51no—
176C3×C42—51no—
177C3×C42C2×AGL(1,𝔽5)11yescharacteristic
178#217—101no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—101no—
181(C2×D3)⋊C4—101no—
182(C2×D3)⋊C4—101no—
183C4⋊Dic3—51no—
184C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190C2×C3⋊C8—102no—
191C2×C3⋊C8—104no—
192C23×C5—61no—
193C22×D5(C2×D3)⋊C411yescharacteristic
194C5×D4—121no—
195C2×C4×C5—61no—
196C2×C4×C5—122no—
197C2×C4×C5(C2×D3)⋊C411yescharacteristic
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5C2×C4×D311yescharacteristic
200C22⋊D5—122no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203C2×Dic5(C2×D3)⋊C411yescharacteristic
204C2×Dic5C2×D1211yescharacteristic
205C2×Dic5C2×#6711yescharacteristic
206C4×D5—22no—
207C4×D5—22no—
208C4×D5—41no—
209Dic10—121no—
210#170—24no—
211#170—64no—
212C2×M16—101no—
213C22×C8—301no—
214#126—301no—
215#125—151no—
216#124—151no—
217#123—301no—
218C22⋊Q8—151no—
219#121—151no—
220C4×Q8—151no—
221C4×D4—31no—
222C4×D4—301no—
223#117—301no—
224C2×C42—51no—
225#97—52no—
226#97—152no—
227#97—301no—
228C4×C8—101no—
229C2×C3×C5#41311yescharacteristic
230C2×C3×C5C2×#10411yescharacteristic
231C2×C3×C5C2×#10411yescharacteristic
232C3×D5—22no—
233C5×D3—81no—
234C23×C3—51no—
235C22×D3—21no—
236C2×C3×C4—51no—
237C2×C3×C4—51no—
238C2×C3×C4—51no—
239C2×C3×C4—102no—
240C2×C3×C4—102no—
241C2×C3×C4—201no—
242C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
243C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
244C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
245#67—202no—
246C2×Dic3—21no—
247C2×Dic3—101no—
248C2×Dic3—101no—
249D12—41no—
250C4×D3—42no—
251Dic6—201no—
252C3×C8—104no—
253C3⋊C8—104no—
254C22×C5—121no—
255C22×C5—121no—
256C22×C5—121no—
257C22×C5C2×(C2×D3)⋊C411yescharacteristic
258C2×D5—21no—
259C2×D5—21no—
260C2×D5#80512yes—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—121no—
264C4×C5#82512yes—
265Dic5—21no—
266Dic5—21no—
267Dic5—21no—
268Dic5—121no—
269Dic5—121no—
270C2×Q8—151no—
271C2×D4—31no—
272C2×D4—301no—
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—51no—
276C22×C4—61no—
277M16—104no—
278C2×C8—102no—
279C2×C8—302no—
280C2×C8—304no—
281C4⋊C4—31no—
282C4⋊C4—151no—
283C4⋊C4—301no—
284C4⋊C4—301no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C22⋊C4—61no—
288C22⋊C4—301no—
289C22⋊C4—301no—
290C22⋊C4—301no—
291C22⋊C4—301no—
292C42—51no—
293C42—51no—
294C42—51no—
295C42—301no—
296C42D3×AGL(1,𝔽5)11yescharacteristic
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—52no—
299C22×C3—101no—
300C22×C3—101no—
301C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—101no—
308C3×C4—101no—
309C3×C4—101no—
310C3×C4#400812yes—
311Dic3—41no—
312Dic3—201no—
313Dic3—201no—
314C2×C5—241no—
315C2×C5C2×#80511yescharacteristic
316C2×C5#513211yescharacteristic
317C2×C5C2×#82511yescharacteristic
318D5—22no—
319C23—51no—
320C23—61no—
321Q8—601no—
322D4—121no—
323D4—602no—
324C2×C4—51no—
325C2×C4—51no—
326C2×C4—51no—
327C2×C4—61no—
328C2×C4—102no—
329C2×C4—102no—
330C2×C4—122no—
331C2×C4—201no—
332C2×C4—301no—
333C2×C4—301no—
334C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
335C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
336C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
337C8—104no—
338C8—304no—
339C2×C3—102no—
340C2×C3#6576111yescharacteristic
341C2×C3C2×#400811yescharacteristic
342C2×C3D5⋊#10411yescharacteristic
343D3—81no—
344C5#6985811yescharacteristic, complemented, Sylow
345C22—52no—
346C22—101no—
347C22—101no—
348C22—121no—
349C22—121no—
350C22—121no—
351C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
352C4—21no—
353C4—21no—
354C4—101no—
355C4—101no—
356C4—101no—
357C4—121no—
358C4—601no—
359C4—601no—
360C4#9115512yes—
361C3#1060439611yescharacteristic, complemented, Sylow
362C2—102no—
363C2—241no—
364C2C2×#9115511yescharacteristic
365C2D5⋊#80511yescharacteristic
366C2#1175181811yescharacteristic
subgroupG/H
centerC2×C4(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 radical#91449C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752335C2semidirect
3. C3×C4×#700C2semidirect
4. #11746506C2semidirect
5. #11746504C2semidirect
26. C4×#700D3semidirect
297. C3×C5#1524semidirect
344. C5#69858semidirect
361. C3#10604396semidirect

Maximal subgroups

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

subgroupindex
#117526822
#117523352
C3×C4×#7002
#117465062
#117465042
#106043963
#698585