Finite Group Databasebeta

← #14283970

Subgroups — #14283970

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#11754415C211yesmaximal, characteristic
2C2×#91231C211yesmaximal, characteristic, complemented
3C3×C4×#704C211yesmaximal, characteristic, complemented
4#11746506C212yesmaximal, complemented
5#11746505C212yesmaximal, complemented
6#10604505—31nomaximal, Hall
7C22×C3⋊#170—21no—
8C2×C3×#704—21no—
9#91819C411yescharacteristic
10C5×#924C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91552—21no—
13#91546—21no—
14#91418C411yescharacteristic
15#91402—21no—
16#91388C2211yescharacteristic
17#91387—21no—
18#91375C2211yescharacteristic
19Dic5×Dic6C411yescharacteristic
20#91231—21no—
21#91231C2212yes—
22C3×#4002C2212yes—
23C3×C4×#170—21no—
24#69858—51nomaximal, Hall
25#65958—31no—
26C4×#704D311yescharacteristic, complemented
27C2×#4002—31no—
28#64927—32no—
29#64870—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32C2×D60C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×#1200—21no—
37C2×C3⋊#170—24no—
38C2×C3⋊#170—22no—
39C3×#704—24no—
40C2×C3×#170—22no—
41#6714—21no—
42C4⋊Dic15C2×C411yescharacteristic
43C5×#217—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×Dic3⋊C4—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51Dic3⋊Dic5—21no—
52#6669—21no—
53#6667—21no—
54#6667—21no—
55#6667—21no—
56Dic3×Dic5—21no—
57#5479—51no—
58C3×C4×M16—51no—
59C2×#803—51no—
60#4465—52no—
61#4464—52no—
62C2×#704—21no—
63C22×#170—61no—
64C5×C22⋊Q8—31no—
65#4093—31no—
66Q8×Dic5—31no—
67#4076—31no—
68C2×C4×Dic5C2×D311yescharacteristic
69#4044—61no—
70#4039—31no—
71#4038—61no—
72#4036—31no—
73#4032—61no—
74#4027—61no—
75#4002—32no—
76#4002—61no—
77#4002C2×D312yes—
78C4×#170—21no—
79#1524—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85#1220—42no—
86C2×Dic15—21no—
87D60—41no—
88C2×C5×Dic3—21no—
89C2×C5×Dic3—21no—
90C5×Dic6—41no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97#1200—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#924AGL(1,𝔽5)11yescharacteristic
106C22×C3⋊C8—101no—
107#876—101no—
108#875—51no—
109C4×D12—51no—
110#872—101no—
111#870—51no—
112C4×Dic6—51no—
113C3×#97—52no—
114C3×C4×C8—101no—
115#803—52no—
116#803—101no—
117C2×C5×Q8—31no—
118C22×C4×C5C4×D311yescharacteristic
119C2×C22⋊D5—61no—
120C22×Dic5D1211yescharacteristic
121C22×Dic5#6711yescharacteristic
122C2×D20—31no—
123C2×C4×D5—61no—
124#704—24no—
125C2×#170—22no—
126C2×#170—64no—
127C2×#170—62no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C5×C22⋊C4—61no—
131#685—61no—
132#685—61no—
133#685—61no—
134#685—61no—
135C4⋊Dic5—31no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138#683—61no—
139C4×Dic5—61no—
140C4×Dic5C4×D311yescharacteristic
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×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#10412yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158Dic15—41no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5#10412yes—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
168C2×#67—101no—
169C2×D12—51no—
170C2×C4×D3—101no—
171C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
172C3×M16—104no—
173C2×C3×C8—102no—
174C3×C42—51no—
175C3×C42—51no—
176C3×C42—51no—
177C3×C42—51no—
178#217—21no—
179(C2×D3)⋊C4—101no—
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—21no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190C2×C3⋊C8—102no—
191C2×C3⋊C8—104no—
192C23×C5(C2×D3)⋊C411yescharacteristic
193C22×D5—61no—
194C5×Q8—121no—
195C2×C4×C5—41no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5C2×C4×D311yescharacteristic
200C22⋊D5—122no—
201C2×Dic5—22no—
202C2×Dic5—22no—
203C2×Dic5—61no—
204C2×Dic5(C2×D3)⋊C411yescharacteristic
205C2×Dic5(C2×D3)⋊C411yescharacteristic
206C2×Dic5C2×D1211yescharacteristic
207C2×Dic5C2×#6711yescharacteristic
208D20—121no—
209C4×D5—122no—
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—31no—
219#121—151no—
220C4×Q8—151no—
221C4×D4—151no—
222C4×D4—301no—
223#117—301no—
224C2×C42—51no—
225#97—52no—
226#97—152no—
227#97—301no—
228C4×C8—101no—
229C2×C3×C5—22no—
230C2×C3×C5#41311yescharacteristic
231C2×C3×C5C2×#10411yescharacteristic
232C2×C3×C5C2×#10411yescharacteristic
233D15—81no—
234C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
235C22×D3—101no—
236C2×C3×C4—41no—
237C2×C3×C4—51no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—102no—
242C2×C3×C4—102no—
243C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
244C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
245#67—202no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—101no—
249D12—201no—
250C4×D3—202no—
251Dic6—41no—
252C3×C8—104no—
253C3⋊C8—104no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5#80512yes—
257C22×C5C2×(C2×D3)⋊C411yescharacteristic
258C2×D5—121no—
259C2×D5—121no—
260C2×D5—121no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—121no—
264C4×C5—121no—
265Dic5—21no—
266Dic5—21no—
267Dic5—21no—
268Dic5—121no—
269Dic5#82512yes—
270C2×Q8—31no—
271C2×D4—151no—
272C2×D4—301no—
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—301no—
276C22×C4D3×AGL(1,𝔽5)11yescharacteristic
277M16—104no—
278C2×C8—102no—
279C2×C8—302no—
280C2×C8—304no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—151no—
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—51no—
296C42—301no—
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—21no—
299C22×C3—21no—
300C22×C3#401012yes—
301C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
302C2×D3—201no—
303C2×D3—201no—
304C2×D3—201no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—52no—
308C3×C4—101no—
309C3×C4—101no—
310C3×C4—101no—
311Dic3—41no—
312Dic3—41no—
313Dic3—201no—
314C2×C5—22no—
315C2×C5C2×#80511yescharacteristic
316C2×C5#513211yescharacteristic
317C2×C5C2×#82511yescharacteristic
318D5—241no—
319C23—301no—
320C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
321Q8—121no—
322D4—601no—
323D4—602no—
324C2×C4—41no—
325C2×C4—51no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—51no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—102no—
332C2×C4—102no—
333C2×C4—301no—
334C2×C4—602no—
335C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
336C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
337C8—104no—
338C8—304no—
339C2×C3—22no—
340C2×C3#6577711yescharacteristic
341C2×C3C2×#401011yescharacteristic
342C2×C3D5⋊#10411yescharacteristic
343D3—401no—
344C5#6985811yescharacteristic, complemented, Sylow
345C22—21no—
346C22—21no—
347C22—601no—
348C22—601no—
349C22—601no—
350C22#9115812yes—
351C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
352C4—21no—
353C4—21no—
354C4—52no—
355C4—101no—
356C4—101no—
357C4—101no—
358C4—121no—
359C4—121no—
360C4—601no—
361C3#1060450511yescharacteristic, complemented, Sylow
362C2—22no—
363C2—1201no—
364C2D5⋊#82511yescharacteristic
365C2C2×#9115811yescharacteristic
366C2#1175200811yescharacteristic
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 radical#91819C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91231C2semidirect
3. C3×C4×#704C2semidirect
4. #11746506C2semidirect
5. #11746505C2semidirect
26. C4×#704D3semidirect
297. C3×C5#1524semidirect
344. C5#69858semidirect
361. C3#10604505semidirect

Maximal subgroups

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

subgroupindex
#117544152
C2×#912312
C3×C4×#7042
#117465062
#117465052
#106045053
#698585