Finite Group Databasebeta

← #14284167

Subgroups — #14284167

Order 1920.

432 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752494C211yesmaximal, characteristic
2#11752342C211yesmaximal, characteristic, complemented
3C3×C4×#700C211yesmaximal, characteristic, complemented
4#11746506C212yesmaximal, complemented
5#11746505C212yesmaximal, complemented
6#10604432—31nomaximal, Hall
7C2×C3×#700—21no—
8C4×D60C411yescharacteristic
9C4×C5×Dic6C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91450C411yescharacteristic
12C4×#1202—21no—
13#91388C2211yescharacteristic
14#91387—21no—
15#91386—21no—
16#91375C2211yescharacteristic
17#91359C411yescharacteristic
18#91348—21no—
19#91232—21no—
20#91231C2212yes—
21C4⋊(C3⋊#170)—21no—
22C3×#4002C2212yes—
23C3×C4×#170—21no—
24#69861—51nomaximal, Hall
25#65914—31no—
26#65683—31no—
27C4×#700D311yescharacteristic, complemented
28#64927—32no—
29#64870—32no—
30C2×D60C2×C411yescharacteristic
31C2×C4×D15—21no—
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×#1202—21no—
37C2×C3⋊#170—22no—
38C2×C3×#170—22no—
39C3×#700—24no—
40C3×C42×C5C2×C411yescharacteristic
41#6714—21no—
42C4⋊Dic15C2×C411yescharacteristic
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×Dic3⋊C4—21no—
45C4×C5×Dic3—21no—
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49Dic3⋊Dic5—21no—
50#6669—21no—
51#6669—21no—
52#6667—21no—
53#6667—21no—
54#6667—21no—
55#6665—21no—
56#5479—51no—
57C3×C4×M16—51no—
58#4926—51no—
59#4465—52no—
60#4464—52no—
61C2×#700—21no—
62C4×C5×Q8—31no—
63#4093—31no—
64#4092—31no—
65#4044—61no—
66#4041—31no—
67#4040—61no—
68#4036—31no—
69C4×D20—31no—
70C4×D20—61no—
71#4018—61no—
72C42×D5C2×D311yescharacteristic
73#4003—61no—
74#4002—32no—
75#4002C2×D312yes—
76C4⋊#170—61no—
77C4×#170—21no—
78#1529—151noSylow
79C22×D15—21no—
80C22×C3×D5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×Dic15—21no—
85D60—41no—
86C4×D15—42no—
87C2×C5×Dic3—21no—
88C2×C5×Dic3—21no—
89C5×Dic6—41no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C3×C4×D5—22no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96#1202—42no—
97C3⋊#170—42no—
98C3×#170—24no—
99C2×C3×M16—101no—
100C2×C3×C42—51no—
101#930—51no—
102#929—101no—
103C4×#67—101no—
104#924—51no—
105#876—101no—
106#875—51no—
107C4×D12—51no—
108#872—101no—
109#870—51no—
110C4×Dic6AGL(1,𝔽5)11yescharacteristic
111C3×#97—52no—
112C3×C4×C8—101no—
113#830—101no—
114C4⋊(C3⋊C8)—101no—
115#803—52no—
116C2×C5×Q8—31no—
117C2×D20—31no—
118C2×D20—61no—
119C2×C4×D5—61no—
120C2×C4×D5C4×D311yescharacteristic
121C2×C4×D5D1211yescharacteristic
122C2×C4×D5#6711yescharacteristic
123C2×#170—22no—
124C2×#170—62no—
125#700—24no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C42×C5—61no—
129C42×C5C4×D311yescharacteristic
130#685—61no—
131#685—61no—
132#685—61no—
133#685—61no—
134#685—61no—
135C4⋊Dic5—31no—
136C4⋊Dic5—61no—
137#683—61no—
138#683—61no—
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142#529—151no—
143#432—151no—
144C4×M16—51no—
145#330—152no—
146#329—152no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C2×D15—41no—
149C2×D15—41no—
150C2×D15—41no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5#10412yes—
157Dic15—41no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C5×Dic3—41no—
162C5×Dic3—41no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C22×C3×C4—51no—
166C2×#67—101no—
167C2×D12—51no—
168C2×C4×D3—101no—
169C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
170C3×M16—104no—
171C2×C3×C8—102no—
172C3×C42—51no—
173C3×C42—51no—
174C3×C42—51no—
175C3×C42C2×AGL(1,𝔽5)11yescharacteristic
176#217—101no—
177(C2×D3)⋊C4—101no—
178(C2×D3)⋊C4—101no—
179(C2×D3)⋊C4—101no—
180(C2×D3)⋊C4—101no—
181C4⋊Dic3—51no—
182C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187C4×Dic3—21no—
188C2×C3⋊C8—102no—
189C22×D5—61no—
190C22×D5(C2×D3)⋊C411yescharacteristic
191C5×Q8—121no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5(C2×D3)⋊C411yescharacteristic
195C2×C4×C5(C2×D3)⋊C411yescharacteristic
196C2×C4×C5C2×C4×D311yescharacteristic
197C2×Dic5—61no—
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5C2×D1211yescharacteristic
200C2×Dic5C2×#6711yescharacteristic
201D20—121no—
202D20—122no—
203C4×D5—22no—
204C4×D5—41no—
205C4×D5—41no—
206C4×D5—122no—
207#170—24no—
208#170—122no—
209C2×M16—101no—
210#126—301no—
211#125—151no—
212#124—151no—
213#123—301no—
214C22⋊Q8—151no—
215#121—151no—
216C4×Q8—31no—
217C4×D4—151no—
218C4×D4—301no—
219#117—301no—
220C2×C42—51no—
221C4⋊C8—301no—
222C22⋊C8—301no—
223#97—52no—
224#97—152no—
225C4×C8—101no—
226C2×C3×C5#41311yescharacteristic
227C2×C3×C5C2×#10411yescharacteristic
228C2×C3×C5#42111yescharacteristic
229D15—81no—
230C3×D5—41no—
231C23×C3—51no—
232C22×D3—101no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—102no—
237C2×C3×C4—201no—
238C2×C3×C4—201no—
239C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
240C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
241C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
242#67—202no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—101no—
246D12—201no—
247C4×D3—202no—
248Dic6—41no—
249C3×C8—104no—
250C3⋊C8—202no—
251C22×C5C2×(C2×D3)⋊C411yescharacteristic
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—21no—
255C2×D5—121no—
256C2×D5—121no—
257C2×D5—121no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—121no—
261C4×C5—121no—
262C4×C5#80512yes—
263Dic5—21no—
264Dic5—21no—
265Dic5—21no—
266Dic5—121no—
267C2×Q8—31no—
268C2×D4—151no—
269C2×D4—301no—
270C22×C4—51no—
271C22×C4—51no—
272C22×C4—51no—
273C22×C4—301no—
274M16—104no—
275C2×C8—102no—
276C2×C8—302no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—151no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—301no—
284C22⋊C4—301no—
285C22⋊C4—301no—
286C22⋊C4—301no—
287C22⋊C4—301no—
288C42—51no—
289C42—51no—
290C42—51no—
291C42—61no—
292C42D3×AGL(1,𝔽5)11yescharacteristic
293C3×C5#152911yescharacteristic, complemented, Hall
294C22×C3—101no—
295C22×C3—101no—
296C22×C3—101no—
297C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
298C2×D3—201no—
299C2×D3—201no—
300C2×D3—201no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—101no—
304C3×C4—101no—
305C3×C4—101no—
306C3×C4#401012yes—
307Dic3—41no—
308Dic3—41no—
309Dic3—201no—
310C2×C5C2×#80511yescharacteristic
311C2×C5#513211yescharacteristic
312C2×C5#513911yescharacteristic
313D5—41no—
314D5—241no—
315C23—51no—
316C23—301no—
317Q8—121no—
318D4—601no—
319D4—602no—
320C2×C4—51no—
321C2×C4—51no—
322C2×C4—51no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—102no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4—301no—
329C2×C4—602no—
330C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
331C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
332C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
333C8—104no—
334C8—602no—
335C2×C3—201no—
336C2×C3#6576111yescharacteristic
337C2×C3C2×#401011yescharacteristic
338C2×C3#6579511yescharacteristic
339D3—401no—
340C5#6986111yescharacteristic, complemented, Sylow
341C22—101no—
342C22—101no—
343C22—101no—
344C22—601no—
345C22—601no—
346C22—601no—
347C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
348C4—21no—
349C4—21no—
350C4—101no—
351C4—101no—
352C4—101no—
353C4—121no—
354C4—121no—
355C4—601no—
356C4#9115812yes—
357C3#1060443211yescharacteristic, complemented, Sylow
358C2—201no—
359C2—1201no—
360C2#1175171711yescharacteristic
361C2C2×#9115811yescharacteristic
362C2#1175181811yescharacteristic
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 radical#91450C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1529
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
2. #11752342C2semidirect
3. C3×C4×#700C2semidirect
4. #11746506C2semidirect
5. #11746505C2semidirect
27. C4×#700D3semidirect
293. C3×C5#1529semidirect
340. C5#69861semidirect
357. C3#10604432semidirect

Maximal subgroups

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

subgroupindex
#117524942
#117523422
C3×C4×#7002
#117465062
#117465052
#106044323
#698615