Finite Group Databasebeta

← #14282500

Subgroups — #14282500

Order 1920.

460 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 106 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
2#11752418C211yesmaximal, characteristic, complemented
3C2×C3×C4×#170C211yesmaximal, characteristic, complemented
4#11746493C212yesmaximal, complemented
5#11746491C212yesmaximal, complemented
6#10604514—31nomaximal, Hall
7C22×C3×#170—21no—
8#91819C411yescharacteristic
9C5×#924C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11#91552—21no—
12#91546—21no—
13#91418C2211yescharacteristic
14#91402—21no—
15#91388C411yescharacteristic
16#91387—21no—
17#91375C411yescharacteristic
18Dic5×Dic6C2211yescharacteristic
19#91241—21no—
20#91231—21no—
21C4⋊(C3⋊#170)C2212yes—
22C3×C4×#170—21no—
23C3×C4×#170C2212yes—
24#69736—51nomaximal, Hall
25#65958—31no—
26#65759—31no—
27C2×C4×#170D311yescharacteristic, complemented
28Q8⋊#170—32no—
29#64871—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—22no—
38C2×C3×#170—24no—
39C2×C3×#170—22no—
40#6714—21no—
41C4⋊Dic15C2×C411yescharacteristic
42C5×#217—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×Dic3⋊C4—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49Dic3⋊Dic5—21no—
50Dic3⋊Dic5—21no—
51#6669—21no—
52#6667—21no—
53#6667—21no—
54#6667—21no—
55Dic3×Dic5—21no—
56#5479—51no—
57C2×C3×C4×C8—51no—
58#4926—51no—
59#4459—52no—
60#4456—52no—
61C22×#170—21no—
62C5×C22⋊Q8—31no—
63#4093—31no—
64Q8×Dic5—31no—
65#4076—31no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4044—61no—
68#4039—31no—
69#4038—61no—
70#4036—31no—
71#4032—61no—
72#4027—61no—
73C22⋊#170—61no—
74#4002—61no—
75C4⋊#170—32no—
76C4×#170—21no—
77C4×#170C2×D312yes—
78#1494—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C22×D15—21no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84#1220—42no—
85C2×Dic15—21no—
86D60—22no—
87C2×C5×Dic3—21no—
88C2×C5×Dic3—21no—
89C5×Dic6—22no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96#1200—42no—
97C3⋊#170—42no—
98C3×#170—24no—
99C22×C3×C8—101no—
100C2×C3×C42—51no—
101#930—51no—
102#929—101no—
103C4×#67—101no—
104#924AGL(1,𝔽5)11yescharacteristic
105#876—101no—
106#875—51no—
107C4×D12—51no—
108#872—101no—
109#870—51no—
110C4×Dic6—51no—
111C3×C4×C8—52no—
112C3×C4×C8—101no—
113#830—101no—
114C4⋊(C3⋊C8)—52no—
115#803—101no—
116C2×C5×Q8—31no—
117C22×C4×C5C4×D311yescharacteristic
118C2×C22⋊D5—61no—
119C22×Dic5D1211yescharacteristic
120C22×Dic5#6711yescharacteristic
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×#170—24no—
124C2×#170—22no—
125C2×#170—62no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C5×C22⋊C4—61no—
129#685—61no—
130#685—61no—
131#685—61no—
132#685—61no—
133C4⋊Dic5—31no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136#683—61no—
137C4×Dic5—61no—
138C4×Dic5C4×D311yescharacteristic
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142#529—151no—
143#432—151no—
144C2×C4×C8—51no—
145Q8⋊C8—152no—
146D4⋊C8—152no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5#10412yes—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×D15—41no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5#13112yes—
156Dic15—41no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5#13512yes—
161C5×Dic3—41no—
162C5×Dic3—41no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
166C2×#67—101no—
167C2×D12—51no—
168C2×C4×D3—101no—
169C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
170C2×C3×C8—102no—
171C2×C3×C8—104no—
172C3×C42—51no—
173C3×C42—51no—
174C3×C42—51no—
175C3×C42—51no—
176#217—21no—
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—101no—
188C2×C3⋊C8—102no—
189C23×C5(C2×D3)⋊C411yescharacteristic
190C22×D5—61no—
191C5×Q8—62no—
192C2×C4×C5—22no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5(C2×D3)⋊C411yescharacteristic
196C2×C4×C5C2×C4×D311yescharacteristic
197C22⋊D5—122no—
198C2×Dic5—22no—
199C2×Dic5—22no—
200C2×Dic5—61no—
201C2×Dic5(C2×D3)⋊C411yescharacteristic
202C2×Dic5(C2×D3)⋊C411yescharacteristic
203C2×Dic5C2×D1211yescharacteristic
204C2×Dic5C2×#6711yescharacteristic
205D20—62no—
206C4×D5—122no—
207#170—24no—
208#170—122no—
209C22×C8—101no—
210#126—301no—
211#125—151no—
212#124—151no—
213#123—301no—
214C22⋊Q8—31no—
215#121—151no—
216C4×Q8—151no—
217C4×D4—151no—
218C4×D4—301no—
219#117—301no—
220C2×C42—51no—
221C4⋊C8—152no—
222C22⋊C8—301no—
223#97—301no—
224C4×C8—52no—
225C4×C8—101no—
226C2×C3×C5—22no—
227C2×C3×C5#40811yescharacteristic
228C2×C3×C5#41611yescharacteristic
229C2×C3×C5C2×#10411yescharacteristic
230D15—81no—
231C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
232C22×D3—101no—
233C2×C3×C4—22no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—51no—
238C2×C3×C4—102no—
239C2×C3×C4—102no—
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—102no—
247C4×D3—202no—
248Dic6—22no—
249C3×C8—104no—
250C3⋊C8—202no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5#80512yes—
254C22×C5C2×(C2×D3)⋊C411yescharacteristic
255C2×D5—121no—
256C2×D5—121no—
257C2×D5—121no—
258C4×C5—21no—
259C4×C5—121no—
260C4×C5—121no—
261C4×C5#90112yes—
262Dic5—21no—
263Dic5—21no—
264Dic5—21no—
265Dic5—121no—
266Dic5#90412yes—
267C2×Q8—31no—
268C2×D4—151no—
269C2×D4—301no—
270C22×C4—51no—
271C22×C4—51no—
272C22×C4—301no—
273C22×C4D3×AGL(1,𝔽5)11yescharacteristic
274C2×C8—102no—
275C2×C8—104no—
276C2×C8—302no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—151no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—61no—
284C22⋊C4—301no—
285C22⋊C4—301no—
286C22⋊C4—301no—
287C22⋊C4—301no—
288C42—51no—
289C42—51no—
290C42—51no—
291C42—51no—
292C42—301no—
293C3×C5#149411yescharacteristic, complemented, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3#401012yes—
297C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
298C2×D3—201no—
299C2×D3—201no—
300C2×D3—201no—
301C3×C4—21no—
302C3×C4—52no—
303C3×C4—101no—
304C3×C4—101no—
305C3×C4—101no—
306C3×C4#413112yes—
307Dic3—41no—
308Dic3—41no—
309Dic3—201no—
310C2×C5—22no—
311C2×C5C2×#80511yescharacteristic
312C2×C5#511011yescharacteristic
313C2×C5#511311yescharacteristic
314D5—241no—
315C23—301no—
316C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
317Q8—62no—
318D4—302no—
319D4—602no—
320C2×C4—22no—
321C2×C4—51no—
322C2×C4—51no—
323C2×C4—51no—
324C2×C4—51no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—102no—
328C2×C4—102no—
329C2×C4—301no—
330C2×C4—602no—
331C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
332C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
333C8—104no—
334C8—602no—
335C2×C3—22no—
336C2×C3#6577511yescharacteristic
337C2×C3C2×#401011yescharacteristic
338C2×C3#6579411yescharacteristic
339D3—401no—
340C5#6973611yescharacteristic, complemented, Sylow
341C22—21no—
342C22—21no—
343C22—601no—
344C22—601no—
345C22—601no—
346C22#9115812yes—
347C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
348C4—21no—
349C4—52no—
350C4—101no—
351C4—101no—
352C4—101no—
353C4—121no—
354C4—121no—
355C4—601no—
356C4#9192712yes—
357C3#1060451411yescharacteristic, complemented, Sylow
358C2—22no—
359C2—1201no—
360C2#1175170411yescharacteristic
361C2C2×#9115811yescharacteristic
362C2#1175199911yescharacteristic
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#1494
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752418C2semidirect
3. C2×C3×C4×#170C2semidirect
4. #11746493C2semidirect
5. #11746491C2semidirect
27. C2×C4×#170D3semidirect
293. C3×C5#1494semidirect
340. C5#69736semidirect
357. C3#10604514semidirect

Maximal subgroups

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

subgroupindex
#117544152
#117524182
C2×C3×C4×#1702
#117464932
#117464912
#106045143
#697365