Finite Group Databasebeta

← #14284438

Subgroups — #14284438

Order 1920.

400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752342C211yesmaximal, characteristic, complemented
3C3×#65684C211yesmaximal, characteristic, complemented
4#11746506C212yesmaximal, complemented
5#11746504C212yesmaximal, complemented
6#10604399—31nomaximal, Hall
7C4×Dic30C411yescharacteristic
8C4×C5×D12C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91449C411yescharacteristic
11#91447—21no—
12C4×#1201—21no—
13#91388C2211yescharacteristic
14#91373C2211yescharacteristic
15#91372—21no—
16#91371—21no—
17#91360C411yescharacteristic
18#91232—21no—
19#91231C2212yes—
20C4⋊(C3⋊#170)—21no—
21C3×#4004—21no—
22C3×#4003—21no—
23C3×#4002C2212yes—
24#70810—51nomaximal, Hall
25#65891—31no—
26#65684D311yescharacteristic, complemented
27#65683—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—
38C2×C3×#170—22no—
39C3×C42×C5C2×C411yescharacteristic
40C4⋊Dic15C2×C411yescharacteristic
41#6712—21no—
42C4×Dic15—21no—
43C5×(C2×D3)⋊C4—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5C2311yescharacteristic
48Dic3⋊Dic5—21no—
49Dic3⋊Dic5—21no—
50#6669—21no—
51(C2×D3)⋊Dic5—21no—
52(C2×D3)⋊Dic5—21no—
53(C2×D3)⋊Dic5—21no—
54#6665—21no—
55#5479—51no—
56C3×#432—51no—
57#4926—51no—
58#4465—52no—
59#4464—52no—
60C4×C5×D4—31no—
61#4084—31no—
62#4082—31no—
63C4×C22⋊D5—61no—
64#4072—61no—
65#4043—31no—
66#4036—31no—
67#4029—61no—
68#4025—61no—
69C42×D5C2×D311yescharacteristic
70C4×Dic10—31no—
71#4004—21no—
72#4003—21no—
73#4003—61no—
74#4002—32no—
75#4002C2×D312yes—
76C4⋊#170—61no—
77#1535—151noSylow
78C22×C5×D3—21no—
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—
85Dic30—41no—
86C2×C5×Dic3—21no—
87C5×D12—41no—
88C4×C5×D3—42no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C3×C4×D5—41no—
93C3×C4×D5—41no—
94C3×C4×D5—41no—
95#1201—42no—
96C3⋊#170—42no—
97C3×#170—42no—
98C2×C3×C42—51no—
99#930—51no—
100#929—101no—
101C4×#67—101no—
102#924—51no—
103#876—101no—
104#875—51no—
105C4×D12AGL(1,𝔽5)11yescharacteristic
106#872—101no—
107#870—51no—
108C4×Dic6—51no—
109C3×C4⋊C8—101no—
110C3×C22⋊C8—101no—
111C3×#97—52no—
112#830—101no—
113C4⋊(C3⋊C8)—101no—
114#803—52no—
115C2×C5×D4—31no—
116C22×C4×C5—61no—
117C2×C22⋊D5—61no—
118C2×C4×D5C4×D311yescharacteristic
119C2×C4×D5D1211yescharacteristic
120C2×C4×D5#6711yescharacteristic
121C2×Dic10—31no—
122C2×#170—22no—
123C2×#170—62no—
124C5×C4⋊C4—31no—
125C5×C22⋊C4—61no—
126C42×C5C4×D311yescharacteristic
127C22⋊Dic5—61no—
128C22⋊Dic5—61no—
129C22⋊Dic5—61no—
130#685—61no—
131C4⋊Dic5—31no—
132C4⋊Dic5—61no—
133C4⋊Dic5—61no—
134#683—61no—
135#683—61no—
136C4×Dic5—61no—
137C4×Dic5D1211yescharacteristic
138C4×Dic5#6711yescharacteristic
139C4×Dic5C22×D311yescharacteristic
140#529—151no—
141#432—51no—
142#432—151no—
143#330—152no—
144#329—152no—
145C22×C3×C5C2×C22⋊C411yescharacteristic
146C2×C5×D3—41no—
147C2×C5×D3—41no—
148C2×C5×D3—41no—
149C2×C3×D5—21no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155Dic15—41no—
156Dic15—41no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C5×Dic3—41no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C2×#67—101no—
165C2×D12C2×AGL(1,𝔽5)11yescharacteristic
166C2×C4×D3—21no—
167C2×Dic6—51no—
168C2×C3×C8—102no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42C2×AGL(1,𝔽5)11yescharacteristic
173#217—101no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—101no—
176(C2×D3)⋊C4—101no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—102no—
186C23×C5—61no—
187C22×D5(C2×D3)⋊C411yescharacteristic
188C5×D4—121no—
189C2×C4×C5—61no—
190C2×C4×C5—122no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C22⋊D5—122no—
195C2×Dic5—61no—
196C2×Dic5—61no—
197C2×Dic5(C2×D3)⋊C411yescharacteristic
198C2×Dic5C2×D1211yescharacteristic
199C2×Dic5C2×#6711yescharacteristic
200C4×D5—41no—
201C4×D5—41no—
202C4×D5—41no—
203Dic10—121no—
204#170—42no—
205#170—122no—
206#126—301no—
207#125—151no—
208#124—151no—
209#123—301no—
210C22⋊Q8—151no—
211#121—151no—
212C4×Q8—151no—
213C4×D4—31no—
214C4×D4—301no—
215#117—301no—
216C2×C42—51no—
217C4⋊C8—101no—
218C4⋊C8—301no—
219C22⋊C8—101no—
220C22⋊C8—301no—
221#97—52no—
222#97—152no—
223C2×C3×C5#41311yescharacteristic
224C2×C3×C5#42111yescharacteristic
225C2×C3×C5#42111yescharacteristic
226C3×D5—41no—
227C5×D3—81no—
228C23×C3—51no—
229C22×D3—21no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—201no—
234C2×C3×C4—201no—
235C2×C3×C4—201no—
236C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
237C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
238C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
239#67—202no—
240C2×Dic3—21no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243D12—41no—
244C4×D3—42no—
245Dic6—201no—
246C3×C8—202no—
247C3⋊C8—202no—
248C22×C5—121no—
249C22×C5—121no—
250C22×C5—121no—
251C22×C5C2×(C2×D3)⋊C411yescharacteristic
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—21no—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—121no—
259Dic5—21no—
260Dic5—21no—
261Dic5—21no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—151no—
265C2×D4—31no—
266C2×D4—301no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4—51no—
270C22×C4—61no—
271C2×C8—102no—
272C2×C8—302no—
273C4⋊C4—31no—
274C4⋊C4—151no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C22⋊C4—61no—
280C22⋊C4—301no—
281C22⋊C4—301no—
282C22⋊C4—301no—
283C22⋊C4—301no—
284C42—51no—
285C42—51no—
286C42—51no—
287C42—301no—
288C42D3×AGL(1,𝔽5)11yescharacteristic
289C3×C5#153511yescharacteristic, complemented, Hall
290C22×C3—101no—
291C22×C3—101no—
292C22×C3—101no—
293C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—101no—
301C3×C4—101no—
302C3×C4—101no—
303Dic3—41no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—241no—
307C2×C5#500511yescharacteristic
308C2×C5#513211yescharacteristic
309C2×C5#513911yescharacteristic
310D5—41no—
311C23—51no—
312C23—61no—
313Q8—601no—
314D4—121no—
315D4—602no—
316C2×C4—51no—
317C2×C4—51no—
318C2×C4—51no—
319C2×C4—61no—
320C2×C4—122no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—301no—
325C2×C4—301no—
326C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
327C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
328C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
329C8—202no—
330C8—602no—
331C2×C3—201no—
332C2×C3#6576111yescharacteristic
333C2×C3#6576911yescharacteristic
334C2×C3#6579511yescharacteristic
335D3—81no—
336C5#7081011yescharacteristic, complemented, Sylow
337C22—101no—
338C22—101no—
339C22—101no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—101no—
348C4—101no—
349C4—101no—
350C4—121no—
351C4—601no—
352C4—601no—
353C3#1060439911yescharacteristic, complemented, Sylow
354C2—201no—
355C2—241no—
356C2#1175171811yescharacteristic
357C2#1175172011yescharacteristic
358C2#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#91449C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1535
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×#65684C2semidirect
4. #11746506C2semidirect
5. #11746504C2semidirect
26. #65684D3semidirect
289. C3×C5#1535semidirect
336. C5#70810semidirect
353. C3#10604399semidirect

Maximal subgroups

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

subgroupindex
#117526822
#117523422
C3×#656842
#117465062
#117465042
#106043993
#708105