Finite Group Databasebeta

← #14298703

Subgroups — #14298703

Order 1920.

472 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 102 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#11754188C211yesmaximal, characteristic
2C2×#91234C211yesmaximal, characteristic
3C2×C3×#4005C211yesmaximal, characteristic
4#11746576C212yesmaximal
5#11746575C212yesmaximal
6#10604387—31nomaximal, Hall
7C22×C3×Dic10C2211yescharacteristic
8C2×#6762C2212yes—
9C2×C3×#704C2212yes—
10#91815C411yescharacteristic
11C5×#926C411yescharacteristic
12#91528C411yescharacteristic
13#91528C411yescharacteristic
14#91528C2211yescharacteristic
15#91528C2211yescharacteristic
16#91331—21no—
17#91331—21no—
18Dic3×Dic10—21no—
19Dic3×Dic10—21no—
20#91234—21no—
21#91234—21no—
22C3×#4005—21no—
23C3×#4005—21no—
24#70101—51nomaximal, Hall
25#65850—31no—
26C2×#4005—31no—
27C2×#4005D311yescharacteristic
28#64867—32no—
29#64867—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2311yescharacteristic
33C2×C3×Dic10—22no—
34C2×C3×Dic10—22no—
35C2×C3×Dic10D411yescharacteristic
36C2×C3×Dic10D411yescharacteristic
37C2×C3×Dic10D411yescharacteristic
38C2×C3×Dic10D411yescharacteristic
39#6762—22no—
40#6762—22no—
41C2×C3⋊#170—22no—
42C3×#704—22no—
43C3×#704—22no—
44C2×C3×#170—22no—
45#6719C2×C411yescharacteristic
46#6719C2×C411yescharacteristic
47C4⋊Dic15—21no—
48C4×Dic15—21no—
49C5×#217C2×C411yescharacteristic
50C5×#217C2×C411yescharacteristic
51C5×C4⋊Dic3—21no—
52C4×C5×Dic3—21no—
53#6668—21no—
54#6668—21no—
55#6668—21no—
56#6668—21no—
57Dic3×Dic5—21no—
58Dic3×Dic5—21no—
59Dic3×Dic5—21no—
60Dic3×Dic5—21no—
61#5812—51no—
62C2×C3×#101—51no—
63C2×#836—51no—
64#4559—52no—
65#4556—52no—
66C22×Dic10C2×D311yescharacteristic
67C2×#704—32no—
68C2×#704C2×D312yes—
69C5×#117—31no—
70#4072—31no—
71#4033—61no—
72#4033—61no—
73#4023—31no—
74#4023—31no—
75#4023—31no—
76#4023—31no—
77C4×Dic10—61no—
78C4×Dic10—61no—
79#4005—21no—
80#4005—21no—
81#4005—61no—
82#4005—61no—
83#1830—151noSylow
84C23×C3×C5C22×C411yescharacteristic
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C2×C3×Dic5C2×D411yescharacteristic
99C2×C3×Dic5#4112yes—
100C2×C3×Dic5#4112yes—
101C3×Dic10—22no—
102C3×Dic10—22no—
103C3×Dic10—22no—
104C3×Dic10—22no—
105C3⋊#170—42no—
106C3×#170—42no—
107C22×C3×Q8—51no—
108C2×C3×M16—52no—
109Q8×Dic3—101no—
110Q8×Dic3—101no—
111Q8×Dic3—101no—
112Q8×Dic3—101no—
113#926—51no—
114#926—51no—
115#926—51no—
116#926—51no—
117#926—51no—
118#926AGL(1,𝔽5)11yescharacteristic
119C2×#208—52no—
120C3×#101—101no—
121C3×#101—101no—
122#836—101no—
123#836—101no—
124C22×C4×C5C4×D311yescharacteristic
125C22×Dic5C4×D311yescharacteristic
126C22×Dic5C22×D311yescharacteristic
127C2×Dic10—22no—
128C2×Dic10—22no—
129C2×Dic10D1211yescharacteristic
130C2×Dic10D1211yescharacteristic
131C2×Dic10#6711yescharacteristic
132C2×Dic10#6711yescharacteristic
133#704—22no—
134#704—22no—
135#704—62no—
136#704—62no—
137C2×#170—22no—
138C2×#170—62no—
139C5×C4⋊C4—61no—
140C5×C22⋊C4—31no—
141C5×C22⋊C4—31no—
142C42×C5—61no—
143C22⋊Dic5—31no—
144C22⋊Dic5—31no—
145C4⋊Dic5—61no—
146#683—61no—
147#683—61no—
148#683—61no—
149#683—61no—
150C4×Dic5—61no—
151C4×Dic5—61no—
152C4×Dic5—61no—
153C4×Dic5—61no—
154C4×Dic5—61no—
155#519—151no—
156C2×#101—51no—
157C2×#101—151no—
158#344—152no—
159#344—152no—
160C22×C3×C5—41no—
161C22×C3×C5C2×C22⋊C411yescharacteristic
162C22×C3×C5#11711yescharacteristic
163C22×C3×C5#11711yescharacteristic
164C3×C4×C5—21no—
165C3×C4×C5—21no—
166Dic15—41no—
167Dic15—41no—
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5#12312yes—
171C3×Dic5#12312yes—
172C5×Dic3—41no—
173C5×Dic3—41no—
174C2×C3×Q8—51no—
175C2×C3×Q8—51no—
176C2×C3×Q8—51no—
177C2×C3×Q8—51no—
178C2×C3×Q8—102no—
179C2×C3×Q8—102no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
183C3×M16—102no—
184C3×M16—102no—
185C2×C3×C8—102no—
186#217—51no—
187#217—51no—
188#217C2×AGL(1,𝔽5)11yescharacteristic
189#217C2×AGL(1,𝔽5)11yescharacteristic
190C4⋊Dic3—21no—
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C4⋊Dic3—101no—
194C4⋊Dic3—101no—
195C4⋊Dic3—101no—
196C4×Dic3—21no—
197C4×Dic3—101no—
198C4×Dic3—101no—
199C4×Dic3—101no—
200C4×Dic3—101no—
201C4×Dic3—101no—
202#208—102no—
203#208—102no—
204C2×C3⋊C8—102no—
205C23×C5C2×C4×D311yescharacteristic
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5(C2×D3)⋊C411yescharacteristic
211C2×C4×C5(C2×D3)⋊C411yescharacteristic
212C2×Dic5—21no—
213C2×Dic5—21no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216C2×Dic5(C2×D3)⋊C411yescharacteristic
217C2×Dic5(C2×D3)⋊C411yescharacteristic
218C2×Dic5C2×D1211yescharacteristic
219C2×Dic5#23712yes—
220C2×Dic5#23712yes—
221C2×Dic5C2×#6711yescharacteristic
222Dic10—22no—
223Dic10—22no—
224Dic10—22no—
225Dic10—22no—
226#170—42no—
227#170—122no—
228C22×Q8—51no—
229C2×M16—52no—
230C2×M16—152no—
231C4×Q8—301no—
232C4×Q8—301no—
233C4×Q8—301no—
234C4×Q8—301no—
235#117—31no—
236#117—151no—
237#117—151no—
238#117—151no—
239#117—151no—
240#117—151no—
241#101—101no—
242#101—101no—
243#101—301no—
244#101—301no—
245C2×C3×C5—21no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5#38111yescharacteristic
249C23×C3C22×AGL(1,𝔽5)11yescharacteristic
250C3×Q8—102no—
251C3×Q8—102no—
252C3×Q8—102no—
253C3×Q8—102no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—52no—
257C2×C3×C4—52no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—101no—
263C2×C3×C4—101no—
264C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
265C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—101no—
269C2×Dic3—101no—
270C3×C8—202no—
271C3⋊C8—202no—
272C22×C5—41no—
273C22×C5#87711yescharacteristic
274C22×C5#87711yescharacteristic
275C22×C5C2×(C2×D3)⋊C411yescharacteristic
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—121no—
279C4×C5—121no—
280Dic5—21no—
281Dic5—21no—
282Dic5—121no—
283Dic5—121no—
284Dic5#88612yes—
285Dic5#93512yes—
286C2×Q8—51no—
287C2×Q8—51no—
288C2×Q8—51no—
289C2×Q8—51no—
290C2×Q8—102no—
291C2×Q8—102no—
292C22×C4—51no—
293C22×C4—51no—
294C22×C4D3×AGL(1,𝔽5)11yescharacteristic
295M16—102no—
296M16—102no—
297M16—302no—
298M16—302no—
299C2×C8—102no—
300C2×C8—302no—
301C4⋊C4—61no—
302C4⋊C4—301no—
303C4⋊C4—301no—
304C4⋊C4—301no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C22⋊C4—31no—
308C22⋊C4—31no—
309C22⋊C4—151no—
310C22⋊C4—151no—
311C42—61no—
312C42—301no—
313C42—301no—
314C42—301no—
315C42—301no—
316C42—301no—
317C3×C5#183011yescharacteristic, complemented, Hall
318C22×C3—41no—
319C22×C3#413011yescharacteristic
320C22×C3#413011yescharacteristic
321C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—52no—
325C3×C4—52no—
326C3×C4—101no—
327C3×C4—101no—
328Dic3—41no—
329Dic3—41no—
330Dic3—201no—
331Dic3—201no—
332C2×C5—21no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5#494311yescharacteristic
336C23C2×D3×AGL(1,𝔽5)11yescharacteristic
337Q8—102no—
338Q8—102no—
339Q8—102no—
340Q8—102no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—52no—
344C2×C4—52no—
345C2×C4—51no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—301no—
354C2×C4—301no—
355C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
356C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
357C8—202no—
358C8—602no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3#6576411yescharacteristic
363C5#7010111yescharacteristic, complemented, Sylow
364C22—41no—
365C22#9192311yescharacteristic
366C22#9192311yescharacteristic
367C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
368C4—21no—
369C4—21no—
370C4—52no—
371C4—52no—
372C4—101no—
373C4—101no—
374C4—121no—
375C4—121no—
376C4—601no—
377C4—601no—
378C3#1060438711yescharacteristic, complemented, Sylow
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1175198411yescharacteristic
subgroupG/H
centerC2#11751984
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5#381
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1830
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
317. C3×C5#1830semidirect
363. C5#70101semidirect
378. C3#10604387semidirect

Maximal subgroups

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

subgroupindex
#117541882
C2×#912342
C2×C3×#40052
#117465762
#117465752
#106043873
#701015