Subgroups — #14417571

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic
2	#11752523	C₂	1	2	yes	maximal
3	C₄×Dic₆₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4689	C₂	1	1	yes	maximal, characteristic
5	C₃×C₄×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748123	C₂	1	2	yes	maximal
7	#11747873	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747832	C₂	1	2	yes	maximal, complemented
10	#11747682	C₂	1	1	yes	maximal, characteristic
11	#11747091	C₂	1	2	yes	maximal, complemented
12	#10610304	—	3	1	no	maximal, Hall
13	C₂×D₃×Dic₁₀	C₂²	1	2	yes	—
14	C₂×Dic₆₀	C₂²	1	1	yes	characteristic
15	C₄×Dic₃₀	C₂²	1	2	yes	—
16	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₅×#872	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
20	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
21	#91400	—	2	2	no	—
22	#91398	—	2	2	no	—
23	#91340	C₂²	1	2	yes	—
24	#91338	C₂²	1	2	yes	—
25	Dic₃×Dic₁₀	C₂²	1	2	yes	—
26	#91325	—	2	2	no	—
27	#91323	—	2	2	no	—
28	C₂×#6662	C₂²	1	2	yes	—
29	D₃×Dic₂₀	C₄	1	8	yes	complemented
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	#91102	C₂²	1	1	yes	characteristic
32	#91100	C₂²	1	2	yes	—
33	C₅×#815	C₂²	1	1	yes	characteristic
34	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
35	C₅×#803	C₂²	1	1	yes	characteristic
36	C₃×#3950	C₂²	1	1	yes	characteristic
37	C₃×#3948	C₂²	1	2	yes	—
38	#90987	C₂²	1	2	yes	—
39	#90974	C₂²	1	2	yes	—
40	#90971	C₂²	1	2	yes	—
41	#79720	—	5	1	no	maximal, Hall
42	C₂²×Dic₂₀	—	3	1	no	—
43	#65850	—	3	2	no	—
44	C₅×#405	—	3	1	no	—
45	#65409	—	3	2	no	—
46	#65395	—	3	1	no	—
47	#65005	—	3	2	no	—
48	#65005	—	3	2	no	—
49	C₄×Dic₂₀	—	3	1	no	—
50	C₄×Dic₂₀	—	3	1	no	—
51	C₄×Dic₂₀	—	3	1	no	—
52	C₄×Dic₂₀	D₃	1	1	yes	characteristic, complemented
53	C₂×Dic₃₀	C₂³	1	2	yes	—
54	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
55	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
56	C₂×#1204	—	2	2	no	—
57	C₂×D₃×Dic₅	—	2	2	no	—
58	D₃×Dic₁₀	—	2	4	no	—
59	D₃×Dic₁₀	C₂×C₄	1	8	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₄⋊Dic₁₅	C₂³	1	2	yes	—
64	#6712	—	2	2	no	—
65	C₄×Dic₁₅	—	2	2	no	—
66	Dic₆₀	C₂×C₄	1	4	yes	—
67	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
68	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
69	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
70	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
71	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
75	C₅×D₃×C₈	C₂×C₄	1	4	yes	—
76	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
77	C₃×#683	—	2	2	no	—
78	C₃×C₄×Dic₅	—	2	2	no	—
79	C₃×Dic₂₀	C₂×C₄	1	4	yes	—
80	#6669	—	2	2	no	—
81	#6668	—	2	2	no	—
82	(C₂×D₃)⋊Dic₅	—	2	2	no	—
83	Dic₃×Dic₅	—	2	2	no	—
84	Dic₃×Dic₅	—	2	2	no	—
85	Dic₃×Dic₅	—	2	2	no	—
86	#6662	C₂×C₄	1	8	yes	—
87	C₂×D₃×Q₁₆	—	5	1	no	—
88	#5572	—	5	2	no	—
89	C₃×C₄×Q₁₆	—	5	1	no	—
90	Dic₃×Q₁₆	—	5	1	no	—
91	#5030	—	5	2	no	—
92	#4880	—	5	1	no	—
93	#4873	—	5	1	no	—
94	#4802	—	5	2	no	—
95	#4789	—	5	2	no	—
96	C₄×Dic₁₂	—	5	1	no	—
97	#4689	D₅	1	1	yes	characteristic
98	C₂²×Dic₁₀	—	3	2	no	—
99	C₂×C₅×M₁₆	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₅×#117	—	3	1	no	—
102	#4072	—	3	2	no	—
103	C₂×Dic₂₀	—	3	2	no	—
104	C₂×Dic₂₀	—	3	1	no	—
105	C₂×Dic₂₀	—	3	8	no	—
106	C₂×Dic₂₀	C₂×D₃	1	1	yes	characteristic
107	#4033	—	6	2	no	—
108	#4033	—	6	2	no	—
109	#4023	—	6	2	no	—
110	#4023	—	6	2	no	—
111	C₄×Dic₁₀	—	3	2	no	—
112	C₄×Dic₁₀	—	3	2	no	—
113	C₄×Dic₁₀	—	3	2	no	—
114	C₄×Dic₁₀	C₂×D₃	1	2	yes	—
115	C₅×#97	—	3	1	no	—
116	C₅×#97	—	3	1	no	—
117	C₄×C₅×C₈	—	3	1	no	—
118	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
119	#3950	—	3	1	no	—
120	#3950	C₂×D₃	1	1	yes	characteristic
121	#3949	—	3	2	no	—
122	#3948	—	3	2	no	—
123	#3948	—	3	2	no	—
124	#3948	—	3	2	no	—
125	#3948	C₂×D₃	1	2	yes	—
126	#2950	—	15	1	no	Sylow
127	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×Dic₁₅	—	2	2	no	—
132	C₂×Dic₁₅	—	2	2	no	—
133	Dic₃₀	—	2	2	no	—
134	Dic₃₀	C₂²×C₄	1	4	yes	—
135	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
139	C₄×C₅×D₃	#41	1	2	yes	—
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₃×Dic₁₀	—	2	2	no	—
143	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
144	#1204	—	2	8	no	—
145	D₃×Dic₅	—	2	8	no	—
146	C₃×C₅×C₈	—	2	1	no	—
147	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₅×C₃⋊C₈	—	2	1	no	—
149	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×D₃×Q₈	—	5	2	no	—
151	C₂×C₃×Q₁₆	—	5	1	no	—
152	C₃×C₄×Q₈	—	5	2	no	—
153	Q₈×Dic₃	—	5	2	no	—
154	C₂×#216	—	5	2	no	—
155	D₃×Q₁₆	—	5	8	no	—
156	C₂×Dic₁₂	—	5	1	no	—
157	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
158	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
159	#892	—	5	2	no	—
160	#892	—	10	2	no	—
161	#887	—	5	2	no	—
162	#887	—	10	2	no	—
163	#872	—	10	2	no	—
164	#872	C₂×D₅	1	1	yes	characteristic
165	C₄×Dic₆	—	5	2	no	—
166	C₄×Dic₆	—	10	2	no	—
167	C₃×#107	—	5	1	no	—
168	C₃×#103	—	5	2	no	—
169	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
170	#835	—	5	2	no	—
171	#818	—	5	1	no	—
172	#816	—	5	2	no	—
173	#815	C₂×D₅	1	1	yes	characteristic
174	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
175	#810	—	5	2	no	—
176	#808	—	5	2	no	—
177	#803	C₂×D₅	1	1	yes	characteristic
178	C₂²×C₄×C₅	—	3	1	no	—
179	C₂²×Dic₅	—	6	2	no	—
180	C₂×Dic₁₀	—	3	2	no	—
181	C₂×Dic₁₀	—	3	8	no	—
182	C₂×Dic₁₀	—	6	4	no	—
183	C₂×Dic₁₀	—	6	2	no	—
184	C₂×Dic₁₀	C₂²×D₃	1	2	yes	—
185	C₅×M₁₆	—	6	2	no	—
186	C₂×C₅×C₈	—	3	1	no	—
187	C₂×C₅×C₈	—	3	4	no	—
188	C₂×C₅×C₈	—	3	1	no	—
189	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	3	1	no	—
192	C₅×C₄⋊C₄	—	3	1	no	—
193	C₅×C₂²⋊C₄	—	3	1	no	—
194	C₅×C₂²⋊C₄	—	3	1	no	—
195	C₄²×C₅	—	3	1	no	—
196	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₂²⋊Dic₅	—	6	2	no	—
198	C₄⋊Dic₅	—	3	2	no	—
199	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
200	#683	—	2	2	no	—
201	#683	—	6	2	no	—
202	#683	—	6	2	no	—
203	#683	—	6	2	no	—
204	C₄×Dic₅	—	2	2	no	—
205	C₄×Dic₅	—	6	2	no	—
206	C₄×Dic₅	—	6	2	no	—
207	C₄×Dic₅	—	6	2	no	—
208	C₄×Dic₅	—	6	2	no	—
209	Dic₂₀	—	3	8	no	—
210	Dic₂₀	—	3	4	no	—
211	Dic₂₀	C₄×D₃	1	4	yes	—
212	C₂²×Q₁₆	—	15	1	no	—
213	#519	—	15	2	no	—
214	#441	—	15	2	no	—
215	#441	—	15	2	no	—
216	C₄×Q₁₆	—	5	1	no	—
217	C₄×Q₁₆	—	15	1	no	—
218	C₄×Q₁₆	—	15	1	no	—
219	C₄×Q₁₆	—	15	1	no	—
220	#427	—	15	1	no	—
221	#419	—	15	2	no	—
222	#405	—	3	1	no	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	1	no	—
225	C₂×C₅×D₃	—	2	1	no	—
226	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
227	C₃×C₄×C₅	—	2	1	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
230	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	Dic₁₅	—	2	4	no	—
232	Dic₁₅	—	4	2	no	—
233	C₃×Dic₅	—	2	4	no	—
234	C₃×Dic₅	—	4	2	no	—
235	C₅×Dic₃	—	2	1	no	—
236	C₅×Dic₃	—	2	1	no	—
237	C₅×Dic₃	C₄×D₄	1	2	yes	—
238	C₂×C₃×Q₈	—	5	2	no	—
239	D₃×Q₈	—	5	8	no	—
240	D₃×Q₈	—	10	4	no	—
241	C₂×C₄×D₃	—	10	2	no	—
242	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
243	C₂×Dic₆	—	5	2	no	—
244	C₂×Dic₆	—	10	2	no	—
245	C₃×Q₁₆	—	5	4	no	—
246	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	—	5	2	no	—
249	C₃×C₄⋊C₄	—	10	2	no	—
250	C₃×C₄²	—	10	2	no	—
251	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
252	#216	—	5	8	no	—
253	(C₂×D₃)⋊C₄	—	10	2	no	—
254	(C₂×D₃)⋊C₄	D₂₀	1	1	yes	characteristic
255	(C₂×D₃)⋊C₄	D₂₀	1	1	yes	characteristic
256	C₄⋊Dic₃	—	5	2	no	—
257	C₄⋊Dic₃	—	10	2	no	—
258	Dic₃⋊C₄	—	10	2	no	—
259	Dic₃⋊C₄	—	10	2	no	—
260	Dic₃⋊C₄	D₂₀	1	1	yes	characteristic
261	Dic₃⋊C₄	D₂₀	1	1	yes	characteristic
262	C₄×Dic₃	—	10	2	no	—
263	C₄×Dic₃	—	10	2	no	—
264	C₄×Dic₃	—	10	2	no	—
265	C₄×Dic₃	—	10	2	no	—
266	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
269	Dic₁₂	—	5	4	no	—
270	ΓL(1,𝔽₂₅)	—	2	2	no	—
271	D₃×C₈	C₄×D₅	1	4	yes	—
272	C₂³×C₅	—	3	1	no	—
273	C₂×C₄×C₅	—	3	1	no	—
274	C₂×C₄×C₅	—	3	2	no	—
275	C₂×C₄×C₅	—	3	2	no	—
276	C₂×C₄×C₅	—	3	1	no	—
277	C₂×C₄×C₅	—	3	1	no	—
278	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
281	C₂×Dic₅	—	2	2	no	—
282	C₂×Dic₅	—	2	2	no	—
283	C₂×Dic₅	—	6	8	no	—
284	C₂×Dic₅	—	6	2	no	—
285	C₂×Dic₅	—	6	2	no	—
286	Dic₁₀	—	2	2	no	—
287	Dic₁₀	—	3	4	no	—
288	Dic₁₀	—	6	8	no	—
289	Dic₁₀	—	6	2	no	—
290	Dic₁₀	C₂×C₄×D₃	1	4	yes	—
291	C₅×C₈	—	2	1	no	—
292	C₅×C₈	—	3	2	no	—
293	C₅×C₈	—	6	1	no	—
294	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
295	C₂²×Q₈	—	15	2	no	—
296	C₂×Q₁₆	—	5	1	no	—
297	C₂×Q₁₆	—	15	8	no	—
298	C₂×Q₁₆	—	15	2	no	—
299	C₂×Q₁₆	—	15	1	no	—
300	C₂×M₁₆	—	3	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₄×Q₈	—	5	2	no	—
303	C₄×Q₈	—	15	2	no	—
304	C₄×Q₈	—	15	2	no	—
305	C₄×Q₈	—	15	2	no	—
306	C₄×Q₈	—	30	2	no	—
307	C₄×Q₈	—	30	2	no	—
308	#117	—	3	1	no	—
309	#117	—	15	2	no	—
310	#117	—	30	2	no	—
311	#117	—	30	2	no	—
312	#107	—	5	1	no	—
313	#107	—	15	1	no	—
314	#106	—	15	2	no	—
315	#103	—	5	2	no	—
316	#103	—	15	2	no	—
317	#103	—	15	2	no	—
318	#103	—	15	2	no	—
319	#97	—	3	1	no	—
320	#97	—	3	1	no	—
321	C₄×C₈	—	3	1	no	—
322	C₄×C₈	D₃×D₅	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×C₅	#578	1	1	yes	characteristic
325	C₂×C₃×C₅	#578	1	1	yes	characteristic
326	C₅×D₃	—	2	2	no	—
327	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
328	C₃×Q₈	—	5	4	no	—
329	C₃×Q₈	—	10	2	no	—
330	C₂×C₃×C₄	—	10	2	no	—
331	C₂×C₃×C₄	—	10	2	no	—
332	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
335	C₂×Dic₃	—	10	2	no	—
336	C₂×Dic₃	—	10	2	no	—
337	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
338	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
339	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
340	C₄×D₃	—	10	8	no	—
341	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
342	C₄×D₃	#709	1	2	yes	—
343	Dic₆	—	5	4	no	—
344	Dic₆	—	10	2	no	—
345	Dic₆	—	10	8	no	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
348	C₃⋊C₈	—	2	1	no	—
349	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
350	C₂²×C₅	—	3	2	no	—
351	C₂²×C₅	—	6	1	no	—
352	C₂²×C₅	—	6	1	no	—
353	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	3	2	no	—
357	C₄×C₅	—	6	1	no	—
358	C₄×C₅	—	6	1	no	—
359	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
360	C₄×C₅	D₃×#41	1	1	yes	characteristic
361	Dic₅	—	2	4	no	—
362	Dic₅	—	4	2	no	—
363	Dic₅	—	6	4	no	—
364	Dic₅	—	12	2	no	—
365	C₂×Q₈	—	5	2	no	—
366	C₂×Q₈	—	15	8	no	—
367	C₂×Q₈	—	15	2	no	—
368	C₂×Q₈	—	30	2	no	—
369	C₂×Q₈	—	30	4	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	30	2	no	—
372	Q₁₆	—	5	4	no	—
373	Q₁₆	—	15	8	no	—
374	Q₁₆	—	15	4	no	—
375	M₁₆	—	6	2	no	—
376	C₂×C₈	—	3	1	no	—
377	C₂×C₈	—	3	4	no	—
378	C₂×C₈	—	3	1	no	—
379	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
380	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
381	C₄⋊C₄	—	3	1	no	—
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	5	2	no	—
384	C₄⋊C₄	—	10	2	no	—
385	C₄⋊C₄	—	15	2	no	—
386	C₄⋊C₄	—	30	2	no	—
387	C₄⋊C₄	—	30	2	no	—
388	C₄⋊C₄	—	30	2	no	—
389	C₂²⋊C₄	—	3	1	no	—
390	C₂²⋊C₄	—	3	1	no	—
391	C₂²⋊C₄	—	30	2	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	10	2	no	—
394	C₄²	—	30	2	no	—
395	C₄²	—	30	2	no	—
396	C₄²	—	30	2	no	—
397	C₄²	—	30	2	no	—
398	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
399	C₃×C₅	#2950	1	1	yes	characteristic, complemented, Hall
400	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	—	2	1	no	—
403	C₂×D₃	C₄×D₂₀	1	2	yes	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	10	4	no	—
407	C₃×C₄	—	20	2	no	—
408	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
409	C₃×C₄	C₂×#709	1	1	yes	characteristic
410	Dic₃	—	2	1	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	—	10	4	no	—
413	Dic₃	—	20	2	no	—
414	Dic₃	C₄×D₂₀	1	2	yes	—
415	C₂×C₅	—	6	2	no	—
416	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
417	C₂×C₅	#5766	1	1	yes	characteristic
418	C₂×C₅	#5771	1	1	yes	characteristic
419	C₂³	—	3	1	no	—
420	Q₈	—	5	4	no	—
421	Q₈	—	10	2	no	—
422	Q₈	—	15	4	no	—
423	Q₈	—	30	8	no	—
424	Q₈	—	30	2	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	10	2	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	—	30	8	no	—
433	C₂×C₄	—	30	2	no	—
434	C₂×C₄	—	30	2	no	—
435	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
436	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	3	2	no	—
440	C₈	—	6	1	no	—
441	C₈	C₄×D₃×D₅	1	2	yes	—
442	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
443	C₂×C₃	#66087	1	1	yes	characteristic
444	C₂×C₃	#66087	1	1	yes	characteristic
445	D₃	—	2	2	no	—
446	C₅	#79720	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	2	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	3	2	no	—
454	C₄	—	6	1	no	—
455	C₄	—	6	1	no	—
456	C₄	—	10	4	no	—
457	C₄	—	20	2	no	—
458	C₄	—	30	4	no	—
459	C₄	—	60	2	no	—
460	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
461	C₄	D₃×#709	1	1	yes	characteristic
462	C₃	#10610304	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	2	no	—
464	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
465	C₂	#11753991	1	1	yes	characteristic
466	C₂	#11754003	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×D₂₀
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2950
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×Dic₆₀	C₂	semidirect
5. C₃×C₄×Dic₂₀	C₂	semidirect
7. #11747873	C₂	semidirect
8. Dic₃×Dic₂₀	C₂	semidirect
9. #11747832	C₂	semidirect
11. #11747091	C₂	semidirect
29. D₃×Dic₂₀	C₄	semidirect
52. C₄×Dic₂₀	D₃	semidirect
399. C₃×C₅	#2950	semidirect
446. C₅	#79720	semidirect
462. C₃	#10610304	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Dic₂₀	2
#11752523	2
C₄×Dic₆₀	2
C₅×#4689	2
C₃×C₄×Dic₂₀	2
#11748123	2
#11747873	2
Dic₃×Dic₂₀	2
#11747832	2
#11747682	2
#11747091	2
#10610304	3
#79720	5