Subgroups — #14417657

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91273	C₂	1	1	yes	maximal, characteristic
2	#11752518	C₂	1	2	yes	maximal, complemented
3	C₄×Dic₆₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748138	C₂	1	2	yes	maximal, complemented
7	#11747873	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747742	C₂	1	2	yes	maximal, complemented
10	D₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747052	C₂	1	2	yes	maximal, complemented
12	#10610293	—	3	1	no	maximal, Hall
13	C₂×#6765	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×D₄₀	C₂²	1	1	yes	characteristic
20	C₃×C₄×D₂₀	C₂²	1	2	yes	—
21	#91442	—	2	2	no	—
22	#91440	—	2	2	no	—
23	D₃×C₄⋊Dic₅	C₂²	1	2	yes	—
24	Dic₃×D₂₀	C₂²	1	2	yes	—
25	#91394	—	2	2	no	—
26	D₅×Dic₃⋊C₄	—	2	2	no	—
27	#91340	C₂²	1	2	yes	—
28	C₂×#6657	C₂²	1	2	yes	—
29	#91273	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×#3953	C₂²	1	2	yes	—
37	C₃×#3950	C₂²	1	1	yes	characteristic
38	#90990	C₂²	1	2	yes	—
39	#90974	C₂²	1	2	yes	—
40	#90965	C₂²	1	2	yes	—
41	#79589	—	5	1	no	maximal, Hall
42	C₂×#4050	—	3	1	no	—
43	#65857	—	3	2	no	—
44	C₅×#405	—	3	1	no	—
45	#65422	—	3	2	no	—
46	C₂×#3950	—	3	1	no	—
47	#64999	—	3	2	no	—
48	#64999	—	3	2	no	—
49	C₄×Dic₂₀	—	3	1	no	—
50	C₄×Dic₂₀	—	3	1	no	—
51	C₄×D₄₀	—	3	1	no	—
52	C₄×D₄₀	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×D₂₀	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₅	—	2	2	no	—
57	C₂×#1201	—	2	2	no	—
58	C₂×D₃×Dic₅	—	2	2	no	—
59	C₂×D₅×Dic₃	—	2	2	no	—
60	C₂×D₅×Dic₃	—	2	2	no	—
61	#6765	—	2	4	no	—
62	#6765	C₂×C₄	1	8	yes	complemented
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₁₅	C₂³	1	2	yes	—
67	#6712	—	2	2	no	—
68	C₄×Dic₁₅	—	2	2	no	—
69	Dic₆₀	C₂×C₄	1	4	yes	complemented
70	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
71	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
72	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
73	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
74	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
78	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
79	C₃×#685	—	2	2	no	—
80	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
81	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
82	Dic₃⋊Dic₅	—	2	2	no	—
83	#6669	—	2	2	no	—
84	#6665	—	2	2	no	—
85	Dic₃×Dic₅	—	2	2	no	—
86	#6657	C₂×C₄	1	8	yes	complemented
87	C₂×#912	—	5	1	no	—
88	#5546	—	5	2	no	—
89	C₃×C₄×D₈	—	5	1	no	—
90	Dic₃×D₈	—	5	1	no	—
91	#5018	—	5	2	no	—
92	D₃×#107	—	5	1	no	—
93	#4873	—	5	1	no	—
94	#4771	—	5	2	no	—
95	#4757	—	5	2	no	—
96	C₄×Dic₁₂	—	5	1	no	—
97	#4689	D₅	1	1	yes	characteristic, complemented
98	C₂×#709	—	3	2	no	—
99	C₂×C₅×M₁₆	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₅×#117	—	3	1	no	—
102	C₂×C₄⋊Dic₅	—	3	2	no	—
103	C₂×Dic₂₀	—	3	1	no	—
104	#4050	—	3	8	no	—
105	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic
106	C₂×#677	—	3	2	no	—
107	#4038	—	6	2	no	—
108	D₅×C₄⋊C₄	—	6	2	no	—
109	#4027	—	6	2	no	—
110	#4027	—	6	2	no	—
111	C₄×D₂₀	—	3	2	no	—
112	C₄×D₂₀	C₂×D₃	1	2	yes	—
113	C₄×Dic₁₀	—	3	2	no	—
114	C₄×Dic₁₀	—	3	2	no	—
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	#3953	—	3	2	no	—
120	#3953	C₂×D₃	1	2	yes	—
121	#3950	—	3	1	no	—
122	#3950	—	3	2	no	—
123	#3950	C₂×D₃	1	1	yes	characteristic
124	#3948	—	3	2	no	—
125	#3948	—	3	2	no	—
126	#2951	—	15	1	no	Sylow
127	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₃×D₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×Dic₁₅	—	2	2	no	—
133	C₂×Dic₁₅	—	2	2	no	—
134	Dic₃₀	—	2	2	no	—
135	Dic₃₀	C₂²×C₄	1	4	yes	—
136	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
140	C₄×C₅×D₃	#41	1	2	yes	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₃×D₂₀	—	2	2	no	—
143	C₃×D₂₀	C₂²×C₄	1	4	yes	—
144	C₃×C₄×D₅	—	8	2	no	—
145	#1201	—	2	8	no	—
146	D₃×Dic₅	—	8	2	no	—
147	D₅×Dic₃	—	2	8	no	—
148	D₅×Dic₃	—	8	2	no	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₅×C₃⋊C₈	—	2	1	no	—
152	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×#237	—	5	2	no	—
154	C₂×C₃×D₈	—	5	1	no	—
155	C₃×C₄×D₄	—	5	2	no	—
156	D₄×Dic₃	—	5	2	no	—
157	C₂×#214	—	5	2	no	—
158	C₄×#67	—	10	2	no	—
159	C₂×Dic₃⋊C₄	—	10	2	no	—
160	#912	—	5	8	no	—
161	C₂×Dic₁₂	—	5	1	no	—
162	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
163	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
164	D₃×C₄⋊C₄	—	5	2	no	—
165	#887	—	5	2	no	—
166	#67⋊C₄	—	10	2	no	—
167	#877	—	10	2	no	—
168	#872	C₂×D₅	1	1	yes	characteristic
169	C₄×Dic₆	—	5	2	no	—
170	C₃×#107	—	5	1	no	—
171	C₃×#102	—	5	2	no	—
172	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
173	#832	—	5	2	no	—
174	#818	—	5	1	no	—
175	#816	—	5	2	no	—
176	#815	C₂×D₅	1	1	yes	characteristic
177	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
178	#810	—	5	2	no	—
179	#807	—	5	2	no	—
180	#803	C₂×D₅	1	1	yes	characteristic
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂×C₂²⋊D₅	—	6	2	no	—
183	C₂²×Dic₅	—	6	2	no	—
184	#709	—	3	8	no	—
185	#709	—	6	4	no	—
186	C₂×D₂₀	C₂²×D₃	1	2	yes	—
187	C₂×C₄×D₅	—	2	2	no	—
188	C₂×C₄×D₅	—	6	2	no	—
189	C₂×C₄×D₅	—	6	2	no	—
190	C₂×Dic₁₀	—	3	2	no	—
191	C₅×M₁₆	—	6	2	no	—
192	C₂×C₅×C₈	—	3	1	no	—
193	C₂×C₅×C₈	—	3	4	no	—
194	C₂×C₅×C₈	—	3	1	no	—
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	3	1	no	—
198	C₅×C₄⋊C₄	—	3	1	no	—
199	C₅×C₂²⋊C₄	—	3	1	no	—
200	C₅×C₂²⋊C₄	—	3	1	no	—
201	C₄²×C₅	—	3	1	no	—
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	#685	—	2	2	no	—
204	#685	—	6	2	no	—
205	C₄⋊Dic₅	—	3	2	no	—
206	C₄⋊Dic₅	—	6	2	no	—
207	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
208	#683	—	6	2	no	—
209	#683	—	6	2	no	—
210	C₄×Dic₅	—	6	2	no	—
211	C₄×Dic₅	—	6	2	no	—
212	Dic₂₀	—	3	4	no	—
213	D₄₀	C₄×D₃	1	4	yes	complemented
214	#677	—	3	8	no	—
215	C₂×#135	—	15	1	no	—
216	#520	—	15	2	no	—
217	#440	—	15	2	no	—
218	#440	—	15	2	no	—
219	C₄×Q₁₆	—	15	1	no	—
220	C₄×Q₁₆	—	15	1	no	—
221	C₄×D₈	—	5	1	no	—
222	C₄×D₈	—	15	1	no	—
223	C₂×#107	—	15	1	no	—
224	#417	—	15	2	no	—
225	#405	—	3	1	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₅×D₃	—	2	1	no	—
228	C₂×C₅×D₃	—	2	1	no	—
229	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
230	C₂×C₃×D₅	—	2	4	no	—
231	C₂×C₃×D₅	—	4	2	no	—
232	C₂×C₃×D₅	—	4	2	no	—
233	C₃×C₄×C₅	—	2	1	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	Dic₁₅	—	2	4	no	—
238	Dic₁₅	—	4	2	no	—
239	C₃×Dic₅	—	4	2	no	—
240	C₅×Dic₃	—	2	1	no	—
241	C₅×Dic₃	—	2	1	no	—
242	C₅×Dic₃	C₄×D₄	1	2	yes	—
243	C₂×C₃×D₄	—	5	2	no	—
244	C₂²×C₃×C₄	—	10	2	no	—
245	C₂×#67	—	10	2	no	—
246	C₂²×Dic₃	—	10	2	no	—
247	C₂²×Dic₃	—	10	2	no	—
248	#237	—	5	8	no	—
249	#237	—	10	4	no	—
250	C₂×C₄×D₃	—	10	2	no	—
251	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
252	C₂×Dic₆	—	5	2	no	—
253	C₃×D₈	—	5	4	no	—
254	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
255	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
256	C₃×C₄⋊C₄	—	5	2	no	—
257	C₃×C₂²⋊C₄	—	10	2	no	—
258	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
259	#217	—	10	2	no	—
260	#214	—	5	8	no	—
261	(C₂×D₃)⋊C₄	D₂₀	1	1	yes	characteristic
262	(C₂×D₃)⋊C₄	D₂₀	1	1	yes	characteristic
263	C₄⋊Dic₃	—	5	2	no	—
264	Dic₃⋊C₄	—	10	2	no	—
265	Dic₃⋊C₄	—	10	2	no	—
266	Dic₃⋊C₄	—	10	2	no	—
267	Dic₃⋊C₄	D₂₀	1	1	yes	characteristic
268	Dic₃⋊C₄	D₂₀	1	1	yes	characteristic
269	C₄×Dic₃	—	10	2	no	—
270	C₄×Dic₃	—	10	2	no	—
271	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
274	Dic₁₂	—	5	4	no	—
275	ΓL(1,𝔽₂₅)	—	2	2	no	—
276	D₃×C₈	C₄×D₅	1	4	yes	complemented
277	C₂³×C₅	—	3	1	no	—
278	C₂²×D₅	—	2	2	no	—
279	C₂×C₄×C₅	—	3	1	no	—
280	C₂×C₄×C₅	—	3	2	no	—
281	C₂×C₄×C₅	—	3	2	no	—
282	C₂×C₄×C₅	—	3	1	no	—
283	C₂×C₄×C₅	—	3	1	no	—
284	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₂²⋊D₅	—	6	8	no	—
288	C₂×Dic₅	—	2	2	no	—
289	C₂×Dic₅	—	6	2	no	—
290	C₂×Dic₅	—	6	2	no	—
291	C₂×Dic₅	—	24	2	no	—
292	D₂₀	—	2	2	no	—
293	D₂₀	C₂×C₄×D₃	1	4	yes	—
294	C₄×D₅	—	6	8	no	—
295	C₄×D₅	—	8	2	no	—
296	C₄×D₅	—	24	2	no	—
297	Dic₁₀	—	3	4	no	—
298	Dic₁₀	—	6	2	no	—
299	C₅×C₈	—	2	1	no	—
300	C₅×C₈	—	3	2	no	—
301	C₅×C₈	—	6	1	no	—
302	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
303	C₂×#41	—	15	2	no	—
304	#135	—	15	8	no	—
305	C₂×Q₁₆	—	15	1	no	—
306	C₂×SD₁₆	—	15	2	no	—
307	C₂×D₈	—	5	1	no	—
308	C₂×M₁₆	—	3	1	no	—
309	C₂²×C₈	—	3	1	no	—
310	C₄×Q₈	—	15	2	no	—
311	C₄×Q₈	—	15	2	no	—
312	C₄×D₄	—	5	2	no	—
313	C₄×D₄	—	15	2	no	—
314	C₄×D₄	—	30	2	no	—
315	C₄×D₄	—	30	2	no	—
316	#117	—	3	1	no	—
317	#117	—	30	2	no	—
318	C₂×C₄⋊C₄	—	15	2	no	—
319	C₂×C₄⋊C₄	—	30	2	no	—
320	#107	—	5	1	no	—
321	#107	—	15	2	no	—
322	#107	—	15	1	no	—
323	#103	—	15	2	no	—
324	#103	—	15	2	no	—
325	#102	—	5	2	no	—
326	#102	—	15	2	no	—
327	#97	—	3	1	no	—
328	#97	—	3	1	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	D₃×D₅	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂×C₃×C₅	#576	1	1	yes	characteristic
333	C₂×C₃×C₅	#578	1	1	yes	characteristic
334	C₃×D₅	—	4	4	no	—
335	C₅×D₃	—	2	2	no	—
336	C₂³×C₃	—	10	2	no	—
337	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
338	C₃×D₄	—	5	4	no	—
339	C₃×D₄	—	10	2	no	—
340	C₂×C₃×C₄	—	10	2	no	—
341	C₂×C₃×C₄	—	40	2	no	—
342	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	#67	—	10	8	no	—
346	C₂×Dic₃	—	10	2	no	—
347	C₂×Dic₃	—	10	8	no	—
348	C₂×Dic₃	—	10	2	no	—
349	C₂×Dic₃	—	40	2	no	—
350	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
351	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
352	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
353	C₄×D₃	—	40	2	no	—
354	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
355	C₄×D₃	#709	1	2	yes	—
356	Dic₆	—	5	4	no	—
357	Dic₆	—	10	2	no	—
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
360	C₃⋊C₈	—	2	1	no	—
361	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
362	C₂²×C₅	—	3	2	no	—
363	C₂²×C₅	—	6	1	no	—
364	C₂²×C₅	—	6	1	no	—
365	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
366	C₂×D₅	—	2	4	no	—
367	C₂×D₅	—	4	2	no	—
368	C₂×D₅	—	4	2	no	—
369	C₄×C₅	—	2	1	no	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	3	2	no	—
372	C₄×C₅	—	6	1	no	—
373	C₄×C₅	—	6	1	no	—
374	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
375	C₄×C₅	D₃×#41	1	1	yes	characteristic
376	Dic₅	—	4	2	no	—
377	Dic₅	—	6	4	no	—
378	Dic₅	—	12	2	no	—
379	#41	—	15	8	no	—
380	#41	—	30	4	no	—
381	C₂×Q₈	—	15	2	no	—
382	C₂×D₄	—	5	2	no	—
383	C₂×D₄	—	30	2	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	10	2	no	—
386	C₂²×C₄	—	30	2	no	—
387	C₂²×C₄	—	30	2	no	—
388	C₂²×C₄	—	30	2	no	—
389	Q₁₆	—	15	4	no	—
390	SD₁₆	—	15	8	no	—
391	D₈	—	5	4	no	—
392	M₁₆	—	6	2	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	—	3	4	no	—
395	C₂×C₈	—	3	1	no	—
396	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
397	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
398	C₄⋊C₄	—	3	1	no	—
399	C₄⋊C₄	—	3	1	no	—
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	—	15	2	no	—
402	C₄⋊C₄	—	30	2	no	—
403	C₄⋊C₄	—	30	2	no	—
404	C₄⋊C₄	—	30	2	no	—
405	C₂²⋊C₄	—	3	1	no	—
406	C₂²⋊C₄	—	3	1	no	—
407	C₂²⋊C₄	—	10	2	no	—
408	C₂²⋊C₄	—	30	2	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	30	2	no	—
411	C₄²	—	30	2	no	—
412	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
413	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	10	4	no	—
415	C₂²×C₃	—	20	2	no	—
416	C₂²×C₃	—	20	2	no	—
417	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	—	2	1	no	—
420	C₂×D₃	C₄×D₂₀	1	2	yes	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	20	2	no	—
424	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
425	C₃×C₄	C₂×#709	1	1	yes	characteristic
426	Dic₃	—	2	1	no	—
427	Dic₃	—	2	1	no	—
428	Dic₃	—	10	4	no	—
429	Dic₃	—	20	2	no	—
430	Dic₃	C₄×D₂₀	1	2	yes	—
431	C₂×C₅	—	6	2	no	—
432	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
433	C₂×C₅	#5757	1	1	yes	characteristic
434	C₂×C₅	#5771	1	1	yes	characteristic
435	D₅	—	4	4	no	—
436	C₂³	—	3	1	no	—
437	C₂³	—	10	2	no	—
438	Q₈	—	15	4	no	—
439	Q₈	—	30	2	no	—
440	D₄	—	5	4	no	—
441	D₄	—	10	2	no	—
442	D₄	—	30	8	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	3	1	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	30	8	no	—
450	C₂×C₄	—	30	2	no	—
451	C₂×C₄	—	30	2	no	—
452	C₂×C₄	—	40	2	no	—
453	C₂×C₄	—	120	2	no	—
454	C₂×C₄	—	120	2	no	—
455	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
456	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
458	C₈	—	2	1	no	—
459	C₈	—	3	2	no	—
460	C₈	—	6	1	no	—
461	C₈	C₄×D₃×D₅	1	2	yes	—
462	C₂×C₃	—	20	4	no	—
463	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
464	C₂×C₃	#66086	1	1	yes	characteristic
465	C₂×C₃	#66087	1	1	yes	characteristic
466	D₃	—	2	2	no	—
467	C₅	#79589	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	3	2	no	—
469	C₂²	—	6	1	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	10	4	no	—
472	C₂²	—	20	2	no	—
473	C₂²	—	20	2	no	—
474	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	3	2	no	—
478	C₄	—	6	1	no	—
479	C₄	—	6	1	no	—
480	C₄	—	20	2	no	—
481	C₄	—	30	4	no	—
482	C₄	—	60	2	no	—
483	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
484	C₄	D₃×#709	1	1	yes	characteristic
485	C₃	#10610293	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	6	2	no	—
487	C₂	—	20	4	no	—
488	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
489	C₂	#11753971	1	1	yes	characteristic
490	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	C₂×#91273	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2951
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
2. #11752518	C₂	semidirect
3. C₄×Dic₆₀	C₂	semidirect
4. C₅×#4689	C₂	semidirect
5. C₃×C₄×D₄₀	C₂	semidirect
6. #11748138	C₂	semidirect
7. #11747873	C₂	semidirect
8. Dic₃×D₄₀	C₂	semidirect
9. #11747742	C₂	semidirect
10. D₃×#3950	C₂	semidirect
11. #11747052	C₂	semidirect
29. #91273	C₄	semidirect
52. C₄×D₄₀	D₃	semidirect
62. #6765	C₂×C₄	semidirect
69. Dic₆₀	C₂×C₄	semidirect
78. C₅×D₃×C₈	C₂×C₄	semidirect
81. C₃×D₄₀	C₂×C₄	semidirect
86. #6657	C₂×C₄	semidirect
97. #4689	D₅	semidirect
213. D₄₀	C₄×D₃	semidirect
276. D₃×C₈	C₄×D₅	semidirect
413. C₃×C₅	#2951	semidirect
467. C₅	#79589	semidirect
485. C₃	#10610293	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91273	2
#11752518	2
C₄×Dic₆₀	2
C₅×#4689	2
C₃×C₄×D₄₀	2
#11748138	2
#11747873	2
Dic₃×D₄₀	2
#11747742	2
D₃×#3950	2
#11747052	2
#10610293	3
#79589	5