Subgroups — #14417367

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄₀	C₂	1	1	yes	maximal, characteristic
2	#11752727	C₂	1	2	yes	maximal, complemented
3	C₄×D₁₂₀	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	#11748107	C₂	1	2	yes	maximal, complemented
7	#11747793	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747741	C₂	1	2	yes	maximal, complemented
10	#11747682	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747023	C₂	1	2	yes	maximal, complemented
12	#10610292	—	3	1	no	maximal, Hall
13	C₂×D₃×D₂₀	C₂²	1	2	yes	—
14	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
15	C₄×D₆₀	C₂²	1	2	yes	complemented
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	complemented
21	#91473	—	2	2	no	—
22	D₅×(C₂×D₃)⋊C₄	—	2	2	no	—
23	#91444	—	2	2	no	—
24	#91428	C₂²	1	2	yes	complemented
25	Dic₃×D₂₀	C₂²	1	2	yes	complemented
26	#91396	—	2	2	no	—
27	#91338	C₂²	1	2	yes	—
28	C₂×#6653	C₂²	1	2	yes	—
29	D₃×D₄₀	C₄	1	8	yes	complemented
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	#91105	C₂²	1	2	yes	complemented
32	#91102	C₂²	1	1	yes	characteristic, complemented
33	C₅×#815	C₂²	1	1	yes	characteristic, complemented
34	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₅×#803	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3953	C₂²	1	2	yes	complemented
37	C₃×#3950	C₂²	1	1	yes	characteristic, complemented
38	#90987	C₂²	1	2	yes	complemented
39	#90968	C₂²	1	2	yes	complemented
40	#90965	C₂²	1	2	yes	complemented
41	#79588	—	5	1	no	maximal, Hall
42	C₂²×D₄₀	—	3	1	no	—
43	#65855	—	3	2	no	—
44	C₅×#405	—	3	1	no	—
45	#65420	—	3	2	no	—
46	#65395	—	3	1	no	—
47	#65000	—	3	2	no	—
48	#65000	—	3	2	no	—
49	C₄×D₄₀	—	3	1	no	—
50	C₄×D₄₀	—	3	1	no	—
51	C₄×D₄₀	—	3	1	no	—
52	C₄×D₄₀	D₃	1	1	yes	characteristic, complemented
53	C₂²×D₃×D₅	—	2	2	no	—
54	C₂×D₆₀	C₂³	1	2	yes	—
55	C₂×C₄×D₁₅	—	2	2	no	—
56	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	—	2	2	no	—
59	C₂×#1202	—	2	2	no	—
60	C₂×#1200	—	2	2	no	—
61	C₂×D₅×Dic₃	—	2	2	no	—
62	D₃×D₂₀	—	2	4	no	—
63	D₃×D₂₀	C₂×C₄	1	8	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	#6714	—	2	2	no	—
68	C₄⋊Dic₁₅	C₂³	1	2	yes	—
69	D₁₂₀	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	#6667	—	2	2	no	—
83	(C₂×D₃)⋊Dic₅	—	2	2	no	—
84	#6665	—	2	2	no	—
85	Dic₃×Dic₅	—	2	2	no	—
86	#6653	C₂×C₄	1	8	yes	complemented
87	C₂×D₃×D₈	—	5	1	no	—
88	#5545	—	5	2	no	—
89	C₃×C₄×D₈	—	5	1	no	—
90	Dic₃×D₈	—	5	1	no	—
91	#5014	—	5	2	no	—
92	#4880	—	5	1	no	—
93	#4872	—	5	1	no	—
94	#4785	—	5	2	no	—
95	#4770	—	5	2	no	—
96	C₄×D₂₄	—	5	1	no	—
97	#4689	D₅	1	1	yes	characteristic, complemented
98	C₂²×D₂₀	—	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×D₄₀	—	3	2	no	—
104	C₂×D₄₀	—	3	1	no	—
105	C₂×D₄₀	—	3	8	no	—
106	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic
107	#4039	—	6	2	no	—
108	#4039	—	6	2	no	—
109	D₅×C₂²⋊C₄	—	6	2	no	—
110	D₅×C₂²⋊C₄	—	6	2	no	—
111	C₄×D₂₀	—	3	2	no	—
112	C₄×D₂₀	—	3	2	no	—
113	C₄×D₂₀	—	3	2	no	—
114	C₄×D₂₀	C₂×D₃	1	2	yes	complemented
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, complemented
119	#3953	—	3	2	no	—
120	#3953	—	3	2	no	—
121	#3953	—	3	2	no	—
122	#3953	C₂×D₃	1	2	yes	complemented
123	#3950	—	3	1	no	—
124	#3950	C₂×D₃	1	1	yes	characteristic, complemented
125	#3949	—	3	2	no	—
126	#2948	—	15	1	no	Sylow
127	C₂²×D₁₅	—	2	2	no	—
128	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₃×D₅	—	2	2	no	—
130	C₂×D₃×D₅	—	2	8	no	—
131	C₂×D₃×D₅	—	8	2	no	—
132	C₂×D₃×D₅	—	8	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×Dic₁₅	—	2	2	no	—
137	D₆₀	—	2	2	no	—
138	D₆₀	C₂²×C₄	1	4	yes	—
139	C₄×D₁₅	—	8	2	no	—
140	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
143	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
144	C₄×C₅×D₃	#41	1	2	yes	—
145	C₂×C₃×Dic₅	—	2	2	no	—
146	C₃×D₂₀	—	2	2	no	—
147	C₃×D₂₀	C₂²×C₄	1	4	yes	—
148	C₃×C₄×D₅	—	8	2	no	—
149	#1202	—	2	8	no	—
150	#1200	—	8	2	no	—
151	D₅×Dic₃	—	8	2	no	—
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
154	C₅×C₃⋊C₈	—	2	1	no	—
155	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×D₃×D₄	—	5	2	no	—
157	C₂×C₃×D₈	—	5	1	no	—
158	C₃×C₄×D₄	—	5	2	no	—
159	D₄×Dic₃	—	5	2	no	—
160	C₂×#213	—	5	2	no	—
161	C₄×#67	—	10	2	no	—
162	C₂×(C₂×D₃)⋊C₄	—	10	2	no	—
163	D₃×D₈	—	5	8	no	—
164	C₂×D₂₄	—	5	1	no	—
165	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
166	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
167	#893	—	5	2	no	—
168	#892	—	5	2	no	—
169	#67⋊C₄	—	10	2	no	—
170	D₃×C₂²⋊C₄	—	10	2	no	—
171	C₄×D₁₂	—	5	2	no	—
172	#872	C₂×D₅	1	1	yes	characteristic
173	C₃×#107	—	5	1	no	—
174	C₃×#102	—	5	2	no	—
175	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
176	#832	—	5	2	no	—
177	#821	—	5	2	no	—
178	#818	—	5	1	no	—
179	#815	C₂×D₅	1	1	yes	characteristic, complemented
180	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
181	#809	—	5	2	no	—
182	#808	—	5	2	no	—
183	#803	C₂×D₅	1	1	yes	characteristic, complemented
184	C₂³×D₅	—	6	2	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₂×D₂₀	—	3	2	no	—
187	C₂×D₂₀	—	3	8	no	—
188	C₂×D₂₀	—	6	4	no	—
189	C₂×D₂₀	—	6	2	no	—
190	C₂×D₂₀	C₂²×D₃	1	2	yes	—
191	C₂×C₄×D₅	—	2	2	no	—
192	C₂×C₄×D₅	—	6	2	no	—
193	C₂×C₄×D₅	—	6	2	no	—
194	C₂×C₄×D₅	—	6	2	no	—
195	C₅×M₁₆	—	6	2	no	—
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	—	3	4	no	—
198	C₂×C₅×C₈	—	3	1	no	—
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×C₂²⋊C₄	—	3	1	no	—
204	C₅×C₂²⋊C₄	—	3	1	no	—
205	C₄²×C₅	—	3	1	no	—
206	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₂²⋊Dic₅	—	6	2	no	—
208	#685	—	2	2	no	—
209	#685	—	6	2	no	—
210	#685	—	6	2	no	—
211	#685	—	6	2	no	—
212	C₄⋊Dic₅	—	3	2	no	—
213	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
214	C₄×Dic₅	—	6	2	no	—
215	D₄₀	—	3	8	no	—
216	D₄₀	—	3	4	no	—
217	D₄₀	C₄×D₃	1	4	yes	complemented
218	C₂²×D₈	—	15	1	no	—
219	#518	—	15	2	no	—
220	#442	—	15	2	no	—
221	#442	—	15	2	no	—
222	C₄×D₈	—	5	1	no	—
223	C₄×D₈	—	15	1	no	—
224	C₄×D₈	—	15	1	no	—
225	C₄×D₈	—	15	1	no	—
226	#427	—	15	1	no	—
227	#418	—	15	2	no	—
228	#405	—	3	1	no	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×D₁₅	—	2	4	no	—
231	C₂×D₁₅	—	4	2	no	—
232	C₂×D₁₅	—	4	2	no	—
233	C₂×C₅×D₃	—	2	1	no	—
234	C₂×C₅×D₃	—	2	1	no	—
235	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
236	C₂×C₃×D₅	—	2	4	no	—
237	C₂×C₃×D₅	—	4	2	no	—
238	C₂×C₃×D₅	—	4	2	no	—
239	D₃×D₅	—	8	8	no	—
240	C₃×C₄×C₅	—	2	1	no	—
241	C₃×C₄×C₅	—	2	1	no	—
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	Dic₁₅	—	4	2	no	—
245	C₃×Dic₅	—	4	2	no	—
246	C₅×Dic₃	—	2	1	no	—
247	C₅×Dic₃	—	2	1	no	—
248	C₅×Dic₃	C₄×D₄	1	2	yes	—
249	C₂³×D₃	—	10	2	no	—
250	C₂×C₃×D₄	—	5	2	no	—
251	C₂²×C₃×C₄	—	10	2	no	—
252	C₂×#67	—	10	2	no	—
253	C₂²×Dic₃	—	10	2	no	—
254	D₃×D₄	—	5	8	no	—
255	D₃×D₄	—	10	4	no	—
256	C₂×D₁₂	—	5	2	no	—
257	C₂×C₄×D₃	—	10	2	no	—
258	C₂×C₄×D₃	—	10	2	no	—
259	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
260	C₃×D₈	—	5	4	no	—
261	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
262	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
263	C₃×C₄⋊C₄	—	5	2	no	—
264	C₃×C₂²⋊C₄	—	10	2	no	—
265	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
266	#217	—	10	2	no	—
267	#213	—	5	8	no	—
268	(C₂×D₃)⋊C₄	—	10	2	no	—
269	(C₂×D₃)⋊C₄	—	10	2	no	—
270	(C₂×D₃)⋊C₄	—	10	2	no	—
271	(C₂×D₃)⋊C₄	D₂₀	1	1	yes	characteristic
272	(C₂×D₃)⋊C₄	D₂₀	1	1	yes	characteristic
273	C₄⋊Dic₃	—	5	2	no	—
274	Dic₃⋊C₄	D₂₀	1	1	yes	characteristic
275	Dic₃⋊C₄	D₂₀	1	1	yes	characteristic
276	C₄×Dic₃	—	10	2	no	—
277	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
278	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
279	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
280	D₂₄	—	5	4	no	—
281	ΓL(1,𝔽₂₅)	—	2	2	no	—
282	D₃×C₈	C₄×D₅	1	4	yes	complemented
283	C₂³×C₅	—	3	1	no	—
284	C₂²×D₅	—	2	2	no	—
285	C₂²×D₅	—	6	8	no	—
286	C₂²×D₅	—	6	2	no	—
287	C₂²×D₅	—	24	2	no	—
288	C₂²×D₅	—	24	2	no	—
289	C₂×C₄×C₅	—	3	1	no	—
290	C₂×C₄×C₅	—	3	2	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	—	3	1	no	—
293	C₂×C₄×C₅	—	3	1	no	—
294	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
297	C₂×Dic₅	—	2	2	no	—
298	C₂×Dic₅	—	6	2	no	—
299	D₂₀	—	2	2	no	—
300	D₂₀	—	3	4	no	—
301	D₂₀	—	6	8	no	—
302	D₂₀	—	6	2	no	—
303	D₂₀	C₂×C₄×D₃	1	4	yes	—
304	C₄×D₅	—	8	2	no	—
305	C₄×D₅	—	24	2	no	—
306	C₄×D₅	—	24	2	no	—
307	C₄×D₅	—	24	2	no	—
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	3	2	no	—
310	C₅×C₈	—	6	1	no	—
311	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
312	C₂²×D₄	—	15	2	no	—
313	C₂×D₈	—	5	1	no	—
314	C₂×D₈	—	15	8	no	—
315	C₂×D₈	—	15	2	no	—
316	C₂×D₈	—	15	1	no	—
317	C₂×M₁₆	—	3	1	no	—
318	C₂²×C₈	—	3	1	no	—
319	C₄×D₄	—	5	2	no	—
320	C₄×D₄	—	15	2	no	—
321	C₄×D₄	—	15	2	no	—
322	C₄×D₄	—	15	2	no	—
323	C₄×D₄	—	30	2	no	—
324	C₄×D₄	—	30	2	no	—
325	#117	—	3	1	no	—
326	#117	—	15	2	no	—
327	C₂×C₂²⋊C₄	—	30	2	no	—
328	C₂×C₂²⋊C₄	—	30	2	no	—
329	#107	—	5	1	no	—
330	#107	—	15	1	no	—
331	#106	—	15	2	no	—
332	#102	—	5	2	no	—
333	#102	—	15	2	no	—
334	#102	—	15	2	no	—
335	#102	—	15	2	no	—
336	#97	—	3	1	no	—
337	#97	—	3	1	no	—
338	C₄×C₈	—	3	1	no	—
339	C₄×C₈	D₃×D₅	1	1	yes	characteristic, complemented
340	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
341	C₂×C₃×C₅	#576	1	1	yes	characteristic
342	C₂×C₃×C₅	#576	1	1	yes	characteristic
343	D₁₅	—	4	4	no	—
344	C₃×D₅	—	4	4	no	—
345	C₅×D₃	—	2	2	no	—
346	C₂³×C₃	—	10	2	no	—
347	C₂²×D₃	—	10	2	no	—
348	C₂²×D₃	—	10	8	no	—
349	C₂²×D₃	—	40	2	no	—
350	C₂²×D₃	—	40	2	no	—
351	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
352	C₃×D₄	—	5	4	no	—
353	C₃×D₄	—	10	2	no	—
354	C₂×C₃×C₄	—	10	2	no	—
355	C₂×C₃×C₄	—	40	2	no	—
356	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
359	#67	—	10	8	no	—
360	C₂×Dic₃	—	10	2	no	—
361	C₂×Dic₃	—	40	2	no	—
362	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
363	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
364	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
365	D₁₂	—	5	4	no	—
366	D₁₂	—	10	2	no	—
367	C₄×D₃	—	40	2	no	—
368	C₄×D₃	—	40	2	no	—
369	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
370	C₄×D₃	#709	1	2	yes	—
371	C₃×C₈	—	2	1	no	—
372	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
373	C₃⋊C₈	—	2	1	no	—
374	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
375	C₂²×C₅	—	3	2	no	—
376	C₂²×C₅	—	6	1	no	—
377	C₂²×C₅	—	6	1	no	—
378	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
379	C₂×D₅	—	2	4	no	—
380	C₂×D₅	—	4	2	no	—
381	C₂×D₅	—	4	2	no	—
382	C₂×D₅	—	6	4	no	—
383	C₂×D₅	—	12	2	no	—
384	C₂×D₅	—	12	2	no	—
385	C₂×D₅	—	24	8	no	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	3	2	no	—
389	C₄×C₅	—	6	1	no	—
390	C₄×C₅	—	6	1	no	—
391	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
392	C₄×C₅	D₃×#41	1	1	yes	characteristic
393	Dic₅	—	4	2	no	—
394	Dic₅	—	12	2	no	—
395	C₂⁴	—	30	2	no	—
396	C₂×D₄	—	5	2	no	—
397	C₂×D₄	—	15	8	no	—
398	C₂×D₄	—	15	2	no	—
399	C₂×D₄	—	30	4	no	—
400	C₂×D₄	—	30	2	no	—
401	C₂²×C₄	—	3	1	no	—
402	C₂²×C₄	—	10	2	no	—
403	C₂²×C₄	—	30	2	no	—
404	C₂²×C₄	—	30	2	no	—
405	C₂²×C₄	—	30	2	no	—
406	D₈	—	5	4	no	—
407	D₈	—	15	8	no	—
408	D₈	—	15	4	no	—
409	M₁₆	—	6	2	no	—
410	C₂×C₈	—	3	1	no	—
411	C₂×C₈	—	3	4	no	—
412	C₂×C₈	—	3	1	no	—
413	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
414	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
415	C₄⋊C₄	—	3	1	no	—
416	C₄⋊C₄	—	3	1	no	—
417	C₄⋊C₄	—	5	2	no	—
418	C₄⋊C₄	—	15	2	no	—
419	C₂²⋊C₄	—	3	1	no	—
420	C₂²⋊C₄	—	3	1	no	—
421	C₂²⋊C₄	—	10	2	no	—
422	C₂²⋊C₄	—	30	2	no	—
423	C₂²⋊C₄	—	30	2	no	—
424	C₂²⋊C₄	—	30	2	no	—
425	C₂²⋊C₄	—	30	2	no	—
426	C₄²	—	3	1	no	—
427	C₄²	—	30	2	no	—
428	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
429	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
430	C₂²×C₃	—	10	4	no	—
431	C₂²×C₃	—	20	2	no	—
432	C₂²×C₃	—	20	2	no	—
433	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
434	C₂×D₃	—	2	1	no	—
435	C₂×D₃	—	2	1	no	—
436	C₂×D₃	—	10	4	no	—
437	C₂×D₃	—	20	2	no	—
438	C₂×D₃	—	20	2	no	—
439	C₂×D₃	—	40	8	no	—
440	C₂×D₃	C₄×D₂₀	1	2	yes	—
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	20	2	no	—
444	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
445	C₃×C₄	C₂×#709	1	1	yes	characteristic
446	Dic₃	—	2	1	no	—
447	Dic₃	—	2	1	no	—
448	Dic₃	—	20	2	no	—
449	Dic₃	C₄×D₂₀	1	2	yes	—
450	C₂×C₅	—	6	2	no	—
451	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
452	C₂×C₅	#5757	1	1	yes	characteristic
453	C₂×C₅	#5769	1	1	yes	characteristic
454	D₅	—	4	4	no	—
455	D₅	—	12	4	no	—
456	C₂³	—	3	1	no	—
457	C₂³	—	10	2	no	—
458	C₂³	—	30	8	no	—
459	C₂³	—	30	2	no	—
460	C₂³	—	120	2	no	—
461	C₂³	—	120	2	no	—
462	D₄	—	5	4	no	—
463	D₄	—	10	2	no	—
464	D₄	—	15	4	no	—
465	D₄	—	30	8	no	—
466	D₄	—	30	2	no	—
467	C₂×C₄	—	3	1	no	—
468	C₂×C₄	—	3	2	no	—
469	C₂×C₄	—	3	2	no	—
470	C₂×C₄	—	3	1	no	—
471	C₂×C₄	—	3	1	no	—
472	C₂×C₄	—	10	2	no	—
473	C₂×C₄	—	30	2	no	—
474	C₂×C₄	—	40	2	no	—
475	C₂×C₄	—	120	2	no	—
476	C₂×C₄	—	120	2	no	—
477	C₂×C₄	—	120	2	no	—
478	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
479	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
481	C₈	—	2	1	no	—
482	C₈	—	3	2	no	—
483	C₈	—	6	1	no	—
484	C₈	C₄×D₃×D₅	1	2	yes	—
485	C₂×C₃	—	20	4	no	—
486	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
487	C₂×C₃	#66086	1	1	yes	characteristic
488	C₂×C₃	#66086	1	1	yes	characteristic
489	D₃	—	2	2	no	—
490	D₃	—	20	4	no	—
491	C₅	#79588	1	1	yes	characteristic, complemented, Sylow
492	C₂²	—	3	2	no	—
493	C₂²	—	6	1	no	—
494	C₂²	—	6	1	no	—
495	C₂²	—	10	4	no	—
496	C₂²	—	20	2	no	—
497	C₂²	—	20	2	no	—
498	C₂²	—	30	4	no	—
499	C₂²	—	60	2	no	—
500	C₂²	—	60	2	no	—
501	C₂²	—	120	8	no	—
502	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	3	2	no	—
506	C₄	—	6	1	no	—
507	C₄	—	6	1	no	—
508	C₄	—	20	2	no	—
509	C₄	—	60	2	no	—
510	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
511	C₄	D₃×#709	1	1	yes	characteristic
512	C₃	#10610292	1	1	yes	characteristic, complemented, Sylow
513	C₂	—	6	2	no	—
514	C₂	—	20	4	no	—
515	C₂	—	60	4	no	—
516	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
517	C₂	#11753971	1	1	yes	characteristic
518	C₂	#11753973	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×D₃×D₄₀	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2948
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. #11752727	C₂	semidirect
3. C₄×D₁₂₀	C₂	semidirect
4. C₅×#4689	C₂	semidirect
5. C₃×C₄×D₄₀	C₂	semidirect
6. #11748107	C₂	semidirect
7. #11747793	C₂	semidirect
8. Dic₃×D₄₀	C₂	semidirect
9. #11747741	C₂	semidirect
10. #11747682	C₂	semidirect
11. #11747023	C₂	semidirect
15. C₄×D₆₀	C₂²	semidirect
20. C₃×C₄×D₂₀	C₂²	semidirect
24. #91428	C₂²	semidirect
25. Dic₃×D₂₀	C₂²	semidirect
29. D₃×D₄₀	C₄	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. #91105	C₂²	semidirect
32. #91102	C₂²	semidirect
33. C₅×#815	C₂²	semidirect
34. C₅×C₈×Dic₃	C₂²	semidirect
35. C₅×#803	C₂²	semidirect
36. C₃×#3953	C₂²	semidirect
37. C₃×#3950	C₂²	semidirect
38. #90987	C₂²	semidirect
39. #90968	C₂²	semidirect
40. #90965	C₂²	semidirect
52. C₄×D₄₀	D₃	semidirect
63. D₃×D₂₀	C₂×C₄	semidirect
69. D₁₂₀	C₂×C₄	semidirect
78. C₅×D₃×C₈	C₂×C₄	semidirect
81. C₃×D₄₀	C₂×C₄	semidirect
86. #6653	C₂×C₄	semidirect
97. #4689	D₅	semidirect
114. C₄×D₂₀	C₂×D₃	semidirect
118. C₄×C₅×C₈	C₂×D₃	semidirect
122. #3953	C₂×D₃	semidirect
124. #3950	C₂×D₃	semidirect
175. C₃×C₄×C₈	C₂×D₅	semidirect
179. #815	C₂×D₅	semidirect
180. C₈×Dic₃	C₂×D₅	semidirect
183. #803	C₂×D₅	semidirect
217. D₄₀	C₄×D₃	semidirect
282. D₃×C₈	C₄×D₅	semidirect
339. C₄×C₈	D₃×D₅	semidirect
429. C₃×C₅	#2948	semidirect
491. C₅	#79588	semidirect
512. C₃	#10610292	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄₀	2
#11752727	2
C₄×D₁₂₀	2
C₅×#4689	2
C₃×C₄×D₄₀	2
#11748107	2
#11747793	2
Dic₃×D₄₀	2
#11747741	2
#11747682	2
#11747023	2
#10610292	3
#79588	5