Subgroups — #14301127

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6658	C₂	1	1	yes	maximal, characteristic
3	#11751040	C₂	1	1	yes	maximal, characteristic
4	C₂×#90971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90968	C₂	1	1	yes	maximal, characteristic
6	C₅×#4524	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745980	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599479	—	3	1	no	maximal, Hall
9	C₂²×D₆₀	C₂²	1	1	yes	characteristic
10	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×#6714	—	2	1	no	—
13	C₂×#6714	—	2	1	no	—
14	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#683	—	2	1	no	—
19	C₂×C₃×C₄×Dic₅	—	2	1	no	—
20	C₃×C₄×Dic₁₀	—	2	2	no	—
21	C₃×C₄×Dic₁₀	—	2	2	no	—
22	C₂×#6658	—	2	2	no	—
23	C₂×#6658	—	2	2	no	—
24	C₂×#6658	C₄	1	4	yes	complemented
25	#90971	—	2	2	no	—
26	#90968	—	2	2	no	—
27	#71633	—	5	1	no	maximal, Hall
28	C₂²×#677	—	3	1	no	—
29	C₂×C₄×Dic₁₀	D₃	1	1	yes	characteristic, complemented
30	C₂×#3953	—	3	1	no	—
31	C₂×#3948	—	3	1	no	—
32	#65228	—	3	1	no	—
33	C₅×#336	—	3	1	no	—
34	#64771	—	3	1	no	—
35	C₂³×D₁₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×Dic₁₅	—	2	1	no	—
40	C₂×D₆₀	—	2	1	no	—
41	C₂×D₆₀	—	2	1	no	—
42	C₂×D₆₀	—	2	1	no	—
43	C₂×D₆₀	—	2	1	no	—
44	C₂×D₆₀	—	2	1	no	—
45	C₂×D₆₀	C₂×C₄	1	2	yes	—
46	C₂²×C₃×Dic₅	—	2	1	no	—
47	C₂²×C₃×Dic₅	—	2	1	no	—
48	C₂×C₃×Dic₁₀	—	2	1	no	—
49	C₂×C₃×Dic₁₀	—	2	1	no	—
50	C₂×C₃×Dic₁₀	—	2	1	no	—
51	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
52	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
53	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	#6714	—	4	2	no	—
57	#6714	—	4	2	no	—
58	C₄⋊Dic₁₅	—	2	1	no	—
59	C₄⋊Dic₁₅	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
66	C₃×C₄⋊Dic₅	—	2	1	no	—
67	C₃×C₄⋊Dic₅	D₄	1	2	yes	—
68	C₃×#683	—	2	4	no	—
69	C₃×C₄×Dic₅	—	2	4	no	—
70	#6658	—	2	8	no	—
71	C₂×C₃×C₄×Q₈	—	5	1	no	—
72	C₂²×#215	—	5	1	no	—
73	C₂×#835	—	5	1	no	—
74	C₂×#809	—	5	1	no	—
75	#4939	—	5	1	no	—
76	#4529	—	5	1	no	—
77	#4524	D₅	1	1	yes	characteristic, complemented
78	C₂²×D₂₀	—	3	1	no	—
79	C₂²×Dic₁₀	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₂²×C₅×C₈	—	3	1	no	—
82	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
83	C₂×#685	—	6	1	no	—
84	C₂×#685	—	6	1	no	—
85	C₂×C₄⋊Dic₅	—	3	1	no	—
86	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
87	C₂×#683	—	2	1	no	—
88	C₂×C₄×Dic₅	—	2	1	no	—
89	C₂×#677	—	3	4	no	—
90	C₂×#677	—	6	2	no	—
91	C₂×#677	—	6	2	no	—
92	C₄×Dic₁₀	—	2	2	no	—
93	C₄×Dic₁₀	—	2	2	no	—
94	#3953	—	6	2	no	—
95	#3948	—	6	2	no	—
96	#1880	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×D₁₅	—	2	2	no	—
99	C₂²×D₁₅	—	4	1	no	—
100	C₂²×D₁₅	—	4	1	no	—
101	C₂²×D₁₅	—	4	1	no	—
102	C₂²×D₁₅	—	4	1	no	—
103	C₂²×D₁₅	—	4	1	no	—
104	C₂²×D₁₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	2	1	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	1	no	—
109	C₂×C₃×C₄×C₅	—	2	1	no	—
110	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	complemented
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
117	C₂×Dic₁₅	—	4	1	no	—
118	C₂×Dic₁₅	—	4	1	no	—
119	C₂×Dic₁₅	—	4	1	no	—
120	D₆₀	—	2	2	no	—
121	D₆₀	—	2	2	no	—
122	D₆₀	—	4	1	no	—
123	D₆₀	—	4	1	no	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	—	2	2	no	—
126	C₂×C₃×Dic₅	—	2	2	no	—
127	C₂×C₃×Dic₅	—	2	2	no	—
128	C₂×C₃×Dic₅	—	4	1	no	—
129	C₂×C₃×Dic₅	—	4	1	no	—
130	C₃×Dic₁₀	—	2	2	no	—
131	C₃×Dic₁₀	—	2	2	no	—
132	C₃×Dic₁₀	—	2	2	no	—
133	C₃×Dic₁₀	C₂²⋊C₄	1	4	yes	complemented
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₅×C₃⋊C₈	—	4	1	no	—
136	C₂²×C₃×Q₈	—	5	1	no	—
137	C₂²×D₁₂	—	5	1	no	—
138	C₃×C₄×Q₈	—	10	2	no	—
139	C₃×C₄×Q₈	—	10	2	no	—
140	C₂×C₃×C₄⋊C₄	—	5	1	no	—
141	C₂×C₃×C₄⋊C₄	—	10	1	no	—
142	C₂×C₃×C₄²	—	10	1	no	—
143	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
144	C₂×#215	—	5	4	no	—
145	C₂×#215	—	10	2	no	—
146	C₂×#215	—	10	2	no	—
147	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
148	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
149	C₂×C₄⋊Dic₃	—	5	1	no	—
150	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
151	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
152	#835	—	10	2	no	—
153	#809	—	10	2	no	—
154	C₂³×D₅	—	6	1	no	—
155	C₂²×C₄×C₅	#67	1	1	yes	characteristic
156	C₂²×C₄×C₅	#67	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂²×Dic₅	—	2	1	no	—
159	C₂²×Dic₅	—	2	1	no	—
160	C₂²×Dic₅	—	6	1	no	—
161	C₂×D₂₀	—	3	2	no	—
162	C₂×D₂₀	—	6	1	no	—
163	C₂×D₂₀	—	6	1	no	—
164	C₂×D₂₀	—	6	1	no	—
165	C₂×D₂₀	—	6	1	no	—
166	C₂×D₂₀	—	6	1	no	—
167	C₂×Dic₁₀	—	2	1	no	—
168	C₂×Dic₁₀	—	2	1	no	—
169	C₂×Dic₁₀	—	2	1	no	—
170	C₂×Dic₁₀	C₄×D₃	1	2	yes	—
171	C₂×Dic₁₀	D₁₂	1	2	yes	—
172	C₂×Dic₁₀	#67	1	2	yes	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	6	1	no	—
175	C₂×C₅×C₈	—	6	1	no	—
176	C₂×C₅×C₈	—	6	1	no	—
177	C₂×C₅×C₈	—	6	1	no	—
178	C₂×C₅×C₈	—	6	1	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	#685	—	12	2	no	—
182	#685	—	12	2	no	—
183	C₄⋊Dic₅	—	2	1	no	—
184	C₄⋊Dic₅	—	6	1	no	—
185	C₄⋊Dic₅	—	6	1	no	—
186	C₄⋊Dic₅	#67	1	2	yes	—
187	#683	—	2	4	no	—
188	C₄×Dic₅	—	2	4	no	—
189	#677	—	6	8	no	—
190	C₂²×SD₁₆	—	15	1	no	—
191	C₂×C₄×Q₈	—	5	1	no	—
192	C₂×#103	—	15	1	no	—
193	C₂×#102	—	15	1	no	—
194	#390	—	15	1	no	—
195	#340	—	15	1	no	—
196	#336	—	3	1	no	—
197	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	#120	1	1	yes	characteristic
199	C₂²×C₃×C₅	#121	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
201	C₂²×C₃×C₅	#135	1	1	yes	characteristic
202	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₃×C₅	#137	1	1	yes	characteristic
204	C₂×D₁₅	—	4	2	no	—
205	C₂×D₁₅	—	4	2	no	—
206	C₂×D₁₅	—	4	2	no	—
207	C₂×D₁₅	—	8	1	no	—
208	C₂×D₁₅	—	8	1	no	—
209	C₂×D₁₅	—	8	1	no	—
210	C₂×D₁₅	—	8	1	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	4	1	no	—
213	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
215	C₃×C₄×C₅	#121	1	1	yes	characteristic
216	C₃×C₄×C₅	#123	1	1	yes	characteristic
217	Dic₁₅	—	8	1	no	—
218	C₃×Dic₅	—	2	4	no	—
219	C₃×Dic₅	—	4	2	no	—
220	C₂³×D₃	—	10	1	no	—
221	C₂×C₃×Q₈	—	5	2	no	—
222	C₂×C₃×Q₈	—	5	2	no	—
223	C₂×C₃×Q₈	—	5	2	no	—
224	C₂×C₃×Q₈	—	10	1	no	—
225	C₂×C₃×Q₈	—	10	1	no	—
226	C₂×C₃×Q₈	—	10	1	no	—
227	C₂²×C₃×C₄	—	10	1	no	—
228	C₂²×C₃×C₄	—	10	1	no	—
229	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
230	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂²×Dic₃	—	10	1	no	—
233	C₂×D₁₂	—	5	2	no	—
234	C₂×D₁₂	—	10	1	no	—
235	C₂×D₁₂	—	10	1	no	—
236	C₂×D₁₂	—	10	1	no	—
237	C₂×D₁₂	—	10	1	no	—
238	C₂×D₁₂	—	10	1	no	—
239	C₃×C₄⋊C₄	—	5	2	no	—
240	C₃×C₄⋊C₄	—	10	4	no	—
241	C₃×C₄⋊C₄	—	10	1	no	—
242	C₃×C₄²	—	2	1	no	—
243	C₃×C₄²	—	2	1	no	—
244	C₃×C₄²	—	10	4	no	—
245	#215	—	10	8	no	—
246	(C₂×D₃)⋊C₄	—	20	2	no	—
247	(C₂×D₃)⋊C₄	—	20	2	no	—
248	C₄⋊Dic₃	—	10	1	no	—
249	C₄⋊Dic₃	—	10	1	no	—
250	C₂×C₃⋊C₈	—	2	1	no	—
251	C₂×C₃⋊C₈	—	2	1	no	—
252	C₂×C₃⋊C₈	—	2	1	no	—
253	C₂×C₃⋊C₈	—	2	1	no	—
254	C₂×C₃⋊C₈	—	2	1	no	—
255	C₂×C₃⋊C₈	C₄×D₅	1	2	yes	—
256	C₂³×C₅	C₂×#67	1	1	yes	characteristic
257	C₂²×D₅	—	6	2	no	—
258	C₂²×D₅	—	12	1	no	—
259	C₂²×D₅	—	12	1	no	—
260	C₂²×D₅	—	12	1	no	—
261	C₂²×D₅	—	12	1	no	—
262	C₂²×D₅	—	12	1	no	—
263	C₂²×D₅	—	12	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	#215	1	2	yes	complemented
270	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
272	C₂×C₄×C₅	#235	1	1	yes	characteristic
273	C₂×C₄×C₅	#235	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
276	C₂×Dic₅	—	2	2	no	—
277	C₂×Dic₅	—	2	2	no	—
278	C₂×Dic₅	—	2	2	no	—
279	C₂×Dic₅	—	2	2	no	—
280	C₂×Dic₅	—	4	1	no	—
281	C₂×Dic₅	—	4	1	no	—
282	C₂×Dic₅	—	12	1	no	—
283	C₂×Dic₅	—	12	1	no	—
284	C₂×Dic₅	—	12	1	no	—
285	D₂₀	—	6	2	no	—
286	D₂₀	—	6	2	no	—
287	D₂₀	—	12	1	no	—
288	D₂₀	—	12	1	no	—
289	Dic₁₀	—	2	2	no	—
290	Dic₁₀	—	2	2	no	—
291	Dic₁₀	—	2	2	no	—
292	Dic₁₀	(C₂×D₃)⋊C₄	1	4	yes	complemented
293	C₅×C₈	—	6	2	no	—
294	C₅×C₈	—	12	1	no	—
295	C₂²×Q₈	—	5	1	no	—
296	C₂²×D₄	—	15	1	no	—
297	C₂×SD₁₆	—	15	4	no	—
298	C₂×SD₁₆	—	30	2	no	—
299	C₂×SD₁₆	—	30	2	no	—
300	C₂²×C₈	—	3	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₄×Q₈	—	10	2	no	—
303	C₄×Q₈	—	10	2	no	—
304	C₂×C₄⋊C₄	—	5	1	no	—
305	C₂×C₄⋊C₄	—	10	1	no	—
306	C₂×C₄⋊C₄	—	15	1	no	—
307	C₂×C₂²⋊C₄	—	30	1	no	—
308	C₂×C₂²⋊C₄	—	30	1	no	—
309	C₂×C₄²	—	10	1	no	—
310	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
311	#103	—	30	2	no	—
312	#102	—	30	2	no	—
313	C₂×C₃×C₅	#386	1	1	yes	characteristic
314	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#440	1	1	yes	characteristic
316	C₂×C₃×C₅	#448	1	1	yes	characteristic
317	C₂×C₃×C₅	#449	1	1	yes	characteristic
318	C₂×C₃×C₅	#460	1	1	yes	characteristic
319	C₂×C₃×C₅	#464	1	1	yes	characteristic
320	D₁₅	—	8	2	no	—
321	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
322	C₂²×D₃	—	10	2	no	—
323	C₂²×D₃	—	20	1	no	—
324	C₂²×D₃	—	20	1	no	—
325	C₂²×D₃	—	20	1	no	—
326	C₂²×D₃	—	20	1	no	—
327	C₂²×D₃	—	20	1	no	—
328	C₂²×D₃	—	20	1	no	—
329	C₃×Q₈	—	5	4	no	—
330	C₃×Q₈	—	10	2	no	—
331	C₃×Q₈	—	10	2	no	—
332	C₃×Q₈	—	10	2	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	10	2	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	—	10	2	no	—
341	C₂×C₃×C₄	—	10	2	no	—
342	C₂×C₃×C₄	—	20	1	no	—
343	C₂×C₃×C₄	—	20	1	no	—
344	C₂×C₃×C₄	#677	1	2	yes	complemented
345	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
346	C₂×C₃×C₄	#709	1	1	yes	characteristic
347	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
348	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
349	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
350	C₂×C₃×C₄	#713	1	1	yes	characteristic
351	C₂×Dic₃	—	20	1	no	—
352	C₂×Dic₃	—	20	1	no	—
353	C₂×Dic₃	—	20	1	no	—
354	D₁₂	—	10	2	no	—
355	D₁₂	—	10	2	no	—
356	D₁₂	—	20	1	no	—
357	D₁₂	—	20	1	no	—
358	C₃⋊C₈	—	2	2	no	—
359	C₃⋊C₈	—	4	1	no	—
360	C₂²×C₅	C₄×#67	1	1	yes	characteristic
361	C₂²×C₅	#930	1	1	yes	characteristic
362	C₂²×C₅	C₂×#215	1	1	yes	characteristic
363	C₂²×C₅	#942	1	1	yes	characteristic
364	C₂²×C₅	#949	1	1	yes	characteristic
365	C₂²×C₅	#950	1	1	yes	characteristic
366	C₂²×C₅	#953	1	1	yes	characteristic
367	C₂×D₅	—	12	2	no	—
368	C₂×D₅	—	12	2	no	—
369	C₂×D₅	—	12	2	no	—
370	C₂×D₅	—	24	1	no	—
371	C₂×D₅	—	24	1	no	—
372	C₂×D₅	—	24	1	no	—
373	C₂×D₅	—	24	1	no	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	4	1	no	—
376	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
377	C₄×C₅	C₄×#67	1	1	yes	characteristic
378	C₄×C₅	#929	1	1	yes	characteristic
379	C₄×C₅	#930	1	1	yes	characteristic
380	Dic₅	—	2	4	no	—
381	Dic₅	—	4	2	no	—
382	Dic₅	—	24	1	no	—
383	C₂⁴	—	30	1	no	—
384	C₂×Q₈	—	5	2	no	—
385	C₂×Q₈	—	5	2	no	—
386	C₂×Q₈	—	5	2	no	—
387	C₂×Q₈	—	10	1	no	—
388	C₂×Q₈	—	10	1	no	—
389	C₂×Q₈	—	10	1	no	—
390	C₂×D₄	—	15	2	no	—
391	C₂×D₄	—	30	1	no	—
392	C₂×D₄	—	30	1	no	—
393	C₂×D₄	—	30	1	no	—
394	C₂×D₄	—	30	1	no	—
395	C₂×D₄	—	30	1	no	—
396	C₂²×C₄	—	10	1	no	—
397	C₂²×C₄	—	10	1	no	—
398	C₂²×C₄	—	30	1	no	—
399	C₂²×C₄	#1202	1	1	yes	characteristic
400	C₂²×C₄	#1202	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
402	SD₁₆	—	30	8	no	—
403	C₂×C₈	—	3	2	no	—
404	C₂×C₈	—	6	1	no	—
405	C₂×C₈	—	6	1	no	—
406	C₂×C₈	—	6	1	no	—
407	C₂×C₈	—	6	1	no	—
408	C₂×C₈	—	6	1	no	—
409	C₄⋊C₄	—	5	2	no	—
410	C₄⋊C₄	—	10	4	no	—
411	C₄⋊C₄	—	10	1	no	—
412	C₄⋊C₄	—	30	1	no	—
413	C₄⋊C₄	—	30	1	no	—
414	C₂²⋊C₄	—	60	2	no	—
415	C₂²⋊C₄	—	60	2	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	10	4	no	—
419	C₃×C₅	#1880	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
421	C₂²×C₃	#4028	1	1	yes	characteristic
422	C₂²×C₃	#4041	1	1	yes	characteristic
423	C₂²×C₃	C₂×#677	1	1	yes	characteristic
424	C₂²×C₃	#4050	1	1	yes	characteristic
425	C₂²×C₃	#4054	1	1	yes	characteristic
426	C₂²×C₃	#4055	1	1	yes	characteristic
427	C₂×D₃	—	20	2	no	—
428	C₂×D₃	—	20	2	no	—
429	C₂×D₃	—	20	2	no	—
430	C₂×D₃	—	40	1	no	—
431	C₂×D₃	—	40	1	no	—
432	C₂×D₃	—	40	1	no	—
433	C₂×D₃	—	40	1	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	10	4	no	—
437	C₃×C₄	—	20	2	no	—
438	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
439	C₃×C₄	#4030	1	1	yes	characteristic
440	C₃×C₄	#4039	1	1	yes	characteristic
441	C₃×C₄	#4040	1	1	yes	characteristic
442	Dic₃	—	40	1	no	—
443	C₂×C₅	C₄×#215	1	1	yes	characteristic
444	C₂×C₅	#5026	1	1	yes	characteristic
445	C₂×C₅	#5027	1	1	yes	characteristic
446	C₂×C₅	#5028	1	1	yes	characteristic
447	C₂×C₅	#5213	1	1	yes	characteristic
448	C₂×C₅	#5227	1	1	yes	characteristic
449	C₂×C₅	#5238	1	1	yes	characteristic
450	D₅	—	24	2	no	—
451	C₂³	—	30	2	no	—
452	C₂³	—	60	1	no	—
453	C₂³	—	60	1	no	—
454	C₂³	—	60	1	no	—
455	C₂³	—	60	1	no	—
456	C₂³	—	60	1	no	—
457	C₂³	—	60	1	no	—
458	C₂³	C₂×#1202	1	1	yes	characteristic
459	Q₈	—	5	4	no	—
460	Q₈	—	10	2	no	—
461	Q₈	—	10	2	no	—
462	Q₈	—	10	2	no	—
463	D₄	—	30	2	no	—
464	D₄	—	30	2	no	—
465	D₄	—	60	1	no	—
466	D₄	—	60	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	10	2	no	—
473	C₂×C₄	—	10	2	no	—
474	C₂×C₄	—	10	2	no	—
475	C₂×C₄	—	10	2	no	—
476	C₂×C₄	—	20	1	no	—
477	C₂×C₄	—	20	1	no	—
478	C₂×C₄	—	60	1	no	—
479	C₂×C₄	—	60	1	no	—
480	C₂×C₄	—	60	1	no	—
481	C₂×C₄	#6658	1	2	yes	complemented
482	C₂×C₄	#6771	1	1	yes	characteristic
483	C₂×C₄	#6773	1	1	yes	characteristic
484	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
485	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
486	C₂×C₄	D₅×#67	1	1	yes	characteristic
487	C₂×C₄	D₅×#67	1	1	yes	characteristic
488	C₈	—	6	2	no	—
489	C₈	—	12	1	no	—
490	C₂×C₃	#64954	1	1	yes	characteristic
491	C₂×C₃	C₄×#677	1	1	yes	characteristic
492	C₂×C₃	#64999	1	1	yes	characteristic
493	C₂×C₃	#65023	1	1	yes	characteristic
494	C₂×C₃	#65027	1	1	yes	characteristic
495	C₂×C₃	#65134	1	1	yes	characteristic
496	C₂×C₃	#65137	1	1	yes	characteristic
497	D₃	—	40	2	no	—
498	C₅	#71633	1	1	yes	characteristic, complemented, Sylow
499	C₂²	—	60	2	no	—
500	C₂²	—	60	2	no	—
501	C₂²	—	60	2	no	—
502	C₂²	—	120	1	no	—
503	C₂²	—	120	1	no	—
504	C₂²	—	120	1	no	—
505	C₂²	—	120	1	no	—
506	C₂²	#91301	1	1	yes	characteristic
507	C₂²	#91311	1	1	yes	characteristic
508	C₂²	C₂×#6658	1	1	yes	characteristic
509	C₂²	#91315	1	1	yes	characteristic
510	C₂²	C₄×#1202	1	1	yes	characteristic
511	C₂²	#91450	1	1	yes	characteristic
512	C₂²	#91564	1	1	yes	characteristic
513	C₄	—	2	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	10	4	no	—
516	C₄	—	20	2	no	—
517	C₄	—	120	1	no	—
518	C₄	#91348	1	1	yes	characteristic
519	C₄	#91444	1	1	yes	characteristic
520	C₄	#91448	1	1	yes	characteristic
521	C₄	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
522	C₃	#10599479	1	1	yes	characteristic, complemented, Sylow
523	C₂	—	120	2	no	—
524	C₂	C₄×#6658	1	1	yes	characteristic
525	C₂	#11747054	1	1	yes	characteristic
526	C₂	#11747064	1	1	yes	characteristic
527	C₂	#11747065	1	1	yes	characteristic
528	C₂	#11748513	1	1	yes	characteristic
529	C₂	#11748532	1	1	yes	characteristic
530	C₂	#11748907	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1202
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1880
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
4. C₂×#90971	C₂	semidirect
6. C₅×#4524	C₂	semidirect
7. #11745980	C₂	semidirect
24. C₂×#6658	C₄	semidirect
29. C₂×C₄×Dic₁₀	D₃	semidirect
77. #4524	D₅	semidirect
110. C₂×C₃×C₄×C₅	SD₁₆	semidirect
133. C₃×Dic₁₀	C₂²⋊C₄	semidirect
269. C₂×C₄×C₅	#215	semidirect
292. Dic₁₀	(C₂×D₃)⋊C₄	semidirect
344. C₂×C₃×C₄	#677	semidirect
419. C₃×C₅	#1880	semidirect
481. C₂×C₄	#6658	semidirect
498. C₅	#71633	semidirect
522. C₃	#10599479	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×Dic₁₀	2
C₂²×#6658	2
#11751040	2
C₂×#90971	2
C₂×#90968	2
C₅×#4524	2
#11745980	2
#10599479	3
#71633	5