Subgroups — #14300129

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91434	C₂	1	1	yes	maximal, characteristic
2	#11751085	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic
4	C₂×#90985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90965	C₂	1	1	yes	maximal, characteristic
6	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745968	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599688	—	3	1	no	maximal, Hall
9	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
10	C₂²×D₅×Dic₃	—	2	1	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	—	2	1	no	—
13	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₂×#6665	—	2	1	no	—
19	#91434	—	2	2	no	—
20	#91434	—	2	2	no	—
21	#91115	—	2	1	no	—
22	C₃×#3941	C₄	1	4	yes	complemented
23	#90985	—	2	2	no	—
24	#90965	—	2	2	no	—
25	#70170	—	5	1	no	maximal, Hall
26	C₂×#4039	—	3	1	no	—
27	C₂×#3953	—	3	1	no	—
28	#65274	—	3	1	no	—
29	C₂×#3941	D₃	1	1	yes	characteristic
30	C₂×#3940	—	3	1	no	—
31	C₅×#340	—	3	1	no	—
32	#64770	—	3	1	no	—
33	C₂³×C₃×D₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₅	—	2	1	no	—
37	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
38	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₂×C₃×D₂₀	—	2	1	no	—
41	C₂×C₃×D₂₀	—	2	1	no	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
44	C₂×C₃×D₂₀	D₄	1	2	yes	—
45	C₂×C₃×D₂₀	Q₈	1	2	yes	—
46	C₂×D₅×Dic₃	—	2	4	no	—
47	C₂×D₅×Dic₃	—	4	2	no	—
48	C₂×D₅×Dic₃	—	4	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	complemented
51	C₄⋊Dic₁₅	—	2	1	no	—
52	C₄⋊Dic₁₅	—	2	1	no	—
53	C₄⋊Dic₁₅	—	4	2	no	—
54	C₄×Dic₁₅	—	2	1	no	—
55	C₄×Dic₁₅	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
64	#6665	—	2	4	no	—
65	C₂×D₄×Dic₃	—	5	1	no	—
66	C₂×C₃×#102	—	5	1	no	—
67	C₂×#832	—	5	1	no	—
68	C₂×#817	—	5	1	no	—
69	#4984	—	5	1	no	—
70	#4550	—	5	1	no	—
71	#4529	D₅	1	1	yes	characteristic, complemented
72	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₄×D₅	—	6	1	no	—
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂×C₅×C₄⋊C₄	—	3	1	no	—
76	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
77	C₂×#685	—	6	1	no	—
78	C₂×C₄⋊Dic₅	—	3	1	no	—
79	C₂×C₄⋊Dic₅	—	6	1	no	—
80	C₂×C₄×Dic₅	—	3	1	no	—
81	C₂²×#168	C₂×D₃	1	1	yes	characteristic
82	#4039	—	6	2	no	—
83	#4039	—	6	2	no	—
84	#3963	—	6	1	no	—
85	#3953	—	6	2	no	—
86	#3941	Dic₃	1	4	yes	complemented
87	#3940	—	6	2	no	—
88	#1864	—	15	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	2	2	no	—
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₂²×C₃×D₅	—	2	2	no	—
93	C₂²×C₃×D₅	—	4	1	no	—
94	C₂²×C₃×D₅	—	4	1	no	—
95	C₂²×C₃×D₅	—	4	1	no	—
96	C₂²×C₃×D₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×Dic₁₅	—	2	1	no	—
107	C₂×Dic₁₅	—	2	1	no	—
108	C₂×Dic₁₅	—	2	1	no	—
109	C₂×Dic₁₅	—	2	1	no	—
110	C₂×Dic₁₅	—	2	1	no	—
111	C₂×Dic₁₅	—	4	1	no	—
112	C₂×Dic₁₅	—	4	1	no	—
113	C₂×Dic₁₅	—	4	1	no	—
114	C₂×Dic₁₅	SD₁₆	1	2	yes	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₃×D₂₀	—	2	2	no	—
119	C₃×D₂₀	—	2	2	no	—
120	C₃×D₂₀	—	2	2	no	—
121	C₃×D₂₀	C₄⋊C₄	1	4	yes	complemented
122	D₅×Dic₃	—	4	8	no	—
123	C₃×#168	—	2	2	no	—
124	C₅×C₃⋊C₈	—	4	1	no	—
125	C₂²×C₃×D₄	—	5	1	no	—
126	C₂³×Dic₃	—	10	1	no	—
127	C₂²×C₃×C₈	—	5	1	no	—
128	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
129	C₂×#217	—	10	1	no	—
130	D₄×Dic₃	—	10	2	no	—
131	D₄×Dic₃	—	10	2	no	—
132	C₂×C₄⋊Dic₃	—	5	1	no	—
133	C₂×C₄⋊Dic₃	—	10	1	no	—
134	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
135	C₂×C₄×Dic₃	—	5	1	no	—
136	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
137	C₃×#102	—	5	4	no	—
138	#832	—	10	2	no	—
139	C₃⋊#95	—	10	1	no	—
140	#817	—	10	2	no	—
141	C₂³×D₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	6	1	no	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂²×Dic₅	—	3	1	no	—
146	C₂²×Dic₅	—	3	1	no	—
147	C₂²×Dic₅	—	6	1	no	—
148	C₂×D₂₀	—	2	1	no	—
149	C₂×D₂₀	—	2	1	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×D₂₀	Dic₆	1	2	yes	—
152	C₂×D₂₀	D₁₂	1	2	yes	—
153	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
154	C₂×C₄×D₅	—	6	4	no	—
155	C₂×C₄×D₅	—	12	2	no	—
156	C₂×C₄×D₅	—	12	2	no	—
157	C₂×C₅×C₈	—	6	1	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₂×C₅×C₈	—	6	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	3	2	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	complemented
164	#685	—	6	4	no	—
165	C₄⋊Dic₅	—	6	1	no	—
166	C₄⋊Dic₅	—	6	1	no	—
167	C₄⋊Dic₅	—	12	2	no	—
168	C₄×Dic₅	—	6	1	no	—
169	C₄×Dic₅	—	6	1	no	—
170	C₂×#168	—	2	1	no	—
171	C₂×#168	—	2	1	no	—
172	C₂×#168	C₂×Dic₃	1	2	yes	complemented
173	C₂×C₄×D₄	—	15	1	no	—
174	C₂×#106	—	15	1	no	—
175	C₂×#102	—	5	1	no	—
176	C₂×#102	—	15	1	no	—
177	#389	—	15	1	no	—
178	#340	—	3	1	no	—
179	#336	—	15	1	no	—
180	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	#120	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
184	C₂²×C₃×C₅	#135	1	1	yes	characteristic
185	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	—	4	2	no	—
189	C₂×C₃×D₅	—	4	2	no	—
190	C₂×C₃×D₅	—	4	2	no	—
191	C₂×C₃×D₅	—	4	2	no	—
192	C₂×C₃×D₅	—	4	2	no	—
193	C₂×C₃×D₅	—	4	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
198	C₃×C₄×C₅	#123	1	1	yes	characteristic
199	Dic₁₅	—	2	2	no	—
200	Dic₁₅	—	4	1	no	—
201	Dic₁₅	—	8	1	no	—
202	C₅×Dic₃	—	4	2	no	—
203	C₂⁴×C₃	—	10	1	no	—
204	C₂×C₃×D₄	—	5	2	no	—
205	C₂×C₃×D₄	—	5	2	no	—
206	C₂×C₃×D₄	—	5	2	no	—
207	C₂×C₃×D₄	—	10	1	no	—
208	C₂×C₃×D₄	—	10	1	no	—
209	C₂×C₃×D₄	—	10	1	no	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
212	C₂²×Dic₃	—	2	1	no	—
213	C₂²×Dic₃	—	5	1	no	—
214	C₂²×Dic₃	—	5	1	no	—
215	C₂²×Dic₃	—	10	4	no	—
216	C₂²×Dic₃	—	10	1	no	—
217	C₂²×Dic₃	—	20	2	no	—
218	C₂²×Dic₃	—	20	2	no	—
219	C₂×C₃×C₈	—	5	2	no	—
220	C₂×C₃×C₈	—	10	1	no	—
221	C₂×C₃×C₈	—	10	1	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	complemented
224	#217	—	10	4	no	—
225	C₄⋊Dic₃	—	2	1	no	—
226	C₄⋊Dic₃	—	10	1	no	—
227	C₄⋊Dic₃	—	10	1	no	—
228	C₄⋊Dic₃	—	20	2	no	—
229	C₄⋊Dic₃	D₂₀	1	2	yes	—
230	C₄×Dic₃	—	10	1	no	—
231	C₄×Dic₃	—	10	1	no	—
232	C₂×C₃⋊C₈	—	2	1	no	—
233	C₂×C₃⋊C₈	—	2	1	no	—
234	C₂×C₃⋊C₈	—	2	1	no	—
235	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
236	C₂²×D₅	—	2	2	no	—
237	C₂²×D₅	—	2	2	no	—
238	C₂²×D₅	—	2	2	no	—
239	C₂²×D₅	—	4	1	no	—
240	C₂²×D₅	—	4	1	no	—
241	C₂²×D₅	—	4	1	no	—
242	C₂²×D₅	—	4	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	6	2	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	—	12	1	no	—
249	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
251	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	#237	1	1	yes	characteristic
253	C₂×C₄×C₅	#237	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
255	C₂×Dic₅	—	3	2	no	—
256	C₂×Dic₅	—	6	1	no	—
257	C₂×Dic₅	—	6	1	no	—
258	C₂×Dic₅	—	6	1	no	—
259	C₂×Dic₅	—	6	1	no	—
260	C₂×Dic₅	—	6	1	no	—
261	C₂×Dic₅	—	12	1	no	—
262	C₂×Dic₅	—	12	1	no	—
263	C₂×Dic₅	—	12	1	no	—
264	D₂₀	—	2	2	no	—
265	D₂₀	—	2	2	no	—
266	D₂₀	—	2	2	no	—
267	D₂₀	C₄⋊Dic₃	1	4	yes	complemented
268	C₄×D₅	—	12	8	no	—
269	C₅×C₈	—	12	1	no	—
270	#168	—	2	2	no	—
271	C₂²×D₄	—	5	1	no	—
272	C₂³×C₄	—	30	1	no	—
273	C₂²×C₈	—	3	1	no	—
274	C₂²×C₈	—	5	1	no	—
275	C₄×D₄	—	30	2	no	—
276	C₄×D₄	—	30	2	no	—
277	C₂×C₄⋊C₄	—	3	1	no	—
278	C₂×C₄⋊C₄	—	15	1	no	—
279	C₂×C₄⋊C₄	—	30	1	no	—
280	C₂×C₄⋊C₄	D₃×D₅	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	30	1	no	—
282	C₂×C₄²	—	15	1	no	—
283	#106	—	30	2	no	—
284	#102	—	5	4	no	—
285	#102	—	30	2	no	—
286	#95	—	30	1	no	—
287	C₂×C₃×C₅	#385	1	1	yes	characteristic
288	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
289	C₂×C₃×C₅	#442	1	1	yes	characteristic
290	C₂×C₃×C₅	#449	1	1	yes	characteristic
291	C₂×C₃×C₅	#450	1	1	yes	characteristic
292	C₂×C₃×C₅	#476	1	1	yes	characteristic
293	C₂×C₃×C₅	#478	1	1	yes	characteristic
294	C₃×D₅	—	4	4	no	—
295	C₂³×C₃	—	10	2	no	—
296	C₂³×C₃	—	10	2	no	—
297	C₂³×C₃	—	10	2	no	—
298	C₂³×C₃	—	20	1	no	—
299	C₂³×C₃	—	20	1	no	—
300	C₂³×C₃	—	20	1	no	—
301	C₂³×C₃	—	20	1	no	—
302	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
303	C₃×D₄	—	5	4	no	—
304	C₃×D₄	—	10	2	no	—
305	C₃×D₄	—	10	2	no	—
306	C₃×D₄	—	10	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
312	C₂×C₃×C₄	#709	1	1	yes	characteristic
313	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
314	C₂×C₃×C₄	#711	1	1	yes	characteristic
315	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
316	C₂×Dic₃	—	2	2	no	—
317	C₂×Dic₃	—	4	1	no	—
318	C₂×Dic₃	—	4	1	no	—
319	C₂×Dic₃	—	5	2	no	—
320	C₂×Dic₃	—	10	1	no	—
321	C₂×Dic₃	—	10	1	no	—
322	C₂×Dic₃	—	10	1	no	—
323	C₂×Dic₃	—	10	1	no	—
324	C₂×Dic₃	—	10	1	no	—
325	C₂×Dic₃	—	20	8	no	—
326	C₂×Dic₃	—	20	1	no	—
327	C₂×Dic₃	—	20	1	no	—
328	C₂×Dic₃	—	20	1	no	—
329	C₃×C₈	—	10	2	no	—
330	C₃⋊C₈	—	4	1	no	—
331	C₂²×C₅	#878	1	1	yes	characteristic
332	C₂²×C₅	#882	1	1	yes	characteristic
333	C₂²×C₅	#911	1	1	yes	characteristic
334	C₂²×C₅	#911	1	1	yes	characteristic
335	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
336	C₂²×C₅	#916	1	1	yes	characteristic
337	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
338	C₂×D₅	—	2	4	no	—
339	C₂×D₅	—	4	2	no	—
340	C₂×D₅	—	4	2	no	—
341	C₂×D₅	—	4	2	no	—
342	C₂×D₅	—	4	2	no	—
343	C₂×D₅	—	4	2	no	—
344	C₂×D₅	—	4	2	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	12	2	no	—
347	C₄×C₅	#878	1	1	yes	characteristic
348	C₄×C₅	#886	1	1	yes	characteristic
349	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
350	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
351	Dic₅	—	6	2	no	—
352	Dic₅	—	12	1	no	—
353	Dic₅	—	24	1	no	—
354	C₂⁴	—	10	1	no	—
355	C₂×D₄	—	5	2	no	—
356	C₂×D₄	—	5	2	no	—
357	C₂×D₄	—	5	2	no	—
358	C₂×D₄	—	10	1	no	—
359	C₂×D₄	—	10	1	no	—
360	C₂×D₄	—	10	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	6	1	no	—
363	C₂²×C₄	—	15	1	no	—
364	C₂²×C₄	—	15	1	no	—
365	C₂²×C₄	—	30	4	no	—
366	C₂²×C₄	—	30	1	no	—
367	C₂²×C₄	—	60	2	no	—
368	C₂²×C₄	—	60	2	no	—
369	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
370	C₂×C₈	—	5	2	no	—
371	C₂×C₈	—	6	1	no	—
372	C₂×C₈	—	6	1	no	—
373	C₂×C₈	—	6	1	no	—
374	C₂×C₈	—	10	1	no	—
375	C₂×C₈	—	10	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	3	2	no	—
378	C₄⋊C₄	—	6	1	no	—
379	C₄⋊C₄	—	30	1	no	—
380	C₄⋊C₄	—	30	1	no	—
381	C₄⋊C₄	—	60	2	no	—
382	C₄⋊C₄	D₅×Dic₃	1	2	yes	complemented
383	C₂²⋊C₄	—	30	4	no	—
384	C₄²	—	30	1	no	—
385	C₄²	—	30	1	no	—
386	C₃×C₅	#1864	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₃	—	10	4	no	—
388	C₂²×C₃	—	20	2	no	—
389	C₂²×C₃	—	20	2	no	—
390	C₂²×C₃	—	20	2	no	—
391	C₂²×C₃	—	20	2	no	—
392	C₂²×C₃	—	20	2	no	—
393	C₂²×C₃	—	20	2	no	—
394	C₂²×C₃	#4027	1	1	yes	characteristic
395	C₂²×C₃	#4028	1	1	yes	characteristic
396	C₂²×C₃	#4042	1	1	yes	characteristic
397	C₂²×C₃	#4057	1	1	yes	characteristic
398	C₂²×C₃	D₅×SD₁₆	1	1	yes	characteristic
399	C₂²×C₃	#4060	1	1	yes	characteristic
400	C₂²×C₃	#4065	1	1	yes	characteristic
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
403	C₃×C₄	#4029	1	1	yes	characteristic
404	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
405	C₃×C₄	#4043	1	1	yes	characteristic
406	Dic₃	—	4	2	no	—
407	Dic₃	—	10	2	no	—
408	Dic₃	—	20	1	no	—
409	Dic₃	—	40	1	no	—
410	C₂×C₅	#4761	1	1	yes	characteristic
411	C₂×C₅	#4763	1	1	yes	characteristic
412	C₂×C₅	#4776	1	1	yes	characteristic
413	C₂×C₅	#4781	1	1	yes	characteristic
414	C₂×C₅	#4950	1	1	yes	characteristic
415	C₂×C₅	#5152	1	1	yes	characteristic
416	C₂×C₅	Dic₃×SD₁₆	1	1	yes	characteristic
417	D₅	—	4	4	no	—
418	C₂³	—	10	2	no	—
419	C₂³	—	10	2	no	—
420	C₂³	—	10	2	no	—
421	C₂³	—	20	1	no	—
422	C₂³	—	20	1	no	—
423	C₂³	—	20	1	no	—
424	C₂³	—	20	1	no	—
425	C₂³	#6790	1	1	yes	characteristic
426	D₄	—	5	4	no	—
427	D₄	—	10	2	no	—
428	D₄	—	10	2	no	—
429	D₄	—	10	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	12	1	no	—
435	C₂×C₄	—	12	1	no	—
436	C₂×C₄	—	15	2	no	—
437	C₂×C₄	—	30	1	no	—
438	C₂×C₄	—	30	1	no	—
439	C₂×C₄	—	30	1	no	—
440	C₂×C₄	—	30	1	no	—
441	C₂×C₄	—	30	1	no	—
442	C₂×C₄	—	60	8	no	—
443	C₂×C₄	—	60	1	no	—
444	C₂×C₄	—	60	1	no	—
445	C₂×C₄	—	60	1	no	—
446	C₂×C₄	D₅×Dic₆	1	1	yes	characteristic
447	C₂×C₄	#6765	1	1	yes	characteristic
448	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
449	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
450	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
451	C₂×C₄	#6780	1	1	yes	characteristic
452	C₈	—	10	2	no	—
453	C₈	—	12	1	no	—
454	C₂×C₃	—	20	4	no	—
455	C₂×C₃	#64957	1	1	yes	characteristic
456	C₂×C₃	#65065	1	1	yes	characteristic
457	C₂×C₃	#65074	1	1	yes	characteristic
458	C₂×C₃	#65077	1	1	yes	characteristic
459	C₂×C₃	#65100	1	1	yes	characteristic
460	C₂×C₃	#65159	1	1	yes	characteristic
461	C₂×C₃	#65180	1	1	yes	characteristic
462	C₅	#70170	1	1	yes	characteristic, complemented, Sylow
463	C₂²	—	10	4	no	—
464	C₂²	—	20	2	no	—
465	C₂²	—	20	2	no	—
466	C₂²	—	20	2	no	—
467	C₂²	—	20	2	no	—
468	C₂²	—	20	2	no	—
469	C₂²	—	20	2	no	—
470	C₂²	#91431	1	1	yes	characteristic
471	C₂²	#91476	1	1	yes	characteristic
472	C₂²	#91482	1	1	yes	characteristic
473	C₂²	#91498	1	1	yes	characteristic
474	C₂²	#91505	1	1	yes	characteristic
475	C₂²	#91521	1	1	yes	characteristic
476	C₂²	#91559	1	1	yes	characteristic
477	C₄	—	4	2	no	—
478	C₄	—	12	2	no	—
479	C₄	—	30	2	no	—
480	C₄	—	60	1	no	—
481	C₄	—	120	1	no	—
482	C₄	D₅×C₄⋊Dic₃	1	1	yes	characteristic
483	C₄	#91414	1	1	yes	characteristic
484	C₄	#91422	1	1	yes	characteristic
485	C₄	Dic₃×D₂₀	1	1	yes	characteristic
486	C₃	#10599688	1	1	yes	characteristic, complemented, Sylow
487	C₂	—	20	4	no	—
488	C₂	#11747255	1	1	yes	characteristic
489	C₂	#11747257	1	1	yes	characteristic
490	C₂	#11747484	1	1	yes	characteristic
491	C₂	#11747518	1	1	yes	characteristic
492	C₂	#11748900	1	1	yes	characteristic
493	C₂	#11748995	1	1	yes	characteristic
494	C₂	#11749239	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#6790
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₄	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₃×D₅
hypocenter	C₃×C₅	#1864
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #11751085	C₂	semidirect
4. C₂×#90985	C₂	semidirect
6. C₅×#4529	C₂	semidirect
7. #11745968	C₂	semidirect
22. C₃×#3941	C₄	semidirect
50. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
63. C₂×C₃×#168	C₂×C₄	semidirect
71. #4529	D₅	semidirect
86. #3941	Dic₃	semidirect
121. C₃×D₂₀	C₄⋊C₄	semidirect
163. C₅×C₄⋊C₄	C₂×Dic₃	semidirect
172. C₂×#168	C₂×Dic₃	semidirect
223. C₃×C₄⋊C₄	C₄×D₅	semidirect
267. D₂₀	C₄⋊Dic₃	semidirect
382. C₄⋊C₄	D₅×Dic₃	semidirect
386. C₃×C₅	#1864	semidirect
462. C₅	#70170	semidirect
486. C₃	#10599688	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91434	2
#11751085	2
C₂×C₃×#3941	2
C₂×#90985	2
C₂×#90965	2
C₅×#4529	2
#11745968	2
#10599688	3
#70170	5