Subgroups — #14299984

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×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	#11751029	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#90988	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90967	C₂	1	1	yes	maximal, characteristic
5	C₂×#90967	C₂	1	1	yes	maximal, characteristic
6	C₃×#64744	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745981	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602399	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	2	1	no	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂×#6712	—	2	1	no	—
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₄×C₅×D₁₂	—	2	2	no	—
18	C₄×C₅×D₁₂	—	2	2	no	—
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
21	#91115	—	2	1	no	—
22	#90988	—	2	2	no	—
23	#90967	—	2	2	no	—
24	#90967	C₄	1	4	yes	complemented
25	#68670	—	5	1	no	maximal, Hall
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₂×#3964	—	3	1	no	—
28	C₂×#3964	—	3	1	no	—
29	C₂×#3939	—	3	1	no	—
30	#65217	—	3	1	no	—
31	#64749	—	3	1	no	—
32	#64744	D₃	1	1	yes	characteristic, complemented
33	C₂³×C₅×D₃	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×Dic₁₅	—	2	1	no	—
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
44	C₂×C₅×D₁₂	D₄	1	2	yes	—
45	C₂×C₅×D₁₂	Q₈	1	2	yes	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₄×C₅×D₃	—	4	2	no	—
48	C₂×C₄×C₅×D₃	—	4	2	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₄⋊Dic₁₅	—	2	1	no	—
52	C₄⋊Dic₁₅	—	2	1	no	—
53	C₄⋊Dic₁₅	—	2	1	no	—
54	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	complemented
55	#6712	—	4	2	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₂×C₃×#168	—	2	1	no	—
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	C₂×C₃×#168	—	2	1	no	—
64	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
65	C₂×C₄×D₁₂	D₅	1	1	yes	characteristic
66	C₂×#821	—	5	1	no	—
67	C₂×#821	—	5	1	no	—
68	C₂×#818	—	5	1	no	—
69	#4928	—	5	1	no	—
70	C₃×#336	—	5	1	no	—
71	#4551	—	5	1	no	—
72	C₂²×C₅×D₄	—	3	1	no	—
73	C₂³×C₄×C₅	—	6	1	no	—
74	C₄×C₅×D₄	—	6	2	no	—
75	C₄×C₅×D₄	—	6	2	no	—
76	C₂×C₅×C₄⋊C₄	—	3	1	no	—
77	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₂×C₄⋊Dic₅	—	3	1	no	—
80	C₂×C₄⋊Dic₅	—	3	1	no	—
81	C₂×#683	—	6	1	no	—
82	C₂²×#168	C₂×D₃	1	1	yes	characteristic
83	C₂²×#168	C₂×D₃	1	1	yes	characteristic
84	#3964	—	3	4	no	—
85	#3964	—	6	2	no	—
86	#3963	—	6	1	no	—
87	#3939	—	6	2	no	—
88	#1862	—	15	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂²×C₅×D₃	—	2	2	no	—
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	—	4	1	no	—
94	C₂²×C₅×D₃	—	4	1	no	—
95	C₂²×C₅×D₃	—	4	1	no	—
96	C₂²×C₅×D₃	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×Dic₁₅	—	2	2	no	—
110	C₂×Dic₁₅	—	4	1	no	—
111	C₂×Dic₁₅	—	4	1	no	—
112	C₂×Dic₁₅	—	4	1	no	—
113	C₂×Dic₁₅	—	4	1	no	—
114	C₂×Dic₁₅	—	4	1	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₅×D₁₂	—	2	2	no	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	C₄⋊C₄	1	4	yes	complemented
122	C₄×C₅×D₃	—	4	8	no	—
123	C₃×#168	—	2	2	no	—
124	C₃×#168	—	4	1	no	—
125	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
126	C₂²×C₄×D₃	—	2	1	no	—
127	C₂²×C₃×C₈	—	5	1	no	—
128	C₂²×C₃×C₈	—	5	1	no	—
129	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
130	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
131	C₂×C₄⋊Dic₃	—	5	1	no	—
132	C₂×C₄⋊Dic₃	—	5	1	no	—
133	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
134	C₂×Dic₃⋊C₄	—	10	1	no	—
135	C₄×D₁₂	—	2	2	no	—
136	C₄×D₁₂	—	2	2	no	—
137	C₃⋊#95	—	10	1	no	—
138	#821	—	5	4	no	—
139	#821	—	10	2	no	—
140	#818	—	10	2	no	—
141	C₂⁴×C₅	—	6	1	no	—
142	C₂×C₅×D₄	—	3	2	no	—
143	C₂×C₅×D₄	—	3	2	no	—
144	C₂×C₅×D₄	—	3	2	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂²×C₄×C₅	—	6	4	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₂²×C₄×C₅	—	12	2	no	—
151	C₂²×C₄×C₅	—	12	2	no	—
152	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
153	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
155	C₂²×Dic₅	—	6	1	no	—
156	C₂²×Dic₅	—	6	1	no	—
157	C₅×C₄⋊C₄	—	3	2	no	—
158	C₅×C₄⋊C₄	—	6	1	no	—
159	C₅×C₂²⋊C₄	—	6	4	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄⋊Dic₅	—	3	2	no	—
163	C₄⋊Dic₅	—	6	1	no	—
164	C₄⋊Dic₅	—	6	1	no	—
165	C₄⋊Dic₅	—	6	1	no	—
166	#683	—	12	2	no	—
167	C₂×#168	—	2	1	no	—
168	C₂×#168	—	2	1	no	—
169	C₂×#168	—	2	1	no	—
170	C₂×#168	—	2	1	no	—
171	C₂×#168	—	2	1	no	—
172	C₂×#168	C₄×D₃	1	2	yes	complemented
173	C₂×C₄×D₄	—	3	1	no	—
174	C₂×#107	—	15	1	no	—
175	C₂×#102	—	15	1	no	—
176	C₂×#102	—	15	1	no	—
177	#389	—	15	1	no	—
178	#340	—	15	1	no	—
179	#336	—	5	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×D₈	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	#137	1	1	yes	characteristic
187	C₂×C₅×D₃	—	2	4	no	—
188	C₂×C₅×D₃	—	4	2	no	—
189	C₂×C₅×D₃	—	4	2	no	—
190	C₂×C₅×D₃	—	4	2	no	—
191	C₂×C₅×D₃	—	4	2	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	4	2	no	—
194	C₃×C₄×C₅	—	2	2	no	—
195	C₃×C₄×C₅	—	4	1	no	—
196	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
198	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
199	C₃×C₄×C₅	#123	1	1	yes	characteristic
200	Dic₁₅	—	4	2	no	—
201	Dic₁₅	—	8	1	no	—
202	C₅×Dic₃	—	4	2	no	—
203	C₂³×D₃	—	2	1	no	—
204	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂²×Dic₃	—	2	1	no	—
208	C₂²×Dic₃	—	10	1	no	—
209	C₂²×Dic₃	—	10	1	no	—
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	Dic₁₀	1	2	yes	—
214	C₂×D₁₂	C₄×D₅	1	2	yes	—
215	C₂×D₁₂	C₂²⋊D₅	1	2	yes	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₂×C₄×D₃	—	4	2	no	—
218	C₂×C₄×D₃	—	4	2	no	—
219	C₂×C₃×C₈	—	5	2	no	—
220	C₂×C₃×C₈	—	10	1	no	—
221	C₂×C₃×C₈	—	10	1	no	—
222	C₂×C₃×C₈	—	10	1	no	—
223	C₂×C₃×C₈	—	10	1	no	—
224	C₂×C₃×C₈	—	10	1	no	—
225	C₃×C₄²	—	2	1	no	—
226	C₃×C₄²	—	2	1	no	—
227	(C₂×D₃)⋊C₄	—	2	4	no	—
228	C₄⋊Dic₃	—	2	1	no	—
229	C₄⋊Dic₃	—	5	2	no	—
230	C₄⋊Dic₃	—	10	1	no	—
231	C₄⋊Dic₃	—	10	1	no	—
232	C₄⋊Dic₃	—	10	1	no	—
233	C₄⋊Dic₃	C₂²⋊D₅	1	2	yes	—
234	Dic₃⋊C₄	—	20	2	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	12	1	no	—
239	C₂³×C₅	—	12	1	no	—
240	C₂³×C₅	—	12	1	no	—
241	C₂³×C₅	—	12	1	no	—
242	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
243	C₅×D₄	—	3	4	no	—
244	C₅×D₄	—	6	2	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	6	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	12	8	no	—
254	C₂×C₄×C₅	—	12	1	no	—
255	C₂×C₄×C₅	—	12	1	no	—
256	C₂×C₄×C₅	D₂₄	1	2	yes	—
257	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×C₄×C₅	#235	1	1	yes	characteristic
259	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	#237	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
263	C₂×Dic₅	—	6	2	no	—
264	C₂×Dic₅	—	12	1	no	—
265	C₂×Dic₅	—	12	1	no	—
266	C₂×Dic₅	—	12	1	no	—
267	C₂×Dic₅	—	12	1	no	—
268	C₂×Dic₅	—	12	1	no	—
269	#168	—	2	2	no	—
270	#168	—	4	1	no	—
271	C₂²×D₄	—	3	1	no	—
272	C₂³×C₄	—	6	1	no	—
273	C₂²×C₈	—	5	1	no	—
274	C₂²×C₈	—	5	1	no	—
275	C₄×D₄	—	6	2	no	—
276	C₄×D₄	—	6	2	no	—
277	C₂×C₄⋊C₄	—	3	1	no	—
278	C₂×C₄⋊C₄	—	15	1	no	—
279	C₂×C₄⋊C₄	—	15	1	no	—
280	C₂×C₄⋊C₄	—	30	1	no	—
281	C₂×C₂²⋊C₄	—	6	1	no	—
282	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
283	#107	—	30	2	no	—
284	#102	—	15	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×D₈	1	1	yes	characteristic
289	C₂×C₃×C₅	#440	1	1	yes	characteristic
290	C₂×C₃×C₅	#447	1	1	yes	characteristic
291	C₂×C₃×C₅	#452	1	1	yes	characteristic
292	C₂×C₃×C₅	#474	1	1	yes	characteristic
293	C₂×C₃×C₅	#478	1	1	yes	characteristic
294	C₅×D₃	—	4	4	no	—
295	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
296	C₂²×D₃	—	2	2	no	—
297	C₂²×D₃	—	2	2	no	—
298	C₂²×D₃	—	2	2	no	—
299	C₂²×D₃	—	4	1	no	—
300	C₂²×D₃	—	4	1	no	—
301	C₂²×D₃	—	4	1	no	—
302	C₂²×D₃	—	4	1	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	#686	1	2	yes	—
309	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	#709	1	1	yes	characteristic
312	C₂×C₃×C₄	#709	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
315	C₂×Dic₃	—	2	2	no	—
316	C₂×Dic₃	—	4	1	no	—
317	C₂×Dic₃	—	4	1	no	—
318	C₂×Dic₃	—	10	2	no	—
319	C₂×Dic₃	—	20	1	no	—
320	C₂×Dic₃	—	20	1	no	—
321	C₂×Dic₃	—	20	1	no	—
322	C₂×Dic₃	—	20	1	no	—
323	C₂×Dic₃	—	20	1	no	—
324	D₁₂	—	2	2	no	—
325	D₁₂	—	2	2	no	—
326	D₁₂	—	2	2	no	—
327	D₁₂	#683	1	4	yes	complemented
328	C₄×D₃	—	4	8	no	—
329	C₃×C₈	—	10	2	no	—
330	C₃×C₈	—	20	1	no	—
331	C₂²×C₅	—	6	4	no	—
332	C₂²×C₅	—	12	2	no	—
333	C₂²×C₅	—	12	2	no	—
334	C₂²×C₅	—	12	2	no	—
335	C₂²×C₅	—	12	2	no	—
336	C₂²×C₅	—	12	2	no	—
337	C₂²×C₅	—	12	2	no	—
338	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
339	C₂²×C₅	#882	1	1	yes	characteristic
340	C₂²×C₅	#897	1	1	yes	characteristic
341	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
342	C₂²×C₅	#904	1	1	yes	characteristic
343	C₂²×C₅	#908	1	1	yes	characteristic
344	C₂²×C₅	#909	1	1	yes	characteristic
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	4	1	no	—
347	C₄×C₅	—	12	2	no	—
348	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
349	C₄×C₅	#883	1	1	yes	characteristic
350	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
351	C₄×C₅	#896	1	1	yes	characteristic
352	Dic₅	—	12	2	no	—
353	Dic₅	—	24	1	no	—
354	C₂⁴	—	6	1	no	—
355	C₂×D₄	—	3	2	no	—
356	C₂×D₄	—	3	2	no	—
357	C₂×D₄	—	3	2	no	—
358	C₂×D₄	—	6	1	no	—
359	C₂×D₄	—	6	1	no	—
360	C₂×D₄	—	6	1	no	—
361	C₂²×C₄	—	6	4	no	—
362	C₂²×C₄	—	6	1	no	—
363	C₂²×C₄	—	12	2	no	—
364	C₂²×C₄	—	12	2	no	—
365	C₂²×C₄	—	30	1	no	—
366	C₂²×C₄	—	30	1	no	—
367	C₂²×C₄	#1203	1	1	yes	characteristic
368	C₂²×C₄	#1203	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
370	C₂×C₈	—	5	2	no	—
371	C₂×C₈	—	10	1	no	—
372	C₂×C₈	—	10	1	no	—
373	C₂×C₈	—	10	1	no	—
374	C₂×C₈	—	10	1	no	—
375	C₂×C₈	—	10	1	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	—	6	1	no	—
378	C₄⋊C₄	—	15	2	no	—
379	C₄⋊C₄	—	30	1	no	—
380	C₄⋊C₄	—	30	1	no	—
381	C₄⋊C₄	—	30	1	no	—
382	C₄⋊C₄	—	60	2	no	—
383	C₂²⋊C₄	—	6	4	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₃×C₅	#1862	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₃	#4070	1	1	yes	characteristic
388	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
389	C₂²×C₃	C₂×#686	1	1	yes	characteristic
390	C₂²×C₃	#4078	1	1	yes	characteristic
391	C₂²×C₃	#4096	1	1	yes	characteristic
392	C₂²×C₃	#4097	1	1	yes	characteristic
393	C₂²×C₃	#4099	1	1	yes	characteristic
394	C₂×D₃	—	2	4	no	—
395	C₂×D₃	—	4	2	no	—
396	C₂×D₃	—	4	2	no	—
397	C₂×D₃	—	4	2	no	—
398	C₂×D₃	—	4	2	no	—
399	C₂×D₃	—	4	2	no	—
400	C₂×D₃	—	4	2	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	C₂×#683	1	1	yes	characteristic
404	C₃×C₄	#4070	1	1	yes	characteristic
405	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
406	C₃×C₄	#4075	1	1	yes	characteristic
407	Dic₃	—	4	2	no	—
408	Dic₃	—	20	2	no	—
409	Dic₃	—	40	1	no	—
410	C₂×C₅	—	12	4	no	—
411	C₂×C₅	#4668	1	1	yes	characteristic
412	C₂×C₅	C₄×D₂₄	1	1	yes	characteristic
413	C₂×C₅	#4710	1	1	yes	characteristic
414	C₂×C₅	#4732	1	1	yes	characteristic
415	C₂×C₅	#4733	1	1	yes	characteristic
416	C₂×C₅	#4846	1	1	yes	characteristic
417	C₂×C₅	#4847	1	1	yes	characteristic
418	C₂³	—	6	2	no	—
419	C₂³	—	6	2	no	—
420	C₂³	—	6	2	no	—
421	C₂³	—	12	1	no	—
422	C₂³	—	12	1	no	—
423	C₂³	—	12	1	no	—
424	C₂³	—	12	1	no	—
425	C₂³	C₂×#1203	1	1	yes	characteristic
426	D₄	—	3	4	no	—
427	D₄	—	6	2	no	—
428	D₄	—	6	2	no	—
429	D₄	—	6	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	12	8	no	—
437	C₂×C₄	—	12	1	no	—
438	C₂×C₄	—	12	1	no	—
439	C₂×C₄	—	30	2	no	—
440	C₂×C₄	—	60	1	no	—
441	C₂×C₄	—	60	1	no	—
442	C₂×C₄	—	60	1	no	—
443	C₂×C₄	—	60	1	no	—
444	C₂×C₄	—	60	1	no	—
445	C₂×C₄	#6654	1	2	yes	—
446	C₂×C₄	#6765	1	1	yes	characteristic
447	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
448	C₂×C₄	#6771	1	1	yes	characteristic
449	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
450	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
451	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
452	C₈	—	10	2	no	—
453	C₈	—	20	1	no	—
454	C₂×C₃	#65296	1	1	yes	characteristic
455	C₂×C₃	#65298	1	1	yes	characteristic
456	C₂×C₃	C₄×#686	1	1	yes	characteristic
457	C₂×C₃	#65307	1	1	yes	characteristic
458	C₂×C₃	#65499	1	1	yes	characteristic
459	C₂×C₃	#65506	1	1	yes	characteristic
460	C₂×C₃	#65528	1	1	yes	characteristic
461	D₃	—	4	4	no	—
462	C₅	#68670	1	1	yes	characteristic, complemented, Sylow
463	C₂²	—	6	4	no	—
464	C₂²	—	12	2	no	—
465	C₂²	—	12	2	no	—
466	C₂²	—	12	2	no	—
467	C₂²	—	12	2	no	—
468	C₂²	—	12	2	no	—
469	C₂²	—	12	2	no	—
470	C₂²	C₂×#6654	1	1	yes	characteristic
471	C₂²	#91303	1	1	yes	characteristic
472	C₂²	#91304	1	1	yes	characteristic
473	C₂²	#91322	1	1	yes	characteristic
474	C₂²	#91365	1	1	yes	characteristic
475	C₂²	C₄×#1203	1	1	yes	characteristic
476	C₂²	#91570	1	1	yes	characteristic
477	C₄	—	2	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	12	2	no	—
480	C₄	—	60	2	no	—
481	C₄	—	120	1	no	—
482	C₄	#91352	1	1	yes	characteristic
483	C₄	D₃×#683	1	1	yes	characteristic
484	C₄	#91441	1	1	yes	characteristic
485	C₄	#91452	1	1	yes	characteristic
486	C₃	#10602399	1	1	yes	characteristic, complemented, Sylow
487	C₂	—	12	4	no	—
488	C₂	#11746894	1	1	yes	characteristic
489	C₂	#11746964	1	1	yes	characteristic
490	C₂	C₄×#6654	1	1	yes	characteristic
491	C₂	#11747056	1	1	yes	characteristic
492	C₂	#11748361	1	1	yes	characteristic
493	C₂	#11748520	1	1	yes	characteristic
494	C₂	#11748722	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1203
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×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1862
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
2. #11751029	C₂	semidirect
3. C₂×#90988	C₂	semidirect
6. C₃×#64744	C₂	semidirect
7. #11745981	C₂	semidirect
24. #90967	C₄	semidirect
32. #64744	D₃	semidirect
54. C₄⋊Dic₁₅	C₂×C₄	semidirect
64. C₂×C₃×#168	C₂×C₄	semidirect
121. C₅×D₁₂	C₄⋊C₄	semidirect
172. C₂×#168	C₄×D₃	semidirect
327. D₁₂	#683	semidirect
386. C₃×C₅	#1862	semidirect
462. C₅	#68670	semidirect
486. C₃	#10602399	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
#11751029	2
C₂×#90988	2
C₂×#90967	2
C₃×#64744	2
#11745981	2
#10602399	3
#68670	5