Subgroups — #14297566

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₅×#5118	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic
4	#11748440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90958	C₂	1	1	yes	maximal, characteristic
6	#11746375	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745987	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601320	—	3	1	no	maximal, Hall
9	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
10	C₂²×D₅×Dic₃	C₄	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₂×#6665	C₄	1	2	yes	—
18	Dic₃×D₂₀	—	2	1	no	—
19	Dic₃×D₂₀	—	2	1	no	—
20	Dic₃×D₂₀	—	2	1	no	—
21	Dic₃×D₂₀	—	2	1	no	—
22	C₅×Dic₃⋊C₈	—	2	1	no	—
23	C₅×Dic₃⋊C₈	—	2	1	no	—
24	C₃×#3955	—	2	2	no	—
25	Dic₃⋊#168	—	2	1	no	—
26	Dic₃⋊#168	—	2	1	no	—
27	#90958	—	2	2	no	—
28	#70063	—	5	1	no	maximal, Hall
29	C₂×C₄×D₂₀	—	3	1	no	—
30	C₅×#423	—	3	1	no	—
31	C₂×#3955	—	3	1	no	—
32	C₂×#3955	D₃	1	1	yes	characteristic
33	#65213	—	3	1	no	—
34	#64774	—	3	1	no	—
35	#64774	—	3	1	no	—
36	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
39	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×D₂₀	—	2	1	no	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	—	2	1	no	—
44	C₂×C₃×D₂₀	—	2	1	no	—
45	C₂×C₃×D₂₀	D₄	1	2	yes	—
46	C₂×C₃×D₂₀	Q₈	1	2	yes	—
47	C₂×D₅×Dic₃	—	2	2	no	—
48	C₂×D₅×Dic₃	—	2	2	no	—
49	C₂×D₅×Dic₃	—	4	4	no	—
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₄⋊Dic₁₅	—	2	1	no	—
54	C₄⋊Dic₁₅	—	2	1	no	—
55	#6710	—	2	1	no	—
56	#6710	—	2	1	no	—
57	C₂×C₃⋊#168	—	2	1	no	—
58	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₅×#208	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₃×#681	—	2	1	no	—
66	C₃×#681	—	2	1	no	—
67	C₂×C₃×#168	—	2	1	no	—
68	#6665	—	2	2	no	—
69	#6665	—	2	2	no	—
70	C₂×D₄×Dic₃	—	5	1	no	—
71	C₂×C₃×#100	—	5	1	no	—
72	C₂×#833	—	5	1	no	—
73	#5118	—	5	1	no	—
74	#5118	D₅	1	1	yes	characteristic, complemented
75	#4554	—	5	1	no	—
76	#4554	—	5	1	no	—
77	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₄×D₅	—	3	2	no	—
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×#685	—	3	2	no	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×#681	—	3	1	no	—
85	C₂×#681	C₂×D₃	1	1	yes	characteristic
86	C₄×D₂₀	—	6	1	no	—
87	C₄×D₂₀	—	6	1	no	—
88	C₄×D₂₀	—	6	1	no	—
89	C₄×D₂₀	—	6	1	no	—
90	C₅×C₄⋊C₈	—	6	1	no	—
91	C₅×C₄⋊C₈	—	6	1	no	—
92	#3955	—	2	2	no	—
93	#3955	—	6	2	no	—
94	C₄⋊#168	—	6	1	no	—
95	C₄⋊#168	—	6	1	no	—
96	#1800	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	2	2	no	—
100	C₂²×C₃×D₅	—	4	2	no	—
101	C₂²×C₃×D₅	—	4	2	no	—
102	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	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	2	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	4	1	no	—
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₃×D₂₀	—	2	2	no	—
118	C₃×D₂₀	—	2	2	no	—
119	C₃×D₂₀	—	2	2	no	—
120	C₃×D₂₀	—	2	2	no	—
121	D₅×Dic₃	—	4	4	no	—
122	D₅×Dic₃	—	4	4	no	—
123	C₃×C₅×C₈	—	4	1	no	—
124	C₃⋊#168	—	4	1	no	—
125	C₃×#168	—	4	1	no	—
126	C₅×C₃⋊C₈	—	4	1	no	—
127	C₂²×C₃×D₄	—	5	1	no	—
128	C₂³×Dic₃	—	5	2	no	—
129	C₂×C₃×M₁₆	—	5	1	no	—
130	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
131	C₂×#217	—	5	2	no	—
132	D₄×Dic₃	—	10	1	no	—
133	D₄×Dic₃	—	10	1	no	—
134	D₄×Dic₃	—	10	1	no	—
135	D₄×Dic₃	—	10	1	no	—
136	C₂×C₄⋊Dic₃	—	5	1	no	—
137	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
138	C₂×#208	—	5	1	no	—
139	C₂×#208	C₂×D₅	1	1	yes	characteristic
140	C₃×#100	—	10	2	no	—
141	#833	—	10	2	no	—
142	Dic₃⋊C₈	—	2	1	no	—
143	Dic₃⋊C₈	—	2	1	no	—
144	Dic₃⋊C₈	—	10	1	no	—
145	Dic₃⋊C₈	—	10	1	no	—
146	C₂³×D₅	C₄×D₃	1	2	yes	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₂²×Dic₅	—	3	2	no	—
151	C₂×D₂₀	—	2	1	no	—
152	C₂×D₂₀	—	2	1	no	—
153	C₂×D₂₀	—	2	1	no	—
154	C₂×D₂₀	—	2	1	no	—
155	C₂×D₂₀	Dic₆	1	2	yes	—
156	C₂×D₂₀	#67	1	2	yes	—
157	C₂×C₄×D₅	—	6	2	no	—
158	C₂×C₄×D₅	—	6	2	no	—
159	C₂×C₄×D₅	—	12	4	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	6	1	no	—
163	C₅×M₁₆	—	6	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₄²×C₅	—	3	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	1	no	—
169	C₄²×C₅	—	3	1	no	—
170	#685	—	6	2	no	—
171	#685	—	6	2	no	—
172	C₄⋊Dic₅	—	6	1	no	—
173	C₄⋊Dic₅	—	6	1	no	—
174	#681	—	2	1	no	—
175	#681	—	2	1	no	—
176	#681	—	6	1	no	—
177	#681	—	6	1	no	—
178	C₂×#168	—	2	1	no	—
179	C₂×#168	—	6	1	no	—
180	C₂×C₄×D₄	—	15	1	no	—
181	#423	—	3	1	no	—
182	#423	—	15	1	no	—
183	C₂×#100	—	5	1	no	—
184	C₂×#100	—	15	1	no	—
185	#343	—	15	1	no	—
186	#343	—	15	1	no	—
187	C₂²×C₃×C₅	—	2	1	no	—
188	C₂²×C₃×C₅	—	2	1	no	—
189	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	#117	1	1	yes	characteristic
192	C₂×C₃×D₅	—	2	4	no	—
193	C₂×C₃×D₅	—	4	4	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	4	no	—
197	C₃×C₄×C₅	#121	1	1	yes	characteristic
198	C₃×C₄×C₅	#121	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
201	Dic₁₅	—	4	2	no	—
202	C₅×Dic₃	—	2	1	no	—
203	C₅×Dic₃	—	2	1	no	—
204	C₅×Dic₃	—	2	1	no	—
205	C₅×Dic₃	#100	1	2	yes	complemented
206	C₂⁴×C₃	—	5	2	no	—
207	C₂×C₃×D₄	—	5	2	no	—
208	C₂×C₃×D₄	—	5	2	no	—
209	C₂×C₃×D₄	—	10	1	no	—
210	C₂×C₃×D₄	—	10	1	no	—
211	C₂×C₃×D₄	—	10	1	no	—
212	C₂×C₃×D₄	—	10	1	no	—
213	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
214	C₂²×Dic₃	—	5	2	no	—
215	C₂²×Dic₃	—	10	2	no	—
216	C₂²×Dic₃	—	10	2	no	—
217	C₂²×Dic₃	—	20	4	no	—
218	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
219	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	2	1	no	—
222	C₃×M₁₆	—	10	1	no	—
223	C₃×M₁₆	—	10	1	no	—
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	10	1	no	—
226	#217	—	10	2	no	—
227	#217	—	10	2	no	—
228	C₄⋊Dic₃	—	10	1	no	—
229	C₄⋊Dic₃	—	10	1	no	—
230	C₄×Dic₃	D₂₀	1	1	yes	characteristic
231	C₄×Dic₃	D₂₀	1	1	yes	characteristic
232	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
233	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
234	#208	—	2	1	no	—
235	#208	—	2	1	no	—
236	#208	—	10	1	no	—
237	#208	—	10	1	no	—
238	C₂×C₃⋊C₈	—	2	1	no	—
239	C₂×C₃⋊C₈	—	10	1	no	—
240	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂²×D₅	—	2	2	no	—
242	C₂²×D₅	—	2	2	no	—
243	C₂²×D₅	—	4	2	no	—
244	C₂²×D₅	—	4	2	no	—
245	C₂²×D₅	Dic₃⋊C₄	1	4	yes	—
246	C₂×C₄×C₅	—	3	1	no	—
247	C₂×C₄×C₅	—	3	1	no	—
248	C₂×C₄×C₅	—	3	1	no	—
249	C₂×C₄×C₅	—	3	1	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	12	1	no	—
252	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
253	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	#237	1	1	yes	characteristic
256	C₂×C₄×C₅	#237	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
258	C₂×Dic₅	—	6	2	no	—
259	C₂×Dic₅	—	12	2	no	—
260	D₂₀	—	2	2	no	—
261	D₂₀	—	2	2	no	—
262	D₂₀	—	2	2	no	—
263	D₂₀	—	2	2	no	—
264	C₄×D₅	—	12	4	no	—
265	C₄×D₅	—	12	4	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	12	1	no	—
268	#168	—	4	1	no	—
269	#168	—	12	1	no	—
270	C₂²×D₄	—	5	1	no	—
271	C₂³×C₄	—	15	2	no	—
272	C₂×M₁₆	—	3	1	no	—
273	C₂×M₁₆	—	5	1	no	—
274	C₂×M₁₆	—	15	1	no	—
275	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
276	C₄×D₄	—	30	1	no	—
277	C₄×D₄	—	30	1	no	—
278	C₄×D₄	—	30	1	no	—
279	C₄×D₄	—	30	1	no	—
280	C₂×C₄⋊C₄	—	15	1	no	—
281	C₂×C₂²⋊C₄	—	15	2	no	—
282	C₂×C₄²	—	3	1	no	—
283	C₄⋊C₈	—	6	1	no	—
284	C₄⋊C₈	—	6	1	no	—
285	C₄⋊C₈	—	30	1	no	—
286	C₄⋊C₈	—	30	1	no	—
287	#100	—	10	2	no	—
288	#100	—	30	2	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	#380	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
293	C₂×C₃×C₅	#413	1	1	yes	characteristic
294	C₃×D₅	—	4	4	no	—
295	C₂³×C₃	—	5	4	no	—
296	C₂³×C₃	—	10	2	no	—
297	C₂³×C₃	—	10	2	no	—
298	C₂³×C₃	—	20	2	no	—
299	C₂³×C₃	—	20	2	no	—
300	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
301	C₃×D₄	—	10	2	no	—
302	C₃×D₄	—	10	2	no	—
303	C₃×D₄	—	10	2	no	—
304	C₃×D₄	—	10	2	no	—
305	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
306	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
307	C₂×C₃×C₄	#711	1	1	yes	characteristic
308	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
309	C₂×C₃×C₄	#713	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
311	C₂×Dic₃	—	2	2	no	—
312	C₂×Dic₃	—	4	1	no	—
313	C₂×Dic₃	—	10	2	no	—
314	C₂×Dic₃	—	20	4	no	—
315	C₂×Dic₃	—	20	4	no	—
316	C₂×Dic₃	—	20	2	no	—
317	C₂×Dic₃	#685	1	1	yes	characteristic
318	C₂×Dic₃	#685	1	1	yes	characteristic
319	C₂×Dic₃	#685	1	1	yes	characteristic
320	C₂×Dic₃	#685	1	1	yes	characteristic
321	C₃×C₈	—	4	1	no	—
322	C₃×C₈	—	20	1	no	—
323	C₃⋊C₈	—	4	1	no	—
324	C₃⋊C₈	—	20	1	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	#877	1	1	yes	characteristic
328	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
330	C₂×D₅	—	2	4	no	—
331	C₂×D₅	—	4	4	no	—
332	C₂×D₅	—	4	2	no	—
333	C₂×D₅	—	4	2	no	—
334	C₂×D₅	—	4	4	no	—
335	C₄×C₅	—	3	2	no	—
336	C₄×C₅	—	6	1	no	—
337	C₄×C₅	—	6	1	no	—
338	C₄×C₅	—	6	1	no	—
339	C₄×C₅	#878	1	1	yes	characteristic
340	C₄×C₅	#878	1	1	yes	characteristic
341	C₄×C₅	#939	1	1	yes	characteristic
342	C₄×C₅	#939	1	1	yes	characteristic
343	Dic₅	—	12	2	no	—
344	C₂⁴	—	5	2	no	—
345	C₂×D₄	—	5	2	no	—
346	C₂×D₄	—	5	2	no	—
347	C₂×D₄	—	10	1	no	—
348	C₂×D₄	—	10	1	no	—
349	C₂×D₄	—	10	1	no	—
350	C₂×D₄	—	10	1	no	—
351	C₂²×C₄	—	3	1	no	—
352	C₂²×C₄	—	3	1	no	—
353	C₂²×C₄	—	15	2	no	—
354	C₂²×C₄	—	30	2	no	—
355	C₂²×C₄	—	30	2	no	—
356	C₂²×C₄	—	60	4	no	—
357	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	6	1	no	—
361	M₁₆	—	6	1	no	—
362	M₁₆	—	10	1	no	—
363	M₁₆	—	10	1	no	—
364	M₁₆	—	30	1	no	—
365	M₁₆	—	30	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	6	1	no	—
368	C₂×C₈	—	10	1	no	—
369	C₂×C₈	—	30	1	no	—
370	C₄⋊C₄	—	30	1	no	—
371	C₄⋊C₄	—	30	1	no	—
372	C₂²⋊C₄	—	30	2	no	—
373	C₂²⋊C₄	—	30	2	no	—
374	C₄²	—	3	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	—	3	1	no	—
377	C₄²	—	3	1	no	—
378	C₃×C₅	#1800	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	2	1	no	—
381	C₂²×C₃	—	10	4	no	—
382	C₂²×C₃	—	20	4	no	—
383	C₂²×C₃	—	20	4	no	—
384	C₂²×C₃	—	20	2	no	—
385	C₂²×C₃	—	20	2	no	—
386	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
387	C₂²×C₃	#4038	1	1	yes	characteristic
388	C₂²×C₃	C₂×#685	1	1	yes	characteristic
389	C₃×C₄	#4041	1	1	yes	characteristic
390	C₃×C₄	#4043	1	1	yes	characteristic
391	C₃×C₄	#4084	1	1	yes	characteristic
392	C₃×C₄	#4092	1	1	yes	characteristic
393	Dic₃	—	2	1	no	—
394	Dic₃	—	2	1	no	—
395	Dic₃	—	2	1	no	—
396	Dic₃	—	20	2	no	—
397	Dic₃	#3955	1	2	yes	complemented
398	C₂×C₅	—	2	1	no	—
399	C₂×C₅	—	2	1	no	—
400	C₂×C₅	D₃×#100	1	1	yes	characteristic
401	C₂×C₅	#4745	1	1	yes	characteristic
402	C₂×C₅	#4942	1	1	yes	characteristic
403	D₅	—	4	4	no	—
404	C₂³	—	5	4	no	—
405	C₂³	—	10	2	no	—
406	C₂³	—	10	2	no	—
407	C₂³	—	20	2	no	—
408	C₂³	—	20	2	no	—
409	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
410	D₄	—	10	2	no	—
411	D₄	—	10	2	no	—
412	D₄	—	10	2	no	—
413	D₄	—	10	2	no	—
414	C₂×C₄	—	3	1	no	—
415	C₂×C₄	—	3	1	no	—
416	C₂×C₄	—	3	1	no	—
417	C₂×C₄	—	3	1	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	12	1	no	—
420	C₂×C₄	—	30	2	no	—
421	C₂×C₄	—	60	4	no	—
422	C₂×C₄	—	60	4	no	—
423	C₂×C₄	—	60	2	no	—
424	C₂×C₄	D₅×Dic₆	1	1	yes	characteristic
425	C₂×C₄	#6766	1	1	yes	characteristic
426	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
427	C₂×C₄	#6780	1	1	yes	characteristic
428	C₂×C₄	D₅×#67	1	1	yes	characteristic
429	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
430	C₈	—	4	1	no	—
431	C₈	—	12	1	no	—
432	C₈	—	20	1	no	—
433	C₈	—	60	1	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	20	4	no	—
437	C₂×C₃	#65276	1	1	yes	characteristic
438	C₂×C₃	C₂×#3955	1	1	yes	characteristic
439	C₂×C₃	#65421	1	1	yes	characteristic
440	C₅	#70063	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	10	4	no	—
444	C₂²	—	20	4	no	—
445	C₂²	—	20	4	no	—
446	C₂²	—	20	2	no	—
447	C₂²	—	20	2	no	—
448	C₂²	D₅×Dic₃⋊C₄	1	1	yes	characteristic
449	C₂²	#91394	1	1	yes	characteristic
450	C₂²	D₃×#685	1	1	yes	characteristic
451	C₄	—	3	2	no	—
452	C₄	—	6	1	no	—
453	C₄	—	6	1	no	—
454	C₄	—	6	1	no	—
455	C₄	—	60	2	no	—
456	C₄	#91409	1	1	yes	characteristic
457	C₄	#91421	1	1	yes	characteristic
458	C₄	#91422	1	1	yes	characteristic
459	C₄	#91549	1	1	yes	characteristic
460	C₃	#10601320	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	20	4	no	—
464	C₂	D₃×#3955	1	1	yes	characteristic
465	C₂	#11748234	1	1	yes	characteristic
466	C₂	#11748878	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#685
commutator	C₂³×C₃×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1800
LCS	G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#5118	C₂	semidirect
4. #11748440	C₂	semidirect
6. #11746375	C₂	semidirect
7. #11745987	C₂	semidirect
74. #5118	D₅	semidirect
205. C₅×Dic₃	#100	semidirect
378. C₃×C₅	#1800	semidirect
397. Dic₃	#3955	semidirect
440. C₅	#70063	semidirect
460. C₃	#10601320	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₃×D₂₀	2
C₅×#5118	2
C₂×C₃×#3955	2
#11748440	2
C₂×#90958	2
#11746375	2
#11745987	2
#10601320	3
#70063	5