Subgroups — D₃×#65000 #14416499

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 500 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	C₄×D₃×D₂₀	C₂	1	2	yes	maximal, complemented
3	#11750812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65000	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×#3953	C₂	1	2	yes	maximal, complemented
7	#11747799	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747796	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747741	C₂	1	2	yes	maximal, complemented
10	D₃×#3949	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747023	C₂	1	2	yes	maximal, complemented
12	C₂×#65000	—	3	1	no	maximal, Hall
13	C₂×D₃×D₂₀	C₂²	1	2	yes	—
14	C₂×C₄×D₃×D₅	—	2	2	no	—
15	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
16	C₄×D₆₀	C₂²	1	2	yes	complemented
17	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
21	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
22	D₃×#685	—	2	2	no	—
23	C₄×#1202	—	2	2	no	—
24	#91428	C₂²	1	2	yes	complemented
25	D₃×C₄⋊Dic₅	C₂²	1	2	yes	—
26	Dic₃×D₂₀	C₂²	1	2	yes	complemented
27	#91395	—	2	2	no	—
28	C₂×#6653	C₂²	1	2	yes	—
29	D₃×D₄₀	C₄	1	8	yes	complemented
30	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
31	#91105	C₂²	1	2	yes	complemented
32	#91101	C₂²	1	1	yes	characteristic, complemented
33	C₅×#815	C₂²	1	1	yes	characteristic, complemented
34	C₅×#815	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×#3949	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	D₃×#442	—	5	1	no	maximal, Hall
42	C₂²×D₄₀	—	3	1	no	—
43	C₂×C₄×D₂₀	—	3	2	no	—
44	C₂×C₅×#97	—	3	1	no	—
45	C₂×#3953	—	3	2	no	—
46	C₂×#3949	—	3	1	no	—
47	#65000	—	3	1	no	—
48	#65000	—	3	2	no	—
49	#65000	—	3	1	no	—
50	#65000	—	3	2	no	—
51	#65000	—	3	1	no	—
52	#65000	D₃	1	1	yes	characteristic, direct product factor
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	D₄	1	2	yes	—
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₃×D₂₀	C₂³	1	2	yes	—
59	C₂×C₃×C₄×D₅	—	2	2	no	—
60	C₂×#1202	—	2	2	no	—
61	C₂×#1200	—	2	2	no	—
62	C₂×D₃×Dic₅	—	2	2	no	—
63	C₂×D₅×Dic₃	—	2	2	no	—
64	D₃×D₂₀	—	2	4	no	—
65	D₃×D₂₀	C₂×C₄	1	8	yes	complemented
66	C₄×D₃×D₅	—	4	8	no	—
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	#6714	—	2	2	no	—
71	C₄⋊Dic₁₅	C₂³	1	2	yes	—
72	D₁₂₀	C₂×C₄	1	4	yes	complemented
73	C₄×C₅×Dic₃	D₄	1	2	yes	—
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×D₃×C₈	—	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	Dic₃⋊Dic₅	—	2	2	no	—
83	#6667	—	2	2	no	—
84	#6665	—	2	2	no	—
85	#6653	C₂×C₄	1	8	yes	complemented
86	C₂×D₃×D₈	—	5	1	no	—
87	C₄×D₃×D₄	—	5	2	no	—
88	C₃×#442	—	5	1	no	—
89	#5152	—	5	1	no	—
90	#5014	—	5	2	no	—
91	#4869	—	5	1	no	—
92	D₃×#106	—	5	1	no	—
93	#4785	—	5	2	no	—
94	D₃×#102	—	5	2	no	—
95	#4711	—	5	1	no	—
96	D₃×#97	D₅	1	1	yes	characteristic, complemented
97	C₂²×D₂₀	—	3	2	no	—
98	C₂²×C₄×D₅	—	6	2	no	—
99	C₂²×C₅×C₈	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₂×#685	—	6	2	no	—
103	C₂×C₄⋊Dic₅	—	3	2	no	—
104	C₂×D₄₀	—	3	2	no	—
105	C₂×D₄₀	—	3	1	no	—
106	C₂×D₄₀	—	3	8	no	—
107	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic
108	C₄×D₂₀	—	3	2	no	—
109	C₄×D₂₀	—	3	2	no	—
110	C₄×D₂₀	—	3	2	no	—
111	C₄×D₂₀	—	6	2	no	—
112	C₄×D₂₀	—	6	2	no	—
113	C₄×D₂₀	C₂×D₃	1	2	yes	complemented
114	C₅×#97	—	3	1	no	—
115	C₅×#97	—	3	1	no	—
116	C₅×#97	—	3	1	no	—
117	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
118	#3953	—	3	2	no	—
119	#3953	—	3	2	no	—
120	#3953	—	3	2	no	—
121	#3953	C₂×D₃	1	2	yes	complemented
122	#3949	—	3	1	no	—
123	#3949	—	3	2	no	—
124	#3949	C₂×D₃	1	1	yes	characteristic, complemented
125	C₂×#442	—	15	1	no	Sylow
126	C₂²×D₁₅	—	2	2	no	—
127	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₃×D₅	—	2	2	no	—
129	C₂×D₃×D₅	—	2	8	no	—
130	C₂×D₃×D₅	—	4	4	no	—
131	C₂×D₃×D₅	—	4	4	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×Dic₁₅	—	2	2	no	—
135	D₆₀	—	2	2	no	—
136	D₆₀	C₂²×C₄	1	4	yes	complemented
137	C₄×D₁₅	—	4	4	no	—
138	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
139	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
140	C₄×C₅×D₃	—	2	4	no	—
141	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₄×C₅×D₃	#41	1	2	yes	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₃×D₂₀	—	2	2	no	—
145	C₃×D₂₀	C₂²×C₄	1	4	yes	complemented
146	C₃×C₄×D₅	—	4	4	no	—
147	#1202	—	2	8	no	—
148	#1200	—	4	4	no	—
149	D₃×Dic₅	—	4	4	no	—
150	D₅×Dic₃	—	4	4	no	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
153	C₅×C₃⋊C₈	—	2	1	no	—
154	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
155	C₂×D₃×D₄	—	5	2	no	—
156	C₂²×C₄×D₃	—	10	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	D₃×D₈	—	5	8	no	—
163	C₂×D₂₄	—	5	1	no	—
164	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
165	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
166	#893	—	5	2	no	—
167	D₃×C₄⋊C₄	—	5	2	no	—
168	#67⋊C₄	—	10	2	no	—
169	D₃×C₂²⋊C₄	—	10	2	no	—
170	C₄×D₁₂	—	5	2	no	—
171	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
172	C₃×#106	—	5	1	no	—
173	C₃×#102	—	5	2	no	—
174	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
175	#832	—	5	2	no	—
176	#821	—	5	2	no	—
177	#817	—	5	1	no	—
178	#815	C₂×D₅	1	1	yes	characteristic, complemented
179	#815	C₂×D₅	1	1	yes	characteristic, complemented
180	#809	—	5	2	no	—
181	#808	—	5	2	no	—
182	#803	C₂×D₅	1	1	yes	characteristic, complemented
183	C₂³×D₅	—	6	2	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	2	no	—
186	C₂²×Dic₅	—	6	2	no	—
187	C₂×D₂₀	—	3	2	no	—
188	C₂×D₂₀	—	3	8	no	—
189	C₂×D₂₀	—	6	4	no	—
190	C₂×D₂₀	—	6	2	no	—
191	C₂×D₂₀	C₂²×D₃	1	2	yes	—
192	C₂×C₄×D₅	—	2	2	no	—
193	C₂×C₄×D₅	—	6	2	no	—
194	C₂×C₄×D₅	—	6	2	no	—
195	C₂×C₄×D₅	—	6	2	no	—
196	C₂×C₄×D₅	—	12	8	no	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	—	3	4	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	—	6	2	no	—
201	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
203	C₄²×C₅	—	3	2	no	—
204	C₄²×C₅	—	3	1	no	—
205	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
206	#685	—	2	2	no	—
207	#685	—	6	2	no	—
208	#685	—	6	2	no	—
209	#685	—	6	2	no	—
210	C₄⋊Dic₅	—	3	2	no	—
211	C₄⋊Dic₅	—	6	2	no	—
212	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
213	D₄₀	—	3	8	no	—
214	D₄₀	—	3	4	no	—
215	D₄₀	C₄×D₃	1	4	yes	complemented
216	C₂²×D₈	—	15	1	no	—
217	C₂×C₄×D₄	—	15	2	no	—
218	#442	—	5	1	no	—
219	#442	—	15	2	no	—
220	#442	—	15	1	no	—
221	#442	—	15	2	no	—
222	#442	—	15	1	no	—
223	#442	—	15	1	no	—
224	C₂×#106	—	15	1	no	—
225	C₂×#102	—	15	2	no	—
226	C₂×#97	—	3	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×D₁₅	—	2	4	no	—
229	C₂×D₁₅	—	4	2	no	—
230	C₂×D₁₅	—	4	2	no	—
231	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
232	C₂×C₅×D₃	AGL(1,ℤ/8)	1	4	yes	—
233	C₂×C₃×D₅	—	2	4	no	—
234	C₂×C₃×D₅	—	4	2	no	—
235	C₂×C₃×D₅	—	4	2	no	—
236	D₃×D₅	—	4	16	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	Dic₁₅	—	4	2	no	—
241	C₃×Dic₅	—	4	2	no	—
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	C₄×D₄	1	2	yes	—
244	C₂³×D₃	—	10	2	no	—
245	C₂×C₃×D₄	—	5	2	no	—
246	C₂²×C₃×C₄	—	10	2	no	—
247	C₂×#67	—	10	2	no	—
248	C₂²×Dic₃	—	10	2	no	—
249	D₃×D₄	—	5	8	no	—
250	D₃×D₄	—	10	4	no	—
251	C₂×D₁₂	—	5	2	no	—
252	C₂×C₄×D₃	—	10	2	no	—
253	C₂×C₄×D₃	—	10	2	no	—
254	C₂×C₄×D₃	—	10	2	no	—
255	C₂×C₄×D₃	—	20	8	no	—
256	C₂×C₄×D₃	D₂₀	1	2	yes	—
257	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
258	C₃×D₈	—	5	4	no	—
259	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₂²⋊C₄	—	10	2	no	—
263	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
264	#217	—	10	2	no	—
265	#213	—	5	8	no	—
266	(C₂×D₃)⋊C₄	—	10	2	no	—
267	(C₂×D₃)⋊C₄	—	10	2	no	—
268	C₄⋊Dic₃	—	5	2	no	—
269	Dic₃⋊C₄	—	10	2	no	—
270	C₄×Dic₃	D₂₀	1	2	yes	—
271	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
274	D₂₄	—	5	4	no	—
275	D₃×C₈	—	2	2	no	—
276	D₃×C₈	C₄×D₅	1	4	yes	complemented
277	C₂³×C₅	—	3	1	no	—
278	C₂²×D₅	—	2	2	no	—
279	C₂²×D₅	—	6	8	no	—
280	C₂²×D₅	—	6	2	no	—
281	C₂²×D₅	—	12	4	no	—
282	C₂²×D₅	—	12	4	no	—
283	C₂×C₄×C₅	—	3	1	no	—
284	C₂×C₄×C₅	—	3	2	no	—
285	C₂×C₄×C₅	—	3	2	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	6	4	no	—
288	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
289	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
290	C₂×Dic₅	—	2	2	no	—
291	C₂×Dic₅	—	6	2	no	—
292	C₂×Dic₅	—	12	4	no	—
293	D₂₀	—	2	2	no	—
294	D₂₀	—	3	4	no	—
295	D₂₀	—	6	8	no	—
296	D₂₀	—	6	2	no	—
297	D₂₀	C₂×C₄×D₃	1	4	yes	complemented
298	C₄×D₅	—	4	4	no	—
299	C₄×D₅	—	12	4	no	—
300	C₄×D₅	—	12	4	no	—
301	C₄×D₅	—	12	4	no	—
302	C₅×C₈	—	2	1	no	—
303	C₅×C₈	—	3	2	no	—
304	C₅×C₈	—	6	1	no	—
305	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
306	C₂²×D₄	—	15	2	no	—
307	C₂³×C₄	—	30	2	no	—
308	C₂×D₈	—	5	1	no	—
309	C₂×D₈	—	15	8	no	—
310	C₂×D₈	—	15	2	no	—
311	C₂×D₈	—	15	1	no	—
312	C₂²×C₈	—	3	1	no	—
313	C₂²×C₈	—	3	1	no	—
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	15	2	no	—
316	C₄×D₄	—	15	2	no	—
317	C₄×D₄	—	15	2	no	—
318	C₄×D₄	—	30	2	no	—
319	C₄×D₄	—	30	2	no	—
320	C₂×C₄⋊C₄	—	15	2	no	—
321	C₂×C₂²⋊C₄	—	30	2	no	—
322	C₂×C₄²	—	3	1	no	—
323	#106	—	5	1	no	—
324	#106	—	15	2	no	—
325	#106	—	15	1	no	—
326	#102	—	5	2	no	—
327	#102	—	15	2	no	—
328	#102	—	15	2	no	—
329	#102	—	15	2	no	—
330	#97	—	3	1	no	—
331	#97	—	3	1	no	—
332	#97	—	3	1	no	—
333	#97	D₃×D₅	1	1	yes	characteristic, complemented
334	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
336	D₁₅	—	4	4	no	—
337	C₃×D₅	—	4	4	no	—
338	C₅×D₃	#442	1	4	yes	complemented
339	C₂³×C₃	—	10	2	no	—
340	C₂²×D₃	—	10	2	no	—
341	C₂²×D₃	—	10	8	no	—
342	C₂²×D₃	—	20	4	no	—
343	C₂²×D₃	—	20	4	no	—
344	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
345	C₃×D₄	—	5	4	no	—
346	C₃×D₄	—	10	2	no	—
347	C₂×C₃×C₄	—	10	2	no	—
348	C₂×C₃×C₄	—	20	4	no	—
349	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
350	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
351	#67	—	10	8	no	—
352	C₂×Dic₃	—	10	2	no	—
353	C₂×Dic₃	—	20	4	no	—
354	C₂×Dic₃	C₂×D₂₀	1	2	yes	—
355	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
356	D₁₂	—	5	4	no	—
357	D₁₂	—	10	2	no	—
358	C₄×D₃	—	2	4	no	—
359	C₄×D₃	—	20	4	no	—
360	C₄×D₃	—	20	4	no	—
361	C₄×D₃	—	20	4	no	—
362	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
363	C₄×D₃	#709	1	2	yes	—
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	C₂×C₄×D₅	1	2	yes	complemented
366	C₃⋊C₈	—	2	1	no	—
367	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	complemented
368	C₂²×C₅	—	3	4	no	—
369	C₂²×C₅	—	3	2	no	—
370	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
371	C₂×D₅	—	2	4	no	—
372	C₂×D₅	—	4	2	no	—
373	C₂×D₅	—	4	2	no	—
374	C₂×D₅	—	6	4	no	—
375	C₂×D₅	—	12	16	no	—
376	C₂×D₅	—	12	2	no	—
377	C₂×D₅	—	12	2	no	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	3	2	no	—
380	C₄×C₅	—	6	2	no	—
381	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
382	C₄×C₅	D₃×#41	1	1	yes	characteristic
383	Dic₅	—	4	2	no	—
384	Dic₅	—	12	2	no	—
385	C₂⁴	—	30	2	no	—
386	C₂×D₄	—	5	2	no	—
387	C₂×D₄	—	15	8	no	—
388	C₂×D₄	—	15	2	no	—
389	C₂×D₄	—	30	4	no	—
390	C₂×D₄	—	30	2	no	—
391	C₂²×C₄	—	3	1	no	—
392	C₂²×C₄	—	3	2	no	—
393	C₂²×C₄	—	10	2	no	—
394	C₂²×C₄	—	30	2	no	—
395	C₂²×C₄	—	30	2	no	—
396	C₂²×C₄	—	30	2	no	—
397	C₂²×C₄	—	30	2	no	—
398	C₂²×C₄	—	60	8	no	—
399	D₈	—	5	4	no	—
400	D₈	—	15	8	no	—
401	D₈	—	15	4	no	—
402	C₂×C₈	—	3	1	no	—
403	C₂×C₈	—	3	4	no	—
404	C₂×C₈	—	3	1	no	—
405	C₂×C₈	—	6	2	no	—
406	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
407	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
408	C₄⋊C₄	—	5	2	no	—
409	C₄⋊C₄	—	15	2	no	—
410	C₄⋊C₄	—	30	2	no	—
411	C₂²⋊C₄	—	10	2	no	—
412	C₂²⋊C₄	—	30	2	no	—
413	C₂²⋊C₄	—	30	2	no	—
414	C₂²⋊C₄	—	30	2	no	—
415	C₄²	—	3	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
418	C₃×C₅	C₂×#442	1	1	yes	characteristic, complemented, Hall
419	C₂²×C₃	—	10	4	no	—
420	C₂²×C₃	—	20	2	no	—
421	C₂²×C₃	—	20	2	no	—
422	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
423	C₂×D₃	—	10	4	no	—
424	C₂×D₃	—	20	2	no	—
425	C₂×D₃	—	20	2	no	—
426	C₂×D₃	—	20	16	no	—
427	C₂×D₃	C₄×D₂₀	1	2	yes	—
428	C₂×D₃	#4054	1	4	yes	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	20	2	no	—
431	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
432	C₃×C₄	C₂×#709	1	1	yes	characteristic
433	Dic₃	—	2	2	no	—
434	Dic₃	—	20	2	no	—
435	Dic₃	C₄×D₂₀	1	2	yes	—
436	C₂×C₅	—	3	4	no	—
437	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
438	C₂×C₅	D₃×AGL(1,ℤ/8)	1	2	yes	—
439	D₅	—	4	4	no	—
440	D₅	—	12	4	no	—
441	C₂³	—	3	1	no	—
442	C₂³	—	10	2	no	—
443	C₂³	—	30	8	no	—
444	C₂³	—	30	2	no	—
445	C₂³	—	60	4	no	—
446	C₂³	—	60	4	no	—
447	D₄	—	5	4	no	—
448	D₄	—	10	2	no	—
449	D₄	—	15	4	no	—
450	D₄	—	30	8	no	—
451	D₄	—	30	2	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	6	4	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	20	4	no	—
459	C₂×C₄	—	30	2	no	—
460	C₂×C₄	—	60	4	no	—
461	C₂×C₄	—	60	4	no	—
462	C₂×C₄	—	60	4	no	—
463	C₂×C₄	—	60	4	no	—
464	C₂×C₄	D₃×D₂₀	1	2	yes	—
465	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	3	2	no	—
468	C₈	—	6	1	no	—
469	C₈	C₄×D₃×D₅	1	2	yes	complemented
470	C₂×C₃	—	20	4	no	—
471	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
472	C₂×C₃	C₂×#4054	1	2	yes	—
473	D₃	—	20	4	no	—
474	D₃	#65000	1	4	yes	direct product factor
475	C₅	D₃×#442	1	1	yes	characteristic, complemented, Sylow
476	C₂²	—	3	2	no	—
477	C₂²	—	3	4	no	—
478	C₂²	—	10	4	no	—
479	C₂²	—	20	2	no	—
480	C₂²	—	20	2	no	—
481	C₂²	—	30	4	no	—
482	C₂²	—	60	16	no	—
483	C₂²	—	60	2	no	—
484	C₂²	—	60	2	no	—
485	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	3	2	no	—
488	C₄	—	6	2	no	—
489	C₄	—	20	2	no	—
490	C₄	—	60	2	no	—
491	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
492	C₄	D₃×#709	1	1	yes	characteristic
493	C₃	C₂×#65000	1	1	yes	characteristic, complemented, Sylow
494	C₂	—	3	4	no	—
495	C₂	—	20	4	no	—
496	C₂	—	60	4	no	—
497	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
498	C₂	D₃×#4054	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃×D₂₀
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×#97	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×D₃×D₄₀	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#97	D₃×D₅
hypocenter	C₃×C₅	C₂×#442
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. C₄×D₃×D₂₀	C₂	semidirect
3. #11750812	C₂	semidirect
4. C₅×D₃×#97	C₂	semidirect
5. C₃×#65000	C₂	semidirect
6. D₃×#3953	C₂	semidirect
7. #11747799	C₂	semidirect
8. #11747796	C₂	semidirect
9. #11747741	C₂	semidirect
10. D₃×#3949	C₂	semidirect
11. #11747023	C₂	semidirect
16. C₄×D₆₀	C₂²	semidirect
21. C₃×C₄×D₂₀	C₂²	semidirect
24. #91428	C₂²	semidirect
26. Dic₃×D₂₀	C₂²	semidirect
29. D₃×D₄₀	C₄	semidirect
30. C₃×C₅×#97	C₂²	semidirect
31. #91105	C₂²	semidirect
32. #91101	C₂²	semidirect
33. C₅×#815	C₂²	semidirect
34. C₅×#815	C₂²	semidirect
35. C₅×#803	C₂²	semidirect
36. C₃×#3953	C₂²	semidirect
37. C₃×#3949	C₂²	semidirect
38. #90987	C₂²	semidirect
39. #90968	C₂²	semidirect
40. #90965	C₂²	semidirect
52. #65000	D₃	direct (N × H)
65. D₃×D₂₀	C₂×C₄	semidirect
72. D₁₂₀	C₂×C₄	semidirect
78. C₅×D₃×C₈	C₂×C₄	semidirect
81. C₃×D₄₀	C₂×C₄	semidirect
85. #6653	C₂×C₄	semidirect
96. D₃×#97	D₅	semidirect
113. C₄×D₂₀	C₂×D₃	semidirect
117. C₅×#97	C₂×D₃	semidirect
121. #3953	C₂×D₃	semidirect
124. #3949	C₂×D₃	semidirect
136. D₆₀	C₂²×C₄	semidirect
145. C₃×D₂₀	C₂²×C₄	semidirect
152. C₃×C₅×C₈	C₂²×C₄	semidirect
154. C₅×C₃⋊C₈	C₂²×C₄	semidirect
174. C₃×#97	C₂×D₅	semidirect
178. #815	C₂×D₅	semidirect
179. #815	C₂×D₅	semidirect
182. #803	C₂×D₅	semidirect
215. D₄₀	C₄×D₃	semidirect
276. D₃×C₈	C₄×D₅	semidirect
297. D₂₀	C₂×C₄×D₃	semidirect
305. C₅×C₈	C₂×C₄×D₃	semidirect
333. #97	D₃×D₅	semidirect
338. C₅×D₃	#442	semidirect
365. C₃×C₈	C₂×C₄×D₅	semidirect
367. C₃⋊C₈	C₂×C₄×D₅	semidirect
418. C₃×C₅	C₂×#442	semidirect
469. C₈	C₄×D₃×D₅	semidirect
474. D₃	#65000	direct (N × H)
475. C₅	D₃×#442	semidirect
493. C₃	C₂×#65000	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
C₄×D₃×D₂₀	2
#11750812	2
C₅×D₃×#97	2
C₃×#65000	2
D₃×#3953	2
#11747799	2
#11747796	2
#11747741	2
D₃×#3949	2
#11747023	2
C₂×#65000	3
D₃×#442	5

Subgroups — D3×#65000 #14416499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65000 #14416499