Subgroups — C₄×#91275 #14416247

Order 1920.

1000 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×#91275	C₂	1	1	yes	maximal, characteristic
2	C₄×#6769	C₂	1	2	yes	maximal, complemented
3	C₄×D₁₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
7	#11747830	C₂	1	2	yes	maximal, complemented
8	#11747793	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747682	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747643	C₂	1	2	yes	maximal, complemented
11	C₄×#6658	C₂	1	2	yes	maximal, complemented
12	C₄×#4050	—	3	1	no	maximal, Hall
13	C₂×#6769	C₂²	1	2	yes	—
14	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
15	C₄×D₆₀	C₂²	1	2	yes	—
16	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
20	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
21	#91446	—	2	2	no	—
22	C₄×#1203	—	2	2	no	—
23	#91428	C₂²	1	2	yes	—
24	#91403	—	2	2	no	—
25	C₄×#1200	—	2	2	no	—
26	#91338	C₂²	1	2	yes	—
27	Dic₃×Dic₁₀	C₂²	1	2	yes	—
28	C₂×#6658	C₂²	1	2	yes	—
29	#91275	C₄	1	8	yes	direct product factor
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	#91105	C₂²	1	2	yes	—
32	#91102	C₂²	1	1	yes	characteristic
33	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
34	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×#3950	C₂²	1	1	yes	characteristic
37	C₃×#3948	C₂²	1	2	yes	—
38	#90987	C₂²	1	2	yes	—
39	#90971	C₂²	1	2	yes	—
40	#90968	C₂²	1	2	yes	—
41	C₄×#919	—	5	1	no	maximal, Hall
42	C₂×#4050	—	3	1	no	—
43	C₄×#709	—	3	2	no	—
44	C₂×C₄×C₅×C₈	—	3	1	no	—
45	#65402	—	3	2	no	—
46	#65395	—	3	1	no	—
47	C₄×Dic₂₀	—	3	1	no	—
48	C₄×Dic₂₀	D₃	1	1	yes	characteristic, complemented
49	C₄×D₄₀	—	3	1	no	—
50	C₄×D₄₀	—	3	1	no	—
51	C₄×#677	—	3	2	no	—
52	C₄×#677	—	3	2	no	—
53	C₂×D₆₀	C₂³	1	2	yes	—
54	C₂×C₄×D₁₅	—	2	2	no	—
55	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
59	C₂×#1203	—	2	2	no	—
60	C₂×#1200	—	2	2	no	—
61	C₂×#1200	—	2	2	no	—
62	#6769	—	2	4	no	—
63	#6769	C₂×C₄	1	8	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	#6714	—	2	2	no	—
68	C₄⋊Dic₁₅	C₂³	1	2	yes	—
69	D₁₂₀	C₂×C₄	1	4	yes	complemented
70	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
71	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
72	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
75	C₅×D₃×C₈	—	2	2	no	—
76	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
77	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
78	C₃×#683	—	2	2	no	—
79	C₃×C₄×Dic₅	—	2	2	no	—
80	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
81	#6668	—	2	2	no	—
82	#6667	—	2	2	no	—
83	(C₂×D₃)⋊Dic₅	—	2	2	no	—
84	Dic₃×Dic₅	—	2	2	no	—
85	Dic₃×Dic₅	—	2	2	no	—
86	#6658	C₂×C₄	1	8	yes	complemented
87	C₂×#919	—	5	1	no	—
88	C₄×#239	—	5	2	no	—
89	C₃×C₄×Q₁₆	—	5	1	no	—
90	Dic₃×Q₁₆	—	5	1	no	—
91	C₄×#215	—	5	2	no	—
92	#4880	—	5	1	no	—
93	#4872	—	5	1	no	—
94	#4804	—	5	2	no	—
95	#4788	—	5	2	no	—
96	C₄×D₂₄	—	5	1	no	—
97	C₄×D₃×C₈	D₅	1	1	yes	characteristic, complemented
98	C₂×#709	—	3	2	no	—
99	C₂²×C₅×C₈	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₄×C₂²⋊D₅	—	6	2	no	—
103	C₄×C₂²⋊D₅	—	6	2	no	—
104	#4072	—	3	2	no	—
105	C₂×Dic₂₀	C₂×D₃	1	1	yes	characteristic
106	#4050	—	3	8	no	—
107	C₂×D₄₀	—	3	1	no	—
108	C₂×#677	—	3	2	no	—
109	C₄×D₂₀	—	3	2	no	—
110	C₄×D₂₀	—	3	2	no	—
111	#4018	—	6	2	no	—
112	C₄²×D₅	—	6	2	no	—
113	C₄×Dic₁₀	—	3	2	no	—
114	C₄×Dic₁₀	C₂×D₃	1	2	yes	—
115	C₄×C₅×C₈	—	3	1	no	—
116	C₄×C₅×C₈	—	3	1	no	—
117	C₄×C₅×C₈	—	3	1	no	—
118	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
119	#3953	—	3	2	no	—
120	#3953	—	3	2	no	—
121	#3950	—	3	1	no	—
122	#3950	C₂×D₃	1	1	yes	characteristic
123	#3949	—	3	2	no	—
124	#3948	—	3	2	no	—
125	#3948	C₂×D₃	1	2	yes	—
126	C₄×#135	—	15	1	no	Sylow
127	C₂²×D₁₅	—	2	2	no	—
128	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×Dic₁₅	—	2	2	no	—
133	D₆₀	—	2	2	no	—
134	D₆₀	C₂²×C₄	1	4	yes	—
135	C₄×D₁₅	—	4	4	no	—
136	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₄×C₅×D₃	—	2	2	no	—
140	C₄×C₅×D₃	—	2	2	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	C₂×C₃×Dic₅	—	2	2	no	—
145	C₃×Dic₁₀	—	2	2	no	—
146	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
147	#1203	—	2	8	no	—
148	#1200	—	2	8	no	—
149	#1200	—	4	4	no	—
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×#239	—	5	2	no	—
155	C₂×C₃×Q₁₆	—	5	1	no	—
156	C₃×C₄×Q₈	—	5	2	no	—
157	Q₈×Dic₃	—	5	2	no	—
158	C₂×#215	—	5	2	no	—
159	#919	—	5	8	no	—
160	C₂×D₂₄	—	5	1	no	—
161	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
162	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
163	#893	—	5	2	no	—
164	#893	—	10	2	no	—
165	#892	—	5	2	no	—
166	#892	—	10	2	no	—
167	C₄×D₁₂	—	5	2	no	—
168	C₄×D₁₂	—	10	2	no	—
169	C₄²×D₃	—	10	2	no	—
170	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
171	C₃×#107	—	5	1	no	—
172	C₃×#103	—	5	2	no	—
173	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
174	#835	—	5	2	no	—
175	#821	—	5	2	no	—
176	#818	—	5	1	no	—
177	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
178	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
179	#809	—	5	2	no	—
180	#808	—	5	2	no	—
181	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂×C₂²⋊D₅	—	6	2	no	—
186	#709	—	3	8	no	—
187	#709	—	6	4	no	—
188	C₂×D₂₀	—	3	2	no	—
189	C₂×C₄×D₅	—	6	2	no	—
190	C₂×C₄×D₅	—	6	2	no	—
191	C₂×C₄×D₅	—	6	2	no	—
192	C₂×Dic₁₀	C₂²×D₃	1	2	yes	—
193	C₂×C₅×C₈	—	3	1	no	—
194	C₂×C₅×C₈	—	3	4	no	—
195	C₂×C₅×C₈	—	3	1	no	—
196	C₂×C₅×C₈	—	6	2	no	—
197	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₄²×C₅	—	3	1	no	—
200	C₄²×C₅	—	3	1	no	—
201	C₄²×C₅	—	3	1	no	—
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂²⋊Dic₅	—	6	2	no	—
204	#685	—	6	2	no	—
205	#685	—	6	2	no	—
206	C₄⋊Dic₅	—	3	2	no	—
207	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
208	#683	—	2	2	no	—
209	#683	—	6	2	no	—
210	C₄×Dic₅	—	2	2	no	—
211	C₄×Dic₅	—	6	2	no	—
212	C₄×Dic₅	—	6	2	no	—
213	Dic₂₀	C₄×D₃	1	4	yes	complemented
214	D₄₀	—	3	4	no	—
215	#677	—	3	8	no	—
216	C₂×#135	—	15	1	no	—
217	C₄×#41	—	15	2	no	—
218	C₄×Q₁₆	—	5	1	no	—
219	C₄×Q₁₆	—	15	1	no	—
220	C₄×SD₁₆	—	15	2	no	—
221	C₄×SD₁₆	—	15	2	no	—
222	C₄×D₈	—	15	1	no	—
223	C₄×D₈	—	15	1	no	—
224	#427	—	15	1	no	—
225	#416	—	15	2	no	—
226	C₂×C₄×C₈	—	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	—	2	1	no	—
232	C₂×C₅×D₃	—	2	1	no	—
233	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	#135	1	2	yes	complemented
236	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	Dic₁₅	—	4	2	no	—
239	C₃×Dic₅	—	2	4	no	—
240	C₃×Dic₅	—	4	2	no	—
241	C₅×Dic₃	—	2	1	no	—
242	C₅×Dic₃	C₄×D₄	1	2	yes	—
243	C₅×Dic₃	#135	1	2	yes	complemented
244	C₂×C₃×Q₈	—	5	2	no	—
245	#239	—	5	8	no	—
246	#239	—	10	4	no	—
247	C₂×D₁₂	—	5	2	no	—
248	C₂×D₁₂	—	10	2	no	—
249	C₂×C₄×D₃	—	10	2	no	—
250	C₂×C₄×D₃	—	10	2	no	—
251	C₂×C₄×D₃	—	10	2	no	—
252	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
253	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
255	C₃×Q₁₆	—	5	4	no	—
256	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
258	C₃×C₄⋊C₄	—	5	2	no	—
259	C₃×C₄⋊C₄	—	10	2	no	—
260	C₃×C₄²	—	10	2	no	—
261	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
262	#215	—	5	8	no	—
263	(C₂×D₃)⋊C₄	—	10	2	no	—
264	(C₂×D₃)⋊C₄	—	10	2	no	—
265	(C₂×D₃)⋊C₄	—	10	2	no	—
266	C₄⋊Dic₃	—	5	2	no	—
267	C₄⋊Dic₃	—	10	2	no	—
268	C₄×Dic₃	—	10	2	no	—
269	C₄×Dic₃	—	10	2	no	—
270	C₄×Dic₃	D₂₀	1	1	yes	characteristic
271	C₄×Dic₃	D₂₀	1	1	yes	characteristic
272	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
275	D₂₄	—	5	4	no	—
276	D₃×C₈	—	2	2	no	—
277	D₃×C₈	C₄×D₅	1	4	yes	complemented
278	C₂³×C₅	—	3	1	no	—
279	C₂²×D₅	—	6	2	no	—
280	C₂×C₄×C₅	—	3	1	no	—
281	C₂×C₄×C₅	—	3	1	no	—
282	C₂×C₄×C₅	—	3	2	no	—
283	C₂×C₄×C₅	—	3	2	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	6	2	no	—
286	C₂×C₄×C₅	—	6	2	no	—
287	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
290	C₂²⋊D₅	—	6	8	no	—
291	C₂×Dic₅	—	2	2	no	—
292	C₂×Dic₅	—	2	2	no	—
293	C₂×Dic₅	—	6	2	no	—
294	D₂₀	—	3	4	no	—
295	D₂₀	—	6	2	no	—
296	C₄×D₅	—	6	8	no	—
297	C₄×D₅	—	12	4	no	—
298	C₄×D₅	—	12	4	no	—
299	Dic₁₀	—	2	2	no	—
300	Dic₁₀	C₂×C₄×D₃	1	4	yes	—
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	—	3	2	no	—
303	C₅×C₈	—	6	1	no	—
304	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
305	C₂×#41	—	15	2	no	—
306	#135	—	15	8	no	—
307	C₂×Q₁₆	—	5	1	no	—
308	C₂×SD₁₆	—	15	2	no	—
309	C₂×D₈	—	15	1	no	—
310	C₂²×C₈	—	3	1	no	—
311	C₂²×C₈	—	3	1	no	—
312	C₄×Q₈	—	5	2	no	—
313	C₄×Q₈	—	15	2	no	—
314	C₄×D₄	—	15	2	no	—
315	C₄×D₄	—	15	2	no	—
316	C₄×D₄	—	30	2	no	—
317	C₄×D₄	—	30	2	no	—
318	#117	—	15	2	no	—
319	#117	—	30	2	no	—
320	C₂×C₄²	—	3	1	no	—
321	C₂×C₄²	—	30	2	no	—
322	#107	—	5	1	no	—
323	#107	—	15	1	no	—
324	#106	—	15	2	no	—
325	#103	—	5	2	no	—
326	#103	—	15	2	no	—
327	#102	—	15	2	no	—
328	#102	—	15	2	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	—	3	1	no	—
331	C₄×C₈	—	3	1	no	—
332	C₄×C₈	D₃×D₅	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
336	D₁₅	—	4	4	no	—
337	C₅×D₃	—	2	2	no	—
338	C₂²×D₃	—	10	2	no	—
339	C₂²×D₃	C₂×D₂₀	1	1	yes	characteristic
340	C₃×Q₈	—	5	4	no	—
341	C₃×Q₈	—	10	2	no	—
342	C₂×C₃×C₄	—	10	2	no	—
343	C₂×C₃×C₄	—	10	2	no	—
344	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
347	C₂×Dic₃	—	10	2	no	—
348	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
349	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
350	C₂×Dic₃	C₂×D₂₀	1	1	yes	characteristic
351	D₁₂	—	5	4	no	—
352	D₁₂	—	10	8	no	—
353	D₁₂	—	10	2	no	—
354	C₄×D₃	—	2	2	no	—
355	C₄×D₃	—	2	2	no	—
356	C₄×D₃	—	10	8	no	—
357	C₄×D₃	—	20	4	no	—
358	C₄×D₃	—	20	4	no	—
359	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
360	C₄×D₃	#709	1	2	yes	—
361	C₃×C₈	—	2	1	no	—
362	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
363	C₃⋊C₈	—	2	1	no	—
364	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
365	C₂²×C₅	—	3	2	no	—
366	C₂²×C₅	—	6	1	no	—
367	C₂²×C₅	—	6	1	no	—
368	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
369	C₂×D₅	—	6	4	no	—
370	C₂×D₅	—	12	2	no	—
371	C₂×D₅	—	12	2	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	3	2	no	—
374	C₄×C₅	—	3	2	no	—
375	C₄×C₅	—	6	1	no	—
376	C₄×C₅	#919	1	2	yes	complemented
377	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
378	C₄×C₅	D₃×#41	1	1	yes	characteristic
379	Dic₅	—	2	4	no	—
380	Dic₅	—	4	2	no	—
381	Dic₅	—	12	2	no	—
382	#41	—	15	8	no	—
383	#41	—	30	4	no	—
384	C₂×Q₈	—	5	2	no	—
385	C₂×D₄	—	15	2	no	—
386	C₂×D₄	—	30	2	no	—
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	1	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	30	2	no	—
391	C₂²×C₄	—	30	2	no	—
392	C₂²×C₄	—	30	2	no	—
393	Q₁₆	—	5	4	no	—
394	SD₁₆	—	15	8	no	—
395	D₈	—	15	4	no	—
396	C₂×C₈	—	3	1	no	—
397	C₂×C₈	—	3	4	no	—
398	C₂×C₈	—	3	1	no	—
399	C₂×C₈	—	6	2	no	—
400	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
402	C₄⋊C₄	—	5	2	no	—
403	C₄⋊C₄	—	10	2	no	—
404	C₄⋊C₄	—	15	2	no	—
405	C₄⋊C₄	—	30	2	no	—
406	C₂²⋊C₄	—	30	2	no	—
407	C₂²⋊C₄	—	30	2	no	—
408	C₂²⋊C₄	—	30	2	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	3	1	no	—
411	C₄²	—	3	1	no	—
412	C₄²	—	10	2	no	—
413	C₄²	—	30	2	no	—
414	C₄²	—	30	2	no	—
415	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
416	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
417	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	—	2	1	no	—
420	C₂×D₃	—	10	4	no	—
421	C₂×D₃	—	20	2	no	—
422	C₂×D₃	—	20	2	no	—
423	C₂×D₃	C₄×D₂₀	1	2	yes	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	10	4	no	—
426	C₃×C₄	—	20	2	no	—
427	C₃×C₄	#4050	1	2	yes	complemented
428	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
429	C₃×C₄	C₂×#709	1	1	yes	characteristic
430	Dic₃	—	2	1	no	—
431	Dic₃	—	20	2	no	—
432	Dic₃	C₄×D₂₀	1	2	yes	—
433	Dic₃	#4050	1	2	yes	complemented
434	C₂×C₅	—	6	2	no	—
435	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
436	C₂×C₅	C₂×#919	1	1	yes	characteristic
437	C₂×C₅	D₃×#135	1	1	yes	characteristic
438	D₅	—	12	4	no	—
439	C₂³	—	3	1	no	—
440	C₂³	—	30	2	no	—
441	Q₈	—	5	4	no	—
442	Q₈	—	10	2	no	—
443	D₄	—	15	4	no	—
444	D₄	—	30	8	no	—
445	D₄	—	30	2	no	—
446	C₂×C₄	—	3	1	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	2	no	—
449	C₂×C₄	—	3	2	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	—	10	2	no	—
455	C₂×C₄	—	30	8	no	—
456	C₂×C₄	—	30	2	no	—
457	C₂×C₄	—	60	4	no	—
458	C₂×C₄	—	60	4	no	—
459	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
460	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	3	2	no	—
464	C₈	—	6	1	no	—
465	C₈	C₄×D₃×D₅	1	2	yes	—
466	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
467	C₂×C₃	C₂×#4050	1	1	yes	characteristic
468	C₂×C₃	C₂×#4050	1	1	yes	characteristic
469	D₃	—	2	2	no	—
470	D₃	—	20	4	no	—
471	C₅	C₄×#919	1	1	yes	characteristic, complemented, Sylow
472	C₂²	—	3	2	no	—
473	C₂²	—	6	1	no	—
474	C₂²	—	6	1	no	—
475	C₂²	—	30	4	no	—
476	C₂²	—	60	2	no	—
477	C₂²	—	60	2	no	—
478	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	3	2	no	—
481	C₄	—	3	2	no	—
482	C₄	—	6	1	no	—
483	C₄	—	10	4	no	—
484	C₄	—	20	2	no	—
485	C₄	—	60	2	no	—
486	C₄	#91275	1	2	yes	direct product factor
487	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
488	C₄	D₃×#709	1	1	yes	characteristic
489	C₃	C₄×#4050	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	6	2	no	—
491	C₂	—	60	4	no	—
492	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
493	C₂	D₃×#4050	1	1	yes	characteristic
494	C₂	C₂×#91275	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₂₀
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#91275	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₄×#135
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×#6769	C₂	semidirect
3. C₄×D₁₂₀	C₂	semidirect
4. C₄×C₅×D₃×C₈	C₂	semidirect
5. C₃×C₄×Dic₂₀	C₂	semidirect
6. Dic₃×Dic₂₀	C₂	semidirect
7. #11747830	C₂	semidirect
8. #11747793	C₂	semidirect
9. #11747682	C₂	semidirect
10. #11747643	C₂	semidirect
11. C₄×#6658	C₂	semidirect
29. #91275	C₄	direct (N × H)
48. C₄×Dic₂₀	D₃	semidirect
63. #6769	C₂×C₄	semidirect
69. D₁₂₀	C₂×C₄	semidirect
76. C₅×D₃×C₈	C₂×C₄	semidirect
80. C₃×Dic₂₀	C₂×C₄	semidirect
86. #6658	C₂×C₄	semidirect
97. C₄×D₃×C₈	D₅	semidirect
213. Dic₂₀	C₄×D₃	semidirect
235. C₃×C₄×C₅	#135	semidirect
243. C₅×Dic₃	#135	semidirect
277. D₃×C₈	C₄×D₅	semidirect
376. C₄×C₅	#919	semidirect
416. C₃×C₅	C₄×#135	semidirect
427. C₃×C₄	#4050	semidirect
433. Dic₃	#4050	semidirect
471. C₅	C₄×#919	semidirect
486. C₄	#91275	direct (N × H)
489. C₃	C₄×#4050	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91275	2
C₄×#6769	2
C₄×D₁₂₀	2
C₄×C₅×D₃×C₈	2
C₃×C₄×Dic₂₀	2
Dic₃×Dic₂₀	2
#11747830	2
#11747793	2
#11747682	2
#11747643	2
C₄×#6658	2
C₄×#4050	3
C₄×#919	5

Subgroups — C4×#91275 #14416247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91275 #14416247