Subgroups — C₃×#10611319 #14417325

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#65879	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65303	C₂	1	2	yes	maximal, complemented
6	C₃×#65169	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65161	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65074	C₂	1	2	yes	maximal, complemented
9	C₃×#65059	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64978	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611319	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
16	C₃×D₄×Dic₅	C₂²	1	2	yes	complemented
17	C₂×C₃×#686	C₂²	1	2	yes	—
18	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
19	C₂×C₃×#685	—	2	2	no	—
20	C₃×D₅×D₈	C₄	1	8	yes	complemented
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×#676	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4039	C₂²	1	2	yes	complemented
25	C₃×#4038	C₂²	1	2	yes	—
26	C₃×#4027	—	2	2	no	—
27	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
28	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
29	C₃×#4018	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3964	C₂²	1	2	yes	complemented
34	C₃×#3953	C₂²	1	2	yes	complemented
35	C₃×#3950	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3941	C₂²	1	2	yes	complemented
39	C₃×#3940	C₂²	1	2	yes	complemented
40	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
41	C₃×#2948	—	5	1	no	maximal, Hall
42	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
43	#65879	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
45	D₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
46	#65303	C₂×C₃	1	2	yes	complemented
47	#65169	C₂×C₃	1	1	yes	characteristic, complemented
48	#65161	C₂×C₃	1	1	yes	characteristic, complemented
49	#65074	C₂×C₃	1	2	yes	complemented
50	#65059	C₂×C₃	1	2	yes	complemented
51	C₄×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
52	#64978	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₃×D₅	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
57	C₂²×C₃×Dic₅	—	2	2	no	—
58	C₃×D₄×D₅	—	2	4	no	—
59	C₃×D₄×D₅	C₂×C₄	1	8	yes	complemented
60	C₂×C₃×D₂₀	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₂²⋊Dic₅	—	2	2	no	—
71	C₃×#686	C₂×C₄	1	8	yes	complemented
72	C₃×#685	—	2	2	no	—
73	C₃×#685	—	2	2	no	—
74	C₃×#685	—	2	2	no	—
75	C₃×#685	D₄	1	1	yes	characteristic
76	C₃×#685	D₄	1	1	yes	characteristic
77	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
78	C₃×#683	D₄	1	1	yes	characteristic
79	C₃×#683	D₄	1	1	yes	characteristic
80	C₃×C₄×Dic₅	—	2	2	no	—
81	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
85	C₃×#676	—	2	2	no	—
86	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
87	C₂²×C₃×D₈	—	5	1	no	—
88	C₃×#518	—	5	2	no	—
89	C₃×#442	—	5	2	no	—
90	C₃×#442	—	5	2	no	—
91	C₃×C₄×D₈	—	5	1	no	—
92	C₃×C₄×D₈	—	5	1	no	—
93	C₃×C₄×D₈	—	5	1	no	—
94	C₃×C₄×D₈	D₅	1	1	yes	characteristic, complemented
95	C₃×#427	—	5	1	no	—
96	C₃×#418	—	5	2	no	—
97	C₃×#405	—	5	1	no	—
98	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
99	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
101	D₄×Dic₅	C₂²×C₃	1	2	yes	complemented
102	C₂×#686	C₂²×C₃	1	2	yes	—
103	C₄×C₂²⋊D₅	—	2	2	no	—
104	C₂×#685	—	2	2	no	—
105	D₅×D₈	C₃×C₄	1	8	yes	complemented
106	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
107	C₂×#676	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
109	#4039	C₂²×C₃	1	2	yes	complemented
110	#4038	C₂²×C₃	1	2	yes	—
111	#4027	—	2	2	no	—
112	D₅×C₂²⋊C₄	—	2	2	no	—
113	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
114	#4018	C₂²×C₃	1	1	yes	characteristic
115	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₅×#102	C₂²×C₃	1	2	yes	complemented
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
118	#3964	C₂²×C₃	1	2	yes	complemented
119	#3953	C₂²×C₃	1	2	yes	complemented
120	#3950	C₂²×C₃	1	1	yes	characteristic, complemented
121	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
123	#3941	C₂²×C₃	1	2	yes	complemented
124	#3940	C₂²×C₃	1	2	yes	complemented
125	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
126	#2948	—	5	1	no	Sylow
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂²×C₃×D₅	—	2	2	no	—
129	C₂²×C₃×D₅	—	2	8	no	—
130	C₂²×C₃×D₅	—	8	2	no	—
131	C₂²×C₃×D₅	—	8	2	no	—
132	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	8	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₂²⋊D₅	—	2	8	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	8	2	no	—
143	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
146	C₃×D₂₀	—	2	2	no	—
147	C₃×D₂₀	C₂²×C₄	1	4	yes	—
148	C₃×C₄×D₅	—	8	2	no	—
149	C₃×C₄×D₅	—	8	2	no	—
150	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
151	C₃×C₄×D₅	#41	1	2	yes	—
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
154	C₃×#168	—	2	1	no	—
155	C₃×#168	C₂²×C₄	1	2	yes	—
156	C₂²×C₃×D₄	—	5	2	no	—
157	C₂×C₃×D₈	—	5	2	no	—
158	C₂×C₃×D₈	—	5	8	no	—
159	C₂×C₃×D₈	—	5	1	no	—
160	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
161	C₂×C₃×M₁₆	—	5	1	no	—
162	C₂²×C₃×C₈	—	5	1	no	—
163	C₃×C₄×D₄	—	5	2	no	—
164	C₃×C₄×D₄	—	5	2	no	—
165	C₃×C₄×D₄	—	5	2	no	—
166	C₃×C₄×D₄	—	10	2	no	—
167	C₃×C₄×D₄	—	10	2	no	—
168	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
169	C₃×#117	—	5	1	no	—
170	C₃×#117	—	5	2	no	—
171	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
172	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
173	C₃×#107	—	5	1	no	—
174	C₃×#107	C₂×D₅	1	1	yes	characteristic, complemented
175	C₃×#106	—	5	2	no	—
176	C₃×#102	—	5	2	no	—
177	C₃×#102	—	5	2	no	—
178	C₃×#102	—	5	2	no	—
179	C₃×#102	C₂×D₅	1	2	yes	complemented
180	C₃×#97	—	5	1	no	—
181	C₃×#97	—	5	1	no	—
182	C₃×C₄×C₈	—	5	1	no	—
183	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
184	C₂³×D₅	—	2	2	no	—
185	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂×C₂²⋊D₅	—	2	2	no	—
188	C₂²×Dic₅	—	2	2	no	—
189	D₄×D₅	—	2	4	no	—
190	D₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
191	C₂×D₂₀	C₂³×C₃	1	2	yes	—
192	C₂×C₄×D₅	—	2	2	no	—
193	C₂×C₄×D₅	—	2	2	no	—
194	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
195	C₅×D₈	C₂×C₃×C₄	1	4	yes	complemented
196	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂²⋊Dic₅	—	2	2	no	—
202	#686	C₂×C₃×C₄	1	8	yes	complemented
203	#685	—	2	2	no	—
204	#685	—	2	2	no	—
205	#685	—	2	2	no	—
206	#685	C₃×D₄	1	1	yes	characteristic
207	#685	C₃×D₄	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
209	#683	C₃×D₄	1	1	yes	characteristic
210	#683	C₃×D₄	1	1	yes	characteristic
211	C₄×Dic₅	—	2	2	no	—
212	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
213	C₂×#168	C₂³×C₃	1	1	yes	characteristic
214	C₂×#168	C₂³×C₃	1	1	yes	characteristic
215	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
216	#676	—	2	2	no	—
217	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
218	C₂²×D₈	—	5	1	no	—
219	#518	—	5	2	no	—
220	#442	—	5	2	no	—
221	#442	—	5	2	no	—
222	C₄×D₈	—	5	1	no	—
223	C₄×D₈	—	5	1	no	—
224	C₄×D₈	—	5	1	no	—
225	C₄×D₈	C₃×D₅	1	1	yes	characteristic, complemented
226	#427	—	5	1	no	—
227	#418	—	5	2	no	—
228	#405	—	5	1	no	—
229	C₂²×C₃×C₅	—	2	4	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₃×D₅	—	2	1	no	—
234	C₂×C₃×D₅	—	2	1	no	—
235	C₂×C₃×D₅	—	2	4	no	—
236	C₂×C₃×D₅	—	4	2	no	—
237	C₂×C₃×D₅	—	4	2	no	—
238	C₂×C₃×D₅	—	8	8	no	—
239	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
240	C₃×C₄×C₅	—	2	1	no	—
241	C₃×C₄×C₅	—	2	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₃×Dic₅	—	2	1	no	—
246	C₃×Dic₅	—	2	1	no	—
247	C₃×Dic₅	—	4	2	no	—
248	C₃×Dic₅	C₄×D₄	1	2	yes	—
249	C₂⁴×C₃	—	10	2	no	—
250	C₂×C₃×D₄	—	5	8	no	—
251	C₂×C₃×D₄	—	5	2	no	—
252	C₂×C₃×D₄	—	10	4	no	—
253	C₂×C₃×D₄	—	10	2	no	—
254	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
255	C₂²×C₃×C₄	—	2	2	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	10	2	no	—
258	C₂²×C₃×C₄	—	10	2	no	—
259	C₂²×C₃×C₄	—	10	2	no	—
260	C₃×D₈	—	5	8	no	—
261	C₃×D₈	—	5	4	no	—
262	C₃×D₈	C₄×D₅	1	4	yes	complemented
263	C₃×M₁₆	—	10	2	no	—
264	C₂×C₃×C₈	—	5	1	no	—
265	C₂×C₃×C₈	—	5	4	no	—
266	C₂×C₃×C₈	—	5	1	no	—
267	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
269	C₃×C₄⋊C₄	—	5	1	no	—
270	C₃×C₄⋊C₄	—	5	1	no	—
271	C₃×C₄⋊C₄	—	5	2	no	—
272	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₂²⋊C₄	—	5	1	no	—
275	C₃×C₂²⋊C₄	—	5	1	no	—
276	C₃×C₂²⋊C₄	—	10	2	no	—
277	C₃×C₂²⋊C₄	—	10	2	no	—
278	C₃×C₂²⋊C₄	—	10	2	no	—
279	C₃×C₂²⋊C₄	—	10	2	no	—
280	C₃×C₄²	—	5	1	no	—
281	C₃×C₄²	—	10	2	no	—
282	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
283	C₂³×C₅	—	2	2	no	—
284	C₂²×D₅	—	2	2	no	—
285	C₂²×D₅	—	2	8	no	—
286	C₂²×D₅	—	8	2	no	—
287	C₂²×D₅	—	8	2	no	—
288	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₅×D₄	—	2	2	no	—
290	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	8	2	no	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
296	C₂²⋊D₅	—	2	8	no	—
297	C₂×Dic₅	—	2	2	no	—
298	C₂×Dic₅	—	8	2	no	—
299	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
302	D₂₀	—	2	2	no	—
303	D₂₀	C₂²×C₃×C₄	1	4	yes	—
304	C₄×D₅	—	8	2	no	—
305	C₄×D₅	—	8	2	no	—
306	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
307	C₄×D₅	C₃×#41	1	2	yes	—
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
310	#168	—	2	1	no	—
311	#168	C₂²×C₃×C₄	1	2	yes	—
312	C₂²×D₄	—	5	2	no	—
313	C₂×D₈	—	5	2	no	—
314	C₂×D₈	—	5	8	no	—
315	C₂×D₈	—	5	1	no	—
316	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
317	C₂×M₁₆	—	5	1	no	—
318	C₂²×C₈	—	5	1	no	—
319	C₄×D₄	—	5	2	no	—
320	C₄×D₄	—	5	2	no	—
321	C₄×D₄	—	5	2	no	—
322	C₄×D₄	—	10	2	no	—
323	C₄×D₄	—	10	2	no	—
324	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
325	#117	—	5	1	no	—
326	#117	—	5	2	no	—
327	C₂×C₂²⋊C₄	—	10	2	no	—
328	C₂×C₂²⋊C₄	—	10	2	no	—
329	#107	—	5	1	no	—
330	#107	C₂×C₃×D₅	1	1	yes	characteristic, complemented
331	#106	—	5	2	no	—
332	#102	—	5	2	no	—
333	#102	—	5	2	no	—
334	#102	—	5	2	no	—
335	#102	C₂×C₃×D₅	1	2	yes	complemented
336	#97	—	5	1	no	—
337	#97	—	5	1	no	—
338	C₄×C₈	—	5	1	no	—
339	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
340	C₂×C₃×C₅	—	4	4	no	—
341	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
342	C₂×C₃×C₅	#576	1	1	yes	characteristic
343	C₂×C₃×C₅	#576	1	1	yes	characteristic
344	C₃×D₅	—	2	2	no	—
345	C₃×D₅	—	4	4	no	—
346	C₂³×C₃	—	2	2	no	—
347	C₂³×C₃	—	5	1	no	—
348	C₂³×C₃	—	10	8	no	—
349	C₂³×C₃	—	10	2	no	—
350	C₂³×C₃	—	40	2	no	—
351	C₂³×C₃	—	40	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	5	4	no	—
354	C₃×D₄	—	10	8	no	—
355	C₃×D₄	—	10	2	no	—
356	C₃×D₄	C₂×C₄×D₅	1	4	yes	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	5	1	no	—
359	C₂×C₃×C₄	—	5	2	no	—
360	C₂×C₃×C₄	—	5	2	no	—
361	C₂×C₃×C₄	—	5	1	no	—
362	C₂×C₃×C₄	—	5	1	no	—
363	C₂×C₃×C₄	—	8	2	no	—
364	C₂×C₃×C₄	—	10	2	no	—
365	C₂×C₃×C₄	—	40	2	no	—
366	C₂×C₃×C₄	—	40	2	no	—
367	C₂×C₃×C₄	—	40	2	no	—
368	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
369	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
371	C₃×C₈	—	2	1	no	—
372	C₃×C₈	—	5	2	no	—
373	C₃×C₈	—	10	1	no	—
374	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
375	C₂²×C₅	—	2	4	no	—
376	C₂²×C₅	—	4	2	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
379	C₂×D₅	—	2	1	no	—
380	C₂×D₅	—	2	1	no	—
381	C₂×D₅	—	2	4	no	—
382	C₂×D₅	—	4	2	no	—
383	C₂×D₅	—	4	2	no	—
384	C₂×D₅	—	8	8	no	—
385	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
390	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
391	Dic₅	—	2	1	no	—
392	Dic₅	—	2	1	no	—
393	Dic₅	—	4	2	no	—
394	Dic₅	C₃×C₄×D₄	1	2	yes	—
395	C₂⁴	—	10	2	no	—
396	C₂×D₄	—	5	8	no	—
397	C₂×D₄	—	5	2	no	—
398	C₂×D₄	—	10	4	no	—
399	C₂×D₄	—	10	2	no	—
400	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	5	1	no	—
403	C₂²×C₄	—	10	2	no	—
404	C₂²×C₄	—	10	2	no	—
405	C₂²×C₄	—	10	2	no	—
406	D₈	—	5	8	no	—
407	D₈	—	5	4	no	—
408	D₈	C₃×C₄×D₅	1	4	yes	complemented
409	M₁₆	—	10	2	no	—
410	C₂×C₈	—	5	1	no	—
411	C₂×C₈	—	5	4	no	—
412	C₂×C₈	—	5	1	no	—
413	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
414	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
415	C₄⋊C₄	—	5	1	no	—
416	C₄⋊C₄	—	5	1	no	—
417	C₄⋊C₄	—	5	2	no	—
418	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	5	1	no	—
421	C₂²⋊C₄	—	5	1	no	—
422	C₂²⋊C₄	—	10	2	no	—
423	C₂²⋊C₄	—	10	2	no	—
424	C₂²⋊C₄	—	10	2	no	—
425	C₂²⋊C₄	—	10	2	no	—
426	C₄²	—	5	1	no	—
427	C₄²	—	10	2	no	—
428	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
429	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
430	C₂²×C₃	—	2	4	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	4	2	no	—
433	C₂²×C₃	—	5	2	no	—
434	C₂²×C₃	—	10	1	no	—
435	C₂²×C₃	—	10	1	no	—
436	C₂²×C₃	—	10	4	no	—
437	C₂²×C₃	—	20	2	no	—
438	C₂²×C₃	—	20	2	no	—
439	C₂²×C₃	—	40	8	no	—
440	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	4	2	no	—
444	C₃×C₄	—	5	2	no	—
445	C₃×C₄	—	10	1	no	—
446	C₃×C₄	—	10	1	no	—
447	C₃×C₄	—	20	2	no	—
448	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
449	C₃×C₄	D₅×#41	1	1	yes	characteristic
450	C₂×C₅	—	4	4	no	—
451	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
452	C₂×C₅	C₃×#576	1	1	yes	characteristic
453	C₂×C₅	C₃×#576	1	1	yes	characteristic
454	D₅	—	2	2	no	—
455	D₅	—	4	4	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	5	1	no	—
458	C₂³	—	10	8	no	—
459	C₂³	—	10	2	no	—
460	C₂³	—	40	2	no	—
461	C₂³	—	40	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	5	4	no	—
464	D₄	—	10	8	no	—
465	D₄	—	10	2	no	—
466	D₄	C₂×C₃×C₄×D₅	1	4	yes	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	5	1	no	—
469	C₂×C₄	—	5	2	no	—
470	C₂×C₄	—	5	2	no	—
471	C₂×C₄	—	5	1	no	—
472	C₂×C₄	—	5	1	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	10	2	no	—
475	C₂×C₄	—	40	2	no	—
476	C₂×C₄	—	40	2	no	—
477	C₂×C₄	—	40	2	no	—
478	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
479	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
480	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
481	C₈	—	2	1	no	—
482	C₈	—	5	2	no	—
483	C₈	—	10	1	no	—
484	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
485	C₂×C₃	—	4	4	no	—
486	C₂×C₃	—	10	2	no	—
487	C₂×C₃	—	20	4	no	—
488	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
489	C₂×C₃	#66091	1	1	yes	characteristic
490	C₂×C₃	#66103	1	1	yes	characteristic
491	C₅	C₃×#2948	1	1	yes	characteristic, complemented, Sylow
492	C₂²	—	2	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	5	2	no	—
496	C₂²	—	10	1	no	—
497	C₂²	—	10	1	no	—
498	C₂²	—	10	4	no	—
499	C₂²	—	20	2	no	—
500	C₂²	—	20	2	no	—
501	C₂²	—	40	8	no	—
502	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	4	2	no	—
506	C₄	—	5	2	no	—
507	C₄	—	10	1	no	—
508	C₄	—	10	1	no	—
509	C₄	—	20	2	no	—
510	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
511	C₄	C₃×D₅×#41	1	1	yes	characteristic
512	C₃	#10611319	1	1	yes	characteristic, direct product factor, Sylow
513	C₂	—	4	4	no	—
514	C₂	—	10	2	no	—
515	C₂	—	20	4	no	—
516	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
517	C₂	C₃×#66091	1	1	yes	characteristic
518	C₂	C₃×#66103	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×D₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₅×D₈	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×D₈	D₅
hypocenter	C₅	C₃×#2948
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₃×#65879	C₂	semidirect
3. C₃×C₄×C₅×D₈	C₂	semidirect
4. C₃×D₈×Dic₅	C₂	semidirect
5. C₃×#65303	C₂	semidirect
6. C₃×#65169	C₂	semidirect
7. C₃×#65161	C₂	semidirect
8. C₃×#65074	C₂	semidirect
9. C₃×#65059	C₂	semidirect
10. C₃×C₄×D₄₀	C₂	semidirect
11. C₃×#64978	C₂	semidirect
12. #10611319	C₃	direct (N × H)
15. C₃×C₄×C₅×D₄	C₂²	semidirect
16. C₃×D₄×Dic₅	C₂²	semidirect
20. C₃×D₅×D₈	C₄	semidirect
24. C₃×#4039	C₂²	semidirect
28. C₃×C₄×D₂₀	C₂²	semidirect
30. C₃×C₅×#107	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₄×C₅×C₈	C₂²	semidirect
33. C₃×#3964	C₂²	semidirect
34. C₃×#3953	C₂²	semidirect
35. C₃×#3950	C₂²	semidirect
36. C₃×#3947	C₂²	semidirect
37. C₃×C₈×Dic₅	C₂²	semidirect
38. C₃×#3941	C₂²	semidirect
39. C₃×#3940	C₂²	semidirect
40. C₃×#3935	C₂²	semidirect
43. #65879	C₂×C₃	semidirect
44. C₄×C₅×D₈	C₂×C₃	semidirect
45. D₈×Dic₅	C₂×C₃	semidirect
46. #65303	C₂×C₃	semidirect
47. #65169	C₂×C₃	semidirect
48. #65161	C₂×C₃	semidirect
49. #65074	C₂×C₃	semidirect
50. #65059	C₂×C₃	semidirect
51. C₄×D₄₀	C₂×C₃	semidirect
52. #64978	C₂×C₃	semidirect
59. C₃×D₄×D₅	C₂×C₄	semidirect
64. C₃×C₅×D₈	C₂×C₄	semidirect
71. C₃×#686	C₂×C₄	semidirect
84. C₃×D₄₀	C₂×C₄	semidirect
86. C₃×C₈×D₅	C₂×C₄	semidirect
94. C₃×C₄×D₈	D₅	semidirect
100. C₄×C₅×D₄	C₂²×C₃	semidirect
101. D₄×Dic₅	C₂²×C₃	semidirect
105. D₅×D₈	C₃×C₄	semidirect
109. #4039	C₂²×C₃	semidirect
113. C₄×D₂₀	C₂²×C₃	semidirect
115. C₅×#107	C₂²×C₃	semidirect
116. C₅×#102	C₂²×C₃	semidirect
117. C₄×C₅×C₈	C₂²×C₃	semidirect
118. #3964	C₂²×C₃	semidirect
119. #3953	C₂²×C₃	semidirect
120. #3950	C₂²×C₃	semidirect
121. #3947	C₂²×C₃	semidirect
122. C₈×Dic₅	C₂²×C₃	semidirect
123. #3941	C₂²×C₃	semidirect
124. #3940	C₂²×C₃	semidirect
125. #3935	C₂²×C₃	semidirect
168. C₃×C₄×D₄	C₂×D₅	semidirect
174. C₃×#107	C₂×D₅	semidirect
179. C₃×#102	C₂×D₅	semidirect
183. C₃×C₄×C₈	C₂×D₅	semidirect
190. D₄×D₅	C₂×C₃×C₄	semidirect
195. C₅×D₈	C₂×C₃×C₄	semidirect
202. #686	C₂×C₃×C₄	semidirect
215. D₄₀	C₂×C₃×C₄	semidirect
217. C₈×D₅	C₂×C₃×C₄	semidirect
225. C₄×D₈	C₃×D₅	semidirect
262. C₃×D₈	C₄×D₅	semidirect
324. C₄×D₄	C₂×C₃×D₅	semidirect
330. #107	C₂×C₃×D₅	semidirect
335. #102	C₂×C₃×D₅	semidirect
339. C₄×C₈	C₂×C₃×D₅	semidirect
408. D₈	C₃×C₄×D₅	semidirect
429. C₃×C₅	#2948	semidirect
491. C₅	C₃×#2948	semidirect
512. C₃	#10611319	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×D₈	2
C₃×#65879	2
C₃×C₄×C₅×D₈	2
C₃×D₈×Dic₅	2
C₃×#65303	2
C₃×#65169	2
C₃×#65161	2
C₃×#65074	2
C₃×#65059	2
C₃×C₄×D₄₀	2
C₃×#64978	2
#10611319	3
C₃×#2948	5

Subgroups — C3×#10611319 #14417325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611319 #14417325