Subgroups — C₃×#10613602 #14439280

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4064	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4060	C₂	1	2	yes	maximal, complemented
3	C₃×#66059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65480	C₂	1	2	yes	maximal, complemented
7	C₃×#65457	C₂	1	2	yes	maximal, complemented
8	C₃×#65375	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65347	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64996	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613602	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₃×#4093	C₂²	1	1	yes	characteristic
21	C₃×#4093	C₂²	1	2	yes	complemented
22	C₂×C₃×#689	C₂²	1	2	yes	complemented
23	C₂×C₃×#688	C₂²	1	2	yes	—
24	C₂×C₃×#688	C₂²	1	2	yes	complemented
25	C₃×#4082	C₂²	1	1	yes	characteristic
26	C₂×C₃×#686	C₂²	1	2	yes	—
27	C₃×#4064	—	2	8	no	—
28	C₃×#4060	—	2	8	no	—
29	C₂×C₃×D₄₀	C₂²	1	2	yes	—
30	C₂×C₃×#677	C₂²	1	2	yes	complemented
31	C₂×C₃×#676	C₂²	1	2	yes	—
32	C₃×#4041	—	2	2	no	—
33	C₃×#4039	—	2	2	no	—
34	C₃×#4031	—	2	2	no	—
35	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
36	C₃×#4021	C₂²	1	1	yes	characteristic
37	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
41	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3153	—	5	1	no	maximal, Hall
43	C₂×#4064	C₂×C₃	1	2	yes	complemented
44	C₂×#4060	C₂×C₃	1	2	yes	complemented
45	#66059	C₂×C₃	1	1	yes	characteristic, complemented
46	D₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
48	#65480	C₂×C₃	1	2	yes	complemented
49	#65457	C₂×C₃	1	2	yes	complemented
50	#65375	C₂×C₃	1	1	yes	characteristic, complemented
51	#65347	C₂×C₃	1	1	yes	characteristic, complemented
52	#65001	C₂×C₃	1	1	yes	characteristic, complemented
53	#64996	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂³×C₃×D₅	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
59	C₃×#713	—	2	4	no	—
60	C₃×#713	—	2	4	no	—
61	C₃×Q₈×D₅	—	2	4	no	—
62	C₃×D₄×D₅	—	2	4	no	—
63	C₂×C₃×D₂₀	—	2	2	no	—
64	C₂×C₃×D₂₀	—	2	2	no	—
65	C₂×C₃×D₂₀	C₂³	1	2	yes	—
66	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	—	2	1	no	—
68	C₂×C₃×C₄×D₅	—	2	2	no	—
69	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
70	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₁₀	—	2	1	no	—
72	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
73	C₃×C₅×Q₁₆	—	2	4	no	—
74	C₃×C₅×SD₁₆	—	2	4	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₂²⋊Dic₅	—	2	2	no	—
80	C₃×#689	—	2	4	no	—
81	C₃×#688	—	2	4	no	—
82	C₃×#688	—	2	4	no	—
83	C₃×#686	—	2	4	no	—
84	C₃×#685	—	2	2	no	—
85	C₃×#685	—	2	2	no	—
86	C₃×#685	—	2	4	no	—
87	C₃×C₄×Dic₅	D₄	1	2	yes	—
88	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×#168	C₂³	1	2	yes	—
90	C₃×D₄₀	—	2	4	no	—
91	C₃×#677	—	2	4	no	—
92	C₃×#676	D₄	1	8	yes	complemented
93	C₂×C₃×#137	—	5	2	no	—
94	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
95	C₃×#532	—	5	1	no	—
96	C₂×C₃×#124	—	5	1	no	—
97	C₃×#497	—	5	1	no	—
98	C₃×#497	D₅	1	1	yes	characteristic, complemented
99	C₃×#496	—	5	1	no	—
100	C₃×#496	—	5	1	no	—
101	C₃×#495	—	5	2	no	—
102	C₃×#495	—	5	2	no	—
103	C₃×C₄×M₁₆	—	5	1	no	—
104	C₂×#713	C₂²×C₃	1	2	yes	—
105	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
109	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×#124	C₂²×C₃	1	1	yes	characteristic
111	#4093	C₂²×C₃	1	1	yes	characteristic
112	#4093	C₂²×C₃	1	2	yes	complemented
113	C₂×#689	C₂²×C₃	1	2	yes	complemented
114	C₂×#688	C₂²×C₃	1	2	yes	—
115	C₂×#688	C₂²×C₃	1	2	yes	complemented
116	#4082	C₂²×C₃	1	1	yes	characteristic
117	C₂×#686	C₂²×C₃	1	2	yes	—
118	#4064	—	2	8	no	—
119	#4060	—	2	8	no	—
120	C₂×D₄₀	C₂²×C₃	1	2	yes	—
121	C₂×#677	C₂²×C₃	1	2	yes	complemented
122	C₂×#676	C₂²×C₃	1	2	yes	—
123	#4041	—	2	2	no	—
124	#4039	—	2	2	no	—
125	#4031	—	2	2	no	—
126	D₅×C₂²⋊C₄	—	2	2	no	—
127	#4021	C₂²×C₃	1	1	yes	characteristic
128	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
130	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
132	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
133	#3153	—	5	1	no	Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×D₅	—	2	1	no	—
136	C₂²×C₃×D₅	—	2	2	no	—
137	C₂²×C₃×D₅	—	4	4	no	—
138	C₂²×C₃×D₅	—	4	2	no	—
139	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₂²⋊D₅	—	4	2	no	—
149	C₂×C₃×Dic₅	—	2	1	no	—
150	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
152	C₃×D₂₀	—	2	2	no	—
153	C₃×D₂₀	—	2	2	no	—
154	C₃×D₂₀	—	2	2	no	—
155	C₃×D₂₀	—	4	4	no	—
156	C₃×D₂₀	—	4	4	no	—
157	C₃×C₄×D₅	—	4	2	no	—
158	C₃×C₄×D₅	—	4	2	no	—
159	C₃×C₄×D₅	—	4	4	no	—
160	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
161	C₃×Dic₁₀	—	2	2	no	—
162	C₃×Dic₁₀	—	4	2	no	—
163	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
164	C₃×#168	C₂×D₄	1	4	yes	—
165	C₂×C₃×#41	—	5	2	no	—
166	C₂²×C₃×Q₈	—	5	1	no	—
167	C₂²×C₃×D₄	—	5	1	no	—
168	C₃×#137	—	10	8	no	—
169	C₃×AGL(1,ℤ/8)	—	10	8	no	—
170	C₂×C₃×Q₁₆	—	5	2	no	—
171	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	complemented
172	C₂×C₃×SD₁₆	—	5	2	no	—
173	C₂×C₃×SD₁₆	—	5	2	no	—
174	C₂×C₃×SD₁₆	—	5	2	no	—
175	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
176	C₂×C₃×D₈	—	5	2	no	—
177	C₂×C₃×D₈	—	5	2	no	—
178	C₂×C₃×M₁₆	—	5	2	no	—
179	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
180	C₃×#127	—	5	1	no	—
181	C₃×#124	—	5	1	no	—
182	C₃×#124	—	5	2	no	—
183	C₃×#124	—	5	1	no	—
184	C₃×#124	—	5	1	no	—
185	C₃×#124	—	10	2	no	—
186	C₃×#124	C₂×D₅	1	1	yes	characteristic
187	C₃×#121	—	10	2	no	—
188	C₃×C₄×D₄	—	10	2	no	—
189	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
190	C₂×C₃×C₄²	—	5	1	no	—
191	C₃×#97	—	5	1	no	—
192	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
193	C₃×C₄×C₈	—	5	2	no	—
194	C₂³×D₅	—	2	1	no	—
195	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
197	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₂²⋊D₅	—	2	1	no	—
199	#713	—	2	4	no	—
200	#713	—	2	4	no	—
201	Q₈×D₅	—	2	4	no	—
202	D₄×D₅	—	2	4	no	—
203	C₂×D₂₀	—	2	2	no	—
204	C₂×D₂₀	—	2	2	no	—
205	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
206	C₂×D₂₀	C₂³×C₃	1	2	yes	—
207	C₂×C₄×D₅	—	2	1	no	—
208	C₂×C₄×D₅	—	2	2	no	—
209	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
210	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×Dic₁₀	—	2	1	no	—
212	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
213	C₅×Q₁₆	—	2	4	no	—
214	C₅×SD₁₆	—	2	4	no	—
215	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
216	C₅×C₄⋊C₄	—	2	2	no	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
219	C₂²⋊Dic₅	—	2	2	no	—
220	#689	—	2	4	no	—
221	#688	—	2	4	no	—
222	#688	—	2	4	no	—
223	#686	—	2	4	no	—
224	#685	—	2	2	no	—
225	#685	—	2	2	no	—
226	#685	—	2	4	no	—
227	C₄×Dic₅	C₃×D₄	1	2	yes	—
228	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
229	C₂×#168	C₂³×C₃	1	2	yes	—
230	D₄₀	—	2	4	no	—
231	#677	—	2	4	no	—
232	#676	C₃×D₄	1	8	yes	complemented
233	C₂×#137	—	5	2	no	—
234	C₂×AGL(1,ℤ/8)	—	5	2	no	—
235	#532	—	5	1	no	—
236	C₂×#124	—	5	1	no	—
237	#497	—	5	1	no	—
238	#497	C₃×D₅	1	1	yes	characteristic, complemented
239	#496	—	5	1	no	—
240	#496	—	5	1	no	—
241	#495	—	5	2	no	—
242	#495	—	5	2	no	—
243	C₄×M₁₆	—	5	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×D₅	—	2	2	no	—
248	C₂×C₃×D₅	—	4	2	no	—
249	C₂×C₃×D₅	—	4	1	no	—
250	C₂×C₃×D₅	—	4	4	no	—
251	C₂×C₃×D₅	—	4	2	no	—
252	C₂×C₃×D₅	—	8	4	no	—
253	C₂×C₃×D₅	#127	1	2	yes	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
258	C₃×Dic₅	—	2	2	no	—
259	C₃×Dic₅	—	4	1	no	—
260	C₃×Dic₅	#127	1	2	yes	—
261	C₂⁴×C₃	—	10	1	no	—
262	C₃×#41	—	10	4	no	—
263	C₃×#41	—	10	4	no	—
264	C₂×C₃×Q₈	—	5	1	no	—
265	C₂×C₃×Q₈	—	10	1	no	—
266	C₂×C₃×Q₈	—	10	4	no	—
267	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
269	C₂×C₃×D₄	—	5	1	no	—
270	C₂×C₃×D₄	—	5	2	no	—
271	C₂×C₃×D₄	—	10	2	no	—
272	C₂×C₃×D₄	—	10	4	no	—
273	C₂×C₃×D₄	—	10	1	no	—
274	C₂×C₃×D₄	—	10	2	no	—
275	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	—	5	1	no	—
277	C₂²×C₃×C₄	—	5	2	no	—
278	C₂²×C₃×C₄	—	10	2	no	—
279	C₂²×C₃×C₄	—	10	1	no	—
280	C₃×Q₁₆	—	2	4	no	—
281	C₃×Q₁₆	—	10	4	no	—
282	C₃×SD₁₆	—	2	4	no	—
283	C₃×SD₁₆	—	10	4	no	—
284	C₃×SD₁₆	—	10	4	no	—
285	C₃×SD₁₆	—	10	4	no	—
286	C₃×D₈	—	10	4	no	—
287	C₃×D₈	—	10	4	no	—
288	C₃×M₁₆	—	5	8	no	—
289	C₂×C₃×C₈	—	5	2	no	—
290	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	—	10	2	no	—
294	C₃×C₂²⋊C₄	—	10	4	no	—
295	C₃×C₂²⋊C₄	—	10	2	no	—
296	C₃×C₂²⋊C₄	—	10	2	no	—
297	C₃×C₄²	—	5	2	no	—
298	C₃×C₄²	—	5	1	no	—
299	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
300	C₂³×C₅	—	2	1	no	—
301	C₂²×D₅	—	2	1	no	—
302	C₂²×D₅	—	2	2	no	—
303	C₂²×D₅	—	4	4	no	—
304	C₂²×D₅	—	4	2	no	—
305	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
306	C₅×Q₈	—	2	2	no	—
307	C₅×Q₈	—	2	2	no	—
308	C₅×Q₈	—	2	2	no	—
309	C₅×D₄	—	2	2	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
313	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
314	C₂²⋊D₅	—	4	2	no	—
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
317	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
318	D₂₀	—	2	2	no	—
319	D₂₀	—	2	2	no	—
320	D₂₀	—	2	2	no	—
321	D₂₀	—	4	4	no	—
322	D₂₀	—	4	4	no	—
323	C₄×D₅	—	4	2	no	—
324	C₄×D₅	—	4	2	no	—
325	C₄×D₅	—	4	4	no	—
326	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
327	Dic₁₀	—	2	2	no	—
328	Dic₁₀	—	4	2	no	—
329	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
330	#168	C₂×C₃×D₄	1	4	yes	—
331	C₂×#41	—	5	2	no	—
332	C₂²×Q₈	—	5	1	no	—
333	C₂²×D₄	—	5	1	no	—
334	#137	—	10	8	no	—
335	AGL(1,ℤ/8)	—	10	8	no	—
336	C₂×Q₁₆	—	5	2	no	—
337	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	complemented
338	C₂×SD₁₆	—	5	2	no	—
339	C₂×SD₁₆	—	5	2	no	—
340	C₂×SD₁₆	—	5	2	no	—
341	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
342	C₂×D₈	—	5	2	no	—
343	C₂×D₈	—	5	2	no	—
344	C₂×M₁₆	—	5	2	no	—
345	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
346	#127	—	5	1	no	—
347	#124	—	5	1	no	—
348	#124	—	5	2	no	—
349	#124	—	5	1	no	—
350	#124	—	5	1	no	—
351	#124	—	10	2	no	—
352	#124	C₂×C₃×D₅	1	1	yes	characteristic
353	#121	—	10	2	no	—
354	C₄×D₄	—	10	2	no	—
355	C₂×C₂²⋊C₄	—	10	2	no	—
356	C₂×C₄²	—	5	1	no	—
357	#97	—	5	1	no	—
358	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
359	C₄×C₈	—	5	2	no	—
360	C₂×C₃×C₅	—	8	1	no	—
361	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
362	C₂×C₃×C₅	#575	1	2	yes	—
363	C₃×D₅	—	2	2	no	—
364	C₃×D₅	—	8	2	no	—
365	C₃×D₅	—	8	1	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂³×C₃	—	5	1	no	—
368	C₂³×C₃	—	10	1	no	—
369	C₂³×C₃	—	10	2	no	—
370	C₂³×C₃	—	20	2	no	—
371	C₂³×C₃	—	20	4	no	—
372	C₃×Q₈	—	2	2	no	—
373	C₃×Q₈	—	2	2	no	—
374	C₃×Q₈	—	2	2	no	—
375	C₃×Q₈	—	10	2	no	—
376	C₃×Q₈	—	20	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	10	2	no	—
379	C₃×D₄	—	10	2	no	—
380	C₃×D₄	—	10	2	no	—
381	C₃×D₄	—	20	4	no	—
382	C₃×D₄	—	20	4	no	—
383	C₃×D₄	—	20	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	5	1	no	—
387	C₂×C₃×C₄	—	5	4	no	—
388	C₂×C₃×C₄	—	5	2	no	—
389	C₂×C₃×C₄	—	10	1	no	—
390	C₂×C₃×C₄	—	20	2	no	—
391	C₂×C₃×C₄	—	20	4	no	—
392	C₂×C₃×C₄	—	20	2	no	—
393	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
394	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
395	C₃×C₈	—	5	4	no	—
396	C₃×C₈	D₄×D₅	1	4	yes	—
397	C₂²×C₅	—	4	2	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
400	C₂×D₅	—	2	2	no	—
401	C₂×D₅	—	4	4	no	—
402	C₂×D₅	—	4	2	no	—
403	C₂×D₅	—	4	2	no	—
404	C₂×D₅	—	4	1	no	—
405	C₂×D₅	—	8	4	no	—
406	C₂×D₅	C₃×#127	1	2	yes	—
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
411	Dic₅	—	2	2	no	—
412	Dic₅	—	4	1	no	—
413	Dic₅	C₃×#127	1	2	yes	—
414	C₂⁴	—	10	1	no	—
415	#41	—	10	4	no	—
416	#41	—	10	4	no	—
417	C₂×Q₈	—	5	1	no	—
418	C₂×Q₈	—	10	1	no	—
419	C₂×Q₈	—	10	4	no	—
420	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
421	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
422	C₂×D₄	—	5	1	no	—
423	C₂×D₄	—	5	2	no	—
424	C₂×D₄	—	10	2	no	—
425	C₂×D₄	—	10	4	no	—
426	C₂×D₄	—	10	1	no	—
427	C₂×D₄	—	10	2	no	—
428	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	2	no	—
431	C₂²×C₄	—	10	2	no	—
432	C₂²×C₄	—	10	1	no	—
433	Q₁₆	—	2	4	no	—
434	Q₁₆	—	10	4	no	—
435	SD₁₆	—	2	4	no	—
436	SD₁₆	—	10	4	no	—
437	SD₁₆	—	10	4	no	—
438	SD₁₆	—	10	4	no	—
439	D₈	—	10	4	no	—
440	D₈	—	10	4	no	—
441	M₁₆	—	5	8	no	—
442	C₂×C₈	—	5	2	no	—
443	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
444	C₄⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	10	2	no	—
447	C₂²⋊C₄	—	10	4	no	—
448	C₂²⋊C₄	—	10	2	no	—
449	C₂²⋊C₄	—	10	2	no	—
450	C₄²	—	5	2	no	—
451	C₄²	—	5	1	no	—
452	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
453	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	4	1	no	—
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	—	5	2	no	—
457	C₂²×C₃	—	10	2	no	—
458	C₂²×C₃	—	20	2	no	—
459	C₂²×C₃	—	20	1	no	—
460	C₂²×C₃	—	20	4	no	—
461	C₂²×C₃	—	20	2	no	—
462	C₂²×C₃	—	40	4	no	—
463	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
464	C₃×C₄	—	2	2	no	—
465	C₃×C₄	—	4	2	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	5	2	no	—
468	C₃×C₄	—	10	2	no	—
469	C₃×C₄	—	20	1	no	—
470	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
471	C₂×C₅	—	8	1	no	—
472	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
473	C₂×C₅	C₃×#575	1	2	yes	—
474	D₅	—	2	2	no	—
475	D₅	—	8	1	no	—
476	D₅	—	8	2	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	5	1	no	—
479	C₂³	—	10	1	no	—
480	C₂³	—	10	2	no	—
481	C₂³	—	20	2	no	—
482	C₂³	—	20	4	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	10	2	no	—
487	Q₈	—	20	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	10	2	no	—
490	D₄	—	10	2	no	—
491	D₄	—	10	2	no	—
492	D₄	—	20	4	no	—
493	D₄	—	20	4	no	—
494	D₄	—	20	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	5	4	no	—
499	C₂×C₄	—	5	2	no	—
500	C₂×C₄	—	10	1	no	—
501	C₂×C₄	—	20	2	no	—
502	C₂×C₄	—	20	4	no	—
503	C₂×C₄	—	20	2	no	—
504	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
505	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
506	C₈	—	5	4	no	—
507	C₈	C₃×D₄×D₅	1	4	yes	—
508	C₂×C₃	—	8	1	no	—
509	C₂×C₃	—	10	2	no	—
510	C₂×C₃	—	40	1	no	—
511	C₂×C₃	—	40	2	no	—
512	C₂×C₃	D₅×#127	1	1	yes	characteristic
513	C₂×C₃	#66111	1	2	yes	—
514	C₅	C₃×#3153	1	1	yes	characteristic, complemented, Sylow
515	C₂²	—	4	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	5	2	no	—
518	C₂²	—	10	2	no	—
519	C₂²	—	20	4	no	—
520	C₂²	—	20	2	no	—
521	C₂²	—	20	2	no	—
522	C₂²	—	20	1	no	—
523	C₂²	—	40	4	no	—
524	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	5	2	no	—
529	C₄	—	10	2	no	—
530	C₄	—	20	1	no	—
531	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
532	C₃	#10613602	1	1	yes	characteristic, direct product factor, Sylow
533	C₂	—	8	1	no	—
534	C₂	—	10	2	no	—
535	C₂	—	40	1	no	—
536	C₂	—	40	2	no	—
537	C₂	C₃×D₅×#127	1	1	yes	characteristic
538	C₂	C₃×#66111	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#497	D₅
hypocenter	C₅	C₃×#3153
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4064	C₂	semidirect
2. C₂×C₃×#4060	C₂	semidirect
3. C₃×#66059	C₂	semidirect
4. C₃×D₅×#124	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×#65480	C₂	semidirect
7. C₃×#65457	C₂	semidirect
8. C₃×#65375	C₂	semidirect
9. C₃×#65347	C₂	semidirect
10. C₃×#65001	C₂	semidirect
11. C₃×#64996	C₂	semidirect
12. #10613602	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×#4093	C₂²	semidirect
22. C₂×C₃×#689	C₂²	semidirect
24. C₂×C₃×#688	C₂²	semidirect
30. C₂×C₃×#677	C₂²	semidirect
37. C₃×#4020	C₂²	semidirect
39. C₃×C₅×#97	C₂²	semidirect
40. C₃×C₈×Dic₅	C₂²	semidirect
41. C₃×#3935	C₂²	semidirect
43. C₂×#4064	C₂×C₃	semidirect
44. C₂×#4060	C₂×C₃	semidirect
45. #66059	C₂×C₃	semidirect
46. D₅×#124	C₂×C₃	semidirect
47. C₅×#497	C₂×C₃	semidirect
48. #65480	C₂×C₃	semidirect
49. #65457	C₂×C₃	semidirect
50. #65375	C₂×C₃	semidirect
51. #65347	C₂×C₃	semidirect
52. #65001	C₂×C₃	semidirect
53. #64996	C₂×C₃	semidirect
92. C₃×#676	D₄	semidirect
98. C₃×#497	D₅	semidirect
107. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
109. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
112. #4093	C₂²×C₃	semidirect
113. C₂×#689	C₂²×C₃	semidirect
115. C₂×#688	C₂²×C₃	semidirect
121. C₂×#677	C₂²×C₃	semidirect
128. #4020	C₂²×C₃	semidirect
130. C₅×#97	C₂²×C₃	semidirect
131. C₈×Dic₅	C₂²×C₃	semidirect
132. #3935	C₂²×C₃	semidirect
171. C₂×C₃×Q₁₆	C₂×D₅	semidirect
179. C₃×C₄⋊Q₈	C₂×D₅	semidirect
192. C₃×#97	C₂×D₅	semidirect
232. #676	C₃×D₄	semidirect
238. #497	C₃×D₅	semidirect
337. C₂×Q₁₆	C₂×C₃×D₅	semidirect
345. C₄⋊Q₈	C₂×C₃×D₅	semidirect
358. #97	C₂×C₃×D₅	semidirect
453. C₃×C₅	#3153	semidirect
514. C₅	C₃×#3153	semidirect
532. C₃	#10613602	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×#4064	2
C₂×C₃×#4060	2
C₃×#66059	2
C₃×D₅×#124	2
C₃×C₅×#497	2
C₃×#65480	2
C₃×#65457	2
C₃×#65375	2
C₃×#65347	2
C₃×#65001	2
C₃×#64996	2
#10613602	3
C₃×#3153	5

Subgroups — C3×#10613602 #14439280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613602 #14439280