Subgroups — C₃×D₅×#578 #14510119

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#578	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66172	C₂	1	2	yes	maximal, complemented
4	C₃×#66113	C₂	1	6	yes	maximal, complemented
5	C₃×D₅×#137	C₂	1	6	yes	maximal, complemented
6	C₃×#66105	C₂	1	3	yes	maximal, complemented
7	C₃×D₅×#135	C₂	1	3	yes	maximal, complemented
8	C₃×#66100	C₂	1	3	yes	maximal, complemented
9	C₂×C₃×D₅×Q₁₆	C₂	1	3	yes	maximal, complemented
10	C₃×#66087	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#578	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	complemented
14	C₃×#4150	—	2	6	no	—
15	C₃×#4150	C₂²	1	6	yes	complemented
16	C₃×#4150	C₂²	1	2	yes	complemented
17	C₃×D₅×#41	—	2	6	no	—
18	C₃×D₅×#41	C₂²	1	6	yes	—
19	C₃×D₅×#41	C₂²	1	1	yes	characteristic
20	C₃×#4147	—	2	2	no	—
21	C₃×#4147	C₂²	1	6	yes	complemented
22	C₂×C₃×Q₈×D₅	—	2	2	no	—
23	C₂×C₃×Q₈×D₅	C₂²	1	6	yes	—
24	C₃×C₅×#137	C₂²	1	6	yes	complemented
25	C₃×C₅×#135	C₂²	1	3	yes	complemented
26	C₂×C₃×C₅×Q₁₆	C₂²	1	3	yes	complemented
27	C₃×C₅×#131	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4097	C₂²	1	6	yes	complemented
29	C₃×#4096	C₂²	1	6	yes	complemented
30	C₃×#4094	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#689	C₂²	1	6	yes	complemented
32	C₃×#4088	C₂²	1	6	yes	complemented
33	C₃×#4065	C₂²	1	3	yes	complemented
34	C₃×#4064	C₂²	1	12	yes	complemented
35	C₃×D₅×Q₁₆	C₂²	1	3	yes	—
36	C₃×D₅×Q₁₆	C₂²	1	6	yes	—
37	C₃×D₅×Q₁₆	C₂²	1	6	yes	complemented
38	C₃×D₅×Q₁₆	C₂²	1	6	yes	complemented
39	C₃×#4062	C₂²	1	6	yes	complemented
40	C₃×#4061	C₂²	1	12	yes	complemented
41	C₃×D₅×SD₁₆	C₂²	1	6	yes	—
42	C₃×#4058	C₂²	1	3	yes	complemented
43	C₃×D₅×D₈	C₂²	1	1	yes	characteristic
44	C₃×#4055	C₂²	1	6	yes	complemented
45	C₃×#4053	C₂²	1	3	yes	complemented
46	C₃×D₅×M₁₆	C₂²	1	3	yes	—
47	C₂×C₃×Dic₂₀	C₂²	1	3	yes	complemented
48	C₃×#4050	C₂²	1	3	yes	complemented
49	C₃×#4047	C₂²	1	3	yes	complemented
50	C₂×C₃×C₈×D₅	C₂²	1	3	yes	—
51	C₂×C₃×#578	—	5	1	no	maximal, Hall
52	D₅×2₋¹⁺⁴	C₂×C₃	1	2	yes	complemented
53	C₅×#578	C₂×C₃	1	1	yes	characteristic, complemented
54	#66172	C₂×C₃	1	2	yes	complemented
55	#66113	C₂×C₃	1	6	yes	complemented
56	D₅×#137	C₂×C₃	1	6	yes	complemented
57	#66105	C₂×C₃	1	3	yes	complemented
58	D₅×#135	C₂×C₃	1	3	yes	complemented
59	#66100	C₂×C₃	1	3	yes	complemented
60	C₂×D₅×Q₁₆	C₂×C₃	1	3	yes	complemented
61	#66087	C₂×C₃	1	1	yes	characteristic, complemented
62	D₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
63	C₃×C₅×#41	—	2	6	no	—
64	C₃×C₅×#41	C₂³	1	6	yes	—
65	C₃×C₅×#41	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×Q₈	—	2	2	no	—
67	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	—
68	C₃×#713	—	2	6	no	—
69	C₃×#713	D₄	1	1	yes	characteristic
70	C₃×#713	C₂³	1	6	yes	—
71	C₃×Q₈×D₅	—	2	2	no	—
72	C₃×Q₈×D₅	—	2	6	no	—
73	C₃×Q₈×D₅	—	2	6	no	—
74	C₃×Q₈×D₅	—	2	6	no	—
75	C₃×Q₈×D₅	D₄	1	1	yes	characteristic
76	C₃×Q₈×D₅	C₂³	1	6	yes	—
77	C₃×Q₈×D₅	C₂³	1	12	yes	—
78	C₃×#711	—	2	6	no	—
79	C₃×#711	—	2	12	no	—
80	C₃×#711	—	2	6	no	—
81	C₃×#711	D₄	1	3	yes	—
82	C₃×#711	C₂³	1	6	yes	—
83	C₃×D₄×D₅	—	2	6	no	—
84	C₃×D₄×D₅	D₄	1	3	yes	—
85	C₃×D₄×D₅	C₂³	1	2	yes	—
86	C₃×#709	—	2	12	no	—
87	C₃×#709	—	2	6	no	—
88	C₃×#709	—	2	6	no	—
89	C₃×#709	C₂³	1	3	yes	—
90	C₃×#709	C₂³	1	6	yes	—
91	C₂×C₃×C₄×D₅	—	2	6	no	—
92	C₂×C₃×C₄×D₅	—	2	6	no	—
93	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
94	C₂×C₃×Dic₁₀	—	2	6	no	—
95	C₂×C₃×Dic₁₀	—	2	6	no	—
96	C₂×C₃×Dic₁₀	C₂³	1	6	yes	—
97	C₃×C₅×Q₁₆	C₂³	1	3	yes	—
98	C₃×C₅×Q₁₆	C₂³	1	6	yes	—
99	C₃×C₅×SD₁₆	C₂³	1	6	yes	—
100	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
101	C₃×C₅×M₁₆	C₂³	1	3	yes	—
102	C₂×C₃×C₅×C₈	C₂³	1	3	yes	—
103	C₃×#689	C₂³	1	12	yes	—
104	C₃×#689	C₂³	1	6	yes	—
105	C₃×#688	C₂³	1	6	yes	—
106	C₃×#687	C₂³	1	6	yes	—
107	C₃×#686	C₂³	1	2	yes	—
108	C₃×#681	C₂³	1	3	yes	—
109	C₂×C₃×#168	C₂³	1	3	yes	—
110	C₃×Dic₂₀	C₂³	1	3	yes	—
111	C₃×Dic₂₀	C₂³	1	6	yes	—
112	C₃×D₄₀	C₂³	1	1	yes	characteristic
113	C₃×#677	C₂³	1	6	yes	—
114	C₃×#676	C₂³	1	6	yes	—
115	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
116	C₃×C₈×D₅	C₂³	1	3	yes	—
117	C₃×C₈×D₅	C₂³	1	3	yes	—
118	C₃×C₈×D₅	C₂³	1	3	yes	—
119	C₂×C₃×2₋¹⁺⁴	—	5	2	no	—
120	C₃×#578	—	5	2	no	—
121	C₃×#578	—	5	6	no	—
122	C₃×#578	—	5	3	no	—
123	C₃×#578	—	5	3	no	—
124	C₃×#578	—	5	1	no	—
125	C₃×#578	D₅	1	1	yes	characteristic, direct product factor
126	C₂×C₃×#137	—	5	6	no	—
127	C₂×C₃×#135	—	5	3	no	—
128	C₂²×C₃×Q₁₆	—	5	3	no	—
129	C₂×C₃×#131	—	5	1	no	—
130	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
131	#4150	—	2	6	no	—
132	#4150	C₂²×C₃	1	6	yes	complemented
133	#4150	C₂²×C₃	1	2	yes	complemented
134	D₅×#41	—	2	6	no	—
135	D₅×#41	C₂²×C₃	1	6	yes	—
136	D₅×#41	C₂²×C₃	1	1	yes	characteristic
137	#4147	—	2	2	no	—
138	#4147	C₂²×C₃	1	6	yes	complemented
139	C₂×Q₈×D₅	—	2	2	no	—
140	C₂×Q₈×D₅	C₂²×C₃	1	6	yes	—
141	C₅×#137	C₂²×C₃	1	6	yes	complemented
142	C₅×#135	C₂²×C₃	1	3	yes	complemented
143	C₂×C₅×Q₁₆	C₂²×C₃	1	3	yes	complemented
144	C₅×#131	C₂²×C₃	1	1	yes	characteristic, complemented
145	#4097	C₂²×C₃	1	6	yes	complemented
146	#4096	C₂²×C₃	1	6	yes	complemented
147	#4094	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₂×#689	C₂²×C₃	1	6	yes	complemented
149	#4088	C₂²×C₃	1	6	yes	complemented
150	#4065	C₂²×C₃	1	3	yes	complemented
151	#4064	C₂²×C₃	1	12	yes	complemented
152	D₅×Q₁₆	C₂²×C₃	1	3	yes	—
153	D₅×Q₁₆	C₂²×C₃	1	6	yes	—
154	D₅×Q₁₆	C₂²×C₃	1	6	yes	complemented
155	D₅×Q₁₆	C₂²×C₃	1	6	yes	complemented
156	#4062	C₂²×C₃	1	6	yes	complemented
157	#4061	C₂²×C₃	1	12	yes	complemented
158	D₅×SD₁₆	C₂²×C₃	1	6	yes	—
159	#4058	C₂²×C₃	1	3	yes	complemented
160	D₅×D₈	C₂²×C₃	1	1	yes	characteristic
161	#4055	C₂²×C₃	1	6	yes	complemented
162	#4053	C₂²×C₃	1	3	yes	complemented
163	D₅×M₁₆	C₂²×C₃	1	3	yes	—
164	C₂×Dic₂₀	C₂²×C₃	1	3	yes	complemented
165	#4050	C₂²×C₃	1	3	yes	complemented
166	#4047	C₂²×C₃	1	3	yes	complemented
167	C₂×C₈×D₅	C₂²×C₃	1	3	yes	—
168	C₂×#578	—	5	1	no	Sylow
169	C₂²×C₃×D₅	—	2	2	no	—
170	C₂²×C₃×D₅	C₂×D₄	1	3	yes	—
171	C₃×C₅×Q₈	—	2	6	no	—
172	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
173	C₃×C₅×Q₈	C₂⁴	1	6	yes	—
174	C₃×C₅×D₄	—	2	6	no	—
175	C₃×C₅×D₄	C₂×D₄	1	3	yes	—
176	C₃×C₅×D₄	C₂⁴	1	2	yes	—
177	C₂×C₃×C₄×C₅	—	2	6	no	—
178	C₂×C₃×C₄×C₅	—	2	6	no	—
179	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
180	C₃×C₂²⋊D₅	—	2	6	no	—
181	C₃×C₂²⋊D₅	—	2	6	no	—
182	C₃×C₂²⋊D₅	—	2	2	no	—
183	C₃×C₂²⋊D₅	C₂×D₄	1	6	yes	—
184	C₂×C₃×Dic₅	—	2	6	no	—
185	C₂×C₃×Dic₅	—	2	6	no	—
186	C₂×C₃×Dic₅	C₂×D₄	1	3	yes	—
187	C₃×D₂₀	—	2	6	no	—
188	C₃×D₂₀	C₂×D₄	1	3	yes	—
189	C₃×D₂₀	C₂⁴	1	2	yes	—
190	C₃×C₄×D₅	—	2	6	no	—
191	C₃×C₄×D₅	—	2	12	no	—
192	C₃×C₄×D₅	—	2	6	no	—
193	C₃×C₄×D₅	—	2	6	no	—
194	C₃×C₄×D₅	C₂×D₄	1	3	yes	—
195	C₃×C₄×D₅	C₂×D₄	1	3	yes	—
196	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
197	C₃×C₄×D₅	C₂⁴	1	3	yes	—
198	C₃×Dic₁₀	—	2	6	no	—
199	C₃×Dic₁₀	—	2	6	no	—
200	C₃×Dic₁₀	—	2	12	no	—
201	C₃×Dic₁₀	C₂×D₄	1	3	yes	—
202	C₃×Dic₁₀	C₂⁴	1	6	yes	—
203	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
204	C₃×C₅×C₈	C₂⁴	1	3	yes	—
205	C₃×#168	C₂⁴	1	1	yes	characteristic
206	C₃×#168	C₂⁴	1	3	yes	—
207	C₃×2₋¹⁺⁴	—	5	6	no	—
208	C₃×2₋¹⁺⁴	—	5	2	no	—
209	C₃×2₋¹⁺⁴	—	5	6	no	—
210	C₃×2₋¹⁺⁴	—	10	2	no	—
211	C₃×2₋¹⁺⁴	—	10	6	no	—
212	C₃×2₋¹⁺⁴	C₂×D₅	1	2	yes	complemented
213	C₂×C₃×#41	—	5	1	no	—
214	C₂×C₃×#41	—	5	6	no	—
215	C₂×C₃×#41	—	10	6	no	—
216	C₂²×C₃×Q₈	—	5	6	no	—
217	C₂²×C₃×Q₈	—	10	2	no	—
218	C₃×#137	—	5	6	no	—
219	C₃×#137	—	5	6	no	—
220	C₃×#137	—	5	12	no	—
221	C₃×#137	—	5	12	no	—
222	C₃×#137	—	5	6	no	—
223	C₃×#137	C₂×D₅	1	6	yes	complemented
224	C₃×#135	—	5	6	no	—
225	C₃×#135	—	5	3	no	—
226	C₃×#135	—	5	6	no	—
227	C₃×#135	—	5	3	no	—
228	C₃×#135	—	5	3	no	—
229	C₃×#135	C₂×D₅	1	3	yes	complemented
230	C₂×C₃×Q₁₆	—	5	6	no	—
231	C₂×C₃×Q₁₆	—	5	3	no	—
232	C₂×C₃×Q₁₆	—	5	6	no	—
233	C₂×C₃×Q₁₆	—	5	6	no	—
234	C₂×C₃×Q₁₆	—	5	6	no	—
235	C₂×C₃×Q₁₆	—	5	3	no	—
236	C₂×C₃×Q₁₆	C₂×D₅	1	3	yes	complemented
237	C₂×C₃×SD₁₆	—	5	6	no	—
238	C₂×C₃×D₈	—	5	1	no	—
239	C₃×#131	—	5	1	no	—
240	C₃×#131	—	5	3	no	—
241	C₃×#131	—	5	3	no	—
242	C₃×#131	C₂×D₅	1	1	yes	characteristic, complemented
243	C₂×C₃×M₁₆	—	5	3	no	—
244	C₂²×C₃×C₈	—	5	3	no	—
245	C₅×#41	—	2	6	no	—
246	C₅×#41	C₂³×C₃	1	6	yes	—
247	C₅×#41	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₅×Q₈	—	2	2	no	—
249	C₂×C₅×Q₈	C₂³×C₃	1	6	yes	—
250	#713	—	2	6	no	—
251	#713	C₃×D₄	1	1	yes	characteristic
252	#713	C₂³×C₃	1	6	yes	—
253	Q₈×D₅	—	2	2	no	—
254	Q₈×D₅	—	2	6	no	—
255	Q₈×D₅	—	2	6	no	—
256	Q₈×D₅	—	2	6	no	—
257	Q₈×D₅	C₃×D₄	1	1	yes	characteristic
258	Q₈×D₅	C₂³×C₃	1	6	yes	—
259	Q₈×D₅	C₂³×C₃	1	12	yes	—
260	#711	—	2	6	no	—
261	#711	—	2	12	no	—
262	#711	—	2	6	no	—
263	#711	C₃×D₄	1	3	yes	—
264	#711	C₂³×C₃	1	6	yes	—
265	D₄×D₅	—	2	6	no	—
266	D₄×D₅	C₃×D₄	1	3	yes	—
267	D₄×D₅	C₂³×C₃	1	2	yes	—
268	#709	—	2	12	no	—
269	#709	—	2	6	no	—
270	#709	—	2	6	no	—
271	#709	C₂³×C₃	1	3	yes	—
272	#709	C₂³×C₃	1	6	yes	—
273	C₂×C₄×D₅	—	2	6	no	—
274	C₂×C₄×D₅	—	2	6	no	—
275	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
276	C₂×Dic₁₀	—	2	6	no	—
277	C₂×Dic₁₀	—	2	6	no	—
278	C₂×Dic₁₀	C₂³×C₃	1	6	yes	—
279	C₅×Q₁₆	C₂³×C₃	1	3	yes	—
280	C₅×Q₁₆	C₂³×C₃	1	6	yes	—
281	C₅×SD₁₆	C₂³×C₃	1	6	yes	—
282	C₅×D₈	C₂³×C₃	1	1	yes	characteristic
283	C₅×M₁₆	C₂³×C₃	1	3	yes	—
284	C₂×C₅×C₈	C₂³×C₃	1	3	yes	—
285	#689	C₂³×C₃	1	6	yes	—
286	#689	C₂³×C₃	1	12	yes	—
287	#688	C₂³×C₃	1	6	yes	—
288	#687	C₂³×C₃	1	6	yes	—
289	#686	C₂³×C₃	1	2	yes	—
290	#681	C₂³×C₃	1	3	yes	—
291	C₂×#168	C₂³×C₃	1	3	yes	—
292	Dic₂₀	C₂³×C₃	1	3	yes	—
293	Dic₂₀	C₂³×C₃	1	6	yes	—
294	D₄₀	C₂³×C₃	1	1	yes	characteristic
295	#677	C₂³×C₃	1	6	yes	—
296	#676	C₂³×C₃	1	6	yes	—
297	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
298	C₈×D₅	C₂³×C₃	1	3	yes	—
299	C₈×D₅	C₂³×C₃	1	3	yes	—
300	C₈×D₅	C₂³×C₃	1	3	yes	—
301	C₂×2₋¹⁺⁴	—	5	2	no	—
302	#578	—	5	2	no	—
303	#578	—	5	6	no	—
304	#578	—	5	3	no	—
305	#578	—	5	3	no	—
306	#578	—	5	1	no	—
307	#578	C₃×D₅	1	1	yes	characteristic, direct product factor
308	C₂×#137	—	5	6	no	—
309	C₂×#135	—	5	3	no	—
310	C₂²×Q₁₆	—	5	3	no	—
311	C₂×#131	—	5	1	no	—
312	C₂²×C₃×C₅	—	2	2	no	—
313	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
314	C₂×C₃×D₅	—	2	6	no	—
315	C₂×C₃×D₅	—	2	2	no	—
316	C₂×C₃×D₅	—	4	4	no	—
317	C₂×C₃×D₅	C₂²×D₄	1	3	yes	—
318	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
319	C₃×C₄×C₅	—	2	6	no	—
320	C₃×C₄×C₅	C₂²×D₄	1	3	yes	—
321	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
322	C₃×Dic₅	—	2	6	no	—
323	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
324	C₃×Dic₅	C₂²×D₄	1	3	yes	—
325	C₃×#41	—	2	6	no	—
326	C₃×#41	—	5	1	no	—
327	C₃×#41	—	5	3	no	—
328	C₃×#41	—	5	3	no	—
329	C₃×#41	—	5	6	no	—
330	C₃×#41	—	5	6	no	—
331	C₃×#41	—	5	6	no	—
332	C₃×#41	—	10	6	no	—
333	C₃×#41	—	10	12	no	—
334	C₃×#41	—	10	6	no	—
335	C₃×#41	—	10	6	no	—
336	C₃×#41	—	10	12	no	—
337	C₃×#41	—	10	6	no	—
338	C₃×#41	—	10	6	no	—
339	C₃×#41	C₂²×D₅	1	6	yes	—
340	C₃×#41	C₂²×D₅	1	1	yes	characteristic
341	C₂×C₃×Q₈	—	2	2	no	—
342	C₂×C₃×Q₈	—	5	1	no	—
343	C₂×C₃×Q₈	—	5	6	no	—
344	C₂×C₃×Q₈	—	5	12	no	—
345	C₂×C₃×Q₈	—	5	6	no	—
346	C₂×C₃×Q₈	—	10	6	no	—
347	C₂×C₃×Q₈	—	10	6	no	—
348	C₂×C₃×Q₈	—	10	6	no	—
349	C₂×C₃×Q₈	—	10	6	no	—
350	C₂×C₃×Q₈	—	10	6	no	—
351	C₂×C₃×Q₈	—	10	2	no	—
352	C₂×C₃×Q₈	C₂²×D₅	1	6	yes	—
353	C₂×C₃×D₄	—	5	3	no	—
354	C₂×C₃×D₄	—	5	2	no	—
355	C₂×C₃×D₄	—	10	6	no	—
356	C₂²×C₃×C₄	—	5	3	no	—
357	C₂²×C₃×C₄	—	10	6	no	—
358	C₂²×C₃×C₄	—	10	6	no	—
359	C₃×Q₁₆	—	5	6	no	—
360	C₃×Q₁₆	—	5	12	no	—
361	C₃×Q₁₆	—	5	3	no	—
362	C₃×Q₁₆	—	5	6	no	—
363	C₃×Q₁₆	C₂²×D₅	1	3	yes	—
364	C₃×Q₁₆	C₂²×D₅	1	6	yes	—
365	C₃×SD₁₆	—	5	6	no	—
366	C₃×SD₁₆	—	5	6	no	—
367	C₃×SD₁₆	—	5	6	no	—
368	C₃×SD₁₆	C₂²×D₅	1	6	yes	—
369	C₃×D₈	—	5	2	no	—
370	C₃×D₈	—	5	1	no	—
371	C₃×D₈	C₂²×D₅	1	1	yes	characteristic
372	C₃×M₁₆	—	5	3	no	—
373	C₃×M₁₆	—	5	6	no	—
374	C₃×M₁₆	C₂²×D₅	1	3	yes	—
375	C₂×C₃×C₈	—	5	3	no	—
376	C₂×C₃×C₈	—	5	1	no	—
377	C₂×C₃×C₈	—	5	3	no	—
378	C₂×C₃×C₈	—	5	3	no	—
379	C₂×C₃×C₈	—	5	3	no	—
380	C₂×C₃×C₈	C₂²×D₅	1	3	yes	—
381	C₂²×D₅	—	2	2	no	—
382	C₂²×D₅	C₂×C₃×D₄	1	3	yes	—
383	C₅×Q₈	—	2	6	no	—
384	C₅×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
385	C₅×Q₈	C₂⁴×C₃	1	6	yes	—
386	C₅×D₄	—	2	6	no	—
387	C₅×D₄	C₂×C₃×D₄	1	3	yes	—
388	C₅×D₄	C₂⁴×C₃	1	2	yes	—
389	C₂×C₄×C₅	—	2	6	no	—
390	C₂×C₄×C₅	—	2	6	no	—
391	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
392	C₂²⋊D₅	—	2	6	no	—
393	C₂²⋊D₅	—	2	6	no	—
394	C₂²⋊D₅	—	2	2	no	—
395	C₂²⋊D₅	C₂×C₃×D₄	1	6	yes	—
396	C₂×Dic₅	—	2	6	no	—
397	C₂×Dic₅	—	2	6	no	—
398	C₂×Dic₅	C₂×C₃×D₄	1	3	yes	—
399	D₂₀	—	2	6	no	—
400	D₂₀	C₂×C₃×D₄	1	3	yes	—
401	D₂₀	C₂⁴×C₃	1	2	yes	—
402	C₄×D₅	—	2	6	no	—
403	C₄×D₅	—	2	12	no	—
404	C₄×D₅	—	2	6	no	—
405	C₄×D₅	—	2	6	no	—
406	C₄×D₅	C₂×C₃×D₄	1	3	yes	—
407	C₄×D₅	C₂×C₃×D₄	1	3	yes	—
408	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
409	C₄×D₅	C₂⁴×C₃	1	3	yes	—
410	Dic₁₀	—	2	6	no	—
411	Dic₁₀	—	2	6	no	—
412	Dic₁₀	—	2	12	no	—
413	Dic₁₀	C₂×C₃×D₄	1	3	yes	—
414	Dic₁₀	C₂⁴×C₃	1	6	yes	—
415	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
416	C₅×C₈	C₂⁴×C₃	1	3	yes	—
417	#168	C₂⁴×C₃	1	1	yes	characteristic
418	#168	C₂⁴×C₃	1	3	yes	—
419	2₋¹⁺⁴	—	5	6	no	—
420	2₋¹⁺⁴	—	5	2	no	—
421	2₋¹⁺⁴	—	5	6	no	—
422	2₋¹⁺⁴	—	10	2	no	—
423	2₋¹⁺⁴	—	10	6	no	—
424	2₋¹⁺⁴	C₂×C₃×D₅	1	2	yes	complemented
425	C₂×#41	—	5	1	no	—
426	C₂×#41	—	5	6	no	—
427	C₂×#41	—	10	6	no	—
428	C₂²×Q₈	—	5	6	no	—
429	C₂²×Q₈	—	10	2	no	—
430	#137	—	5	6	no	—
431	#137	—	5	6	no	—
432	#137	—	5	12	no	—
433	#137	—	5	12	no	—
434	#137	—	5	6	no	—
435	#137	C₂×C₃×D₅	1	6	yes	complemented
436	#135	—	5	6	no	—
437	#135	—	5	3	no	—
438	#135	—	5	6	no	—
439	#135	—	5	3	no	—
440	#135	—	5	3	no	—
441	#135	C₂×C₃×D₅	1	3	yes	complemented
442	C₂×Q₁₆	—	5	6	no	—
443	C₂×Q₁₆	—	5	3	no	—
444	C₂×Q₁₆	—	5	6	no	—
445	C₂×Q₁₆	—	5	6	no	—
446	C₂×Q₁₆	—	5	6	no	—
447	C₂×Q₁₆	—	5	3	no	—
448	C₂×Q₁₆	C₂×C₃×D₅	1	3	yes	complemented
449	C₂×SD₁₆	—	5	6	no	—
450	C₂×D₈	—	5	1	no	—
451	#131	—	5	1	no	—
452	#131	—	5	3	no	—
453	#131	—	5	3	no	—
454	#131	C₂×C₃×D₅	1	1	yes	characteristic, complemented
455	C₂×M₁₆	—	5	3	no	—
456	C₂²×C₈	—	5	3	no	—
457	C₂×C₃×C₅	—	2	3	no	—
458	C₂×C₃×C₅	—	4	2	no	—
459	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
460	C₃×D₅	—	2	3	no	—
461	C₃×D₅	—	4	2	no	—
462	C₃×D₅	#578	1	2	yes	direct product factor
463	C₂³×C₃	—	5	3	no	—
464	C₂³×C₃	—	10	2	no	—
465	C₃×Q₈	—	2	6	no	—
466	C₃×Q₈	—	5	3	no	—
467	C₃×Q₈	—	5	6	no	—
468	C₃×Q₈	—	10	6	no	—
469	C₃×Q₈	—	10	12	no	—
470	C₃×Q₈	—	10	6	no	—
471	C₃×Q₈	D₄×D₅	1	1	yes	characteristic
472	C₃×Q₈	C₂³×D₅	1	6	yes	—
473	C₃×D₄	—	2	6	no	—
474	C₃×D₄	—	5	6	no	—
475	C₃×D₄	—	5	3	no	—
476	C₃×D₄	—	5	2	no	—
477	C₃×D₄	—	10	6	no	—
478	C₃×D₄	—	10	2	no	—
479	C₃×D₄	—	10	6	no	—
480	C₃×D₄	—	10	6	no	—
481	C₃×D₄	D₄×D₅	1	3	yes	—
482	C₃×D₄	C₂³×D₅	1	2	yes	—
483	C₂×C₃×C₄	—	2	6	no	—
484	C₂×C₃×C₄	—	2	6	no	—
485	C₂×C₃×C₄	—	5	3	no	—
486	C₂×C₃×C₄	—	5	3	no	—
487	C₂×C₃×C₄	—	5	3	no	—
488	C₂×C₃×C₄	—	5	1	no	—
489	C₂×C₃×C₄	—	5	3	no	—
490	C₂×C₃×C₄	—	10	6	no	—
491	C₂×C₃×C₄	—	10	6	no	—
492	C₂×C₃×C₄	—	10	12	no	—
493	C₂×C₃×C₄	—	10	6	no	—
494	C₂×C₃×C₄	—	10	6	no	—
495	C₂×C₃×C₄	—	10	6	no	—
496	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
497	C₃×C₈	—	5	1	no	—
498	C₃×C₈	—	5	3	no	—
499	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
500	C₃×C₈	C₂³×D₅	1	3	yes	—
501	C₂²×C₅	—	2	2	no	—
502	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
503	C₂×D₅	—	2	6	no	—
504	C₂×D₅	—	2	2	no	—
505	C₂×D₅	—	4	4	no	—
506	C₂×D₅	C₂²×C₃×D₄	1	3	yes	—
507	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
508	C₄×C₅	—	2	6	no	—
509	C₄×C₅	C₂²×C₃×D₄	1	3	yes	—
510	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
511	Dic₅	—	2	6	no	—
512	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
513	Dic₅	C₂²×C₃×D₄	1	3	yes	—
514	#41	—	2	6	no	—
515	#41	—	5	1	no	—
516	#41	—	5	3	no	—
517	#41	—	5	3	no	—
518	#41	—	5	6	no	—
519	#41	—	5	6	no	—
520	#41	—	5	6	no	—
521	#41	—	10	6	no	—
522	#41	—	10	12	no	—
523	#41	—	10	6	no	—
524	#41	—	10	6	no	—
525	#41	—	10	12	no	—
526	#41	—	10	6	no	—
527	#41	—	10	6	no	—
528	#41	C₂²×C₃×D₅	1	6	yes	—
529	#41	C₂²×C₃×D₅	1	1	yes	characteristic
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	5	1	no	—
532	C₂×Q₈	—	5	6	no	—
533	C₂×Q₈	—	5	12	no	—
534	C₂×Q₈	—	5	6	no	—
535	C₂×Q₈	—	10	6	no	—
536	C₂×Q₈	—	10	6	no	—
537	C₂×Q₈	—	10	6	no	—
538	C₂×Q₈	—	10	6	no	—
539	C₂×Q₈	—	10	6	no	—
540	C₂×Q₈	—	10	2	no	—
541	C₂×Q₈	C₂²×C₃×D₅	1	6	yes	—
542	C₂×D₄	—	5	3	no	—
543	C₂×D₄	—	5	2	no	—
544	C₂×D₄	—	10	6	no	—
545	C₂²×C₄	—	5	3	no	—
546	C₂²×C₄	—	10	6	no	—
547	C₂²×C₄	—	10	6	no	—
548	Q₁₆	—	5	6	no	—
549	Q₁₆	—	5	12	no	—
550	Q₁₆	—	5	3	no	—
551	Q₁₆	—	5	6	no	—
552	Q₁₆	C₂²×C₃×D₅	1	3	yes	—
553	Q₁₆	C₂²×C₃×D₅	1	6	yes	—
554	SD₁₆	—	5	6	no	—
555	SD₁₆	—	5	6	no	—
556	SD₁₆	—	5	6	no	—
557	SD₁₆	C₂²×C₃×D₅	1	6	yes	—
558	D₈	—	5	2	no	—
559	D₈	—	5	1	no	—
560	D₈	C₂²×C₃×D₅	1	1	yes	characteristic
561	M₁₆	—	5	3	no	—
562	M₁₆	—	5	6	no	—
563	M₁₆	C₂²×C₃×D₅	1	3	yes	—
564	C₂×C₈	—	5	3	no	—
565	C₂×C₈	—	5	1	no	—
566	C₂×C₈	—	5	3	no	—
567	C₂×C₈	—	5	3	no	—
568	C₂×C₈	—	5	3	no	—
569	C₂×C₈	C₂²×C₃×D₅	1	3	yes	—
570	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
571	C₂²×C₃	—	2	2	no	—
572	C₂²×C₃	—	5	1	no	—
573	C₂²×C₃	—	5	3	no	—
574	C₂²×C₃	—	10	6	no	—
575	C₂²×C₃	—	10	2	no	—
576	C₂²×C₃	—	20	4	no	—
577	C₂²×C₃	C₂×D₄×D₅	1	3	yes	—
578	C₃×C₄	—	2	6	no	—
579	C₃×C₄	—	5	1	no	—
580	C₃×C₄	—	5	3	no	—
581	C₃×C₄	—	10	6	no	—
582	C₃×C₄	C₂×D₄×D₅	1	3	yes	—
583	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
584	C₂×C₅	—	2	3	no	—
585	C₂×C₅	—	4	2	no	—
586	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
587	D₅	—	2	3	no	—
588	D₅	—	4	2	no	—
589	D₅	C₃×#578	1	2	yes	direct product factor
590	C₂³	—	5	3	no	—
591	C₂³	—	10	2	no	—
592	Q₈	—	2	6	no	—
593	Q₈	—	5	3	no	—
594	Q₈	—	5	6	no	—
595	Q₈	—	10	6	no	—
596	Q₈	—	10	12	no	—
597	Q₈	—	10	6	no	—
598	Q₈	C₃×D₄×D₅	1	1	yes	characteristic
599	Q₈	C₂³×C₃×D₅	1	6	yes	—
600	D₄	—	2	6	no	—
601	D₄	—	5	6	no	—
602	D₄	—	5	3	no	—
603	D₄	—	5	2	no	—
604	D₄	—	10	6	no	—
605	D₄	—	10	2	no	—
606	D₄	—	10	6	no	—
607	D₄	—	10	6	no	—
608	D₄	C₃×D₄×D₅	1	3	yes	—
609	D₄	C₂³×C₃×D₅	1	2	yes	—
610	C₂×C₄	—	2	6	no	—
611	C₂×C₄	—	2	6	no	—
612	C₂×C₄	—	5	3	no	—
613	C₂×C₄	—	5	3	no	—
614	C₂×C₄	—	5	3	no	—
615	C₂×C₄	—	5	1	no	—
616	C₂×C₄	—	5	3	no	—
617	C₂×C₄	—	10	6	no	—
618	C₂×C₄	—	10	6	no	—
619	C₂×C₄	—	10	12	no	—
620	C₂×C₄	—	10	6	no	—
621	C₂×C₄	—	10	6	no	—
622	C₂×C₄	—	10	6	no	—
623	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
624	C₈	—	5	1	no	—
625	C₈	—	5	3	no	—
626	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
627	C₈	C₂³×C₃×D₅	1	3	yes	—
628	C₂×C₃	—	2	3	no	—
629	C₂×C₃	—	4	2	no	—
630	C₂×C₃	—	5	2	no	—
631	C₂×C₃	—	10	3	no	—
632	C₂×C₃	—	20	2	no	—
633	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
634	C₅	C₂×C₃×#578	1	1	yes	characteristic, complemented, Sylow
635	C₂²	—	2	2	no	—
636	C₂²	—	5	1	no	—
637	C₂²	—	5	3	no	—
638	C₂²	—	10	6	no	—
639	C₂²	—	10	2	no	—
640	C₂²	—	20	4	no	—
641	C₂²	C₂×C₃×D₄×D₅	1	3	yes	—
642	C₄	—	2	6	no	—
643	C₄	—	5	1	no	—
644	C₄	—	5	3	no	—
645	C₄	—	10	6	no	—
646	C₄	C₂×C₃×D₄×D₅	1	3	yes	—
647	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
648	C₃	D₅×#578	1	1	yes	characteristic, direct product factor, Sylow
649	C₂	—	2	3	no	—
650	C₂	—	4	2	no	—
651	C₂	—	5	2	no	—
652	C₂	—	10	3	no	—
653	C₂	—	20	2	no	—
654	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#578	C₂
socle	C₂×C₃×C₅	C₂³×D₄
hypercenter	C₃×#578	D₅
hypocenter	C₅	C₂×C₃×#578
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41 ◁ C₃×#578

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×2₋¹⁺⁴	C₂	semidirect
2. C₃×C₅×#578	C₂	semidirect
3. C₃×#66172	C₂	semidirect
4. C₃×#66113	C₂	semidirect
5. C₃×D₅×#137	C₂	semidirect
6. C₃×#66105	C₂	semidirect
7. C₃×D₅×#135	C₂	semidirect
8. C₃×#66100	C₂	semidirect
9. C₂×C₃×D₅×Q₁₆	C₂	semidirect
10. C₃×#66087	C₂	semidirect
11. C₃×D₅×#131	C₂	semidirect
12. D₅×#578	C₃	direct (N × H)
13. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
15. C₃×#4150	C₂²	semidirect
16. C₃×#4150	C₂²	semidirect
21. C₃×#4147	C₂²	semidirect
24. C₃×C₅×#137	C₂²	semidirect
25. C₃×C₅×#135	C₂²	semidirect
26. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
27. C₃×C₅×#131	C₂²	semidirect
28. C₃×#4097	C₂²	semidirect
29. C₃×#4096	C₂²	semidirect
30. C₃×#4094	C₂²	semidirect
31. C₂×C₃×#689	C₂²	semidirect
32. C₃×#4088	C₂²	semidirect
33. C₃×#4065	C₂²	semidirect
34. C₃×#4064	C₂²	semidirect
37. C₃×D₅×Q₁₆	C₂²	semidirect
38. C₃×D₅×Q₁₆	C₂²	semidirect
39. C₃×#4062	C₂²	semidirect
40. C₃×#4061	C₂²	semidirect
42. C₃×#4058	C₂²	semidirect
44. C₃×#4055	C₂²	semidirect
45. C₃×#4053	C₂²	semidirect
47. C₂×C₃×Dic₂₀	C₂²	semidirect
48. C₃×#4050	C₂²	semidirect
49. C₃×#4047	C₂²	semidirect
52. D₅×2₋¹⁺⁴	C₂×C₃	semidirect
53. C₅×#578	C₂×C₃	semidirect
54. #66172	C₂×C₃	semidirect
55. #66113	C₂×C₃	semidirect
56. D₅×#137	C₂×C₃	semidirect
57. #66105	C₂×C₃	semidirect
58. D₅×#135	C₂×C₃	semidirect
59. #66100	C₂×C₃	semidirect
60. C₂×D₅×Q₁₆	C₂×C₃	semidirect
61. #66087	C₂×C₃	semidirect
62. D₅×#131	C₂×C₃	semidirect
125. C₃×#578	D₅	direct (N × H)
130. C₅×2₋¹⁺⁴	C₂²×C₃	semidirect
132. #4150	C₂²×C₃	semidirect
133. #4150	C₂²×C₃	semidirect
138. #4147	C₂²×C₃	semidirect
141. C₅×#137	C₂²×C₃	semidirect
142. C₅×#135	C₂²×C₃	semidirect
143. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
144. C₅×#131	C₂²×C₃	semidirect
145. #4097	C₂²×C₃	semidirect
146. #4096	C₂²×C₃	semidirect
147. #4094	C₂²×C₃	semidirect
148. C₂×#689	C₂²×C₃	semidirect
149. #4088	C₂²×C₃	semidirect
150. #4065	C₂²×C₃	semidirect
151. #4064	C₂²×C₃	semidirect
154. D₅×Q₁₆	C₂²×C₃	semidirect
155. D₅×Q₁₆	C₂²×C₃	semidirect
156. #4062	C₂²×C₃	semidirect
157. #4061	C₂²×C₃	semidirect
159. #4058	C₂²×C₃	semidirect
161. #4055	C₂²×C₃	semidirect
162. #4053	C₂²×C₃	semidirect
164. C₂×Dic₂₀	C₂²×C₃	semidirect
165. #4050	C₂²×C₃	semidirect
166. #4047	C₂²×C₃	semidirect
212. C₃×2₋¹⁺⁴	C₂×D₅	semidirect
223. C₃×#137	C₂×D₅	semidirect
229. C₃×#135	C₂×D₅	semidirect
236. C₂×C₃×Q₁₆	C₂×D₅	semidirect
242. C₃×#131	C₂×D₅	semidirect
307. #578	C₃×D₅	direct (N × H)
424. 2₋¹⁺⁴	C₂×C₃×D₅	semidirect
435. #137	C₂×C₃×D₅	semidirect
441. #135	C₂×C₃×D₅	semidirect
448. C₂×Q₁₆	C₂×C₃×D₅	semidirect
454. #131	C₂×C₃×D₅	semidirect
462. C₃×D₅	#578	direct (N × H)
570. C₃×C₅	C₂×#578	semidirect
589. D₅	C₃×#578	direct (N × H)
634. C₅	C₂×C₃×#578	semidirect
648. C₃	D₅×#578	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×2₋¹⁺⁴	2
C₃×C₅×#578	2
C₃×#66172	2
C₃×#66113	2
C₃×D₅×#137	2
C₃×#66105	2
C₃×D₅×#135	2
C₃×#66100	2
C₂×C₃×D₅×Q₁₆	2
C₃×#66087	2
C₃×D₅×#131	2
D₅×#578	3
C₂×C₃×#578	5

Subgroups — C3×D5×#578 #14510119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#578 #14510119