Subgroups — C₃×#10610286 #14415452

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65858	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64995	C₂	1	2	yes	maximal, complemented
9	C₃×#64995	C₂	1	2	yes	maximal, complemented
10	C₃×#64977	C₂	1	2	yes	maximal, complemented
11	C₃×C₈×D₂₀	C₂	1	2	yes	maximal, complemented
12	#10610286	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×#4053	—	2	4	no	—
21	C₃×D₅×M₁₆	—	2	4	no	—
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×#676	C₂²	1	2	yes	complemented
24	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
25	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
26	C₃×#4043	C₄	1	1	yes	characteristic
27	C₃×#4043	C₄	1	1	yes	characteristic
28	C₃×#4041	C₄	1	1	yes	characteristic
29	C₃×#4041	C₄	1	1	yes	characteristic
30	C₃×#4032	C₄	1	2	yes	—
31	C₃×#4028	C₄	1	2	yes	—
32	C₃×C₄×D₂₀	C₂²	1	2	yes	—
33	C₃×C₄×D₂₀	C₂²	1	2	yes	—
34	C₃×C₅×#97	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
36	C₃×#3952	C₂²	1	1	yes	characteristic
37	C₃×#3952	C₂²	1	1	yes	characteristic
38	C₃×#3952	C₂²	1	1	yes	characteristic
39	C₃×#3952	C₂²	1	1	yes	characteristic
40	C₃×#3952	C₂²	1	2	yes	complemented
41	C₃×#3952	C₂²	1	2	yes	complemented
42	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
43	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
44	C₃×#2933	—	5	1	no	maximal, Hall
45	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
47	#65858	C₂×C₃	1	1	yes	characteristic
48	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
49	#65399	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#3952	C₂×C₃	1	1	yes	characteristic, complemented
51	#65288	C₂×C₃	1	1	yes	characteristic, complemented
52	#64995	C₂×C₃	1	2	yes	complemented
53	#64995	C₂×C₃	1	2	yes	complemented
54	#64977	C₂×C₃	1	2	yes	complemented
55	C₈×D₂₀	C₂×C₃	1	2	yes	complemented
56	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₃×#709	—	2	2	no	—
61	C₃×#709	—	2	2	no	—
62	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
64	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₄×D₅	—	2	2	no	—
66	C₂×C₃×C₄×D₅	—	2	2	no	—
67	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
72	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
73	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
74	C₂×C₃×C₅×C₈	—	2	2	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₃×C₄²×C₅	C₂³	1	2	yes	—
82	C₃×#685	C₂×C₄	1	2	yes	—
83	C₃×#685	C₂×C₄	1	2	yes	—
84	C₃×#685	C₂×C₄	1	2	yes	—
85	C₃×#685	C₂×C₄	1	2	yes	—
86	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
87	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
88	C₃×#681	—	2	2	no	—
89	C₂×C₃×#168	—	2	2	no	—
90	C₂×C₃×#168	C₂³	1	1	yes	characteristic
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₃×#676	—	2	4	no	—
94	C₃×#676	—	2	4	no	—
95	C₃×C₈×D₅	—	2	4	no	—
96	C₃×C₈×D₅	—	2	4	no	—
97	C₂×C₃×#131	—	5	1	no	—
98	C₂²×C₃×M₁₆	—	5	1	no	—
99	C₃×#525	—	5	1	no	—
100	C₃×#436	—	5	2	no	—
101	C₃×#435	—	5	2	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×C₈×D₄	—	5	2	no	—
104	C₃×#424	—	5	1	no	—
105	C₃×#408	—	5	1	no	—
106	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
107	C₃×#405	D₅	1	1	yes	characteristic, complemented
108	C₂×#709	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
111	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₅×#117	C₂²×C₃	1	1	yes	characteristic
113	C₂×#681	C₂²×C₃	1	1	yes	characteristic
114	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
115	#4053	—	2	4	no	—
116	D₅×M₁₆	—	2	4	no	—
117	C₂×#676	C₂²×C₃	1	2	yes	—
118	C₂×#676	C₂²×C₃	1	2	yes	complemented
119	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
120	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
121	#4043	C₃×C₄	1	1	yes	characteristic
122	#4043	C₃×C₄	1	1	yes	characteristic
123	#4041	C₃×C₄	1	1	yes	characteristic
124	#4041	C₃×C₄	1	1	yes	characteristic
125	#4032	C₃×C₄	1	2	yes	—
126	#4028	C₃×C₄	1	2	yes	—
127	C₄×D₂₀	C₂²×C₃	1	2	yes	—
128	C₄×D₂₀	C₂²×C₃	1	2	yes	—
129	C₅×#97	C₂²×C₃	1	2	yes	complemented
130	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
131	#3952	C₂²×C₃	1	1	yes	characteristic
132	#3952	C₂²×C₃	1	1	yes	characteristic
133	#3952	C₂²×C₃	1	1	yes	characteristic
134	#3952	C₂²×C₃	1	1	yes	characteristic
135	#3952	C₂²×C₃	1	2	yes	complemented
136	#3952	C₂²×C₃	1	2	yes	complemented
137	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
138	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
139	#2933	—	5	1	no	Sylow
140	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₃×D₅	—	2	2	no	—
142	C₂²×C₃×D₅	—	2	2	no	—
143	C₂²×C₃×D₅	—	4	1	no	—
144	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
146	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₃×C₂²⋊D₅	—	2	4	no	—
154	C₂×C₃×Dic₅	—	2	2	no	—
155	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
156	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	C₃×D₂₀	—	2	4	no	—
159	C₃×D₂₀	—	2	2	no	—
160	C₃×D₂₀	—	4	2	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×C₄×D₅	—	2	2	no	—
163	C₃×C₄×D₅	—	2	1	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	1	no	—
166	C₃×C₄×D₅	—	2	1	no	—
167	C₃×C₄×D₅	—	2	1	no	—
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×Dic₁₀	—	2	2	no	—
170	C₃×C₅×C₈	—	2	1	no	—
171	C₃×C₅×C₈	—	2	1	no	—
172	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
173	C₃×#168	—	2	1	no	—
174	C₃×#168	—	2	2	no	—
175	C₃×#168	—	2	1	no	—
176	C₂×C₃×#41	—	5	1	no	—
177	C₂³×C₃×C₄	—	5	1	no	—
178	C₃×#131	—	10	4	no	—
179	C₂×C₃×M₁₆	—	5	1	no	—
180	C₂×C₃×M₁₆	—	5	2	no	—
181	C₂×C₃×M₁₆	—	5	2	no	—
182	C₂×C₃×M₁₆	—	10	4	no	—
183	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
184	C₂²×C₃×C₈	—	5	1	no	—
185	C₂²×C₃×C₈	—	5	2	no	—
186	C₂²×C₃×C₈	—	5	2	no	—
187	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
188	C₃×#123	—	5	2	no	—
189	C₃×C₂²⋊Q₈	—	5	1	no	—
190	C₃×C₂²⋊Q₈	—	5	1	no	—
191	C₃×#121	—	5	1	no	—
192	C₃×#121	—	5	1	no	—
193	C₃×#120	—	5	2	no	—
194	C₃×C₄×D₄	—	5	2	no	—
195	C₃×C₄×D₄	—	5	2	no	—
196	C₃×#117	C₂×D₅	1	1	yes	characteristic
197	C₃×C₄⋊C₈	—	5	2	no	—
198	C₃×C₄⋊C₈	—	5	2	no	—
199	C₃×C₂²⋊C₈	—	5	1	no	—
200	C₃×C₂²⋊C₈	—	5	1	no	—
201	C₃×C₂²⋊C₈	—	5	1	no	—
202	C₃×C₂²⋊C₈	—	5	1	no	—
203	C₃×C₂²⋊C₈	—	5	2	no	—
204	C₃×C₂²⋊C₈	—	5	2	no	—
205	C₃×#97	C₂×D₅	1	2	yes	complemented
206	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
207	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
210	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
211	#709	—	2	2	no	—
212	#709	—	2	2	no	—
213	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
214	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
215	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
216	C₂×C₄×D₅	—	2	2	no	—
217	C₂×C₄×D₅	—	2	2	no	—
218	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
220	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
223	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
224	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
225	C₂×C₅×C₈	—	2	2	no	—
226	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
229	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
231	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
232	C₄²×C₅	C₂³×C₃	1	2	yes	—
233	#685	C₂×C₃×C₄	1	2	yes	—
234	#685	C₂×C₃×C₄	1	2	yes	—
235	#685	C₂×C₃×C₄	1	2	yes	—
236	#685	C₂×C₃×C₄	1	2	yes	—
237	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
238	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
239	#681	—	2	2	no	—
240	C₂×#168	—	2	2	no	—
241	C₂×#168	C₂³×C₃	1	1	yes	characteristic
242	C₂×#168	C₂³×C₃	1	1	yes	characteristic
243	C₂×#168	C₂³×C₃	1	2	yes	—
244	#676	—	2	4	no	—
245	#676	—	2	4	no	—
246	C₈×D₅	—	2	4	no	—
247	C₈×D₅	—	2	4	no	—
248	C₂×#131	—	5	1	no	—
249	C₂²×M₁₆	—	5	1	no	—
250	#525	—	5	1	no	—
251	#436	—	5	2	no	—
252	#435	—	5	2	no	—
253	#435	—	5	2	no	—
254	C₈×D₄	—	5	2	no	—
255	#424	—	5	1	no	—
256	#408	—	5	1	no	—
257	C₂×C₂²⋊C₈	—	5	1	no	—
258	#405	C₃×D₅	1	1	yes	characteristic, complemented
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₃×D₅	—	2	1	no	—
264	C₂×C₃×D₅	—	2	1	no	—
265	C₂×C₃×D₅	—	2	1	no	—
266	C₂×C₃×D₅	—	2	2	no	—
267	C₂×C₃×D₅	—	2	2	no	—
268	C₂×C₃×D₅	—	2	1	no	—
269	C₂×C₃×D₅	—	2	1	no	—
270	C₂×C₃×D₅	—	2	2	no	—
271	C₂×C₃×D₅	—	4	4	no	—
272	C₂×C₃×D₅	#131	1	2	yes	complemented
273	C₃×C₄×C₅	—	2	2	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
276	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
278	C₃×Dic₅	—	2	2	no	—
279	C₃×Dic₅	—	2	1	no	—
280	C₃×Dic₅	—	2	1	no	—
281	C₂⁴×C₃	—	5	1	no	—
282	C₃×#41	—	10	2	no	—
283	C₃×#41	—	10	2	no	—
284	C₂×C₃×Q₈	—	5	1	no	—
285	C₂×C₃×D₄	—	5	2	no	—
286	C₂×C₃×D₄	—	5	2	no	—
287	C₂×C₃×D₄	—	5	1	no	—
288	C₂×C₃×D₄	—	5	2	no	—
289	C₂²×C₃×C₄	—	5	1	no	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₂²×C₃×C₄	—	5	1	no	—
293	C₂²×C₃×C₄	—	5	2	no	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	10	2	no	—
296	C₂²×C₃×C₄	—	10	2	no	—
297	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₃×M₁₆	—	10	2	no	—
299	C₃×M₁₆	—	10	4	no	—
300	C₃×M₁₆	—	10	4	no	—
301	C₃×M₁₆	D₂₀	1	4	yes	complemented
302	C₂×C₃×C₈	—	2	2	no	—
303	C₂×C₃×C₈	—	5	1	no	—
304	C₂×C₃×C₈	—	5	1	no	—
305	C₂×C₃×C₈	—	5	2	no	—
306	C₂×C₃×C₈	—	10	2	no	—
307	C₂×C₃×C₈	—	10	4	no	—
308	C₂×C₃×C₈	—	10	4	no	—
309	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
310	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
311	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
312	C₃×C₄⋊C₄	—	5	2	no	—
313	C₃×C₄⋊C₄	—	5	2	no	—
314	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
315	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	—	5	2	no	—
317	C₃×C₂²⋊C₄	—	5	2	no	—
318	C₃×C₂²⋊C₄	—	5	2	no	—
319	C₃×C₂²⋊C₄	—	5	2	no	—
320	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
321	C₃×C₄²	C₂²×D₅	1	2	yes	—
322	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
323	C₂²×D₅	—	2	2	no	—
324	C₂²×D₅	—	2	2	no	—
325	C₂²×D₅	—	4	1	no	—
326	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
327	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
328	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
330	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
331	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
333	C₂×C₄×C₅	C₃×#41	1	2	yes	—
334	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
335	C₂²⋊D₅	—	2	4	no	—
336	C₂×Dic₅	—	2	2	no	—
337	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
338	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
340	D₂₀	—	2	4	no	—
341	D₂₀	—	2	2	no	—
342	D₂₀	—	4	2	no	—
343	C₄×D₅	—	2	2	no	—
344	C₄×D₅	—	2	2	no	—
345	C₄×D₅	—	2	1	no	—
346	C₄×D₅	—	2	2	no	—
347	C₄×D₅	—	2	1	no	—
348	C₄×D₅	—	2	1	no	—
349	C₄×D₅	—	2	1	no	—
350	C₄×D₅	—	2	2	no	—
351	Dic₁₀	—	2	2	no	—
352	C₅×C₈	—	2	1	no	—
353	C₅×C₈	—	2	1	no	—
354	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
355	#168	—	2	1	no	—
356	#168	—	2	2	no	—
357	#168	—	2	1	no	—
358	C₂×#41	—	5	1	no	—
359	C₂³×C₄	—	5	1	no	—
360	#131	—	10	4	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	2	no	—
363	C₂×M₁₆	—	5	2	no	—
364	C₂×M₁₆	—	10	4	no	—
365	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	2	no	—
368	C₂²×C₈	—	5	2	no	—
369	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
370	#123	—	5	2	no	—
371	C₂²⋊Q₈	—	5	1	no	—
372	C₂²⋊Q₈	—	5	1	no	—
373	#121	—	5	1	no	—
374	#121	—	5	1	no	—
375	#120	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	5	2	no	—
378	#117	C₂×C₃×D₅	1	1	yes	characteristic
379	C₄⋊C₈	—	5	2	no	—
380	C₄⋊C₈	—	5	2	no	—
381	C₂²⋊C₈	—	5	1	no	—
382	C₂²⋊C₈	—	5	1	no	—
383	C₂²⋊C₈	—	5	1	no	—
384	C₂²⋊C₈	—	5	1	no	—
385	C₂²⋊C₈	—	5	2	no	—
386	C₂²⋊C₈	—	5	2	no	—
387	#97	C₂×C₃×D₅	1	2	yes	complemented
388	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
389	C₂×C₃×C₅	—	2	2	no	—
390	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
391	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
392	C₂×C₃×C₅	#568	1	1	yes	characteristic
393	C₃×D₅	—	2	2	no	—
394	C₃×D₅	—	4	2	no	—
395	C₃×D₅	—	4	1	no	—
396	C₂³×C₃	—	5	1	no	—
397	C₂³×C₃	—	5	1	no	—
398	C₂³×C₃	—	5	2	no	—
399	C₂³×C₃	—	10	2	no	—
400	C₂³×C₃	—	10	2	no	—
401	C₂³×C₃	—	20	1	no	—
402	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
403	C₃×Q₈	—	10	2	no	—
404	C₃×D₄	—	10	4	no	—
405	C₃×D₄	—	10	4	no	—
406	C₃×D₄	—	10	2	no	—
407	C₃×D₄	—	20	2	no	—
408	C₂×C₃×C₄	—	5	1	no	—
409	C₂×C₃×C₄	—	5	1	no	—
410	C₂×C₃×C₄	—	5	2	no	—
411	C₂×C₃×C₄	—	10	2	no	—
412	C₂×C₃×C₄	—	10	1	no	—
413	C₂×C₃×C₄	—	10	2	no	—
414	C₂×C₃×C₄	—	10	1	no	—
415	C₂×C₃×C₄	—	10	1	no	—
416	C₂×C₃×C₄	—	10	1	no	—
417	C₂×C₃×C₄	—	10	2	no	—
418	C₂×C₃×C₄	—	10	2	no	—
419	C₂×C₃×C₄	—	10	2	no	—
420	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
421	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
424	C₂×C₃×C₄	#709	1	2	yes	—
425	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
426	C₃×C₈	—	2	1	no	—
427	C₃×C₈	—	2	1	no	—
428	C₃×C₈	—	10	1	no	—
429	C₃×C₈	—	10	2	no	—
430	C₃×C₈	—	10	1	no	—
431	C₃×C₈	C₂×D₂₀	1	4	yes	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
435	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
436	C₂×D₅	—	2	1	no	—
437	C₂×D₅	—	2	1	no	—
438	C₂×D₅	—	2	2	no	—
439	C₂×D₅	—	2	1	no	—
440	C₂×D₅	—	2	1	no	—
441	C₂×D₅	—	2	2	no	—
442	C₂×D₅	—	2	1	no	—
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	4	4	no	—
445	C₂×D₅	C₃×#131	1	2	yes	complemented
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	2	no	—
448	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
449	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
450	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
451	Dic₅	—	2	2	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	—	2	1	no	—
454	C₂⁴	—	5	1	no	—
455	#41	—	10	2	no	—
456	#41	—	10	2	no	—
457	C₂×Q₈	—	5	1	no	—
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	5	2	no	—
460	C₂×D₄	—	5	1	no	—
461	C₂×D₄	—	5	2	no	—
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	1	no	—
464	C₂²×C₄	—	5	1	no	—
465	C₂²×C₄	—	5	1	no	—
466	C₂²×C₄	—	5	2	no	—
467	C₂²×C₄	—	5	1	no	—
468	C₂²×C₄	—	10	2	no	—
469	C₂²×C₄	—	10	2	no	—
470	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
471	M₁₆	—	10	2	no	—
472	M₁₆	—	10	4	no	—
473	M₁₆	—	10	4	no	—
474	M₁₆	C₃×D₂₀	1	4	yes	complemented
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	2	no	—
479	C₂×C₈	—	10	2	no	—
480	C₂×C₈	—	10	4	no	—
481	C₂×C₈	—	10	4	no	—
482	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
483	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
484	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
488	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
489	C₂²⋊C₄	—	5	2	no	—
490	C₂²⋊C₄	—	5	2	no	—
491	C₂²⋊C₄	—	5	2	no	—
492	C₂²⋊C₄	—	5	2	no	—
493	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
494	C₄²	C₂²×C₃×D₅	1	2	yes	—
495	C₃×C₅	#2933	1	1	yes	characteristic, complemented, Hall
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	5	2	no	—
499	C₂²×C₃	—	10	1	no	—
500	C₂²×C₃	—	10	1	no	—
501	C₂²×C₃	—	10	1	no	—
502	C₂²×C₃	—	10	2	no	—
503	C₂²×C₃	—	10	2	no	—
504	C₂²×C₃	—	10	1	no	—
505	C₂²×C₃	—	10	1	no	—
506	C₂²×C₃	—	10	2	no	—
507	C₂²×C₃	—	20	4	no	—
508	C₂²×C₃	C₄×D₂₀	1	2	yes	—
509	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
510	C₃×C₄	—	2	2	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	10	1	no	—
513	C₃×C₄	—	10	1	no	—
514	C₃×C₄	—	10	2	no	—
515	C₃×C₄	C₄×D₂₀	1	2	yes	—
516	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
517	C₃×C₄	C₂×#709	1	1	yes	characteristic
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
520	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
521	C₂×C₅	C₃×#568	1	1	yes	characteristic
522	D₅	—	2	2	no	—
523	D₅	—	4	1	no	—
524	D₅	—	4	2	no	—
525	C₂³	—	5	1	no	—
526	C₂³	—	5	1	no	—
527	C₂³	—	5	2	no	—
528	C₂³	—	10	2	no	—
529	C₂³	—	10	2	no	—
530	C₂³	—	20	1	no	—
531	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
532	Q₈	—	10	2	no	—
533	D₄	—	10	4	no	—
534	D₄	—	10	4	no	—
535	D₄	—	10	2	no	—
536	D₄	—	20	2	no	—
537	C₂×C₄	—	5	1	no	—
538	C₂×C₄	—	5	1	no	—
539	C₂×C₄	—	5	2	no	—
540	C₂×C₄	—	10	2	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	10	2	no	—
543	C₂×C₄	—	10	1	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	—	10	1	no	—
546	C₂×C₄	—	10	2	no	—
547	C₂×C₄	—	10	2	no	—
548	C₂×C₄	—	10	2	no	—
549	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
550	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
551	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
552	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
553	C₂×C₄	C₃×#709	1	2	yes	—
554	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	10	1	no	—
558	C₈	—	10	1	no	—
559	C₈	—	10	2	no	—
560	C₈	C₂×C₃×D₂₀	1	4	yes	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	10	2	no	—
563	C₂×C₃	—	20	1	no	—
564	C₂×C₃	—	20	2	no	—
565	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
566	C₂×C₃	D₅×#131	1	1	yes	characteristic
567	C₂×C₃	#66084	1	1	yes	characteristic
568	C₅	C₃×#2933	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	5	2	no	—
572	C₂²	—	10	1	no	—
573	C₂²	—	10	1	no	—
574	C₂²	—	10	1	no	—
575	C₂²	—	10	2	no	—
576	C₂²	—	10	2	no	—
577	C₂²	—	10	1	no	—
578	C₂²	—	10	1	no	—
579	C₂²	—	10	2	no	—
580	C₂²	—	20	4	no	—
581	C₂²	C₃×C₄×D₂₀	1	2	yes	—
582	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	10	1	no	—
586	C₄	—	10	1	no	—
587	C₄	—	10	2	no	—
588	C₄	C₃×C₄×D₂₀	1	2	yes	—
589	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
590	C₄	C₂×C₃×#709	1	1	yes	characteristic
591	C₃	#10610286	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	10	2	no	—
594	C₂	—	20	1	no	—
595	C₂	—	20	2	no	—
596	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
597	C₂	C₃×D₅×#131	1	1	yes	characteristic
598	C₂	C₃×#66084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65858	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2933
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4053	C₂	semidirect
2. C₂×C₃×D₅×M₁₆	C₂	semidirect
4. C₃×C₅×#405	C₂	semidirect
5. C₃×#65399	C₂	semidirect
6. C₂×C₃×#3952	C₂	semidirect
7. C₃×#65288	C₂	semidirect
8. C₃×#64995	C₂	semidirect
9. C₃×#64995	C₂	semidirect
10. C₃×#64977	C₂	semidirect
11. C₃×C₈×D₂₀	C₂	semidirect
12. #10610286	C₃	direct (N × H)
23. C₂×C₃×#676	C₂²	semidirect
25. C₂×C₃×C₈×D₅	C₂²	semidirect
34. C₃×C₅×#97	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
40. C₃×#3952	C₂²	semidirect
41. C₃×#3952	C₂²	semidirect
42. C₃×C₄⋊#168	C₂²	semidirect
43. C₃×C₄⋊#168	C₂²	semidirect
45. C₂×#4053	C₂×C₃	semidirect
46. C₂×D₅×M₁₆	C₂×C₃	semidirect
48. C₅×#405	C₂×C₃	semidirect
49. #65399	C₂×C₃	semidirect
50. C₂×#3952	C₂×C₃	semidirect
51. #65288	C₂×C₃	semidirect
52. #64995	C₂×C₃	semidirect
53. #64995	C₂×C₃	semidirect
54. #64977	C₂×C₃	semidirect
55. C₈×D₂₀	C₂×C₃	semidirect
73. C₃×C₅×M₁₆	D₄	semidirect
107. C₃×#405	D₅	semidirect
118. C₂×#676	C₂²×C₃	semidirect
120. C₂×C₈×D₅	C₂²×C₃	semidirect
129. C₅×#97	C₂²×C₃	semidirect
130. C₄×C₅×C₈	C₂²×C₃	semidirect
135. #3952	C₂²×C₃	semidirect
136. #3952	C₂²×C₃	semidirect
137. C₄⋊#168	C₂²×C₃	semidirect
138. C₄⋊#168	C₂²×C₃	semidirect
205. C₃×#97	C₂×D₅	semidirect
206. C₃×C₄×C₈	C₂×D₅	semidirect
224. C₅×M₁₆	C₃×D₄	semidirect
258. #405	C₃×D₅	semidirect
272. C₂×C₃×D₅	#131	semidirect
301. C₃×M₁₆	D₂₀	semidirect
387. #97	C₂×C₃×D₅	semidirect
388. C₄×C₈	C₂×C₃×D₅	semidirect
445. C₂×D₅	C₃×#131	semidirect
474. M₁₆	C₃×D₂₀	semidirect
495. C₃×C₅	#2933	semidirect
568. C₅	C₃×#2933	semidirect
591. C₃	#10610286	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×#4053	2
C₂×C₃×D₅×M₁₆	2
C₃×#65858	2
C₃×C₅×#405	2
C₃×#65399	2
C₂×C₃×#3952	2
C₃×#65288	2
C₃×#64995	2
C₃×#64977	2
C₃×C₈×D₂₀	2
#10610286	3
C₃×#2933	5

Subgroups — C3×#10610286 #14415452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610286 #14415452