Subgroups — C₃×#10610331 #14411801

Order 1920.

1548 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4047	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65399	C₂	1	2	yes	maximal, complemented
6	C₃×#65016	C₂	1	4	yes	maximal, complemented
7	C₃×#65015	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
9	#10610331	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	C₄	1	2	yes	—
12	C₂×C₃×#709	—	2	8	no	—
13	C₂×C₃×#709	C₄	1	2	yes	—
14	C₂×C₃×#709	C₄	1	1	yes	characteristic
15	C₂×C₃×#709	C₄	1	1	yes	characteristic
16	C₂×C₃×#709	C₂²	1	1	yes	characteristic
17	C₂×C₃×#709	C₂²	1	2	yes	—
18	C₂×C₃×#709	C₂²	1	1	yes	characteristic
19	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
21	C₂²×C₃×Dic₁₀	C₄	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
23	C₂×C₃×#681	C₂²	1	2	yes	complemented
24	C₃×#4047	—	2	8	no	—
25	C₂×C₃×#676	C₂²	1	4	yes	complemented
26	C₂×C₃×C₈×D₅	C₂²	1	4	yes	complemented
27	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
30	C₃×C₂²⋊#168	C₂²	1	2	yes	—
31	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
32	C₃×#3952	C₂²	1	4	yes	complemented
33	C₃×#3952	C₂²	1	4	yes	complemented
34	C₃×#2880	—	5	1	no	maximal, Hall
35	C₂²×#709	C₂×C₃	1	1	yes	characteristic
36	C₂×#4047	C₂×C₃	1	2	yes	complemented
37	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
38	#65496	C₂×C₃	1	1	yes	characteristic, complemented
39	#65399	C₂×C₃	1	2	yes	complemented
40	#65016	C₂×C₃	1	4	yes	complemented
41	#65015	C₂×C₃	1	2	yes	complemented
42	D₅×C₂²⋊C₈	C₂×C₃	1	2	yes	complemented
43	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
53	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
57	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
58	C₃×#709	—	2	4	no	—
59	C₃×#709	—	2	8	no	—
60	C₃×#709	—	2	4	no	—
61	C₃×#709	—	2	8	no	—
62	C₃×#709	—	2	4	no	—
63	C₃×#709	D₄	1	8	yes	—
64	C₂×C₃×D₂₀	—	2	4	no	—
65	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
66	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	—	2	8	no	—
69	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
70	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
71	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
72	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
73	C₂×C₃×Dic₁₀	—	2	4	no	—
74	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
76	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	—	2	4	no	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₃×#681	—	2	4	no	—
81	C₂×C₃×#168	C₂³	1	4	yes	—
82	C₃×#676	—	2	8	no	—
83	C₃×C₈×D₅	—	2	8	no	—
84	C₂²×C₃×#41	—	5	1	no	—
85	C₂×C₃×#131	—	5	2	no	—
86	C₃×#408	—	5	2	no	—
87	C₃×#408	—	5	4	no	—
88	C₃×#407	—	5	1	no	—
89	C₃×#407	—	5	2	no	—
90	C₂×C₃×C₂²⋊C₈	—	5	2	no	—
91	C₂×C₃×C₂²⋊C₈	D₅	1	1	yes	characteristic, complemented
92	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₂²⋊D₅	C₃×C₄	1	2	yes	—
94	C₂×#709	—	2	8	no	—
95	C₂×#709	C₃×C₄	1	2	yes	—
96	C₂×#709	C₃×C₄	1	1	yes	characteristic
97	C₂×#709	C₃×C₄	1	1	yes	characteristic
98	C₂×#709	C₂²×C₃	1	1	yes	characteristic
99	C₂×#709	C₂²×C₃	1	2	yes	—
100	C₂×#709	C₂²×C₃	1	1	yes	characteristic
101	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic
102	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
103	C₂²×Dic₁₀	C₃×C₄	1	1	yes	characteristic
104	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
105	C₂×#681	C₂²×C₃	1	2	yes	complemented
106	#4047	—	2	8	no	—
107	C₂×#676	C₂²×C₃	1	4	yes	complemented
108	C₂×C₈×D₅	C₂²×C₃	1	4	yes	complemented
109	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
110	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
111	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
112	C₂²⋊#168	C₂²×C₃	1	2	yes	—
113	C₂²⋊#168	C₂²×C₃	1	2	yes	complemented
114	#3952	C₂²×C₃	1	4	yes	complemented
115	#3952	C₂²×C₃	1	4	yes	complemented
116	#2880	—	5	1	no	Sylow
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	4	1	no	—
120	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₃×D₅	—	2	4	no	—
124	C₂²×C₃×D₅	—	2	4	no	—
125	C₂²×C₃×D₅	—	4	2	no	—
126	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
127	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₂²⋊D₅	—	2	4	no	—
139	C₃×C₂²⋊D₅	—	2	4	no	—
140	C₃×C₂²⋊D₅	—	2	4	no	—
141	C₃×C₂²⋊D₅	C₂²⋊C₄	1	8	yes	—
142	C₂×C₃×Dic₅	—	2	4	no	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
145	C₃×D₂₀	—	2	4	no	—
146	C₃×D₂₀	—	2	2	no	—
147	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
148	C₃×C₄×D₅	—	2	4	no	—
149	C₃×C₄×D₅	—	2	4	no	—
150	C₃×C₄×D₅	—	2	4	no	—
151	C₃×C₄×D₅	C₂×D₄	1	8	yes	—
152	C₃×Dic₁₀	—	2	2	no	—
153	C₃×Dic₁₀	—	2	4	no	—
154	C₃×Dic₁₀	C₂²⋊C₄	1	4	yes	—
155	C₃×C₅×C₈	—	2	2	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₃×#168	—	2	4	no	—
158	C₂×C₃×#41	—	5	2	no	—
159	C₂×C₃×#41	—	5	1	no	—
160	C₂×C₃×#41	—	5	1	no	—
161	C₂×C₃×#41	—	5	1	no	—
162	C₂×C₃×#41	—	5	2	no	—
163	C₂×C₃×#41	—	5	1	no	—
164	C₂×C₃×#41	—	10	8	no	—
165	C₂²×C₃×Q₈	—	5	1	no	—
166	C₂²×C₃×D₄	—	5	2	no	—
167	C₂²×C₃×D₄	—	5	1	no	—
168	C₂³×C₃×C₄	—	5	2	no	—
169	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
170	C₃×#131	—	10	8	no	—
171	C₂×C₃×M₁₆	—	5	2	no	—
172	C₂×C₃×M₁₆	—	5	4	no	—
173	C₂²×C₃×C₈	—	5	4	no	—
174	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
175	C₃×C₂²⋊C₈	—	5	2	no	—
176	C₃×C₂²⋊C₈	—	5	2	no	—
177	C₃×C₂²⋊C₈	—	5	4	no	—
178	C₃×C₂²⋊C₈	—	5	4	no	—
179	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
180	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
181	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	complemented
182	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
184	C₂²×C₄×C₅	—	2	4	no	—
185	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₂²⋊D₅	—	2	8	no	—
192	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
193	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
194	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
195	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
196	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
197	#709	—	2	4	no	—
198	#709	—	2	8	no	—
199	#709	—	2	4	no	—
200	#709	—	2	8	no	—
201	#709	—	2	4	no	—
202	#709	C₃×D₄	1	8	yes	—
203	C₂×D₂₀	—	2	4	no	—
204	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
205	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×D₅	—	2	8	no	—
208	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
209	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
210	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
211	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
212	C₂×Dic₁₀	—	2	4	no	—
213	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
214	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
215	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×C₅×C₈	—	2	4	no	—
217	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
218	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
219	#681	—	2	4	no	—
220	C₂×#168	C₂³×C₃	1	4	yes	—
221	#676	—	2	8	no	—
222	C₈×D₅	—	2	8	no	—
223	C₂²×#41	—	5	1	no	—
224	C₂×#131	—	5	2	no	—
225	#408	—	5	2	no	—
226	#408	—	5	4	no	—
227	#407	—	5	1	no	—
228	#407	—	5	2	no	—
229	C₂×C₂²⋊C₈	—	5	2	no	—
230	C₂×C₂²⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
231	C₂²×C₃×C₅	—	2	1	no	—
232	C₂²×C₃×C₅	—	2	1	no	—
233	C₂²×C₃×C₅	—	2	1	no	—
234	C₂²×C₃×C₅	—	2	1	no	—
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	1	no	—
237	C₂²×C₃×C₅	—	2	1	no	—
238	C₂²×C₃×C₅	—	4	4	no	—
239	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂²×C₃×C₅	#131	1	2	yes	complemented
241	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₂×C₃×D₅	—	2	2	no	—
243	C₂×C₃×D₅	—	2	2	no	—
244	C₂×C₃×D₅	—	2	2	no	—
245	C₂×C₃×D₅	—	2	2	no	—
246	C₂×C₃×D₅	—	2	2	no	—
247	C₂×C₃×D₅	—	4	8	no	—
248	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	4	yes	—
249	C₃×C₄×C₅	—	2	1	no	—
250	C₃×C₄×C₅	—	2	1	no	—
251	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
252	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
253	C₃×Dic₅	—	2	2	no	—
254	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
255	C₂⁴×C₃	—	5	2	no	—
256	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
257	C₃×#41	—	5	8	no	—
258	C₃×#41	—	10	8	no	—
259	C₃×#41	—	10	8	no	—
260	C₃×#41	—	10	4	no	—
261	C₃×#41	—	10	4	no	—
262	C₃×#41	—	10	4	no	—
263	C₂×C₃×Q₈	—	5	1	no	—
264	C₂×C₃×Q₈	—	5	2	no	—
265	C₂×C₃×Q₈	—	5	1	no	—
266	C₂×C₃×Q₈	—	10	4	no	—
267	C₂×C₃×D₄	—	5	2	no	—
268	C₂×C₃×D₄	—	5	2	no	—
269	C₂×C₃×D₄	—	5	2	no	—
270	C₂×C₃×D₄	—	5	2	no	—
271	C₂×C₃×D₄	—	5	1	no	—
272	C₂×C₃×D₄	—	5	2	no	—
273	C₂×C₃×D₄	—	5	1	no	—
274	C₂×C₃×D₄	—	10	4	no	—
275	C₂×C₃×D₄	—	10	8	no	—
276	C₂²×C₃×C₄	—	2	4	no	—
277	C₂²×C₃×C₄	—	5	2	no	—
278	C₂²×C₃×C₄	—	5	2	no	—
279	C₂²×C₃×C₄	—	5	2	no	—
280	C₂²×C₃×C₄	—	5	2	no	—
281	C₂²×C₃×C₄	—	5	2	no	—
282	C₂²×C₃×C₄	—	10	8	no	—
283	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
289	C₃×M₁₆	—	10	8	no	—
290	C₃×M₁₆	—	10	4	no	—
291	C₂×C₃×C₈	—	2	4	no	—
292	C₂×C₃×C₈	—	5	4	no	—
293	C₂×C₃×C₈	—	10	8	no	—
294	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
295	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	4	1	no	—
299	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
300	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₂²×D₅	—	2	4	no	—
303	C₂²×D₅	—	2	4	no	—
304	C₂²×D₅	—	4	2	no	—
305	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
306	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
316	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
317	C₂²⋊D₅	—	2	4	no	—
318	C₂²⋊D₅	—	2	4	no	—
319	C₂²⋊D₅	—	2	4	no	—
320	C₂²⋊D₅	C₃×C₂²⋊C₄	1	8	yes	—
321	C₂×Dic₅	—	2	4	no	—
322	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
323	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
324	D₂₀	—	2	4	no	—
325	D₂₀	—	2	2	no	—
326	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
327	C₄×D₅	—	2	4	no	—
328	C₄×D₅	—	2	4	no	—
329	C₄×D₅	—	2	4	no	—
330	C₄×D₅	C₂×C₃×D₄	1	8	yes	—
331	Dic₁₀	—	2	2	no	—
332	Dic₁₀	—	2	4	no	—
333	Dic₁₀	C₃×C₂²⋊C₄	1	4	yes	—
334	C₅×C₈	—	2	2	no	—
335	C₅×C₈	—	2	2	no	—
336	#168	—	2	4	no	—
337	C₂×#41	—	5	2	no	—
338	C₂×#41	—	5	1	no	—
339	C₂×#41	—	5	1	no	—
340	C₂×#41	—	5	1	no	—
341	C₂×#41	—	5	2	no	—
342	C₂×#41	—	5	1	no	—
343	C₂×#41	—	10	8	no	—
344	C₂²×Q₈	—	5	1	no	—
345	C₂²×D₄	—	5	2	no	—
346	C₂²×D₄	—	5	1	no	—
347	C₂³×C₄	—	5	2	no	—
348	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
349	#131	—	10	8	no	—
350	C₂×M₁₆	—	5	2	no	—
351	C₂×M₁₆	—	5	4	no	—
352	C₂²×C₈	—	5	4	no	—
353	C₂²×C₈	C₂×C₃×D₅	1	2	yes	complemented
354	C₂²⋊C₈	—	5	2	no	—
355	C₂²⋊C₈	—	5	2	no	—
356	C₂²⋊C₈	—	5	4	no	—
357	C₂²⋊C₈	—	5	4	no	—
358	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
359	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
360	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	complemented
361	C₂×C₃×C₅	—	2	2	no	—
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	—	4	1	no	—
364	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
366	C₂×C₃×C₅	#568	1	1	yes	characteristic
367	C₃×D₅	—	2	4	no	—
368	C₃×D₅	—	4	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	—	4	1	no	—
372	C₂³×C₃	—	5	2	no	—
373	C₂³×C₃	—	5	2	no	—
374	C₂³×C₃	—	10	4	no	—
375	C₂³×C₃	—	10	4	no	—
376	C₂³×C₃	—	20	2	no	—
377	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
378	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
379	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
380	C₃×Q₈	—	5	4	no	—
381	C₃×Q₈	—	10	4	no	—
382	C₃×Q₈	—	10	2	no	—
383	C₃×D₄	—	5	8	no	—
384	C₃×D₄	—	5	4	no	—
385	C₃×D₄	—	10	4	no	—
386	C₃×D₄	—	10	4	no	—
387	C₃×D₄	—	10	4	no	—
388	C₃×D₄	—	10	4	no	—
389	C₃×D₄	—	10	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	5	2	no	—
396	C₂×C₃×C₄	—	5	8	no	—
397	C₂×C₃×C₄	—	5	2	no	—
398	C₂×C₃×C₄	—	10	4	no	—
399	C₂×C₃×C₄	—	10	4	no	—
400	C₂×C₃×C₄	—	10	4	no	—
401	C₂×C₃×C₄	—	10	4	no	—
402	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
405	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
406	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	2	no	—
409	C₃×C₈	—	10	4	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	1	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	4	4	no	—
418	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
419	C₂²×C₅	C₃×#131	1	2	yes	complemented
420	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	2	2	no	—
423	C₂×D₅	—	2	2	no	—
424	C₂×D₅	—	2	2	no	—
425	C₂×D₅	—	2	2	no	—
426	C₂×D₅	—	4	8	no	—
427	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
431	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
432	Dic₅	—	2	2	no	—
433	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
434	C₂⁴	—	5	2	no	—
435	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
436	#41	—	5	8	no	—
437	#41	—	10	8	no	—
438	#41	—	10	8	no	—
439	#41	—	10	4	no	—
440	#41	—	10	4	no	—
441	#41	—	10	4	no	—
442	C₂×Q₈	—	5	1	no	—
443	C₂×Q₈	—	5	2	no	—
444	C₂×Q₈	—	5	1	no	—
445	C₂×Q₈	—	10	4	no	—
446	C₂×D₄	—	5	2	no	—
447	C₂×D₄	—	5	2	no	—
448	C₂×D₄	—	5	2	no	—
449	C₂×D₄	—	5	2	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	—	5	2	no	—
452	C₂×D₄	—	5	1	no	—
453	C₂×D₄	—	10	4	no	—
454	C₂×D₄	—	10	8	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	5	2	no	—
457	C₂²×C₄	—	5	2	no	—
458	C₂²×C₄	—	5	2	no	—
459	C₂²×C₄	—	5	2	no	—
460	C₂²×C₄	—	5	2	no	—
461	C₂²×C₄	—	10	8	no	—
462	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
463	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
464	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
468	M₁₆	—	10	8	no	—
469	M₁₆	—	10	4	no	—
470	C₂×C₈	—	2	4	no	—
471	C₂×C₈	—	5	4	no	—
472	C₂×C₈	—	10	8	no	—
473	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
474	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
475	C₃×C₅	#2880	1	1	yes	characteristic, complemented, Hall
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	4	4	no	—
484	C₂²×C₃	—	5	4	no	—
485	C₂²×C₃	—	10	2	no	—
486	C₂²×C₃	—	10	2	no	—
487	C₂²×C₃	—	10	2	no	—
488	C₂²×C₃	—	10	2	no	—
489	C₂²×C₃	—	10	2	no	—
490	C₂²×C₃	—	20	8	no	—
491	C₂²×C₃	D₅×C₂²⋊C₄	1	2	yes	—
492	C₂²×C₃	#4047	1	2	yes	complemented
493	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	5	4	no	—
497	C₃×C₄	—	10	2	no	—
498	C₃×C₄	D₅×C₂²⋊C₄	1	2	yes	—
499	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
500	C₂×C₅	—	2	2	no	—
501	C₂×C₅	—	2	2	no	—
502	C₂×C₅	—	4	1	no	—
503	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
504	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
505	C₂×C₅	C₃×#568	1	1	yes	characteristic
506	D₅	—	2	4	no	—
507	D₅	—	4	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	5	2	no	—
512	C₂³	—	5	2	no	—
513	C₂³	—	10	4	no	—
514	C₂³	—	10	4	no	—
515	C₂³	—	20	2	no	—
516	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
517	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
518	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
519	Q₈	—	5	4	no	—
520	Q₈	—	10	4	no	—
521	Q₈	—	10	2	no	—
522	D₄	—	5	8	no	—
523	D₄	—	5	4	no	—
524	D₄	—	10	4	no	—
525	D₄	—	10	4	no	—
526	D₄	—	10	4	no	—
527	D₄	—	10	4	no	—
528	D₄	—	10	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	5	2	no	—
535	C₂×C₄	—	5	8	no	—
536	C₂×C₄	—	5	2	no	—
537	C₂×C₄	—	10	4	no	—
538	C₂×C₄	—	10	4	no	—
539	C₂×C₄	—	10	4	no	—
540	C₂×C₄	—	10	4	no	—
541	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
542	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
543	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
544	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
545	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	10	4	no	—
549	C₂×C₃	—	2	2	no	—
550	C₂×C₃	—	2	2	no	—
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	—	10	4	no	—
553	C₂×C₃	—	20	2	no	—
554	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
555	C₂×C₃	C₂×#4047	1	1	yes	characteristic
556	C₂×C₃	#66079	1	1	yes	characteristic
557	C₅	C₃×#2880	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	5	4	no	—
567	C₂²	—	10	2	no	—
568	C₂²	—	10	2	no	—
569	C₂²	—	10	2	no	—
570	C₂²	—	10	2	no	—
571	C₂²	—	10	2	no	—
572	C₂²	—	20	8	no	—
573	C₂²	C₃×D₅×C₂²⋊C₄	1	2	yes	—
574	C₂²	C₃×#4047	1	2	yes	complemented
575	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	5	4	no	—
579	C₄	—	10	2	no	—
580	C₄	C₃×D₅×C₂²⋊C₄	1	2	yes	—
581	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
582	C₃	#10610331	1	1	yes	characteristic, direct product factor, Sylow
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	10	4	no	—
587	C₂	—	20	2	no	—
588	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
589	C₂	C₂×C₃×#4047	1	1	yes	characteristic
590	C₂	C₃×#66079	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	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×#709	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₂²⋊C₈	D₅
hypocenter	C₅	C₃×#2880
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4047	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
4. C₃×#65496	C₂	semidirect
5. C₃×#65399	C₂	semidirect
6. C₃×#65016	C₂	semidirect
7. C₃×#65015	C₂	semidirect
8. C₃×D₅×C₂²⋊C₈	C₂	semidirect
9. #10610331	C₃	direct (N × H)
22. C₂²×C₃×C₅×C₈	C₂²	semidirect
23. C₂×C₃×#681	C₂²	semidirect
25. C₂×C₃×#676	C₂²	semidirect
26. C₂×C₃×C₈×D₅	C₂²	semidirect
29. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
31. C₃×C₂²⋊#168	C₂²	semidirect
32. C₃×#3952	C₂²	semidirect
33. C₃×#3952	C₂²	semidirect
36. C₂×#4047	C₂×C₃	semidirect
37. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
38. #65496	C₂×C₃	semidirect
39. #65399	C₂×C₃	semidirect
40. #65016	C₂×C₃	semidirect
41. #65015	C₂×C₃	semidirect
42. D₅×C₂²⋊C₈	C₂×C₃	semidirect
91. C₂×C₃×C₂²⋊C₈	D₅	semidirect
104. C₂²×C₅×C₈	C₂²×C₃	semidirect
105. C₂×#681	C₂²×C₃	semidirect
107. C₂×#676	C₂²×C₃	semidirect
108. C₂×C₈×D₅	C₂²×C₃	semidirect
111. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
113. C₂²⋊#168	C₂²×C₃	semidirect
114. #3952	C₂²×C₃	semidirect
115. #3952	C₂²×C₃	semidirect
174. C₂²×C₃×C₈	C₂×D₅	semidirect
181. C₃×C₂²⋊C₈	C₂×D₅	semidirect
230. C₂×C₂²⋊C₈	C₃×D₅	semidirect
240. C₂²×C₃×C₅	#131	semidirect
353. C₂²×C₈	C₂×C₃×D₅	semidirect
360. C₂²⋊C₈	C₂×C₃×D₅	semidirect
419. C₂²×C₅	C₃×#131	semidirect
475. C₃×C₅	#2880	semidirect
492. C₂²×C₃	#4047	semidirect
557. C₅	C₃×#2880	semidirect
574. C₂²	C₃×#4047	semidirect
582. C₃	#10610331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#709	2
C₂×C₃×#4047	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×#65496	2
C₃×#65399	2
C₃×#65016	2
C₃×#65015	2
C₃×D₅×C₂²⋊C₈	2
#10610331	3
C₃×#2880	5

Subgroups — C3×#10610331 #14411801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610331 #14411801