Subgroups — C₃×#10610445 #14412159

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic
2	C₃×#66079	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#413	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65526	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3955	C₂	1	2	yes	maximal, complemented
6	C₃×#65040	C₂	1	4	yes	maximal, complemented
7	C₃×D₅×#100	C₂	1	4	yes	maximal, complemented
8	#10610445	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₃×#4149	—	2	4	no	—
11	C₃×#4149	—	2	4	no	—
12	C₂×C₃×#713	C₂²	1	2	yes	—
13	C₂×C₃×D₄×D₅	C₄	1	4	yes	—
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₂×C₃×#709	C₄	1	2	yes	—
16	C₂×C₃×#709	C₂²	1	1	yes	characteristic
17	C₂²×C₃×D₂₀	C₄	1	2	yes	—
18	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃×#681	C₂²	1	2	yes	complemented
21	C₃×#4053	—	2	4	no	—
22	C₃×D₅×M₁₆	C₂²	1	8	yes	complemented
23	C₃×#4047	—	2	4	no	—
24	C₃×C₅×#101	C₂²	1	2	yes	complemented
25	C₃×C₅×#100	C₂²	1	2	yes	complemented
26	C₃×#3968	C₂²	1	2	yes	complemented
27	C₃×#3965	C₂²	1	2	yes	complemented
28	C₃×#3955	C₂²	1	8	yes	complemented
29	C₃×#2888	—	5	1	no	maximal, Hall
30	C₂×#4149	C₂×C₃	1	1	yes	characteristic
31	#66079	C₂×C₃	1	2	yes	complemented
32	C₅×#413	C₂×C₃	1	1	yes	characteristic, complemented
33	#65526	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3955	C₂×C₃	1	2	yes	complemented
35	#65040	C₂×C₃	1	4	yes	complemented
36	D₅×#100	C₂×C₃	1	4	yes	complemented
37	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
38	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
39	C₃×C₅×#41	—	2	2	no	—
40	C₃×C₅×#41	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
47	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
48	C₃×#713	—	2	8	no	—
49	C₃×D₄×D₅	—	2	16	no	—
50	C₃×D₄×D₅	—	2	8	no	—
51	C₃×#709	—	2	4	no	—
52	C₃×#709	—	2	4	no	—
53	C₃×#709	D₄	1	4	yes	—
54	C₃×#709	D₄	1	4	yes	—
55	C₂×C₃×D₂₀	—	2	2	no	—
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	—	2	4	no	—
58	C₂×C₃×D₂₀	—	2	4	no	—
59	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
60	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
61	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×D₂₀	C₂³	1	2	yes	—
63	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
64	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
65	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
66	C₃×C₅×M₁₆	—	2	2	no	—
67	C₃×C₅×M₁₆	C₂³	1	4	yes	—
68	C₂×C₃×C₅×C₈	—	2	2	no	—
69	C₃×#681	—	2	2	no	—
70	C₃×#681	C₂³	1	4	yes	—
71	C₂×C₃×#168	—	2	2	no	—
72	C₃×#676	—	2	8	no	—
73	C₃×C₈×D₅	—	2	8	no	—
74	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
75	C₃×#568	—	5	2	no	—
76	C₃×#413	—	5	1	no	—
77	C₃×#413	—	5	4	no	—
78	C₃×#413	D₅	1	1	yes	characteristic, complemented
79	C₂×C₃×#100	—	5	2	no	—
80	C₂×C₃×#100	—	5	4	no	—
81	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
82	#4149	—	2	4	no	—
83	#4149	—	2	4	no	—
84	C₂×#713	C₂²×C₃	1	2	yes	—
85	C₂×D₄×D₅	C₃×C₄	1	4	yes	—
86	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
87	C₂×#709	C₃×C₄	1	2	yes	—
88	C₂×#709	C₂²×C₃	1	1	yes	characteristic
89	C₂²×D₂₀	C₃×C₄	1	2	yes	—
90	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
92	C₂×#681	C₂²×C₃	1	2	yes	complemented
93	#4053	—	2	4	no	—
94	D₅×M₁₆	C₂²×C₃	1	8	yes	complemented
95	#4047	—	2	4	no	—
96	C₅×#101	C₂²×C₃	1	2	yes	complemented
97	C₅×#100	C₂²×C₃	1	2	yes	complemented
98	#3968	C₂²×C₃	1	2	yes	complemented
99	#3965	C₂²×C₃	1	2	yes	complemented
100	#3955	C₂²×C₃	1	8	yes	complemented
101	#2888	—	5	1	no	Sylow
102	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
103	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₃×D₅	—	2	4	no	—
105	C₂²×C₃×D₅	—	2	8	no	—
106	C₂²×C₃×D₅	—	8	4	no	—
107	C₂²×C₃×D₅	—	8	2	no	—
108	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
109	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
110	C₃×C₅×Q₈	—	2	2	no	—
111	C₃×C₅×D₄	—	2	4	no	—
112	C₃×C₅×D₄	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₂²⋊D₅	—	2	8	no	—
121	C₃×C₂²⋊D₅	C₂²⋊C₄	1	8	yes	—
122	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
123	C₃×D₂₀	—	2	8	no	—
124	C₃×D₂₀	—	2	2	no	—
125	C₃×D₂₀	—	2	2	no	—
126	C₃×D₂₀	—	2	4	no	—
127	C₃×D₂₀	C₂²⋊C₄	1	2	yes	—
128	C₃×D₂₀	C₂²⋊C₄	1	2	yes	—
129	C₃×C₄×D₅	—	2	8	no	—
130	C₃×C₄×D₅	C₂×D₄	1	8	yes	—
131	C₃×Dic₁₀	C₂²⋊C₄	1	2	yes	—
132	C₃×Dic₁₀	C₂²⋊C₄	1	2	yes	—
133	C₃×C₅×C₈	—	2	4	no	—
134	C₃×#168	—	2	4	no	—
135	C₃×H(5,𝔽₂)	—	10	4	no	—
136	C₃×H(5,𝔽₂)	—	10	4	no	—
137	C₂×C₃×#41	—	5	2	no	—
138	C₂×C₃×#41	—	5	2	no	—
139	C₂×C₃×#41	—	5	1	no	—
140	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
141	C₂²×C₃×D₄	—	5	4	no	—
142	C₂²×C₃×D₄	—	5	2	no	—
143	C₂²×C₃×D₄	—	5	2	no	—
144	C₂²×C₃×D₄	—	5	1	no	—
145	C₃×#131	—	10	4	no	—
146	C₃×#131	—	10	4	no	—
147	C₂×C₃×M₁₆	—	5	2	no	—
148	C₂×C₃×M₁₆	—	5	8	no	—
149	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	complemented
150	C₃×#101	—	5	2	no	—
151	C₃×#101	C₂×D₅	1	2	yes	complemented
152	C₃×#100	—	5	2	no	—
153	C₃×#100	—	5	8	no	—
154	C₃×#100	C₂×D₅	1	2	yes	complemented
155	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
156	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
157	C₅×#41	—	2	2	no	—
158	C₅×#41	—	2	2	no	—
159	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
161	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
165	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
166	#713	—	2	8	no	—
167	D₄×D₅	—	2	16	no	—
168	D₄×D₅	—	2	8	no	—
169	#709	—	2	4	no	—
170	#709	—	2	4	no	—
171	#709	C₃×D₄	1	4	yes	—
172	#709	C₃×D₄	1	4	yes	—
173	C₂×D₂₀	—	2	2	no	—
174	C₂×D₂₀	—	2	2	no	—
175	C₂×D₂₀	—	2	4	no	—
176	C₂×D₂₀	—	2	4	no	—
177	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
178	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
179	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
180	C₂×D₂₀	C₂³×C₃	1	2	yes	—
181	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
182	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
183	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
184	C₅×M₁₆	—	2	2	no	—
185	C₅×M₁₆	C₂³×C₃	1	4	yes	—
186	C₂×C₅×C₈	—	2	2	no	—
187	#681	—	2	2	no	—
188	#681	C₂³×C₃	1	4	yes	—
189	C₂×#168	—	2	2	no	—
190	#676	—	2	8	no	—
191	C₈×D₅	—	2	8	no	—
192	C₂×H(5,𝔽₂)	—	5	1	no	—
193	#568	—	5	2	no	—
194	#413	—	5	1	no	—
195	#413	—	5	4	no	—
196	#413	C₃×D₅	1	1	yes	characteristic, complemented
197	C₂×#100	—	5	2	no	—
198	C₂×#100	—	5	4	no	—
199	C₂²×C₃×C₅	—	2	2	no	—
200	C₂²×C₃×C₅	—	4	1	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₃×D₅	—	2	4	no	—
205	C₂×C₃×D₅	—	4	2	no	—
206	C₂×C₃×D₅	—	4	4	no	—
207	C₂×C₃×D₅	—	8	8	no	—
208	C₂×C₃×D₅	—	8	4	no	—
209	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	4	yes	—
210	C₃×C₄×C₅	—	2	2	no	—
211	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
214	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
215	C₂⁴×C₃	—	5	4	no	—
216	C₂⁴×C₃	—	5	2	no	—
217	C₃×#41	—	2	2	no	—
218	C₃×#41	—	2	2	no	—
219	C₃×#41	—	5	4	no	—
220	C₃×#41	—	5	4	no	—
221	C₃×#41	—	10	4	no	—
222	C₃×#41	—	10	4	no	—
223	C₃×#41	—	10	8	no	—
224	C₂×C₃×Q₈	—	5	1	no	—
225	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
226	C₂×C₃×D₄	—	5	2	no	—
227	C₂×C₃×D₄	—	5	4	no	—
228	C₂×C₃×D₄	—	5	1	no	—
229	C₂×C₃×D₄	—	5	4	no	—
230	C₂×C₃×D₄	—	5	2	no	—
231	C₂×C₃×D₄	—	5	2	no	—
232	C₂×C₃×D₄	—	10	4	no	—
233	C₂×C₃×D₄	—	10	4	no	—
234	C₂×C₃×D₄	—	10	8	no	—
235	C₂×C₃×D₄	—	10	16	no	—
236	C₂×C₃×D₄	—	10	2	no	—
237	C₂×C₃×D₄	—	10	2	no	—
238	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
239	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	—	5	2	no	—
241	C₂²×C₃×C₄	—	5	4	no	—
242	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
243	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₃×M₁₆	—	2	2	no	—
245	C₃×M₁₆	—	5	4	no	—
246	C₃×M₁₆	—	10	8	no	—
247	C₃×M₁₆	—	10	2	no	—
248	C₃×M₁₆	C₂²×D₅	1	4	yes	—
249	C₂×C₃×C₈	—	2	2	no	—
250	C₂×C₃×C₈	—	10	8	no	—
251	C₂×C₃×C₈	—	10	2	no	—
252	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
253	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
254	C₂²×D₅	—	2	4	no	—
255	C₂²×D₅	—	2	8	no	—
256	C₂²×D₅	—	8	4	no	—
257	C₂²×D₅	—	8	2	no	—
258	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
259	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
260	C₅×Q₈	—	2	2	no	—
261	C₅×D₄	—	2	4	no	—
262	C₅×D₄	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
270	C₂²⋊D₅	—	2	8	no	—
271	C₂²⋊D₅	C₃×C₂²⋊C₄	1	8	yes	—
272	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
273	D₂₀	—	2	8	no	—
274	D₂₀	—	2	2	no	—
275	D₂₀	—	2	2	no	—
276	D₂₀	—	2	4	no	—
277	D₂₀	C₃×C₂²⋊C₄	1	2	yes	—
278	D₂₀	C₃×C₂²⋊C₄	1	2	yes	—
279	C₄×D₅	—	2	8	no	—
280	C₄×D₅	C₂×C₃×D₄	1	8	yes	—
281	Dic₁₀	C₃×C₂²⋊C₄	1	2	yes	—
282	Dic₁₀	C₃×C₂²⋊C₄	1	2	yes	—
283	C₅×C₈	—	2	4	no	—
284	#168	—	2	4	no	—
285	H(5,𝔽₂)	—	10	4	no	—
286	H(5,𝔽₂)	—	10	4	no	—
287	C₂×#41	—	5	2	no	—
288	C₂×#41	—	5	2	no	—
289	C₂×#41	—	5	1	no	—
290	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
291	C₂²×D₄	—	5	4	no	—
292	C₂²×D₄	—	5	2	no	—
293	C₂²×D₄	—	5	2	no	—
294	C₂²×D₄	—	5	1	no	—
295	#131	—	10	4	no	—
296	#131	—	10	4	no	—
297	C₂×M₁₆	—	5	2	no	—
298	C₂×M₁₆	—	5	8	no	—
299	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	complemented
300	#101	—	5	2	no	—
301	#101	C₂×C₃×D₅	1	2	yes	complemented
302	#100	—	5	2	no	—
303	#100	—	5	8	no	—
304	#100	C₂×C₃×D₅	1	2	yes	complemented
305	C₂×C₃×C₅	—	2	1	no	—
306	C₂×C₃×C₅	—	2	2	no	—
307	C₂×C₃×C₅	—	4	2	no	—
308	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
309	C₃×D₅	—	2	4	no	—
310	C₃×D₅	—	4	4	no	—
311	C₂³×C₃	—	5	2	no	—
312	C₂³×C₃	—	5	4	no	—
313	C₂³×C₃	—	10	8	no	—
314	C₂³×C₃	—	10	4	no	—
315	C₂³×C₃	—	40	2	no	—
316	C₂³×C₃	—	40	4	no	—
317	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
318	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
319	C₃×Q₈	—	2	2	no	—
320	C₃×Q₈	—	5	2	no	—
321	C₃×Q₈	—	5	2	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	2	2	no	—
324	C₃×D₄	—	5	8	no	—
325	C₃×D₄	—	5	2	no	—
326	C₃×D₄	—	5	2	no	—
327	C₃×D₄	—	10	8	no	—
328	C₃×D₄	—	10	8	no	—
329	C₃×D₄	—	10	4	no	—
330	C₃×D₄	—	10	2	no	—
331	C₃×D₄	—	10	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	5	8	no	—
336	C₂×C₃×C₄	—	10	8	no	—
337	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
340	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
341	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
342	C₃×C₈	—	2	4	no	—
343	C₃×C₈	—	10	4	no	—
344	C₂²×C₅	—	2	2	no	—
345	C₂²×C₅	—	4	1	no	—
346	C₂²×C₅	—	4	2	no	—
347	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
348	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
349	C₂×D₅	—	2	4	no	—
350	C₂×D₅	—	4	2	no	—
351	C₂×D₅	—	4	4	no	—
352	C₂×D₅	—	8	8	no	—
353	C₂×D₅	—	8	4	no	—
354	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
357	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
358	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
359	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
360	C₂⁴	—	5	4	no	—
361	C₂⁴	—	5	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	5	4	no	—
365	#41	—	5	4	no	—
366	#41	—	10	4	no	—
367	#41	—	10	4	no	—
368	#41	—	10	8	no	—
369	C₂×Q₈	—	5	1	no	—
370	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
371	C₂×D₄	—	5	2	no	—
372	C₂×D₄	—	5	4	no	—
373	C₂×D₄	—	5	1	no	—
374	C₂×D₄	—	5	4	no	—
375	C₂×D₄	—	5	2	no	—
376	C₂×D₄	—	5	2	no	—
377	C₂×D₄	—	10	4	no	—
378	C₂×D₄	—	10	4	no	—
379	C₂×D₄	—	10	8	no	—
380	C₂×D₄	—	10	16	no	—
381	C₂×D₄	—	10	2	no	—
382	C₂×D₄	—	10	2	no	—
383	C₂×D₄	C₃×C₄×D₅	1	2	yes	—
384	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
385	C₂²×C₄	—	5	2	no	—
386	C₂²×C₄	—	5	4	no	—
387	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
388	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
389	M₁₆	—	2	2	no	—
390	M₁₆	—	5	4	no	—
391	M₁₆	—	10	8	no	—
392	M₁₆	—	10	2	no	—
393	M₁₆	C₂²×C₃×D₅	1	4	yes	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	10	8	no	—
396	C₂×C₈	—	10	2	no	—
397	C₃×C₅	#2888	1	1	yes	characteristic, complemented, Hall
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	4	1	no	—
400	C₂²×C₃	—	4	2	no	—
401	C₂²×C₃	—	5	4	no	—
402	C₂²×C₃	—	10	4	no	—
403	C₂²×C₃	—	20	2	no	—
404	C₂²×C₃	—	20	4	no	—
405	C₂²×C₃	—	40	4	no	—
406	C₂²×C₃	—	40	8	no	—
407	C₂²×C₃	D₅×C₂²⋊C₄	1	2	yes	—
408	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
409	C₃×C₄	—	2	2	no	—
410	C₃×C₄	—	5	4	no	—
411	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
413	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
414	C₂×C₅	—	2	1	no	—
415	C₂×C₅	—	2	2	no	—
416	C₂×C₅	—	4	2	no	—
417	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
418	D₅	—	2	4	no	—
419	D₅	—	4	4	no	—
420	C₂³	—	5	2	no	—
421	C₂³	—	5	4	no	—
422	C₂³	—	10	8	no	—
423	C₂³	—	10	4	no	—
424	C₂³	—	40	2	no	—
425	C₂³	—	40	4	no	—
426	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
427	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
428	Q₈	—	2	2	no	—
429	Q₈	—	5	2	no	—
430	Q₈	—	5	2	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	2	no	—
433	D₄	—	5	8	no	—
434	D₄	—	5	2	no	—
435	D₄	—	5	2	no	—
436	D₄	—	10	8	no	—
437	D₄	—	10	8	no	—
438	D₄	—	10	4	no	—
439	D₄	—	10	2	no	—
440	D₄	—	10	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	5	2	no	—
444	C₂×C₄	—	5	8	no	—
445	C₂×C₄	—	10	8	no	—
446	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
447	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
448	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
449	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
450	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
451	C₈	—	2	4	no	—
452	C₈	—	10	4	no	—
453	C₂×C₃	—	2	1	no	—
454	C₂×C₃	—	2	2	no	—
455	C₂×C₃	—	4	2	no	—
456	C₂×C₃	—	10	4	no	—
457	C₂×C₃	—	20	4	no	—
458	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
459	C₅	C₃×#2888	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	5	4	no	—
464	C₂²	—	10	4	no	—
465	C₂²	—	20	2	no	—
466	C₂²	—	20	4	no	—
467	C₂²	—	40	4	no	—
468	C₂²	—	40	8	no	—
469	C₂²	C₃×D₅×C₂²⋊C₄	1	2	yes	—
470	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
471	C₄	—	2	2	no	—
472	C₄	—	5	4	no	—
473	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
474	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
475	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
476	C₃	#10610445	1	1	yes	characteristic, direct product factor, Sylow
477	C₂	—	2	1	no	—
478	C₂	—	2	2	no	—
479	C₂	—	4	2	no	—
480	C₂	—	10	4	no	—
481	C₂	—	20	4	no	—
482	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₅×C₂²⋊C₄
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#413	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₃×#4149	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#413	D₅
hypocenter	C₅	C₃×#2888
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#413

Complements

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

N	H ≅ G/N	type
2. C₃×#66079	C₂	semidirect
3. C₃×C₅×#413	C₂	semidirect
4. C₃×#65526	C₂	semidirect
5. C₂×C₃×#3955	C₂	semidirect
6. C₃×#65040	C₂	semidirect
7. C₃×D₅×#100	C₂	semidirect
8. #10610445	C₃	direct (N × H)
19. C₂×C₃×C₅×M₁₆	C₂²	semidirect
20. C₂×C₃×#681	C₂²	semidirect
22. C₃×D₅×M₁₆	C₂²	semidirect
24. C₃×C₅×#101	C₂²	semidirect
25. C₃×C₅×#100	C₂²	semidirect
26. C₃×#3968	C₂²	semidirect
27. C₃×#3965	C₂²	semidirect
28. C₃×#3955	C₂²	semidirect
31. #66079	C₂×C₃	semidirect
32. C₅×#413	C₂×C₃	semidirect
33. #65526	C₂×C₃	semidirect
34. C₂×#3955	C₂×C₃	semidirect
35. #65040	C₂×C₃	semidirect
36. D₅×#100	C₂×C₃	semidirect
78. C₃×#413	D₅	semidirect
91. C₂×C₅×M₁₆	C₂²×C₃	semidirect
92. C₂×#681	C₂²×C₃	semidirect
94. D₅×M₁₆	C₂²×C₃	semidirect
96. C₅×#101	C₂²×C₃	semidirect
97. C₅×#100	C₂²×C₃	semidirect
98. #3968	C₂²×C₃	semidirect
99. #3965	C₂²×C₃	semidirect
100. #3955	C₂²×C₃	semidirect
149. C₂×C₃×M₁₆	C₂×D₅	semidirect
151. C₃×#101	C₂×D₅	semidirect
154. C₃×#100	C₂×D₅	semidirect
196. #413	C₃×D₅	semidirect
299. C₂×M₁₆	C₂×C₃×D₅	semidirect
301. #101	C₂×C₃×D₅	semidirect
304. #100	C₂×C₃×D₅	semidirect
397. C₃×C₅	#2888	semidirect
459. C₅	C₃×#2888	semidirect
476. C₃	#10610445	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×#4149	2
C₃×#66079	2
C₃×C₅×#413	2
C₃×#65526	2
C₂×C₃×#3955	2
C₃×#65040	2
C₃×D₅×#100	2
#10610445	3
C₃×#2888	5

Subgroups — C3×#10610445 #14412159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610445 #14412159