Subgroups — C₃×#10615147 #14425528

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66283	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4088	C₂	1	2	yes	maximal, complemented
4	C₃×#65526	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65384	C₂	1	4	yes	maximal, complemented
6	C₃×#65350	C₂	1	4	yes	maximal, complemented
7	C₃×#65294	C₂	1	2	yes	maximal, complemented
8	#10615147	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₃×#4150	—	2	2	no	—
12	C₃×#4149	—	2	2	no	—
13	C₃×D₅×#41	—	2	4	no	—
14	C₃×#4147	C₂²	1	2	yes	—
15	C₃×#4144	—	2	2	no	—
16	C₃×#4144	C₂²	1	2	yes	—
17	C₂×C₃×#709	—	2	2	no	—
18	C₂×C₃×#709	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃×C₅×#124	C₂²	1	2	yes	complemented
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#689	—	2	2	no	—
25	C₃×#4088	—	2	4	no	—
26	C₃×#4088	C₂²	1	8	yes	complemented
27	C₂×C₃×#688	—	2	2	no	—
28	C₂×C₃×#681	C₂²	1	2	yes	complemented
29	C₃×#3968	C₂²	1	2	yes	complemented
30	C₃×#3965	C₂²	1	2	yes	complemented
31	C₃×#3937	C₂²	1	8	yes	complemented
32	C₃×#3022	—	5	1	no	maximal, Hall
33	#66283	C₂×C₃	1	1	yes	characteristic
34	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#4088	C₂×C₃	1	2	yes	complemented
36	#65526	C₂×C₃	1	1	yes	characteristic, complemented
37	#65384	C₂×C₃	1	4	yes	complemented
38	#65350	C₂×C₃	1	4	yes	complemented
39	#65294	C₂×C₃	1	2	yes	complemented
40	C₃×C₅×#41	—	2	2	no	—
41	C₃×C₅×#41	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
48	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
53	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
54	C₃×#713	—	2	4	no	—
55	C₃×Q₈×D₅	—	2	4	no	—
56	C₃×#711	—	2	8	no	—
57	C₃×#711	—	2	4	no	—
58	C₃×D₄×D₅	—	2	8	no	—
59	C₃×D₄×D₅	—	2	4	no	—
60	C₃×#709	—	2	4	no	—
61	C₃×#709	—	2	4	no	—
62	C₃×#709	—	2	2	no	—
63	C₃×#709	—	2	4	no	—
64	C₃×#709	—	2	2	no	—
65	C₃×#709	D₄	1	4	yes	—
66	C₃×#709	C₂³	1	4	yes	—
67	C₂×C₃×D₂₀	—	2	2	no	—
68	C₂×C₃×D₂₀	D₄	1	2	yes	—
69	C₂×C₃×C₄×D₅	—	2	4	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×Dic₁₀	—	2	2	no	—
72	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₃×#689	—	2	8	no	—
79	C₃×#688	—	2	8	no	—
80	C₃×#681	—	2	2	no	—
81	C₃×#681	C₂³	1	4	yes	—
82	C₂×C₃×#168	—	2	2	no	—
83	C₃×#585	—	5	1	no	—
84	C₂×C₃×#137	—	5	2	no	—
85	C₃×#536	D₅	1	1	yes	characteristic, complemented
86	C₃×#456	—	5	4	no	—
87	C₃×#455	—	5	4	no	—
88	C₃×#421	—	5	2	no	—
89	C₃×#413	—	5	1	no	—
90	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
92	#4150	—	2	2	no	—
93	#4149	—	2	2	no	—
94	D₅×#41	—	2	4	no	—
95	#4147	C₂²×C₃	1	2	yes	—
96	#4144	—	2	2	no	—
97	#4144	C₂²×C₃	1	2	yes	—
98	C₂×#709	—	2	2	no	—
99	C₂×#709	C₂²×C₃	1	2	yes	—
100	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
101	C₅×#124	C₂²×C₃	1	2	yes	complemented
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	—	2	2	no	—
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₂×#689	—	2	2	no	—
106	#4088	—	2	4	no	—
107	#4088	C₂²×C₃	1	8	yes	complemented
108	C₂×#688	—	2	2	no	—
109	C₂×#681	C₂²×C₃	1	2	yes	complemented
110	#3968	C₂²×C₃	1	2	yes	complemented
111	#3965	C₂²×C₃	1	2	yes	complemented
112	#3937	C₂²×C₃	1	8	yes	complemented
113	#3022	—	5	1	no	Sylow
114	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₃×D₅	—	2	4	no	—
117	C₂²×C₃×D₅	—	2	2	no	—
118	C₃×C₅×Q₈	—	2	2	no	—
119	C₃×C₅×Q₈	—	2	4	no	—
120	C₃×C₅×Q₈	—	4	1	no	—
121	C₃×C₅×Q₈	—	4	1	no	—
122	C₃×C₅×D₄	—	2	4	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	4	2	no	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₃×C₂²⋊D₅	—	2	8	no	—
135	C₃×C₂²⋊D₅	—	2	4	no	—
136	C₃×C₂²⋊D₅	—	2	4	no	—
137	C₂×C₃×Dic₅	—	2	4	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₃×D₂₀	—	2	4	no	—
140	C₃×D₂₀	—	2	2	no	—
141	C₃×D₂₀	C₂×D₄	1	4	yes	—
142	C₃×C₄×D₅	—	2	8	no	—
143	C₃×C₄×D₅	—	2	4	no	—
144	C₃×C₄×D₅	—	2	4	no	—
145	C₃×Dic₁₀	—	2	4	no	—
146	C₃×Dic₁₀	—	2	2	no	—
147	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
148	C₃×#168	—	2	4	no	—
149	C₃×2₋¹⁺⁴	—	5	2	no	—
150	C₃×2₋¹⁺⁴	—	10	2	no	—
151	C₃×H(5,𝔽₂)	—	5	2	no	—
152	C₃×H(5,𝔽₂)	—	10	2	no	—
153	C₃×H(5,𝔽₂)	—	10	2	no	—
154	C₂×C₃×#41	—	5	2	no	—
155	C₂×C₃×#41	—	10	4	no	—
156	C₂×C₃×#41	—	10	2	no	—
157	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
158	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
159	C₃×#137	—	5	8	no	—
160	C₃×#137	—	10	4	no	—
161	C₂×C₃×Q₁₆	—	10	2	no	—
162	C₂×C₃×SD₁₆	—	10	2	no	—
163	C₂×C₃×M₁₆	—	5	2	no	—
164	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	complemented
165	C₃×#124	C₂×D₅	1	2	yes	complemented
166	C₃×#123	—	2	2	no	—
167	C₃×C₂²⋊Q₈	—	2	2	no	—
168	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
169	C₃×#104	—	5	8	no	—
170	C₃×#101	—	5	2	no	—
171	C₃×#100	—	5	2	no	—
172	C₅×#41	—	2	2	no	—
173	C₅×#41	—	2	2	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	2	no	—
176	C₂×C₅×Q₈	—	2	2	no	—
177	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
178	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
180	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₂²⋊D₅	—	2	4	no	—
185	C₂×C₂²⋊D₅	—	2	2	no	—
186	#713	—	2	4	no	—
187	Q₈×D₅	—	2	4	no	—
188	#711	—	2	8	no	—
189	#711	—	2	4	no	—
190	D₄×D₅	—	2	8	no	—
191	D₄×D₅	—	2	4	no	—
192	#709	—	2	4	no	—
193	#709	—	2	4	no	—
194	#709	—	2	2	no	—
195	#709	—	2	4	no	—
196	#709	—	2	2	no	—
197	#709	C₃×D₄	1	4	yes	—
198	#709	C₂³×C₃	1	4	yes	—
199	C₂×D₂₀	—	2	2	no	—
200	C₂×D₂₀	C₃×D₄	1	2	yes	—
201	C₂×C₄×D₅	—	2	4	no	—
202	C₂×C₄×D₅	—	2	2	no	—
203	C₂×Dic₁₀	—	2	2	no	—
204	C₂×Dic₁₀	C₃×D₄	1	2	yes	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	4	no	—
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₄²×C₅	C₂³×C₃	1	2	yes	—
210	#689	—	2	8	no	—
211	#688	—	2	8	no	—
212	#681	—	2	2	no	—
213	#681	C₂³×C₃	1	4	yes	—
214	C₂×#168	—	2	2	no	—
215	#585	—	5	1	no	—
216	C₂×#137	—	5	2	no	—
217	#536	C₃×D₅	1	1	yes	characteristic, complemented
218	#456	—	5	4	no	—
219	#455	—	5	4	no	—
220	#421	—	5	2	no	—
221	#413	—	5	1	no	—
222	C₂²×C₃×C₅	—	2	2	no	—
223	C₂²×C₃×C₅	—	4	1	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	#120	1	2	yes	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₃×D₅	—	2	4	no	—
228	C₂×C₃×D₅	—	8	2	no	—
229	C₂×C₃×D₅	—	8	4	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	#120	1	1	yes	characteristic
234	C₃×C₄×C₅	#120	1	1	yes	characteristic
235	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
236	C₃×Dic₅	—	2	4	no	—
237	C₃×#41	—	2	2	no	—
238	C₃×#41	—	2	2	no	—
239	C₃×#41	—	5	4	no	—
240	C₃×#41	—	5	4	no	—
241	C₃×#41	—	10	4	no	—
242	C₃×#41	—	10	4	no	—
243	C₃×#41	—	10	4	no	—
244	C₃×#41	—	10	8	no	—
245	C₃×#41	—	10	4	no	—
246	C₃×#41	—	10	2	no	—
247	C₃×#41	—	10	2	no	—
248	C₃×#41	—	10	4	no	—
249	C₂×C₃×Q₈	—	2	1	no	—
250	C₂×C₃×Q₈	—	2	2	no	—
251	C₂×C₃×Q₈	—	2	2	no	—
252	C₂×C₃×Q₈	—	5	2	no	—
253	C₂×C₃×Q₈	—	10	2	no	—
254	C₂×C₃×Q₈	—	10	4	no	—
255	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
256	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
257	C₂×C₃×D₄	—	5	2	no	—
258	C₂×C₃×D₄	—	10	2	no	—
259	C₂×C₃×D₄	—	10	4	no	—
260	C₂×C₃×D₄	—	10	8	no	—
261	C₂×C₃×D₄	—	10	2	no	—
262	C₂×C₃×D₄	—	10	4	no	—
263	C₂×C₃×D₄	C₂²⋊D₅	1	2	yes	—
264	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
265	C₂²×C₃×C₄	—	2	1	no	—
266	C₂²×C₃×C₄	—	10	4	no	—
267	C₂²×C₃×C₄	—	10	2	no	—
268	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
269	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
270	C₃×Q₁₆	—	10	8	no	—
271	C₃×SD₁₆	—	10	8	no	—
272	C₃×M₁₆	—	5	4	no	—
273	C₃×M₁₆	—	10	2	no	—
274	C₂×C₃×C₈	—	10	2	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	—	2	4	no	—
277	C₃×C₂²⋊C₄	—	2	1	no	—
278	C₃×C₂²⋊C₄	—	2	4	no	—
279	C₃×C₄²	C₂²×D₅	1	2	yes	—
280	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
281	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂²×D₅	—	2	4	no	—
283	C₂²×D₅	—	2	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	—	2	4	no	—
286	C₅×Q₈	—	4	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×D₄	—	2	4	no	—
289	C₅×D₄	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	4	2	no	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
296	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
300	C₂²⋊D₅	—	2	8	no	—
301	C₂²⋊D₅	—	2	4	no	—
302	C₂²⋊D₅	—	2	4	no	—
303	C₂×Dic₅	—	2	4	no	—
304	C₂×Dic₅	—	2	2	no	—
305	D₂₀	—	2	4	no	—
306	D₂₀	—	2	2	no	—
307	D₂₀	C₂×C₃×D₄	1	4	yes	—
308	C₄×D₅	—	2	8	no	—
309	C₄×D₅	—	2	4	no	—
310	C₄×D₅	—	2	4	no	—
311	Dic₁₀	—	2	4	no	—
312	Dic₁₀	—	2	2	no	—
313	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
314	#168	—	2	4	no	—
315	2₋¹⁺⁴	—	5	2	no	—
316	2₋¹⁺⁴	—	10	2	no	—
317	H(5,𝔽₂)	—	5	2	no	—
318	H(5,𝔽₂)	—	10	2	no	—
319	H(5,𝔽₂)	—	10	2	no	—
320	C₂×#41	—	5	2	no	—
321	C₂×#41	—	10	4	no	—
322	C₂×#41	—	10	2	no	—
323	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
324	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
325	#137	—	5	8	no	—
326	#137	—	10	4	no	—
327	C₂×Q₁₆	—	10	2	no	—
328	C₂×SD₁₆	—	10	2	no	—
329	C₂×M₁₆	—	5	2	no	—
330	C₄⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
331	#124	C₂×C₃×D₅	1	2	yes	complemented
332	#123	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
335	#104	—	5	8	no	—
336	#101	—	5	2	no	—
337	#100	—	5	2	no	—
338	C₂×C₃×C₅	—	2	1	no	—
339	C₂×C₃×C₅	—	2	2	no	—
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
342	C₃×D₅	—	4	4	no	—
343	C₂³×C₃	—	10	4	no	—
344	C₂³×C₃	—	10	2	no	—
345	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
346	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	2	4	no	—
349	C₃×Q₈	—	4	1	no	—
350	C₃×Q₈	—	4	1	no	—
351	C₃×Q₈	—	5	4	no	—
352	C₃×Q₈	—	10	4	no	—
353	C₃×Q₈	—	10	2	no	—
354	C₃×D₄	—	2	4	no	—
355	C₃×D₄	—	2	2	no	—
356	C₃×D₄	—	5	4	no	—
357	C₃×D₄	—	10	4	no	—
358	C₃×D₄	—	10	8	no	—
359	C₃×D₄	—	10	4	no	—
360	C₃×D₄	—	10	4	no	—
361	C₃×D₄	—	10	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	—	10	8	no	—
368	C₂×C₃×C₄	—	10	4	no	—
369	C₂×C₃×C₄	—	10	2	no	—
370	C₂×C₃×C₄	—	10	4	no	—
371	C₂×C₃×C₄	—	10	4	no	—
372	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
373	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
374	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
377	C₃×C₈	—	10	4	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	2	no	—
381	C₂²×C₅	C₃×#120	1	2	yes	—
382	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
383	C₂×D₅	—	2	4	no	—
384	C₂×D₅	—	8	2	no	—
385	C₂×D₅	—	8	4	no	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	C₃×#120	1	1	yes	characteristic
390	C₄×C₅	C₃×#120	1	1	yes	characteristic
391	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
392	Dic₅	—	2	4	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	5	4	no	—
396	#41	—	5	4	no	—
397	#41	—	10	4	no	—
398	#41	—	10	4	no	—
399	#41	—	10	4	no	—
400	#41	—	10	8	no	—
401	#41	—	10	4	no	—
402	#41	—	10	2	no	—
403	#41	—	10	2	no	—
404	#41	—	10	4	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	5	2	no	—
409	C₂×Q₈	—	10	2	no	—
410	C₂×Q₈	—	10	4	no	—
411	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
412	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
413	C₂×D₄	—	5	2	no	—
414	C₂×D₄	—	10	2	no	—
415	C₂×D₄	—	10	4	no	—
416	C₂×D₄	—	10	8	no	—
417	C₂×D₄	—	10	2	no	—
418	C₂×D₄	—	10	4	no	—
419	C₂×D₄	C₃×C₂²⋊D₅	1	2	yes	—
420	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	10	4	no	—
423	C₂²×C₄	—	10	2	no	—
424	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
425	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
426	Q₁₆	—	10	8	no	—
427	SD₁₆	—	10	8	no	—
428	M₁₆	—	5	4	no	—
429	M₁₆	—	10	2	no	—
430	C₂×C₈	—	10	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₄²	C₂²×C₃×D₅	1	2	yes	—
436	C₃×C₅	#3022	1	1	yes	characteristic, complemented, Hall
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	4	1	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	10	4	no	—
441	C₂²×C₃	—	40	2	no	—
442	C₂²×C₃	—	40	4	no	—
443	C₂²×C₃	#4083	1	2	yes	—
444	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	4	2	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	10	4	no	—
449	C₃×C₄	#4083	1	1	yes	characteristic
450	C₃×C₄	#4083	1	1	yes	characteristic
451	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	2	no	—
454	C₂×C₅	—	4	2	no	—
455	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
456	D₅	—	4	4	no	—
457	C₂³	—	10	4	no	—
458	C₂³	—	10	2	no	—
459	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
460	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
461	Q₈	—	2	2	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	4	1	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	5	4	no	—
466	Q₈	—	10	4	no	—
467	Q₈	—	10	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	5	4	no	—
471	D₄	—	10	4	no	—
472	D₄	—	10	8	no	—
473	D₄	—	10	4	no	—
474	D₄	—	10	4	no	—
475	D₄	—	10	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	10	8	no	—
482	C₂×C₄	—	10	4	no	—
483	C₂×C₄	—	10	2	no	—
484	C₂×C₄	—	10	4	no	—
485	C₂×C₄	—	10	4	no	—
486	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
487	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
488	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
489	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
491	C₈	—	10	4	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	2	no	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	—	20	4	no	—
496	C₂×C₃	C₂×#4083	1	1	yes	characteristic
497	C₅	C₃×#3022	1	1	yes	characteristic, complemented, Sylow
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	10	4	no	—
502	C₂²	—	40	2	no	—
503	C₂²	—	40	4	no	—
504	C₂²	C₃×#4083	1	2	yes	—
505	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	10	4	no	—
510	C₄	C₃×#4083	1	1	yes	characteristic
511	C₄	C₃×#4083	1	1	yes	characteristic
512	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
513	C₃	#10615147	1	1	yes	characteristic, direct product factor, Sylow
514	C₂	—	2	1	no	—
515	C₂	—	2	2	no	—
516	C₂	—	4	2	no	—
517	C₂	—	20	4	no	—
518	C₂	C₂×C₃×#4083	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×#4083
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#536	C₂
socle	C₂×C₃×C₅	C₂×#120
prime radical	C₃×#66283	C₂
hypercenter	C₃×#536	D₅
hypocenter	C₅	C₃×#3022
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#536

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#536	C₂	semidirect
3. C₂×C₃×#4088	C₂	semidirect
4. C₃×#65526	C₂	semidirect
5. C₃×#65384	C₂	semidirect
6. C₃×#65350	C₂	semidirect
7. C₃×#65294	C₂	semidirect
8. #10615147	C₃	direct (N × H)
10. C₂²×C₃×C₅×Q₈	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×#124	C₂²	semidirect
23. C₃×C₅×#117	C₂²	semidirect
26. C₃×#4088	C₂²	semidirect
28. C₂×C₃×#681	C₂²	semidirect
29. C₃×#3968	C₂²	semidirect
30. C₃×#3965	C₂²	semidirect
31. C₃×#3937	C₂²	semidirect
34. C₅×#536	C₂×C₃	semidirect
35. C₂×#4088	C₂×C₃	semidirect
36. #65526	C₂×C₃	semidirect
37. #65384	C₂×C₃	semidirect
38. #65350	C₂×C₃	semidirect
39. #65294	C₂×C₃	semidirect
85. C₃×#536	D₅	semidirect
91. C₂²×C₅×Q₈	C₂²×C₃	semidirect
100. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
101. C₅×#124	C₂²×C₃	semidirect
104. C₅×#117	C₂²×C₃	semidirect
107. #4088	C₂²×C₃	semidirect
109. C₂×#681	C₂²×C₃	semidirect
110. #3968	C₂²×C₃	semidirect
111. #3965	C₂²×C₃	semidirect
112. #3937	C₂²×C₃	semidirect
158. C₂²×C₃×Q₈	C₂×D₅	semidirect
164. C₃×C₄⋊Q₈	C₂×D₅	semidirect
165. C₃×#124	C₂×D₅	semidirect
168. C₃×#117	C₂×D₅	semidirect
217. #536	C₃×D₅	semidirect
324. C₂²×Q₈	C₂×C₃×D₅	semidirect
330. C₄⋊Q₈	C₂×C₃×D₅	semidirect
331. #124	C₂×C₃×D₅	semidirect
334. #117	C₂×C₃×D₅	semidirect
436. C₃×C₅	#3022	semidirect
497. C₅	C₃×#3022	semidirect
513. C₃	#10615147	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×#66283	2
C₃×C₅×#536	2
C₂×C₃×#4088	2
C₃×#65526	2
C₃×#65384	2
C₃×#65350	2
C₃×#65294	2
#10615147	3
C₃×#3022	5

Subgroups — C3×#10615147 #14425528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615147 #14425528