Subgroups — C₃×#10615844 #14424430

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66164	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65527	C₂	1	4	yes	maximal, complemented
6	C₃×#65523	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65516	C₂	1	4	yes	maximal, complemented
9	C₃×#65514	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615844	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
12	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
13	C₂×C₃×C₅×#41	—	2	2	no	—
14	C₂×C₃×C₅×#41	—	2	1	no	—
15	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₅×Q₈	—	2	1	no	—
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
21	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
22	C₃×#4095	—	2	4	no	—
23	C₃×#4093	—	2	1	no	—
24	C₂×C₃×#688	—	2	4	no	—
25	C₂×C₃×#688	C₂²	1	4	yes	—
26	C₂×C₃×#688	C₂²	1	2	yes	—
27	C₃×#4086	—	2	1	no	—
28	C₃×#4083	—	2	2	no	—
29	C₂×C₃×#686	C₂²	1	2	yes	—
30	C₃×#4076	C₂²	1	4	yes	—
31	C₃×#4072	C₂²	1	1	yes	characteristic
32	C₂×C₃×#681	C₂²	1	1	yes	characteristic
33	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
34	C₃×#3967	C₂²	1	4	yes	complemented
35	C₃×#3967	C₂²	1	2	yes	complemented
36	C₃×#3964	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
38	C₃×#3010	—	5	1	no	maximal, Hall
39	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
40	#66164	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×#4095	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×#688	C₂×C₃	1	1	yes	characteristic, complemented
43	#65527	C₂×C₃	1	4	yes	complemented
44	#65523	C₂×C₃	1	1	yes	characteristic, complemented
45	#65522	C₂×C₃	1	1	yes	characteristic, complemented
46	#65516	C₂×C₃	1	4	yes	complemented
47	#65514	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×D₅	—	2	1	no	—
49	C₃×C₅×#41	—	2	16	no	—
50	C₃×C₅×#41	—	2	8	no	—
51	C₃×C₅×#41	—	2	4	no	—
52	C₃×C₅×#41	—	2	4	no	—
53	C₃×C₅×#41	—	2	2	no	—
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	D₄	1	4	yes	complemented
57	C₂×C₃×C₅×Q₈	—	2	8	no	—
58	C₂×C₃×C₅×Q₈	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	—	2	4	no	—
60	C₂×C₃×C₅×Q₈	—	2	1	no	—
61	C₂×C₃×C₅×Q₈	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	—	2	2	no	—
63	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
65	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×D₄	—	2	1	no	—
68	C₂×C₃×C₅×D₄	—	2	2	no	—
69	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
70	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
71	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	—	2	1	no	—
73	C₂²×C₃×C₄×C₅	—	2	2	no	—
74	C₂²×C₃×C₄×C₅	—	2	1	no	—
75	C₂²×C₃×C₄×C₅	—	2	2	no	—
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
79	C₂×C₃×D₂₀	—	2	2	no	—
80	C₂×C₃×D₂₀	—	2	2	no	—
81	C₂×C₃×D₂₀	—	2	1	no	—
82	C₂×C₃×D₂₀	C₂³	1	2	yes	—
83	C₃×C₂²⋊Dic₅	—	2	1	no	—
84	C₃×#688	—	2	8	no	—
85	C₃×#688	—	2	4	no	—
86	C₃×#686	—	2	4	no	—
87	C₃×#685	—	2	4	no	—
88	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
89	C₃×C₄×Dic₅	—	2	1	no	—
90	C₃×#681	—	2	2	no	—
91	C₂×C₃×#168	—	2	2	no	—
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₂×C₃×#168	C₂³	1	2	yes	—
94	C₂×C₃×2₋¹⁺⁴	D₅	1	1	yes	characteristic, complemented
95	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
96	C₂²×C₃×SD₁₆	—	5	1	no	—
97	C₃×#535	—	5	1	no	—
98	C₃×#449	—	5	4	no	—
99	C₃×#448	—	5	4	no	—
100	C₃×#419	—	5	1	no	—
101	C₃×#416	—	5	1	no	—
102	C₃×#408	—	5	1	no	—
103	C₅×2₋¹⁺⁴	—	2	4	no	—
104	C₅×2₋¹⁺⁴	—	2	4	no	—
105	C₂×C₅×#41	—	2	2	no	—
106	C₂×C₅×#41	—	2	1	no	—
107	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
110	C₂²×C₅×Q₈	—	2	1	no	—
111	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
112	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
113	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
114	#4095	—	2	4	no	—
115	#4093	—	2	1	no	—
116	C₂×#688	—	2	4	no	—
117	C₂×#688	C₂²×C₃	1	4	yes	—
118	C₂×#688	C₂²×C₃	1	2	yes	—
119	#4086	—	2	1	no	—
120	#4083	—	2	2	no	—
121	C₂×#686	C₂²×C₃	1	2	yes	—
122	#4076	C₂²×C₃	1	4	yes	—
123	#4072	C₂²×C₃	1	1	yes	characteristic
124	C₂×#681	C₂²×C₃	1	1	yes	characteristic
125	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
126	#3967	C₂²×C₃	1	4	yes	complemented
127	#3967	C₂²×C₃	1	2	yes	complemented
128	#3964	C₂²×C₃	1	2	yes	complemented
129	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
130	#3010	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₃×D₅	—	2	2	no	—
135	C₂²×C₃×D₅	—	4	2	no	—
136	C₂²×C₃×D₅	—	8	2	no	—
137	C₃×C₅×Q₈	—	2	8	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	4	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
143	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
144	C₃×C₅×D₄	—	2	8	no	—
145	C₃×C₅×D₄	—	2	4	no	—
146	C₃×C₅×D₄	—	2	4	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	1	no	—
149	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	—	2	8	no	—
151	C₂×C₃×C₄×C₅	—	2	8	no	—
152	C₂×C₃×C₄×C₅	—	2	4	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	4	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₂²⋊D₅	—	8	4	no	—
164	C₂×C₃×Dic₅	—	2	2	no	—
165	C₃×D₂₀	—	2	2	no	—
166	C₃×D₂₀	—	2	2	no	—
167	C₃×D₂₀	—	4	2	no	—
168	C₃×#168	—	2	2	no	—
169	C₃×#168	—	2	2	no	—
170	C₃×2₋¹⁺⁴	—	2	4	no	—
171	C₃×2₋¹⁺⁴	—	2	4	no	—
172	C₂×C₃×#41	—	2	2	no	—
173	C₂×C₃×#41	—	2	1	no	—
174	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
175	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
176	C₂×C₃×#41	C₂×D₅	1	2	yes	complemented
177	C₂²×C₃×Q₈	—	2	1	no	—
178	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
179	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	complemented
180	C₂²×C₃×D₄	—	5	1	no	—
181	C₃×AGL(1,ℤ/8)	—	10	4	no	—
182	C₂×C₃×SD₁₆	—	5	4	no	—
183	C₂×C₃×SD₁₆	—	5	2	no	—
184	C₂×C₃×SD₁₆	—	10	4	no	—
185	C₂×C₃×D₈	—	5	2	no	—
186	C₂×C₃×M₁₆	—	5	1	no	—
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₃×#127	—	10	1	no	—
189	C₃×#124	—	10	1	no	—
190	C₃×#121	—	5	4	no	—
191	C₃×#120	—	10	2	no	—
192	C₃×#117	—	5	1	no	—
193	C₃×#103	—	5	2	no	—
194	C₃×#103	—	5	4	no	—
195	C₃×#102	—	5	2	no	—
196	C₃×C₂²⋊C₈	—	5	4	no	—
197	C₂³×D₅	—	2	1	no	—
198	C₅×#41	—	2	16	no	—
199	C₅×#41	—	2	8	no	—
200	C₅×#41	—	2	4	no	—
201	C₅×#41	—	2	4	no	—
202	C₅×#41	—	2	2	no	—
203	C₅×#41	—	2	2	no	—
204	C₅×#41	—	2	2	no	—
205	C₅×#41	C₃×D₄	1	4	yes	complemented
206	C₂×C₅×Q₈	—	2	8	no	—
207	C₂×C₅×Q₈	—	2	4	no	—
208	C₂×C₅×Q₈	—	2	4	no	—
209	C₂×C₅×Q₈	—	2	1	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	2	2	no	—
212	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
213	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
214	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
215	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
219	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
220	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
226	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₂²⋊D₅	—	2	4	no	—
228	C₂×D₂₀	—	2	2	no	—
229	C₂×D₂₀	—	2	2	no	—
230	C₂×D₂₀	—	2	1	no	—
231	C₂×D₂₀	C₂³×C₃	1	2	yes	—
232	C₂²⋊Dic₅	—	2	1	no	—
233	#688	—	2	8	no	—
234	#688	—	2	4	no	—
235	#686	—	2	4	no	—
236	#685	—	2	4	no	—
237	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
238	C₄×Dic₅	—	2	1	no	—
239	#681	—	2	2	no	—
240	C₂×#168	—	2	2	no	—
241	C₂×#168	C₂³×C₃	1	2	yes	—
242	C₂×#168	C₂³×C₃	1	2	yes	—
243	C₂×2₋¹⁺⁴	C₃×D₅	1	1	yes	characteristic, complemented
244	C₂×AGL(1,ℤ/8)	—	5	1	no	—
245	C₂²×SD₁₆	—	5	1	no	—
246	#535	—	5	1	no	—
247	#449	—	5	4	no	—
248	#448	—	5	4	no	—
249	#419	—	5	1	no	—
250	#416	—	5	1	no	—
251	#408	—	5	1	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	2	2	no	—
254	C₂²×C₃×C₅	—	2	2	no	—
255	C₂²×C₃×C₅	—	2	4	no	—
256	C₂²×C₃×C₅	—	4	2	no	—
257	C₂²×C₃×C₅	#120	1	2	yes	—
258	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₃×D₅	—	4	2	no	—
260	C₂×C₃×D₅	—	4	4	no	—
261	C₂×C₃×D₅	—	8	4	no	—
262	C₃×C₄×C₅	—	2	4	no	—
263	C₃×C₄×C₅	—	2	2	no	—
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	#120	1	2	yes	—
266	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₃×Dic₅	—	4	2	no	—
269	C₂⁴×C₃	—	10	1	no	—
270	C₃×#41	—	2	16	no	—
271	C₃×#41	—	2	8	no	—
272	C₃×#41	—	2	4	no	—
273	C₃×#41	—	2	4	no	—
274	C₃×#41	—	2	2	no	—
275	C₃×#41	—	2	2	no	—
276	C₃×#41	—	2	2	no	—
277	C₃×#41	C₂²⋊D₅	1	4	yes	complemented
278	C₂×C₃×Q₈	—	2	8	no	—
279	C₂×C₃×Q₈	—	2	4	no	—
280	C₂×C₃×Q₈	—	2	4	no	—
281	C₂×C₃×Q₈	—	2	1	no	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
285	C₂×C₃×Q₈	C₂²⋊D₅	1	4	yes	complemented
286	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
287	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	—	2	2	no	—
290	C₂×C₃×D₄	—	5	2	no	—
291	C₂×C₃×D₄	—	10	4	no	—
292	C₂×C₃×D₄	—	10	2	no	—
293	C₂×C₃×D₄	—	10	2	no	—
294	C₂×C₃×D₄	—	10	1	no	—
295	C₂×C₃×D₄	C₂²⋊D₅	1	2	yes	—
296	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
297	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
298	C₂²×C₃×C₄	—	2	1	no	—
299	C₂²×C₃×C₄	—	2	2	no	—
300	C₂²×C₃×C₄	—	2	1	no	—
301	C₂²×C₃×C₄	—	2	2	no	—
302	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
303	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
304	C₃×SD₁₆	—	10	8	no	—
305	C₃×SD₁₆	—	10	4	no	—
306	C₃×D₈	—	10	4	no	—
307	C₃×M₁₆	—	10	2	no	—
308	C₂×C₃×C₈	—	5	2	no	—
309	C₂×C₃×C₈	—	5	2	no	—
310	C₂×C₃×C₈	—	10	2	no	—
311	C₃×C₄⋊C₄	—	5	2	no	—
312	C₃×C₂²⋊C₄	—	10	1	no	—
313	C₃×C₂²⋊C₄	—	10	4	no	—
314	C₃×C₄²	—	10	1	no	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
317	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂²×D₅	—	2	2	no	—
319	C₂²×D₅	—	4	2	no	—
320	C₂²×D₅	—	8	2	no	—
321	C₅×Q₈	—	2	8	no	—
322	C₅×Q₈	—	2	2	no	—
323	C₅×Q₈	—	2	4	no	—
324	C₅×Q₈	—	2	1	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
327	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
328	C₅×D₄	—	2	8	no	—
329	C₅×D₄	—	2	4	no	—
330	C₅×D₄	—	2	4	no	—
331	C₅×D₄	—	2	2	no	—
332	C₅×D₄	—	2	1	no	—
333	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
334	C₂×C₄×C₅	—	2	8	no	—
335	C₂×C₄×C₅	—	2	8	no	—
336	C₂×C₄×C₅	—	2	4	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	4	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
343	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
345	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
346	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
347	C₂²⋊D₅	—	8	4	no	—
348	C₂×Dic₅	—	2	2	no	—
349	D₂₀	—	2	2	no	—
350	D₂₀	—	2	2	no	—
351	D₂₀	—	4	2	no	—
352	#168	—	2	2	no	—
353	#168	—	2	2	no	—
354	2₋¹⁺⁴	—	2	4	no	—
355	2₋¹⁺⁴	—	2	4	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
359	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
360	C₂×#41	C₂×C₃×D₅	1	2	yes	complemented
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
363	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	complemented
364	C₂²×D₄	—	5	1	no	—
365	AGL(1,ℤ/8)	—	10	4	no	—
366	C₂×SD₁₆	—	5	4	no	—
367	C₂×SD₁₆	—	5	2	no	—
368	C₂×SD₁₆	—	10	4	no	—
369	C₂×D₈	—	5	2	no	—
370	C₂×M₁₆	—	5	1	no	—
371	C₂²×C₈	—	5	1	no	—
372	#127	—	10	1	no	—
373	#124	—	10	1	no	—
374	#121	—	5	4	no	—
375	#120	—	10	2	no	—
376	#117	—	5	1	no	—
377	#103	—	5	2	no	—
378	#103	—	5	4	no	—
379	#102	—	5	2	no	—
380	C₂²⋊C₈	—	5	4	no	—
381	C₂×C₃×C₅	—	2	2	no	—
382	C₂×C₃×C₅	—	4	2	no	—
383	C₂×C₃×C₅	—	4	2	no	—
384	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
385	C₂×C₃×C₅	#577	1	2	yes	—
386	C₃×D₅	—	8	2	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	10	2	no	—
389	C₂³×C₃	—	20	2	no	—
390	C₂³×C₃	—	40	2	no	—
391	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
392	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
393	C₃×Q₈	—	2	8	no	—
394	C₃×Q₈	—	2	2	no	—
395	C₃×Q₈	—	2	4	no	—
396	C₃×Q₈	—	2	1	no	—
397	C₃×Q₈	—	2	2	no	—
398	C₃×Q₈	C₂×C₂²⋊D₅	1	2	yes	—
399	C₃×Q₈	C₂×C₂²⋊D₅	1	4	yes	—
400	C₃×D₄	—	2	8	no	—
401	C₃×D₄	—	2	4	no	—
402	C₃×D₄	—	2	4	no	—
403	C₃×D₄	—	2	2	no	—
404	C₃×D₄	—	2	1	no	—
405	C₃×D₄	—	10	2	no	—
406	C₃×D₄	—	10	2	no	—
407	C₃×D₄	—	20	2	no	—
408	C₃×D₄	—	40	4	no	—
409	C₃×D₄	C₂×C₂²⋊D₅	1	2	yes	—
410	C₂×C₃×C₄	—	2	8	no	—
411	C₂×C₃×C₄	—	2	8	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	10	2	no	—
419	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
420	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
423	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
424	C₃×C₈	—	10	2	no	—
425	C₃×C₈	—	10	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	4	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	C₃×#120	1	2	yes	—
432	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
433	C₂×D₅	—	4	4	no	—
434	C₂×D₅	—	4	2	no	—
435	C₂×D₅	—	8	4	no	—
436	C₄×C₅	—	2	4	no	—
437	C₄×C₅	—	2	2	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	C₃×#120	1	2	yes	—
440	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
441	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
442	Dic₅	—	4	2	no	—
443	C₂⁴	—	10	1	no	—
444	#41	—	2	16	no	—
445	#41	—	2	8	no	—
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	C₃×C₂²⋊D₅	1	4	yes	complemented
452	C₂×Q₈	—	2	8	no	—
453	C₂×Q₈	—	2	4	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
459	C₂×Q₈	C₃×C₂²⋊D₅	1	4	yes	complemented
460	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
461	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	10	4	no	—
466	C₂×D₄	—	10	2	no	—
467	C₂×D₄	—	10	2	no	—
468	C₂×D₄	—	10	1	no	—
469	C₂×D₄	C₃×C₂²⋊D₅	1	2	yes	—
470	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
477	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
478	SD₁₆	—	10	8	no	—
479	SD₁₆	—	10	4	no	—
480	D₈	—	10	4	no	—
481	M₁₆	—	10	2	no	—
482	C₂×C₈	—	5	2	no	—
483	C₂×C₈	—	5	2	no	—
484	C₂×C₈	—	10	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₂²⋊C₄	—	10	1	no	—
487	C₂²⋊C₄	—	10	4	no	—
488	C₄²	—	10	1	no	—
489	C₃×C₅	#3010	1	1	yes	characteristic, complemented, Hall
490	C₂²×C₃	—	2	2	no	—
491	C₂²×C₃	—	2	4	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	4	2	no	—
495	C₂²×C₃	—	20	4	no	—
496	C₂²×C₃	—	20	2	no	—
497	C₂²×C₃	—	40	4	no	—
498	C₂²×C₃	#4099	1	2	yes	—
499	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
500	C₃×C₄	—	2	4	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	20	2	no	—
504	C₃×C₄	#4099	1	2	yes	—
505	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
506	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	4	2	no	—
509	C₂×C₅	—	4	2	no	—
510	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
511	C₂×C₅	C₃×#577	1	2	yes	—
512	D₅	—	8	2	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	10	2	no	—
515	C₂³	—	20	2	no	—
516	C₂³	—	40	2	no	—
517	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
518	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
519	Q₈	—	2	8	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	4	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	2	2	no	—
524	Q₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
525	Q₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
526	D₄	—	2	8	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	1	no	—
531	D₄	—	10	2	no	—
532	D₄	—	10	2	no	—
533	D₄	—	20	2	no	—
534	D₄	—	40	4	no	—
535	D₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
536	C₂×C₄	—	2	8	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	10	2	no	—
545	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
546	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
547	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
548	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
549	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
550	C₈	—	10	2	no	—
551	C₈	—	10	2	no	—
552	C₂×C₃	—	2	2	no	—
553	C₂×C₃	—	4	2	no	—
554	C₂×C₃	—	4	2	no	—
555	C₂×C₃	—	40	2	no	—
556	C₂×C₃	#66171	1	2	yes	—
557	C₂×C₃	C₂×#4099	1	1	yes	characteristic
558	C₅	C₃×#3010	1	1	yes	characteristic, complemented, Sylow
559	C₂²	—	2	2	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	20	4	no	—
565	C₂²	—	20	2	no	—
566	C₂²	—	40	4	no	—
567	C₂²	C₃×#4099	1	2	yes	—
568	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
569	C₄	—	2	4	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	20	2	no	—
573	C₄	C₃×#4099	1	2	yes	—
574	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
575	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
576	C₃	#10615844	1	1	yes	characteristic, direct product factor, Sylow
577	C₂	—	2	2	no	—
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	—	40	2	no	—
581	C₂	C₃×#66171	1	2	yes	—
582	C₂	C₂×C₃×#4099	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×2₋¹⁺⁴	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×2₋¹⁺⁴	D₅
hypocenter	C₅	C₃×#3010
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×2₋¹⁺⁴	C₂	semidirect
2. C₃×#66164	C₂	semidirect
3. C₂×C₃×#4095	C₂	semidirect
4. C₂²×C₃×#688	C₂	semidirect
5. C₃×#65527	C₂	semidirect
6. C₃×#65523	C₂	semidirect
7. C₃×#65522	C₂	semidirect
8. C₃×#65516	C₂	semidirect
9. C₃×#65514	C₂	semidirect
10. #10615844	C₃	direct (N × H)
17. C₂×C₃×C₅×#41	C₂²	semidirect
20. C₂²×C₃×C₅×Q₈	C₂²	semidirect
34. C₃×#3967	C₂²	semidirect
35. C₃×#3967	C₂²	semidirect
36. C₃×#3964	C₂²	semidirect
37. C₃×C₂²⋊#168	C₂²	semidirect
39. C₂×C₅×2₋¹⁺⁴	C₂×C₃	semidirect
40. #66164	C₂×C₃	semidirect
41. C₂×#4095	C₂×C₃	semidirect
42. C₂²×#688	C₂×C₃	semidirect
43. #65527	C₂×C₃	semidirect
44. #65523	C₂×C₃	semidirect
45. #65522	C₂×C₃	semidirect
46. #65516	C₂×C₃	semidirect
47. #65514	C₂×C₃	semidirect
56. C₃×C₅×#41	D₄	semidirect
64. C₂×C₃×C₅×Q₈	D₄	semidirect
94. C₂×C₃×2₋¹⁺⁴	D₅	semidirect
109. C₂×C₅×#41	C₂²×C₃	semidirect
112. C₂²×C₅×Q₈	C₂²×C₃	semidirect
126. #3967	C₂²×C₃	semidirect
127. #3967	C₂²×C₃	semidirect
128. #3964	C₂²×C₃	semidirect
129. C₂²⋊#168	C₂²×C₃	semidirect
176. C₂×C₃×#41	C₂×D₅	semidirect
179. C₂²×C₃×Q₈	C₂×D₅	semidirect
205. C₅×#41	C₃×D₄	semidirect
213. C₂×C₅×Q₈	C₃×D₄	semidirect
243. C₂×2₋¹⁺⁴	C₃×D₅	semidirect
277. C₃×#41	C₂²⋊D₅	semidirect
285. C₂×C₃×Q₈	C₂²⋊D₅	semidirect
360. C₂×#41	C₂×C₃×D₅	semidirect
363. C₂²×Q₈	C₂×C₃×D₅	semidirect
451. #41	C₃×C₂²⋊D₅	semidirect
459. C₂×Q₈	C₃×C₂²⋊D₅	semidirect
489. C₃×C₅	#3010	semidirect
558. C₅	C₃×#3010	semidirect
576. C₃	#10615844	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×C₅×2₋¹⁺⁴	2
C₃×#66164	2
C₂×C₃×#4095	2
C₂²×C₃×#688	2
C₃×#65527	2
C₃×#65523	2
C₃×#65522	2
C₃×#65516	2
C₃×#65514	2
#10615844	3
C₃×#3010	5

Subgroups — C3×#10615844 #14424430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615844 #14424430