Subgroups — C₃×#10610941 #14413504

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 504 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
2	C₃×#65857	C₂	1	1	yes	maximal, characteristic
3	C₃×#65838	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65170	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#107	C₂	1	2	yes	maximal, complemented
10	C₃×#65150	C₂	1	2	yes	maximal, complemented
11	C₃×#65149	C₂	1	2	yes	maximal, complemented
12	#10610941	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
18	C₃×#4072	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
21	C₃×#4053	C₄	1	8	yes	complemented
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
24	C₃×#4039	—	2	1	no	—
25	C₃×#4038	C₂²	1	2	yes	—
26	C₃×#4038	C₂²	1	2	yes	—
27	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₃×#4033	—	2	1	no	—
30	C₃×#4027	—	2	2	no	—
31	C₃×C₄×D₂₀	—	2	1	no	—
32	C₃×C₄×Dic₁₀	—	2	1	no	—
33	C₃×C₅×#107	C₂²	1	2	yes	—
34	C₃×C₅×#106	C₂²	1	2	yes	—
35	C₃×#3950	C₂²	1	2	yes	—
36	C₃×#3949	C₂²	1	2	yes	—
37	C₃×#3940	C₂²	1	1	yes	characteristic
38	C₃×#3940	C₂²	1	1	yes	characteristic
39	C₃×#3939	C₂²	1	1	yes	characteristic
40	C₃×#3939	C₂²	1	1	yes	characteristic
41	C₃×#3939	C₂²	1	2	yes	—
42	C₃×#3939	C₂²	1	2	yes	—
43	C₃×#2913	—	5	1	no	maximal, Hall
44	C₂×#4053	C₂×C₃	1	1	yes	characteristic
45	#65857	C₂×C₃	1	1	yes	characteristic
46	#65838	C₂×C₃	1	1	yes	characteristic
47	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
48	#65410	C₂×C₃	1	1	yes	characteristic, complemented
49	#65287	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#3939	C₂×C₃	1	1	yes	characteristic, complemented
51	#65170	C₂×C₃	1	2	yes	complemented
52	D₅×#107	C₂×C₃	1	2	yes	complemented
53	#65150	C₂×C₃	1	2	yes	complemented
54	#65149	C₂×C₃	1	2	yes	complemented
55	C₂²×C₃×C₄×C₅	—	2	1	no	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
58	C₂²×C₃×Dic₅	—	2	1	no	—
59	C₃×#709	C₂×C₄	1	4	yes	—
60	C₃×#709	Q₈	1	4	yes	—
61	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	—	2	2	no	—
64	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
65	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
66	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₄²×C₅	—	2	1	no	—
74	C₃×C₂²⋊Dic₅	—	2	1	no	—
75	C₃×#685	—	2	2	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×C₄⋊Dic₅	—	2	1	no	—
78	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
79	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
80	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
81	C₃×#683	—	2	2	no	—
82	C₃×#683	—	2	2	no	—
83	C₃×C₄×Dic₅	—	2	1	no	—
84	C₃×C₄×Dic₅	—	2	2	no	—
85	C₃×C₄×Dic₅	—	2	2	no	—
86	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×#676	C₂×C₄	1	8	yes	complemented
90	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
91	C₂×C₃×#131	—	5	1	no	—
92	C₃×#520	—	5	1	no	—
93	C₃×#520	—	5	1	no	—
94	C₃×#428	—	5	1	no	—
95	C₃×#428	—	5	2	no	—
96	C₃×#428	—	5	2	no	—
97	C₃×#428	D₅	1	1	yes	characteristic, complemented
98	C₃×#427	—	5	1	no	—
99	C₃×#427	—	5	2	no	—
100	C₂×C₃×#107	—	5	1	no	—
101	C₂×C₃×#107	—	5	2	no	—
102	C₂×#709	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₄×C₂²⋊D₅	—	2	2	no	—
107	#4072	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
109	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
110	#4053	C₃×C₄	1	8	yes	complemented
111	C₂×#676	C₂²×C₃	1	2	yes	—
112	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
113	#4039	—	2	1	no	—
114	#4038	C₂²×C₃	1	2	yes	—
115	#4038	C₂²×C₃	1	2	yes	—
116	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
117	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	#4033	—	2	1	no	—
119	#4027	—	2	2	no	—
120	C₄×D₂₀	—	2	1	no	—
121	C₄×Dic₁₀	—	2	1	no	—
122	C₅×#107	C₂²×C₃	1	2	yes	—
123	C₅×#106	C₂²×C₃	1	2	yes	—
124	#3950	C₂²×C₃	1	2	yes	—
125	#3949	C₂²×C₃	1	2	yes	—
126	#3940	C₂²×C₃	1	1	yes	characteristic
127	#3940	C₂²×C₃	1	1	yes	characteristic
128	#3939	C₂²×C₃	1	1	yes	characteristic
129	#3939	C₂²×C₃	1	1	yes	characteristic
130	#3939	C₂²×C₃	1	2	yes	—
131	#3939	C₂²×C₃	1	2	yes	—
132	#2913	—	5	1	no	Sylow
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	8	1	no	—
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₃×C₂²⋊D₅	C₄⋊C₄	1	8	yes	—
144	C₂×C₃×Dic₅	—	2	1	no	—
145	C₂×C₃×Dic₅	—	2	1	no	—
146	C₂×C₃×Dic₅	—	2	2	no	—
147	C₂×C₃×Dic₅	—	8	1	no	—
148	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
149	C₃×D₂₀	C₄⋊C₄	1	4	yes	—
150	C₃×C₄×D₅	—	8	2	no	—
151	C₃×C₄×D₅	—	8	2	no	—
152	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
153	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
154	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	—
155	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
156	C₃×#168	C₂²×C₄	1	2	yes	—
157	C₃×#168	C₂²×C₄	1	2	yes	—
158	C₂×C₃×#41	—	5	1	no	—
159	C₃×#131	—	5	8	no	—
160	C₂×C₃×M₁₆	—	5	2	no	—
161	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
162	C₂²×C₃×C₈	—	5	1	no	—
163	C₂²×C₃×C₈	—	5	2	no	—
164	C₃×C₄×Q₈	—	10	1	no	—
165	C₃×C₄×Q₈	—	10	1	no	—
166	C₃×C₄×D₄	—	10	1	no	—
167	C₃×C₄×D₄	—	10	2	no	—
168	C₃×C₄×D₄	—	10	1	no	—
169	C₃×C₄×D₄	—	10	2	no	—
170	C₃×#117	—	5	1	no	—
171	C₃×#117	—	5	2	no	—
172	C₃×#117	—	5	2	no	—
173	C₃×#117	C₂×D₅	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	—	5	1	no	—
175	C₂×C₃×C₄⋊C₄	—	5	2	no	—
176	C₂×C₃×C₄⋊C₄	—	5	2	no	—
177	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
178	C₃×#107	—	5	2	no	—
179	C₃×#107	—	5	1	no	—
180	C₃×#107	—	5	2	no	—
181	C₃×#107	—	5	2	no	—
182	C₃×#107	—	5	1	no	—
183	C₃×#107	C₂×D₅	1	2	yes	—
184	C₃×#106	—	5	2	no	—
185	C₃×#106	—	5	1	no	—
186	C₃×#106	—	5	1	no	—
187	C₃×#106	C₂×D₅	1	2	yes	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
191	C₂²×Dic₅	—	2	1	no	—
192	#709	C₂×C₃×C₄	1	4	yes	—
193	#709	C₃×Q₈	1	4	yes	—
194	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
195	C₂×C₄×D₅	—	2	2	no	—
196	C₂×C₄×D₅	—	2	2	no	—
197	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
198	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
199	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
200	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
203	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₂²⋊Dic₅	—	2	1	no	—
208	#685	—	2	2	no	—
209	#685	—	2	2	no	—
210	C₄⋊Dic₅	—	2	1	no	—
211	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
212	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
214	#683	—	2	2	no	—
215	#683	—	2	2	no	—
216	C₄×Dic₅	—	2	1	no	—
217	C₄×Dic₅	—	2	2	no	—
218	C₄×Dic₅	—	2	2	no	—
219	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
220	C₂×#168	C₂³×C₃	1	1	yes	characteristic
221	C₂×#168	C₂³×C₃	1	1	yes	characteristic
222	#676	C₂×C₃×C₄	1	8	yes	complemented
223	C₈×D₅	C₂×C₃×C₄	1	8	yes	complemented
224	C₂×#131	—	5	1	no	—
225	#520	—	5	1	no	—
226	#520	—	5	1	no	—
227	#428	—	5	1	no	—
228	#428	—	5	2	no	—
229	#428	—	5	2	no	—
230	#428	C₃×D₅	1	1	yes	characteristic, complemented
231	#427	—	5	1	no	—
232	#427	—	5	2	no	—
233	C₂×#107	—	5	1	no	—
234	C₂×#107	—	5	2	no	—
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	1	no	—
237	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
238	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₃×D₅	—	2	2	no	—
240	C₂×C₃×D₅	—	2	2	no	—
241	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
242	C₃×C₄×C₅	—	4	1	no	—
243	C₃×C₄×C₅	—	4	2	no	—
244	C₃×C₄×C₅	—	4	1	no	—
245	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
246	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
247	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
248	C₃×Dic₅	—	4	1	no	—
249	C₃×Dic₅	—	4	2	no	—
250	C₃×Dic₅	—	4	1	no	—
251	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
252	C₃×#41	—	5	4	no	—
253	C₃×#41	—	5	4	no	—
254	C₂×C₃×Q₈	—	5	1	no	—
255	C₂×C₃×D₄	—	5	2	no	—
256	C₂×C₃×D₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	5	2	no	—
259	C₂²×C₃×C₄	—	10	2	no	—
260	C₂²×C₃×C₄	—	10	2	no	—
261	C₂²×C₃×C₄	—	10	1	no	—
262	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
263	C₃×M₁₆	—	5	8	no	—
264	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
265	C₂×C₃×C₈	—	5	4	no	—
266	C₂×C₃×C₈	—	5	1	no	—
267	C₂×C₃×C₈	—	5	1	no	—
268	C₂×C₃×C₈	—	5	8	no	—
269	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	5	1	no	—
272	C₃×C₄⋊C₄	—	5	2	no	—
273	C₃×C₄⋊C₄	—	5	1	no	—
274	C₃×C₄⋊C₄	—	10	2	no	—
275	C₃×C₄⋊C₄	—	10	2	no	—
276	C₃×C₄⋊C₄	—	10	1	no	—
277	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
280	C₃×C₂²⋊C₄	—	2	1	no	—
281	C₃×C₂²⋊C₄	—	10	2	no	—
282	C₃×C₂²⋊C₄	—	10	2	no	—
283	C₃×C₂²⋊C₄	—	10	1	no	—
284	C₃×C₄²	—	2	1	no	—
285	C₃×C₄²	—	10	2	no	—
286	C₃×C₄²	—	10	2	no	—
287	C₃×C₄²	—	10	1	no	—
288	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	8	1	no	—
294	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
297	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
298	C₂²⋊D₅	C₃×C₄⋊C₄	1	8	yes	—
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	2	no	—
302	C₂×Dic₅	—	8	1	no	—
303	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
304	D₂₀	C₃×C₄⋊C₄	1	4	yes	—
305	C₄×D₅	—	8	2	no	—
306	C₄×D₅	—	8	2	no	—
307	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
308	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
309	Dic₁₀	C₃×C₄⋊C₄	1	4	yes	—
310	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
311	#168	C₂²×C₃×C₄	1	2	yes	—
312	#168	C₂²×C₃×C₄	1	2	yes	—
313	C₂×#41	—	5	1	no	—
314	#131	—	5	8	no	—
315	C₂×M₁₆	—	5	2	no	—
316	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
317	C₂²×C₈	—	5	1	no	—
318	C₂²×C₈	—	5	2	no	—
319	C₄×Q₈	—	10	1	no	—
320	C₄×Q₈	—	10	1	no	—
321	C₄×D₄	—	10	1	no	—
322	C₄×D₄	—	10	2	no	—
323	C₄×D₄	—	10	1	no	—
324	C₄×D₄	—	10	2	no	—
325	#117	—	5	1	no	—
326	#117	—	5	2	no	—
327	#117	—	5	2	no	—
328	#117	C₂×C₃×D₅	1	1	yes	characteristic
329	C₂×C₄⋊C₄	—	5	1	no	—
330	C₂×C₄⋊C₄	—	5	2	no	—
331	C₂×C₄⋊C₄	—	5	2	no	—
332	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
333	#107	—	5	2	no	—
334	#107	—	5	1	no	—
335	#107	—	5	2	no	—
336	#107	—	5	2	no	—
337	#107	—	5	1	no	—
338	#107	C₂×C₃×D₅	1	2	yes	—
339	#106	—	5	2	no	—
340	#106	—	5	1	no	—
341	#106	—	5	1	no	—
342	#106	C₂×C₃×D₅	1	2	yes	—
343	C₂×C₃×C₅	—	2	2	no	—
344	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₃×C₅	#576	1	1	yes	characteristic
346	C₂×C₃×C₅	#578	1	1	yes	characteristic
347	C₃×D₅	—	2	4	no	—
348	C₂³×C₃	—	5	2	no	—
349	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
350	C₃×Q₈	—	5	4	no	—
351	C₃×D₄	—	5	8	no	—
352	C₃×D₄	—	5	4	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	5	2	no	—
357	C₂×C₃×C₄	—	5	4	no	—
358	C₂×C₃×C₄	—	5	4	no	—
359	C₂×C₃×C₄	—	8	1	no	—
360	C₂×C₃×C₄	—	10	1	no	—
361	C₂×C₃×C₄	—	10	1	no	—
362	C₂×C₃×C₄	—	10	2	no	—
363	C₂×C₃×C₄	—	40	2	no	—
364	C₂×C₃×C₄	—	40	2	no	—
365	C₂×C₃×C₄	—	40	1	no	—
366	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
367	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
368	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
369	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
370	C₃×C₈	—	5	2	no	—
371	C₃×C₈	—	5	2	no	—
372	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
373	C₂²×C₅	—	2	1	no	—
374	C₂²×C₅	—	2	1	no	—
375	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
376	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
377	C₂×D₅	—	2	2	no	—
378	C₂×D₅	—	2	2	no	—
379	C₂×D₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	—	4	2	no	—
382	C₄×C₅	—	4	1	no	—
383	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
384	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
385	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
386	Dic₅	—	4	1	no	—
387	Dic₅	—	4	2	no	—
388	Dic₅	—	4	1	no	—
389	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
390	#41	—	5	4	no	—
391	#41	—	5	4	no	—
392	C₂×Q₈	—	5	1	no	—
393	C₂×D₄	—	5	2	no	—
394	C₂×D₄	—	5	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	5	2	no	—
397	C₂²×C₄	—	10	2	no	—
398	C₂²×C₄	—	10	2	no	—
399	C₂²×C₄	—	10	1	no	—
400	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
401	M₁₆	—	5	8	no	—
402	M₁₆	C₃×C₄×D₅	1	4	yes	complemented
403	C₂×C₈	—	5	4	no	—
404	C₂×C₈	—	5	1	no	—
405	C₂×C₈	—	5	1	no	—
406	C₂×C₈	—	5	8	no	—
407	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	—	5	2	no	—
411	C₄⋊C₄	—	5	1	no	—
412	C₄⋊C₄	—	10	2	no	—
413	C₄⋊C₄	—	10	2	no	—
414	C₄⋊C₄	—	10	1	no	—
415	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
416	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
417	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	10	2	no	—
420	C₂²⋊C₄	—	10	2	no	—
421	C₂²⋊C₄	—	10	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	10	2	no	—
424	C₄²	—	10	2	no	—
425	C₄²	—	10	1	no	—
426	C₃×C₅	#2913	1	1	yes	characteristic, complemented, Hall
427	C₂²×C₃	—	2	1	no	—
428	C₂²×C₃	—	2	1	no	—
429	C₂²×C₃	—	5	4	no	—
430	C₂²×C₃	—	10	2	no	—
431	C₂²×C₃	—	10	2	no	—
432	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
433	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	5	4	no	—
438	C₃×C₄	—	20	1	no	—
439	C₃×C₄	—	20	2	no	—
440	C₃×C₄	—	20	1	no	—
441	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
442	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
443	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
444	C₂×C₅	—	2	2	no	—
445	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
446	C₂×C₅	C₃×#576	1	1	yes	characteristic
447	C₂×C₅	C₃×#578	1	1	yes	characteristic
448	D₅	—	2	4	no	—
449	C₂³	—	5	2	no	—
450	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
451	Q₈	—	5	4	no	—
452	D₄	—	5	8	no	—
453	D₄	—	5	4	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	5	2	no	—
458	C₂×C₄	—	5	4	no	—
459	C₂×C₄	—	5	4	no	—
460	C₂×C₄	—	8	1	no	—
461	C₂×C₄	—	10	1	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	1	no	—
464	C₂×C₄	—	40	2	no	—
465	C₂×C₄	—	40	2	no	—
466	C₂×C₄	—	40	1	no	—
467	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
468	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
469	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
470	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
471	C₈	—	5	2	no	—
472	C₈	—	5	2	no	—
473	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
474	C₂×C₃	—	2	2	no	—
475	C₂×C₃	—	10	4	no	—
476	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
477	C₂×C₃	#66108	1	1	yes	characteristic
478	C₂×C₃	#66113	1	1	yes	characteristic
479	C₅	C₃×#2913	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	5	4	no	—
483	C₂²	—	10	2	no	—
484	C₂²	—	10	2	no	—
485	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
486	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
487	C₄	—	4	2	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	5	4	no	—
491	C₄	—	20	1	no	—
492	C₄	—	20	2	no	—
493	C₄	—	20	1	no	—
494	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
495	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
496	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
497	C₃	#10610941	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	2	2	no	—
499	C₂	—	10	4	no	—
500	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
501	C₂	C₃×#66108	1	1	yes	characteristic
502	C₂	C₃×#66113	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#428	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#428	D₅
hypocenter	C₅	C₃×#2913
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#428

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#428	C₂	semidirect
5. C₃×#65410	C₂	semidirect
6. C₃×#65287	C₂	semidirect
7. C₂×C₃×#3939	C₂	semidirect
8. C₃×#65170	C₂	semidirect
9. C₃×D₅×#107	C₂	semidirect
10. C₃×#65150	C₂	semidirect
11. C₃×#65149	C₂	semidirect
12. #10610941	C₃	direct (N × H)
21. C₃×#4053	C₄	semidirect
47. C₅×#428	C₂×C₃	semidirect
48. #65410	C₂×C₃	semidirect
49. #65287	C₂×C₃	semidirect
50. C₂×#3939	C₂×C₃	semidirect
51. #65170	C₂×C₃	semidirect
52. D₅×#107	C₂×C₃	semidirect
53. #65150	C₂×C₃	semidirect
54. #65149	C₂×C₃	semidirect
66. C₃×C₅×M₁₆	C₂×C₄	semidirect
86. C₂×C₃×#168	C₂×C₄	semidirect
89. C₃×#676	C₂×C₄	semidirect
90. C₃×C₈×D₅	C₂×C₄	semidirect
97. C₃×#428	D₅	semidirect
110. #4053	C₃×C₄	semidirect
199. C₅×M₁₆	C₂×C₃×C₄	semidirect
219. C₂×#168	C₂×C₃×C₄	semidirect
222. #676	C₂×C₃×C₄	semidirect
223. C₈×D₅	C₂×C₃×C₄	semidirect
230. #428	C₃×D₅	semidirect
264. C₃×M₁₆	C₄×D₅	semidirect
402. M₁₆	C₃×C₄×D₅	semidirect
426. C₃×C₅	#2913	semidirect
479. C₅	C₃×#2913	semidirect
497. C₃	#10610941	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
C₃×#65857	2
C₃×#65838	2
C₃×C₅×#428	2
C₃×#65410	2
C₃×#65287	2
C₂×C₃×#3939	2
C₃×#65170	2
C₃×D₅×#107	2
C₃×#65150	2
C₃×#65149	2
#10610941	3
C₃×#2913	5

Subgroups — C3×#10610941 #14413504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610941 #14413504