Subgroups — C₃×#10607693 #14320968

Order 1920.

1000 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×#4033	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
3	C₃×#65274	C₂	1	1	yes	maximal, characteristic
4	C₃×#65267	C₂	1	2	yes	maximal
5	C₃×C₄⋊C₄×Dic₅	C₂	1	2	yes	maximal
6	C₃×C₄⋊C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
7	C₃×#65263	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
9	C₃×#65218	C₂	1	1	yes	maximal, characteristic
10	C₃×#64944	C₂	1	2	yes	maximal
11	C₃×#64937	C₂	1	2	yes	maximal
12	#10607693	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×#683	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
29	C₃×#4033	C₄	1	8	yes	complemented
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×#3963	C₂²	1	2	yes	—
32	C₃×#3963	C₂²	1	2	yes	—
33	C₃×#3963	C₂²	1	2	yes	—
34	C₃×#3963	C₂²	1	2	yes	—
35	C₃×#3963	C₂²	1	2	yes	—
36	C₃×#3963	C₂²	1	2	yes	—
37	C₃×#2295	—	5	1	no	maximal, Hall
38	C₂×#4033	C₂×C₃	1	1	yes	characteristic
39	C₅×#389	C₂×C₃	1	1	yes	characteristic
40	#65274	C₂×C₃	1	1	yes	characteristic
41	#65267	C₂×C₃	1	2	yes	—
42	C₄⋊C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
43	C₄⋊C₄×Dic₅	C₂×C₃	1	2	yes	—
44	#65263	C₂×C₃	1	1	yes	characteristic
45	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
46	#65218	C₂×C₃	1	1	yes	characteristic
47	#64944	C₂×C₃	1	2	yes	—
48	#64937	C₂×C₃	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
56	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×Dic₁₀	—	2	2	no	—
61	C₂×C₃×Dic₁₀	—	2	2	no	—
62	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
66	C₃×C₄²×C₅	—	2	2	no	—
67	C₃×C₄⋊Dic₅	—	2	2	no	—
68	C₃×C₄⋊Dic₅	—	2	4	no	—
69	C₃×#683	C₂×C₄	1	8	yes	—
70	C₃×C₄×Dic₅	—	2	2	no	—
71	C₃×C₄×Dic₅	—	2	2	no	—
72	C₃×C₄×Dic₅	—	2	2	no	—
73	C₃×C₄×Dic₅	—	2	2	no	—
74	C₃×C₄×Dic₅	—	2	4	no	—
75	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
76	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	—
77	C₃×C₄×Dic₅	Q₈	1	4	yes	complemented
78	C₂×C₃×C₄×Q₈	—	5	1	no	—
79	C₃×#391	—	5	1	no	—
80	C₃×#391	—	5	1	no	—
81	C₃×#389	—	5	1	no	—
82	C₃×#389	D₅	1	1	yes	characteristic
83	C₃×#387	—	5	2	no	—
84	C₃×#387	—	5	2	no	—
85	C₃×C₄×C₄⋊C₄	—	5	1	no	—
86	C₃×C₄×C₄⋊C₄	—	5	2	no	—
87	C₃×#376	—	5	2	no	—
88	C₃×C₄³	—	5	1	no	—
89	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
95	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
96	C₂×#683	C₂²×C₃	1	2	yes	—
97	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
98	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
103	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
105	#4033	C₃×C₄	1	8	yes	complemented
106	C₅×#95	C₂²×C₃	1	2	yes	—
107	#3963	C₂²×C₃	1	2	yes	—
108	#3963	C₂²×C₃	1	2	yes	—
109	#3963	C₂²×C₃	1	2	yes	—
110	#3963	C₂²×C₃	1	2	yes	—
111	#3963	C₂²×C₃	1	2	yes	—
112	#3963	C₂²×C₃	1	2	yes	—
113	#2295	—	5	1	no	Sylow
114	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
127	C₂×C₃×C₄×C₅	#41	1	2	yes	—
128	C₂×C₃×C₄×C₅	#41	1	2	yes	—
129	C₂×C₃×C₄×C₅	#41	1	2	yes	—
130	C₂×C₃×Dic₅	—	2	1	no	—
131	C₂×C₃×Dic₅	—	2	1	no	—
132	C₂×C₃×Dic₅	—	2	1	no	—
133	C₂×C₃×Dic₅	—	2	1	no	—
134	C₂×C₃×Dic₅	—	2	1	no	—
135	C₂×C₃×Dic₅	—	2	1	no	—
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₂×C₃×Dic₅	—	2	2	no	—
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
145	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
146	C₂×C₃×Dic₅	#41	1	2	yes	—
147	C₂×C₃×Dic₅	#41	1	2	yes	—
148	C₃×Dic₁₀	—	2	8	no	—
149	C₂²×C₃×Q₈	—	5	1	no	—
150	C₃×C₄×Q₈	—	5	8	no	—
151	C₂×C₃×C₄⋊C₄	—	5	2	no	—
152	C₂×C₃×C₄⋊C₄	—	5	2	no	—
153	C₂×C₃×C₄⋊C₄	—	5	1	no	—
154	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
157	C₂×C₃×C₄²	—	5	1	no	—
158	C₂×C₃×C₄²	—	5	1	no	—
159	C₂×C₃×C₄²	—	5	2	no	—
160	C₂×C₃×C₄²	—	5	1	no	—
161	C₂×C₃×C₄²	—	5	1	no	—
162	C₂×C₃×C₄²	—	5	1	no	—
163	C₂×C₃×C₄²	—	5	1	no	—
164	C₂×C₃×C₄²	—	5	2	no	—
165	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
166	C₃×#95	—	5	2	no	—
167	C₃×#95	—	5	2	no	—
168	C₃×#95	—	5	2	no	—
169	C₃×#95	—	5	2	no	—
170	C₃×#95	—	5	2	no	—
171	C₃×#95	—	5	2	no	—
172	C₃×#95	C₂×D₅	1	2	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
174	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
179	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
180	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
181	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
182	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
184	C₂×Dic₁₀	—	2	2	no	—
185	C₂×Dic₁₀	—	2	2	no	—
186	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
187	C₅×C₄⋊C₄	—	2	4	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
190	C₄²×C₅	—	2	2	no	—
191	C₄⋊Dic₅	—	2	2	no	—
192	C₄⋊Dic₅	—	2	4	no	—
193	#683	C₂×C₃×C₄	1	8	yes	—
194	C₄×Dic₅	—	2	2	no	—
195	C₄×Dic₅	—	2	2	no	—
196	C₄×Dic₅	—	2	2	no	—
197	C₄×Dic₅	—	2	2	no	—
198	C₄×Dic₅	—	2	4	no	—
199	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
200	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	—
201	C₄×Dic₅	C₃×Q₈	1	4	yes	complemented
202	C₂×C₄×Q₈	—	5	1	no	—
203	#391	—	5	1	no	—
204	#391	—	5	1	no	—
205	#389	—	5	1	no	—
206	#389	C₃×D₅	1	1	yes	characteristic
207	#387	—	5	2	no	—
208	#387	—	5	2	no	—
209	C₄×C₄⋊C₄	—	5	1	no	—
210	C₄×C₄⋊C₄	—	5	2	no	—
211	#376	—	5	2	no	—
212	C₄³	—	5	1	no	—
213	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
214	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
215	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
216	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
217	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	#117	1	4	yes	—
225	C₃×Dic₅	—	2	4	no	—
226	C₃×Dic₅	—	2	2	no	—
227	C₃×Dic₅	—	2	2	no	—
228	C₃×Dic₅	—	2	2	no	—
229	C₃×Dic₅	—	4	2	no	—
230	C₃×Dic₅	C₄×Q₈	1	4	yes	—
231	C₂×C₃×Q₈	—	5	4	no	—
232	C₂×C₃×Q₈	—	10	2	no	—
233	C₂×C₃×Q₈	—	10	2	no	—
234	C₂²×C₃×C₄	—	5	1	no	—
235	C₂²×C₃×C₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	2	no	—
237	C₂²×C₃×C₄	—	5	1	no	—
238	C₂²×C₃×C₄	—	5	1	no	—
239	C₂²×C₃×C₄	—	5	2	no	—
240	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
241	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
242	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
245	C₃×C₄⋊C₄	—	2	4	no	—
246	C₃×C₄⋊C₄	—	2	2	no	—
247	C₃×C₄⋊C₄	—	5	8	no	—
248	C₃×C₄⋊C₄	—	10	4	no	—
249	C₃×C₄⋊C₄	—	10	2	no	—
250	C₃×C₄⋊C₄	C₄×D₅	1	4	yes	—
251	C₃×C₄²	—	2	2	no	—
252	C₃×C₄²	—	5	4	no	—
253	C₃×C₄²	—	5	8	no	—
254	C₃×C₄²	—	5	4	no	—
255	C₃×C₄²	—	10	2	no	—
256	C₃×C₄²	—	10	2	no	—
257	C₃×C₄²	—	10	4	no	—
258	C₃×C₄²	—	10	2	no	—
259	C₃×C₄²	—	10	2	no	—
260	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
271	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
272	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
273	C₂×C₄×C₅	C₃×#41	1	2	yes	—
274	C₂×C₄×C₅	C₃×#41	1	2	yes	—
275	C₂×C₄×C₅	C₃×#41	1	2	yes	—
276	C₂×Dic₅	—	2	1	no	—
277	C₂×Dic₅	—	2	1	no	—
278	C₂×Dic₅	—	2	1	no	—
279	C₂×Dic₅	—	2	1	no	—
280	C₂×Dic₅	—	2	1	no	—
281	C₂×Dic₅	—	2	1	no	—
282	C₂×Dic₅	—	2	2	no	—
283	C₂×Dic₅	—	2	2	no	—
284	C₂×Dic₅	—	2	2	no	—
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
288	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
289	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
290	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
291	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
292	C₂×Dic₅	C₃×#41	1	2	yes	—
293	C₂×Dic₅	C₃×#41	1	2	yes	—
294	Dic₁₀	—	2	8	no	—
295	C₂²×Q₈	—	5	1	no	—
296	C₄×Q₈	—	5	8	no	—
297	C₂×C₄⋊C₄	—	5	2	no	—
298	C₂×C₄⋊C₄	—	5	2	no	—
299	C₂×C₄⋊C₄	—	5	1	no	—
300	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
303	C₂×C₄²	—	5	1	no	—
304	C₂×C₄²	—	5	2	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	5	1	no	—
307	C₂×C₄²	—	5	1	no	—
308	C₂×C₄²	—	5	1	no	—
309	C₂×C₄²	—	5	1	no	—
310	C₂×C₄²	—	5	2	no	—
311	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
312	#95	—	5	2	no	—
313	#95	—	5	2	no	—
314	#95	—	5	2	no	—
315	#95	—	5	2	no	—
316	#95	—	5	2	no	—
317	#95	—	5	2	no	—
318	#95	C₂×C₃×D₅	1	2	yes	—
319	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
320	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
321	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
322	C₂×C₃×C₅	#529	1	1	yes	characteristic
323	C₂×C₃×C₅	#529	1	1	yes	characteristic
324	C₂×C₃×C₅	#533	1	1	yes	characteristic
325	C₂×C₃×C₅	#533	1	1	yes	characteristic
326	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
327	C₃×Q₈	—	10	8	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	—	5	2	no	—
339	C₂×C₃×C₄	—	5	2	no	—
340	C₂×C₃×C₄	—	5	2	no	—
341	C₂×C₃×C₄	—	5	4	no	—
342	C₂×C₃×C₄	—	5	2	no	—
343	C₂×C₃×C₄	—	5	2	no	—
344	C₂×C₃×C₄	—	10	1	no	—
345	C₂×C₃×C₄	—	10	1	no	—
346	C₂×C₃×C₄	—	10	2	no	—
347	C₂×C₃×C₄	—	10	1	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	10	1	no	—
351	C₂×C₃×C₄	—	10	1	no	—
352	C₂×C₃×C₄	—	10	2	no	—
353	C₂×C₃×C₄	—	10	2	no	—
354	C₂×C₃×C₄	—	10	2	no	—
355	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
356	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
357	C₂×C₃×C₄	#711	1	2	yes	—
358	C₂×C₃×C₄	#711	1	2	yes	—
359	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
360	C₂×C₃×C₄	#713	1	2	yes	—
361	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
362	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
363	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
364	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
365	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
366	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
367	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
368	C₄×C₅	—	2	4	no	—
369	C₄×C₅	—	2	2	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	4	2	no	—
372	C₄×C₅	C₃×#117	1	4	yes	—
373	Dic₅	—	2	4	no	—
374	Dic₅	—	2	2	no	—
375	Dic₅	—	2	2	no	—
376	Dic₅	—	2	2	no	—
377	Dic₅	—	4	2	no	—
378	Dic₅	C₃×C₄×Q₈	1	4	yes	—
379	C₂×Q₈	—	5	4	no	—
380	C₂×Q₈	—	10	2	no	—
381	C₂×Q₈	—	10	2	no	—
382	C₂²×C₄	—	5	1	no	—
383	C₂²×C₄	—	5	1	no	—
384	C₂²×C₄	—	5	2	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	C₂²×C₄	—	5	2	no	—
388	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
389	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
390	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	5	8	no	—
396	C₄⋊C₄	—	10	4	no	—
397	C₄⋊C₄	—	10	2	no	—
398	C₄⋊C₄	C₃×C₄×D₅	1	4	yes	—
399	C₄²	—	2	2	no	—
400	C₄²	—	5	4	no	—
401	C₄²	—	5	8	no	—
402	C₄²	—	5	4	no	—
403	C₄²	—	10	2	no	—
404	C₄²	—	10	2	no	—
405	C₄²	—	10	4	no	—
406	C₄²	—	10	2	no	—
407	C₄²	—	10	2	no	—
408	C₃×C₅	#2295	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
410	C₂²×C₃	C₂×#711	1	1	yes	characteristic
411	C₂²×C₃	C₂×#711	1	1	yes	characteristic
412	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
413	C₂²×C₃	C₂×#713	1	1	yes	characteristic
414	C₂²×C₃	D₅×#41	1	1	yes	characteristic
415	C₂²×C₃	D₅×#41	1	1	yes	characteristic
416	C₃×C₄	—	2	4	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	4	2	no	—
420	C₃×C₄	—	5	4	no	—
421	C₃×C₄	—	10	2	no	—
422	C₃×C₄	—	10	4	no	—
423	C₃×C₄	—	10	2	no	—
424	C₃×C₄	—	10	2	no	—
425	C₃×C₄	—	20	2	no	—
426	C₃×C₄	#4038	1	4	yes	—
427	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
428	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
429	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
430	C₂×C₅	C₃×#529	1	1	yes	characteristic
431	C₂×C₅	C₃×#529	1	1	yes	characteristic
432	C₂×C₅	C₃×#533	1	1	yes	characteristic
433	C₂×C₅	C₃×#533	1	1	yes	characteristic
434	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
435	Q₈	—	10	8	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	5	2	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	5	2	no	—
448	C₂×C₄	—	5	2	no	—
449	C₂×C₄	—	5	4	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	10	1	no	—
453	C₂×C₄	—	10	1	no	—
454	C₂×C₄	—	10	2	no	—
455	C₂×C₄	—	10	1	no	—
456	C₂×C₄	—	10	1	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	10	1	no	—
459	C₂×C₄	—	10	1	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	10	2	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
464	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
465	C₂×C₄	C₃×#711	1	2	yes	—
466	C₂×C₄	C₃×#711	1	2	yes	—
467	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
468	C₂×C₄	C₃×#713	1	2	yes	—
469	C₂×C₃	C₂×#4038	1	1	yes	characteristic
470	C₂×C₃	C₄×#711	1	1	yes	characteristic
471	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
472	C₂×C₃	#65934	1	1	yes	characteristic
473	C₂×C₃	#65956	1	1	yes	characteristic
474	C₂×C₃	#66025	1	1	yes	characteristic
475	C₂×C₃	#66062	1	1	yes	characteristic
476	C₅	C₃×#2295	1	1	yes	characteristic, complemented, Sylow
477	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
478	C₂²	C₂×C₃×#711	1	1	yes	characteristic
479	C₂²	C₂×C₃×#711	1	1	yes	characteristic
480	C₂²	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
481	C₂²	C₂×C₃×#713	1	1	yes	characteristic
482	C₂²	C₃×D₅×#41	1	1	yes	characteristic
483	C₂²	C₃×D₅×#41	1	1	yes	characteristic
484	C₄	—	2	4	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	5	4	no	—
489	C₄	—	10	2	no	—
490	C₄	—	10	2	no	—
491	C₄	—	10	2	no	—
492	C₄	—	10	4	no	—
493	C₄	—	20	2	no	—
494	C₄	C₃×#4038	1	4	yes	—
495	C₃	#10607693	1	1	yes	characteristic, direct product factor, Sylow
496	C₂	C₂×C₃×#4038	1	1	yes	characteristic
497	C₂	C₃×C₄×#711	1	1	yes	characteristic
498	C₂	C₃×C₄×Q₈×D₅	1	1	yes	characteristic
499	C₂	C₃×#65934	1	1	yes	characteristic
500	C₂	C₃×#65956	1	1	yes	characteristic
501	C₂	C₃×#66025	1	1	yes	characteristic
502	C₂	C₃×#66062	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#389	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#389	D₅
hypocenter	C₅	C₃×#2295
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#389

Complements

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

N	H ≅ G/N	type
12. #10607693	C₃	direct (N × H)
29. C₃×#4033	C₄	semidirect
77. C₃×C₄×Dic₅	Q₈	semidirect
105. #4033	C₃×C₄	semidirect
201. C₄×Dic₅	C₃×Q₈	semidirect
408. C₃×C₅	#2295	semidirect
476. C₅	C₃×#2295	semidirect
495. C₃	#10607693	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×#4033	2
C₃×C₅×#389	2
C₃×#65274	2
C₃×#65267	2
C₃×C₄⋊C₄×Dic₅	2
C₃×#65263	2
C₃×C₄²×Dic₅	2
C₃×#65218	2
C₃×#64944	2
C₃×#64937	2
#10607693	3
C₃×#2295	5

Subgroups — C3×#10607693 #14320968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10607693 #14320968