Subgroups — C₃×#10599546 #14294479

Order 1920.

808 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×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64775	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64752	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64743	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599546	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×#685	—	2	1	no	—
14	C₃×#4072	C₂²	1	1	yes	characteristic
15	C₂×C₃×#683	—	2	1	no	—
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#681	C₂²	1	1	yes	characteristic
18	C₃×D₅×M₁₆	—	2	2	no	—
19	C₃×D₅×M₁₆	C₄	1	4	yes	complemented
20	C₂×C₃×#676	—	2	1	no	—
21	C₂×C₃×C₈×D₅	—	2	1	no	—
22	C₃×#4038	C₄	1	2	yes	complemented
23	C₃×D₅×C₄⋊C₄	C₄	1	2	yes	complemented
24	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
25	C₃×#4023	—	2	1	no	—
26	C₃×#4018	—	2	1	no	—
27	C₃×#4018	—	2	2	no	—
28	C₃×#4018	C₄	1	4	yes	complemented
29	C₃×C₄²×D₅	—	2	1	no	—
30	C₃×#1733	—	5	1	no	maximal, Hall
31	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
32	D₅×#117	C₂×C₃	1	1	yes	characteristic
33	C₂×#4018	C₂×C₃	1	1	yes	characteristic
34	C₅×#339	C₂×C₃	1	1	yes	characteristic, complemented
35	#64775	C₂×C₃	1	1	yes	characteristic, complemented
36	#64752	C₂×C₃	1	1	yes	characteristic, complemented
37	#64743	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	—	2	1	no	—
42	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	—	2	2	no	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
51	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
60	C₃×C₂²⋊Dic₅	—	2	1	no	—
61	C₃×#685	—	2	4	no	—
62	C₃×#685	—	2	2	no	—
63	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
64	C₃×#683	—	2	4	no	—
65	C₃×#683	—	2	2	no	—
66	C₃×C₄×Dic₅	—	2	1	no	—
67	C₃×C₄×Dic₅	—	2	1	no	—
68	C₃×C₄×Dic₅	—	2	2	no	—
69	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
70	C₃×#681	—	2	1	no	—
71	C₃×#681	C₂×C₄	1	2	yes	complemented
72	C₂×C₃×#168	—	2	1	no	—
73	C₃×#676	—	2	4	no	—
74	C₃×C₈×D₅	—	2	4	no	—
75	C₂²×C₃×M₁₆	—	5	1	no	—
76	C₂×C₃×#117	—	5	1	no	—
77	C₂×C₃×#117	—	5	1	no	—
78	C₃×#339	—	5	1	no	—
79	C₃×#339	—	5	1	no	—
80	C₃×#339	—	5	1	no	—
81	C₃×#339	D₅	1	1	yes	characteristic, complemented
82	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
84	C₅×#117	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×#685	—	2	1	no	—
87	#4072	C₂²×C₃	1	1	yes	characteristic
88	C₂×#683	—	2	1	no	—
89	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
90	C₂×#681	C₂²×C₃	1	1	yes	characteristic
91	D₅×M₁₆	—	2	2	no	—
92	D₅×M₁₆	C₃×C₄	1	4	yes	complemented
93	C₂×#676	—	2	1	no	—
94	C₂×C₈×D₅	—	2	1	no	—
95	#4038	C₃×C₄	1	2	yes	complemented
96	D₅×C₄⋊C₄	C₃×C₄	1	2	yes	complemented
97	D₅×C₂²⋊C₄	—	2	1	no	—
98	#4023	—	2	1	no	—
99	#4018	—	2	2	no	—
100	#4018	—	2	1	no	—
101	#4018	C₃×C₄	1	4	yes	complemented
102	C₄²×D₅	—	2	1	no	—
103	#1733	—	5	1	no	Sylow
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	4	2	no	—
122	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
124	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
126	C₃×C₄×D₅	—	4	4	no	—
127	C₃×C₄×D₅	C₄²	1	2	yes	—
128	C₃×C₄×D₅	C₄²	1	2	yes	—
129	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
130	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
131	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
132	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
133	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
134	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
135	C₃×C₅×C₈	—	2	2	no	—
136	C₃×#168	—	2	2	no	—
137	C₂³×C₃×C₄	—	5	1	no	—
138	C₂×C₃×M₁₆	—	5	1	no	—
139	C₂×C₃×M₁₆	—	5	4	no	—
140	C₂×C₃×M₁₆	—	10	1	no	—
141	C₂×C₃×M₁₆	—	10	2	no	—
142	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
143	C₂²×C₃×C₈	—	10	1	no	—
144	C₃×#117	—	5	4	no	—
145	C₃×#117	—	5	1	no	—
146	C₃×#117	—	5	2	no	—
147	C₃×#117	—	10	2	no	—
148	C₃×#117	—	10	1	no	—
149	C₃×#117	—	10	1	no	—
150	C₃×#117	C₂×D₅	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	—	5	2	no	—
152	C₂×C₃×C₄⋊C₄	—	10	1	no	—
153	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
154	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
155	C₂×C₃×C₄²	—	5	1	no	—
156	C₂×C₃×C₄²	—	10	1	no	—
157	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
158	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²×Dic₅	—	2	1	no	—
162	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
163	C₂×C₄×D₅	—	2	2	no	—
164	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
165	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
171	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
172	C₅×M₁₆	—	2	1	no	—
173	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	complemented
174	C₂×C₅×C₈	—	2	1	no	—
175	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
180	C₂²⋊Dic₅	—	2	1	no	—
181	#685	—	2	4	no	—
182	#685	—	2	2	no	—
183	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
184	#683	—	2	4	no	—
185	#683	—	2	2	no	—
186	C₄×Dic₅	—	2	1	no	—
187	C₄×Dic₅	—	2	1	no	—
188	C₄×Dic₅	—	2	2	no	—
189	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
190	#681	—	2	1	no	—
191	#681	C₂×C₃×C₄	1	2	yes	complemented
192	C₂×#168	—	2	1	no	—
193	#676	—	2	4	no	—
194	C₈×D₅	—	2	4	no	—
195	C₂²×M₁₆	—	5	1	no	—
196	C₂×#117	—	5	1	no	—
197	C₂×#117	—	5	1	no	—
198	#339	—	5	1	no	—
199	#339	—	5	1	no	—
200	#339	—	5	1	no	—
201	#339	C₃×D₅	1	1	yes	characteristic, complemented
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₃×D₅	—	2	2	no	—
207	C₂×C₃×D₅	—	2	2	no	—
208	C₂×C₃×D₅	—	4	2	no	—
209	C₂×C₃×D₅	—	4	2	no	—
210	C₂×C₃×D₅	#95	1	2	yes	—
211	C₂×C₃×D₅	#95	1	2	yes	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
215	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₃×Dic₅	—	4	2	no	—
219	C₃×Dic₅	—	4	2	no	—
220	C₃×Dic₅	#95	1	2	yes	—
221	C₃×Dic₅	#95	1	2	yes	—
222	C₂⁴×C₃	—	5	1	no	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	—	5	1	no	—
225	C₂²×C₃×C₄	—	5	1	no	—
226	C₂²×C₃×C₄	—	5	1	no	—
227	C₂²×C₃×C₄	—	5	2	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	—	5	2	no	—
230	C₂²×C₃×C₄	—	5	1	no	—
231	C₂²×C₃×C₄	—	5	1	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	10	2	no	—
234	C₂²×C₃×C₄	—	10	1	no	—
235	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
236	C₃×M₁₆	—	2	1	no	—
237	C₃×M₁₆	—	5	2	no	—
238	C₃×M₁₆	—	10	4	no	—
239	C₃×M₁₆	—	10	1	no	—
240	C₃×M₁₆	C₄×D₅	1	2	yes	complemented
241	C₂×C₃×C₈	—	2	1	no	—
242	C₂×C₃×C₈	—	10	4	no	—
243	C₂×C₃×C₈	—	10	1	no	—
244	C₃×C₄⋊C₄	—	5	2	no	—
245	C₃×C₄⋊C₄	—	10	2	no	—
246	C₃×C₄⋊C₄	—	10	4	no	—
247	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
248	C₃×C₂²⋊C₄	—	2	1	no	—
249	C₃×C₂²⋊C₄	—	10	2	no	—
250	C₃×C₂²⋊C₄	—	10	4	no	—
251	C₃×C₂²⋊C₄	—	10	1	no	—
252	C₃×C₄²	—	2	1	no	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	—	5	2	no	—
255	C₃×C₄²	—	10	2	no	—
256	C₃×C₄²	—	10	1	no	—
257	C₃×C₄²	—	10	1	no	—
258	C₃×C₄²	C₄×D₅	1	2	yes	complemented
259	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×D₅	C₃×C₂²⋊C₄	1	2	yes	—
264	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	2	2	no	—
276	C₂×Dic₅	—	4	2	no	—
277	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
279	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
281	C₄×D₅	—	4	4	no	—
282	C₄×D₅	C₃×C₄²	1	2	yes	—
283	C₄×D₅	C₃×C₄²	1	2	yes	—
284	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
285	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
286	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
287	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
288	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
289	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
290	C₅×C₈	—	2	2	no	—
291	#168	—	2	2	no	—
292	C₂³×C₄	—	5	1	no	—
293	C₂×M₁₆	—	5	1	no	—
294	C₂×M₁₆	—	5	4	no	—
295	C₂×M₁₆	—	10	1	no	—
296	C₂×M₁₆	—	10	2	no	—
297	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂²×C₈	—	10	1	no	—
299	#117	—	5	4	no	—
300	#117	—	5	1	no	—
301	#117	—	5	2	no	—
302	#117	—	10	1	no	—
303	#117	—	10	2	no	—
304	#117	—	10	1	no	—
305	#117	C₂×C₃×D₅	1	1	yes	characteristic
306	C₂×C₄⋊C₄	—	5	2	no	—
307	C₂×C₄⋊C₄	—	10	1	no	—
308	C₂×C₂²⋊C₄	—	10	1	no	—
309	C₂×C₂²⋊C₄	—	10	1	no	—
310	C₂×C₄²	—	5	1	no	—
311	C₂×C₄²	—	10	1	no	—
312	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
313	C₂×C₃×C₅	—	2	1	no	—
314	C₂×C₃×C₅	—	2	1	no	—
315	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
316	C₂×C₃×C₅	#421	1	2	yes	—
317	C₃×D₅	—	2	2	no	—
318	C₃×D₅	—	2	2	no	—
319	C₂³×C₃	—	5	1	no	—
320	C₂³×C₃	—	5	1	no	—
321	C₂³×C₃	—	5	2	no	—
322	C₂³×C₃	—	5	2	no	—
323	C₂³×C₃	—	20	2	no	—
324	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	—	5	1	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	1	no	—
331	C₂×C₃×C₄	—	5	2	no	—
332	C₂×C₃×C₄	—	5	2	no	—
333	C₂×C₃×C₄	—	5	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	5	2	no	—
336	C₂×C₃×C₄	—	5	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	—	10	2	no	—
341	C₂×C₃×C₄	—	10	2	no	—
342	C₂×C₃×C₄	—	20	4	no	—
343	C₂×C₃×C₄	—	20	2	no	—
344	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
347	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
348	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
349	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
350	C₃×C₈	—	2	2	no	—
351	C₃×C₈	—	10	2	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
355	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
356	C₂×D₅	—	2	2	no	—
357	C₂×D₅	—	2	2	no	—
358	C₂×D₅	—	4	2	no	—
359	C₂×D₅	—	4	2	no	—
360	C₂×D₅	C₃×#95	1	2	yes	—
361	C₂×D₅	C₃×#95	1	2	yes	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
365	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
366	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
367	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
368	Dic₅	—	4	2	no	—
369	Dic₅	—	4	2	no	—
370	Dic₅	C₃×#95	1	2	yes	—
371	Dic₅	C₃×#95	1	2	yes	—
372	C₂⁴	—	5	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	5	1	no	—
377	C₂²×C₄	—	5	2	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	5	1	no	—
380	C₂²×C₄	—	5	1	no	—
381	C₂²×C₄	—	5	2	no	—
382	C₂²×C₄	—	5	2	no	—
383	C₂²×C₄	—	10	2	no	—
384	C₂²×C₄	—	10	1	no	—
385	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
386	M₁₆	—	2	1	no	—
387	M₁₆	—	5	2	no	—
388	M₁₆	—	10	4	no	—
389	M₁₆	—	10	1	no	—
390	M₁₆	C₃×C₄×D₅	1	2	yes	complemented
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	10	4	no	—
393	C₂×C₈	—	10	1	no	—
394	C₄⋊C₄	—	5	2	no	—
395	C₄⋊C₄	—	10	2	no	—
396	C₄⋊C₄	—	10	4	no	—
397	C₄⋊C₄	C₃×C₄×D₅	1	2	yes	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	10	2	no	—
400	C₂²⋊C₄	—	10	4	no	—
401	C₂²⋊C₄	—	10	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	5	2	no	—
405	C₄²	—	10	2	no	—
406	C₄²	—	10	1	no	—
407	C₄²	—	10	1	no	—
408	C₄²	C₃×C₄×D₅	1	2	yes	complemented
409	C₃×C₅	#1733	1	1	yes	characteristic, complemented, Hall
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	5	2	no	—
412	C₂²×C₃	—	5	2	no	—
413	C₂²×C₃	—	10	2	no	—
414	C₂²×C₃	—	10	2	no	—
415	C₂²×C₃	—	20	2	no	—
416	C₂²×C₃	—	20	2	no	—
417	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
418	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	—	4	2	no	—
422	C₃×C₄	—	5	2	no	—
423	C₃×C₄	—	5	2	no	—
424	C₃×C₄	—	20	2	no	—
425	C₃×C₄	—	20	2	no	—
426	C₃×C₄	C₄²×D₅	1	1	yes	characteristic
427	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
429	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
433	C₂×C₅	C₃×#421	1	2	yes	—
434	D₅	—	2	2	no	—
435	D₅	—	2	2	no	—
436	C₂³	—	5	1	no	—
437	C₂³	—	5	1	no	—
438	C₂³	—	5	2	no	—
439	C₂³	—	5	2	no	—
440	C₂³	—	20	2	no	—
441	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	5	1	no	—
448	C₂×C₄	—	5	2	no	—
449	C₂×C₄	—	5	2	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	2	no	—
454	C₂×C₄	—	5	2	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	5	2	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	20	4	no	—
460	C₂×C₄	—	20	2	no	—
461	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
462	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
463	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
464	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
465	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
466	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	10	2	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	10	2	no	—
472	C₂×C₃	—	10	2	no	—
473	C₂×C₃	D₅×#95	1	1	yes	characteristic
474	C₂×C₃	#65110	1	2	yes	—
475	C₅	C₃×#1733	1	1	yes	characteristic, complemented, Sylow
476	C₂²	—	2	2	no	—
477	C₂²	—	5	2	no	—
478	C₂²	—	5	2	no	—
479	C₂²	—	10	2	no	—
480	C₂²	—	10	2	no	—
481	C₂²	—	20	2	no	—
482	C₂²	—	20	2	no	—
483	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
484	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
485	C₂²	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	5	2	no	—
489	C₄	—	5	2	no	—
490	C₄	—	20	2	no	—
491	C₄	—	20	2	no	—
492	C₄	C₃×C₄²×D₅	1	1	yes	characteristic
493	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
494	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
495	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
496	C₃	#10599546	1	1	yes	characteristic, direct product factor, Sylow
497	C₂	—	2	1	no	—
498	C₂	—	2	1	no	—
499	C₂	—	10	2	no	—
500	C₂	—	10	2	no	—
501	C₂	C₃×D₅×#95	1	1	yes	characteristic
502	C₂	C₃×#65110	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#339	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#339	D₅
hypocenter	C₅	C₃×#1733
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#339

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#339	C₂	semidirect
5. C₃×#64775	C₂	semidirect
6. C₃×#64752	C₂	semidirect
7. C₃×#64743	C₂	semidirect
8. #10599546	C₃	direct (N × H)
19. C₃×D₅×M₁₆	C₄	semidirect
22. C₃×#4038	C₄	semidirect
23. C₃×D₅×C₄⋊C₄	C₄	semidirect
28. C₃×#4018	C₄	semidirect
34. C₅×#339	C₂×C₃	semidirect
35. #64775	C₂×C₃	semidirect
36. #64752	C₂×C₃	semidirect
37. #64743	C₂×C₃	semidirect
53. C₃×C₅×M₁₆	C₂×C₄	semidirect
59. C₃×C₄²×C₅	C₂×C₄	semidirect
69. C₃×C₄×Dic₅	C₂×C₄	semidirect
71. C₃×#681	C₂×C₄	semidirect
81. C₃×#339	D₅	semidirect
92. D₅×M₁₆	C₃×C₄	semidirect
95. #4038	C₃×C₄	semidirect
96. D₅×C₄⋊C₄	C₃×C₄	semidirect
101. #4018	C₃×C₄	semidirect
173. C₅×M₁₆	C₂×C₃×C₄	semidirect
179. C₄²×C₅	C₂×C₃×C₄	semidirect
189. C₄×Dic₅	C₂×C₃×C₄	semidirect
191. #681	C₂×C₃×C₄	semidirect
201. #339	C₃×D₅	semidirect
240. C₃×M₁₆	C₄×D₅	semidirect
258. C₃×C₄²	C₄×D₅	semidirect
390. M₁₆	C₃×C₄×D₅	semidirect
408. C₄²	C₃×C₄×D₅	semidirect
409. C₃×C₅	#1733	semidirect
475. C₅	C₃×#1733	semidirect
496. C₃	#10599546	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×D₅×M₁₆	2
C₃×D₅×#117	2
C₂×C₃×#4018	2
C₃×C₅×#339	2
C₃×#64775	2
C₃×#64752	2
C₃×#64743	2
#10599546	3
C₃×#1733	5

Subgroups — C3×#10599546 #14294479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599546 #14294479