Subgroups — C₃×#10602780 #14294777

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic
4	C₃×#64774	C₂	1	4	yes	maximal, complemented
5	#10602780	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₅×M₁₆	—	2	2	no	—
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₃×C₅×M₁₆	C₄	1	4	yes	complemented
10	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	—	2	1	no	—
12	C₂×C₃×C₂²⋊Dic₅	C₄	1	2	yes	—
13	C₃×#4072	—	2	1	no	—
14	C₃×#4072	—	2	1	no	—
15	C₃×#4072	—	2	1	no	—
16	C₃×#4072	—	2	1	no	—
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
19	C₂×C₃×#681	—	2	2	no	—
20	C₂×C₃×#681	—	2	1	no	—
21	C₂×C₃×#681	C₄	1	4	yes	complemented
22	C₂×C₃×#681	C₂²	1	2	yes	—
23	C₂²×C₃×#168	—	2	1	no	—
24	C₃×#1742	—	5	1	no	maximal, Hall
25	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
26	C₂×#4072	C₂×C₃	1	1	yes	characteristic
27	C₂²×#681	C₂×C₃	1	1	yes	characteristic
28	#64774	C₂×C₃	1	4	yes	complemented
29	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
41	C₃×C₅×M₁₆	—	2	4	no	—
42	C₃×C₅×M₁₆	—	2	2	no	—
43	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
44	C₂×C₃×C₅×C₈	—	2	4	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₃×C₂²⋊Dic₅	—	2	2	no	—
47	C₃×C₂²⋊Dic₅	—	2	2	no	—
48	C₃×C₄⋊Dic₅	—	2	2	no	—
49	C₃×C₄⋊Dic₅	—	2	2	no	—
50	C₃×C₄×Dic₅	—	2	2	no	—
51	C₃×C₄×Dic₅	—	2	2	no	—
52	C₃×#681	—	2	4	no	—
53	C₃×#681	—	2	2	no	—
54	C₃×#681	C₂×C₄	1	4	yes	—
55	C₂×C₃×#168	—	2	4	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₂²×C₃×M₁₆	—	5	1	no	—
58	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic
59	C₂×C₃×#117	—	5	1	no	—
60	C₃×#343	—	5	4	no	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₅×M₁₆	—	2	2	no	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	C₃×C₄	1	4	yes	complemented
65	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
66	C₂²×C₅×C₈	—	2	1	no	—
67	C₂×C₂²⋊Dic₅	C₃×C₄	1	2	yes	—
68	#4072	—	2	1	no	—
69	#4072	—	2	1	no	—
70	#4072	—	2	1	no	—
71	#4072	—	2	1	no	—
72	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
74	C₂×#681	—	2	1	no	—
75	C₂×#681	—	2	2	no	—
76	C₂×#681	C₃×C₄	1	4	yes	complemented
77	C₂×#681	C₂²×C₃	1	2	yes	—
78	C₂²×#168	—	2	1	no	—
79	#1742	—	5	1	no	Sylow
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	C₄²	1	2	yes	—
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
85	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×Dic₅	—	2	4	no	—
105	C₂×C₃×Dic₅	—	4	4	no	—
106	C₃×C₅×C₈	—	2	4	no	—
107	C₃×#168	—	2	4	no	—
108	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
109	C₂×C₃×M₁₆	—	2	2	no	—
110	C₂×C₃×M₁₆	—	2	1	no	—
111	C₂×C₃×M₁₆	—	5	4	no	—
112	C₂×C₃×M₁₆	—	5	2	no	—
113	C₂×C₃×M₁₆	—	10	1	no	—
114	C₂×C₃×M₁₆	—	10	2	no	—
115	C₂×C₃×M₁₆	Dic₅	1	4	yes	complemented
116	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
117	C₂²×C₃×C₈	—	2	1	no	—
118	C₂²×C₃×C₈	—	10	1	no	—
119	C₃×#117	—	10	1	no	—
120	C₃×#117	—	10	1	no	—
121	C₃×#117	—	10	1	no	—
122	C₃×#117	—	10	1	no	—
123	C₂×C₃×C₄⋊C₄	—	5	2	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
125	C₂×C₃×C₄²	—	5	2	no	—
126	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
133	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
138	C₅×M₁₆	—	2	4	no	—
139	C₅×M₁₆	—	2	2	no	—
140	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	—
141	C₂×C₅×C₈	—	2	4	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂²⋊Dic₅	—	2	2	no	—
144	C₂²⋊Dic₅	—	2	2	no	—
145	C₄⋊Dic₅	—	2	2	no	—
146	C₄⋊Dic₅	—	2	2	no	—
147	C₄×Dic₅	—	2	2	no	—
148	C₄×Dic₅	—	2	2	no	—
149	#681	—	2	4	no	—
150	#681	—	2	2	no	—
151	#681	C₂×C₃×C₄	1	4	yes	—
152	C₂×#168	—	2	4	no	—
153	C₂×#168	—	2	2	no	—
154	C₂²×M₁₆	—	5	1	no	—
155	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic
156	C₂×#117	—	5	1	no	—
157	#343	—	5	4	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	4	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	#95	1	2	yes	—
164	C₂²×C₃×C₅	#95	1	2	yes	—
165	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₃×C₄×C₅	#95	1	2	yes	—
169	C₃×C₄×C₅	#95	1	2	yes	—
170	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₃×Dic₅	—	4	4	no	—
175	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	—	5	4	no	—
177	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
178	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
180	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
181	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
187	C₃×M₁₆	—	2	4	no	—
188	C₃×M₁₆	—	2	2	no	—
189	C₃×M₁₆	—	5	4	no	—
190	C₃×M₁₆	—	10	4	no	—
191	C₃×M₁₆	—	10	2	no	—
192	C₃×M₁₆	C₂×Dic₅	1	4	yes	—
193	C₂×C₃×C₈	—	2	4	no	—
194	C₂×C₃×C₈	—	2	2	no	—
195	C₂×C₃×C₈	—	10	4	no	—
196	C₂×C₃×C₈	—	10	2	no	—
197	C₃×C₄⋊C₄	—	10	2	no	—
198	C₃×C₄⋊C₄	—	10	2	no	—
199	C₃×C₂²⋊C₄	—	10	2	no	—
200	C₃×C₂²⋊C₄	—	10	2	no	—
201	C₃×C₄²	—	10	2	no	—
202	C₃×C₄²	—	10	2	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	C₃×C₄²	1	2	yes	—
205	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
208	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
210	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
217	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
220	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
221	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
227	C₂×Dic₅	—	2	4	no	—
228	C₂×Dic₅	—	4	4	no	—
229	C₅×C₈	—	2	4	no	—
230	#168	—	2	4	no	—
231	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	5	4	no	—
235	C₂×M₁₆	—	5	2	no	—
236	C₂×M₁₆	—	10	1	no	—
237	C₂×M₁₆	—	10	2	no	—
238	C₂×M₁₆	C₃×Dic₅	1	4	yes	complemented
239	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	10	1	no	—
242	#117	—	10	1	no	—
243	#117	—	10	1	no	—
244	#117	—	10	1	no	—
245	#117	—	10	1	no	—
246	C₂×C₄⋊C₄	—	5	2	no	—
247	C₂×C₂²⋊C₄	—	5	2	no	—
248	C₂×C₄²	—	5	2	no	—
249	C₂×C₃×C₅	—	2	2	no	—
250	C₂×C₃×C₅	—	2	2	no	—
251	C₂×C₃×C₅	—	2	1	no	—
252	C₂×C₃×C₅	—	2	1	no	—
253	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
254	C₂×C₃×C₅	#413	1	2	yes	—
255	C₂³×C₃	—	4	2	no	—
256	C₂³×C₃	C₄×Dic₅	1	2	yes	—
257	C₂³×C₃	#683	1	2	yes	—
258	C₂³×C₃	#685	1	1	yes	characteristic
259	C₂³×C₃	#685	1	1	yes	characteristic
260	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
261	C₂×C₃×C₄	—	10	4	no	—
262	C₂×C₃×C₄	—	20	4	no	—
263	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
264	C₂×C₃×C₄	#683	1	2	yes	—
265	C₂×C₃×C₄	#683	1	2	yes	—
266	C₂×C₃×C₄	#683	1	2	yes	—
267	C₂×C₃×C₄	C₄⋊Dic₅	1	2	yes	—
268	C₂×C₃×C₄	C₄⋊Dic₅	1	2	yes	—
269	C₂×C₃×C₄	#685	1	1	yes	characteristic
270	C₂×C₃×C₄	#685	1	2	yes	—
271	C₂×C₃×C₄	#685	1	2	yes	—
272	C₂×C₃×C₄	#685	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
274	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
275	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
281	C₃×C₈	—	2	4	no	—
282	C₃×C₈	—	10	4	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	C₃×#95	1	2	yes	—
289	C₂²×C₅	C₃×#95	1	2	yes	—
290	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
291	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
293	C₄×C₅	C₃×#95	1	2	yes	—
294	C₄×C₅	C₃×#95	1	2	yes	—
295	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
298	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
299	Dic₅	—	4	4	no	—
300	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
301	C₂²×C₄	—	5	4	no	—
302	C₂²×C₄	C₃×Dic₁₀	1	2	yes	—
303	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
305	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
306	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
308	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
309	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
310	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
311	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	5	4	no	—
315	M₁₆	—	10	4	no	—
316	M₁₆	—	10	2	no	—
317	M₁₆	C₂×C₃×Dic₅	1	4	yes	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	10	4	no	—
321	C₂×C₈	—	10	2	no	—
322	C₄⋊C₄	—	10	2	no	—
323	C₄⋊C₄	—	10	2	no	—
324	C₂²⋊C₄	—	10	2	no	—
325	C₂²⋊C₄	—	10	2	no	—
326	C₄²	—	10	2	no	—
327	C₄²	—	10	2	no	—
328	C₃×C₅	#1742	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	4	2	no	—
333	C₂²×C₃	—	4	2	no	—
334	C₂²×C₃	#3963	1	2	yes	—
335	C₂²×C₃	#3963	1	2	yes	—
336	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
337	C₂²×C₃	C₂×#683	1	1	yes	characteristic
338	C₂²×C₃	C₂×#685	1	1	yes	characteristic
339	C₃×C₄	—	20	4	no	—
340	C₃×C₄	#3963	1	2	yes	—
341	C₃×C₄	#3963	1	2	yes	—
342	C₃×C₄	C₂×#683	1	1	yes	characteristic
343	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
344	C₃×C₄	C₂×#685	1	1	yes	characteristic
345	C₃×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	2	2	no	—
348	C₂×C₅	—	2	1	no	—
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
351	C₂×C₅	C₃×#413	1	2	yes	—
352	C₂³	—	4	2	no	—
353	C₂³	C₃×C₄×Dic₅	1	2	yes	—
354	C₂³	C₃×#683	1	2	yes	—
355	C₂³	C₃×#685	1	1	yes	characteristic
356	C₂³	C₃×#685	1	1	yes	characteristic
357	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
358	C₂×C₄	—	10	4	no	—
359	C₂×C₄	—	20	4	no	—
360	C₂×C₄	C₃×C₄×Dic₅	1	2	yes	—
361	C₂×C₄	C₃×#683	1	2	yes	—
362	C₂×C₄	C₃×#683	1	2	yes	—
363	C₂×C₄	C₃×#683	1	2	yes	—
364	C₂×C₄	C₃×C₄⋊Dic₅	1	2	yes	—
365	C₂×C₄	C₃×C₄⋊Dic₅	1	2	yes	—
366	C₂×C₄	C₃×#685	1	1	yes	characteristic
367	C₂×C₄	C₃×#685	1	1	yes	characteristic
368	C₂×C₄	C₃×#685	1	2	yes	—
369	C₂×C₄	C₃×#685	1	2	yes	—
370	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
371	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
372	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
373	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
374	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
376	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
377	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
378	C₈	—	2	4	no	—
379	C₈	—	10	4	no	—
380	C₂×C₃	—	2	2	no	—
381	C₂×C₃	—	2	2	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	#65421	1	2	yes	—
385	C₂×C₃	C₂×#3963	1	1	yes	characteristic
386	C₅	C₃×#1742	1	1	yes	characteristic, complemented, Sylow
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₃×#3963	1	2	yes	—
393	C₂²	C₃×#3963	1	2	yes	—
394	C₂²	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
395	C₂²	C₂×C₃×#683	1	1	yes	characteristic
396	C₂²	C₂×C₃×#685	1	1	yes	characteristic
397	C₄	—	20	4	no	—
398	C₄	C₃×#3963	1	2	yes	—
399	C₄	C₃×#3963	1	2	yes	—
400	C₄	C₂×C₃×#683	1	1	yes	characteristic
401	C₄	C₂×C₃×C₄⋊Dic₅	1	1	yes	characteristic
402	C₄	C₂×C₃×#685	1	1	yes	characteristic
403	C₄	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
404	C₃	#10602780	1	1	yes	characteristic, direct product factor, Sylow
405	C₂	—	2	2	no	—
406	C₂	—	2	2	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	C₃×#65421	1	2	yes	—
410	C₂	C₂×C₃×#3963	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#685
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₃×#1742
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×#64774	C₂	semidirect
5. #10602780	C₃	direct (N × H)
9. C₂×C₃×C₅×M₁₆	C₄	semidirect
21. C₂×C₃×#681	C₄	semidirect
28. #64774	C₂×C₃	semidirect
64. C₂×C₅×M₁₆	C₃×C₄	semidirect
76. C₂×#681	C₃×C₄	semidirect
115. C₂×C₃×M₁₆	Dic₅	semidirect
238. C₂×M₁₆	C₃×Dic₅	semidirect
328. C₃×C₅	#1742	semidirect
386. C₅	C₃×#1742	semidirect
404. C₃	#10602780	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×M₁₆	2
C₂×C₃×#4072	2
C₂²×C₃×#681	2
C₃×#64774	2
#10602780	3
C₃×#1742	5

Subgroups — C3×#10602780 #14294777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602780 #14294777