Subgroups — C₃×#10602371 #14294485

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	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×#64743	C₂	1	4	yes	maximal, complemented
5	#10602371	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×C₅×#117	—	2	2	no	—
8	C₃×C₅×#117	C₄	1	4	yes	complemented
9	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
10	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
11	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
12	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
13	C₃×#4072	—	2	1	no	—
14	C₃×#4072	—	2	1	no	—
15	C₃×#4072	C₄	1	2	yes	complemented
16	C₃×#4072	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊Dic₅	C₄	1	2	yes	complemented
18	C₂×C₃×C₄×Dic₅	—	2	1	no	—
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×#1733	—	5	1	no	maximal, Hall
25	C₂×C₅×#117	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	#64743	C₂×C₃	1	4	yes	complemented
29	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
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	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	—	2	2	no	—
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
44	C₃×C₄²×C₅	—	2	2	no	—
45	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
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	C₂×C₄	1	4	yes	—
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	complemented
55	C₂×C₃×#168	—	2	4	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₂²×C₃×M₁₆	—	5	1	no	—
58	C₂×C₃×#117	—	5	1	no	—
59	C₂×C₃×#117	D₅	1	1	yes	characteristic
60	C₃×#339	—	5	4	no	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₅×#117	—	2	2	no	—
63	C₅×#117	C₃×C₄	1	4	yes	complemented
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
67	C₂×C₂²⋊Dic₅	—	2	1	no	—
68	#4072	—	2	1	no	—
69	#4072	—	2	1	no	—
70	#4072	C₃×C₄	1	2	yes	complemented
71	#4072	C₂²×C₃	1	2	yes	—
72	C₂×C₄⋊Dic₅	C₃×C₄	1	2	yes	complemented
73	C₂×C₄×Dic₅	—	2	1	no	—
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	#1733	—	5	1	no	Sylow
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	4	4	no	—
88	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²⋊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	C₄⋊C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₃×Dic₅	—	2	4	no	—
107	C₂×C₃×Dic₅	—	4	4	no	—
108	C₃×#168	—	2	4	no	—
109	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
110	C₂×C₃×M₁₆	—	5	4	no	—
111	C₂×C₃×M₁₆	—	5	2	no	—
112	C₂×C₃×M₁₆	—	10	1	no	—
113	C₂×C₃×M₁₆	—	10	2	no	—
114	C₂²×C₃×C₈	—	10	1	no	—
115	C₃×#117	—	2	2	no	—
116	C₃×#117	—	5	2	no	—
117	C₃×#117	—	5	2	no	—
118	C₃×#117	—	10	1	no	—
119	C₃×#117	—	10	1	no	—
120	C₃×#117	Dic₅	1	4	yes	complemented
121	C₂×C₃×C₄⋊C₄	—	2	1	no	—
122	C₂×C₃×C₄⋊C₄	—	5	2	no	—
123	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
125	C₂×C₃×C₄²	—	10	1	no	—
126	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
127	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×C₃×C₄	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×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
137	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂²×Dic₅	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₂²⋊C₄	—	2	4	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
144	C₂²⋊Dic₅	—	2	2	no	—
145	C₂²⋊Dic₅	—	2	2	no	—
146	C₄⋊Dic₅	—	2	2	no	—
147	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
148	C₄×Dic₅	—	2	2	no	—
149	C₄×Dic₅	—	2	2	no	—
150	#681	—	2	4	no	—
151	#681	—	2	2	no	—
152	#681	C₂×C₃×C₄	1	4	yes	complemented
153	C₂×#168	—	2	4	no	—
154	C₂×#168	—	2	2	no	—
155	C₂²×M₁₆	—	5	1	no	—
156	C₂×#117	—	5	1	no	—
157	C₂×#117	C₃×D₅	1	1	yes	characteristic
158	#339	—	5	4	no	—
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	—	4	2	no	—
164	C₂²×C₃×C₅	#95	1	2	yes	—
165	C₂²×C₃×C₅	#95	1	2	yes	—
166	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₃×C₄×C₅	—	4	4	no	—
170	C₃×C₄×C₅	#95	1	2	yes	—
171	C₃×C₄×C₅	#95	1	2	yes	—
172	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₃×Dic₅	—	4	4	no	—
177	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	—	10	2	no	—
180	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
181	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
184	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
185	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
187	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₃×M₁₆	—	5	4	no	—
191	C₃×M₁₆	—	10	4	no	—
192	C₃×M₁₆	—	10	2	no	—
193	C₂×C₃×C₈	—	10	4	no	—
194	C₂×C₃×C₈	—	10	2	no	—
195	C₃×C₄⋊C₄	—	2	4	no	—
196	C₃×C₄⋊C₄	—	5	4	no	—
197	C₃×C₄⋊C₄	—	10	2	no	—
198	C₃×C₂²⋊C₄	—	2	4	no	—
199	C₃×C₂²⋊C₄	—	10	2	no	—
200	C₃×C₂²⋊C₄	—	10	2	no	—
201	C₃×C₄²	—	2	2	no	—
202	C₃×C₄²	—	10	2	no	—
203	C₃×C₄²	—	10	2	no	—
204	C₃×C₄²	C₂×Dic₅	1	4	yes	complemented
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
209	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
210	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	4	4	no	—
213	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
214	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
215	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
221	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
222	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
223	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
224	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
225	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
231	C₂×Dic₅	—	2	4	no	—
232	C₂×Dic₅	—	4	4	no	—
233	#168	—	2	4	no	—
234	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂×M₁₆	—	5	4	no	—
236	C₂×M₁₆	—	5	2	no	—
237	C₂×M₁₆	—	10	1	no	—
238	C₂×M₁₆	—	10	2	no	—
239	C₂²×C₈	—	10	1	no	—
240	#117	—	2	2	no	—
241	#117	—	5	2	no	—
242	#117	—	5	2	no	—
243	#117	—	10	1	no	—
244	#117	—	10	1	no	—
245	#117	C₃×Dic₅	1	4	yes	complemented
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	5	2	no	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	10	1	no	—
250	C₂×C₄²	—	10	1	no	—
251	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
252	C₂×C₃×C₅	—	2	1	no	—
253	C₂×C₃×C₅	—	2	2	no	—
254	C₂×C₃×C₅	—	2	2	no	—
255	C₂×C₃×C₅	—	2	1	no	—
256	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
257	C₂×C₃×C₅	#421	1	2	yes	—
258	C₂³×C₃	—	4	2	no	—
259	C₂³×C₃	#683	1	2	yes	—
260	C₂³×C₃	#685	1	1	yes	characteristic
261	C₂³×C₃	#685	1	1	yes	characteristic
262	C₂³×C₃	C₂²⋊Dic₅	1	2	yes	—
263	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	4	4	no	—
266	C₂×C₃×C₄	—	10	4	no	—
267	C₂×C₃×C₄	—	20	4	no	—
268	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
269	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
270	C₂×C₃×C₄	#683	1	2	yes	—
271	C₂×C₃×C₄	#683	1	2	yes	—
272	C₂×C₃×C₄	#683	1	2	yes	—
273	C₂×C₃×C₄	C₄⋊Dic₅	1	2	yes	—
274	C₂×C₃×C₄	C₄⋊Dic₅	1	2	yes	—
275	C₂×C₃×C₄	#685	1	1	yes	characteristic
276	C₂×C₃×C₄	#685	1	1	yes	characteristic
277	C₂×C₃×C₄	#685	1	2	yes	—
278	C₂×C₃×C₄	#685	1	2	yes	—
279	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
280	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
286	C₃×C₈	—	10	4	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	C₃×#95	1	2	yes	—
293	C₂²×C₅	C₃×#95	1	2	yes	—
294	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
297	C₄×C₅	—	4	4	no	—
298	C₄×C₅	C₃×#95	1	2	yes	—
299	C₄×C₅	C₃×#95	1	2	yes	—
300	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
301	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
302	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
303	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
304	Dic₅	—	4	4	no	—
305	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	10	2	no	—
308	C₂²×C₄	C₃×Dic₁₀	1	2	yes	—
309	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
310	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
311	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
312	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
313	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
315	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
316	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
317	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
318	M₁₆	—	5	4	no	—
319	M₁₆	—	10	4	no	—
320	M₁₆	—	10	2	no	—
321	C₂×C₈	—	10	4	no	—
322	C₂×C₈	—	10	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	5	4	no	—
325	C₄⋊C₄	—	10	2	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	10	2	no	—
328	C₂²⋊C₄	—	10	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	10	2	no	—
331	C₄²	—	10	2	no	—
332	C₄²	C₂×C₃×Dic₅	1	4	yes	complemented
333	C₃×C₅	#1733	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	#3963	1	2	yes	—
340	C₂²×C₃	#3963	1	2	yes	—
341	C₂²×C₃	C₂×#683	1	1	yes	characteristic
342	C₂²×C₃	C₂×#685	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
344	C₃×C₄	—	4	4	no	—
345	C₃×C₄	—	20	4	no	—
346	C₃×C₄	#3963	1	2	yes	—
347	C₃×C₄	#3963	1	2	yes	—
348	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
349	C₃×C₄	C₂×#683	1	1	yes	characteristic
350	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
351	C₃×C₄	C₂×#685	1	1	yes	characteristic
352	C₂×C₅	—	2	1	no	—
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	—	2	2	no	—
355	C₂×C₅	—	2	1	no	—
356	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
357	C₂×C₅	C₃×#421	1	2	yes	—
358	C₂³	—	4	2	no	—
359	C₂³	C₃×#683	1	2	yes	—
360	C₂³	C₃×#685	1	1	yes	characteristic
361	C₂³	C₃×#685	1	1	yes	characteristic
362	C₂³	C₃×C₂²⋊Dic₅	1	2	yes	—
363	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	20	4	no	—
368	C₂×C₄	C₃×C₄×Dic₅	1	2	yes	—
369	C₂×C₄	C₃×C₄×Dic₅	1	2	yes	—
370	C₂×C₄	C₃×#683	1	2	yes	—
371	C₂×C₄	C₃×#683	1	2	yes	—
372	C₂×C₄	C₃×#683	1	2	yes	—
373	C₂×C₄	C₃×C₄⋊Dic₅	1	2	yes	—
374	C₂×C₄	C₃×C₄⋊Dic₅	1	2	yes	—
375	C₂×C₄	C₃×#685	1	1	yes	characteristic
376	C₂×C₄	C₃×#685	1	1	yes	characteristic
377	C₂×C₄	C₃×#685	1	2	yes	—
378	C₂×C₄	C₃×#685	1	2	yes	—
379	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
380	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
381	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
382	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
386	C₈	—	10	4	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	2	2	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	#65294	1	2	yes	—
392	C₂×C₃	C₂×#3963	1	1	yes	characteristic
393	C₅	C₃×#1733	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	C₃×#3963	1	2	yes	—
400	C₂²	C₃×#3963	1	2	yes	—
401	C₂²	C₂×C₃×#683	1	1	yes	characteristic
402	C₂²	C₂×C₃×#685	1	1	yes	characteristic
403	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
404	C₄	—	4	4	no	—
405	C₄	—	20	4	no	—
406	C₄	C₃×#3963	1	2	yes	—
407	C₄	C₃×#3963	1	2	yes	—
408	C₄	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
409	C₄	C₂×C₃×#683	1	1	yes	characteristic
410	C₄	C₂×C₃×C₄⋊Dic₅	1	1	yes	characteristic
411	C₄	C₂×C₃×#685	1	1	yes	characteristic
412	C₃	#10602371	1	1	yes	characteristic, direct product factor, Sylow
413	C₂	—	2	1	no	—
414	C₂	—	2	2	no	—
415	C₂	—	2	2	no	—
416	C₂	—	2	1	no	—
417	C₂	C₃×#65294	1	2	yes	—
418	C₂	C₂×C₃×#3963	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#1733
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
4. C₃×#64743	C₂	semidirect
5. #10602371	C₃	direct (N × H)
8. C₃×C₅×#117	C₄	semidirect
15. C₃×#4072	C₄	semidirect
17. C₂×C₃×C₄⋊Dic₅	C₄	semidirect
21. C₂×C₃×#681	C₄	semidirect
28. #64743	C₂×C₃	semidirect
45. C₃×C₄²×C₅	C₂×C₄	semidirect
54. C₃×#681	C₂×C₄	semidirect
63. C₅×#117	C₃×C₄	semidirect
70. #4072	C₃×C₄	semidirect
72. C₂×C₄⋊Dic₅	C₃×C₄	semidirect
76. C₂×#681	C₃×C₄	semidirect
120. C₃×#117	Dic₅	semidirect
143. C₄²×C₅	C₂×C₃×C₄	semidirect
152. #681	C₂×C₃×C₄	semidirect
204. C₃×C₄²	C₂×Dic₅	semidirect
245. #117	C₃×Dic₅	semidirect
332. C₄²	C₂×C₃×Dic₅	semidirect
333. C₃×C₅	#1733	semidirect
393. C₅	C₃×#1733	semidirect
412. C₃	#10602371	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×#117	2
C₂×C₃×#4072	2
C₂²×C₃×#681	2
C₃×#64743	2
#10602371	3
C₃×#1733	5

Subgroups — C3×#10602371 #14294485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602371 #14294485