Subgroups — C₃×#10610281 #14411523

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 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	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
3	C₃×#65856	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64997	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#97	C₂	1	2	yes	maximal, complemented
10	C₃×#64978	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#676	C₂	1	2	yes	maximal, complemented
12	#10610281	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	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×#4053	C₄	1	8	yes	complemented
21	C₃×#4047	C₄	1	8	yes	complemented
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×#676	C₂²	1	2	yes	—
24	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
25	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
26	C₃×#4039	C₄	1	2	yes	—
27	C₃×#4033	C₄	1	2	yes	—
28	C₃×#4027	C₄	1	4	yes	—
29	C₃×#4018	C₂²	1	2	yes	—
30	C₃×C₄²×D₅	C₂²	1	2	yes	—
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
33	C₃×#3947	C₂²	1	1	yes	characteristic
34	C₃×#3947	C₂²	1	1	yes	characteristic
35	C₃×#3947	C₂²	1	1	yes	characteristic
36	C₃×#3947	C₂²	1	1	yes	characteristic
37	C₃×#3947	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×#3935	C₂²	1	2	yes	—
40	C₃×C₄×#168	C₂²	1	2	yes	—
41	C₃×#2875	—	5	1	no	maximal, Hall
42	C₂×#4053	C₂×C₃	1	1	yes	characteristic
43	C₂×#4047	C₂×C₃	1	1	yes	characteristic
44	#65856	C₂×C₃	1	1	yes	characteristic
45	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
46	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
48	#65286	C₂×C₃	1	1	yes	characteristic, complemented
49	#64997	C₂×C₃	1	2	yes	complemented
50	D₅×#97	C₂×C₃	1	2	yes	complemented
51	#64978	C₂×C₃	1	2	yes	complemented
52	C₄×#676	C₂×C₃	1	2	yes	complemented
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
56	C₃×#709	C₂×C₄	1	4	yes	—
57	C₃×#709	C₂×C₄	1	4	yes	—
58	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
60	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
61	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	2	yes	—
70	C₃×#685	C₂×C₄	1	4	yes	—
71	C₃×#683	C₂×C₄	1	4	yes	—
72	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
73	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
74	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₃×#681	C₂×C₄	1	4	yes	complemented
77	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₂×C₃×#168	C₂³	1	2	yes	—
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₃×#676	C₂×C₄	1	8	yes	complemented
82	C₃×#676	C₂×C₄	1	8	yes	complemented
83	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
84	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
85	C₂×C₃×#131	—	5	1	no	—
86	C₂×C₃×#131	—	5	1	no	—
87	C₃×C₄×#41	—	5	1	no	—
88	C₃×#405	—	5	1	no	—
89	C₃×#405	—	5	2	no	—
90	C₃×#405	—	5	2	no	—
91	C₃×#405	D₅	1	1	yes	characteristic, complemented
92	C₃×C₄×M₁₆	—	5	1	no	—
93	C₃×C₄×M₁₆	—	5	2	no	—
94	C₂×C₃×#97	—	5	1	no	—
95	C₂×C₃×#97	—	5	2	no	—
96	C₂×#709	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
99	C₅×#117	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂×#681	C₂²×C₃	1	1	yes	characteristic
102	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
103	#4053	C₃×C₄	1	8	yes	complemented
104	#4047	C₃×C₄	1	8	yes	complemented
105	C₂×#676	C₂²×C₃	1	2	yes	—
106	C₂×#676	C₂²×C₃	1	2	yes	—
107	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
108	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
109	#4039	C₃×C₄	1	2	yes	—
110	#4033	C₃×C₄	1	2	yes	—
111	#4027	C₃×C₄	1	4	yes	—
112	#4018	C₂²×C₃	1	2	yes	—
113	C₄²×D₅	C₂²×C₃	1	2	yes	—
114	C₅×#97	C₂²×C₃	1	2	yes	—
115	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
116	#3947	C₂²×C₃	1	1	yes	characteristic
117	#3947	C₂²×C₃	1	1	yes	characteristic
118	#3947	C₂²×C₃	1	1	yes	characteristic
119	#3947	C₂²×C₃	1	1	yes	characteristic
120	#3947	C₂²×C₃	1	2	yes	—
121	C₈×Dic₅	C₂²×C₃	1	2	yes	—
122	#3935	C₂²×C₃	1	2	yes	—
123	C₄×#168	C₂²×C₃	1	2	yes	—
124	#2875	—	5	1	no	Sylow
125	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₃×C₂²⋊D₅	C₄²	1	8	yes	—
133	C₂×C₃×Dic₅	—	4	2	no	—
134	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
137	C₃×D₂₀	C₄²	1	4	yes	—
138	C₃×C₄×D₅	—	4	4	no	—
139	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
140	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
141	C₃×Dic₁₀	C₄²	1	4	yes	—
142	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
144	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
145	C₃×#168	C₂²×C₄	1	2	yes	—
146	C₃×#168	C₂²×C₄	1	4	yes	—
147	C₃×#168	C₂²×C₄	1	2	yes	—
148	C₂×C₃×#41	—	5	1	no	—
149	C₃×#131	—	5	8	no	—
150	C₃×#131	—	5	8	no	—
151	C₂×C₃×M₁₆	—	5	1	no	—
152	C₂×C₃×M₁₆	—	5	2	no	—
153	C₂×C₃×M₁₆	—	5	2	no	—
154	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	2	no	—
157	C₂²×C₃×C₈	—	5	2	no	—
158	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
159	C₃×C₄×Q₈	—	5	2	no	—
160	C₃×C₄×D₄	—	5	2	no	—
161	C₃×C₄×D₄	—	5	4	no	—
162	C₃×#117	—	5	2	no	—
163	C₃×#117	C₂×D₅	1	1	yes	characteristic
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×C₃×C₄²	—	5	2	no	—
166	C₃×#97	—	5	1	no	—
167	C₃×#97	—	5	2	no	—
168	C₃×#97	—	5	1	no	—
169	C₃×#97	—	5	1	no	—
170	C₃×#97	—	5	1	no	—
171	C₃×#97	—	5	2	no	—
172	C₃×#97	C₂×D₅	1	2	yes	—
173	C₃×C₄×C₈	—	5	2	no	—
174	C₃×C₄×C₈	—	5	2	no	—
175	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
178	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
179	#709	C₂×C₃×C₄	1	4	yes	—
180	#709	C₂×C₃×C₄	1	4	yes	—
181	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
183	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
184	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
185	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
186	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
187	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
190	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
191	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
192	C₄²×C₅	C₂³×C₃	1	2	yes	—
193	#685	C₂×C₃×C₄	1	4	yes	—
194	#683	C₂×C₃×C₄	1	4	yes	—
195	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
196	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
197	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
198	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
199	#681	C₂×C₃×C₄	1	4	yes	complemented
200	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
201	C₂×#168	C₂³×C₃	1	1	yes	characteristic
202	C₂×#168	C₂³×C₃	1	2	yes	—
203	C₂×#168	C₂³×C₃	1	1	yes	characteristic
204	#676	C₂×C₃×C₄	1	8	yes	complemented
205	#676	C₂×C₃×C₄	1	8	yes	complemented
206	C₈×D₅	C₂×C₃×C₄	1	8	yes	complemented
207	C₈×D₅	C₂×C₃×C₄	1	8	yes	complemented
208	C₂×#131	—	5	1	no	—
209	C₂×#131	—	5	1	no	—
210	C₄×#41	—	5	1	no	—
211	#405	—	5	1	no	—
212	#405	—	5	2	no	—
213	#405	—	5	2	no	—
214	#405	C₃×D₅	1	1	yes	characteristic, complemented
215	C₄×M₁₆	—	5	1	no	—
216	C₄×M₁₆	—	5	2	no	—
217	C₂×#97	—	5	1	no	—
218	C₂×#97	—	5	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
221	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₃×D₅	—	2	4	no	—
223	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
224	C₃×C₄×C₅	—	2	4	no	—
225	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
226	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₃×Dic₅	—	2	2	no	—
229	C₃×Dic₅	—	2	2	no	—
230	C₃×Dic₅	C₂×C₄²	1	4	yes	—
231	C₃×#41	—	5	4	no	—
232	C₃×#41	—	5	4	no	—
233	C₂×C₃×Q₈	—	5	1	no	—
234	C₂×C₃×D₄	—	5	2	no	—
235	C₂×C₃×D₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	2	no	—
237	C₂²×C₃×C₄	—	5	2	no	—
238	C₂²×C₃×C₄	—	5	4	no	—
239	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
240	C₃×M₁₆	—	5	4	no	—
241	C₃×M₁₆	—	5	8	no	—
242	C₃×M₁₆	—	5	8	no	—
243	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
244	C₂×C₃×C₈	—	5	4	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	C₂×C₃×C₈	—	5	2	no	—
247	C₂×C₃×C₈	—	5	1	no	—
248	C₂×C₃×C₈	—	5	8	no	—
249	C₂×C₃×C₈	—	5	8	no	—
250	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
251	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	5	4	no	—
255	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
256	C₃×C₂²⋊C₄	—	5	4	no	—
257	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
258	C₃×C₄²	—	5	4	no	—
259	C₃×C₄²	—	5	2	no	—
260	C₃×C₄²	—	5	1	no	—
261	C₃×C₄²	—	5	1	no	—
262	C₃×C₄²	C₂²×D₅	1	2	yes	—
263	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
268	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
270	C₂²⋊D₅	C₃×C₄²	1	8	yes	—
271	C₂×Dic₅	—	4	2	no	—
272	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
273	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
274	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
275	D₂₀	C₃×C₄²	1	4	yes	—
276	C₄×D₅	—	4	4	no	—
277	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
278	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
279	Dic₁₀	C₃×C₄²	1	4	yes	—
280	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
281	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
282	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
283	#168	C₂²×C₃×C₄	1	2	yes	—
284	#168	C₂²×C₃×C₄	1	4	yes	—
285	#168	C₂²×C₃×C₄	1	2	yes	—
286	C₂×#41	—	5	1	no	—
287	#131	—	5	8	no	—
288	#131	—	5	8	no	—
289	C₂×M₁₆	—	5	1	no	—
290	C₂×M₁₆	—	5	2	no	—
291	C₂×M₁₆	—	5	2	no	—
292	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
293	C₂²×C₈	—	5	1	no	—
294	C₂²×C₈	—	5	2	no	—
295	C₂²×C₈	—	5	2	no	—
296	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
297	C₄×Q₈	—	5	2	no	—
298	C₄×D₄	—	5	2	no	—
299	C₄×D₄	—	5	4	no	—
300	#117	—	5	2	no	—
301	#117	C₂×C₃×D₅	1	1	yes	characteristic
302	C₂×C₄²	—	5	1	no	—
303	C₂×C₄²	—	5	2	no	—
304	#97	—	5	1	no	—
305	#97	—	5	2	no	—
306	#97	—	5	1	no	—
307	#97	—	5	1	no	—
308	#97	—	5	1	no	—
309	#97	—	5	2	no	—
310	#97	C₂×C₃×D₅	1	2	yes	—
311	C₄×C₈	—	5	2	no	—
312	C₄×C₈	—	5	2	no	—
313	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
316	C₂×C₃×C₅	#568	1	2	yes	—
317	C₃×D₅	—	2	4	no	—
318	C₂³×C₃	—	5	2	no	—
319	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
320	C₃×Q₈	—	5	4	no	—
321	C₃×D₄	—	5	8	no	—
322	C₃×D₄	—	5	4	no	—
323	C₂×C₃×C₄	—	5	2	no	—
324	C₂×C₃×C₄	—	5	4	no	—
325	C₂×C₃×C₄	—	5	4	no	—
326	C₂×C₃×C₄	—	5	2	no	—
327	C₂×C₃×C₄	—	5	2	no	—
328	C₂×C₃×C₄	—	20	4	no	—
329	C₂×C₃×C₄	—	20	2	no	—
330	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
331	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
333	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
335	C₃×C₈	—	5	2	no	—
336	C₃×C₈	—	5	4	no	—
337	C₃×C₈	—	5	2	no	—
338	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
339	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
340	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
343	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
344	C₂×D₅	—	2	4	no	—
345	C₂×D₅	C₂×C₃×C₄²	1	4	yes	—
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
348	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
349	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
350	Dic₅	—	2	2	no	—
351	Dic₅	—	2	2	no	—
352	Dic₅	C₂×C₃×C₄²	1	4	yes	—
353	#41	—	5	4	no	—
354	#41	—	5	4	no	—
355	C₂×Q₈	—	5	1	no	—
356	C₂×D₄	—	5	2	no	—
357	C₂×D₄	—	5	1	no	—
358	C₂²×C₄	—	5	2	no	—
359	C₂²×C₄	—	5	2	no	—
360	C₂²×C₄	—	5	4	no	—
361	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
362	M₁₆	—	5	4	no	—
363	M₁₆	—	5	8	no	—
364	M₁₆	—	5	8	no	—
365	M₁₆	C₃×C₄×D₅	1	4	yes	complemented
366	C₂×C₈	—	5	4	no	—
367	C₂×C₈	—	5	2	no	—
368	C₂×C₈	—	5	1	no	—
369	C₂×C₈	—	5	1	no	—
370	C₂×C₈	—	5	8	no	—
371	C₂×C₈	—	5	8	no	—
372	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
373	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
374	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
375	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
376	C₄⋊C₄	—	5	4	no	—
377	C₄⋊C₄	C₃×C₄×D₅	1	2	yes	—
378	C₂²⋊C₄	—	5	4	no	—
379	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
380	C₄²	—	5	4	no	—
381	C₄²	—	5	2	no	—
382	C₄²	—	5	1	no	—
383	C₄²	—	5	1	no	—
384	C₄²	C₂²×C₃×D₅	1	2	yes	—
385	C₃×C₅	#2875	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	5	4	no	—
388	C₂²×C₃	—	10	4	no	—
389	C₂²×C₃	C₄²×D₅	1	2	yes	—
390	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	—	5	4	no	—
393	C₃×C₄	—	10	2	no	—
394	C₃×C₄	—	10	2	no	—
395	C₃×C₄	C₄²×D₅	1	2	yes	—
396	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
397	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
398	C₂×C₅	—	2	2	no	—
399	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
400	C₂×C₅	C₃×#568	1	2	yes	—
401	D₅	—	2	4	no	—
402	C₂³	—	5	2	no	—
403	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
404	Q₈	—	5	4	no	—
405	D₄	—	5	8	no	—
406	D₄	—	5	4	no	—
407	C₂×C₄	—	5	2	no	—
408	C₂×C₄	—	5	4	no	—
409	C₂×C₄	—	5	4	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	20	4	no	—
413	C₂×C₄	—	20	2	no	—
414	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
415	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
416	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
417	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
418	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
419	C₈	—	5	2	no	—
420	C₈	—	5	2	no	—
421	C₈	—	5	4	no	—
422	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
423	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
424	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	—	10	4	no	—
427	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
428	C₂×C₃	#66084	1	2	yes	—
429	C₅	C₃×#2875	1	1	yes	characteristic, complemented, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	5	4	no	—
432	C₂²	—	10	4	no	—
433	C₂²	C₃×C₄²×D₅	1	2	yes	—
434	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	5	4	no	—
437	C₄	—	10	2	no	—
438	C₄	—	10	2	no	—
439	C₄	C₃×C₄²×D₅	1	2	yes	—
440	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
441	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
442	C₃	#10610281	1	1	yes	characteristic, direct product factor, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	10	4	no	—
445	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
446	C₂	C₃×#66084	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2875
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#405	C₂	semidirect
5. C₃×M₁₆×Dic₅	C₂	semidirect
6. C₂×C₃×#3947	C₂	semidirect
7. C₃×#65286	C₂	semidirect
8. C₃×#64997	C₂	semidirect
9. C₃×D₅×#97	C₂	semidirect
10. C₃×#64978	C₂	semidirect
11. C₃×C₄×#676	C₂	semidirect
12. #10610281	C₃	direct (N × H)
20. C₃×#4053	C₄	semidirect
21. C₃×#4047	C₄	semidirect
45. C₅×#405	C₂×C₃	semidirect
46. M₁₆×Dic₅	C₂×C₃	semidirect
47. C₂×#3947	C₂×C₃	semidirect
48. #65286	C₂×C₃	semidirect
49. #64997	C₂×C₃	semidirect
50. D₅×#97	C₂×C₃	semidirect
51. #64978	C₂×C₃	semidirect
52. C₄×#676	C₂×C₃	semidirect
62. C₃×C₅×M₁₆	C₂×C₄	semidirect
63. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
76. C₃×#681	C₂×C₄	semidirect
77. C₂×C₃×#168	C₂×C₄	semidirect
81. C₃×#676	C₂×C₄	semidirect
82. C₃×#676	C₂×C₄	semidirect
83. C₃×C₈×D₅	C₂×C₄	semidirect
84. C₃×C₈×D₅	C₂×C₄	semidirect
91. C₃×#405	D₅	semidirect
103. #4053	C₃×C₄	semidirect
104. #4047	C₃×C₄	semidirect
185. C₅×M₁₆	C₂×C₃×C₄	semidirect
186. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
199. #681	C₂×C₃×C₄	semidirect
200. C₂×#168	C₂×C₃×C₄	semidirect
204. #676	C₂×C₃×C₄	semidirect
205. #676	C₂×C₃×C₄	semidirect
206. C₈×D₅	C₂×C₃×C₄	semidirect
207. C₈×D₅	C₂×C₃×C₄	semidirect
214. #405	C₃×D₅	semidirect
243. C₃×M₁₆	C₄×D₅	semidirect
250. C₂×C₃×C₈	C₄×D₅	semidirect
365. M₁₆	C₃×C₄×D₅	semidirect
372. C₂×C₈	C₃×C₄×D₅	semidirect
385. C₃×C₅	#2875	semidirect
429. C₅	C₃×#2875	semidirect
442. C₃	#10610281	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
C₂×C₃×#4047	2
C₃×#65856	2
C₃×C₅×#405	2
C₃×M₁₆×Dic₅	2
C₂×C₃×#3947	2
C₃×#65286	2
C₃×#64997	2
C₃×D₅×#97	2
C₃×#64978	2
C₃×C₄×#676	2
#10610281	3
C₃×#2875	5

Subgroups — C3×#10610281 #14411523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610281 #14411523