Subgroups — C₂×C₃×#66159 #14480465

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66159	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4090	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4082	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4081	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4070	C₂	1	4	yes	maximal, complemented
9	C₂×#66159	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	—	2	8	no	—
11	C₂×C₃×C₅×#41	C₂²	1	8	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
18	C₂²×C₃×Dic₁₀	—	2	8	no	—
19	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
20	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
21	C₂²×C₃×Dic₁₀	C₂²	1	8	yes	complemented
22	C₂×C₃×C₂²⋊Dic₅	C₂²	1	8	yes	—
23	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
24	C₃×#4090	C₂²	1	16	yes	complemented
25	C₃×#4082	C₂²	1	16	yes	complemented
26	C₃×#4081	C₂²	1	32	yes	complemented
27	C₃×#4072	C₂²	1	8	yes	complemented
28	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
29	C₃×#4070	C₂²	1	32	yes	complemented
30	C₂×C₃×#683	C₂²	1	8	yes	—
31	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
32	C₂×C₃×#536	—	5	1	no	maximal, Hall
33	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic
34	C₂³×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
35	#66159	C₂×C₃	1	16	yes	direct product factor
36	C₂×#4090	C₂×C₃	1	2	yes	complemented
37	C₂×#4082	C₂×C₃	1	2	yes	complemented
38	C₂×#4081	C₂×C₃	1	4	yes	complemented
39	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×#4070	C₂×C₃	1	4	yes	complemented
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×#41	—	2	32	no	—
44	C₂×C₃×C₅×Q₈	—	2	4	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
46	C₂×C₃×C₅×D₄	—	2	8	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	—	2	8	no	—
51	C₂²×C₃×C₄×C₅	D₄	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
57	C₂²×C₃×Dic₅	—	2	8	no	—
58	C₂²×C₃×Dic₅	C₂³	1	8	yes	—
59	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
60	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
61	C₂×C₃×Dic₁₀	—	2	8	no	—
62	C₂×C₃×Dic₁₀	—	2	8	no	—
63	C₂×C₃×Dic₁₀	—	2	32	no	—
64	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
65	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
66	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
67	C₃×C₂²⋊Dic₅	C₂³	1	32	yes	—
68	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
69	C₃×#683	C₂³	1	32	yes	—
70	C₃×C₄×Dic₅	C₂³	1	8	yes	—
71	C₂²×C₃×#41	D₅	1	1	yes	characteristic
72	C₂³×C₃×Q₈	—	5	1	no	—
73	C₃×#536	—	5	16	no	—
74	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
75	C₂×C₃×#124	—	5	2	no	—
76	C₂×C₃×#123	—	5	4	no	—
77	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
78	C₂×C₃×#117	—	5	1	no	—
79	C₂×C₅×#41	—	2	8	no	—
80	C₂×C₅×#41	C₂²×C₃	1	8	yes	—
81	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
85	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
86	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
87	C₂²×Dic₁₀	—	2	8	no	—
88	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
89	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
90	C₂²×Dic₁₀	C₂²×C₃	1	8	yes	complemented
91	C₂×C₂²⋊Dic₅	C₂²×C₃	1	8	yes	—
92	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
93	#4090	C₂²×C₃	1	16	yes	complemented
94	#4082	C₂²×C₃	1	16	yes	complemented
95	#4081	C₂²×C₃	1	32	yes	complemented
96	#4072	C₂²×C₃	1	8	yes	complemented
97	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
98	#4070	C₂²×C₃	1	32	yes	complemented
99	C₂×#683	C₂²×C₃	1	8	yes	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
101	C₂×#536	—	5	1	no	Sylow
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	—	2	4	no	—
104	C₂³×C₃×C₅	—	2	8	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
106	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
108	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
109	C₃×C₅×Q₈	—	2	8	no	—
110	C₃×C₅×D₄	—	2	16	no	—
111	C₃×C₅×D₄	—	2	8	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	16	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
120	C₂×C₃×Dic₅	—	2	16	no	—
121	C₂×C₃×Dic₅	—	2	8	no	—
122	C₂×C₃×Dic₅	—	2	8	no	—
123	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
124	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
125	C₃×Dic₁₀	—	2	16	no	—
126	C₃×Dic₁₀	—	2	16	no	—
127	C₂×C₃×#41	—	2	8	no	—
128	C₂×C₃×#41	C₂×D₅	1	8	yes	—
129	C₂²×C₃×Q₈	—	5	2	no	—
130	C₂²×C₃×Q₈	—	5	2	no	—
131	C₂²×C₃×Q₈	—	5	8	no	—
132	C₂²×C₃×Q₈	—	10	8	no	—
133	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
134	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
135	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
136	C₂³×C₃×C₄	—	5	2	no	—
137	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
138	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
139	C₃×C₄⋊Q₈	—	5	16	no	—
140	C₃×#124	—	5	16	no	—
141	C₃×#123	—	5	32	no	—
142	C₃×C₂²⋊Q₈	—	5	32	no	—
143	C₃×#117	—	5	8	no	—
144	C₂×C₃×C₄⋊C₄	—	5	2	no	—
145	C₂×C₃×C₄⋊C₄	—	5	8	no	—
146	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
147	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
148	C₂×C₃×C₄²	—	5	2	no	—
149	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
150	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₅×#41	—	2	32	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
154	C₂×C₅×D₄	—	2	8	no	—
155	C₂×C₅×D₄	—	2	4	no	—
156	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
157	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
158	C₂²×C₄×C₅	—	2	8	no	—
159	C₂²×C₄×C₅	C₃×D₄	1	8	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
165	C₂²×Dic₅	—	2	8	no	—
166	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
167	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
168	C₂²×Dic₅	C₂³×C₃	1	8	yes	—
169	C₂×Dic₁₀	—	2	8	no	—
170	C₂×Dic₁₀	—	2	8	no	—
171	C₂×Dic₁₀	—	2	32	no	—
172	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
173	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
174	C₂²⋊Dic₅	C₂³×C₃	1	32	yes	—
175	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
176	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
177	#683	C₂³×C₃	1	32	yes	—
178	C₄×Dic₅	C₂³×C₃	1	8	yes	—
179	C₂²×#41	C₃×D₅	1	1	yes	characteristic
180	C₂³×Q₈	—	5	1	no	—
181	#536	—	5	16	no	—
182	C₂×C₄⋊Q₈	—	5	2	no	—
183	C₂×#124	—	5	2	no	—
184	C₂×#123	—	5	4	no	—
185	C₂×C₂²⋊Q₈	—	5	4	no	—
186	C₂×#117	—	5	1	no	—
187	C₂²×C₃×C₅	—	2	8	no	—
188	C₂²×C₃×C₅	—	2	4	no	—
189	C₂²×C₃×C₅	—	2	4	no	—
190	C₂²×C₃×C₅	—	2	8	no	—
191	C₂²×C₃×C₅	—	4	8	no	—
192	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
194	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
195	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
196	C₃×C₄×C₅	—	2	4	no	—
197	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
198	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
199	C₃×Dic₅	—	2	8	no	—
200	C₃×Dic₅	—	2	8	no	—
201	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
202	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
203	C₃×#41	—	2	32	no	—
204	C₂×C₃×Q₈	—	2	4	no	—
205	C₂×C₃×Q₈	—	5	8	no	—
206	C₂×C₃×Q₈	—	5	8	no	—
207	C₂×C₃×Q₈	—	10	8	no	—
208	C₂×C₃×Q₈	—	10	8	no	—
209	C₂×C₃×Q₈	—	10	32	no	—
210	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
211	C₂×C₃×D₄	—	2	8	no	—
212	C₂×C₃×D₄	—	2	4	no	—
213	C₂×C₃×D₄	C₂²×D₅	1	8	yes	—
214	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
215	C₂²×C₃×C₄	—	2	8	no	—
216	C₂²×C₃×C₄	—	5	8	no	—
217	C₂²×C₃×C₄	—	5	4	no	—
218	C₂²×C₃×C₄	—	5	4	no	—
219	C₂²×C₃×C₄	—	10	8	no	—
220	C₂²×C₃×C₄	C₂²⋊D₅	1	8	yes	—
221	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
222	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
224	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₃×C₄⋊C₄	—	5	32	no	—
227	C₃×C₄⋊C₄	—	5	8	no	—
228	C₃×C₂²⋊C₄	—	5	8	no	—
229	C₃×C₂²⋊C₄	—	5	32	no	—
230	C₃×C₄²	—	5	8	no	—
231	C₂³×C₅	—	2	4	no	—
232	C₂³×C₅	—	2	4	no	—
233	C₂³×C₅	—	2	8	no	—
234	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
235	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
236	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
237	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
238	C₅×Q₈	—	2	8	no	—
239	C₅×D₄	—	2	16	no	—
240	C₅×D₄	—	2	8	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	16	no	—
243	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	16	yes	—
246	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
247	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
248	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
249	C₂×Dic₅	—	2	16	no	—
250	C₂×Dic₅	—	2	8	no	—
251	C₂×Dic₅	—	2	8	no	—
252	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
253	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
254	Dic₁₀	—	2	16	no	—
255	Dic₁₀	—	2	16	no	—
256	C₂×#41	—	2	8	no	—
257	C₂×#41	C₂×C₃×D₅	1	8	yes	—
258	C₂²×Q₈	—	5	2	no	—
259	C₂²×Q₈	—	5	2	no	—
260	C₂²×Q₈	—	5	8	no	—
261	C₂²×Q₈	—	10	8	no	—
262	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
263	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
264	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
265	C₂³×C₄	—	5	2	no	—
266	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
267	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
268	C₄⋊Q₈	—	5	16	no	—
269	#124	—	5	16	no	—
270	#123	—	5	32	no	—
271	C₂²⋊Q₈	—	5	32	no	—
272	#117	—	5	8	no	—
273	C₂×C₄⋊C₄	—	5	2	no	—
274	C₂×C₄⋊C₄	—	5	8	no	—
275	C₂×C₂²⋊C₄	—	5	2	no	—
276	C₂×C₂²⋊C₄	—	5	8	no	—
277	C₂×C₄²	—	5	2	no	—
278	C₂×C₃×C₅	—	2	4	no	—
279	C₂×C₃×C₅	—	4	4	no	—
280	C₂×C₃×C₅	#536	1	4	yes	complemented
281	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
282	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
283	C₂³×C₃	—	2	4	no	—
284	C₂³×C₃	—	2	8	no	—
285	C₂³×C₃	—	2	4	no	—
286	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
287	C₂³×C₃	C₂³×D₅	1	4	yes	—
288	C₂³×C₃	C₂³×D₅	1	2	yes	—
289	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
290	C₃×Q₈	—	2	8	no	—
291	C₃×Q₈	—	10	16	no	—
292	C₃×Q₈	—	10	16	no	—
293	C₃×D₄	—	2	16	no	—
294	C₃×D₄	—	2	8	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	16	no	—
297	C₂×C₃×C₄	—	5	8	no	—
298	C₂×C₃×C₄	—	5	8	no	—
299	C₂×C₃×C₄	—	10	8	no	—
300	C₂×C₃×C₄	—	10	16	no	—
301	C₂×C₃×C₄	—	10	8	no	—
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
303	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
304	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	16	yes	—
305	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
306	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
307	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	8	no	—
310	C₂²×C₅	—	2	4	no	—
311	C₂²×C₅	—	2	8	no	—
312	C₂²×C₅	—	4	8	no	—
313	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
314	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
315	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
316	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
317	C₄×C₅	—	2	4	no	—
318	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
319	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
320	Dic₅	—	2	8	no	—
321	Dic₅	—	2	8	no	—
322	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
323	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
324	#41	—	2	32	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	5	8	no	—
327	C₂×Q₈	—	5	8	no	—
328	C₂×Q₈	—	10	8	no	—
329	C₂×Q₈	—	10	8	no	—
330	C₂×Q₈	—	10	32	no	—
331	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	C₂²×C₃×D₅	1	8	yes	—
335	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	5	4	no	—
338	C₂²×C₄	—	5	4	no	—
339	C₂²×C₄	—	5	8	no	—
340	C₂²×C₄	—	10	8	no	—
341	C₂²×C₄	C₃×C₂²⋊D₅	1	8	yes	—
342	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
343	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
344	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
347	C₄⋊C₄	—	5	8	no	—
348	C₄⋊C₄	—	5	32	no	—
349	C₂²⋊C₄	—	5	8	no	—
350	C₂²⋊C₄	—	5	32	no	—
351	C₄²	—	5	8	no	—
352	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	2	8	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	8	no	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	4	8	no	—
358	C₂²×C₃	#4150	1	4	yes	—
359	C₂²×C₃	C₂²×C₂²⋊D₅	1	4	yes	—
360	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
361	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
362	C₃×C₄	—	2	4	no	—
363	C₃×C₄	—	10	8	no	—
364	C₃×C₄	—	10	8	no	—
365	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
366	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
367	C₂×C₅	—	2	4	no	—
368	C₂×C₅	—	4	4	no	—
369	C₂×C₅	C₃×#536	1	4	yes	complemented
370	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
371	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	8	no	—
374	C₂³	—	2	4	no	—
375	C₂³	C₂×C₃×C₂²⋊D₅	1	4	yes	—
376	C₂³	C₂³×C₃×D₅	1	4	yes	—
377	C₂³	C₂³×C₃×D₅	1	2	yes	—
378	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
379	Q₈	—	2	8	no	—
380	Q₈	—	10	16	no	—
381	Q₈	—	10	16	no	—
382	D₄	—	2	16	no	—
383	D₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	16	no	—
386	C₂×C₄	—	5	8	no	—
387	C₂×C₄	—	5	8	no	—
388	C₂×C₄	—	10	8	no	—
389	C₂×C₄	—	10	16	no	—
390	C₂×C₄	—	10	8	no	—
391	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
392	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
393	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	16	yes	—
394	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
395	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
396	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
397	C₂×C₃	—	2	4	no	—
398	C₂×C₃	—	4	4	no	—
399	C₂×C₃	#66159	1	4	yes	direct product factor
400	C₂×C₃	C₂×#4150	1	2	yes	—
401	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
402	C₅	C₂×C₃×#536	1	1	yes	characteristic, complemented, Sylow
403	C₂²	—	2	4	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	8	no	—
408	C₂²	C₃×#4150	1	4	yes	—
409	C₂²	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
410	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
411	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	10	8	no	—
414	C₄	—	10	8	no	—
415	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
416	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
417	C₃	C₂×#66159	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	2	4	no	—
419	C₂	—	4	4	no	—
420	C₂	C₃×#66159	1	4	yes	direct product factor
421	C₂	C₂×C₃×#4150	1	2	yes	—
422	C₂	C₂³×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting, prime radical	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₃×#41	D₅
hypocenter	C₅	C₂×C₃×#536
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₁₀	C₂	semidirect
3. C₃×#66159	C₂	direct (N × H)
4. C₂×C₃×#4090	C₂	semidirect
5. C₂×C₃×#4082	C₂	semidirect
6. C₂×C₃×#4081	C₂	semidirect
7. C₂×C₃×#4072	C₂	semidirect
8. C₂×C₃×#4070	C₂	semidirect
9. C₂×#66159	C₃	direct (N × H)
21. C₂²×C₃×Dic₁₀	C₂²	semidirect
24. C₃×#4090	C₂²	semidirect
25. C₃×#4082	C₂²	semidirect
26. C₃×#4081	C₂²	semidirect
27. C₃×#4072	C₂²	semidirect
29. C₃×#4070	C₂²	semidirect
34. C₂³×Dic₁₀	C₂×C₃	semidirect
35. #66159	C₂×C₃	direct (N × H)
36. C₂×#4090	C₂×C₃	semidirect
37. C₂×#4082	C₂×C₃	semidirect
38. C₂×#4081	C₂×C₃	semidirect
39. C₂×#4072	C₂×C₃	semidirect
40. C₂×#4070	C₂×C₃	semidirect
90. C₂²×Dic₁₀	C₂²×C₃	semidirect
93. #4090	C₂²×C₃	semidirect
94. #4082	C₂²×C₃	semidirect
95. #4081	C₂²×C₃	semidirect
96. #4072	C₂²×C₃	semidirect
98. #4070	C₂²×C₃	semidirect
280. C₂×C₃×C₅	#536	semidirect
352. C₃×C₅	C₂×#536	semidirect
369. C₂×C₅	C₃×#536	semidirect
399. C₂×C₃	#66159	direct (N × H)
402. C₅	C₂×C₃×#536	semidirect
417. C₃	C₂×#66159	direct (N × H)
420. C₂	C₃×#66159	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×#41	2
C₂³×C₃×Dic₁₀	2
C₃×#66159	2
C₂×C₃×#4090	2
C₂×C₃×#4082	2
C₂×C₃×#4081	2
C₂×C₃×#4072	2
C₂×C₃×#4070	2
C₂×#66159	3
C₂×C₃×#536	5

Subgroups — C2×C3×#66159 #14480465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66159 #14480465