Subgroups — C₃×#10605482 #14319715

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4039	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄⋊C₄×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#685	C₂	1	4	yes	maximal, complemented
6	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64955	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×#95	C₂	1	2	yes	maximal, complemented
9	#10605482	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#685	C₂²	1	4	yes	—
17	C₂×C₃×#685	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
21	C₃×#4039	C₄	1	16	yes	complemented
22	C₃×C₄×D₂₀	C₄	1	8	yes	complemented
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×#3963	C₂²	1	1	yes	characteristic
25	C₃×#3963	C₂²	1	4	yes	—
26	C₃×#3963	C₂²	1	1	yes	characteristic
27	C₃×#3963	C₂²	1	2	yes	—
28	C₃×#2275	—	5	1	no	maximal, Hall
29	C₂×#4039	C₂×C₃	1	2	yes	—
30	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
32	C₄⋊C₄×Dic₅	C₂×C₃	1	2	yes	complemented
33	C₄×#685	C₂×C₃	1	4	yes	complemented
34	#65221	C₂×C₃	1	1	yes	characteristic, complemented
35	#64955	C₂×C₃	1	2	yes	complemented
36	D₅×#95	C₂×C₃	1	2	yes	complemented
37	C₂³×C₃×D₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
45	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
46	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	—
47	C₂×C₃×C₄×D₅	—	4	4	no	—
48	C₂×C₃×C₄×D₅	—	4	4	no	—
49	C₂×C₃×C₄×D₅	—	4	4	no	—
50	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	complemented
51	C₂×C₃×C₄×D₅	C₂×C₄	1	16	yes	complemented
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
53	C₃×C₄²×C₅	—	4	2	no	—
54	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
55	C₃×#685	C₂×C₄	1	8	yes	complemented
56	C₃×#685	C₂×C₄	1	16	yes	complemented
57	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	complemented
58	C₃×C₄×Dic₅	—	4	4	no	—
59	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	complemented
60	C₂×C₃×C₄×D₄	—	5	2	no	—
61	C₂×C₃×C₄×D₄	—	5	1	no	—
62	C₃×C₄×C₄⋊C₄	—	5	2	no	—
63	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
64	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
65	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
66	C₃×#376	—	5	1	no	—
67	C₂×C₃×#95	—	5	2	no	—
68	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
70	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×#685	C₂²×C₃	1	2	yes	—
75	C₂×#685	C₂²×C₃	1	4	yes	—
76	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
78	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
79	#4039	C₃×C₄	1	16	yes	complemented
80	C₄×D₂₀	C₃×C₄	1	8	yes	complemented
81	C₅×#95	C₂²×C₃	1	2	yes	—
82	#3963	C₂²×C₃	1	1	yes	characteristic
83	#3963	C₂²×C₃	1	4	yes	—
84	#3963	C₂²×C₃	1	1	yes	characteristic
85	#3963	C₂²×C₃	1	2	yes	—
86	#2275	—	5	1	no	Sylow
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₂²×C₃×D₅	—	2	2	no	—
89	C₂²×C₃×D₅	—	2	4	no	—
90	C₂²×C₃×D₅	—	2	2	no	—
91	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
92	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	2	4	no	—
105	C₂×C₃×Dic₅	—	2	2	no	—
106	C₂×C₃×Dic₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
109	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
110	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
111	C₃×D₂₀	C₄²	1	16	yes	complemented
112	C₃×C₄×D₅	—	4	16	no	—
113	C₃×C₄×D₅	—	4	8	no	—
114	C₂²×C₃×D₄	—	5	1	no	—
115	C₂³×C₃×C₄	—	5	4	no	—
116	C₂³×C₃×C₄	—	5	2	no	—
117	C₃×C₄×D₄	—	5	16	no	—
118	C₃×C₄×D₄	—	5	8	no	—
119	C₂×C₃×C₄⋊C₄	—	5	1	no	—
120	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
121	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
122	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
123	C₂×C₃×C₄²	—	5	2	no	—
124	C₂×C₃×C₄²	—	5	4	no	—
125	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	C₃×#95	—	5	1	no	—
128	C₃×#95	—	5	4	no	—
129	C₃×#95	—	5	2	no	—
130	C₃×#95	—	5	1	no	—
131	C₃×#95	C₂×D₅	1	2	yes	—
132	C₂³×D₅	C₂³×C₃	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
138	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
139	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
140	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
141	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	—
142	C₂×C₄×D₅	—	4	4	no	—
143	C₂×C₄×D₅	—	4	4	no	—
144	C₂×C₄×D₅	—	4	4	no	—
145	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
146	C₂×C₄×D₅	C₂×C₃×C₄	1	16	yes	complemented
147	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
148	C₄²×C₅	—	4	2	no	—
149	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
150	#685	C₂×C₃×C₄	1	8	yes	complemented
151	#685	C₂×C₃×C₄	1	16	yes	complemented
152	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	complemented
153	C₄×Dic₅	—	4	4	no	—
154	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	complemented
155	C₂×C₄×D₄	—	5	2	no	—
156	C₂×C₄×D₄	—	5	1	no	—
157	C₄×C₄⋊C₄	—	5	2	no	—
158	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
159	C₄×C₂²⋊C₄	—	5	4	no	—
160	C₄×C₂²⋊C₄	—	5	2	no	—
161	#376	—	5	1	no	—
162	C₂×#95	—	5	2	no	—
163	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
165	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
167	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₃×D₅	—	2	4	no	—
169	C₂×C₃×D₅	—	2	8	no	—
170	C₂×C₃×D₅	—	2	4	no	—
171	C₂×C₃×D₅	—	2	8	no	—
172	C₂×C₃×D₅	C₂×C₄²	1	8	yes	—
173	C₃×C₄×C₅	—	2	2	no	—
174	C₃×C₄×C₅	—	2	8	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
177	C₃×Dic₅	—	2	4	no	—
178	C₃×Dic₅	—	2	4	no	—
179	C₃×Dic₅	—	2	4	no	—
180	C₂⁴×C₃	—	5	2	no	—
181	C₂×C₃×D₄	—	5	8	no	—
182	C₂×C₃×D₄	—	5	4	no	—
183	C₂²×C₃×C₄	—	5	2	no	—
184	C₂²×C₃×C₄	—	5	2	no	—
185	C₂²×C₃×C₄	—	5	2	no	—
186	C₂²×C₃×C₄	—	5	16	no	—
187	C₂²×C₃×C₄	—	5	8	no	—
188	C₂²×C₃×C₄	—	20	4	no	—
189	C₂²×C₃×C₄	—	20	4	no	—
190	C₂²×C₃×C₄	—	20	4	no	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
194	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
195	C₃×C₄⋊C₄	—	5	4	no	—
196	C₃×C₄⋊C₄	C₄×D₅	1	8	yes	complemented
197	C₃×C₂²⋊C₄	—	5	16	no	—
198	C₃×C₂²⋊C₄	—	5	8	no	—
199	C₃×C₄²	—	4	2	no	—
200	C₃×C₄²	—	5	8	no	—
201	C₃×C₄²	—	20	4	no	—
202	C₃×C₄²	C₄×D₅	1	4	yes	complemented
203	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₂²×D₅	—	2	2	no	—
205	C₂²×D₅	—	2	4	no	—
206	C₂²×D₅	—	2	2	no	—
207	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
208	C₂²×D₅	C₂²×C₃×C₄	1	8	yes	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×Dic₅	—	2	2	no	—
220	C₂×Dic₅	—	2	4	no	—
221	C₂×Dic₅	—	2	2	no	—
222	C₂×Dic₅	—	2	2	no	—
223	C₂×Dic₅	—	2	2	no	—
224	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
225	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
226	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
227	D₂₀	C₃×C₄²	1	16	yes	complemented
228	C₄×D₅	—	4	16	no	—
229	C₄×D₅	—	4	8	no	—
230	C₂²×D₄	—	5	1	no	—
231	C₂³×C₄	—	5	4	no	—
232	C₂³×C₄	—	5	2	no	—
233	C₄×D₄	—	5	16	no	—
234	C₄×D₄	—	5	8	no	—
235	C₂×C₄⋊C₄	—	5	1	no	—
236	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
237	C₂×C₂²⋊C₄	—	5	4	no	—
238	C₂×C₂²⋊C₄	—	5	2	no	—
239	C₂×C₄²	—	5	2	no	—
240	C₂×C₄²	—	5	4	no	—
241	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
242	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
243	#95	—	5	1	no	—
244	#95	—	5	4	no	—
245	#95	—	5	2	no	—
246	#95	—	5	1	no	—
247	#95	C₂×C₃×D₅	1	2	yes	—
248	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
249	C₂×C₃×C₅	#518	1	1	yes	characteristic
250	C₂×C₃×C₅	#518	1	2	yes	—
251	C₂×C₃×C₅	#520	1	1	yes	characteristic
252	C₂×C₃×C₅	#520	1	2	yes	—
253	C₃×D₅	—	2	8	no	—
254	C₂³×C₃	—	5	4	no	—
255	C₂³×C₃	—	5	8	no	—
256	C₂³×C₃	—	10	2	no	—
257	C₂³×C₃	—	10	2	no	—
258	C₂³×C₃	—	10	4	no	—
259	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
260	C₃×D₄	—	5	16	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	5	4	no	—
267	C₂×C₃×C₄	—	5	4	no	—
268	C₂×C₃×C₄	—	5	4	no	—
269	C₂×C₃×C₄	—	10	2	no	—
270	C₂×C₃×C₄	—	10	2	no	—
271	C₂×C₃×C₄	—	10	2	no	—
272	C₂×C₃×C₄	—	10	4	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	20	8	no	—
275	C₂×C₃×C₄	—	20	16	no	—
276	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
277	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
278	C₂×C₃×C₄	C₂×C₄×D₅	1	8	yes	—
279	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
280	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
281	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
282	C₂²×C₅	C₂³×C₃×C₄	1	2	yes	—
283	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
284	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂×D₅	—	2	4	no	—
287	C₂×D₅	—	2	8	no	—
288	C₂×D₅	—	2	8	no	—
289	C₂×D₅	—	2	4	no	—
290	C₂×D₅	C₂×C₃×C₄²	1	8	yes	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	8	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	C₂×C₃×C₄²	1	4	yes	—
295	Dic₅	—	2	4	no	—
296	Dic₅	—	2	4	no	—
297	Dic₅	—	2	4	no	—
298	C₂⁴	—	5	2	no	—
299	C₂×D₄	—	5	8	no	—
300	C₂×D₄	—	5	4	no	—
301	C₂²×C₄	—	5	2	no	—
302	C₂²×C₄	—	5	2	no	—
303	C₂²×C₄	—	5	2	no	—
304	C₂²×C₄	—	5	16	no	—
305	C₂²×C₄	—	5	8	no	—
306	C₂²×C₄	—	20	4	no	—
307	C₂²×C₄	—	20	4	no	—
308	C₂²×C₄	—	20	4	no	—
309	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
312	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
313	C₄⋊C₄	—	5	4	no	—
314	C₄⋊C₄	C₃×C₄×D₅	1	8	yes	complemented
315	C₂²⋊C₄	—	5	16	no	—
316	C₂²⋊C₄	—	5	8	no	—
317	C₄²	—	4	2	no	—
318	C₄²	—	5	8	no	—
319	C₄²	—	20	4	no	—
320	C₄²	C₃×C₄×D₅	1	4	yes	complemented
321	C₃×C₅	#2275	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	—	5	8	no	—
323	C₂²×C₃	—	10	4	no	—
324	C₂²×C₃	—	10	4	no	—
325	C₂²×C₃	—	10	8	no	—
326	C₂²×C₃	—	10	8	no	—
327	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
328	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
329	C₂²×C₃	#4144	1	1	yes	characteristic
330	C₂²×C₃	#4147	1	1	yes	characteristic
331	C₂²×C₃	#4149	1	2	yes	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	8	no	—
335	C₃×C₄	—	10	4	no	—
336	C₃×C₄	—	10	4	no	—
337	C₃×C₄	—	10	4	no	—
338	C₃×C₄	C₄²×D₅	1	4	yes	—
339	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
340	C₂×C₅	C₃×#518	1	1	yes	characteristic
341	C₂×C₅	C₃×#518	1	2	yes	—
342	C₂×C₅	C₃×#520	1	2	yes	—
343	C₂×C₅	C₃×#520	1	1	yes	characteristic
344	D₅	—	2	8	no	—
345	C₂³	—	5	4	no	—
346	C₂³	—	5	8	no	—
347	C₂³	—	10	2	no	—
348	C₂³	—	10	2	no	—
349	C₂³	—	10	4	no	—
350	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
351	D₄	—	5	16	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	5	4	no	—
358	C₂×C₄	—	5	4	no	—
359	C₂×C₄	—	5	4	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	—	10	2	no	—
362	C₂×C₄	—	10	2	no	—
363	C₂×C₄	—	10	4	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	20	8	no	—
366	C₂×C₄	—	20	16	no	—
367	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
368	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
369	C₂×C₄	C₂×C₃×C₄×D₅	1	8	yes	—
370	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
371	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
372	C₂×C₃	—	10	8	no	—
373	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
374	C₂×C₃	#65838	1	1	yes	characteristic
375	C₂×C₃	#65855	1	1	yes	characteristic
376	C₂×C₃	#65879	1	2	yes	—
377	C₂×C₃	#65908	1	2	yes	—
378	C₅	C₃×#2275	1	1	yes	characteristic, complemented, Sylow
379	C₂²	—	5	8	no	—
380	C₂²	—	10	4	no	—
381	C₂²	—	10	8	no	—
382	C₂²	—	10	8	no	—
383	C₂²	—	10	4	no	—
384	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
385	C₂²	C₂²×C₃×C₄×D₅	1	2	yes	—
386	C₂²	C₃×#4144	1	1	yes	characteristic
387	C₂²	C₃×#4147	1	1	yes	characteristic
388	C₂²	C₃×#4149	1	2	yes	—
389	C₄	—	2	2	no	—
390	C₄	—	2	8	no	—
391	C₄	—	2	2	no	—
392	C₄	—	10	4	no	—
393	C₄	—	10	4	no	—
394	C₄	—	10	4	no	—
395	C₄	C₃×C₄²×D₅	1	4	yes	—
396	C₃	#10605482	1	1	yes	characteristic, direct product factor, Sylow
397	C₂	—	10	8	no	—
398	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
399	C₂	C₃×#65838	1	1	yes	characteristic
400	C₂	C₃×#65855	1	1	yes	characteristic
401	C₂	C₃×#65879	1	2	yes	—
402	C₂	C₃×#65908	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2275
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×C₄⋊C₄×Dic₅	C₂	semidirect
5. C₃×C₄×#685	C₂	semidirect
6. C₃×#65221	C₂	semidirect
7. C₃×#64955	C₂	semidirect
8. C₃×D₅×#95	C₂	semidirect
9. #10605482	C₃	direct (N × H)
21. C₃×#4039	C₄	semidirect
22. C₃×C₄×D₂₀	C₄	semidirect
31. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
32. C₄⋊C₄×Dic₅	C₂×C₃	semidirect
33. C₄×#685	C₂×C₃	semidirect
34. #65221	C₂×C₃	semidirect
35. #64955	C₂×C₃	semidirect
36. D₅×#95	C₂×C₃	semidirect
50. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
51. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
52. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
54. C₃×C₄²×C₅	C₂×C₄	semidirect
55. C₃×#685	C₂×C₄	semidirect
56. C₃×#685	C₂×C₄	semidirect
57. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
59. C₃×C₄×Dic₅	C₂×C₄	semidirect
63. C₃×C₄×C₄⋊C₄	D₅	semidirect
79. #4039	C₃×C₄	semidirect
80. C₄×D₂₀	C₃×C₄	semidirect
111. C₃×D₂₀	C₄²	semidirect
145. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
146. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
147. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
149. C₄²×C₅	C₂×C₃×C₄	semidirect
150. #685	C₂×C₃×C₄	semidirect
151. #685	C₂×C₃×C₄	semidirect
152. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
154. C₄×Dic₅	C₂×C₃×C₄	semidirect
158. C₄×C₄⋊C₄	C₃×D₅	semidirect
196. C₃×C₄⋊C₄	C₄×D₅	semidirect
202. C₃×C₄²	C₄×D₅	semidirect
227. D₂₀	C₃×C₄²	semidirect
314. C₄⋊C₄	C₃×C₄×D₅	semidirect
320. C₄²	C₃×C₄×D₅	semidirect
321. C₃×C₅	#2275	semidirect
378. C₅	C₃×#2275	semidirect
396. C₃	#10605482	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×#4039	2
C₂×C₃×C₄×D₂₀	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄⋊C₄×Dic₅	2
C₃×C₄×#685	2
C₃×#65221	2
C₃×#64955	2
C₃×D₅×#95	2
#10605482	3
C₃×#2275	5

Subgroups — C3×#10605482 #14319715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605482 #14319715