Subgroups — C₃×#10610284 #14414921

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65858	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65415	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64995	C₂	1	4	yes	maximal, complemented
9	C₃×C₈×D₂₀	C₂	1	4	yes	maximal, complemented
10	#10610284	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×#709	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₃×#4047	—	2	4	no	—
19	C₂×C₃×#676	C₂²	1	2	yes	complemented
20	C₂×C₃×C₈×D₅	—	2	4	no	—
21	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
24	C₃×#4043	C₄	1	2	yes	—
25	C₃×#4041	C₄	1	2	yes	—
26	C₃×#4032	C₄	1	2	yes	—
27	C₃×#4028	C₄	1	2	yes	—
28	C₃×C₄×D₂₀	C₂²	1	4	yes	—
29	C₃×C₅×#97	C₂²	1	2	yes	complemented
30	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
31	C₃×#3952	C₂²	1	4	yes	—
32	C₃×#3952	C₂²	1	4	yes	complemented
33	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
34	C₃×#2929	—	5	1	no	maximal, Hall
35	C₂×#4047	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
37	#65858	C₂×C₃	1	1	yes	characteristic
38	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
39	#65418	C₂×C₃	1	1	yes	characteristic, complemented
40	#65415	C₂×C₃	1	1	yes	characteristic, complemented
41	#65288	C₂×C₃	1	1	yes	characteristic, complemented
42	#64995	C₂×C₃	1	4	yes	complemented
43	C₈×D₂₀	C₂×C₃	1	4	yes	complemented
44	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
47	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
48	C₃×#709	—	2	2	no	—
49	C₃×#709	—	2	2	no	—
50	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
52	C₂×C₃×C₄×D₅	—	2	2	no	—
53	C₂×C₃×C₄×D₅	—	2	2	no	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
57	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
58	C₃×C₅×M₁₆	—	2	2	no	—
59	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	2	yes	—
66	C₃×#685	C₂×C₄	1	4	yes	—
67	C₃×#685	C₂×C₄	1	4	yes	—
68	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
69	C₃×#681	—	2	2	no	—
70	C₂×C₃×#168	—	2	2	no	—
71	C₂×C₃×#168	C₂³	1	2	yes	—
72	C₂×C₃×#168	C₂³	1	2	yes	—
73	C₃×#676	—	2	4	no	—
74	C₃×C₈×D₅	—	2	4	no	—
75	C₃×C₈×D₅	—	2	4	no	—
76	C₃×C₈×D₅	—	2	4	no	—
77	C₂×C₃×#131	—	5	1	no	—
78	C₂³×C₃×C₈	—	5	1	no	—
79	C₃×#525	—	5	1	no	—
80	C₃×#435	—	5	4	no	—
81	C₃×C₈×D₄	—	5	4	no	—
82	C₃×#424	—	5	1	no	—
83	C₃×#408	—	5	1	no	—
84	C₃×#407	—	5	1	no	—
85	C₃×#405	D₅	1	1	yes	characteristic, complemented
86	C₂×#709	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
90	C₅×#117	C₂²×C₃	1	1	yes	characteristic
91	C₂×#681	C₂²×C₃	1	1	yes	characteristic
92	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
93	#4047	—	2	4	no	—
94	C₂×#676	C₂²×C₃	1	2	yes	complemented
95	C₂×C₈×D₅	—	2	4	no	—
96	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
97	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
98	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
99	#4043	C₃×C₄	1	2	yes	—
100	#4041	C₃×C₄	1	2	yes	—
101	#4032	C₃×C₄	1	2	yes	—
102	#4028	C₃×C₄	1	2	yes	—
103	C₄×D₂₀	C₂²×C₃	1	4	yes	—
104	C₅×#97	C₂²×C₃	1	2	yes	complemented
105	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
106	#3952	C₂²×C₃	1	4	yes	—
107	#3952	C₂²×C₃	1	4	yes	complemented
108	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
109	#2929	—	5	1	no	Sylow
110	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₃×D₅	—	2	2	no	—
112	C₂²×C₃×D₅	—	2	4	no	—
113	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
114	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₂²⋊D₅	—	2	4	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
124	C₃×D₂₀	—	2	8	no	—
125	C₃×D₂₀	—	2	2	no	—
126	C₃×C₄×D₅	—	2	4	no	—
127	C₃×C₄×D₅	—	2	2	no	—
128	C₃×C₄×D₅	—	2	2	no	—
129	C₃×C₄×D₅	—	2	2	no	—
130	C₃×C₄×D₅	—	2	2	no	—
131	C₃×Dic₁₀	—	2	2	no	—
132	C₃×C₅×C₈	—	2	2	no	—
133	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
134	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₃×#168	—	2	2	no	—
136	C₃×#168	—	2	2	no	—
137	C₂×C₃×#41	—	5	1	no	—
138	C₂³×C₃×C₄	—	5	1	no	—
139	C₃×#131	—	10	4	no	—
140	C₂×C₃×M₁₆	—	5	1	no	—
141	C₂×C₃×M₁₆	—	5	2	no	—
142	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
143	C₂²×C₃×C₈	—	5	1	no	—
144	C₂²×C₃×C₈	—	5	2	no	—
145	C₂²×C₃×C₈	—	5	2	no	—
146	C₂²×C₃×C₈	—	5	2	no	—
147	C₂²×C₃×C₈	—	10	4	no	—
148	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
149	C₃×#123	—	5	2	no	—
150	C₃×C₂²⋊Q₈	—	5	2	no	—
151	C₃×#121	—	5	2	no	—
152	C₃×#120	—	5	2	no	—
153	C₃×C₄×D₄	—	5	4	no	—
154	C₃×#117	C₂×D₅	1	1	yes	characteristic
155	C₃×C₄⋊C₈	—	5	4	no	—
156	C₃×C₂²⋊C₈	—	5	4	no	—
157	C₃×C₂²⋊C₈	—	5	4	no	—
158	C₃×#97	C₂×D₅	1	2	yes	complemented
159	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
160	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
163	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
164	#709	—	2	2	no	—
165	#709	—	2	2	no	—
166	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
168	C₂×C₄×D₅	—	2	2	no	—
169	C₂×C₄×D₅	—	2	2	no	—
170	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
171	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
172	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
173	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
174	C₅×M₁₆	—	2	2	no	—
175	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
176	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
177	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
179	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
180	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
181	C₄²×C₅	C₂³×C₃	1	2	yes	—
182	#685	C₂×C₃×C₄	1	4	yes	—
183	#685	C₂×C₃×C₄	1	4	yes	—
184	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
185	#681	—	2	2	no	—
186	C₂×#168	—	2	2	no	—
187	C₂×#168	C₂³×C₃	1	2	yes	—
188	C₂×#168	C₂³×C₃	1	2	yes	—
189	#676	—	2	4	no	—
190	C₈×D₅	—	2	4	no	—
191	C₈×D₅	—	2	4	no	—
192	C₈×D₅	—	2	4	no	—
193	C₂×#131	—	5	1	no	—
194	C₂³×C₈	—	5	1	no	—
195	#525	—	5	1	no	—
196	#435	—	5	4	no	—
197	C₈×D₄	—	5	4	no	—
198	#424	—	5	1	no	—
199	#408	—	5	1	no	—
200	#407	—	5	1	no	—
201	#405	C₃×D₅	1	1	yes	characteristic, complemented
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
204	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₃×D₅	—	2	8	no	—
206	C₂×C₃×D₅	—	2	2	no	—
207	C₂×C₃×D₅	—	2	2	no	—
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	4	no	—
210	C₂×C₃×D₅	#131	1	4	yes	complemented
211	C₃×C₄×C₅	—	2	4	no	—
212	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₃×Dic₅	—	2	2	no	—
216	C₃×Dic₅	—	2	2	no	—
217	C₂⁴×C₃	—	5	1	no	—
218	C₃×#41	—	10	2	no	—
219	C₃×#41	—	10	2	no	—
220	C₂×C₃×Q₈	—	5	1	no	—
221	C₂×C₃×D₄	—	5	2	no	—
222	C₂×C₃×D₄	—	5	4	no	—
223	C₂×C₃×D₄	—	5	1	no	—
224	C₂²×C₃×C₄	—	5	1	no	—
225	C₂²×C₃×C₄	—	5	2	no	—
226	C₂²×C₃×C₄	—	5	2	no	—
227	C₂²×C₃×C₄	—	5	2	no	—
228	C₂²×C₃×C₄	—	10	2	no	—
229	C₂²×C₃×C₄	—	10	2	no	—
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₃×M₁₆	—	2	2	no	—
232	C₃×M₁₆	—	10	2	no	—
233	C₃×M₁₆	—	10	4	no	—
234	C₂×C₃×C₈	—	5	2	no	—
235	C₂×C₃×C₈	—	5	2	no	—
236	C₂×C₃×C₈	—	10	2	no	—
237	C₂×C₃×C₈	—	10	4	no	—
238	C₂×C₃×C₈	—	10	4	no	—
239	C₂×C₃×C₈	—	10	4	no	—
240	C₂×C₃×C₈	D₂₀	1	4	yes	complemented
241	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
242	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
244	C₃×C₄⋊C₄	—	5	4	no	—
245	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
246	C₃×C₂²⋊C₄	—	5	4	no	—
247	C₃×C₂²⋊C₄	—	5	4	no	—
248	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
249	C₃×C₄²	C₂²×D₅	1	2	yes	—
250	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	2	4	no	—
253	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
254	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
255	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
256	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₃×#41	1	2	yes	—
259	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
260	C₂²⋊D₅	—	2	4	no	—
261	C₂×Dic₅	—	2	2	no	—
262	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
264	D₂₀	—	2	8	no	—
265	D₂₀	—	2	2	no	—
266	C₄×D₅	—	2	4	no	—
267	C₄×D₅	—	2	2	no	—
268	C₄×D₅	—	2	2	no	—
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	—	2	2	no	—
271	Dic₁₀	—	2	2	no	—
272	C₅×C₈	—	2	2	no	—
273	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
274	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
275	#168	—	2	2	no	—
276	#168	—	2	2	no	—
277	C₂×#41	—	5	1	no	—
278	C₂³×C₄	—	5	1	no	—
279	#131	—	10	4	no	—
280	C₂×M₁₆	—	5	1	no	—
281	C₂×M₁₆	—	5	2	no	—
282	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	2	no	—
285	C₂²×C₈	—	5	2	no	—
286	C₂²×C₈	—	5	2	no	—
287	C₂²×C₈	—	10	4	no	—
288	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
289	#123	—	5	2	no	—
290	C₂²⋊Q₈	—	5	2	no	—
291	#121	—	5	2	no	—
292	#120	—	5	2	no	—
293	C₄×D₄	—	5	4	no	—
294	#117	C₂×C₃×D₅	1	1	yes	characteristic
295	C₄⋊C₈	—	5	4	no	—
296	C₂²⋊C₈	—	5	4	no	—
297	C₂²⋊C₈	—	5	4	no	—
298	#97	C₂×C₃×D₅	1	2	yes	complemented
299	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	2	yes	—
303	C₃×D₅	—	2	4	no	—
304	C₃×D₅	—	4	2	no	—
305	C₂³×C₃	—	5	2	no	—
306	C₂³×C₃	—	5	2	no	—
307	C₂³×C₃	—	10	4	no	—
308	C₂³×C₃	—	10	2	no	—
309	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
310	C₃×Q₈	—	10	2	no	—
311	C₃×D₄	—	10	8	no	—
312	C₃×D₄	—	10	4	no	—
313	C₃×D₄	—	10	2	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	5	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	2	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	10	4	no	—
322	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
325	C₂×C₃×C₄	#709	1	2	yes	—
326	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
327	C₃×C₈	—	2	2	no	—
328	C₃×C₈	—	10	2	no	—
329	C₃×C₈	—	10	2	no	—
330	C₃×C₈	C₂×D₂₀	1	2	yes	—
331	C₃×C₈	C₂×D₂₀	1	2	yes	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
334	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
335	C₂×D₅	—	2	8	no	—
336	C₂×D₅	—	2	2	no	—
337	C₂×D₅	—	2	2	no	—
338	C₂×D₅	—	2	4	no	—
339	C₂×D₅	—	2	2	no	—
340	C₂×D₅	C₃×#131	1	4	yes	complemented
341	C₄×C₅	—	2	4	no	—
342	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
343	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
345	Dic₅	—	2	2	no	—
346	Dic₅	—	2	2	no	—
347	C₂⁴	—	5	1	no	—
348	#41	—	10	2	no	—
349	#41	—	10	2	no	—
350	C₂×Q₈	—	5	1	no	—
351	C₂×D₄	—	5	2	no	—
352	C₂×D₄	—	5	4	no	—
353	C₂×D₄	—	5	1	no	—
354	C₂²×C₄	—	5	1	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	—	5	2	no	—
357	C₂²×C₄	—	5	2	no	—
358	C₂²×C₄	—	10	2	no	—
359	C₂²×C₄	—	10	2	no	—
360	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	10	2	no	—
363	M₁₆	—	10	4	no	—
364	C₂×C₈	—	5	2	no	—
365	C₂×C₈	—	5	2	no	—
366	C₂×C₈	—	10	2	no	—
367	C₂×C₈	—	10	4	no	—
368	C₂×C₈	—	10	4	no	—
369	C₂×C₈	—	10	4	no	—
370	C₂×C₈	C₃×D₂₀	1	4	yes	complemented
371	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
372	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₄⋊C₄	—	5	4	no	—
375	C₄⋊C₄	C₃×C₄×D₅	1	2	yes	—
376	C₂²⋊C₄	—	5	4	no	—
377	C₂²⋊C₄	—	5	4	no	—
378	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
379	C₄²	C₂²×C₃×D₅	1	2	yes	—
380	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	5	4	no	—
383	C₂²×C₃	—	10	8	no	—
384	C₂²×C₃	—	10	2	no	—
385	C₂²×C₃	—	10	2	no	—
386	C₂²×C₃	—	10	2	no	—
387	C₂²×C₃	—	10	4	no	—
388	C₂²×C₃	C₄×D₂₀	1	2	yes	—
389	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	10	2	no	—
392	C₃×C₄	—	10	2	no	—
393	C₃×C₄	C₄×D₂₀	1	2	yes	—
394	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
395	C₃×C₄	C₂×#709	1	1	yes	characteristic
396	C₂×C₅	—	2	2	no	—
397	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
398	C₂×C₅	C₂×C₃×#131	1	2	yes	—
399	D₅	—	2	4	no	—
400	D₅	—	4	2	no	—
401	C₂³	—	5	2	no	—
402	C₂³	—	5	2	no	—
403	C₂³	—	10	4	no	—
404	C₂³	—	10	2	no	—
405	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
406	Q₈	—	10	2	no	—
407	D₄	—	10	8	no	—
408	D₄	—	10	4	no	—
409	D₄	—	10	2	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	10	2	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	4	no	—
418	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
419	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
420	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
421	C₂×C₄	C₃×#709	1	2	yes	—
422	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	10	2	no	—
425	C₈	—	10	2	no	—
426	C₈	C₂×C₃×D₂₀	1	2	yes	—
427	C₈	C₂×C₃×D₂₀	1	2	yes	—
428	C₂×C₃	—	2	2	no	—
429	C₂×C₃	—	10	4	no	—
430	C₂×C₃	—	20	2	no	—
431	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
432	C₂×C₃	D₅×#131	1	2	yes	—
433	C₅	C₃×#2929	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	2	no	—
435	C₂²	—	5	4	no	—
436	C₂²	—	10	8	no	—
437	C₂²	—	10	2	no	—
438	C₂²	—	10	2	no	—
439	C₂²	—	10	2	no	—
440	C₂²	—	10	4	no	—
441	C₂²	C₃×C₄×D₂₀	1	2	yes	—
442	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
443	C₄	—	2	4	no	—
444	C₄	—	10	2	no	—
445	C₄	—	10	2	no	—
446	C₄	C₃×C₄×D₂₀	1	2	yes	—
447	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
448	C₄	C₂×C₃×#709	1	1	yes	characteristic
449	C₃	#10610284	1	1	yes	characteristic, direct product factor, Sylow
450	C₂	—	2	2	no	—
451	C₂	—	10	4	no	—
452	C₂	—	20	2	no	—
453	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
454	C₂	C₃×D₅×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65858	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2929
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4047	C₂	semidirect
2. C₂²×C₃×C₈×D₅	C₂	semidirect
4. C₃×C₅×#405	C₂	semidirect
5. C₃×#65418	C₂	semidirect
6. C₃×#65415	C₂	semidirect
7. C₃×#65288	C₂	semidirect
8. C₃×#64995	C₂	semidirect
9. C₃×C₈×D₂₀	C₂	semidirect
10. #10610284	C₃	direct (N × H)
19. C₂×C₃×#676	C₂²	semidirect
23. C₂×C₃×C₈×D₅	C₂²	semidirect
29. C₃×C₅×#97	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
32. C₃×#3952	C₂²	semidirect
33. C₃×C₄⋊#168	C₂²	semidirect
35. C₂×#4047	C₂×C₃	semidirect
36. C₂²×C₈×D₅	C₂×C₃	semidirect
38. C₅×#405	C₂×C₃	semidirect
39. #65418	C₂×C₃	semidirect
40. #65415	C₂×C₃	semidirect
41. #65288	C₂×C₃	semidirect
42. #64995	C₂×C₃	semidirect
43. C₈×D₂₀	C₂×C₃	semidirect
59. C₂×C₃×C₅×C₈	D₄	semidirect
85. C₃×#405	D₅	semidirect
94. C₂×#676	C₂²×C₃	semidirect
98. C₂×C₈×D₅	C₂²×C₃	semidirect
104. C₅×#97	C₂²×C₃	semidirect
105. C₄×C₅×C₈	C₂²×C₃	semidirect
107. #3952	C₂²×C₃	semidirect
108. C₄⋊#168	C₂²×C₃	semidirect
158. C₃×#97	C₂×D₅	semidirect
159. C₃×C₄×C₈	C₂×D₅	semidirect
175. C₂×C₅×C₈	C₃×D₄	semidirect
201. #405	C₃×D₅	semidirect
210. C₂×C₃×D₅	#131	semidirect
240. C₂×C₃×C₈	D₂₀	semidirect
298. #97	C₂×C₃×D₅	semidirect
299. C₄×C₈	C₂×C₃×D₅	semidirect
340. C₂×D₅	C₃×#131	semidirect
370. C₂×C₈	C₃×D₂₀	semidirect
380. C₃×C₅	#2929	semidirect
433. C₅	C₃×#2929	semidirect
449. C₃	#10610284	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×#4047	2
C₂²×C₃×C₈×D₅	2
C₃×#65858	2
C₃×C₅×#405	2
C₃×#65418	2
C₃×#65415	2
C₃×#65288	2
C₃×#64995	2
C₃×C₈×D₂₀	2
#10610284	3
C₃×#2929	5

Subgroups — C3×#10610284 #14414921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610284 #14414921