Subgroups — C₃×#10610388 #14415221

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66166	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65018	C₂	1	4	yes	maximal, complemented
9	C₃×#65014	C₂	1	4	yes	maximal, complemented
10	#10610388	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	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×#4094	—	2	4	no	—
16	C₃×#4093	C₄	1	1	yes	characteristic
17	C₃×#4090	C₄	1	1	yes	characteristic
18	C₃×#4086	C₄	1	1	yes	characteristic
19	C₃×#4085	C₄	1	4	yes	—
20	C₃×#4082	C₄	1	1	yes	characteristic
21	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₂×C₃×#681	C₂²	1	2	yes	—
25	C₂²×C₃×#168	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
27	C₃×#4053	—	2	4	no	—
28	C₂×C₃×#676	C₂²	1	2	yes	—
29	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
30	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₃×#3952	C₂²	1	4	yes	—
32	C₃×#3946	C₂²	1	4	yes	—
33	C₃×C₈×Dic₅	C₂²	1	2	yes	—
34	C₃×C₈×Dic₅	C₂²	1	2	yes	—
35	C₃×#2931	—	5	1	no	maximal, Hall
36	#66166	C₂×C₃	1	1	yes	characteristic
37	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
40	#65407	C₂×C₃	1	1	yes	characteristic, complemented
41	#65399	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
43	#65018	C₂×C₃	1	4	yes	complemented
44	#65014	C₂×C₃	1	4	yes	complemented
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
54	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
55	C₃×#709	—	2	2	no	—
56	C₃×#709	—	2	2	no	—
57	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
59	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×M₁₆	—	2	2	no	—
61	C₂×C₃×C₅×C₈	—	2	2	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
65	C₃×#685	C₂×C₄	1	4	yes	—
66	C₃×#683	C₂×C₄	1	4	yes	—
67	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
68	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄×Dic₅	C₂³	1	2	yes	—
70	C₃×#681	—	2	2	no	—
71	C₃×#681	—	2	4	no	—
72	C₂×C₃×#168	—	2	4	no	—
73	C₂×C₃×#168	D₄	1	4	yes	complemented
74	C₂×C₃×#168	C₂³	1	2	yes	—
75	C₂×C₃×#168	C₂³	1	1	yes	characteristic
76	C₂×C₃×#168	C₂³	1	1	yes	characteristic
77	C₃×#676	—	2	4	no	—
78	C₃×C₈×D₅	—	2	4	no	—
79	C₂×C₃×#131	—	5	1	no	—
80	C₂×C₃×#131	—	5	1	no	—
81	C₃×#532	—	5	1	no	—
82	C₃×#436	—	5	4	no	—
83	C₃×C₈×D₄	—	5	4	no	—
84	C₃×#423	—	5	1	no	—
85	C₃×#408	—	5	1	no	—
86	C₃×#408	D₅	1	1	yes	characteristic, complemented
87	C₂×C₃×C₄×C₈	—	5	1	no	—
88	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
89	C₂×#709	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
92	#4094	—	2	4	no	—
93	#4093	C₃×C₄	1	1	yes	characteristic
94	#4090	C₃×C₄	1	1	yes	characteristic
95	#4086	C₃×C₄	1	1	yes	characteristic
96	#4085	C₃×C₄	1	4	yes	—
97	#4082	C₃×C₄	1	1	yes	characteristic
98	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
99	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×#681	C₂²×C₃	1	1	yes	characteristic
101	C₂×#681	C₂²×C₃	1	2	yes	—
102	C₂²×#168	C₂²×C₃	1	2	yes	—
103	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
104	#4053	—	2	4	no	—
105	C₂×#676	C₂²×C₃	1	2	yes	—
106	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
107	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
108	#3952	C₂²×C₃	1	4	yes	—
109	#3946	C₂²×C₃	1	4	yes	—
110	C₈×Dic₅	C₂²×C₃	1	2	yes	—
111	C₈×Dic₅	C₂²×C₃	1	2	yes	—
112	#2931	—	5	1	no	Sylow
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
116	C₃×C₅×Q₈	—	2	2	no	—
117	C₃×C₅×D₄	—	2	4	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	#41	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₃×C₂²⋊D₅	—	2	4	no	—
127	C₃×C₂²⋊D₅	—	2	8	no	—
128	C₂×C₃×Dic₅	—	2	4	no	—
129	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
132	C₃×D₂₀	—	2	2	no	—
133	C₃×C₄×D₅	—	2	2	no	—
134	C₃×C₄×D₅	—	2	2	no	—
135	C₃×Dic₁₀	—	2	2	no	—
136	C₃×C₅×C₈	—	2	2	no	—
137	C₃×C₅×C₈	—	2	2	no	—
138	C₃×#168	—	2	2	no	—
139	C₃×#168	C₂×D₄	1	2	yes	—
140	C₃×#168	C₂×D₄	1	2	yes	—
141	C₂×C₃×#41	—	5	1	no	—
142	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
143	C₃×#131	—	10	4	no	—
144	C₃×#131	—	10	4	no	—
145	C₂×C₃×M₁₆	—	5	1	no	—
146	C₂×C₃×M₁₆	—	5	2	no	—
147	C₂×C₃×M₁₆	—	5	2	no	—
148	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
149	C₂²×C₃×C₈	—	5	1	no	—
150	C₂²×C₃×C₈	—	5	2	no	—
151	C₂²×C₃×C₈	—	5	2	no	—
152	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
153	C₃×C₄⋊Q₈	—	5	1	no	—
154	C₃×#127	—	5	1	no	—
155	C₃×#124	—	5	1	no	—
156	C₃×#124	—	5	1	no	—
157	C₃×#121	—	5	4	no	—
158	C₃×C₄×D₄	—	5	4	no	—
159	C₂×C₃×C₄²	—	5	1	no	—
160	C₃×C₄⋊C₈	—	5	4	no	—
161	C₃×C₂²⋊C₈	—	5	4	no	—
162	C₃×C₂²⋊C₈	C₂×D₅	1	4	yes	—
163	C₃×C₄×C₈	—	5	2	no	—
164	C₃×C₄×C₈	—	5	2	no	—
165	C₅×#41	—	2	2	no	—
166	C₅×#41	—	2	2	no	—
167	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
170	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
173	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
174	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
175	#709	—	2	2	no	—
176	#709	—	2	2	no	—
177	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
179	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
180	C₅×M₁₆	—	2	2	no	—
181	C₂×C₅×C₈	—	2	2	no	—
182	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
183	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
184	C₂²⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
185	#685	C₂×C₃×C₄	1	4	yes	—
186	#683	C₂×C₃×C₄	1	4	yes	—
187	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
189	C₄×Dic₅	C₂³×C₃	1	2	yes	—
190	#681	—	2	2	no	—
191	#681	—	2	4	no	—
192	C₂×#168	—	2	4	no	—
193	C₂×#168	C₃×D₄	1	4	yes	complemented
194	C₂×#168	C₂³×C₃	1	2	yes	—
195	C₂×#168	C₂³×C₃	1	1	yes	characteristic
196	C₂×#168	C₂³×C₃	1	1	yes	characteristic
197	#676	—	2	4	no	—
198	C₈×D₅	—	2	4	no	—
199	C₂×#131	—	5	1	no	—
200	C₂×#131	—	5	1	no	—
201	#532	—	5	1	no	—
202	#436	—	5	4	no	—
203	C₈×D₄	—	5	4	no	—
204	#423	—	5	1	no	—
205	#408	—	5	1	no	—
206	#408	C₃×D₅	1	1	yes	characteristic, complemented
207	C₂×C₄×C₈	—	5	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
212	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₃×D₅	—	2	2	no	—
214	C₂×C₃×D₅	—	2	4	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
217	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₃×Dic₅	—	2	2	no	—
220	C₃×Dic₅	—	2	2	no	—
221	C₃×Dic₅	#131	1	4	yes	complemented
222	C₃×#41	—	2	2	no	—
223	C₃×#41	—	2	2	no	—
224	C₃×#41	—	10	2	no	—
225	C₃×#41	—	10	2	no	—
226	C₂×C₃×Q₈	—	5	1	no	—
227	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
228	C₂×C₃×D₄	—	5	4	no	—
229	C₂×C₃×D₄	—	5	2	no	—
230	C₂×C₃×D₄	—	5	1	no	—
231	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
232	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
236	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
237	C₃×M₁₆	—	2	2	no	—
238	C₃×M₁₆	—	10	4	no	—
239	C₃×M₁₆	—	10	4	no	—
240	C₃×M₁₆	—	10	2	no	—
241	C₂×C₃×C₈	—	2	2	no	—
242	C₂×C₃×C₈	—	5	4	no	—
243	C₂×C₃×C₈	—	5	1	no	—
244	C₂×C₃×C₈	—	5	1	no	—
245	C₂×C₃×C₈	—	5	2	no	—
246	C₂×C₃×C₈	—	10	4	no	—
247	C₂×C₃×C₈	—	10	4	no	—
248	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
249	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
250	C₃×C₄⋊C₄	—	5	4	no	—
251	C₃×C₂²⋊C₄	—	5	4	no	—
252	C₃×C₂²⋊C₄	—	5	4	no	—
253	C₃×C₄²	—	5	1	no	—
254	C₃×C₄²	—	5	1	no	—
255	C₃×C₄²	—	5	2	no	—
256	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
257	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
259	C₅×Q₈	—	2	2	no	—
260	C₅×D₄	—	2	4	no	—
261	C₅×D₄	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₃×#41	1	2	yes	—
268	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
269	C₂²⋊D₅	—	2	4	no	—
270	C₂²⋊D₅	—	2	8	no	—
271	C₂×Dic₅	—	2	4	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	—	2	2	no	—
276	C₄×D₅	—	2	2	no	—
277	C₄×D₅	—	2	2	no	—
278	Dic₁₀	—	2	2	no	—
279	C₅×C₈	—	2	2	no	—
280	C₅×C₈	—	2	2	no	—
281	#168	—	2	2	no	—
282	#168	C₂×C₃×D₄	1	2	yes	—
283	#168	C₂×C₃×D₄	1	2	yes	—
284	C₂×#41	—	5	1	no	—
285	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
286	#131	—	10	4	no	—
287	#131	—	10	4	no	—
288	C₂×M₁₆	—	5	1	no	—
289	C₂×M₁₆	—	5	2	no	—
290	C₂×M₁₆	—	5	2	no	—
291	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
292	C₂²×C₈	—	5	1	no	—
293	C₂²×C₈	—	5	2	no	—
294	C₂²×C₈	—	5	2	no	—
295	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
296	C₄⋊Q₈	—	5	1	no	—
297	#127	—	5	1	no	—
298	#124	—	5	1	no	—
299	#124	—	5	1	no	—
300	#121	—	5	4	no	—
301	C₄×D₄	—	5	4	no	—
302	C₂×C₄²	—	5	1	no	—
303	C₄⋊C₈	—	5	4	no	—
304	C₂²⋊C₈	—	5	4	no	—
305	C₂²⋊C₈	C₂×C₃×D₅	1	4	yes	—
306	C₄×C₈	—	5	2	no	—
307	C₄×C₈	—	5	2	no	—
308	C₂×C₃×C₅	—	2	2	no	—
309	C₂×C₃×C₅	—	4	2	no	—
310	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×#131	1	2	yes	—
312	C₃×D₅	—	4	2	no	—
313	C₂³×C₃	—	5	2	no	—
314	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
315	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	10	2	no	—
318	C₃×D₄	—	2	4	no	—
319	C₃×D₄	—	2	2	no	—
320	C₃×D₄	—	10	8	no	—
321	C₃×D₄	—	10	4	no	—
322	C₃×D₄	—	10	2	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	5	2	no	—
326	C₂×C₃×C₄	—	5	2	no	—
327	C₂×C₃×C₄	—	5	2	no	—
328	C₂×C₃×C₄	—	10	4	no	—
329	C₂×C₃×C₄	—	10	2	no	—
330	C₂×C₃×C₄	—	10	2	no	—
331	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
334	C₂×C₃×C₄	#711	1	2	yes	—
335	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
336	C₃×C₈	—	2	2	no	—
337	C₃×C₈	—	2	2	no	—
338	C₃×C₈	—	5	2	no	—
339	C₃×C₈	—	5	2	no	—
340	C₃×C₈	—	10	2	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	4	no	—
343	C₂²×C₅	—	2	2	no	—
344	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
345	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
346	C₂×D₅	—	2	4	no	—
347	C₂×D₅	—	2	2	no	—
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
350	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
352	Dic₅	—	2	2	no	—
353	Dic₅	—	2	2	no	—
354	Dic₅	C₃×#131	1	4	yes	complemented
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	10	2	no	—
358	#41	—	10	2	no	—
359	C₂×Q₈	—	5	1	no	—
360	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
361	C₂×D₄	—	5	4	no	—
362	C₂×D₄	—	5	2	no	—
363	C₂×D₄	—	5	1	no	—
364	C₂×D₄	C₃×C₄×D₅	1	2	yes	—
365	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
366	C₂²×C₄	—	5	2	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
369	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
370	M₁₆	—	2	2	no	—
371	M₁₆	—	10	4	no	—
372	M₁₆	—	10	4	no	—
373	M₁₆	—	10	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	5	4	no	—
376	C₂×C₈	—	5	1	no	—
377	C₂×C₈	—	5	1	no	—
378	C₂×C₈	—	5	2	no	—
379	C₂×C₈	—	10	4	no	—
380	C₂×C₈	—	10	4	no	—
381	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
382	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
383	C₄⋊C₄	—	5	4	no	—
384	C₂²⋊C₄	—	5	4	no	—
385	C₂²⋊C₄	—	5	4	no	—
386	C₄²	—	5	1	no	—
387	C₄²	—	5	1	no	—
388	C₄²	—	5	2	no	—
389	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	10	2	no	—
394	C₂²×C₃	—	10	4	no	—
395	C₂²×C₃	#4027	1	2	yes	—
396	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	5	4	no	—
399	C₃×C₄	—	10	2	no	—
400	C₃×C₄	—	10	2	no	—
401	C₃×C₄	#4027	1	2	yes	—
402	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
403	C₃×C₄	C₂×#711	1	1	yes	characteristic
404	C₂×C₅	—	2	2	no	—
405	C₂×C₅	—	4	2	no	—
406	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
407	C₂×C₅	C₂×C₃×#131	1	2	yes	—
408	D₅	—	4	2	no	—
409	C₂³	—	5	2	no	—
410	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
411	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	10	2	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	2	no	—
416	D₄	—	10	8	no	—
417	D₄	—	10	4	no	—
418	D₄	—	10	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	10	4	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	10	2	no	—
427	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
428	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
429	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
430	C₂×C₄	C₃×#711	1	2	yes	—
431	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	5	2	no	—
435	C₈	—	5	2	no	—
436	C₈	—	10	2	no	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	4	2	no	—
439	C₂×C₃	—	20	2	no	—
440	C₂×C₃	C₂×#4027	1	1	yes	characteristic
441	C₂×C₃	D₅×#131	1	2	yes	—
442	C₅	C₃×#2931	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	10	2	no	—
447	C₂²	—	10	4	no	—
448	C₂²	C₃×#4027	1	2	yes	—
449	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	5	4	no	—
452	C₄	—	10	2	no	—
453	C₄	—	10	2	no	—
454	C₄	C₃×#4027	1	2	yes	—
455	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
456	C₄	C₂×C₃×#711	1	1	yes	characteristic
457	C₃	#10610388	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	2	2	no	—
459	C₂	—	4	2	no	—
460	C₂	—	20	2	no	—
461	C₂	C₂×C₃×#4027	1	1	yes	characteristic
462	C₂	C₃×D₅×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#408	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#66166	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#408	D₅
hypocenter	C₅	C₃×#2931
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₂×C₃×#4053	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₃×#65407	C₂	semidirect
6. C₃×#65399	C₂	semidirect
7. C₂×C₃×C₈×Dic₅	C₂	semidirect
8. C₃×#65018	C₂	semidirect
9. C₃×#65014	C₂	semidirect
10. #10610388	C₃	direct (N × H)
37. C₂×#4094	C₂×C₃	semidirect
38. C₂×#4053	C₂×C₃	semidirect
39. C₅×#408	C₂×C₃	semidirect
40. #65407	C₂×C₃	semidirect
41. #65399	C₂×C₃	semidirect
42. C₂×C₈×Dic₅	C₂×C₃	semidirect
43. #65018	C₂×C₃	semidirect
44. #65014	C₂×C₃	semidirect
73. C₂×C₃×#168	D₄	semidirect
86. C₃×#408	D₅	semidirect
193. C₂×#168	C₃×D₄	semidirect
206. #408	C₃×D₅	semidirect
221. C₃×Dic₅	#131	semidirect
354. Dic₅	C₃×#131	semidirect
389. C₃×C₅	#2931	semidirect
442. C₅	C₃×#2931	semidirect
457. C₃	#10610388	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#66166	2
C₂×C₃×#4094	2
C₂×C₃×#4053	2
C₃×C₅×#408	2
C₃×#65407	2
C₃×#65399	2
C₂×C₃×C₈×Dic₅	2
C₃×#65018	2
C₃×#65014	2
#10610388	3
C₃×#2931	5

Subgroups — C3×#10610388 #14415221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610388 #14415221