Subgroups — C₅×D₃×#407 #14411621

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5126	C₂	1	2	yes	maximal, complemented
6	C₅×#4726	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#407	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₄	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	8	no	—
13	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
17	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
18	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
22	C₂×C₅×#208	C₂²	1	2	yes	complemented
23	C₅×D₃×M₁₆	—	2	8	no	—
24	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
25	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
26	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
27	C₅×#830	C₂²	1	4	yes	complemented
28	C₅×(C₂×D₃)⋊C₈	C₂²	1	8	yes	complemented
29	D₃×#407	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂⁴×C₄×C₅	—	3	1	no	—
31	C₂²×C₅×M₁₆	—	3	2	no	—
32	C₅×#407	—	3	4	no	—
33	C₅×#407	—	3	1	no	—
34	C₅×#407	—	3	2	no	—
35	C₅×#407	D₃	1	1	yes	characteristic, direct product factor
36	C₂×C₅×C₂²⋊C₈	—	3	4	no	—
37	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₅×D₃	—	2	4	no	—
39	C₂³×C₅×D₃	—	2	8	no	—
40	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	4	no	—
45	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	—	2	4	no	—
50	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
52	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
53	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×C₅×D₃	—	2	4	no	—
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₂×C₄×C₅×D₃	—	2	4	no	—
57	C₂×C₄×C₅×D₃	—	2	8	no	—
58	C₂×C₄×C₅×D₃	—	2	8	no	—
59	C₂×C₄×C₅×D₃	—	2	8	no	—
60	C₂×C₄×C₅×D₃	—	2	8	no	—
61	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
63	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
65	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
69	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
70	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₃×C₅×M₁₆	—	2	4	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	4	yes	complemented
74	C₅×#208	—	2	4	no	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	complemented
76	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
77	C₅×D₃×C₈	—	2	8	no	—
78	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
79	C₂×D₃×M₁₆	C₂×C₅	1	2	yes	complemented
80	C₃×#407	C₂×C₅	1	1	yes	characteristic, complemented
81	#5207	C₂×C₅	1	1	yes	characteristic, complemented
82	#5126	C₂×C₅	1	2	yes	complemented
83	#4726	C₂×C₅	1	4	yes	complemented
84	D₃×C₂²⋊C₈	C₂×C₅	1	4	yes	complemented
85	C₂⁵×C₅	—	3	1	no	—
86	C₂³×C₄×C₅	—	3	1	no	—
87	C₂³×C₄×C₅	—	3	1	no	—
88	C₂³×C₄×C₅	—	3	1	no	—
89	C₂³×C₄×C₅	—	3	2	no	—
90	C₂³×C₄×C₅	—	3	2	no	—
91	C₂³×C₄×C₅	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	2	no	—
93	C₂³×C₄×C₅	—	3	2	no	—
94	C₂³×C₄×C₅	—	3	1	no	—
95	C₂³×C₄×C₅	—	6	8	no	—
96	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
97	C₂×C₅×M₁₆	—	3	2	no	—
98	C₂×C₅×M₁₆	—	3	4	no	—
99	C₂×C₅×M₁₆	—	6	8	no	—
100	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
101	C₂²×C₅×C₈	—	3	4	no	—
102	C₅×C₂²⋊C₈	—	3	4	no	—
103	C₅×C₂²⋊C₈	—	3	8	no	—
104	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	complemented
105	C₂×#407	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	4	no	—
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
110	C₂²×C₅×D₃	—	2	32	no	—
111	C₂²×C₅×D₃	—	2	2	no	—
112	C₂²×C₅×D₃	—	2	4	no	—
113	C₂²×C₅×D₃	—	2	4	no	—
114	C₂²×C₅×D₃	—	2	4	no	—
115	C₂²×C₅×D₃	—	2	4	no	—
116	C₂²×C₅×D₃	—	2	4	no	—
117	C₂²×C₅×D₃	—	2	4	no	—
118	C₂²×C₅×D₃	—	2	4	no	—
119	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
120	C₂²×C₅×D₃	M₁₆	1	8	yes	complemented
121	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	4	no	—
126	C₂×C₃×C₄×C₅	—	2	4	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	—	2	4	no	—
133	C₂×C₅×Dic₃	—	2	4	no	—
134	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
135	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
136	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×C₅×D₃	—	2	4	no	—
139	C₄×C₅×D₃	—	2	4	no	—
140	C₄×C₅×D₃	—	2	4	no	—
141	C₄×C₅×D₃	—	2	4	no	—
142	C₄×C₅×D₃	—	2	4	no	—
143	C₄×C₅×D₃	—	2	4	no	—
144	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
145	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
146	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
147	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
148	C₃×C₅×C₈	—	2	4	no	—
149	C₅×C₃⋊C₈	—	2	4	no	—
150	C₂⁴×D₃	C₄×C₅	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂³×Dic₃	C₄×C₅	1	1	yes	characteristic
153	C₂²×C₄×D₃	—	2	8	no	—
154	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
155	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
156	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
157	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
158	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
159	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
160	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
161	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
163	C₂×#208	C₂²×C₅	1	2	yes	complemented
164	D₃×M₁₆	—	2	8	no	—
165	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	complemented
166	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
167	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
168	#830	C₂²×C₅	1	4	yes	complemented
169	(C₂×D₃)⋊C₈	C₂²×C₅	1	8	yes	complemented
170	C₂⁴×C₅	—	3	1	no	—
171	C₂⁴×C₅	—	3	2	no	—
172	C₂⁴×C₅	—	3	2	no	—
173	C₂⁴×C₅	—	3	1	no	—
174	C₂⁴×C₅	—	6	4	no	—
175	C₂⁴×C₅	—	6	8	no	—
176	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	—	2	4	no	—
178	C₂²×C₄×C₅	—	3	1	no	—
179	C₂²×C₄×C₅	—	3	1	no	—
180	C₂²×C₄×C₅	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	8	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	2	no	—
185	C₂²×C₄×C₅	—	3	2	no	—
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	2	no	—
188	C₂²×C₄×C₅	—	3	2	no	—
189	C₂²×C₄×C₅	—	3	2	no	—
190	C₂²×C₄×C₅	—	3	2	no	—
191	C₂²×C₄×C₅	—	3	2	no	—
192	C₂²×C₄×C₅	—	3	2	no	—
193	C₂²×C₄×C₅	—	6	4	no	—
194	C₂²×C₄×C₅	—	6	8	no	—
195	C₂²×C₄×C₅	—	6	8	no	—
196	C₂²×C₄×C₅	—	6	8	no	—
197	C₂²×C₄×C₅	—	6	8	no	—
198	C₂²×C₄×C₅	—	6	4	no	—
199	C₂²×C₄×C₅	—	6	4	no	—
200	C₂²×C₄×C₅	—	6	4	no	—
201	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
203	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
204	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₅×M₁₆	—	2	4	no	—
206	C₅×M₁₆	—	6	8	no	—
207	C₅×M₁₆	—	6	4	no	—
208	C₂×C₅×C₈	—	3	4	no	—
209	C₂×C₅×C₈	—	6	8	no	—
210	C₂×C₅×C₈	C₂²×D₃	1	4	yes	complemented
211	C₂⁴×C₄	—	3	1	no	—
212	C₂²×M₁₆	—	3	2	no	—
213	#407	—	3	1	no	—
214	#407	—	3	2	no	—
215	#407	—	3	4	no	—
216	#407	C₅×D₃	1	1	yes	characteristic, direct product factor
217	C₂×C₂²⋊C₈	—	3	4	no	—
218	C₂²×C₃×C₅	—	2	8	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	—	2	2	no	—
221	C₂²×C₃×C₅	—	2	2	no	—
222	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
224	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₅×D₃	—	2	16	no	—
226	C₂×C₅×D₃	—	2	8	no	—
227	C₂×C₅×D₃	—	2	2	no	—
228	C₂×C₅×D₃	—	2	2	no	—
229	C₂×C₅×D₃	—	2	2	no	—
230	C₂×C₅×D₃	—	2	8	no	—
231	C₂×C₅×D₃	—	2	16	no	—
232	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	—
235	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
238	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
239	C₅×Dic₃	—	2	2	no	—
240	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
241	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂³×D₃	—	2	4	no	—
244	C₂³×D₃	—	2	8	no	—
245	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
246	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
247	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
249	C₂²×C₃×C₄	—	2	4	no	—
250	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
252	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
253	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂²×Dic₃	—	2	4	no	—
255	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
256	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
257	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
258	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
259	C₂×C₄×D₃	—	2	4	no	—
260	C₂×C₄×D₃	—	2	4	no	—
261	C₂×C₄×D₃	—	2	4	no	—
262	C₂×C₄×D₃	—	2	8	no	—
263	C₂×C₄×D₃	—	2	8	no	—
264	C₂×C₄×D₃	—	2	8	no	—
265	C₂×C₄×D₃	—	2	8	no	—
266	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
267	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
268	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
269	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
270	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
271	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
274	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
275	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
277	C₃×M₁₆	—	2	4	no	—
278	C₂×C₃×C₈	C₂³×C₅	1	4	yes	complemented
279	#208	—	2	4	no	—
280	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
281	ΓL(1,𝔽₂₅)	—	2	8	no	—
282	D₃×C₈	—	2	8	no	—
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	2	4	no	—
285	C₂³×C₅	—	3	1	no	—
286	C₂³×C₅	—	3	4	no	—
287	C₂³×C₅	—	3	8	no	—
288	C₂³×C₅	—	3	1	no	—
289	C₂³×C₅	—	3	2	no	—
290	C₂³×C₅	—	6	4	no	—
291	C₂³×C₅	—	6	4	no	—
292	C₂³×C₅	—	6	4	no	—
293	C₂³×C₅	—	6	4	no	—
294	C₂³×C₅	—	6	4	no	—
295	C₂³×C₅	—	6	4	no	—
296	C₂³×C₅	—	6	32	no	—
297	C₂³×C₅	—	6	2	no	—
298	C₂³×C₅	—	6	4	no	—
299	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
300	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	4	no	—
303	C₂×C₄×C₅	—	2	4	no	—
304	C₂×C₄×C₅	—	3	4	no	—
305	C₂×C₄×C₅	—	3	1	no	—
306	C₂×C₄×C₅	—	3	1	no	—
307	C₂×C₄×C₅	—	3	4	no	—
308	C₂×C₄×C₅	—	3	4	no	—
309	C₂×C₄×C₅	—	3	4	no	—
310	C₂×C₄×C₅	—	3	4	no	—
311	C₂×C₄×C₅	—	3	2	no	—
312	C₂×C₄×C₅	—	6	4	no	—
313	C₂×C₄×C₅	—	6	4	no	—
314	C₂×C₄×C₅	—	6	4	no	—
315	C₂×C₄×C₅	—	6	4	no	—
316	C₂×C₄×C₅	—	6	4	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	6	4	no	—
320	C₂×C₄×C₅	—	6	4	no	—
321	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
322	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
323	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
324	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×C₈	—	2	4	no	—
326	C₅×C₈	—	6	4	no	—
327	C₂⁵	—	3	1	no	—
328	C₂³×C₄	—	3	1	no	—
329	C₂³×C₄	—	3	1	no	—
330	C₂³×C₄	—	3	1	no	—
331	C₂³×C₄	—	3	2	no	—
332	C₂³×C₄	—	3	2	no	—
333	C₂³×C₄	—	3	1	no	—
334	C₂³×C₄	—	3	2	no	—
335	C₂³×C₄	—	3	2	no	—
336	C₂³×C₄	—	3	1	no	—
337	C₂³×C₄	—	6	8	no	—
338	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
339	C₂×M₁₆	—	3	2	no	—
340	C₂×M₁₆	—	3	4	no	—
341	C₂×M₁₆	—	6	8	no	—
342	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
343	C₂²×C₈	—	3	4	no	—
344	C₂²⋊C₈	—	3	4	no	—
345	C₂²⋊C₈	—	3	8	no	—
346	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
347	C₂×C₃×C₅	—	2	2	no	—
348	C₂×C₃×C₅	—	2	4	no	—
349	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
350	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
351	C₅×D₃	—	2	2	no	—
352	C₅×D₃	—	2	4	no	—
353	C₅×D₃	#407	1	4	yes	direct product factor
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	2	4	no	—
356	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
357	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
358	C₂²×D₃	—	2	32	no	—
359	C₂²×D₃	—	2	2	no	—
360	C₂²×D₃	—	2	4	no	—
361	C₂²×D₃	—	2	4	no	—
362	C₂²×D₃	—	2	4	no	—
363	C₂²×D₃	—	2	4	no	—
364	C₂²×D₃	—	2	4	no	—
365	C₂²×D₃	—	2	4	no	—
366	C₂²×D₃	—	2	4	no	—
367	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
368	C₂²×D₃	C₅×M₁₆	1	8	yes	complemented
369	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
371	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	—	2	4	no	—
375	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
376	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
378	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
379	C₂×Dic₃	—	2	2	no	—
380	C₂×Dic₃	—	2	4	no	—
381	C₂×Dic₃	—	2	4	no	—
382	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
383	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
384	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
385	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
386	C₄×D₃	—	2	4	no	—
387	C₄×D₃	—	2	4	no	—
388	C₄×D₃	—	2	4	no	—
389	C₄×D₃	—	2	4	no	—
390	C₄×D₃	—	2	4	no	—
391	C₄×D₃	—	2	4	no	—
392	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
393	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
394	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
395	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
396	C₃×C₈	—	2	4	no	—
397	C₃⋊C₈	—	2	4	no	—
398	C₂²×C₅	—	2	8	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	—	3	2	no	—
403	C₂²×C₅	—	3	4	no	—
404	C₂²×C₅	—	3	2	no	—
405	C₂²×C₅	—	3	4	no	—
406	C₂²×C₅	—	6	8	no	—
407	C₂²×C₅	—	6	16	no	—
408	C₂²×C₅	—	6	8	no	—
409	C₂²×C₅	—	6	16	no	—
410	C₂²×C₅	—	6	2	no	—
411	C₂²×C₅	—	6	2	no	—
412	C₂²×C₅	—	6	2	no	—
413	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
414	C₂²×C₅	D₃×M₁₆	1	4	yes	complemented
415	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	3	2	no	—
418	C₄×C₅	—	3	2	no	—
419	C₄×C₅	—	6	2	no	—
420	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
421	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
422	C₂⁴	—	3	1	no	—
423	C₂⁴	—	3	2	no	—
424	C₂⁴	—	3	2	no	—
425	C₂⁴	—	3	1	no	—
426	C₂⁴	—	6	4	no	—
427	C₂⁴	—	6	8	no	—
428	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	8	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	6	4	no	—
446	C₂²×C₄	—	6	8	no	—
447	C₂²×C₄	—	6	8	no	—
448	C₂²×C₄	—	6	8	no	—
449	C₂²×C₄	—	6	8	no	—
450	C₂²×C₄	—	6	4	no	—
451	C₂²×C₄	—	6	4	no	—
452	C₂²×C₄	—	6	4	no	—
453	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
454	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
455	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
456	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
457	M₁₆	—	2	4	no	—
458	M₁₆	—	6	8	no	—
459	M₁₆	—	6	4	no	—
460	C₂×C₈	—	3	4	no	—
461	C₂×C₈	—	6	8	no	—
462	C₂×C₈	C₂²×C₅×D₃	1	4	yes	complemented
463	C₃×C₅	C₂×#407	1	1	yes	characteristic, complemented, Hall
464	C₂²×C₃	—	2	8	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
469	C₂²×C₃	C₂×C₅×M₁₆	1	4	yes	complemented
470	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
471	C₂×D₃	—	2	16	no	—
472	C₂×D₃	—	2	8	no	—
473	C₂×D₃	—	2	2	no	—
474	C₂×D₃	—	2	2	no	—
475	C₂×D₃	—	2	2	no	—
476	C₂×D₃	—	2	8	no	—
477	C₂×D₃	—	2	16	no	—
478	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
479	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
480	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	—
481	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	complemented
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
484	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
485	Dic₃	—	2	2	no	—
486	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
487	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
488	C₂×C₅	—	2	2	no	—
489	C₂×C₅	—	2	4	no	—
490	C₂×C₅	—	3	4	no	—
491	C₂×C₅	—	6	2	no	—
492	C₂×C₅	—	6	4	no	—
493	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
494	C₂×C₅	C₂×D₃×M₁₆	1	2	yes	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	3	1	no	—
498	C₂³	—	3	4	no	—
499	C₂³	—	3	8	no	—
500	C₂³	—	3	1	no	—
501	C₂³	—	3	2	no	—
502	C₂³	—	6	4	no	—
503	C₂³	—	6	4	no	—
504	C₂³	—	6	4	no	—
505	C₂³	—	6	4	no	—
506	C₂³	—	6	4	no	—
507	C₂³	—	6	4	no	—
508	C₂³	—	6	32	no	—
509	C₂³	—	6	2	no	—
510	C₂³	—	6	4	no	—
511	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
512	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	3	4	no	—
517	C₂×C₄	—	3	1	no	—
518	C₂×C₄	—	3	1	no	—
519	C₂×C₄	—	3	4	no	—
520	C₂×C₄	—	3	4	no	—
521	C₂×C₄	—	3	4	no	—
522	C₂×C₄	—	3	4	no	—
523	C₂×C₄	—	3	2	no	—
524	C₂×C₄	—	6	4	no	—
525	C₂×C₄	—	6	4	no	—
526	C₂×C₄	—	6	4	no	—
527	C₂×C₄	—	6	4	no	—
528	C₂×C₄	—	6	4	no	—
529	C₂×C₄	—	6	4	no	—
530	C₂×C₄	—	6	2	no	—
531	C₂×C₄	—	6	4	no	—
532	C₂×C₄	—	6	4	no	—
533	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
534	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
535	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
536	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
537	C₈	—	2	4	no	—
538	C₈	—	6	4	no	—
539	C₂×C₃	—	2	2	no	—
540	C₂×C₃	—	2	4	no	—
541	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
542	C₂×C₃	C₂²×C₅×M₁₆	1	2	yes	—
543	D₃	—	2	2	no	—
544	D₃	—	2	4	no	—
545	D₃	C₅×#407	1	4	yes	direct product factor
546	C₅	D₃×#407	1	1	yes	characteristic, direct product factor, Sylow
547	C₂²	—	2	8	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	3	2	no	—
552	C₂²	—	3	4	no	—
553	C₂²	—	3	2	no	—
554	C₂²	—	3	4	no	—
555	C₂²	—	6	8	no	—
556	C₂²	—	6	16	no	—
557	C₂²	—	6	8	no	—
558	C₂²	—	6	16	no	—
559	C₂²	—	6	2	no	—
560	C₂²	—	6	2	no	—
561	C₂²	—	6	2	no	—
562	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
563	C₂²	C₅×D₃×M₁₆	1	4	yes	complemented
564	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	3	2	no	—
567	C₄	—	3	2	no	—
568	C₄	—	6	2	no	—
569	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
570	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
571	C₃	C₂×C₅×#407	1	1	yes	characteristic, complemented, Sylow
572	C₂	—	2	2	no	—
573	C₂	—	2	4	no	—
574	C₂	—	3	4	no	—
575	C₂	—	6	2	no	—
576	C₂	—	6	4	no	—
577	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
578	C₂	C₂×C₅×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#407	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂⁴×C₅×D₃	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#407	D₃
hypocenter	C₃	C₂×C₅×#407
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#407

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₃×C₅×#407	C₂	semidirect
4. C₅×#5207	C₂	semidirect
5. C₅×#5126	C₂	semidirect
6. C₅×#4726	C₂	semidirect
7. C₅×D₃×C₂²⋊C₈	C₂	semidirect
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
22. C₂×C₅×#208	C₂²	semidirect
24. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
25. C₂×C₅×D₃×C₈	C₂²	semidirect
26. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
27. C₅×#830	C₂²	semidirect
28. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
29. D₃×#407	C₅	direct (N × H)
35. C₅×#407	D₃	direct (N × H)
73. C₂×C₃×C₅×C₈	C₂³	semidirect
75. C₂×C₅×C₃⋊C₈	C₂³	semidirect
79. C₂×D₃×M₁₆	C₂×C₅	semidirect
80. C₃×#407	C₂×C₅	semidirect
81. #5207	C₂×C₅	semidirect
82. #5126	C₂×C₅	semidirect
83. #4726	C₂×C₅	semidirect
84. D₃×C₂²⋊C₈	C₂×C₅	semidirect
100. C₂×C₅×M₁₆	C₂×D₃	semidirect
104. C₅×C₂²⋊C₈	C₂×D₃	semidirect
120. C₂²×C₅×D₃	M₁₆	semidirect
162. C₂×C₃×M₁₆	C₂²×C₅	semidirect
163. C₂×#208	C₂²×C₅	semidirect
165. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
166. C₂×D₃×C₈	C₂²×C₅	semidirect
167. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
168. #830	C₂²×C₅	semidirect
169. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
210. C₂×C₅×C₈	C₂²×D₃	semidirect
216. #407	C₅×D₃	direct (N × H)
223. C₂²×C₃×C₅	C₂×M₁₆	semidirect
235. C₂×C₅×D₃	C₂×M₁₆	semidirect
278. C₂×C₃×C₈	C₂³×C₅	semidirect
280. C₂×C₃⋊C₈	C₂³×C₅	semidirect
342. C₂×M₁₆	C₂×C₅×D₃	semidirect
346. C₂²⋊C₈	C₂×C₅×D₃	semidirect
353. C₅×D₃	#407	direct (N × H)
368. C₂²×D₃	C₅×M₁₆	semidirect
414. C₂²×C₅	D₃×M₁₆	semidirect
462. C₂×C₈	C₂²×C₅×D₃	semidirect
463. C₃×C₅	C₂×#407	semidirect
469. C₂²×C₃	C₂×C₅×M₁₆	semidirect
481. C₂×D₃	C₂×C₅×M₁₆	semidirect
545. D₃	C₅×#407	direct (N × H)
546. C₅	D₃×#407	direct (N × H)
563. C₂²	C₅×D₃×M₁₆	semidirect
571. C₃	C₂×C₅×#407	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂×C₅×D₃×M₁₆	2
C₃×C₅×#407	2
C₅×#5207	2
C₅×#5126	2
C₅×#4726	2
C₅×D₃×C₂²⋊C₈	2
C₂×C₅×#407	3
D₃×#407	5

Subgroups — C5×D3×#407 #14411621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#407 #14411621