Subgroups — C₅×M₁₆×D₁₂ #14415687

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5126	C₂	1	2	yes	maximal, complemented
5	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4706	C₂	1	4	yes	maximal, complemented
7	C₅×#4688	C₂	1	2	yes	maximal, complemented
8	C₅×C₈×D₁₂	C₂	1	2	yes	maximal, complemented
9	C₅×D₄×M₁₆	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
16	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
17	C₂×C₅×#208	C₂²	1	2	yes	—
18	C₅×D₃×M₁₆	—	2	8	no	—
19	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
20	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
21	C₄×C₅×D₁₂	C₄	1	2	yes	—
22	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
23	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
24	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
26	C₄×C₅×D₁₂	C₂²	1	2	yes	—
27	C₃×C₅×#97	C₂²	1	2	yes	complemented
28	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
29	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
30	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
32	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
33	M₁₆×D₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×M₁₆	—	3	2	no	—
35	C₂×C₄×C₅×D₄	—	3	1	no	—
36	C₅×#436	—	3	2	no	—
37	C₅×#435	—	3	4	no	—
38	C₅×C₈×D₄	—	3	2	no	—
39	C₅×#423	—	3	1	no	—
40	C₅×#407	—	3	2	no	—
41	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
42	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
47	C₂×C₅×D₁₂	—	2	4	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	—	2	4	no	—
52	C₂×C₄×C₅×D₃	—	2	4	no	—
53	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₃×C₅×M₁₆	—	2	2	no	—
58	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
66	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
67	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
68	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
70	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
71	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₅×#208	—	2	4	no	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
74	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
75	C₅×D₃×C₈	—	2	8	no	—
76	C₂×D₃×M₁₆	C₂×C₅	1	2	yes	complemented
77	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
78	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
79	#5126	C₂×C₅	1	2	yes	complemented
80	#4924	C₂×C₅	1	1	yes	characteristic, complemented
81	#4706	C₂×C₅	1	4	yes	complemented
82	#4688	C₂×C₅	1	2	yes	complemented
83	C₈×D₁₂	C₂×C₅	1	2	yes	complemented
84	C₂²×C₅×D₄	—	3	1	no	—
85	C₂³×C₄×C₅	—	3	2	no	—
86	C₂×C₅×M₁₆	—	3	2	no	—
87	C₂×C₅×M₁₆	—	3	4	no	—
88	C₂×C₅×M₁₆	—	6	8	no	—
89	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
91	C₂²×C₅×C₈	—	3	4	no	—
92	C₄×C₅×D₄	—	3	1	no	—
93	C₄×C₅×D₄	—	3	2	no	—
94	C₄×C₅×D₄	—	3	1	no	—
95	C₄×C₅×D₄	—	3	1	no	—
96	C₄×C₅×D₄	—	3	2	no	—
97	C₄×C₅×D₄	—	3	1	no	—
98	C₂×C₅×C₄⋊C₄	—	3	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
100	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
101	C₅×C₄⋊C₈	—	3	2	no	—
102	C₅×C₄⋊C₈	—	3	2	no	—
103	C₅×C₂²⋊C₈	—	3	4	no	—
104	C₅×C₂²⋊C₈	—	3	4	no	—
105	C₅×#97	C₂×D₃	1	2	yes	complemented
106	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
107	D₄×M₁₆	—	3	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₅×D₃	—	2	4	no	—
110	C₂²×C₅×D₃	—	2	4	no	—
111	C₂²×C₅×D₃	—	4	2	no	—
112	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	4	1	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₅×Dic₃	—	2	4	no	—
125	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
126	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
127	C₅×D₁₂	—	2	4	no	—
128	C₅×D₁₂	—	2	2	no	—
129	C₅×D₁₂	M₁₆	1	4	yes	direct product factor
130	C₄×C₅×D₃	—	2	4	no	—
131	C₄×C₅×D₃	—	2	4	no	—
132	C₄×C₅×D₃	—	2	2	no	—
133	C₄×C₅×D₃	—	2	2	no	—
134	C₄×C₅×D₃	—	2	2	no	—
135	C₄×C₅×D₃	—	2	2	no	—
136	C₃×C₅×C₈	—	2	2	no	—
137	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
138	C₅×C₃⋊C₈	—	2	4	no	—
139	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
140	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
141	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
145	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
146	C₂×#208	C₂²×C₅	1	2	yes	—
147	D₃×M₁₆	—	2	8	no	—
148	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	complemented
149	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
150	C₄×D₁₂	C₄×C₅	1	2	yes	—
151	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
152	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
153	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
154	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
155	C₄×D₁₂	C₂²×C₅	1	2	yes	—
156	C₃×#97	C₂²×C₅	1	2	yes	complemented
157	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
158	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
159	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
160	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
161	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
162	C₂⁴×C₅	—	3	2	no	—
163	C₂×C₅×D₄	—	3	1	no	—
164	C₂×C₅×D₄	—	3	2	no	—
165	C₂×C₅×D₄	—	3	1	no	—
166	C₂×C₅×D₄	—	6	4	no	—
167	C₂²×C₄×C₅	—	3	2	no	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	—	3	2	no	—
170	C₂²×C₄×C₅	—	3	2	no	—
171	C₂²×C₄×C₅	—	3	2	no	—
172	C₂²×C₄×C₅	—	6	4	no	—
173	C₂²×C₄×C₅	—	6	4	no	—
174	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₅×M₁₆	—	2	2	no	—
178	C₅×M₁₆	—	6	4	no	—
179	C₅×M₁₆	—	6	8	no	—
180	C₅×M₁₆	D₁₂	1	4	yes	direct product factor
181	C₂×C₅×C₈	—	3	4	no	—
182	C₂×C₅×C₈	—	6	8	no	—
183	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
184	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
185	C₅×C₄⋊C₄	—	3	2	no	—
186	C₅×C₄⋊C₄	—	3	1	no	—
187	C₅×C₄⋊C₄	—	3	1	no	—
188	C₅×C₂²⋊C₄	—	3	2	no	—
189	C₅×C₂²⋊C₄	—	3	2	no	—
190	C₅×C₂²⋊C₄	—	3	2	no	—
191	C₅×C₂²⋊C₄	—	3	2	no	—
192	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
193	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
194	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
195	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²×M₁₆	—	3	2	no	—
197	C₂×C₄×D₄	—	3	1	no	—
198	#436	—	3	2	no	—
199	#435	—	3	4	no	—
200	C₈×D₄	—	3	2	no	—
201	#423	—	3	1	no	—
202	#407	—	3	2	no	—
203	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₅×D₃	—	2	2	no	—
209	C₂×C₅×D₃	—	2	2	no	—
210	C₂×C₅×D₃	—	2	2	no	—
211	C₂×C₅×D₃	—	2	2	no	—
212	C₂×C₅×D₃	—	2	2	no	—
213	C₂×C₅×D₃	—	4	8	no	—
214	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
219	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
220	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₅×Dic₃	—	2	2	no	—
223	C₅×Dic₃	—	2	2	no	—
224	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
229	C₂×D₁₂	—	2	4	no	—
230	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
231	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄×D₃	—	2	4	no	—
234	C₂×C₄×D₃	—	2	4	no	—
235	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
238	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
239	C₃×M₁₆	—	2	2	no	—
240	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
241	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
242	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
243	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
244	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
245	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
246	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
247	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
248	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
249	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
251	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
252	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
253	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
254	#208	—	2	4	no	—
255	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
256	ΓL(1,𝔽₂₅)	—	2	8	no	—
257	D₃×C₈	—	2	8	no	—
258	C₂³×C₅	—	3	2	no	—
259	C₂³×C₅	—	3	2	no	—
260	C₂³×C₅	—	6	4	no	—
261	C₂³×C₅	—	6	4	no	—
262	C₂³×C₅	—	12	2	no	—
263	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₅×D₄	—	3	4	no	—
265	C₅×D₄	—	6	4	no	—
266	C₅×D₄	—	6	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	4	1	no	—
271	C₂×C₄×C₅	—	6	4	no	—
272	C₂×C₄×C₅	—	6	4	no	—
273	C₂×C₄×C₅	—	6	4	no	—
274	C₂×C₄×C₅	—	6	2	no	—
275	C₂×C₄×C₅	—	6	2	no	—
276	C₂×C₄×C₅	—	6	2	no	—
277	C₂×C₄×C₅	—	6	2	no	—
278	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
284	C₂×C₄×C₅	#235	1	2	yes	—
285	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₅×C₈	—	2	2	no	—
287	C₅×C₈	—	6	4	no	—
288	C₅×C₈	C₂×D₁₂	1	4	yes	complemented
289	C₂²×D₄	—	3	1	no	—
290	C₂³×C₄	—	3	2	no	—
291	C₂×M₁₆	—	3	2	no	—
292	C₂×M₁₆	—	3	4	no	—
293	C₂×M₁₆	—	6	8	no	—
294	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
295	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
296	C₂²×C₈	—	3	4	no	—
297	C₄×D₄	—	3	1	no	—
298	C₄×D₄	—	3	2	no	—
299	C₄×D₄	—	3	1	no	—
300	C₄×D₄	—	3	1	no	—
301	C₄×D₄	—	3	2	no	—
302	C₄×D₄	—	3	1	no	—
303	C₂×C₄⋊C₄	—	3	1	no	—
304	C₂×C₂²⋊C₄	—	3	2	no	—
305	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
306	C₄⋊C₈	—	3	2	no	—
307	C₄⋊C₈	—	3	2	no	—
308	C₂²⋊C₈	—	3	4	no	—
309	C₂²⋊C₈	—	3	4	no	—
310	#97	C₂×C₅×D₃	1	2	yes	complemented
311	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#568	1	1	yes	characteristic
316	C₅×D₃	—	2	4	no	—
317	C₅×D₃	—	4	2	no	—
318	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂²×D₃	—	2	4	no	—
320	C₂²×D₃	—	2	4	no	—
321	C₂²×D₃	—	4	2	no	—
322	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
323	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	4	1	no	—
326	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₃×C₄	C₅×#41	1	2	yes	—
333	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
334	C₂×Dic₃	—	2	4	no	—
335	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
336	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
337	D₁₂	—	2	4	no	—
338	D₁₂	—	2	2	no	—
339	D₁₂	C₅×M₁₆	1	4	yes	direct product factor
340	C₄×D₃	—	2	4	no	—
341	C₄×D₃	—	2	4	no	—
342	C₄×D₃	—	2	2	no	—
343	C₄×D₃	—	2	2	no	—
344	C₄×D₃	—	2	2	no	—
345	C₄×D₃	—	2	2	no	—
346	C₃×C₈	—	2	2	no	—
347	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
348	C₃⋊C₈	—	2	4	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	3	4	no	—
352	C₂²×C₅	—	6	2	no	—
353	C₂²×C₅	—	6	2	no	—
354	C₂²×C₅	—	6	2	no	—
355	C₂²×C₅	—	6	2	no	—
356	C₂²×C₅	—	6	2	no	—
357	C₂²×C₅	—	12	8	no	—
358	C₂²×C₅	C₄×D₁₂	1	2	yes	—
359	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	6	2	no	—
364	C₄×C₅	—	6	2	no	—
365	C₄×C₅	C₄×D₁₂	1	2	yes	—
366	C₄×C₅	D₃×M₁₆	1	2	yes	complemented
367	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
368	C₄×C₅	C₂×#235	1	1	yes	characteristic
369	C₂⁴	—	3	2	no	—
370	C₂×D₄	—	3	1	no	—
371	C₂×D₄	—	3	2	no	—
372	C₂×D₄	—	3	1	no	—
373	C₂×D₄	—	6	4	no	—
374	C₂²×C₄	—	3	2	no	—
375	C₂²×C₄	—	3	2	no	—
376	C₂²×C₄	—	3	2	no	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₂²×C₄	—	6	4	no	—
380	C₂²×C₄	—	6	4	no	—
381	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
382	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
384	M₁₆	—	2	2	no	—
385	M₁₆	—	6	4	no	—
386	M₁₆	—	6	8	no	—
387	M₁₆	C₅×D₁₂	1	4	yes	direct product factor
388	C₂×C₈	—	3	4	no	—
389	C₂×C₈	—	6	8	no	—
390	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
391	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	—	3	1	no	—
394	C₄⋊C₄	—	3	1	no	—
395	C₂²⋊C₄	—	3	2	no	—
396	C₂²⋊C₄	—	3	2	no	—
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
400	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
401	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
402	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
407	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	2	2	no	—
410	C₂×D₃	—	2	2	no	—
411	C₂×D₃	—	2	2	no	—
412	C₂×D₃	—	2	2	no	—
413	C₂×D₃	—	4	8	no	—
414	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	complemented
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
419	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	complemented
420	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
422	Dic₃	—	2	2	no	—
423	Dic₃	—	2	2	no	—
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	6	4	no	—
426	C₂×C₅	—	12	2	no	—
427	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
428	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
429	C₂×C₅	#5745	1	1	yes	characteristic
430	C₂³	—	3	2	no	—
431	C₂³	—	3	2	no	—
432	C₂³	—	6	4	no	—
433	C₂³	—	6	4	no	—
434	C₂³	—	12	2	no	—
435	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
436	D₄	—	3	4	no	—
437	D₄	—	6	4	no	—
438	D₄	—	6	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	3	2	no	—
441	C₂×C₄	—	3	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	6	4	no	—
444	C₂×C₄	—	6	4	no	—
445	C₂×C₄	—	6	4	no	—
446	C₂×C₄	—	6	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
455	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
456	C₂×C₄	C₅×#235	1	2	yes	—
457	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	6	4	no	—
460	C₈	C₂×C₅×D₁₂	1	4	yes	complemented
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
463	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
464	C₂×C₃	C₅×#568	1	1	yes	characteristic
465	D₃	—	2	4	no	—
466	D₃	—	4	2	no	—
467	C₅	M₁₆×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	3	4	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	—	6	2	no	—
474	C₂²	—	6	2	no	—
475	C₂²	—	6	2	no	—
476	C₂²	—	12	8	no	—
477	C₂²	C₄×C₅×D₁₂	1	2	yes	—
478	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	6	2	no	—
483	C₄	—	6	2	no	—
484	C₄	C₄×C₅×D₁₂	1	2	yes	—
485	C₄	C₅×D₃×M₁₆	1	2	yes	complemented
486	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
487	C₄	C₂×C₅×#235	1	1	yes	characteristic
488	C₃	C₅×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	6	4	no	—
491	C₂	—	12	2	no	—
492	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
493	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
494	C₂	C₅×#5745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×D₄×M₁₆
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₅×#5126	C₂	semidirect
5. C₅×#4924	C₂	semidirect
6. C₅×#4706	C₂	semidirect
7. C₅×#4688	C₂	semidirect
8. C₅×C₈×D₁₂	C₂	semidirect
19. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
20. C₂×C₅×D₃×C₈	C₂²	semidirect
27. C₃×C₅×#97	C₂²	semidirect
28. C₃×C₄×C₅×C₈	C₂²	semidirect
29. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
30. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
31. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
32. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
33. M₁₆×D₁₂	C₅	direct (N × H)
41. C₄×C₅×M₁₆	D₃	semidirect
58. C₃×C₅×M₁₆	D₄	semidirect
76. C₂×D₃×M₁₆	C₂×C₅	semidirect
78. C₃×C₄×M₁₆	C₂×C₅	semidirect
79. #5126	C₂×C₅	semidirect
80. #4924	C₂×C₅	semidirect
81. #4706	C₂×C₅	semidirect
82. #4688	C₂×C₅	semidirect
83. C₈×D₁₂	C₂×C₅	semidirect
105. C₅×#97	C₂×D₃	semidirect
106. C₄×C₅×C₈	C₂×D₃	semidirect
129. C₅×D₁₂	M₁₆	direct (N × H)
137. C₃×C₅×C₈	C₂×D₄	semidirect
148. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
149. C₂×D₃×C₈	C₂²×C₅	semidirect
156. C₃×#97	C₂²×C₅	semidirect
157. C₃×C₄×C₈	C₂²×C₅	semidirect
158. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
159. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
160. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
161. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
180. C₅×M₁₆	D₁₂	direct (N × H)
203. C₄×M₁₆	C₅×D₃	semidirect
214. C₂×C₅×D₃	C₂×M₁₆	semidirect
219. C₃×C₄×C₅	C₂×M₁₆	semidirect
240. C₃×M₁₆	C₅×D₄	semidirect
288. C₅×C₈	C₂×D₁₂	semidirect
310. #97	C₂×C₅×D₃	semidirect
311. C₄×C₈	C₂×C₅×D₃	semidirect
339. D₁₂	C₅×M₁₆	direct (N × H)
347. C₃×C₈	C₂×C₅×D₄	semidirect
366. C₄×C₅	D₃×M₁₆	semidirect
387. M₁₆	C₅×D₁₂	direct (N × H)
403. C₃×C₅	D₄×M₁₆	semidirect
414. C₂×D₃	C₂×C₅×M₁₆	semidirect
419. C₃×C₄	C₂×C₅×M₁₆	semidirect
460. C₈	C₂×C₅×D₁₂	semidirect
467. C₅	M₁₆×D₁₂	direct (N × H)
485. C₄	C₅×D₃×M₁₆	semidirect
488. C₃	C₅×D₄×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×M₁₆	2
C₅×#5126	2
C₅×#4924	2
C₅×#4706	2
C₅×#4688	2
C₅×C₈×D₁₂	2
C₅×D₄×M₁₆	3
M₁₆×D₁₂	5

Subgroups — C5×M16×D12 #14415687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×M₁₆×D₁₂ #14415687