Subgroups — C₂×#11751650 #14411275

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅⋊ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#91149	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×ΓL(1,𝔽₁₆)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#11751650	C₂	1	8	yes	maximal, direct product factor
9	C₂×M₁₆×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
10	C₂²×D₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
11	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
13	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×#6740	C₄	1	2	yes	complemented
17	C₂×#6739	C₄	1	2	yes	complemented
18	C₂×Dic₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
19	C₄×D₃×AGL(1,𝔽₅)	C₄	1	4	yes	—
20	C₄×D₃×AGL(1,𝔽₅)	C₂²	1	4	yes	—
21	D₅⋊ΓL(1,𝔽₂₅)	C₄	1	4	yes	complemented
22	D₅⋊ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
23	C₂×#6705	C₄	1	1	yes	characteristic, complemented
24	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic, complemented
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×#6651	C₄	1	1	yes	characteristic, complemented
27	C₂×#6650	C₄	1	1	yes	characteristic, complemented
28	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	D₅×ΓL(1,𝔽₂₅)	C₄	1	4	yes	complemented
30	D₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
31	C₈×ΓL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
32	C₃×#3992	C₂²	1	4	yes	complemented
33	#91149	C₂²	1	4	yes	complemented
34	ΓL(1,𝔽₁₆)⋊C₈	C₂²	1	4	yes	complemented
35	C₂×#4707	—	5	1	no	maximal, Hall
36	C₂²×C₄×AGL(1,𝔽₅)	—	3	1	no	—
37	C₂×D₅⋊M₁₆	—	3	1	no	—
38	C₂×D₅×M₁₆	—	3	1	no	—
39	M₁₆×AGL(1,𝔽₅)	—	3	8	no	—
40	C₂×#3992	—	3	1	no	—
41	C₂×#3992	D₃	1	1	yes	characteristic, complemented
42	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
43	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
44	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
46	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
47	C₂×D₃×AGL(1,𝔽₅)	—	2	8	no	—
48	C₂×D₃×AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
49	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₂×#1200	C₂×C₄	1	1	yes	characteristic
53	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
54	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
55	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
56	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
57	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
58	C₄×D₃×D₅	C₂³	1	2	yes	—
59	C₂×C₃⋊#170	C₂×C₄	1	2	yes	complemented
60	C₄×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
61	C₄×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
62	D₅⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	complemented
63	D₅⋊(C₃⋊C₈)	C₂³	1	2	yes	—
64	C₂×C₃×#170	C₂×C₄	1	2	yes	complemented
65	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
66	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
67	C₃×D₅⋊C₈	C₂×C₄	1	2	yes	complemented
68	C₃×D₅⋊C₈	C₂³	1	2	yes	—
69	#6740	C₂×C₄	1	8	yes	complemented
70	#6739	C₂×C₄	1	8	yes	complemented
71	Dic₃×AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
72	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic, complemented
74	#6705	C₂×C₄	1	4	yes	complemented
75	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
76	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
77	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic, complemented
78	C₃×C₈×D₅	C₂×C₄	1	2	yes	complemented
79	C₃×C₈×D₅	C₂³	1	2	yes	—
80	#6651	C₂×C₄	1	4	yes	complemented
81	#6650	C₂×C₄	1	4	yes	complemented
82	D₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
83	D₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
85	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
86	C₂×C₄²×D₃	—	5	1	no	—
87	C₂×C₃×#97	—	5	1	no	—
88	C₂×C₈×Dic₃	—	5	1	no	—
89	C₂×C₈×Dic₃	—	5	1	no	—
90	C₂×#803	—	5	1	no	—
91	#4707	—	5	8	no	—
92	C₂³×AGL(1,𝔽₅)	—	3	2	no	—
93	C₂²×C₄×D₅	—	3	1	no	—
94	C₂×#704	—	3	2	no	—
95	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
96	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
97	C₂×C₄×AGL(1,𝔽₅)	—	3	4	no	—
98	C₂×C₄×AGL(1,𝔽₅)	—	3	4	no	—
99	C₂×C₄×AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
100	D₅⋊M₁₆	—	3	4	no	—
101	D₅⋊M₁₆	—	3	4	no	—
102	C₂×#700	—	3	2	no	—
103	C₂×D₅⋊C₈	—	3	1	no	—
104	C₂×D₅⋊C₈	C₂×D₃	1	1	yes	characteristic
105	C₂×C₅×M₁₆	—	3	1	no	—
106	C₂×#681	—	3	1	no	—
107	D₅×M₁₆	—	3	4	no	—
108	D₅×M₁₆	—	3	4	no	—
109	C₂×#676	—	3	1	no	—
110	C₂×#676	—	3	1	no	—
111	C₂×C₈×D₅	—	3	1	no	—
112	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
113	#3992	—	3	4	no	—
114	#3992	C₂×D₃	1	4	yes	complemented
115	C₈×AGL(1,𝔽₅)	—	3	4	no	—
116	C₈×AGL(1,𝔽₅)	—	3	4	no	—
117	C₂×C₄×M₁₆	—	15	1	no	Sylow
118	C₂²×D₁₅	C₄²	1	1	yes	characteristic
119	C₂²×C₅×D₃	C₄²	1	1	yes	characteristic
120	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₃×D₅	—	2	4	no	—
122	C₂×D₃×D₅	C₄²	1	2	yes	—
123	C₂×D₃×D₅	C₂²×C₄	1	2	yes	—
124	C₂×ΓL(1,𝔽₁₆)	M₁₆	1	8	yes	complemented
125	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	4	yes	—
126	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
127	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	4	yes	—
128	D₃×AGL(1,𝔽₅)	—	2	16	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₁₅	C₄²	1	1	yes	characteristic
131	C₄×D₁₅	C₄²	1	2	yes	—
132	C₄×D₁₅	C₂²×C₄	1	2	yes	—
133	C₂×C₅×Dic₃	C₄²	1	1	yes	characteristic
134	C₄×C₅×D₃	C₄²	1	2	yes	—
135	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
136	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
137	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
138	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
141	#1200	C₄²	1	2	yes	—
142	#1200	C₂²×C₄	1	2	yes	—
143	D₃×Dic₅	C₄²	1	2	yes	—
144	D₃×Dic₅	C₂²×C₄	1	2	yes	—
145	D₅×Dic₃	C₄²	1	2	yes	—
146	D₅×Dic₃	C₂²×C₄	1	2	yes	—
147	C₃⋊#170	C₂²×C₄	1	4	yes	complemented
148	C₃×#170	C₂²×C₄	1	4	yes	complemented
149	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
150	C₃⋊#168	C₂²×C₄	1	2	yes	complemented
151	C₃×#168	C₂²×C₄	1	2	yes	complemented
152	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
153	C₂²×C₄×D₃	—	5	1	no	—
154	C₂²×C₄×D₃	—	5	2	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	1	no	—
157	C₂×C₃×C₄²	—	5	1	no	—
158	C₂×C₄×Dic₃	—	5	2	no	—
159	C₂×C₄×Dic₃	—	5	1	no	—
160	C₂²×C₃⋊C₈	—	5	1	no	—
161	C₂²×C₃⋊C₈	—	5	1	no	—
162	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
163	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
164	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
165	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
167	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
168	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
169	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
170	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
171	C₂×ΓL(1,𝔽₂₅)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
172	C₄²×D₃	—	5	4	no	—
173	C₄²×D₃	—	5	4	no	—
174	C₃×#97	—	5	4	no	—
175	C₈×Dic₃	—	5	4	no	—
176	C₈×Dic₃	—	5	4	no	—
177	#803	—	5	4	no	—
178	C₂³×D₅	—	3	1	no	—
179	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
180	C₂²×AGL(1,𝔽₅)	—	3	8	no	—
181	C₂²×AGL(1,𝔽₅)	—	6	8	no	—
182	C₂²×AGL(1,𝔽₅)	C₄×D₃	1	2	yes	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×Dic₅	—	3	1	no	—
185	C₂×C₄×D₅	—	3	1	no	—
186	C₂×C₄×D₅	—	3	1	no	—
187	C₂×C₄×D₅	—	3	1	no	—
188	C₂×C₄×D₅	—	3	2	no	—
189	C₂×C₄×D₅	—	3	2	no	—
190	C₂×C₄×D₅	—	3	2	no	—
191	C₂×C₄×D₅	—	3	2	no	—
192	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
193	#704	—	3	8	no	—
194	C₂×#170	—	3	2	no	—
195	C₂×#170	C₄×D₃	1	2	yes	complemented
196	C₄×AGL(1,𝔽₅)	—	3	8	no	—
197	C₄×AGL(1,𝔽₅)	—	3	2	no	—
198	C₄×AGL(1,𝔽₅)	—	3	2	no	—
199	C₄×AGL(1,𝔽₅)	C₄×D₃	1	2	yes	—
200	C₄×AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
201	#700	—	3	8	no	—
202	D₅⋊C₈	—	3	2	no	—
203	D₅⋊C₈	—	3	2	no	—
204	D₅⋊C₈	C₄×D₃	1	2	yes	complemented
205	D₅⋊C₈	C₂²×D₃	1	2	yes	—
206	C₅×M₁₆	—	3	4	no	—
207	C₂×C₅×C₈	—	3	1	no	—
208	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic, complemented
209	#681	—	3	4	no	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	C₄×D₃	1	1	yes	characteristic, complemented
212	#676	—	3	4	no	—
213	#676	—	3	4	no	—
214	C₈×D₅	—	3	2	no	—
215	C₈×D₅	—	3	2	no	—
216	C₈×D₅	C₄×D₃	1	2	yes	complemented
217	C₈×D₅	C₂²×D₃	1	2	yes	—
218	C₂²×M₁₆	—	15	1	no	—
219	C₂²×M₁₆	—	15	1	no	—
220	C₂²×C₄²	—	15	1	no	—
221	C₄×M₁₆	—	15	8	no	—
222	C₂×#97	—	5	1	no	—
223	C₂×#97	—	15	1	no	—
224	C₂×C₄×C₈	—	15	1	no	—
225	C₂×C₄×C₈	—	15	1	no	—
226	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
227	C₂×D₁₅	—	2	2	no	—
228	C₂×D₁₅	C₂×C₄²	1	2	yes	—
229	C₂×C₅×D₃	—	2	2	no	—
230	C₂×C₅×D₃	C₂×C₄²	1	2	yes	—
231	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
232	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
233	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
234	D₃×D₅	—	2	4	no	—
235	D₃×D₅	—	2	4	no	—
236	ΓL(1,𝔽₁₆)	C₂×M₁₆	1	8	yes	complemented
237	C₃×AGL(1,𝔽₅)	—	2	4	no	—
238	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
240	Dic₁₅	C₂×C₄²	1	2	yes	—
241	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
242	C₃×Dic₅	C₂³×C₄	1	1	yes	characteristic
243	C₅×Dic₃	C₂×C₄²	1	2	yes	—
244	C₂³×D₃	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	1	no	—
246	C₂²×C₃×C₄	—	5	2	no	—
247	C₂²×Dic₃	—	5	2	no	—
248	C₂²×Dic₃	—	5	1	no	—
249	C₂×C₄×D₃	—	5	1	no	—
250	C₂×C₄×D₃	—	5	1	no	—
251	C₂×C₄×D₃	—	5	1	no	—
252	C₂×C₄×D₃	—	5	2	no	—
253	C₂×C₄×D₃	—	5	2	no	—
254	C₂×C₄×D₃	—	5	2	no	—
255	C₂×C₄×D₃	—	5	2	no	—
256	C₂×C₄×D₃	—	5	8	no	—
257	C₂×C₄×D₃	—	10	8	no	—
258	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₂×C₃×C₈	—	5	2	no	—
260	C₂×C₃×C₈	—	5	2	no	—
261	C₂×C₃×C₈	—	5	2	no	—
262	C₂×C₃×C₈	—	5	1	no	—
263	C₂×C₃×C₈	—	5	2	no	—
264	C₂×C₃×C₈	—	5	2	no	—
265	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
266	C₃×C₄²	—	5	2	no	—
267	C₃×C₄²	—	5	2	no	—
268	C₄×Dic₃	—	5	2	no	—
269	C₄×Dic₃	—	5	8	no	—
270	C₄×Dic₃	—	5	2	no	—
271	C₂×C₃⋊C₈	—	5	2	no	—
272	C₂×C₃⋊C₈	—	5	2	no	—
273	C₂×C₃⋊C₈	—	5	2	no	—
274	C₂×C₃⋊C₈	—	5	1	no	—
275	C₂×C₃⋊C₈	—	5	2	no	—
276	C₂×C₃⋊C₈	—	5	2	no	—
277	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
278	ΓL(1,𝔽₂₅)	—	5	8	no	—
279	ΓL(1,𝔽₂₅)	—	5	8	no	—
280	ΓL(1,𝔽₂₅)	—	5	4	no	—
281	ΓL(1,𝔽₂₅)	—	5	4	no	—
282	ΓL(1,𝔽₂₅)	—	5	4	no	—
283	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
284	C₂³×C₅	—	3	1	no	—
285	C₂²×D₅	—	3	1	no	—
286	C₂²×D₅	—	3	2	no	—
287	C₂²×D₅	—	3	2	no	—
288	C₂²×D₅	—	6	4	no	—
289	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
290	C₂×AGL(1,𝔽₅)	—	2	4	no	—
291	C₂×AGL(1,𝔽₅)	—	3	8	no	—
292	C₂×AGL(1,𝔽₅)	—	3	4	no	—
293	C₂×AGL(1,𝔽₅)	—	6	16	no	—
294	C₂×AGL(1,𝔽₅)	C₂×C₄×D₃	1	4	yes	—
295	C₂×C₄×C₅	—	3	1	no	—
296	C₂×C₄×C₅	—	3	2	no	—
297	C₂×C₄×C₅	—	3	2	no	—
298	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
299	C₂×Dic₅	—	3	1	no	—
300	C₂×Dic₅	—	3	2	no	—
301	C₂×Dic₅	—	3	2	no	—
302	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
303	C₄×D₅	—	3	2	no	—
304	C₄×D₅	—	3	2	no	—
305	C₄×D₅	—	3	2	no	—
306	C₄×D₅	—	3	2	no	—
307	C₄×D₅	—	3	2	no	—
308	C₄×D₅	—	3	2	no	—
309	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
310	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
311	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
312	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
313	#170	—	3	4	no	—
314	#170	C₂×C₄×D₃	1	4	yes	complemented
315	C₅×C₈	—	3	2	no	—
316	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
317	#168	—	3	2	no	—
318	#168	C₂×C₄×D₃	1	2	yes	complemented
319	C₂³×C₄	—	15	1	no	—
320	C₂³×C₄	—	15	2	no	—
321	C₂×M₁₆	—	3	1	no	—
322	C₂×M₁₆	—	15	1	no	—
323	C₂×M₁₆	—	15	4	no	—
324	C₂×M₁₆	—	15	4	no	—
325	C₂×M₁₆	—	15	1	no	—
326	C₂×M₁₆	—	15	2	no	—
327	C₂×M₁₆	—	15	4	no	—
328	C₂×M₁₆	—	15	4	no	—
329	C₂×M₁₆	—	15	2	no	—
330	C₂×M₁₆	—	15	1	no	—
331	C₂²×C₈	—	5	1	no	—
332	C₂²×C₈	—	5	1	no	—
333	C₂²×C₈	—	15	1	no	—
334	C₂²×C₈	—	15	1	no	—
335	C₂×C₄²	—	5	1	no	—
336	C₂×C₄²	—	15	4	no	—
337	C₂×C₄²	—	15	4	no	—
338	C₂×C₄²	—	15	1	no	—
339	C₂×C₄²	—	15	2	no	—
340	#97	—	5	4	no	—
341	#97	—	15	4	no	—
342	C₄×C₈	—	15	4	no	—
343	C₄×C₈	—	15	4	no	—
344	C₂×C₃×C₅	C₄×M₁₆	1	2	yes	complemented
345	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
346	D₁₅	—	2	2	no	—
347	C₃×D₅	C₄×M₁₆	1	2	yes	complemented
348	C₃×D₅	C₂²×M₁₆	1	2	yes	—
349	C₅×D₃	—	2	2	no	—
350	C₂³×C₃	—	5	1	no	—
351	C₂²×D₃	—	5	1	no	—
352	C₂²×D₃	—	5	2	no	—
353	C₂²×D₃	—	5	2	no	—
354	C₂²×D₃	—	10	4	no	—
355	C₂²×D₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
356	C₂×C₃×C₄	—	5	1	no	—
357	C₂×C₃×C₄	—	5	1	no	—
358	C₂×C₃×C₄	—	5	1	no	—
359	C₂×C₃×C₄	—	5	1	no	—
360	C₂×C₃×C₄	—	5	1	no	—
361	C₂×C₃×C₄	—	5	4	no	—
362	C₂×C₃×C₄	—	10	4	no	—
363	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂×Dic₃	—	5	8	no	—
365	C₂×Dic₃	—	5	4	no	—
366	C₂×Dic₃	—	5	1	no	—
367	C₂×Dic₃	—	5	2	no	—
368	C₂×Dic₃	—	5	2	no	—
369	C₂×Dic₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₄×D₃	—	5	2	no	—
371	C₄×D₃	—	5	2	no	—
372	C₄×D₃	—	5	2	no	—
373	C₄×D₃	—	5	2	no	—
374	C₄×D₃	—	5	2	no	—
375	C₄×D₃	—	5	2	no	—
376	C₄×D₃	—	10	16	no	—
377	C₄×D₃	C₄×AGL(1,𝔽₅)	1	2	yes	—
378	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
379	C₃×C₈	—	5	4	no	—
380	C₃×C₈	—	5	2	no	—
381	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
382	C₃⋊C₈	—	5	4	no	—
383	C₃⋊C₈	—	5	2	no	—
384	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
385	C₂²×C₅	—	3	2	no	—
386	C₂²×C₅	—	6	2	no	—
387	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
388	C₂×D₅	—	3	2	no	—
389	C₂×D₅	—	6	2	no	—
390	C₂×D₅	—	6	4	no	—
391	C₂×D₅	—	6	4	no	—
392	C₂×D₅	C₄²×D₃	1	1	yes	characteristic
393	C₂×D₅	D₃×M₁₆	1	4	yes	—
394	C₂×D₅	C₂²×C₄×D₃	1	1	yes	characteristic
395	AGL(1,𝔽₅)	—	2	4	no	—
396	AGL(1,𝔽₅)	—	3	8	no	—
397	C₄×C₅	—	3	2	no	—
398	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
399	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
400	Dic₅	—	3	2	no	—
401	Dic₅	C₄²×D₃	1	1	yes	characteristic
402	Dic₅	C₂²×C₄×D₃	1	1	yes	characteristic
403	C₂⁴	—	15	1	no	—
404	C₂²×C₄	—	3	1	no	—
405	C₂²×C₄	—	5	1	no	—
406	C₂²×C₄	—	5	2	no	—
407	C₂²×C₄	—	15	2	no	—
408	C₂²×C₄	—	15	2	no	—
409	C₂²×C₄	—	15	1	no	—
410	C₂²×C₄	—	15	2	no	—
411	C₂²×C₄	—	15	2	no	—
412	C₂²×C₄	—	15	1	no	—
413	C₂²×C₄	—	15	1	no	—
414	C₂²×C₄	—	15	8	no	—
415	C₂²×C₄	—	15	2	no	—
416	C₂²×C₄	—	15	1	no	—
417	C₂²×C₄	—	30	8	no	—
418	M₁₆	—	3	4	no	—
419	M₁₆	—	15	4	no	—
420	M₁₆	—	15	4	no	—
421	M₁₆	—	15	8	no	—
422	M₁₆	—	15	8	no	—
423	M₁₆	—	15	4	no	—
424	C₂×C₈	—	3	1	no	—
425	C₂×C₈	—	5	2	no	—
426	C₂×C₈	—	5	2	no	—
427	C₂×C₈	—	5	2	no	—
428	C₂×C₈	—	5	1	no	—
429	C₂×C₈	—	5	2	no	—
430	C₂×C₈	—	5	2	no	—
431	C₂×C₈	—	15	2	no	—
432	C₂×C₈	—	15	2	no	—
433	C₂×C₈	—	15	2	no	—
434	C₂×C₈	—	15	2	no	—
435	C₂×C₈	—	15	2	no	—
436	C₂×C₈	—	15	1	no	—
437	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
438	C₄²	—	5	2	no	—
439	C₄²	—	5	2	no	—
440	C₄²	—	15	2	no	—
441	C₄²	—	15	2	no	—
442	C₄²	—	15	8	no	—
443	C₃×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic, complemented, Hall
444	C₂²×C₃	—	5	4	no	—
445	C₂²×C₃	—	5	1	no	—
446	C₂²×C₃	—	5	1	no	—
447	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
448	C₂×D₃	—	2	2	no	—
449	C₂×D₃	—	5	2	no	—
450	C₂×D₃	—	10	4	no	—
451	C₂×D₃	—	10	4	no	—
452	C₂×D₃	—	10	2	no	—
453	C₂×D₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
454	C₃×C₄	—	5	1	no	—
455	C₃×C₄	—	5	1	no	—
456	C₃×C₄	—	10	4	no	—
457	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
458	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
459	Dic₃	—	5	8	no	—
460	Dic₃	—	5	2	no	—
461	Dic₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
462	C₂×C₅	—	6	2	no	—
463	C₂×C₅	#4707	1	2	yes	complemented
464	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
465	D₅	—	6	2	no	—
466	D₅	#4707	1	2	yes	complemented
467	D₅	C₂×D₃×M₁₆	1	2	yes	—
468	C₂³	—	3	1	no	—
469	C₂³	—	5	1	no	—
470	C₂³	—	15	2	no	—
471	C₂³	—	15	2	no	—
472	C₂³	—	15	1	no	—
473	C₂³	—	30	4	no	—
474	C₂×C₄	—	3	1	no	—
475	C₂×C₄	—	3	2	no	—
476	C₂×C₄	—	3	2	no	—
477	C₂×C₄	—	5	1	no	—
478	C₂×C₄	—	5	1	no	—
479	C₂×C₄	—	5	1	no	—
480	C₂×C₄	—	5	1	no	—
481	C₂×C₄	—	5	1	no	—
482	C₂×C₄	—	5	4	no	—
483	C₂×C₄	—	10	4	no	—
484	C₂×C₄	—	15	2	no	—
485	C₂×C₄	—	15	2	no	—
486	C₂×C₄	—	15	2	no	—
487	C₂×C₄	—	15	2	no	—
488	C₂×C₄	—	15	2	no	—
489	C₂×C₄	—	15	2	no	—
490	C₂×C₄	—	15	4	no	—
491	C₂×C₄	—	15	8	no	—
492	C₂×C₄	—	15	1	no	—
493	C₂×C₄	—	15	2	no	—
494	C₂×C₄	—	15	2	no	—
495	C₂×C₄	—	30	16	no	—
496	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
497	C₈	—	3	2	no	—
498	C₈	—	5	4	no	—
499	C₈	—	5	2	no	—
500	C₈	—	15	4	no	—
501	C₈	—	15	2	no	—
502	C₈	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	complemented
503	C₂×C₃	—	5	2	no	—
504	C₂×C₃	—	5	2	no	—
505	C₂×C₃	M₁₆×AGL(1,𝔽₅)	1	2	yes	complemented
506	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
507	D₃	—	2	2	no	—
508	D₃	—	10	2	no	—
509	C₅	C₂×#4707	1	1	yes	characteristic, complemented, Sylow
510	C₂²	—	3	2	no	—
511	C₂²	—	5	1	no	—
512	C₂²	—	5	1	no	—
513	C₂²	—	5	4	no	—
514	C₂²	—	6	2	no	—
515	C₂²	—	15	2	no	—
516	C₂²	—	30	4	no	—
517	C₂²	—	30	4	no	—
518	C₂²	—	30	2	no	—
519	C₂²	C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
520	C₄	—	3	2	no	—
521	C₄	—	5	1	no	—
522	C₄	—	5	1	no	—
523	C₄	—	10	4	no	—
524	C₄	—	15	8	no	—
525	C₄	—	15	2	no	—
526	C₄	C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
527	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
528	C₃	C₂×M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	5	2	no	—
530	C₂	—	5	2	no	—
531	C₂	—	6	2	no	—
532	C₂	—	30	2	no	—
533	C₂	#11751650	1	2	yes	direct product factor
534	C₂	C₂×C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₈×ΓL(1,𝔽₁₆)	C₂	semidirect
5. C₂×C₃×#3992	C₂	semidirect
6. C₂×#91149	C₂	semidirect
7. C₂×ΓL(1,𝔽₁₆)⋊C₈	C₂	semidirect
8. #11751650	C₂	direct (N × H)
16. C₂×#6740	C₄	semidirect
17. C₂×#6739	C₄	semidirect
21. D₅⋊ΓL(1,𝔽₂₅)	C₄	semidirect
23. C₂×#6705	C₄	semidirect
24. C₂×C₅×ΓL(1,𝔽₂₅)	C₄	semidirect
26. C₂×#6651	C₄	semidirect
27. C₂×#6650	C₄	semidirect
29. D₅×ΓL(1,𝔽₂₅)	C₄	semidirect
31. C₈×ΓL(1,𝔽₁₆)	C₂²	semidirect
32. C₃×#3992	C₂²	semidirect
33. #91149	C₂²	semidirect
34. ΓL(1,𝔽₁₆)⋊C₈	C₂²	semidirect
41. C₂×#3992	D₃	semidirect
59. C₂×C₃⋊#170	C₂×C₄	semidirect
62. D₅⋊(C₃⋊C₈)	C₂×C₄	semidirect
64. C₂×C₃×#170	C₂×C₄	semidirect
67. C₃×D₅⋊C₈	C₂×C₄	semidirect
69. #6740	C₂×C₄	semidirect
70. #6739	C₂×C₄	semidirect
72. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
73. C₂×C₃⋊#168	C₂×C₄	semidirect
74. #6705	C₂×C₄	semidirect
75. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
76. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
77. C₂×C₃×#168	C₂×C₄	semidirect
78. C₃×C₈×D₅	C₂×C₄	semidirect
80. #6651	C₂×C₄	semidirect
81. #6650	C₂×C₄	semidirect
82. D₅×C₃⋊C₈	C₂×C₄	semidirect
114. #3992	C₂×D₃	semidirect
124. C₂×ΓL(1,𝔽₁₆)	M₁₆	semidirect
147. C₃⋊#170	C₂²×C₄	semidirect
148. C₃×#170	C₂²×C₄	semidirect
149. C₃×C₅×C₈	C₂²×C₄	semidirect
150. C₃⋊#168	C₂²×C₄	semidirect
151. C₃×#168	C₂²×C₄	semidirect
152. C₅×C₃⋊C₈	C₂²×C₄	semidirect
171. C₂×ΓL(1,𝔽₂₅)	AGL(1,𝔽₅)	semidirect
195. C₂×#170	C₄×D₃	semidirect
204. D₅⋊C₈	C₄×D₃	semidirect
208. C₂×C₅×C₈	C₄×D₃	semidirect
211. C₂×#168	C₄×D₃	semidirect
216. C₈×D₅	C₄×D₃	semidirect
236. ΓL(1,𝔽₁₆)	C₂×M₁₆	semidirect
265. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
277. C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	semidirect
283. ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	semidirect
314. #170	C₂×C₄×D₃	semidirect
316. C₅×C₈	C₂×C₄×D₃	semidirect
318. #168	C₂×C₄×D₃	semidirect
344. C₂×C₃×C₅	C₄×M₁₆	semidirect
347. C₃×D₅	C₄×M₁₆	semidirect
381. C₃×C₈	C₂²×AGL(1,𝔽₅)	semidirect
384. C₃⋊C₈	C₂²×AGL(1,𝔽₅)	semidirect
437. C₂×C₈	D₃×AGL(1,𝔽₅)	semidirect
443. C₃×C₅	C₂×C₄×M₁₆	semidirect
463. C₂×C₅	#4707	semidirect
466. D₅	#4707	semidirect
502. C₈	C₂×D₃×AGL(1,𝔽₅)	semidirect
505. C₂×C₃	M₁₆×AGL(1,𝔽₅)	semidirect
509. C₅	C₂×#4707	semidirect
528. C₃	C₂×M₁₆×AGL(1,𝔽₅)	semidirect
533. C₂	#11751650	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×C₄×D₃×AGL(1,𝔽₅)	2
C₂×D₅⋊ΓL(1,𝔽₂₅)	2
C₂×D₅×ΓL(1,𝔽₂₅)	2
C₂×C₈×ΓL(1,𝔽₁₆)	2
C₂×C₃×#3992	2
C₂×#91149	2
C₂×ΓL(1,𝔽₁₆)⋊C₈	2
#11751650	2
C₂×M₁₆×AGL(1,𝔽₅)	3
C₂×#4707	5

Subgroups — C2×#11751650 #14411275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751650 #14411275