Subgroups — C₂×C₄×C₃⋊D₃×#1043 #72230555

Order 14400.

11952 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊Dic₃×#1043	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₃⋊(C₃⋊#1043)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₃⋊D₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₃⋊(C₃⋊(C₅⋊D₅))	C₄	1	1	yes	characteristic, complemented
5	C₂×#14268255	C₄	1	1	yes	characteristic, complemented
6	C₂×C₃⋊Dic₃×C₅⋊D₅	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊D₃×#1039	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×C₅²×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
9	C₂×C₃²×C₄×#1043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₃⋊D₃×#1043	C₂	1	8	yes	maximal, direct product factor
11	C₃⋊Dic₃×#1043	C₂²	1	8	yes	complemented
12	C₂×C₃²×C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic
13	C₄×C₃⋊(C₃⋊#1043)	C₂²	1	4	yes	complemented
14	C₄×C₃⋊D₃×C₅⋊D₅	C₄	1	4	yes	complemented
15	C₄×C₃⋊D₃×C₅⋊D₅	C₂²	1	4	yes	—
16	C₃²×C₄×#1043	C₂²	1	4	yes	complemented
17	C₂×C₄×D₃×#1043	—	3	4	no	maximal
18	C₂×C₄×C₃⋊D₃×AGL(1,𝔽₅)	—	5	6	no	maximal
19	C₂×Dic₃×#1043	—	3	8	no	—
20	C₄×D₃×#1043	—	3	32	no	—
21	C₂×C₄×C₃⋊#1043	—	3	4	no	—
22	C₂×C₄×D₃×C₅⋊D₅	—	3	4	no	—
23	C₂×C₃×C₄×#1043	D₃	1	4	yes	complemented
24	C₂²×C₃⋊D₃×#1043	C₂	1	2	yes	maximal
25	C₂²×C₃⋊(C₃⋊#1043)	C₂²	1	2	yes	—
26	C₂²×C₃⋊D₃×C₅⋊D₅	C₂²	1	1	yes	characteristic
27	C₂²×C₃²×#1043	C₂²	1	2	yes	—
28	C₂²×D₃×#1043	—	3	8	no	—
29	C₂×C₃⋊D₃×#1043	C₄	1	16	yes	direct product factor
30	C₂×C₃⋊D₃×#1043	C₂²	1	8	yes	—
31	C₂²×C₃²×C₅⋊D₅	C₂³	1	1	yes	characteristic
32	C₂²×C₅²×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃⋊D₃×C₅⋊D₅	C₂×C₄	1	2	yes	—
35	C₂×C₃⋊D₃×C₅⋊D₅	C₂×C₄	1	8	yes	—
36	C₂×C₃⋊D₃×C₅⋊D₅	C₂³	1	2	yes	—
37	C₂×C₃⋊(C₃⋊#1043)	C₂×C₄	1	8	yes	complemented
38	C₂×C₃⋊(C₃⋊#1043)	C₂³	1	4	yes	—
39	C₂×C₃²×#1043	C₂×C₄	1	8	yes	complemented
40	C₂×C₃²×#1043	C₂³	1	4	yes	—
41	C₃⋊D₃×#1043	C₂×C₄	1	32	yes	direct product factor
42	C₂×C₃²×C₄×C₅²	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂×C₃⋊(C₃⋊#1039)	C₂×C₄	1	1	yes	characteristic, complemented
44	C₄×C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₄	1	4	yes	complemented
45	C₂×C₅²×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
46	C₄×C₅²×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
47	C₂×C₃²×#1039	C₂×C₄	1	1	yes	characteristic, complemented
48	C₃²×C₄×C₅⋊D₅	C₂×C₄	1	2	yes	complemented
49	C₃²×C₄×C₅⋊D₅	C₂³	1	2	yes	—
50	#14268255	C₂×C₄	1	4	yes	complemented
51	C₃⋊D₃×#1039	C₂×C₄	1	4	yes	complemented
52	C₃⋊Dic₃×C₅⋊D₅	C₂×C₄	1	2	yes	complemented
53	C₃⋊Dic₃×C₅⋊D₅	C₂³	1	2	yes	—
54	C₂²×C₄×#1043	—	9	1	no	Hall
55	C₂²×C₃⋊D₃×AGL(1,𝔽₅)	—	5	12	no	—
56	C₂×C₄×D₅×C₃⋊D₃	—	5	6	no	—
57	C₂×C₄×C₃⋊ΓL(1,𝔽₁₆)	—	5	6	no	—
58	C₂×C₃²×C₄×AGL(1,𝔽₅)	—	5	6	no	—
59	C₂×AGL(1,𝔽₅)×C₃⋊Dic₃	—	5	12	no	—
60	C₄×C₃⋊D₃×AGL(1,𝔽₅)	—	5	48	no	—
61	C₂²×D₃×C₅⋊D₅	—	3	4	no	—
62	C₂²×C₃⋊#1043	—	3	8	no	—
63	C₂²×C₃×#1043	C₂×D₃	1	8	yes	—
64	C₂×D₃×#1043	—	3	64	no	—
65	C₂×D₃×#1043	—	3	32	no	—
66	C₂×C₄×C₃⋊(C₅⋊D₅)	—	3	4	no	—
67	C₂×C₄×C₅²×D₃	—	3	4	no	—
68	C₂×C₃×C₄×C₅⋊D₅	C₂×D₃	1	4	yes	—
69	C₂×#10597113	—	3	4	no	—
70	C₂×D₃×#1039	—	3	4	no	—
71	C₂×Dic₃×C₅⋊D₅	—	3	4	no	—
72	C₄×D₃×C₅⋊D₅	—	3	16	no	—
73	C₄×D₃×C₅⋊D₅	—	3	16	no	—
74	C₄×C₃⋊#1043	—	3	16	no	—
75	C₃×C₄×#1043	C₂×D₃	1	16	yes	complemented
76	Dic₃×#1043	—	3	32	no	—
77	C₂×C₄×D₃×AGL(1,𝔽₅)	—	15	24	no	—
78	C₂²×C₃²×C₅²	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃⋊(C₃⋊(C₅⋊D₅))	C₄²	1	4	yes	complemented
80	C₂×C₃⋊(C₃⋊(C₅⋊D₅))	C₂²×C₄	1	2	yes	—
81	C₂×C₅²×C₃⋊D₃	C₄²	1	4	yes	complemented
82	C₂×C₅²×C₃⋊D₃	C₂²×C₄	1	2	yes	—
83	C₂×C₃²×C₅⋊D₅	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₃²×C₅⋊D₅	C₂²×C₄	1	4	yes	—
85	C₂×C₃²×C₅⋊D₅	C₂⁴	1	1	yes	characteristic
86	C₃⋊D₃×C₅⋊D₅	C₄²	1	8	yes	complemented
87	C₃⋊D₃×C₅⋊D₅	C₂²×C₄	1	8	yes	—
88	C₃⋊(C₃⋊#1043)	C₂²×C₄	1	8	yes	complemented
89	C₃²×#1043	C₂²×C₄	1	8	yes	complemented
90	C₃²×C₄×C₅²	C₂²×C₄	1	2	yes	complemented
91	C₃⋊(C₃⋊#1039)	C₂²×C₄	1	2	yes	complemented
92	C₅²×C₃⋊Dic₃	C₂²×C₄	1	2	yes	complemented
93	C₃²×#1039	C₂²×C₄	1	2	yes	complemented
94	C₂³×#1043	—	9	2	no	—
95	C₂²×C₄×C₅⋊D₅	—	9	1	no	—
96	C₂×C₄×#1043	—	9	2	no	—
97	C₂×C₄×#1043	—	9	1	no	—
98	C₂×C₄×#1043	—	9	8	no	—
99	C₂×C₄×#1043	C₃⋊D₃	1	1	yes	characteristic, direct product factor
100	C₂²×D₅×C₃⋊D₃	—	5	6	no	—
101	C₂²×C₃⋊ΓL(1,𝔽₁₆)	—	5	12	no	—
102	C₂²×C₃²×AGL(1,𝔽₅)	—	5	12	no	—
103	C₂×C₃⋊D₃×AGL(1,𝔽₅)	—	5	96	no	—
104	C₂×C₃⋊D₃×AGL(1,𝔽₅)	—	5	48	no	—
105	C₂×C₄×C₃⋊D₁₅	—	5	6	no	—
106	C₂×C₄×C₅×C₃⋊D₃	AGL(1,𝔽₅)	1	6	yes	complemented
107	C₂×C₃²×C₄×D₅	—	5	6	no	—
108	C₂×#67137	—	5	6	no	—
109	C₂×C₃⋊D₃×Dic₅	—	5	6	no	—
110	C₂×D₅×C₃⋊Dic₃	—	5	6	no	—
111	C₄×D₅×C₃⋊D₃	—	5	24	no	—
112	C₄×D₅×C₃⋊D₃	—	5	24	no	—
113	C₄×C₃⋊ΓL(1,𝔽₁₆)	—	5	24	no	—
114	C₃²×C₄×AGL(1,𝔽₅)	—	5	24	no	—
115	AGL(1,𝔽₅)×C₃⋊Dic₃	—	5	48	no	—
116	C₂²×C₃⋊(C₅⋊D₅)	—	3	4	no	—
117	C₂²×C₅²×D₃	—	3	4	no	—
118	C₂²×C₃×C₅⋊D₅	C₂²×D₃	1	4	yes	—
119	C₂×D₃×C₅⋊D₅	—	3	32	no	—
120	C₂×D₃×C₅⋊D₅	—	3	8	no	—
121	C₂×D₃×C₅⋊D₅	—	3	8	no	—
122	C₂×C₃⋊#1043	—	3	32	no	—
123	C₂×C₃⋊#1043	—	3	16	no	—
124	C₂×C₃×#1043	C₄×D₃	1	32	yes	complemented
125	C₂×C₃×#1043	C₂²×D₃	1	16	yes	—
126	D₃×#1043	—	3	128	no	—
127	C₂×C₃×C₄×C₅²	C₄×D₃	1	4	yes	complemented
128	C₂×C₃⋊#1039	—	3	4	no	—
129	C₄×C₃⋊(C₅⋊D₅)	—	3	16	no	—
130	C₂×C₅²×Dic₃	—	3	4	no	—
131	C₄×C₅²×D₃	—	3	16	no	—
132	C₂×C₃×#1039	C₄×D₃	1	4	yes	complemented
133	C₃×C₄×C₅⋊D₅	C₄×D₃	1	8	yes	complemented
134	C₃×C₄×C₅⋊D₅	C₂²×D₃	1	8	yes	—
135	#10597113	—	3	16	no	—
136	D₃×#1039	—	3	16	no	—
137	Dic₃×C₅⋊D₅	—	3	8	no	—
138	Dic₃×C₅⋊D₅	—	3	8	no	—
139	C₂×C₄²×C₃⋊D₃	—	25	1	no	Hall
140	C₂²×D₃×AGL(1,𝔽₅)	—	15	48	no	—
141	C₂×C₄×D₃×D₅	—	15	24	no	—
142	C₂×C₄×ΓL(1,𝔽₁₆)	—	15	24	no	—
143	C₂×C₃×C₄×AGL(1,𝔽₅)	—	5	24	no	—
144	C₂×Dic₃×AGL(1,𝔽₅)	—	15	48	no	—
145	C₄×D₃×AGL(1,𝔽₅)	—	15	192	no	—
146	C₂×C₃²×C₅²	C₂×C₄²	1	2	yes	complemented
147	C₂×C₃²×C₅²	C₂³×C₄	1	1	yes	characteristic
148	C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₄²	1	4	yes	complemented
149	C₅²×C₃⋊D₃	C₂×C₄²	1	4	yes	complemented
150	C₃²×C₅⋊D₅	C₂×C₄²	1	2	yes	complemented
151	C₃²×C₅⋊D₅	C₂³×C₄	1	2	yes	—
152	C₂³×C₅⋊D₅	—	9	1	no	—
153	C₂²×#1043	—	9	2	no	—
154	C₂²×#1043	—	9	16	no	—
155	C₂²×#1043	—	9	8	no	—
156	C₂²×#1043	C₂×C₃⋊D₃	1	2	yes	—
157	C₂²×C₄×C₅²	—	9	1	no	—
158	C₂²×#1039	—	9	1	no	—
159	C₂×C₄×C₅⋊D₅	—	9	1	no	—
160	C₂×C₄×C₅⋊D₅	—	9	1	no	—
161	C₂×C₄×C₅⋊D₅	—	9	1	no	—
162	C₂×C₄×C₅⋊D₅	—	9	4	no	—
163	C₂×C₄×C₅⋊D₅	—	9	4	no	—
164	C₂×C₄×C₅⋊D₅	C₂×C₃⋊D₃	1	1	yes	characteristic
165	C₄×#1043	—	9	8	no	—
166	C₄×#1043	—	9	4	no	—
167	C₄×#1043	C₂×C₃⋊D₃	1	4	yes	direct product factor
168	C₂²×C₃⋊D₁₅	—	5	6	no	—
169	C₂²×C₅×C₃⋊D₃	C₂×AGL(1,𝔽₅)	1	6	yes	—
170	C₂²×C₃²×D₅	—	5	6	no	—
171	C₂×D₅×C₃⋊D₃	—	5	48	no	—
172	C₂×D₅×C₃⋊D₃	—	5	12	no	—
173	C₂×D₅×C₃⋊D₃	—	5	12	no	—
174	C₂×C₃⋊ΓL(1,𝔽₁₆)	—	5	24	no	—
175	C₂×C₃⋊ΓL(1,𝔽₁₆)	—	5	48	no	—
176	C₂×C₃²×AGL(1,𝔽₅)	—	5	24	no	—
177	C₂×C₃²×AGL(1,𝔽₅)	—	5	48	no	—
178	C₃⋊D₃×AGL(1,𝔽₅)	—	5	192	no	—
179	C₂×C₃²×C₄×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	complemented
180	C₂×C₃⋊Dic₁₅	—	5	6	no	—
181	C₄×C₃⋊D₁₅	—	5	24	no	—
182	C₂×C₅×C₃⋊Dic₃	C₂×AGL(1,𝔽₅)	1	6	yes	complemented
183	C₄×C₅×C₃⋊D₃	C₂×AGL(1,𝔽₅)	1	24	yes	complemented
184	C₂×C₃²×Dic₅	—	5	6	no	—
185	C₃²×C₄×D₅	—	5	12	no	—
186	C₃²×C₄×D₅	—	5	12	no	—
187	#67137	—	5	24	no	—
188	C₃⋊D₃×Dic₅	—	5	24	no	—
189	D₅×C₃⋊Dic₃	—	5	12	no	—
190	D₅×C₃⋊Dic₃	—	5	12	no	—
191	C₂²×C₄×AGL(1,𝔽₅)	—	45	6	no	—
192	C₂²×C₃×C₅²	C₂×C₄×D₃	1	4	yes	—
193	C₂×C₃⋊(C₅⋊D₅)	—	3	16	no	—
194	C₂×C₃⋊(C₅⋊D₅)	—	3	8	no	—
195	C₂×C₅²×D₃	—	3	16	no	—
196	C₂×C₅²×D₃	—	3	8	no	—
197	C₂×C₃×C₅⋊D₅	C₂×C₄×D₃	1	4	yes	—
198	C₂×C₃×C₅⋊D₅	C₂×C₄×D₃	1	16	yes	—
199	C₂×C₃×C₅⋊D₅	C₂³×D₃	1	4	yes	—
200	D₃×C₅⋊D₅	—	3	32	no	—
201	D₃×C₅⋊D₅	—	3	32	no	—
202	C₃⋊#1043	—	3	32	no	—
203	C₃×#1043	C₂×C₄×D₃	1	32	yes	complemented
204	C₃×C₄×C₅²	C₂×C₄×D₃	1	8	yes	complemented
205	C₃⋊#1039	—	3	8	no	—
206	C₅²×Dic₃	—	3	8	no	—
207	C₃×#1039	C₂×C₄×D₃	1	8	yes	complemented
208	C₂²×C₄×C₃⋊D₃	—	25	2	no	—
209	C₂²×C₄×C₃⋊D₃	—	25	1	no	—
210	C₂×C₃²×C₄²	—	25	1	no	—
211	C₂×C₄×C₃⋊Dic₃	—	25	1	no	—
212	C₂×C₄×C₃⋊Dic₃	—	25	2	no	—
213	C₄²×C₃⋊D₃	—	25	8	no	—
214	C₂²×D₃×D₅	—	15	24	no	—
215	C₂²×ΓL(1,𝔽₁₆)	—	15	48	no	—
216	C₂²×C₃×AGL(1,𝔽₅)	—	5	48	no	—
217	C₂×D₃×AGL(1,𝔽₅)	—	15	192	no	—
218	C₂×D₃×AGL(1,𝔽₅)	—	15	384	no	—
219	C₂×C₄×D₁₅	—	15	24	no	—
220	C₂×C₄×C₅×D₃	—	3	24	no	—
221	C₂×C₃×C₄×D₅	—	5	24	no	—
222	C₂×#1200	—	15	24	no	—
223	C₂×D₃×Dic₅	—	15	24	no	—
224	C₂×D₅×Dic₃	—	15	24	no	—
225	C₄×D₃×D₅	—	15	96	no	—
226	C₄×D₃×D₅	—	15	96	no	—
227	C₄×ΓL(1,𝔽₁₆)	—	15	96	no	—
228	C₃×C₄×AGL(1,𝔽₅)	—	5	96	no	—
229	Dic₃×AGL(1,𝔽₅)	—	15	192	no	—
230	C₃²×C₅²	C₂²×C₄²	1	1	yes	characteristic, complemented, Hall
231	C₂³×C₅²	—	9	1	no	—
232	C₂²×C₅⋊D₅	—	9	1	no	—
233	C₂²×C₅⋊D₅	—	9	2	no	—
234	C₂²×C₅⋊D₅	—	9	2	no	—
235	C₂²×C₅⋊D₅	—	9	8	no	—
236	C₂²×C₅⋊D₅	C₂²×C₃⋊D₃	1	1	yes	characteristic
237	C₂×#1043	—	9	4	no	—
238	C₂×#1043	—	9	8	no	—
239	C₂×#1043	—	9	32	no	—
240	C₂×#1043	C₄×C₃⋊D₃	1	8	yes	direct product factor
241	C₂×#1043	C₂²×C₃⋊D₃	1	4	yes	—
242	C₂×C₄×C₅²	—	9	1	no	—
243	C₂×C₄×C₅²	—	9	4	no	—
244	C₂×C₄×C₅²	C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
245	C₂×#1039	—	9	1	no	—
246	C₂×#1039	—	9	4	no	—
247	C₂×#1039	C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
248	C₄×C₅⋊D₅	—	9	2	no	—
249	C₄×C₅⋊D₅	—	9	2	no	—
250	C₄×C₅⋊D₅	—	9	4	no	—
251	C₄×C₅⋊D₅	—	9	4	no	—
252	C₄×C₅⋊D₅	C₄×C₃⋊D₃	1	2	yes	complemented
253	C₄×C₅⋊D₅	C₂²×C₃⋊D₃	1	2	yes	—
254	C₂×C₄²×D₃	—	75	4	no	—
255	C₂²×C₃²×C₅	C₂²×AGL(1,𝔽₅)	1	6	yes	—
256	C₂×C₃⋊D₁₅	—	5	24	no	—
257	C₂×C₃⋊D₁₅	—	5	12	no	—
258	C₂×C₅×C₃⋊D₃	C₄×AGL(1,𝔽₅)	1	24	yes	complemented
259	C₂×C₅×C₃⋊D₃	C₂²×AGL(1,𝔽₅)	1	12	yes	—
260	C₂×C₃²×D₅	—	5	24	no	—
261	C₂×C₃²×D₅	—	5	6	no	—
262	C₂×C₃²×D₅	—	5	6	no	—
263	D₅×C₃⋊D₃	—	5	48	no	—
264	D₅×C₃⋊D₃	—	5	48	no	—
265	C₃⋊ΓL(1,𝔽₁₆)	—	5	48	no	—
266	C₃²×AGL(1,𝔽₅)	—	5	48	no	—
267	C₃²×C₄×C₅	C₂²×AGL(1,𝔽₅)	1	12	yes	complemented
268	C₃⋊Dic₁₅	—	5	12	no	—
269	C₅×C₃⋊Dic₃	C₂²×AGL(1,𝔽₅)	1	12	yes	complemented
270	C₃²×Dic₅	—	5	12	no	—
271	C₂³×AGL(1,𝔽₅)	—	45	12	no	—
272	C₂²×C₄×D₅	—	45	6	no	—
273	C₂×C₄×AGL(1,𝔽₅)	—	5	6	no	—
274	C₂×C₄×AGL(1,𝔽₅)	—	45	48	no	—
275	C₂×C₄×AGL(1,𝔽₅)	—	45	6	no	—
276	C₂×C₄×AGL(1,𝔽₅)	—	45	12	no	—
277	C₂×C₃×C₅²	C₄²×D₃	1	8	yes	complemented
278	C₂×C₃×C₅²	C₂²×C₄×D₃	1	4	yes	—
279	C₃⋊(C₅⋊D₅)	—	3	16	no	—
280	C₅²×D₃	—	3	16	no	—
281	C₃×C₅⋊D₅	C₄²×D₃	1	8	yes	complemented
282	C₃×C₅⋊D₅	C₂²×C₄×D₃	1	8	yes	—
283	C₂³×C₃⋊D₃	—	25	1	no	—
284	C₂²×C₃²×C₄	—	25	2	no	—
285	C₂²×C₃²×C₄	—	25	1	no	—
286	C₂²×C₃⋊Dic₃	—	25	2	no	—
287	C₂²×C₃⋊Dic₃	—	25	1	no	—
288	C₂×C₄×C₃⋊D₃	—	25	8	no	—
289	C₂×C₄×C₃⋊D₃	—	25	16	no	—
290	C₂×C₄×C₃⋊D₃	—	25	1	no	—
291	C₂×C₄×C₃⋊D₃	—	25	1	no	—
292	C₂×C₄×C₃⋊D₃	—	25	1	no	—
293	C₂×C₄×C₃⋊D₃	—	25	4	no	—
294	C₂×C₄×C₃⋊D₃	—	25	4	no	—
295	C₂×C₄×C₃⋊D₃	#1043	1	1	yes	characteristic, direct product factor
296	C₃²×C₄²	—	25	4	no	—
297	C₄×C₃⋊Dic₃	—	25	4	no	—
298	C₄×C₃⋊Dic₃	—	25	8	no	—
299	C₂²×D₁₅	—	15	24	no	—
300	C₂²×C₅×D₃	—	3	24	no	—
301	C₂²×C₃×D₅	—	5	24	no	—
302	C₂×D₃×D₅	—	15	48	no	—
303	C₂×D₃×D₅	—	15	48	no	—
304	C₂×D₃×D₅	—	15	192	no	—
305	C₂×ΓL(1,𝔽₁₆)	—	15	96	no	—
306	C₂×ΓL(1,𝔽₁₆)	—	15	192	no	—
307	C₂×C₃×AGL(1,𝔽₅)	—	5	96	no	—
308	C₂×C₃×AGL(1,𝔽₅)	—	5	192	no	—
309	D₃×AGL(1,𝔽₅)	—	15	768	no	—
310	C₂×C₃×C₄×C₅	D₃×AGL(1,𝔽₅)	1	24	yes	complemented
311	C₂×Dic₁₅	—	15	24	no	—
312	C₄×D₁₅	—	15	96	no	—
313	C₂×C₅×Dic₃	—	3	24	no	—
314	C₄×C₅×D₃	—	3	96	no	—
315	C₂×C₃×Dic₅	—	5	24	no	—
316	C₃×C₄×D₅	—	5	48	no	—
317	C₃×C₄×D₅	—	5	48	no	—
318	#1200	—	15	96	no	—
319	D₃×Dic₅	—	15	96	no	—
320	D₅×Dic₃	—	15	48	no	—
321	D₅×Dic₃	—	15	48	no	—
322	C₂²×C₅²	—	9	4	no	—
323	C₂²×C₅²	—	9	2	no	—
324	C₂²×C₅²	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
325	C₂×C₅⋊D₅	—	9	4	no	—
326	C₂×C₅⋊D₅	—	9	2	no	—
327	C₂×C₅⋊D₅	—	9	8	no	—
328	C₂×C₅⋊D₅	—	9	8	no	—
329	C₂×C₅⋊D₅	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
330	C₂×C₅⋊D₅	C₂×C₄×C₃⋊D₃	1	4	yes	—
331	C₂×C₅⋊D₅	C₂³×C₃⋊D₃	1	1	yes	characteristic
332	#1043	—	9	8	no	—
333	#1043	C₂×C₄×C₃⋊D₃	1	8	yes	direct product factor
334	C₄×C₅²	—	9	2	no	—
335	C₄×C₅²	C₂×C₄×C₃⋊D₃	1	2	yes	complemented
336	#1039	—	9	2	no	—
337	#1039	C₂×C₄×C₃⋊D₃	1	2	yes	complemented
338	C₂²×C₄×D₃	—	75	4	no	—
339	C₂²×C₄×D₃	—	75	8	no	—
340	C₂×C₃×C₄²	—	25	4	no	—
341	C₂×C₄×Dic₃	—	75	8	no	—
342	C₂×C₄×Dic₃	—	75	4	no	—
343	C₄²×D₃	—	75	32	no	—
344	C₂×C₃²×C₅	C₂×C₄×AGL(1,𝔽₅)	1	12	yes	complemented
345	C₂×C₃²×C₅	C₂³×AGL(1,𝔽₅)	1	6	yes	—
346	C₃⋊D₁₅	—	5	24	no	—
347	C₅×C₃⋊D₃	C₂×C₄×AGL(1,𝔽₅)	1	24	yes	complemented
348	C₃²×D₅	—	5	12	no	—
349	C₃²×D₅	—	5	12	no	—
350	C₂³×D₅	—	45	6	no	—
351	C₂²×AGL(1,𝔽₅)	—	5	12	no	—
352	C₂²×AGL(1,𝔽₅)	—	45	48	no	—
353	C₂²×AGL(1,𝔽₅)	—	45	96	no	—
354	C₂²×AGL(1,𝔽₅)	—	45	12	no	—
355	C₂²×C₄×C₅	—	9	6	no	—
356	C₂²×Dic₅	—	45	6	no	—
357	C₂×C₄×D₅	—	5	6	no	—
358	C₂×C₄×D₅	—	45	24	no	—
359	C₂×C₄×D₅	—	45	24	no	—
360	C₂×C₄×D₅	—	45	6	no	—
361	C₂×C₄×D₅	—	45	6	no	—
362	C₂×C₄×D₅	—	45	6	no	—
363	C₄×AGL(1,𝔽₅)	—	5	24	no	—
364	C₄×AGL(1,𝔽₅)	—	45	24	no	—
365	C₄×AGL(1,𝔽₅)	—	45	48	no	—
366	C₃×C₅²	C₂×C₄²×D₃	1	4	yes	complemented
367	C₂³×C₃²	—	25	1	no	—
368	C₂²×C₃⋊D₃	—	25	1	no	—
369	C₂²×C₃⋊D₃	—	25	8	no	—
370	C₂²×C₃⋊D₃	—	25	2	no	—
371	C₂²×C₃⋊D₃	—	25	2	no	—
372	C₂²×C₃⋊D₃	C₂×#1043	1	1	yes	characteristic
373	C₂×C₃²×C₄	—	25	4	no	—
374	C₂×C₃²×C₄	—	25	8	no	—
375	C₂×C₃²×C₄	—	25	1	no	—
376	C₂×C₃²×C₄	—	25	2	no	—
377	C₂×C₃²×C₄	—	25	2	no	—
378	C₂×C₃²×C₄	C₂×#1043	1	1	yes	characteristic, complemented
379	C₂×C₃⋊Dic₃	—	25	4	no	—
380	C₂×C₃⋊Dic₃	—	25	8	no	—
381	C₂×C₃⋊Dic₃	—	25	1	no	—
382	C₂×C₃⋊Dic₃	—	25	2	no	—
383	C₂×C₃⋊Dic₃	—	25	2	no	—
384	C₂×C₃⋊Dic₃	C₂×#1043	1	1	yes	characteristic, complemented
385	C₄×C₃⋊D₃	—	25	32	no	—
386	C₄×C₃⋊D₃	—	25	4	no	—
387	C₄×C₃⋊D₃	—	25	4	no	—
388	C₄×C₃⋊D₃	—	25	4	no	—
389	C₄×C₃⋊D₃	C₂×#1043	1	4	yes	direct product factor
390	C₂²×C₄²	—	225	1	no	Sylow
391	C₂²×C₃×C₅	C₂×D₃×AGL(1,𝔽₅)	1	24	yes	—
392	C₂×D₁₅	—	15	96	no	—
393	C₂×D₁₅	—	15	48	no	—
394	C₂×C₅×D₃	—	3	96	no	—
395	C₂×C₅×D₃	—	3	48	no	—
396	C₂×C₃×D₅	—	5	96	no	—
397	C₂×C₃×D₅	—	5	24	no	—
398	C₂×C₃×D₅	—	5	24	no	—
399	D₃×D₅	—	15	192	no	—
400	D₃×D₅	—	15	192	no	—
401	ΓL(1,𝔽₁₆)	—	15	192	no	—
402	C₃×AGL(1,𝔽₅)	—	5	192	no	—
403	C₃×C₄×C₅	C₂×D₃×AGL(1,𝔽₅)	1	48	yes	complemented
404	Dic₁₅	—	15	48	no	—
405	C₃×Dic₅	—	5	48	no	—
406	C₅×Dic₃	—	3	48	no	—
407	C₂×C₅²	—	9	4	no	—
408	C₂×C₅²	C₄²×C₃⋊D₃	1	2	yes	complemented
409	C₂×C₅²	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
410	C₅⋊D₅	—	9	4	no	—
411	C₅⋊D₅	C₄²×C₃⋊D₃	1	2	yes	complemented
412	C₅⋊D₅	C₂²×C₄×C₃⋊D₃	1	2	yes	—
413	C₂³×D₃	—	75	4	no	—
414	C₂²×C₃×C₄	—	25	8	no	—
415	C₂²×C₃×C₄	—	25	4	no	—
416	C₂²×Dic₃	—	75	4	no	—
417	C₂²×Dic₃	—	75	8	no	—
418	C₂×C₄×D₃	—	3	4	no	—
419	C₂×C₄×D₃	—	75	16	no	—
420	C₂×C₄×D₃	—	75	16	no	—
421	C₂×C₄×D₃	—	75	4	no	—
422	C₂×C₄×D₃	—	75	4	no	—
423	C₂×C₄×D₃	—	75	32	no	—
424	C₂×C₄×D₃	—	75	64	no	—
425	C₂×C₄×D₃	—	75	4	no	—
426	C₃×C₄²	—	25	16	no	—
427	C₄×Dic₃	—	75	32	no	—
428	C₄×Dic₃	—	75	16	no	—
429	C₃²×C₅	C₂²×C₄×AGL(1,𝔽₅)	1	6	yes	complemented
430	C₂³×C₅	—	9	6	no	—
431	C₂²×D₅	—	5	6	no	—
432	C₂²×D₅	—	45	12	no	—
433	C₂²×D₅	—	45	12	no	—
434	C₂²×D₅	—	45	48	no	—
435	C₂²×D₅	—	45	6	no	—
436	C₂×AGL(1,𝔽₅)	—	5	48	no	—
437	C₂×AGL(1,𝔽₅)	—	5	24	no	—
438	C₂×AGL(1,𝔽₅)	—	45	192	no	—
439	C₂×AGL(1,𝔽₅)	—	45	24	no	—
440	C₂×AGL(1,𝔽₅)	—	45	48	no	—
441	C₂×C₄×C₅	—	9	6	no	—
442	C₂×C₄×C₅	—	9	24	no	—
443	C₂×C₄×C₅	C₃⋊D₃×AGL(1,𝔽₅)	1	6	yes	complemented
444	C₂×Dic₅	—	5	6	no	—
445	C₂×Dic₅	—	45	24	no	—
446	C₂×Dic₅	—	45	6	no	—
447	C₄×D₅	—	5	12	no	—
448	C₄×D₅	—	5	12	no	—
449	C₄×D₅	—	45	24	no	—
450	C₄×D₅	—	45	12	no	—
451	C₄×D₅	—	45	12	no	—
452	C₄×D₅	—	45	24	no	—
453	C₂²×C₃²	—	25	4	no	—
454	C₂²×C₃²	—	25	1	no	—
455	C₂²×C₃²	—	25	1	no	—
456	C₂²×C₃²	C₂²×#1043	1	1	yes	characteristic
457	C₂×C₃⋊D₃	—	25	4	no	—
458	C₂×C₃⋊D₃	—	25	2	no	—
459	C₂×C₃⋊D₃	—	25	8	no	—
460	C₂×C₃⋊D₃	—	25	8	no	—
461	C₂×C₃⋊D₃	C₄×#1043	1	4	yes	direct product factor
462	C₂×C₃⋊D₃	C₂²×#1043	1	2	yes	—
463	C₃²×C₄	—	25	8	no	—
464	C₃²×C₄	—	25	2	no	—
465	C₃²×C₄	C₂²×#1043	1	2	yes	complemented
466	C₃⋊Dic₃	—	25	8	no	—
467	C₃⋊Dic₃	—	25	2	no	—
468	C₃⋊Dic₃	C₂²×#1043	1	2	yes	complemented
469	C₂³×C₄	—	225	1	no	—
470	C₂³×C₄	—	225	2	no	—
471	C₂×C₄²	—	25	1	no	—
472	C₂×C₄²	—	225	8	no	—
473	C₂×C₄²	—	225	2	no	—
474	C₂×C₄²	—	225	1	no	—
475	C₂×C₃×C₅	C₄×D₃×AGL(1,𝔽₅)	1	48	yes	complemented
476	C₂×C₃×C₅	C₂²×D₃×AGL(1,𝔽₅)	1	24	yes	—
477	D₁₅	—	15	96	no	—
478	C₃×D₅	—	5	48	no	—
479	C₃×D₅	—	5	48	no	—
480	C₅×D₃	—	3	96	no	—
481	C₅²	C₂×C₄²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
482	C₂³×C₃	—	25	4	no	—
483	C₂²×D₃	—	3	4	no	—
484	C₂²×D₃	—	75	8	no	—
485	C₂²×D₃	—	75	8	no	—
486	C₂²×D₃	—	75	32	no	—
487	C₂²×D₃	—	75	4	no	—
488	C₂×C₃×C₄	—	25	16	no	—
489	C₂×C₃×C₄	—	25	32	no	—
490	C₂×C₃×C₄	—	25	4	no	—
491	C₂×C₃×C₄	—	25	8	no	—
492	C₂×C₃×C₄	—	25	8	no	—
493	C₂×C₃×C₄	D₃×#1043	1	4	yes	complemented
494	C₂×Dic₃	—	3	4	no	—
495	C₂×Dic₃	—	75	8	no	—
496	C₂×Dic₃	—	75	8	no	—
497	C₂×Dic₃	—	75	16	no	—
498	C₂×Dic₃	—	75	32	no	—
499	C₂×Dic₃	—	75	4	no	—
500	C₄×D₃	—	3	16	no	—
501	C₄×D₃	—	75	16	no	—
502	C₄×D₃	—	75	16	no	—
503	C₄×D₃	—	75	128	no	—
504	C₄×D₃	—	75	16	no	—
505	C₂²×C₅	—	9	12	no	—
506	C₂²×C₅	—	9	24	no	—
507	C₂²×C₅	C₂×C₃⋊D₃×AGL(1,𝔽₅)	1	6	yes	—
508	C₂×D₅	—	5	6	no	—
509	C₂×D₅	—	5	6	no	—
510	C₂×D₅	—	5	24	no	—
511	C₂×D₅	—	45	48	no	—
512	C₂×D₅	—	45	48	no	—
513	C₂×D₅	—	45	12	no	—
514	C₂×D₅	—	45	24	no	—
515	AGL(1,𝔽₅)	—	5	48	no	—
516	AGL(1,𝔽₅)	—	45	48	no	—
517	C₄×C₅	—	9	12	no	—
518	C₄×C₅	C₂×C₃⋊D₃×AGL(1,𝔽₅)	1	12	yes	complemented
519	Dic₅	—	5	12	no	—
520	Dic₅	—	45	12	no	—
521	C₂×C₃²	—	25	2	no	—
522	C₂×C₃²	—	25	2	no	—
523	C₂×C₃²	C₂×C₄×#1043	1	2	yes	complemented
524	C₂×C₃²	C₂³×#1043	1	1	yes	characteristic
525	C₃⋊D₃	—	25	4	no	—
526	C₃⋊D₃	C₂×C₄×#1043	1	4	yes	direct product factor
527	C₂⁴	—	225	1	no	—
528	C₂²×C₄	—	9	1	no	—
529	C₂²×C₄	—	25	2	no	—
530	C₂²×C₄	—	25	1	no	—
531	C₂²×C₄	—	225	4	no	—
532	C₂²×C₄	—	225	1	no	—
533	C₂²×C₄	—	225	4	no	—
534	C₂²×C₄	—	225	1	no	—
535	C₂²×C₄	—	225	1	no	—
536	C₂²×C₄	—	225	8	no	—
537	C₂²×C₄	—	225	16	no	—
538	C₂²×C₄	—	225	2	no	—
539	C₂²×C₄	—	225	1	no	—
540	C₄²	—	25	4	no	—
541	C₄²	—	225	8	no	—
542	C₄²	—	225	4	no	—
543	C₃×C₅	C₂×C₄×D₃×AGL(1,𝔽₅)	1	24	yes	complemented
544	C₂²×C₃	—	25	4	no	—
545	C₂²×C₃	—	25	4	no	—
546	C₂²×C₃	—	25	16	no	—
547	C₂²×C₃	C₂×D₃×#1043	1	4	yes	—
548	C₂×D₃	—	3	8	no	—
549	C₂×D₃	—	3	16	no	—
550	C₂×D₃	—	75	32	no	—
551	C₂×D₃	—	75	32	no	—
552	C₂×D₃	—	75	8	no	—
553	C₂×D₃	—	75	16	no	—
554	C₃×C₄	—	25	32	no	—
555	C₃×C₄	—	25	8	no	—
556	C₃×C₄	C₂×D₃×#1043	1	8	yes	complemented
557	Dic₃	—	3	8	no	—
558	Dic₃	—	75	32	no	—
559	Dic₃	—	75	8	no	—
560	C₂×C₅	—	9	24	no	—
561	C₂×C₅	C₄×C₃⋊D₃×AGL(1,𝔽₅)	1	12	yes	complemented
562	C₂×C₅	C₂²×C₃⋊D₃×AGL(1,𝔽₅)	1	6	yes	—
563	D₅	—	5	12	no	—
564	D₅	—	5	12	no	—
565	D₅	—	45	24	no	—
566	C₃²	C₂²×C₄×#1043	1	1	yes	characteristic, complemented, Sylow
567	C₂³	—	9	1	no	—
568	C₂³	—	25	1	no	—
569	C₂³	—	225	2	no	—
570	C₂³	—	225	2	no	—
571	C₂³	—	225	8	no	—
572	C₂³	—	225	1	no	—
573	C₂×C₄	—	9	1	no	—
574	C₂×C₄	—	9	4	no	—
575	C₂×C₄	—	25	4	no	—
576	C₂×C₄	—	25	8	no	—
577	C₂×C₄	—	25	1	no	—
578	C₂×C₄	—	25	2	no	—
579	C₂×C₄	—	25	2	no	—
580	C₂×C₄	—	225	4	no	—
581	C₂×C₄	—	225	2	no	—
582	C₂×C₄	—	225	2	no	—
583	C₂×C₄	—	225	4	no	—
584	C₂×C₄	—	225	32	no	—
585	C₂×C₄	—	225	4	no	—
586	C₂×C₄	—	225	8	no	—
587	C₂×C₄	—	225	1	no	—
588	C₂×C₄	—	225	4	no	—
589	C₂×C₄	C₃⋊D₃×#1043	1	1	yes	characteristic, direct product factor
590	C₂×C₃	—	25	8	no	—
591	C₂×C₃	—	25	8	no	—
592	C₂×C₃	C₂²×D₃×#1043	1	4	yes	—
593	C₂×C₃	C₄×D₃×#1043	1	8	yes	complemented
594	D₃	—	3	16	no	—
595	D₃	—	75	16	no	—
596	C₅	C₂×C₄×C₃⋊D₃×AGL(1,𝔽₅)	1	6	yes	complemented
597	C₂²	—	9	2	no	—
598	C₂²	—	9	4	no	—
599	C₂²	—	25	1	no	—
600	C₂²	—	25	1	no	—
601	C₂²	—	25	4	no	—
602	C₂²	—	225	8	no	—
603	C₂²	—	225	8	no	—
604	C₂²	—	225	2	no	—
605	C₂²	—	225	4	no	—
606	C₂²	C₂×C₃⋊D₃×#1043	1	1	yes	characteristic
607	C₄	—	9	2	no	—
608	C₄	—	25	8	no	—
609	C₄	—	25	2	no	—
610	C₄	—	225	8	no	—
611	C₄	—	225	2	no	—
612	C₄	C₂×C₃⋊D₃×#1043	1	2	yes	direct product factor
613	C₃	C₂×C₄×D₃×#1043	1	4	yes	complemented
614	C₂	—	9	4	no	—
615	C₂	—	25	2	no	—
616	C₂	—	25	2	no	—
617	C₂	—	225	4	no	—
618	C₂	C₂²×C₃⋊D₃×#1043	1	1	yes	characteristic
619	C₂	C₄×C₃⋊D₃×#1043	1	2	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄	C₃⋊D₃×#1043
commutator, hypocenter	C₃²×C₅²	C₂²×C₄²
Frattini	C₂	C₂²×C₃⋊D₃×#1043
Fitting	C₂×C₃²×C₄×C₅²	C₂×C₄
socle	C₂²×C₃²×C₅²	C₂²×C₄
prime radical	C₂²×C₃⋊D₃×C₅⋊D₅	C₂²
cosocle	C₂×C₃²×C₅⋊D₅	C₂⁴
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊Dic₃×#1043	C₂	semidirect
2. C₂×C₄×C₃⋊(C₃⋊#1043)	C₂	semidirect
4. C₂×C₄×C₃⋊(C₃⋊(C₅⋊D₅))	C₄	semidirect
5. C₂×#14268255	C₄	semidirect
7. C₂×C₃⋊D₃×#1039	C₄	semidirect
8. C₂×C₄×C₅²×C₃⋊D₃	C₄	semidirect
9. C₂×C₃²×C₄×#1043	C₂	semidirect
10. C₄×C₃⋊D₃×#1043	C₂	direct (N × H)
11. C₃⋊Dic₃×#1043	C₂²	semidirect
13. C₄×C₃⋊(C₃⋊#1043)	C₂²	semidirect
14. C₄×C₃⋊D₃×C₅⋊D₅	C₄	semidirect
16. C₃²×C₄×#1043	C₂²	semidirect
23. C₂×C₃×C₄×#1043	D₃	semidirect
29. C₂×C₃⋊D₃×#1043	C₄	direct (N × H)
37. C₂×C₃⋊(C₃⋊#1043)	C₂×C₄	semidirect
39. C₂×C₃²×#1043	C₂×C₄	semidirect
41. C₃⋊D₃×#1043	C₂×C₄	direct (N × H)
42. C₂×C₃²×C₄×C₅²	C₂×C₄	semidirect
43. C₂×C₃⋊(C₃⋊#1039)	C₂×C₄	semidirect
44. C₄×C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₄	semidirect
45. C₂×C₅²×C₃⋊Dic₃	C₂×C₄	semidirect
46. C₄×C₅²×C₃⋊D₃	C₂×C₄	semidirect
47. C₂×C₃²×#1039	C₂×C₄	semidirect
48. C₃²×C₄×C₅⋊D₅	C₂×C₄	semidirect
50. #14268255	C₂×C₄	semidirect
51. C₃⋊D₃×#1039	C₂×C₄	semidirect
52. C₃⋊Dic₃×C₅⋊D₅	C₂×C₄	semidirect
75. C₃×C₄×#1043	C₂×D₃	semidirect
79. C₂×C₃⋊(C₃⋊(C₅⋊D₅))	C₄²	semidirect
81. C₂×C₅²×C₃⋊D₃	C₄²	semidirect
86. C₃⋊D₃×C₅⋊D₅	C₄²	semidirect
88. C₃⋊(C₃⋊#1043)	C₂²×C₄	semidirect
89. C₃²×#1043	C₂²×C₄	semidirect
90. C₃²×C₄×C₅²	C₂²×C₄	semidirect
91. C₃⋊(C₃⋊#1039)	C₂²×C₄	semidirect
92. C₅²×C₃⋊Dic₃	C₂²×C₄	semidirect
93. C₃²×#1039	C₂²×C₄	semidirect
99. C₂×C₄×#1043	C₃⋊D₃	direct (N × H)
106. C₂×C₄×C₅×C₃⋊D₃	AGL(1,𝔽₅)	semidirect
124. C₂×C₃×#1043	C₄×D₃	semidirect
127. C₂×C₃×C₄×C₅²	C₄×D₃	semidirect
132. C₂×C₃×#1039	C₄×D₃	semidirect
133. C₃×C₄×C₅⋊D₅	C₄×D₃	semidirect
146. C₂×C₃²×C₅²	C₂×C₄²	semidirect
148. C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₄²	semidirect
149. C₅²×C₃⋊D₃	C₂×C₄²	semidirect
150. C₃²×C₅⋊D₅	C₂×C₄²	semidirect
167. C₄×#1043	C₂×C₃⋊D₃	direct (N × H)
179. C₂×C₃²×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
182. C₂×C₅×C₃⋊Dic₃	C₂×AGL(1,𝔽₅)	semidirect
183. C₄×C₅×C₃⋊D₃	C₂×AGL(1,𝔽₅)	semidirect
203. C₃×#1043	C₂×C₄×D₃	semidirect
204. C₃×C₄×C₅²	C₂×C₄×D₃	semidirect
207. C₃×#1039	C₂×C₄×D₃	semidirect
230. C₃²×C₅²	C₂²×C₄²	semidirect
240. C₂×#1043	C₄×C₃⋊D₃	direct (N × H)
244. C₂×C₄×C₅²	C₄×C₃⋊D₃	semidirect
247. C₂×#1039	C₄×C₃⋊D₃	semidirect
252. C₄×C₅⋊D₅	C₄×C₃⋊D₃	semidirect
258. C₂×C₅×C₃⋊D₃	C₄×AGL(1,𝔽₅)	semidirect
267. C₃²×C₄×C₅	C₂²×AGL(1,𝔽₅)	semidirect
269. C₅×C₃⋊Dic₃	C₂²×AGL(1,𝔽₅)	semidirect
277. C₂×C₃×C₅²	C₄²×D₃	semidirect
281. C₃×C₅⋊D₅	C₄²×D₃	semidirect
295. C₂×C₄×C₃⋊D₃	#1043	direct (N × H)
310. C₂×C₃×C₄×C₅	D₃×AGL(1,𝔽₅)	semidirect
333. #1043	C₂×C₄×C₃⋊D₃	direct (N × H)
335. C₄×C₅²	C₂×C₄×C₃⋊D₃	semidirect
337. #1039	C₂×C₄×C₃⋊D₃	semidirect
344. C₂×C₃²×C₅	C₂×C₄×AGL(1,𝔽₅)	semidirect
347. C₅×C₃⋊D₃	C₂×C₄×AGL(1,𝔽₅)	semidirect
366. C₃×C₅²	C₂×C₄²×D₃	semidirect
378. C₂×C₃²×C₄	C₂×#1043	semidirect
384. C₂×C₃⋊Dic₃	C₂×#1043	semidirect
389. C₄×C₃⋊D₃	C₂×#1043	direct (N × H)
403. C₃×C₄×C₅	C₂×D₃×AGL(1,𝔽₅)	semidirect
408. C₂×C₅²	C₄²×C₃⋊D₃	semidirect
411. C₅⋊D₅	C₄²×C₃⋊D₃	semidirect
429. C₃²×C₅	C₂²×C₄×AGL(1,𝔽₅)	semidirect
443. C₂×C₄×C₅	C₃⋊D₃×AGL(1,𝔽₅)	semidirect
461. C₂×C₃⋊D₃	C₄×#1043	direct (N × H)
465. C₃²×C₄	C₂²×#1043	semidirect
468. C₃⋊Dic₃	C₂²×#1043	semidirect
475. C₂×C₃×C₅	C₄×D₃×AGL(1,𝔽₅)	semidirect
481. C₅²	C₂×C₄²×C₃⋊D₃	semidirect
493. C₂×C₃×C₄	D₃×#1043	semidirect
518. C₄×C₅	C₂×C₃⋊D₃×AGL(1,𝔽₅)	semidirect
523. C₂×C₃²	C₂×C₄×#1043	semidirect
526. C₃⋊D₃	C₂×C₄×#1043	direct (N × H)
543. C₃×C₅	C₂×C₄×D₃×AGL(1,𝔽₅)	semidirect
556. C₃×C₄	C₂×D₃×#1043	semidirect
561. C₂×C₅	C₄×C₃⋊D₃×AGL(1,𝔽₅)	semidirect
566. C₃²	C₂²×C₄×#1043	semidirect
589. C₂×C₄	C₃⋊D₃×#1043	direct (N × H)
593. C₂×C₃	C₄×D₃×#1043	semidirect
596. C₅	C₂×C₄×C₃⋊D₃×AGL(1,𝔽₅)	semidirect
612. C₄	C₂×C₃⋊D₃×#1043	direct (N × H)
613. C₃	C₂×C₄×D₃×#1043	semidirect
619. C₂	C₄×C₃⋊D₃×#1043	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⋊Dic₃×#1043	2
C₂×C₄×C₃⋊(C₃⋊#1043)	2
C₂×C₄×C₃⋊D₃×C₅⋊D₅	2
C₂×C₃²×C₄×#1043	2
C₄×C₃⋊D₃×#1043	2
C₂×C₄×D₃×#1043	3
C₂×C₄×C₃⋊D₃×AGL(1,𝔽₅)	5
C₂²×C₃⋊D₃×#1043	2

Subgroups — C2×C4×C3⋊D3×#1043 #72230555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃⋊D₃×#1043 #72230555