Subgroups — C₃×#10617447 #14417015

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66266	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66258	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₃×#65794	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4007	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65735	C₂	1	2	yes	maximal, complemented
7	C₃×SD₁₆×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	C₃×#65731	C₂	1	2	yes	maximal, complemented
9	C₃×D₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
10	C₃×#65728	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65727	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617447	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
16	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
17	C₃×D₄×AGL(1,𝔽₅)	—	2	2	no	—
18	C₃×D₄×AGL(1,𝔽₅)	—	2	1	no	—
19	C₃×D₄×AGL(1,𝔽₅)	—	2	1	no	—
20	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
21	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
22	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
23	C₃×#4130	—	2	1	no	—
24	C₃×#4130	C₂²	1	1	yes	characteristic
25	C₃×#4130	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
27	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic, complemented
30	C₃×#4095	C₄	1	1	yes	characteristic, complemented
31	C₃×#4078	C₄	1	1	yes	characteristic, complemented
32	C₃×#4060	C₄	1	2	yes	complemented
33	C₃×D₅×SD₁₆	C₂²	1	2	yes	—
34	C₃×#4057	C₄	1	2	yes	complemented
35	C₃×D₅×D₈	C₂²	1	2	yes	—
36	C₃×#4054	C₄	1	1	yes	characteristic, complemented
37	C₃×D₅×M₁₆	C₂²	1	1	yes	characteristic
38	C₃×#4009	C₂²	1	1	yes	characteristic, complemented
39	C₃×#4009	C₂²	1	1	yes	characteristic, complemented
40	C₃×#4007	C₂²	1	2	yes	—
41	C₃×#4007	C₂²	1	2	yes	—
42	C₃×#4007	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4007	C₂²	1	1	yes	characteristic, complemented
44	C₃×#3994	C₂²	1	2	yes	complemented
45	C₃×#3993	C₂²	1	2	yes	complemented
46	C₃×#3992	C₂²	1	2	yes	complemented
47	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
48	C₃×#2946	—	5	1	no	maximal, Hall
49	#66266	C₂×C₃	1	1	yes	characteristic, complemented
50	#66258	C₂×C₃	1	1	yes	characteristic, complemented
51	D₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
52	#65794	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×#4007	C₂×C₃	1	1	yes	characteristic, complemented
54	#65735	C₂×C₃	1	2	yes	complemented
55	SD₁₆×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
56	#65731	C₂×C₃	1	2	yes	complemented
57	D₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
58	#65728	C₂×C₃	1	1	yes	characteristic, complemented
59	#65727	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂³×C₃×D₅	—	2	1	no	—
61	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
62	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
63	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
64	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
65	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
68	C₃×#713	C₂×C₄	1	1	yes	characteristic, complemented
69	C₃×Q₈×D₅	C₂³	1	1	yes	characteristic
70	C₃×#711	—	2	1	no	—
71	C₃×#711	C₂×C₄	1	1	yes	characteristic, complemented
72	C₃×D₄×D₅	—	2	1	no	—
73	C₃×D₄×D₅	—	2	1	no	—
74	C₃×D₄×D₅	—	2	1	no	—
75	C₃×D₄×D₅	C₂×C₄	1	2	yes	complemented
76	C₃×D₄×D₅	C₂³	1	2	yes	—
77	C₃×D₄×D₅	C₂³	1	1	yes	characteristic
78	C₃×#709	—	2	1	no	—
79	C₃×#709	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
81	C₂×C₃×C₄×D₅	—	2	1	no	—
82	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
83	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
84	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
85	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
86	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
87	C₃×C₂²⋊AGL(1,𝔽₅)	D₄	1	2	yes	—
88	C₂×C₃×#170	—	2	1	no	—
89	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
90	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
91	C₃×C₄⋊AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
92	C₃×C₄⋊AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
93	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
94	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
95	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
96	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
97	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
98	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
99	C₃×D₅⋊C₈	—	2	1	no	—
100	C₃×D₅⋊C₈	C₂³	1	1	yes	characteristic
101	C₃×D₅⋊C₈	C₂³	1	1	yes	characteristic
102	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
103	C₃×C₅×D₈	C₂×C₄	1	2	yes	complemented
104	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic, complemented
105	C₃×#688	C₂×C₄	1	2	yes	complemented
106	C₃×#687	C₂×C₄	1	2	yes	complemented
107	C₃×#686	C₂×C₄	1	2	yes	complemented
108	C₃×#686	C₂×C₄	1	2	yes	complemented
109	C₃×#681	C₂×C₄	1	1	yes	characteristic, complemented
110	C₃×D₄₀	C₂×C₄	1	2	yes	complemented
111	C₃×#677	C₂×C₄	1	2	yes	complemented
112	C₃×#676	C₂×C₄	1	2	yes	complemented
113	C₃×C₈×D₅	C₂³	1	2	yes	—
114	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
115	C₃×#520	—	5	1	no	—
116	C₃×#518	—	5	1	no	—
117	C₃×#442	—	5	2	no	—
118	C₃×#440	—	5	2	no	—
119	C₃×C₄×SD₁₆	—	5	2	no	—
120	C₃×C₄×D₈	—	5	2	no	—
121	C₃×#428	—	5	1	no	—
122	C₃×#416	—	5	1	no	—
123	C₂×C₃×#102	—	5	1	no	—
124	C₃×#405	—	5	1	no	—
125	D₅×#41	C₂²×C₃	1	1	yes	characteristic
126	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
128	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	complemented
129	D₄×AGL(1,𝔽₅)	—	2	2	no	—
130	D₄×AGL(1,𝔽₅)	—	2	1	no	—
131	D₄×AGL(1,𝔽₅)	—	2	1	no	—
132	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
133	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
134	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	complemented
135	#4130	—	2	1	no	—
136	#4130	C₂²×C₃	1	1	yes	characteristic
137	#4130	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
139	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
140	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
141	C₅×AGL(1,ℤ/8)	C₃×C₄	1	1	yes	characteristic, complemented
142	#4095	C₃×C₄	1	1	yes	characteristic, complemented
143	#4078	C₃×C₄	1	1	yes	characteristic, complemented
144	#4060	C₃×C₄	1	2	yes	complemented
145	D₅×SD₁₆	C₂²×C₃	1	2	yes	—
146	#4057	C₃×C₄	1	2	yes	complemented
147	D₅×D₈	C₂²×C₃	1	2	yes	—
148	#4054	C₃×C₄	1	1	yes	characteristic, complemented
149	D₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
150	#4009	C₂²×C₃	1	1	yes	characteristic, complemented
151	#4009	C₂²×C₃	1	1	yes	characteristic, complemented
152	#4007	C₂²×C₃	1	2	yes	—
153	#4007	C₂²×C₃	1	2	yes	—
154	#4007	C₂²×C₃	1	1	yes	characteristic, complemented
155	#4007	C₂²×C₃	1	1	yes	characteristic, complemented
156	#3994	C₂²×C₃	1	2	yes	complemented
157	#3993	C₂²×C₃	1	2	yes	complemented
158	#3992	C₂²×C₃	1	2	yes	complemented
159	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	complemented
160	#2946	—	5	1	no	Sylow
161	C₂³×C₃×C₅	—	2	1	no	—
162	C₂²×C₃×D₅	—	2	1	no	—
163	C₂²×C₃×D₅	—	2	1	no	—
164	C₂²×C₃×D₅	—	2	2	no	—
165	C₂²×C₃×D₅	—	2	2	no	—
166	C₂²×C₃×D₅	—	8	1	no	—
167	C₂²×C₃×D₅	—	8	1	no	—
168	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
170	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
171	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
172	C₂×C₃×AGL(1,𝔽₅)	—	8	2	no	—
173	C₂×C₃×AGL(1,𝔽₅)	—	8	2	no	—
174	C₂×C₃×AGL(1,𝔽₅)	—	8	2	no	—
175	C₂×C₃×AGL(1,𝔽₅)	—	8	1	no	—
176	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
177	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
178	C₃×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
179	C₃×C₅×D₄	—	2	1	no	—
180	C₃×C₅×D₄	—	2	1	no	—
181	C₃×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
182	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₃×C₂²⋊D₅	—	2	1	no	—
186	C₃×C₂²⋊D₅	—	2	1	no	—
187	C₃×C₂²⋊D₅	—	2	2	no	—
188	C₃×C₂²⋊D₅	—	2	1	no	—
189	C₃×C₂²⋊D₅	—	2	2	no	—
190	C₂×C₃×Dic₅	—	2	1	no	—
191	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
192	C₃×D₂₀	—	2	1	no	—
193	C₃×D₂₀	—	2	1	no	—
194	C₃×D₂₀	C₂²×C₄	1	2	yes	—
195	C₃×D₂₀	C₂²×C₄	1	1	yes	characteristic
196	C₃×C₄×D₅	—	2	1	no	—
197	C₃×C₄×D₅	—	2	1	no	—
198	C₃×C₄×D₅	—	2	1	no	—
199	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
200	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
201	C₃×C₄×D₅	#41	1	1	yes	characteristic
202	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
203	C₃×Dic₁₀	—	2	1	no	—
204	C₃×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
205	C₃×#170	—	2	1	no	—
206	C₃×#170	—	2	1	no	—
207	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
208	C₃×#168	C₂²×C₄	1	2	yes	—
209	C₂×C₃×#41	—	5	1	no	—
210	C₂²×C₃×D₄	—	5	1	no	—
211	C₃×AGL(1,ℤ/8)	—	5	1	no	—
212	C₃×AGL(1,ℤ/8)	—	5	1	no	—
213	C₃×AGL(1,ℤ/8)	—	5	2	no	—
214	C₃×AGL(1,ℤ/8)	—	5	2	no	—
215	C₃×AGL(1,ℤ/8)	—	5	1	no	—
216	C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
217	C₂×C₃×SD₁₆	—	5	2	no	—
218	C₂×C₃×D₈	—	5	2	no	—
219	C₂×C₃×M₁₆	—	5	1	no	—
220	C₂²×C₃×C₈	—	5	1	no	—
221	C₃×C₄×Q₈	—	5	2	no	—
222	C₃×C₄×D₄	—	5	2	no	—
223	C₃×C₄×D₄	—	5	2	no	—
224	C₃×C₄×D₄	—	5	2	no	—
225	C₃×C₄×D₄	—	10	2	no	—
226	C₃×C₄×D₄	—	10	1	no	—
227	C₃×C₄×D₄	—	10	1	no	—
228	C₃×#117	—	5	1	no	—
229	C₃×#117	—	5	1	no	—
230	C₃×#117	—	10	1	no	—
231	C₂×C₃×C₄⋊C₄	—	5	1	no	—
232	C₂×C₃×C₄⋊C₄	—	10	1	no	—
233	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
234	C₃×#107	—	5	2	no	—
235	C₃×#106	—	5	2	no	—
236	C₃×#103	—	5	1	no	—
237	C₃×#103	—	5	1	no	—
238	C₃×#102	—	5	2	no	—
239	C₃×#102	—	5	2	no	—
240	C₃×#102	—	5	1	no	—
241	C₃×#102	—	5	1	no	—
242	C₃×#97	—	5	2	no	—
243	C₃×C₄×C₈	—	5	2	no	—
244	C₂³×D₅	—	2	1	no	—
245	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
246	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
247	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
248	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
249	C₅×#41	C₂×C₃×C₄	1	1	yes	characteristic, complemented
250	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
251	C₂×C₂²⋊D₅	—	2	1	no	—
252	#713	C₂×C₃×C₄	1	1	yes	characteristic, complemented
253	Q₈×D₅	C₂³×C₃	1	1	yes	characteristic
254	#711	—	2	1	no	—
255	#711	C₂×C₃×C₄	1	1	yes	characteristic, complemented
256	D₄×D₅	—	2	1	no	—
257	D₄×D₅	—	2	1	no	—
258	D₄×D₅	—	2	1	no	—
259	D₄×D₅	C₂×C₃×C₄	1	2	yes	complemented
260	D₄×D₅	C₂³×C₃	1	2	yes	—
261	D₄×D₅	C₂³×C₃	1	1	yes	characteristic
262	#709	—	2	1	no	—
263	#709	C₂×C₃×C₄	1	1	yes	characteristic, complemented
264	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
265	C₂×C₄×D₅	—	2	1	no	—
266	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
267	C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
268	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
269	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
270	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
271	C₂²⋊AGL(1,𝔽₅)	C₃×D₄	1	2	yes	—
272	C₂×#170	—	2	1	no	—
273	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
274	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
275	C₄⋊AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
276	C₄⋊AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
277	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
278	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
279	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
280	C₄×AGL(1,𝔽₅)	—	2	2	no	—
281	C₄×AGL(1,𝔽₅)	—	2	1	no	—
282	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
283	D₅⋊C₈	—	2	1	no	—
284	D₅⋊C₈	C₂³×C₃	1	1	yes	characteristic
285	D₅⋊C₈	C₂³×C₃	1	1	yes	characteristic
286	C₅×SD₁₆	C₂×C₃×C₄	1	2	yes	complemented
287	C₅×D₈	C₂×C₃×C₄	1	2	yes	complemented
288	C₅×M₁₆	C₂×C₃×C₄	1	1	yes	characteristic, complemented
289	#688	C₂×C₃×C₄	1	2	yes	complemented
290	#687	C₂×C₃×C₄	1	2	yes	complemented
291	#686	C₂×C₃×C₄	1	2	yes	complemented
292	#686	C₂×C₃×C₄	1	2	yes	complemented
293	#681	C₂×C₃×C₄	1	1	yes	characteristic, complemented
294	D₄₀	C₂×C₃×C₄	1	2	yes	complemented
295	#677	C₂×C₃×C₄	1	2	yes	complemented
296	#676	C₂×C₃×C₄	1	2	yes	complemented
297	C₈×D₅	C₂³×C₃	1	2	yes	—
298	C₂×AGL(1,ℤ/8)	—	5	1	no	—
299	#520	—	5	1	no	—
300	#518	—	5	1	no	—
301	#442	—	5	2	no	—
302	#440	—	5	2	no	—
303	C₄×SD₁₆	—	5	2	no	—
304	C₄×D₈	—	5	2	no	—
305	#428	—	5	1	no	—
306	#416	—	5	1	no	—
307	C₂×#102	—	5	1	no	—
308	#405	—	5	1	no	—
309	C₂²×C₃×C₅	—	2	1	no	—
310	C₂²×C₃×C₅	—	2	2	no	—
311	C₂²×C₃×C₅	—	8	1	no	—
312	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
313	C₂×C₃×D₅	—	2	1	no	—
314	C₂×C₃×D₅	—	2	1	no	—
315	C₂×C₃×D₅	—	2	1	no	—
316	C₂×C₃×D₅	—	2	2	no	—
317	C₂×C₃×D₅	—	4	1	no	—
318	C₂×C₃×D₅	—	4	2	no	—
319	C₂×C₃×D₅	—	4	2	no	—
320	C₂×C₃×D₅	—	4	1	no	—
321	C₂×C₃×D₅	—	8	2	no	—
322	C₂×C₃×D₅	—	8	1	no	—
323	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
325	C₃×AGL(1,𝔽₅)	—	2	2	no	—
326	C₃×AGL(1,𝔽₅)	—	2	2	no	—
327	C₃×AGL(1,𝔽₅)	—	4	2	no	—
328	C₃×AGL(1,𝔽₅)	—	4	1	no	—
329	C₃×AGL(1,𝔽₅)	—	4	1	no	—
330	C₃×C₄×C₅	—	2	1	no	—
331	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
332	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
333	C₃×Dic₅	—	2	1	no	—
334	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
335	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
336	C₂⁴×C₃	—	10	1	no	—
337	C₃×#41	—	5	1	no	—
338	C₃×#41	—	5	1	no	—
339	C₃×#41	—	5	1	no	—
340	C₃×#41	—	10	1	no	—
341	C₃×#41	—	10	1	no	—
342	C₃×#41	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
343	C₂×C₃×Q₈	—	5	1	no	—
344	C₂×C₃×D₄	—	5	1	no	—
345	C₂×C₃×D₄	—	5	2	no	—
346	C₂×C₃×D₄	—	5	2	no	—
347	C₂×C₃×D₄	—	5	1	no	—
348	C₂×C₃×D₄	—	10	1	no	—
349	C₂×C₃×D₄	—	10	1	no	—
350	C₂×C₃×D₄	—	10	1	no	—
351	C₂×C₃×D₄	—	10	1	no	—
352	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
353	C₂²×C₃×C₄	—	5	1	no	—
354	C₂²×C₃×C₄	—	10	1	no	—
355	C₂²×C₃×C₄	—	10	2	no	—
356	C₂²×C₃×C₄	—	10	2	no	—
357	C₂²×C₃×C₄	—	10	2	no	—
358	C₂²×C₃×C₄	—	10	1	no	—
359	C₃×SD₁₆	—	5	2	no	—
360	C₃×SD₁₆	—	5	2	no	—
361	C₃×SD₁₆	—	5	2	no	—
362	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
363	C₃×D₈	—	5	2	no	—
364	C₃×D₈	—	5	2	no	—
365	C₃×D₈	—	5	2	no	—
366	C₃×D₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
367	C₃×M₁₆	—	5	1	no	—
368	C₃×M₁₆	—	5	2	no	—
369	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
370	C₂×C₃×C₈	—	5	2	no	—
371	C₂×C₃×C₈	—	5	1	no	—
372	C₂×C₃×C₈	—	5	1	no	—
373	C₂×C₃×C₈	—	10	1	no	—
374	C₂×C₃×C₈	—	10	1	no	—
375	C₃×C₄⋊C₄	—	5	1	no	—
376	C₃×C₄⋊C₄	—	5	1	no	—
377	C₃×C₄⋊C₄	—	5	2	no	—
378	C₃×C₄⋊C₄	—	5	1	no	—
379	C₃×C₄⋊C₄	—	5	1	no	—
380	C₃×C₄⋊C₄	—	10	1	no	—
381	C₃×C₄⋊C₄	—	10	2	no	—
382	C₃×C₂²⋊C₄	—	5	2	no	—
383	C₃×C₂²⋊C₄	—	10	2	no	—
384	C₃×C₂²⋊C₄	—	10	2	no	—
385	C₃×C₂²⋊C₄	—	10	2	no	—
386	C₃×C₂²⋊C₄	—	10	1	no	—
387	C₃×C₄²	—	5	2	no	—
388	C₃×C₄²	—	10	1	no	—
389	C₃×C₄²	—	10	2	no	—
390	C₂³×C₅	—	2	1	no	—
391	C₂²×D₅	—	2	1	no	—
392	C₂²×D₅	—	2	1	no	—
393	C₂²×D₅	—	2	2	no	—
394	C₂²×D₅	—	2	2	no	—
395	C₂²×D₅	—	8	1	no	—
396	C₂²×D₅	—	8	1	no	—
397	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
398	C₂×AGL(1,𝔽₅)	—	2	2	no	—
399	C₂×AGL(1,𝔽₅)	—	2	1	no	—
400	C₂×AGL(1,𝔽₅)	—	2	1	no	—
401	C₂×AGL(1,𝔽₅)	—	8	2	no	—
402	C₂×AGL(1,𝔽₅)	—	8	2	no	—
403	C₂×AGL(1,𝔽₅)	—	8	2	no	—
404	C₂×AGL(1,𝔽₅)	—	8	1	no	—
405	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	2	yes	—
406	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	2	yes	—
407	C₅×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₅×D₄	—	2	1	no	—
409	C₅×D₄	—	2	1	no	—
410	C₅×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
411	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
414	C₂²⋊D₅	—	2	1	no	—
415	C₂²⋊D₅	—	2	1	no	—
416	C₂²⋊D₅	—	2	2	no	—
417	C₂²⋊D₅	—	2	1	no	—
418	C₂²⋊D₅	—	2	2	no	—
419	C₂×Dic₅	—	2	1	no	—
420	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
421	D₂₀	—	2	1	no	—
422	D₂₀	—	2	1	no	—
423	D₂₀	C₂²×C₃×C₄	1	2	yes	—
424	D₂₀	C₂²×C₃×C₄	1	1	yes	characteristic
425	C₄×D₅	—	2	1	no	—
426	C₄×D₅	—	2	1	no	—
427	C₄×D₅	—	2	1	no	—
428	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
429	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
430	C₄×D₅	C₃×#41	1	1	yes	characteristic
431	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
432	Dic₁₀	—	2	1	no	—
433	Dic₁₀	C₂²×C₃×C₄	1	1	yes	characteristic
434	#170	—	2	1	no	—
435	#170	—	2	1	no	—
436	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
437	#168	C₂²×C₃×C₄	1	2	yes	—
438	C₂×#41	—	5	1	no	—
439	C₂²×D₄	—	5	1	no	—
440	AGL(1,ℤ/8)	—	5	1	no	—
441	AGL(1,ℤ/8)	—	5	1	no	—
442	AGL(1,ℤ/8)	—	5	2	no	—
443	AGL(1,ℤ/8)	—	5	2	no	—
444	AGL(1,ℤ/8)	—	5	1	no	—
445	AGL(1,ℤ/8)	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
446	C₂×SD₁₆	—	5	2	no	—
447	C₂×D₈	—	5	2	no	—
448	C₂×M₁₆	—	5	1	no	—
449	C₂²×C₈	—	5	1	no	—
450	C₄×Q₈	—	5	2	no	—
451	C₄×D₄	—	5	2	no	—
452	C₄×D₄	—	5	2	no	—
453	C₄×D₄	—	5	2	no	—
454	C₄×D₄	—	10	2	no	—
455	C₄×D₄	—	10	1	no	—
456	C₄×D₄	—	10	1	no	—
457	#117	—	5	1	no	—
458	#117	—	5	1	no	—
459	#117	—	10	1	no	—
460	C₂×C₄⋊C₄	—	5	1	no	—
461	C₂×C₄⋊C₄	—	10	1	no	—
462	C₂×C₂²⋊C₄	—	10	2	no	—
463	#107	—	5	2	no	—
464	#106	—	5	2	no	—
465	#103	—	5	1	no	—
466	#103	—	5	1	no	—
467	#102	—	5	2	no	—
468	#102	—	5	2	no	—
469	#102	—	5	1	no	—
470	#102	—	5	1	no	—
471	#97	—	5	2	no	—
472	C₄×C₈	—	5	2	no	—
473	C₂×C₃×C₅	—	2	1	no	—
474	C₂×C₃×C₅	—	4	2	no	—
475	C₂×C₃×C₅	—	4	1	no	—
476	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
477	C₃×D₅	—	2	1	no	—
478	C₃×D₅	—	4	1	no	—
479	C₃×D₅	—	4	2	no	—
480	C₃×D₅	#576	1	1	yes	characteristic
481	C₃×D₅	#577	1	1	yes	characteristic
482	C₂³×C₃	—	2	1	no	—
483	C₂³×C₃	—	5	1	no	—
484	C₂³×C₃	—	10	1	no	—
485	C₂³×C₃	—	10	2	no	—
486	C₂³×C₃	—	10	2	no	—
487	C₂³×C₃	—	10	1	no	—
488	C₂³×C₃	—	40	1	no	—
489	C₂³×C₃	—	40	1	no	—
490	C₃×Q₈	—	5	1	no	—
491	C₃×Q₈	—	10	1	no	—
492	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
493	C₃×D₄	—	2	1	no	—
494	C₃×D₄	—	2	1	no	—
495	C₃×D₄	—	5	1	no	—
496	C₃×D₄	—	5	2	no	—
497	C₃×D₄	—	10	1	no	—
498	C₃×D₄	—	10	2	no	—
499	C₃×D₄	—	10	2	no	—
500	C₃×D₄	—	10	1	no	—
501	C₃×D₄	—	10	1	no	—
502	C₃×D₄	—	10	1	no	—
503	C₃×D₄	—	10	1	no	—
504	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
505	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	5	1	no	—
508	C₂×C₃×C₄	—	5	1	no	—
509	C₂×C₃×C₄	—	5	1	no	—
510	C₂×C₃×C₄	—	5	1	no	—
511	C₂×C₃×C₄	—	5	1	no	—
512	C₂×C₃×C₄	—	5	2	no	—
513	C₂×C₃×C₄	—	5	2	no	—
514	C₂×C₃×C₄	—	10	1	no	—
515	C₂×C₃×C₄	—	10	1	no	—
516	C₂×C₃×C₄	—	10	1	no	—
517	C₂×C₃×C₄	—	10	1	no	—
518	C₂×C₃×C₄	—	10	1	no	—
519	C₂×C₃×C₄	—	10	1	no	—
520	C₂×C₃×C₄	—	10	2	no	—
521	C₂×C₃×C₄	—	40	2	no	—
522	C₂×C₃×C₄	—	40	2	no	—
523	C₂×C₃×C₄	—	40	2	no	—
524	C₂×C₃×C₄	—	40	1	no	—
525	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
526	C₃×C₈	—	5	2	no	—
527	C₃×C₈	—	10	1	no	—
528	C₃×C₈	—	10	1	no	—
529	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
530	C₂²×C₅	—	2	1	no	—
531	C₂²×C₅	—	2	2	no	—
532	C₂²×C₅	—	8	1	no	—
533	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
534	C₂×D₅	—	2	1	no	—
535	C₂×D₅	—	2	1	no	—
536	C₂×D₅	—	2	1	no	—
537	C₂×D₅	—	2	2	no	—
538	C₂×D₅	—	4	1	no	—
539	C₂×D₅	—	4	2	no	—
540	C₂×D₅	—	4	2	no	—
541	C₂×D₅	—	4	1	no	—
542	C₂×D₅	—	8	2	no	—
543	C₂×D₅	—	8	1	no	—
544	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
545	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
546	AGL(1,𝔽₅)	—	2	2	no	—
547	AGL(1,𝔽₅)	—	2	2	no	—
548	AGL(1,𝔽₅)	—	4	2	no	—
549	AGL(1,𝔽₅)	—	4	1	no	—
550	AGL(1,𝔽₅)	—	4	1	no	—
551	C₄×C₅	—	2	1	no	—
552	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
553	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
554	Dic₅	—	2	1	no	—
555	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
556	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
557	C₂⁴	—	10	1	no	—
558	#41	—	5	1	no	—
559	#41	—	5	1	no	—
560	#41	—	5	1	no	—
561	#41	—	10	1	no	—
562	#41	—	10	1	no	—
563	#41	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
564	C₂×Q₈	—	5	1	no	—
565	C₂×D₄	—	5	1	no	—
566	C₂×D₄	—	5	2	no	—
567	C₂×D₄	—	5	2	no	—
568	C₂×D₄	—	5	1	no	—
569	C₂×D₄	—	10	1	no	—
570	C₂×D₄	—	10	1	no	—
571	C₂×D₄	—	10	1	no	—
572	C₂×D₄	—	10	1	no	—
573	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
574	C₂²×C₄	—	5	1	no	—
575	C₂²×C₄	—	10	1	no	—
576	C₂²×C₄	—	10	2	no	—
577	C₂²×C₄	—	10	2	no	—
578	C₂²×C₄	—	10	2	no	—
579	C₂²×C₄	—	10	1	no	—
580	SD₁₆	—	5	2	no	—
581	SD₁₆	—	5	2	no	—
582	SD₁₆	—	5	2	no	—
583	SD₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
584	D₈	—	5	2	no	—
585	D₈	—	5	2	no	—
586	D₈	—	5	2	no	—
587	D₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
588	M₁₆	—	5	1	no	—
589	M₁₆	—	5	2	no	—
590	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
591	C₂×C₈	—	5	2	no	—
592	C₂×C₈	—	5	1	no	—
593	C₂×C₈	—	5	1	no	—
594	C₂×C₈	—	10	1	no	—
595	C₂×C₈	—	10	1	no	—
596	C₄⋊C₄	—	5	1	no	—
597	C₄⋊C₄	—	5	1	no	—
598	C₄⋊C₄	—	5	2	no	—
599	C₄⋊C₄	—	5	1	no	—
600	C₄⋊C₄	—	5	1	no	—
601	C₄⋊C₄	—	10	1	no	—
602	C₄⋊C₄	—	10	2	no	—
603	C₂²⋊C₄	—	5	2	no	—
604	C₂²⋊C₄	—	10	2	no	—
605	C₂²⋊C₄	—	10	2	no	—
606	C₂²⋊C₄	—	10	2	no	—
607	C₂²⋊C₄	—	10	1	no	—
608	C₄²	—	5	2	no	—
609	C₄²	—	10	1	no	—
610	C₄²	—	10	2	no	—
611	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	5	1	no	—
615	C₂²×C₃	—	5	1	no	—
616	C₂²×C₃	—	8	1	no	—
617	C₂²×C₃	—	10	1	no	—
618	C₂²×C₃	—	10	1	no	—
619	C₂²×C₃	—	10	1	no	—
620	C₂²×C₃	—	10	2	no	—
621	C₂²×C₃	—	20	1	no	—
622	C₂²×C₃	—	20	2	no	—
623	C₂²×C₃	—	20	2	no	—
624	C₂²×C₃	—	20	1	no	—
625	C₂²×C₃	—	40	1	no	—
626	C₂²×C₃	—	40	2	no	—
627	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	5	1	no	—
630	C₃×C₄	—	5	1	no	—
631	C₃×C₄	—	10	2	no	—
632	C₃×C₄	—	10	2	no	—
633	C₃×C₄	—	10	1	no	—
634	C₃×C₄	—	20	1	no	—
635	C₃×C₄	—	20	2	no	—
636	C₃×C₄	—	20	1	no	—
637	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
638	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
639	C₂×C₅	—	2	1	no	—
640	C₂×C₅	—	4	2	no	—
641	C₂×C₅	—	4	1	no	—
642	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
643	D₅	—	2	1	no	—
644	D₅	—	4	2	no	—
645	D₅	—	4	1	no	—
646	D₅	C₃×#576	1	1	yes	characteristic
647	D₅	C₃×#577	1	1	yes	characteristic
648	C₂³	—	2	1	no	—
649	C₂³	—	5	1	no	—
650	C₂³	—	10	1	no	—
651	C₂³	—	10	2	no	—
652	C₂³	—	10	2	no	—
653	C₂³	—	10	1	no	—
654	C₂³	—	40	1	no	—
655	C₂³	—	40	1	no	—
656	Q₈	—	5	1	no	—
657	Q₈	—	10	1	no	—
658	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	5	1	no	—
662	D₄	—	5	2	no	—
663	D₄	—	10	1	no	—
664	D₄	—	10	2	no	—
665	D₄	—	10	2	no	—
666	D₄	—	10	1	no	—
667	D₄	—	10	1	no	—
668	D₄	—	10	1	no	—
669	D₄	—	10	1	no	—
670	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
671	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	5	1	no	—
674	C₂×C₄	—	5	1	no	—
675	C₂×C₄	—	5	1	no	—
676	C₂×C₄	—	5	1	no	—
677	C₂×C₄	—	5	1	no	—
678	C₂×C₄	—	5	2	no	—
679	C₂×C₄	—	5	2	no	—
680	C₂×C₄	—	10	1	no	—
681	C₂×C₄	—	10	1	no	—
682	C₂×C₄	—	10	1	no	—
683	C₂×C₄	—	10	1	no	—
684	C₂×C₄	—	10	1	no	—
685	C₂×C₄	—	10	1	no	—
686	C₂×C₄	—	10	2	no	—
687	C₂×C₄	—	40	2	no	—
688	C₂×C₄	—	40	2	no	—
689	C₂×C₄	—	40	2	no	—
690	C₂×C₄	—	40	1	no	—
691	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
692	C₈	—	5	2	no	—
693	C₈	—	10	1	no	—
694	C₈	—	10	1	no	—
695	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
696	C₂×C₃	—	2	1	no	—
697	C₂×C₃	—	4	2	no	—
698	C₂×C₃	—	4	1	no	—
699	C₂×C₃	—	5	1	no	—
700	C₂×C₃	—	5	1	no	—
701	C₂×C₃	—	10	1	no	—
702	C₂×C₃	—	20	2	no	—
703	C₂×C₃	—	20	1	no	—
704	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
705	C₅	C₃×#2946	1	1	yes	characteristic, complemented, Sylow
706	C₂²	—	2	1	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	5	1	no	—
709	C₂²	—	5	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	10	1	no	—
712	C₂²	—	10	1	no	—
713	C₂²	—	10	1	no	—
714	C₂²	—	10	2	no	—
715	C₂²	—	20	1	no	—
716	C₂²	—	20	2	no	—
717	C₂²	—	20	2	no	—
718	C₂²	—	20	1	no	—
719	C₂²	—	40	1	no	—
720	C₂²	—	40	2	no	—
721	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
722	C₄	—	2	1	no	—
723	C₄	—	5	1	no	—
724	C₄	—	5	1	no	—
725	C₄	—	10	2	no	—
726	C₄	—	10	2	no	—
727	C₄	—	10	1	no	—
728	C₄	—	20	1	no	—
729	C₄	—	20	2	no	—
730	C₄	—	20	1	no	—
731	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
732	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
733	C₃	#10617447	1	1	yes	characteristic, direct product factor, Sylow
734	C₂	—	2	1	no	—
735	C₂	—	4	2	no	—
736	C₂	—	4	1	no	—
737	C₂	—	5	1	no	—
738	C₂	—	5	1	no	—
739	C₂	—	10	1	no	—
740	C₂	—	20	2	no	—
741	C₂	—	20	1	no	—
742	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×D₅×AGL(1,ℤ/8)	C₂
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2946
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×#66266	C₂	semidirect
2. C₃×#66258	C₂	semidirect
4. C₃×#65794	C₂	semidirect
5. C₂×C₃×#4007	C₂	semidirect
6. C₃×#65735	C₂	semidirect
7. C₃×SD₁₆×AGL(1,𝔽₅)	C₂	semidirect
8. C₃×#65731	C₂	semidirect
9. C₃×D₈×AGL(1,𝔽₅)	C₂	semidirect
10. C₃×#65728	C₂	semidirect
11. C₃×#65727	C₂	semidirect
12. #10617447	C₃	direct (N × H)
16. C₃×Q₈×AGL(1,𝔽₅)	C₂²	semidirect
22. C₃×D₄×AGL(1,𝔽₅)	C₂²	semidirect
29. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
30. C₃×#4095	C₄	semidirect
31. C₃×#4078	C₄	semidirect
32. C₃×#4060	C₄	semidirect
34. C₃×#4057	C₄	semidirect
36. C₃×#4054	C₄	semidirect
38. C₃×#4009	C₂²	semidirect
39. C₃×#4009	C₂²	semidirect
42. C₃×#4007	C₂²	semidirect
43. C₃×#4007	C₂²	semidirect
44. C₃×#3994	C₂²	semidirect
45. C₃×#3993	C₂²	semidirect
46. C₃×#3992	C₂²	semidirect
47. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
49. #66266	C₂×C₃	semidirect
50. #66258	C₂×C₃	semidirect
52. #65794	C₂×C₃	semidirect
53. C₂×#4007	C₂×C₃	semidirect
54. #65735	C₂×C₃	semidirect
55. SD₁₆×AGL(1,𝔽₅)	C₂×C₃	semidirect
56. #65731	C₂×C₃	semidirect
57. D₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
58. #65728	C₂×C₃	semidirect
59. #65727	C₂×C₃	semidirect
65. C₃×C₅×#41	C₂×C₄	semidirect
66. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
68. C₃×#713	C₂×C₄	semidirect
71. C₃×#711	C₂×C₄	semidirect
75. C₃×D₄×D₅	C₂×C₄	semidirect
79. C₃×#709	C₂×C₄	semidirect
80. C₂×C₃×D₂₀	C₂×C₄	semidirect
102. C₃×C₅×SD₁₆	C₂×C₄	semidirect
103. C₃×C₅×D₈	C₂×C₄	semidirect
104. C₃×C₅×M₁₆	C₂×C₄	semidirect
105. C₃×#688	C₂×C₄	semidirect
106. C₃×#687	C₂×C₄	semidirect
107. C₃×#686	C₂×C₄	semidirect
108. C₃×#686	C₂×C₄	semidirect
109. C₃×#681	C₂×C₄	semidirect
110. C₃×D₄₀	C₂×C₄	semidirect
111. C₃×#677	C₂×C₄	semidirect
112. C₃×#676	C₂×C₄	semidirect
128. Q₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
134. D₄×AGL(1,𝔽₅)	C₂²×C₃	semidirect
141. C₅×AGL(1,ℤ/8)	C₃×C₄	semidirect
142. #4095	C₃×C₄	semidirect
143. #4078	C₃×C₄	semidirect
144. #4060	C₃×C₄	semidirect
146. #4057	C₃×C₄	semidirect
148. #4054	C₃×C₄	semidirect
150. #4009	C₂²×C₃	semidirect
151. #4009	C₂²×C₃	semidirect
154. #4007	C₂²×C₃	semidirect
155. #4007	C₂²×C₃	semidirect
156. #3994	C₂²×C₃	semidirect
157. #3993	C₂²×C₃	semidirect
158. #3992	C₂²×C₃	semidirect
159. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
216. C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)	semidirect
249. C₅×#41	C₂×C₃×C₄	semidirect
250. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
252. #713	C₂×C₃×C₄	semidirect
255. #711	C₂×C₃×C₄	semidirect
259. D₄×D₅	C₂×C₃×C₄	semidirect
263. #709	C₂×C₃×C₄	semidirect
264. C₂×D₂₀	C₂×C₃×C₄	semidirect
286. C₅×SD₁₆	C₂×C₃×C₄	semidirect
287. C₅×D₈	C₂×C₃×C₄	semidirect
288. C₅×M₁₆	C₂×C₃×C₄	semidirect
289. #688	C₂×C₃×C₄	semidirect
290. #687	C₂×C₃×C₄	semidirect
291. #686	C₂×C₃×C₄	semidirect
292. #686	C₂×C₃×C₄	semidirect
293. #681	C₂×C₃×C₄	semidirect
294. D₄₀	C₂×C₃×C₄	semidirect
295. #677	C₂×C₃×C₄	semidirect
296. #676	C₂×C₃×C₄	semidirect
342. C₃×#41	C₂×AGL(1,𝔽₅)	semidirect
352. C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
362. C₃×SD₁₆	C₂×AGL(1,𝔽₅)	semidirect
366. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
369. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
445. AGL(1,ℤ/8)	C₃×AGL(1,𝔽₅)	semidirect
563. #41	C₂×C₃×AGL(1,𝔽₅)	semidirect
573. C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
583. SD₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
587. D₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
590. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
611. C₃×C₅	#2946	semidirect
705. C₅	C₃×#2946	semidirect
733. C₃	#10617447	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×#66266	2
C₃×#66258	2
C₃×D₅×AGL(1,ℤ/8)	2
C₃×#65794	2
C₂×C₃×#4007	2
C₃×#65735	2
C₃×SD₁₆×AGL(1,𝔽₅)	2
C₃×#65731	2
C₃×D₈×AGL(1,𝔽₅)	2
C₃×#65728	2
C₃×#65727	2
#10617447	3
C₃×#2946	5

Subgroups — C3×#10617447 #14417015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617447 #14417015