Subgroups — C₃×#10617451 #14417186

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 700 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
2	C₃×#66262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#137	C₂	1	1	yes	maximal, characteristic
4	C₃×#65794	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#4009	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65739	C₂	1	2	yes	maximal, complemented
7	C₃×Q₁₆×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	C₃×#65735	C₂	1	2	yes	maximal, complemented
9	C₃×SD₁₆×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	#10617451	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
15	C₃×Q₈×AGL(1,𝔽₅)	—	2	1	no	—
16	C₃×Q₈×AGL(1,𝔽₅)	—	2	1	no	—
17	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	2	yes	—
18	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	2	yes	—
19	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	2	yes	—
20	C₃×D₄×AGL(1,𝔽₅)	—	2	2	no	—
21	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
22	C₃×#4130	—	2	2	no	—
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×#137	C₄	1	1	yes	characteristic, complemented
30	C₃×#4097	C₄	1	1	yes	characteristic, complemented
31	C₃×#4088	C₄	1	1	yes	characteristic, complemented
32	C₃×#4064	C₄	1	2	yes	complemented
33	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
34	C₃×#4061	C₄	1	2	yes	complemented
35	C₃×D₅×SD₁₆	C₂²	1	2	yes	—
36	C₃×#4055	C₄	1	1	yes	characteristic, complemented
37	C₃×D₅×M₁₆	C₂²	1	1	yes	characteristic
38	C₃×#4009	C₂²	1	2	yes	—
39	C₃×#4009	C₂²	1	2	yes	—
40	C₃×#4009	C₂²	1	1	yes	characteristic
41	C₃×#4009	C₂²	1	1	yes	characteristic
42	C₃×#4007	C₂²	1	1	yes	characteristic
43	C₃×#4007	C₂²	1	1	yes	characteristic
44	C₃×#3994	C₂²	1	2	yes	—
45	C₃×#3993	C₂²	1	2	yes	—
46	C₃×#3992	C₂²	1	2	yes	—
47	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	2	yes	—
48	C₃×#2947	—	5	1	no	maximal, Hall
49	#66266	C₂×C₃	1	1	yes	characteristic
50	#66262	C₂×C₃	1	1	yes	characteristic, complemented
51	D₅×#137	C₂×C₃	1	1	yes	characteristic
52	#65794	C₂×C₃	1	1	yes	characteristic
53	C₂×#4009	C₂×C₃	1	1	yes	characteristic, complemented
54	#65739	C₂×C₃	1	2	yes	complemented
55	Q₁₆×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
56	#65735	C₂×C₃	1	2	yes	complemented
57	SD₁₆×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	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
61	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
62	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
64	C₃×#713	C₂×C₄	1	1	yes	characteristic
65	C₃×Q₈×D₅	—	2	1	no	—
66	C₃×Q₈×D₅	—	2	1	no	—
67	C₃×Q₈×D₅	C₂×C₄	1	2	yes	complemented
68	C₃×Q₈×D₅	C₂³	1	2	yes	—
69	C₃×Q₈×D₅	C₂³	1	1	yes	characteristic
70	C₃×#711	—	2	1	no	—
71	C₃×#711	C₂×C₄	1	1	yes	characteristic
72	C₃×D₄×D₅	—	2	1	no	—
73	C₃×D₄×D₅	C₂³	1	1	yes	characteristic
74	C₃×#709	—	2	1	no	—
75	C₃×#709	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₅	—	2	1	no	—
77	C₂×C₃×C₄×D₅	—	2	1	no	—
78	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×Dic₁₀	—	2	1	no	—
80	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
81	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
82	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
83	C₃×C₂²⋊AGL(1,𝔽₅)	D₄	1	2	yes	—
84	C₂×C₃×#170	—	2	1	no	—
85	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
86	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
87	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
88	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
89	C₃×C₄⋊AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
90	C₃×C₄⋊AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
91	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
92	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
93	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
94	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
95	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
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×Q₁₆	C₂×C₄	1	2	yes	complemented
103	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
104	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic, complemented
105	C₃×#689	C₂×C₄	1	2	yes	complemented
106	C₃×#689	C₂×C₄	1	2	yes	complemented
107	C₃×#688	C₂×C₄	1	2	yes	complemented
108	C₃×#687	C₂×C₄	1	2	yes	complemented
109	C₃×#681	C₂×C₄	1	1	yes	characteristic, complemented
110	C₃×Dic₂₀	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×#137	—	5	1	no	—
115	C₃×#520	—	5	1	no	—
116	C₃×#519	—	5	1	no	—
117	C₃×#441	—	5	2	no	—
118	C₃×#440	—	5	2	no	—
119	C₃×C₄×Q₁₆	—	5	2	no	—
120	C₃×C₄×SD₁₆	—	5	2	no	—
121	C₃×#428	—	5	1	no	—
122	C₃×#416	—	5	1	no	—
123	C₂×C₃×#103	—	5	1	no	—
124	C₃×#405	—	5	1	no	—
125	D₅×#41	C₂²×C₃	1	1	yes	characteristic
126	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
127	Q₈×AGL(1,𝔽₅)	—	2	1	no	—
128	Q₈×AGL(1,𝔽₅)	—	2	1	no	—
129	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
130	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
131	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
132	D₄×AGL(1,𝔽₅)	—	2	2	no	—
133	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
134	#4130	—	2	2	no	—
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×#137	C₃×C₄	1	1	yes	characteristic, complemented
142	#4097	C₃×C₄	1	1	yes	characteristic, complemented
143	#4088	C₃×C₄	1	1	yes	characteristic, complemented
144	#4064	C₃×C₄	1	2	yes	complemented
145	D₅×Q₁₆	C₂²×C₃	1	2	yes	—
146	#4061	C₃×C₄	1	2	yes	complemented
147	D₅×SD₁₆	C₂²×C₃	1	2	yes	—
148	#4055	C₃×C₄	1	1	yes	characteristic, complemented
149	D₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
150	#4009	C₂²×C₃	1	1	yes	characteristic
151	#4009	C₂²×C₃	1	1	yes	characteristic
152	#4009	C₂²×C₃	1	2	yes	—
153	#4009	C₂²×C₃	1	2	yes	—
154	#4007	C₂²×C₃	1	1	yes	characteristic
155	#4007	C₂²×C₃	1	1	yes	characteristic
156	#3994	C₂²×C₃	1	2	yes	—
157	#3993	C₂²×C₃	1	2	yes	—
158	#3992	C₂²×C₃	1	2	yes	—
159	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
160	#2947	—	5	1	no	Sylow
161	C₂²×C₃×D₅	—	2	1	no	—
162	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
164	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
165	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
166	C₂×C₃×AGL(1,𝔽₅)	—	8	2	no	—
167	C₂×C₃×AGL(1,𝔽₅)	—	8	1	no	—
168	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
169	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
170	C₃×C₅×Q₈	—	2	1	no	—
171	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
172	C₃×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
173	C₃×C₅×D₄	—	2	1	no	—
174	C₃×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₃×C₂²⋊D₅	—	2	1	no	—
179	C₃×C₂²⋊D₅	—	2	1	no	—
180	C₃×C₂²⋊D₅	—	2	1	no	—
181	C₂×C₃×Dic₅	—	2	1	no	—
182	C₂×C₃×Dic₅	—	2	1	no	—
183	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
184	C₃×D₂₀	—	2	1	no	—
185	C₃×D₂₀	C₂²×C₄	1	1	yes	characteristic
186	C₃×C₄×D₅	—	2	2	no	—
187	C₃×C₄×D₅	—	2	1	no	—
188	C₃×C₄×D₅	—	2	2	no	—
189	C₃×C₄×D₅	—	2	1	no	—
190	C₃×C₄×D₅	—	2	1	no	—
191	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
192	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
193	C₃×C₄×D₅	#41	1	1	yes	characteristic
194	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
195	C₃×Dic₁₀	—	2	1	no	—
196	C₃×Dic₁₀	—	2	2	no	—
197	C₃×Dic₁₀	—	2	2	no	—
198	C₃×Dic₁₀	—	2	1	no	—
199	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
200	C₃×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
201	C₃×#170	—	2	1	no	—
202	C₃×#170	—	2	1	no	—
203	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
204	C₃×#168	C₂²×C₄	1	2	yes	—
205	C₂×C₃×#41	—	5	1	no	—
206	C₂²×C₃×Q₈	—	5	1	no	—
207	C₃×#137	—	5	1	no	—
208	C₃×#137	—	5	1	no	—
209	C₃×#137	—	5	2	no	—
210	C₃×#137	—	5	2	no	—
211	C₃×#137	—	5	1	no	—
212	C₃×#137	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
213	C₂×C₃×Q₁₆	—	5	2	no	—
214	C₂×C₃×SD₁₆	—	5	2	no	—
215	C₂×C₃×M₁₆	—	5	1	no	—
216	C₂²×C₃×C₈	—	5	1	no	—
217	C₃×C₄×Q₈	—	5	2	no	—
218	C₃×C₄×Q₈	—	5	2	no	—
219	C₃×C₄×Q₈	—	5	2	no	—
220	C₃×C₄×Q₈	—	10	1	no	—
221	C₃×C₄×Q₈	—	10	1	no	—
222	C₃×C₄×D₄	—	5	2	no	—
223	C₃×C₄×D₄	—	10	2	no	—
224	C₃×#117	—	5	1	no	—
225	C₃×#117	—	5	1	no	—
226	C₃×#117	—	10	2	no	—
227	C₃×#117	—	10	1	no	—
228	C₂×C₃×C₄⋊C₄	—	5	1	no	—
229	C₂×C₃×C₄⋊C₄	—	10	1	no	—
230	C₃×#107	—	5	2	no	—
231	C₃×#106	—	5	2	no	—
232	C₃×#103	—	5	2	no	—
233	C₃×#103	—	5	2	no	—
234	C₃×#103	—	5	1	no	—
235	C₃×#103	—	5	1	no	—
236	C₃×#102	—	5	1	no	—
237	C₃×#102	—	5	1	no	—
238	C₃×#97	—	5	2	no	—
239	C₃×C₄×C₈	—	5	2	no	—
240	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
241	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
242	C₅×#41	C₂×C₃×C₄	1	1	yes	characteristic
243	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
244	#713	C₂×C₃×C₄	1	1	yes	characteristic
245	Q₈×D₅	—	2	1	no	—
246	Q₈×D₅	—	2	1	no	—
247	Q₈×D₅	C₂×C₃×C₄	1	2	yes	complemented
248	Q₈×D₅	C₂³×C₃	1	2	yes	—
249	Q₈×D₅	C₂³×C₃	1	1	yes	characteristic
250	#711	—	2	1	no	—
251	#711	C₂×C₃×C₄	1	1	yes	characteristic
252	D₄×D₅	—	2	1	no	—
253	D₄×D₅	C₂³×C₃	1	1	yes	characteristic
254	#709	—	2	1	no	—
255	#709	C₂×C₃×C₄	1	1	yes	characteristic
256	C₂×C₄×D₅	—	2	1	no	—
257	C₂×C₄×D₅	—	2	1	no	—
258	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
259	C₂×Dic₁₀	—	2	1	no	—
260	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
261	C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
262	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
263	C₂²⋊AGL(1,𝔽₅)	C₃×D₄	1	2	yes	—
264	C₂×#170	—	2	1	no	—
265	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
266	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
267	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
268	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
269	C₄⋊AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
270	C₄⋊AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
271	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
272	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
273	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
274	C₄×AGL(1,𝔽₅)	—	2	2	no	—
275	C₄×AGL(1,𝔽₅)	—	2	2	no	—
276	C₄×AGL(1,𝔽₅)	—	2	2	no	—
277	C₄×AGL(1,𝔽₅)	—	2	1	no	—
278	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
279	D₅⋊C₈	—	2	1	no	—
280	D₅⋊C₈	C₂³×C₃	1	1	yes	characteristic
281	D₅⋊C₈	C₂³×C₃	1	1	yes	characteristic
282	C₅×Q₁₆	C₂×C₃×C₄	1	2	yes	complemented
283	C₅×SD₁₆	C₂×C₃×C₄	1	2	yes	complemented
284	C₅×M₁₆	C₂×C₃×C₄	1	1	yes	characteristic, complemented
285	#689	C₂×C₃×C₄	1	2	yes	complemented
286	#689	C₂×C₃×C₄	1	2	yes	complemented
287	#688	C₂×C₃×C₄	1	2	yes	complemented
288	#687	C₂×C₃×C₄	1	2	yes	complemented
289	#681	C₂×C₃×C₄	1	1	yes	characteristic, complemented
290	Dic₂₀	C₂×C₃×C₄	1	2	yes	complemented
291	#677	C₂×C₃×C₄	1	2	yes	complemented
292	#676	C₂×C₃×C₄	1	2	yes	complemented
293	C₈×D₅	C₂³×C₃	1	2	yes	—
294	C₂×#137	—	5	1	no	—
295	#520	—	5	1	no	—
296	#519	—	5	1	no	—
297	#441	—	5	2	no	—
298	#440	—	5	2	no	—
299	C₄×Q₁₆	—	5	2	no	—
300	C₄×SD₁₆	—	5	2	no	—
301	#428	—	5	1	no	—
302	#416	—	5	1	no	—
303	C₂×#103	—	5	1	no	—
304	#405	—	5	1	no	—
305	C₂²×C₃×C₅	—	2	1	no	—
306	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
307	C₂×C₃×D₅	—	2	1	no	—
308	C₂×C₃×D₅	—	2	1	no	—
309	C₂×C₃×D₅	—	2	1	no	—
310	C₂×C₃×D₅	—	4	1	no	—
311	C₂×C₃×D₅	—	4	1	no	—
312	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
313	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
314	C₃×AGL(1,𝔽₅)	—	2	2	no	—
315	C₃×AGL(1,𝔽₅)	—	2	2	no	—
316	C₃×AGL(1,𝔽₅)	—	4	1	no	—
317	C₃×AGL(1,𝔽₅)	—	4	2	no	—
318	C₃×AGL(1,𝔽₅)	—	4	1	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	2	1	no	—
321	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
322	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
323	C₃×Dic₅	—	2	2	no	—
324	C₃×Dic₅	—	2	1	no	—
325	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
326	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
327	C₃×#41	—	5	1	no	—
328	C₃×#41	—	5	1	no	—
329	C₃×#41	—	5	1	no	—
330	C₃×#41	—	10	1	no	—
331	C₃×#41	—	10	1	no	—
332	C₃×#41	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
333	C₂×C₃×Q₈	—	5	2	no	—
334	C₂×C₃×Q₈	—	5	1	no	—
335	C₂×C₃×Q₈	—	5	2	no	—
336	C₂×C₃×Q₈	—	5	1	no	—
337	C₂×C₃×Q₈	—	10	1	no	—
338	C₂×C₃×Q₈	—	10	1	no	—
339	C₂×C₃×Q₈	—	10	1	no	—
340	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
341	C₂×C₃×D₄	—	5	1	no	—
342	C₂×C₃×D₄	—	10	1	no	—
343	C₂²×C₃×C₄	—	5	1	no	—
344	C₂²×C₃×C₄	—	10	1	no	—
345	C₂²×C₃×C₄	—	10	1	no	—
346	C₂²×C₃×C₄	—	10	2	no	—
347	C₂²×C₃×C₄	—	10	1	no	—
348	C₃×Q₁₆	—	5	2	no	—
349	C₃×Q₁₆	—	5	2	no	—
350	C₃×Q₁₆	—	5	2	no	—
351	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
352	C₃×SD₁₆	—	5	2	no	—
353	C₃×SD₁₆	—	5	2	no	—
354	C₃×SD₁₆	—	5	2	no	—
355	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
356	C₃×M₁₆	—	5	1	no	—
357	C₃×M₁₆	—	5	2	no	—
358	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
359	C₂×C₃×C₈	—	5	2	no	—
360	C₂×C₃×C₈	—	5	1	no	—
361	C₂×C₃×C₈	—	5	1	no	—
362	C₂×C₃×C₈	—	10	1	no	—
363	C₂×C₃×C₈	—	10	1	no	—
364	C₃×C₄⋊C₄	—	5	1	no	—
365	C₃×C₄⋊C₄	—	5	1	no	—
366	C₃×C₄⋊C₄	—	5	1	no	—
367	C₃×C₄⋊C₄	—	5	1	no	—
368	C₃×C₄⋊C₄	—	5	2	no	—
369	C₃×C₄⋊C₄	—	10	1	no	—
370	C₃×C₄⋊C₄	—	10	2	no	—
371	C₃×C₄⋊C₄	—	10	2	no	—
372	C₃×C₄⋊C₄	—	10	2	no	—
373	C₃×C₂²⋊C₄	—	5	2	no	—
374	C₃×C₂²⋊C₄	—	10	2	no	—
375	C₃×C₂²⋊C₄	—	10	1	no	—
376	C₃×C₄²	—	5	2	no	—
377	C₃×C₄²	—	10	1	no	—
378	C₃×C₄²	—	10	2	no	—
379	C₃×C₄²	—	10	2	no	—
380	C₃×C₄²	—	10	2	no	—
381	C₂²×D₅	—	2	1	no	—
382	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
383	C₂×AGL(1,𝔽₅)	—	2	1	no	—
384	C₂×AGL(1,𝔽₅)	—	2	1	no	—
385	C₂×AGL(1,𝔽₅)	—	2	2	no	—
386	C₂×AGL(1,𝔽₅)	—	8	2	no	—
387	C₂×AGL(1,𝔽₅)	—	8	1	no	—
388	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	2	yes	—
389	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	2	yes	—
390	C₅×Q₈	—	2	1	no	—
391	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
392	C₅×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
393	C₅×D₄	—	2	1	no	—
394	C₅×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
398	C₂²⋊D₅	—	2	1	no	—
399	C₂²⋊D₅	—	2	1	no	—
400	C₂²⋊D₅	—	2	1	no	—
401	C₂×Dic₅	—	2	1	no	—
402	C₂×Dic₅	—	2	1	no	—
403	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
404	D₂₀	—	2	1	no	—
405	D₂₀	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₄×D₅	—	2	2	no	—
407	C₄×D₅	—	2	1	no	—
408	C₄×D₅	—	2	2	no	—
409	C₄×D₅	—	2	1	no	—
410	C₄×D₅	—	2	1	no	—
411	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
412	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
413	C₄×D₅	C₃×#41	1	1	yes	characteristic
414	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
415	Dic₁₀	—	2	1	no	—
416	Dic₁₀	—	2	2	no	—
417	Dic₁₀	—	2	2	no	—
418	Dic₁₀	—	2	1	no	—
419	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
420	Dic₁₀	C₂²×C₃×C₄	1	1	yes	characteristic
421	#170	—	2	1	no	—
422	#170	—	2	1	no	—
423	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
424	#168	C₂²×C₃×C₄	1	2	yes	—
425	C₂×#41	—	5	1	no	—
426	C₂²×Q₈	—	5	1	no	—
427	#137	—	5	1	no	—
428	#137	—	5	1	no	—
429	#137	—	5	2	no	—
430	#137	—	5	2	no	—
431	#137	—	5	1	no	—
432	#137	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
433	C₂×Q₁₆	—	5	2	no	—
434	C₂×SD₁₆	—	5	2	no	—
435	C₂×M₁₆	—	5	1	no	—
436	C₂²×C₈	—	5	1	no	—
437	C₄×Q₈	—	5	2	no	—
438	C₄×Q₈	—	5	2	no	—
439	C₄×Q₈	—	5	2	no	—
440	C₄×Q₈	—	10	1	no	—
441	C₄×Q₈	—	10	1	no	—
442	C₄×D₄	—	5	2	no	—
443	C₄×D₄	—	10	2	no	—
444	#117	—	5	1	no	—
445	#117	—	5	1	no	—
446	#117	—	10	2	no	—
447	#117	—	10	1	no	—
448	C₂×C₄⋊C₄	—	5	1	no	—
449	C₂×C₄⋊C₄	—	10	1	no	—
450	#107	—	5	2	no	—
451	#106	—	5	2	no	—
452	#103	—	5	2	no	—
453	#103	—	5	2	no	—
454	#103	—	5	1	no	—
455	#103	—	5	1	no	—
456	#102	—	5	1	no	—
457	#102	—	5	1	no	—
458	#97	—	5	2	no	—
459	C₄×C₈	—	5	2	no	—
460	C₂×C₃×C₅	—	2	1	no	—
461	C₂×C₃×C₅	—	4	1	no	—
462	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
463	C₃×D₅	—	2	1	no	—
464	C₃×D₅	—	4	1	no	—
465	C₃×D₅	#577	1	1	yes	characteristic
466	C₃×D₅	#578	1	1	yes	characteristic
467	C₂³×C₃	—	5	1	no	—
468	C₂³×C₃	—	10	1	no	—
469	C₃×Q₈	—	2	1	no	—
470	C₃×Q₈	—	5	2	no	—
471	C₃×Q₈	—	5	1	no	—
472	C₃×Q₈	—	10	2	no	—
473	C₃×Q₈	—	10	2	no	—
474	C₃×Q₈	—	10	1	no	—
475	C₃×Q₈	—	10	1	no	—
476	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
477	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₃×D₄	—	2	1	no	—
479	C₃×D₄	—	5	1	no	—
480	C₃×D₄	—	10	1	no	—
481	C₃×D₄	—	10	1	no	—
482	C₃×D₄	—	10	1	no	—
483	C₃×D₄	—	10	1	no	—
484	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	5	1	no	—
488	C₂×C₃×C₄	—	5	1	no	—
489	C₂×C₃×C₄	—	5	1	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	5	1	no	—
492	C₂×C₃×C₄	—	5	2	no	—
493	C₂×C₃×C₄	—	5	2	no	—
494	C₂×C₃×C₄	—	10	1	no	—
495	C₂×C₃×C₄	—	10	1	no	—
496	C₂×C₃×C₄	—	10	2	no	—
497	C₂×C₃×C₄	—	10	2	no	—
498	C₂×C₃×C₄	—	10	1	no	—
499	C₂×C₃×C₄	—	10	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	—	10	1	no	—
503	C₂×C₃×C₄	—	10	2	no	—
504	C₂×C₃×C₄	—	40	2	no	—
505	C₂×C₃×C₄	—	40	1	no	—
506	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₃×C₈	—	5	2	no	—
508	C₃×C₈	—	10	1	no	—
509	C₃×C₈	—	10	1	no	—
510	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
511	C₂²×C₅	—	2	1	no	—
512	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
513	C₂×D₅	—	2	1	no	—
514	C₂×D₅	—	2	1	no	—
515	C₂×D₅	—	2	1	no	—
516	C₂×D₅	—	4	1	no	—
517	C₂×D₅	—	4	1	no	—
518	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
519	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
520	AGL(1,𝔽₅)	—	2	2	no	—
521	AGL(1,𝔽₅)	—	2	2	no	—
522	AGL(1,𝔽₅)	—	4	1	no	—
523	AGL(1,𝔽₅)	—	4	2	no	—
524	AGL(1,𝔽₅)	—	4	1	no	—
525	C₄×C₅	—	2	2	no	—
526	C₄×C₅	—	2	1	no	—
527	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
528	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
529	Dic₅	—	2	2	no	—
530	Dic₅	—	2	1	no	—
531	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
532	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
533	#41	—	5	1	no	—
534	#41	—	5	1	no	—
535	#41	—	5	1	no	—
536	#41	—	10	1	no	—
537	#41	—	10	1	no	—
538	#41	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
539	C₂×Q₈	—	5	2	no	—
540	C₂×Q₈	—	5	1	no	—
541	C₂×Q₈	—	5	2	no	—
542	C₂×Q₈	—	5	1	no	—
543	C₂×Q₈	—	10	1	no	—
544	C₂×Q₈	—	10	1	no	—
545	C₂×Q₈	—	10	1	no	—
546	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
547	C₂×D₄	—	5	1	no	—
548	C₂×D₄	—	10	1	no	—
549	C₂²×C₄	—	5	1	no	—
550	C₂²×C₄	—	10	1	no	—
551	C₂²×C₄	—	10	1	no	—
552	C₂²×C₄	—	10	2	no	—
553	C₂²×C₄	—	10	1	no	—
554	Q₁₆	—	5	2	no	—
555	Q₁₆	—	5	2	no	—
556	Q₁₆	—	5	2	no	—
557	Q₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
558	SD₁₆	—	5	2	no	—
559	SD₁₆	—	5	2	no	—
560	SD₁₆	—	5	2	no	—
561	SD₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
562	M₁₆	—	5	1	no	—
563	M₁₆	—	5	2	no	—
564	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
565	C₂×C₈	—	5	2	no	—
566	C₂×C₈	—	5	1	no	—
567	C₂×C₈	—	5	1	no	—
568	C₂×C₈	—	10	1	no	—
569	C₂×C₈	—	10	1	no	—
570	C₄⋊C₄	—	5	1	no	—
571	C₄⋊C₄	—	5	1	no	—
572	C₄⋊C₄	—	5	1	no	—
573	C₄⋊C₄	—	5	1	no	—
574	C₄⋊C₄	—	5	2	no	—
575	C₄⋊C₄	—	10	1	no	—
576	C₄⋊C₄	—	10	2	no	—
577	C₄⋊C₄	—	10	2	no	—
578	C₄⋊C₄	—	10	2	no	—
579	C₂²⋊C₄	—	5	2	no	—
580	C₂²⋊C₄	—	10	2	no	—
581	C₂²⋊C₄	—	10	1	no	—
582	C₄²	—	5	2	no	—
583	C₄²	—	10	1	no	—
584	C₄²	—	10	2	no	—
585	C₄²	—	10	2	no	—
586	C₄²	—	10	2	no	—
587	C₃×C₅	#2947	1	1	yes	characteristic, complemented, Hall
588	C₂²×C₃	—	2	1	no	—
589	C₂²×C₃	—	5	1	no	—
590	C₂²×C₃	—	5	1	no	—
591	C₂²×C₃	—	10	1	no	—
592	C₂²×C₃	—	10	1	no	—
593	C₂²×C₃	—	10	1	no	—
594	C₂²×C₃	—	20	1	no	—
595	C₂²×C₃	—	20	1	no	—
596	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	2	2	no	—
599	C₃×C₄	—	5	1	no	—
600	C₃×C₄	—	5	1	no	—
601	C₃×C₄	—	10	2	no	—
602	C₃×C₄	—	10	2	no	—
603	C₃×C₄	—	10	1	no	—
604	C₃×C₄	—	10	2	no	—
605	C₃×C₄	—	20	1	no	—
606	C₃×C₄	—	20	1	no	—
607	C₃×C₄	—	20	2	no	—
608	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
609	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
610	C₂×C₅	—	2	1	no	—
611	C₂×C₅	—	4	1	no	—
612	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
613	D₅	—	2	1	no	—
614	D₅	—	4	1	no	—
615	D₅	C₃×#577	1	1	yes	characteristic
616	D₅	C₃×#578	1	1	yes	characteristic
617	C₂³	—	5	1	no	—
618	C₂³	—	10	1	no	—
619	Q₈	—	2	1	no	—
620	Q₈	—	5	2	no	—
621	Q₈	—	5	1	no	—
622	Q₈	—	10	2	no	—
623	Q₈	—	10	2	no	—
624	Q₈	—	10	1	no	—
625	Q₈	—	10	1	no	—
626	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
627	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
628	D₄	—	2	1	no	—
629	D₄	—	5	1	no	—
630	D₄	—	10	1	no	—
631	D₄	—	10	1	no	—
632	D₄	—	10	1	no	—
633	D₄	—	10	1	no	—
634	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	5	1	no	—
638	C₂×C₄	—	5	1	no	—
639	C₂×C₄	—	5	1	no	—
640	C₂×C₄	—	5	1	no	—
641	C₂×C₄	—	5	1	no	—
642	C₂×C₄	—	5	2	no	—
643	C₂×C₄	—	5	2	no	—
644	C₂×C₄	—	10	1	no	—
645	C₂×C₄	—	10	1	no	—
646	C₂×C₄	—	10	2	no	—
647	C₂×C₄	—	10	2	no	—
648	C₂×C₄	—	10	1	no	—
649	C₂×C₄	—	10	1	no	—
650	C₂×C₄	—	10	1	no	—
651	C₂×C₄	—	10	1	no	—
652	C₂×C₄	—	10	1	no	—
653	C₂×C₄	—	10	2	no	—
654	C₂×C₄	—	40	2	no	—
655	C₂×C₄	—	40	1	no	—
656	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
657	C₈	—	5	2	no	—
658	C₈	—	10	1	no	—
659	C₈	—	10	1	no	—
660	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
661	C₂×C₃	—	2	1	no	—
662	C₂×C₃	—	4	1	no	—
663	C₂×C₃	—	5	1	no	—
664	C₂×C₃	—	5	1	no	—
665	C₂×C₃	—	10	1	no	—
666	C₂×C₃	—	20	1	no	—
667	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
668	C₅	C₃×#2947	1	1	yes	characteristic, complemented, Sylow
669	C₂²	—	2	1	no	—
670	C₂²	—	5	1	no	—
671	C₂²	—	5	1	no	—
672	C₂²	—	10	1	no	—
673	C₂²	—	10	1	no	—
674	C₂²	—	10	1	no	—
675	C₂²	—	20	1	no	—
676	C₂²	—	20	1	no	—
677	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	5	1	no	—
681	C₄	—	5	1	no	—
682	C₄	—	10	2	no	—
683	C₄	—	10	2	no	—
684	C₄	—	10	1	no	—
685	C₄	—	10	2	no	—
686	C₄	—	20	2	no	—
687	C₄	—	20	1	no	—
688	C₄	—	20	1	no	—
689	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
690	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
691	C₃	#10617451	1	1	yes	characteristic, direct product factor, Sylow
692	C₂	—	2	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	5	1	no	—
695	C₂	—	5	1	no	—
696	C₂	—	10	1	no	—
697	C₂	—	20	1	no	—
698	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×#137	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×D₅×#41	C₂²
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₃×#137	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2947
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#137

Complements

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

N	H ≅ G/N	type
2. C₃×#66262	C₂	semidirect
5. C₂×C₃×#4009	C₂	semidirect
6. C₃×#65739	C₂	semidirect
7. C₃×Q₁₆×AGL(1,𝔽₅)	C₂	semidirect
8. C₃×#65735	C₂	semidirect
9. C₃×SD₁₆×AGL(1,𝔽₅)	C₂	semidirect
10. C₃×#65728	C₂	semidirect
11. C₃×#65727	C₂	semidirect
12. #10617451	C₃	direct (N × H)
29. C₃×C₅×#137	C₄	semidirect
30. C₃×#4097	C₄	semidirect
31. C₃×#4088	C₄	semidirect
32. C₃×#4064	C₄	semidirect
34. C₃×#4061	C₄	semidirect
36. C₃×#4055	C₄	semidirect
50. #66262	C₂×C₃	semidirect
53. C₂×#4009	C₂×C₃	semidirect
54. #65739	C₂×C₃	semidirect
55. Q₁₆×AGL(1,𝔽₅)	C₂×C₃	semidirect
56. #65735	C₂×C₃	semidirect
57. SD₁₆×AGL(1,𝔽₅)	C₂×C₃	semidirect
58. #65728	C₂×C₃	semidirect
59. #65727	C₂×C₃	semidirect
63. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
67. C₃×Q₈×D₅	C₂×C₄	semidirect
80. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
102. C₃×C₅×Q₁₆	C₂×C₄	semidirect
103. C₃×C₅×SD₁₆	C₂×C₄	semidirect
104. C₃×C₅×M₁₆	C₂×C₄	semidirect
105. C₃×#689	C₂×C₄	semidirect
106. C₃×#689	C₂×C₄	semidirect
107. C₃×#688	C₂×C₄	semidirect
108. C₃×#687	C₂×C₄	semidirect
109. C₃×#681	C₂×C₄	semidirect
110. C₃×Dic₂₀	C₂×C₄	semidirect
111. C₃×#677	C₂×C₄	semidirect
112. C₃×#676	C₂×C₄	semidirect
141. C₅×#137	C₃×C₄	semidirect
142. #4097	C₃×C₄	semidirect
143. #4088	C₃×C₄	semidirect
144. #4064	C₃×C₄	semidirect
146. #4061	C₃×C₄	semidirect
148. #4055	C₃×C₄	semidirect
212. C₃×#137	AGL(1,𝔽₅)	semidirect
243. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
247. Q₈×D₅	C₂×C₃×C₄	semidirect
260. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
282. C₅×Q₁₆	C₂×C₃×C₄	semidirect
283. C₅×SD₁₆	C₂×C₃×C₄	semidirect
284. C₅×M₁₆	C₂×C₃×C₄	semidirect
285. #689	C₂×C₃×C₄	semidirect
286. #689	C₂×C₃×C₄	semidirect
287. #688	C₂×C₃×C₄	semidirect
288. #687	C₂×C₃×C₄	semidirect
289. #681	C₂×C₃×C₄	semidirect
290. Dic₂₀	C₂×C₃×C₄	semidirect
291. #677	C₂×C₃×C₄	semidirect
292. #676	C₂×C₃×C₄	semidirect
340. C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	semidirect
351. C₃×Q₁₆	C₂×AGL(1,𝔽₅)	semidirect
355. C₃×SD₁₆	C₂×AGL(1,𝔽₅)	semidirect
358. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
432. #137	C₃×AGL(1,𝔽₅)	semidirect
546. C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
557. Q₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
561. SD₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
564. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
587. C₃×C₅	#2947	semidirect
668. C₅	C₃×#2947	semidirect
691. C₃	#10617451	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×#66262	2
C₃×D₅×#137	2
C₃×#65794	2
C₂×C₃×#4009	2
C₃×#65739	2
C₃×Q₁₆×AGL(1,𝔽₅)	2
C₃×#65735	2
C₃×SD₁₆×AGL(1,𝔽₅)	2
C₃×#65728	2
C₃×#65727	2
#10617451	3
C₃×#2947	5

Subgroups — C3×#10617451 #14417186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617451 #14417186