Subgroups — C₃×#10617116 #14418991

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65856	C₂	1	1	yes	maximal, characteristic
2	C₃×#65754	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#704	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65707	C₂	1	2	yes	maximal, complemented
5	C₃×#65704	C₂	1	2	yes	maximal, complemented
6	C₃×#65695	C₂	1	2	yes	maximal, complemented
7	C₃×#65694	C₂	1	2	yes	maximal, complemented
8	C₃×#65680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65678	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×#700	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617116	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₄	1	1	yes	characteristic
14	C₂×C₃×#704	C₂²	1	2	yes	—
15	C₂×C₃×#700	C₂²	1	2	yes	—
16	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
17	C₃×C₅×#117	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₃×#4039	C₄	1	1	yes	characteristic
20	C₃×#4039	C₂²	1	1	yes	characteristic
21	C₃×#4033	C₄	1	1	yes	characteristic
22	C₃×#4033	C₂²	1	1	yes	characteristic
23	C₃×#4027	C₄	1	1	yes	characteristic
24	C₃×#4027	C₄	1	1	yes	characteristic
25	C₃×#4027	C₂²	1	1	yes	characteristic
26	C₃×#4027	C₂²	1	1	yes	characteristic
27	C₃×#4018	C₄	1	1	yes	characteristic
28	C₃×#4018	C₄	1	1	yes	characteristic
29	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊#170	C₂²	1	2	yes	—
32	C₃×#4004	C₂²	1	2	yes	—
33	C₃×#4004	C₂²	1	2	yes	—
34	C₃×#4003	C₂²	1	2	yes	—
35	C₃×#4003	C₂²	1	2	yes	—
36	C₃×#4002	C₂²	1	2	yes	—
37	C₃×#4002	C₂²	1	2	yes	—
38	C₃×C₄⋊#170	C₂²	1	2	yes	—
39	C₃×C₄×#170	C₂²	1	1	yes	characteristic
40	C₃×C₄×#170	C₂²	1	1	yes	characteristic
41	C₃×C₄×#170	C₂²	1	2	yes	—
42	C₃×C₄×#170	C₂²	1	1	yes	characteristic
43	C₃×C₄×#170	C₂²	1	1	yes	characteristic
44	C₃×#2965	—	5	1	no	maximal, Hall
45	#65856	C₂×C₃	1	1	yes	characteristic
46	#65754	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#704	C₂×C₃	1	1	yes	characteristic, complemented
48	#65707	C₂×C₃	1	2	yes	complemented
49	#65704	C₂×C₃	1	2	yes	complemented
50	#65695	C₂×C₃	1	2	yes	complemented
51	#65694	C₂×C₃	1	2	yes	complemented
52	#65680	C₂×C₃	1	1	yes	characteristic, complemented
53	#65678	C₂×C₃	1	1	yes	characteristic, complemented
54	C₄×#700	C₂×C₃	1	1	yes	characteristic, complemented
55	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
61	C₃×#709	—	2	4	no	—
62	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
70	C₃×#704	—	2	4	no	—
71	C₂×C₃×#170	C₂³	1	2	yes	—
72	C₂×C₃×#170	C₂³	1	2	yes	—
73	C₂×C₃×#170	C₂³	1	2	yes	—
74	C₂×C₃×#170	C₂³	1	2	yes	—
75	C₃×#700	—	2	4	no	—
76	C₃×D₅⋊C₈	—	2	4	no	—
77	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
83	C₃×#685	C₂×C₄	1	1	yes	characteristic
84	C₃×#685	C₂×C₄	1	1	yes	characteristic
85	C₃×#685	C₂×C₄	1	1	yes	characteristic
86	C₃×#685	C₂×C₄	1	1	yes	characteristic
87	C₃×#683	C₂×C₄	1	1	yes	characteristic
88	C₃×#683	C₂×C₄	1	1	yes	characteristic
89	C₃×#683	C₂×C₄	1	1	yes	characteristic
90	C₃×#683	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
96	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
97	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
98	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
99	C₃×C₄×#41	—	5	1	no	—
100	C₃×#446	—	5	2	no	—
101	C₃×#436	—	5	2	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×#435	—	5	2	no	—
104	C₃×#431	—	5	1	no	—
105	C₃×#431	—	5	1	no	—
106	C₃×#431	—	5	1	no	—
107	C₃×C₄×M₁₆	—	5	1	no	—
108	C₃×C₄×M₁₆	—	5	1	no	—
109	C₂×C₃×C₄×C₈	—	5	1	no	—
110	C₂×#709	C₃×C₄	1	1	yes	characteristic
111	C₂×#704	C₂²×C₃	1	2	yes	—
112	C₂×#700	C₂²×C₃	1	2	yes	—
113	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
114	C₅×#117	C₃×C₄	1	1	yes	characteristic
115	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
116	#4039	C₃×C₄	1	1	yes	characteristic
117	#4039	C₂²×C₃	1	1	yes	characteristic
118	#4033	C₃×C₄	1	1	yes	characteristic
119	#4033	C₂²×C₃	1	1	yes	characteristic
120	#4027	C₃×C₄	1	1	yes	characteristic
121	#4027	C₃×C₄	1	1	yes	characteristic
122	#4027	C₂²×C₃	1	1	yes	characteristic
123	#4027	C₂²×C₃	1	1	yes	characteristic
124	#4018	C₃×C₄	1	1	yes	characteristic
125	#4018	C₃×C₄	1	1	yes	characteristic
126	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
127	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
128	C₂²⋊#170	C₂²×C₃	1	2	yes	—
129	#4004	C₂²×C₃	1	2	yes	—
130	#4004	C₂²×C₃	1	2	yes	—
131	#4003	C₂²×C₃	1	2	yes	—
132	#4003	C₂²×C₃	1	2	yes	—
133	#4002	C₂²×C₃	1	2	yes	—
134	#4002	C₂²×C₃	1	2	yes	—
135	C₄⋊#170	C₂²×C₃	1	2	yes	—
136	C₄×#170	C₂²×C₃	1	1	yes	characteristic
137	C₄×#170	C₂²×C₃	1	1	yes	characteristic
138	C₄×#170	C₂²×C₃	1	2	yes	—
139	C₄×#170	C₂²×C₃	1	1	yes	characteristic
140	C₄×#170	C₂²×C₃	1	1	yes	characteristic
141	#2965	—	5	1	no	Sylow
142	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₃×C₂²⋊D₅	—	2	2	no	—
153	C₃×C₂²⋊D₅	—	2	2	no	—
154	C₂×C₃×Dic₅	—	2	2	no	—
155	C₂×C₃×Dic₅	—	2	2	no	—
156	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
162	C₃×D₂₀	—	2	2	no	—
163	C₃×C₄×D₅	—	2	2	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	2	no	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×C₄×D₅	—	2	2	no	—
168	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
169	C₃×Dic₁₀	—	2	2	no	—
170	C₃×#170	—	2	2	no	—
171	C₃×#170	—	2	2	no	—
172	C₃×#170	—	2	2	no	—
173	C₃×#170	#41	1	4	yes	complemented
174	C₂×C₃×#41	—	5	1	no	—
175	C₂×C₃×M₁₆	—	5	2	no	—
176	C₂×C₃×M₁₆	—	5	2	no	—
177	C₂²×C₃×C₈	—	5	2	no	—
178	C₃×C₄×Q₈	—	5	1	no	—
179	C₃×C₄×Q₈	—	5	1	no	—
180	C₃×C₄×D₄	—	5	1	no	—
181	C₃×C₄×D₄	—	5	1	no	—
182	C₃×C₄×D₄	—	5	1	no	—
183	C₃×C₄×D₄	—	5	1	no	—
184	C₃×C₄×D₄	—	5	1	no	—
185	C₃×C₄×D₄	—	5	1	no	—
186	C₃×#117	—	5	1	no	—
187	C₃×#117	—	5	1	no	—
188	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic
189	C₂×C₃×C₄²	—	5	1	no	—
190	C₂×C₃×C₄²	—	5	1	no	—
191	C₂×C₃×C₄²	—	5	1	no	—
192	C₃×C₄⋊C₈	—	5	2	no	—
193	C₃×C₄⋊C₈	—	5	2	no	—
194	C₃×C₄⋊C₈	—	5	2	no	—
195	C₃×C₂²⋊C₈	—	5	2	no	—
196	C₃×C₂²⋊C₈	—	5	2	no	—
197	C₃×C₂²⋊C₈	—	5	2	no	—
198	C₃×#97	—	5	2	no	—
199	C₃×#97	—	5	2	no	—
200	C₃×C₄×C₈	—	5	1	no	—
201	C₃×C₄×C₈	—	5	1	no	—
202	C₃×C₄×C₈	—	5	2	no	—
203	C₃×C₄×C₈	—	5	1	no	—
204	C₃×C₄×C₈	—	5	1	no	—
205	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
210	#709	—	2	4	no	—
211	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
212	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
214	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
219	#704	—	2	4	no	—
220	C₂×#170	C₂³×C₃	1	2	yes	—
221	C₂×#170	C₂³×C₃	1	2	yes	—
222	C₂×#170	C₂³×C₃	1	2	yes	—
223	C₂×#170	C₂³×C₃	1	2	yes	—
224	#700	—	2	4	no	—
225	D₅⋊C₈	—	2	4	no	—
226	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
227	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
228	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
229	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
230	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
231	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
232	#685	C₂×C₃×C₄	1	1	yes	characteristic
233	#685	C₂×C₃×C₄	1	1	yes	characteristic
234	#685	C₂×C₃×C₄	1	1	yes	characteristic
235	#685	C₂×C₃×C₄	1	1	yes	characteristic
236	#683	C₂×C₃×C₄	1	1	yes	characteristic
237	#683	C₂×C₃×C₄	1	1	yes	characteristic
238	#683	C₂×C₃×C₄	1	1	yes	characteristic
239	#683	C₂×C₃×C₄	1	1	yes	characteristic
240	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
241	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
242	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
243	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
244	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
245	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
246	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
247	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
248	C₄×#41	—	5	1	no	—
249	#446	—	5	2	no	—
250	#436	—	5	2	no	—
251	#435	—	5	2	no	—
252	#435	—	5	2	no	—
253	#431	—	5	1	no	—
254	#431	—	5	1	no	—
255	#431	—	5	1	no	—
256	C₄×M₁₆	—	5	1	no	—
257	C₄×M₁₆	—	5	1	no	—
258	C₂×C₄×C₈	—	5	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₃×D₅	—	2	1	no	—
264	C₂×C₃×D₅	—	2	1	no	—
265	C₂×C₃×D₅	—	2	1	no	—
266	C₂×C₃×D₅	—	2	1	no	—
267	C₂×C₃×D₅	—	2	1	no	—
268	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	—	2	1	no	—
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
275	C₃×Dic₅	—	2	1	no	—
276	C₃×Dic₅	—	2	1	no	—
277	C₃×Dic₅	—	2	1	no	—
278	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
279	C₃×Dic₅	#131	1	2	yes	—
280	C₃×Dic₅	C₂×#41	1	2	yes	—
281	C₃×#41	—	10	4	no	—
282	C₂×C₃×Q₈	—	5	1	no	—
283	C₂×C₃×D₄	—	5	1	no	—
284	C₂×C₃×D₄	—	5	1	no	—
285	C₂×C₃×D₄	—	5	1	no	—
286	C₂²×C₃×C₄	—	5	1	no	—
287	C₂²×C₃×C₄	—	5	1	no	—
288	C₂²×C₃×C₄	—	5	1	no	—
289	C₂²×C₃×C₄	—	5	1	no	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₂²×C₃×C₄	—	5	1	no	—
293	C₂²×C₃×C₄	—	5	1	no	—
294	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₃×M₁₆	—	10	4	no	—
296	C₃×M₁₆	—	10	4	no	—
297	C₂×C₃×C₈	—	5	2	no	—
298	C₂×C₃×C₈	—	5	2	no	—
299	C₂×C₃×C₈	—	5	2	no	—
300	C₂×C₃×C₈	—	5	2	no	—
301	C₂×C₃×C₈	—	10	4	no	—
302	C₃×C₄⋊C₄	—	5	1	no	—
303	C₃×C₄⋊C₄	—	5	1	no	—
304	C₃×C₄⋊C₄	—	5	1	no	—
305	C₃×C₄⋊C₄	—	5	1	no	—
306	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	—	5	1	no	—
309	C₃×C₂²⋊C₄	—	5	1	no	—
310	C₃×C₂²⋊C₄	—	5	1	no	—
311	C₃×C₂²⋊C₄	—	5	1	no	—
312	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₃×C₄²	—	5	1	no	—
315	C₃×C₄²	—	5	1	no	—
316	C₃×C₄²	—	5	1	no	—
317	C₃×C₄²	—	5	1	no	—
318	C₃×C₄²	—	5	1	no	—
319	C₃×C₄²	—	5	1	no	—
320	C₃×C₄²	—	5	1	no	—
321	C₃×C₄²	—	5	1	no	—
322	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
323	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
325	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
334	C₂²⋊D₅	—	2	2	no	—
335	C₂²⋊D₅	—	2	2	no	—
336	C₂×Dic₅	—	2	2	no	—
337	C₂×Dic₅	—	2	2	no	—
338	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
340	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
341	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
343	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
344	D₂₀	—	2	2	no	—
345	C₄×D₅	—	2	2	no	—
346	C₄×D₅	—	2	2	no	—
347	C₄×D₅	—	2	2	no	—
348	C₄×D₅	—	2	2	no	—
349	C₄×D₅	—	2	2	no	—
350	C₄×D₅	C₃×M₁₆	1	4	yes	complemented
351	Dic₁₀	—	2	2	no	—
352	#170	—	2	2	no	—
353	#170	—	2	2	no	—
354	#170	—	2	2	no	—
355	#170	C₃×#41	1	4	yes	complemented
356	C₂×#41	—	5	1	no	—
357	C₂×M₁₆	—	5	2	no	—
358	C₂×M₁₆	—	5	2	no	—
359	C₂²×C₈	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×D₄	—	5	1	no	—
363	C₄×D₄	—	5	1	no	—
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	5	1	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	5	1	no	—
368	#117	—	5	1	no	—
369	#117	—	5	1	no	—
370	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₂×C₄²	—	5	1	no	—
372	C₂×C₄²	—	5	1	no	—
373	C₂×C₄²	—	5	1	no	—
374	C₄⋊C₈	—	5	2	no	—
375	C₄⋊C₈	—	5	2	no	—
376	C₄⋊C₈	—	5	2	no	—
377	C₂²⋊C₈	—	5	2	no	—
378	C₂²⋊C₈	—	5	2	no	—
379	C₂²⋊C₈	—	5	2	no	—
380	#97	—	5	2	no	—
381	#97	—	5	2	no	—
382	C₄×C₈	—	5	1	no	—
383	C₄×C₈	—	5	1	no	—
384	C₄×C₈	—	5	2	no	—
385	C₄×C₈	—	5	1	no	—
386	C₄×C₈	—	5	1	no	—
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
391	C₃×D₅	—	2	2	no	—
392	C₃×D₅	—	4	1	no	—
393	C₂³×C₃	—	5	1	no	—
394	C₂³×C₃	—	5	1	no	—
395	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
396	C₃×Q₈	—	10	2	no	—
397	C₃×D₄	—	10	2	no	—
398	C₃×D₄	—	10	2	no	—
399	C₃×D₄	—	10	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	5	1	no	—
402	C₂×C₃×C₄	—	5	1	no	—
403	C₂×C₃×C₄	—	5	1	no	—
404	C₂×C₃×C₄	—	5	4	no	—
405	C₂×C₃×C₄	—	5	1	no	—
406	C₂×C₃×C₄	—	5	1	no	—
407	C₂×C₃×C₄	—	5	1	no	—
408	C₂×C₃×C₄	—	10	2	no	—
409	C₂×C₃×C₄	—	10	2	no	—
410	C₂×C₃×C₄	—	10	2	no	—
411	C₂×C₃×C₄	—	10	2	no	—
412	C₂×C₃×C₄	—	10	2	no	—
413	C₂×C₃×C₄	—	10	2	no	—
414	C₂×C₃×C₄	—	10	2	no	—
415	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₃×C₈	—	5	4	no	—
422	C₃×C₈	—	10	2	no	—
423	C₃×C₈	—	10	2	no	—
424	C₃×C₈	—	10	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	2	1	no	—
433	C₂×D₅	—	2	1	no	—
434	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
441	Dic₅	—	2	1	no	—
442	Dic₅	—	2	1	no	—
443	Dic₅	—	2	1	no	—
444	Dic₅	C₂×C₃×M₁₆	1	2	yes	—
445	Dic₅	C₃×#131	1	2	yes	—
446	Dic₅	C₂×C₃×#41	1	2	yes	—
447	#41	—	10	4	no	—
448	C₂×Q₈	—	5	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	—	5	1	no	—
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	1	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
461	M₁₆	—	10	4	no	—
462	M₁₆	—	10	4	no	—
463	C₂×C₈	—	5	2	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	5	2	no	—
466	C₂×C₈	—	5	2	no	—
467	C₂×C₈	—	10	4	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
473	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
474	C₂²⋊C₄	—	5	1	no	—
475	C₂²⋊C₄	—	5	1	no	—
476	C₂²⋊C₄	—	5	1	no	—
477	C₂²⋊C₄	—	5	1	no	—
478	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
480	C₄²	—	5	1	no	—
481	C₄²	—	5	1	no	—
482	C₄²	—	5	1	no	—
483	C₄²	—	5	1	no	—
484	C₄²	—	5	1	no	—
485	C₄²	—	5	1	no	—
486	C₄²	—	5	1	no	—
487	C₄²	—	5	1	no	—
488	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
489	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
490	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	5	2	no	—
495	C₂²×C₃	—	10	1	no	—
496	C₂²×C₃	—	10	1	no	—
497	C₂²×C₃	—	10	1	no	—
498	C₂²×C₃	—	10	1	no	—
499	C₂²×C₃	—	10	1	no	—
500	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	5	2	no	—
507	C₃×C₄	—	5	2	no	—
508	C₃×C₄	—	5	2	no	—
509	C₃×C₄	—	10	1	no	—
510	C₃×C₄	—	10	1	no	—
511	C₃×C₄	—	10	1	no	—
512	C₃×C₄	D₅⋊M₁₆	1	2	yes	—
513	C₂×C₅	—	4	1	no	—
514	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
515	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
516	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
517	D₅	—	2	2	no	—
518	D₅	—	4	1	no	—
519	C₂³	—	5	1	no	—
520	C₂³	—	5	1	no	—
521	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
522	Q₈	—	10	2	no	—
523	D₄	—	10	2	no	—
524	D₄	—	10	2	no	—
525	D₄	—	10	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	5	1	no	—
528	C₂×C₄	—	5	1	no	—
529	C₂×C₄	—	5	1	no	—
530	C₂×C₄	—	5	4	no	—
531	C₂×C₄	—	5	1	no	—
532	C₂×C₄	—	5	1	no	—
533	C₂×C₄	—	5	1	no	—
534	C₂×C₄	—	10	2	no	—
535	C₂×C₄	—	10	2	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	2	no	—
538	C₂×C₄	—	10	2	no	—
539	C₂×C₄	—	10	2	no	—
540	C₂×C₄	—	10	2	no	—
541	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
543	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
544	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
545	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
546	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
547	C₈	—	5	4	no	—
548	C₈	—	10	2	no	—
549	C₈	—	10	2	no	—
550	C₈	—	10	2	no	—
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	—	10	2	no	—
553	C₂×C₃	—	20	1	no	—
554	C₂×C₃	C₂×D₅⋊M₁₆	1	1	yes	characteristic
555	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
556	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
557	C₅	C₃×#2965	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	5	2	no	—
562	C₂²	—	10	1	no	—
563	C₂²	—	10	1	no	—
564	C₂²	—	10	1	no	—
565	C₂²	—	10	1	no	—
566	C₂²	—	10	1	no	—
567	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	5	2	no	—
574	C₄	—	5	2	no	—
575	C₄	—	5	2	no	—
576	C₄	—	10	1	no	—
577	C₄	—	10	1	no	—
578	C₄	—	10	1	no	—
579	C₄	C₃×D₅⋊M₁₆	1	2	yes	—
580	C₃	#10617116	1	1	yes	characteristic, direct product factor, Sylow
581	C₂	—	4	1	no	—
582	C₂	—	10	2	no	—
583	C₂	—	20	1	no	—
584	C₂	C₂×C₃×D₅⋊M₁₆	1	1	yes	characteristic
585	C₂	C₃×D₅⋊#131	1	1	yes	characteristic
586	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#117	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2965
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₃×#65754	C₂	semidirect
3. C₃×C₄×#704	C₂	semidirect
4. C₃×#65707	C₂	semidirect
5. C₃×#65704	C₂	semidirect
6. C₃×#65695	C₂	semidirect
7. C₃×#65694	C₂	semidirect
8. C₃×#65680	C₂	semidirect
9. C₃×#65678	C₂	semidirect
10. C₃×C₄×#700	C₂	semidirect
11. C₃×C₄×D₅⋊C₈	C₂	semidirect
12. #10617116	C₃	direct (N × H)
46. #65754	C₂×C₃	semidirect
47. C₄×#704	C₂×C₃	semidirect
48. #65707	C₂×C₃	semidirect
49. #65704	C₂×C₃	semidirect
50. #65695	C₂×C₃	semidirect
51. #65694	C₂×C₃	semidirect
52. #65680	C₂×C₃	semidirect
53. #65678	C₂×C₃	semidirect
54. C₄×#700	C₂×C₃	semidirect
55. C₄×D₅⋊C₈	C₂×C₃	semidirect
168. C₃×C₄×D₅	M₁₆	semidirect
173. C₃×#170	#41	semidirect
350. C₄×D₅	C₃×M₁₆	semidirect
355. #170	C₃×#41	semidirect
490. C₃×C₅	#2965	semidirect
557. C₅	C₃×#2965	semidirect
580. C₃	#10617116	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×#65856	2
C₃×#65754	2
C₃×C₄×#704	2
C₃×#65707	2
C₃×#65704	2
C₃×#65695	2
C₃×#65694	2
C₃×#65680	2
C₃×#65678	2
C₃×C₄×#700	2
C₃×C₄×D₅⋊C₈	2
#10617116	3
C₃×#2965	5

Subgroups — C3×#10617116 #14418991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617116 #14418991