Subgroups — C₃×#10617233 #14419163

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65934	C₂	1	1	yes	maximal, characteristic
2	C₃×#65774	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65773	C₂	1	2	yes	maximal, complemented
4	C₃×D₄×#170	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65759	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65709	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65703	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65697	C₂	1	2	yes	maximal, complemented
11	C₃×#65691	C₂	1	2	yes	maximal, complemented
12	#10617233	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#704	C₂²	1	2	yes	—
14	C₂²×C₃×#170	C₂²	1	2	yes	—
15	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
17	C₃×C₅×#121	C₄	1	1	yes	characteristic
18	C₃×#4082	C₄	1	1	yes	characteristic
19	C₃×#4081	C₄	1	2	yes	—
20	C₃×D₄×Dic₅	C₂²	1	2	yes	—
21	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₃×#4070	C₄	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₃×#4036	C₄	1	1	yes	characteristic
25	C₃×#4033	C₂²	1	1	yes	characteristic
26	C₃×#4025	C₄	1	2	yes	—
27	C₃×#4023	C₂²	1	2	yes	—
28	C₃×C₂²⋊#170	C₂²	1	2	yes	—
29	C₃×C₂²⋊#170	C₂²	1	2	yes	—
30	C₃×C₂²⋊#170	C₂²	1	2	yes	—
31	C₃×#4004	C₂²	1	2	yes	—
32	C₃×#4002	C₂²	1	2	yes	—
33	C₃×#4002	C₂²	1	2	yes	—
34	C₃×C₄⋊#170	C₂²	1	2	yes	—
35	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
37	C₃×C₄×#170	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
42	C₃×#2966	—	5	1	no	maximal, Hall
43	#65934	C₂×C₃	1	1	yes	characteristic
44	#65774	C₂×C₃	1	1	yes	characteristic, complemented
45	#65773	C₂×C₃	1	2	yes	complemented
46	D₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
47	D₄×#170	C₂×C₃	1	2	yes	complemented
48	#65759	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
50	#65709	C₂×C₃	1	1	yes	characteristic, complemented
51	#65703	C₂×C₃	1	1	yes	characteristic, complemented
52	#65697	C₂×C₃	1	2	yes	complemented
53	#65691	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
60	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
61	C₃×#704	—	2	4	no	—
62	C₂×C₃×#170	—	2	4	no	—
63	C₂×C₃×#170	—	2	2	no	—
64	C₂×C₃×#170	—	2	2	no	—
65	C₂×C₃×#170	C₂³	1	1	yes	characteristic
66	C₂×C₃×#170	C₂³	1	1	yes	characteristic
67	C₂×C₃×#170	C₂³	1	2	yes	—
68	C₂×C₃×#170	C₂³	1	2	yes	—
69	C₂×C₃×#170	C₂³	1	1	yes	characteristic
70	C₂×C₃×#170	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
74	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
75	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
76	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
77	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
78	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×#683	C₂×C₄	1	2	yes	—
80	C₃×#683	C₂×C₄	1	2	yes	—
81	C₃×#683	C₂×C₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄×Dic₅	C₂³	1	2	yes	—
86	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
87	C₃×#529	—	5	1	no	—
88	C₃×#446	—	5	1	no	—
89	C₃×C₈×Q₈	—	5	1	no	—
90	C₃×#436	—	5	1	no	—
91	C₃×#435	—	5	2	no	—
92	C₃×C₈×D₄	—	5	1	no	—
93	C₃×C₈×D₄	—	5	2	no	—
94	C₃×#433	—	5	2	no	—
95	C₃×#432	—	5	1	no	—
96	C₃×#405	—	5	2	no	—
97	C₂×C₃×C₄×C₈	—	5	1	no	—
98	C₂×#704	C₂²×C₃	1	2	yes	—
99	C₂²×#170	C₂²×C₃	1	2	yes	—
100	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
101	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
102	C₅×#121	C₃×C₄	1	1	yes	characteristic
103	#4082	C₃×C₄	1	1	yes	characteristic
104	#4081	C₃×C₄	1	2	yes	—
105	D₄×Dic₅	C₂²×C₃	1	2	yes	—
106	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
107	#4070	C₃×C₄	1	1	yes	characteristic
108	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
109	#4036	C₃×C₄	1	1	yes	characteristic
110	#4033	C₂²×C₃	1	1	yes	characteristic
111	#4025	C₃×C₄	1	2	yes	—
112	#4023	C₂²×C₃	1	2	yes	—
113	C₂²⋊#170	C₂²×C₃	1	2	yes	—
114	C₂²⋊#170	C₂²×C₃	1	2	yes	—
115	C₂²⋊#170	C₂²×C₃	1	2	yes	—
116	#4004	C₂²×C₃	1	2	yes	—
117	#4002	C₂²×C₃	1	2	yes	—
118	#4002	C₂²×C₃	1	2	yes	—
119	C₄⋊#170	C₂²×C₃	1	2	yes	—
120	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
121	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
122	C₄×#170	C₂²×C₃	1	1	yes	characteristic
123	C₄×#170	C₂²×C₃	1	2	yes	—
124	C₄×#170	C₂²×C₃	1	1	yes	characteristic
125	C₄×#170	C₂²×C₃	1	1	yes	characteristic
126	C₄×#170	C₂²×C₃	1	1	yes	characteristic
127	#2966	—	5	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₅×D₄	—	2	4	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	—	2	1	no	—
138	C₂×C₃×Dic₅	—	2	1	no	—
139	C₂×C₃×Dic₅	—	2	2	no	—
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
145	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
146	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
147	C₃×Dic₁₀	—	2	2	no	—
148	C₃×#170	—	2	1	no	—
149	C₃×#170	—	2	1	no	—
150	C₃×#170	—	2	2	no	—
151	C₃×#170	—	2	2	no	—
152	C₃×#170	#41	1	2	yes	—
153	C₃×#170	#41	1	2	yes	—
154	C₂×C₃×M₁₆	—	5	2	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	1	no	—
157	C₂²×C₃×C₈	—	5	2	no	—
158	C₃×#126	—	5	2	no	—
159	C₃×#125	—	5	1	no	—
160	C₃×#124	—	5	1	no	—
161	C₃×#123	—	5	2	no	—
162	C₃×C₂²⋊Q₈	—	5	1	no	—
163	C₃×#121	AGL(1,𝔽₅)	1	1	yes	characteristic
164	C₃×C₄×Q₈	—	5	1	no	—
165	C₃×C₄×D₄	—	5	2	no	—
166	C₃×C₄×D₄	—	5	1	no	—
167	C₃×#117	—	5	2	no	—
168	C₂×C₃×C₄²	—	5	1	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×C₄⋊C₈	—	5	1	no	—
171	C₃×C₄⋊C₈	—	5	2	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₂²⋊C₈	—	5	2	no	—
174	C₃×C₂²⋊C₈	—	5	2	no	—
175	C₃×C₂²⋊C₈	—	5	2	no	—
176	C₃×#97	—	5	2	no	—
177	C₃×#97	—	5	2	no	—
178	C₃×C₄×C₈	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	—	5	1	no	—
181	C₃×C₄×C₈	—	5	1	no	—
182	C₃×C₄×C₈	—	5	2	no	—
183	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
184	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
188	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
189	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
190	#704	—	2	4	no	—
191	C₂×#170	—	2	4	no	—
192	C₂×#170	—	2	2	no	—
193	C₂×#170	—	2	2	no	—
194	C₂×#170	C₂³×C₃	1	1	yes	characteristic
195	C₂×#170	C₂³×C₃	1	1	yes	characteristic
196	C₂×#170	C₂³×C₃	1	2	yes	—
197	C₂×#170	C₂³×C₃	1	2	yes	—
198	C₂×#170	C₂³×C₃	1	1	yes	characteristic
199	C₂×#170	C₂³×C₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
201	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
202	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
203	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
204	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
205	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
206	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
207	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
208	#683	C₂×C₃×C₄	1	2	yes	—
209	#683	C₂×C₃×C₄	1	2	yes	—
210	#683	C₂×C₃×C₄	1	2	yes	—
211	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
212	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
214	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
215	C₄×Dic₅	C₂³×C₃	1	2	yes	—
216	#529	—	5	1	no	—
217	#446	—	5	1	no	—
218	C₈×Q₈	—	5	1	no	—
219	#436	—	5	1	no	—
220	#435	—	5	2	no	—
221	C₈×D₄	—	5	1	no	—
222	C₈×D₄	—	5	2	no	—
223	#433	—	5	2	no	—
224	#432	—	5	1	no	—
225	#405	—	5	2	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂²×C₃×C₅	—	2	1	no	—
228	C₂²×C₃×C₅	—	2	1	no	—
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	—	2	2	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	#131	1	2	yes	—
233	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	#131	1	2	yes	—
237	C₃×Dic₅	—	2	1	no	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	2	2	no	—
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	—	2	1	no	—
242	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
243	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
244	C₂×C₃×Q₈	—	5	1	no	—
245	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
246	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
247	C₂²×C₃×C₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	5	2	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
251	C₃×M₁₆	—	10	4	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	2	no	—
257	C₂×C₃×C₈	—	5	2	no	—
258	C₂×C₃×C₈	—	10	2	no	—
259	C₂×C₃×C₈	—	10	4	no	—
260	C₂×C₃×C₈	—	10	2	no	—
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₄⋊C₄	—	5	2	no	—
263	C₃×C₄⋊C₄	—	5	2	no	—
264	C₃×C₄⋊C₄	—	5	1	no	—
265	C₃×C₄⋊C₄	—	5	2	no	—
266	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₃×C₂²⋊C₄	—	5	2	no	—
268	C₃×C₂²⋊C₄	—	5	2	no	—
269	C₃×C₂²⋊C₄	—	5	2	no	—
270	C₃×C₂²⋊C₄	—	5	2	no	—
271	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
272	C₃×C₄²	—	5	1	no	—
273	C₃×C₄²	—	5	1	no	—
274	C₃×C₄²	—	5	1	no	—
275	C₃×C₄²	—	5	1	no	—
276	C₃×C₄²	—	5	2	no	—
277	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
278	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₅×D₄	—	2	4	no	—
280	C₅×D₄	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
284	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	2	1	no	—
287	C₂×Dic₅	—	2	1	no	—
288	C₂×Dic₅	—	2	2	no	—
289	C₂×Dic₅	—	2	2	no	—
290	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
291	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
292	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
293	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
294	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
295	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
296	Dic₁₀	—	2	2	no	—
297	#170	—	2	1	no	—
298	#170	—	2	1	no	—
299	#170	—	2	2	no	—
300	#170	—	2	2	no	—
301	#170	C₃×#41	1	2	yes	—
302	#170	C₃×#41	1	2	yes	—
303	C₂×M₁₆	—	5	2	no	—
304	C₂²×C₈	—	5	1	no	—
305	C₂²×C₈	—	5	1	no	—
306	C₂²×C₈	—	5	2	no	—
307	#126	—	5	2	no	—
308	#125	—	5	1	no	—
309	#124	—	5	1	no	—
310	#123	—	5	2	no	—
311	C₂²⋊Q₈	—	5	1	no	—
312	#121	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₄×Q₈	—	5	1	no	—
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	5	1	no	—
316	#117	—	5	2	no	—
317	C₂×C₄²	—	5	1	no	—
318	C₄⋊C₈	—	5	1	no	—
319	C₄⋊C₈	—	5	1	no	—
320	C₄⋊C₈	—	5	2	no	—
321	C₄⋊C₈	—	5	2	no	—
322	C₂²⋊C₈	—	5	2	no	—
323	C₂²⋊C₈	—	5	2	no	—
324	C₂²⋊C₈	—	5	2	no	—
325	#97	—	5	2	no	—
326	#97	—	5	2	no	—
327	C₄×C₈	—	5	1	no	—
328	C₄×C₈	—	5	1	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	2	no	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	—	4	2	no	—
334	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
337	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
338	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
339	C₃×Q₈	—	10	2	no	—
340	C₃×D₄	—	2	4	no	—
341	C₃×D₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	5	1	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	5	1	no	—
346	C₂×C₃×C₄	—	5	1	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	5	2	no	—
349	C₂×C₃×C₄	—	10	1	no	—
350	C₂×C₃×C₄	—	10	1	no	—
351	C₂×C₃×C₄	—	10	2	no	—
352	C₂×C₃×C₄	—	10	2	no	—
353	C₂×C₃×C₄	—	10	2	no	—
354	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
356	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
357	C₃×C₈	—	5	2	no	—
358	C₃×C₈	—	5	2	no	—
359	C₃×C₈	—	10	1	no	—
360	C₃×C₈	—	10	1	no	—
361	C₃×C₈	—	10	2	no	—
362	C₃×C₈	—	10	2	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	C₃×#131	1	2	yes	—
369	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	C₃×#131	1	2	yes	—
373	Dic₅	—	2	2	no	—
374	Dic₅	—	2	1	no	—
375	Dic₅	—	2	1	no	—
376	Dic₅	—	2	1	no	—
377	Dic₅	—	2	2	no	—
378	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
379	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
380	C₂×Q₈	—	5	1	no	—
381	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
382	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₂²×C₄	—	5	1	no	—
384	C₂²×C₄	—	5	2	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
387	M₁₆	—	10	4	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	5	2	no	—
393	C₂×C₈	—	5	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	4	no	—
396	C₂×C₈	—	10	2	no	—
397	C₄⋊C₄	—	5	2	no	—
398	C₄⋊C₄	—	5	2	no	—
399	C₄⋊C₄	—	5	1	no	—
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	—	5	2	no	—
402	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₂²⋊C₄	—	5	2	no	—
404	C₂²⋊C₄	—	5	2	no	—
405	C₂²⋊C₄	—	5	2	no	—
406	C₂²⋊C₄	—	5	2	no	—
407	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
408	C₄²	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	2	no	—
411	C₄²	—	5	1	no	—
412	C₄²	—	5	1	no	—
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	2	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	#4131	1	2	yes	—
420	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	5	1	no	—
424	C₃×C₄	—	5	1	no	—
425	C₃×C₄	—	10	1	no	—
426	C₃×C₄	—	10	1	no	—
427	C₃×C₄	—	10	2	no	—
428	C₃×C₄	—	10	1	no	—
429	C₃×C₄	—	10	2	no	—
430	C₃×C₄	#4131	1	2	yes	—
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	4	2	no	—
433	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
434	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
435	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
436	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
437	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
438	Q₈	—	10	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	1	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	5	2	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	1	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	10	2	no	—
453	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
455	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
456	C₈	—	5	2	no	—
457	C₈	—	5	2	no	—
458	C₈	—	10	1	no	—
459	C₈	—	10	1	no	—
460	C₈	—	10	2	no	—
461	C₈	—	10	2	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	—	4	2	no	—
464	C₂×C₃	C₂×#4131	1	1	yes	characteristic
465	C₂×C₃	C₂×#4131	1	1	yes	characteristic
466	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₅	C₃×#2966	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	C₃×#4131	1	2	yes	—
474	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	2	no	—
477	C₄	—	5	1	no	—
478	C₄	—	5	1	no	—
479	C₄	—	10	1	no	—
480	C₄	—	10	1	no	—
481	C₄	—	10	2	no	—
482	C₄	—	10	1	no	—
483	C₄	—	10	2	no	—
484	C₄	C₃×#4131	1	2	yes	—
485	C₃	#10617233	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	4	2	no	—
488	C₂	C₂×C₃×#4131	1	1	yes	characteristic
489	C₂	C₂×C₃×#4131	1	1	yes	characteristic
490	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting, prime radical	C₃×C₅×#121	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#121	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2966
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
2. C₃×#65774	C₂	semidirect
3. C₃×#65773	C₂	semidirect
4. C₃×D₄×#170	C₂	semidirect
5. C₃×D₄×#170	C₂	semidirect
6. C₃×#65759	C₂	semidirect
7. C₂×C₃×C₄×#170	C₂	semidirect
8. C₃×#65709	C₂	semidirect
9. C₃×#65703	C₂	semidirect
10. C₃×#65697	C₂	semidirect
11. C₃×#65691	C₂	semidirect
12. #10617233	C₃	direct (N × H)
44. #65774	C₂×C₃	semidirect
45. #65773	C₂×C₃	semidirect
46. D₄×#170	C₂×C₃	semidirect
47. D₄×#170	C₂×C₃	semidirect
48. #65759	C₂×C₃	semidirect
49. C₂×C₄×#170	C₂×C₃	semidirect
50. #65709	C₂×C₃	semidirect
51. #65703	C₂×C₃	semidirect
52. #65697	C₂×C₃	semidirect
53. #65691	C₂×C₃	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	C₃×#2966	semidirect
485. C₃	#10617233	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×#65934	2
C₃×#65774	2
C₃×#65773	2
C₃×D₄×#170	2
C₃×#65759	2
C₂×C₃×C₄×#170	2
C₃×#65709	2
C₃×#65703	2
C₃×#65697	2
C₃×#65691	2
#10617233	3
C₃×#2966	5

Subgroups — C3×#10617233 #14419163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617233 #14419163