Subgroups — C₃×#10617312 #14419159

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×#66014	C₂	1	1	yes	maximal, characteristic
2	C₃×#65788	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₈×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65774	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65697	C₂	1	2	yes	maximal, complemented
7	C₃×#65694	C₂	1	2	yes	maximal, complemented
8	C₃×#65692	C₂	1	2	yes	maximal, complemented
9	C₃×#65691	C₂	1	2	yes	maximal, complemented
10	C₃×#65683	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617312	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	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#124	C₄	1	1	yes	characteristic
18	C₃×#4092	C₄	1	1	yes	characteristic
19	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
20	C₃×#4084	C₄	1	1	yes	characteristic
21	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₃×#4029	C₄	1	2	yes	—
23	C₃×#4027	C₂²	1	2	yes	—
24	C₃×#4025	C₄	1	2	yes	—
25	C₃×#4023	C₂²	1	2	yes	—
26	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
27	C₃×#4016	C₄	1	1	yes	characteristic
28	C₃×C₂²⋊#170	C₂²	1	2	yes	—
29	C₃×C₂²⋊#170	C₂²	1	2	yes	—
30	C₃×#4004	C₂²	1	2	yes	—
31	C₃×#4003	C₂²	1	2	yes	—
32	C₃×#4002	C₂²	1	2	yes	—
33	C₃×#4002	C₂²	1	2	yes	—
34	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊#170	C₂²	1	2	yes	—
37	C₃×C₄×#170	C₂²	1	1	yes	characteristic
38	C₃×C₄×#170	C₂²	1	1	yes	characteristic
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×#2966	—	5	1	no	maximal, Hall
43	#66014	C₂×C₃	1	1	yes	characteristic
44	#65788	C₂×C₃	1	1	yes	characteristic, complemented
45	Q₈×#170	C₂×C₃	1	1	yes	characteristic, complemented
46	#65774	C₂×C₃	1	1	yes	characteristic, complemented
47	D₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
48	#65697	C₂×C₃	1	2	yes	complemented
49	#65694	C₂×C₃	1	2	yes	complemented
50	#65692	C₂×C₃	1	2	yes	complemented
51	#65691	C₂×C₃	1	2	yes	complemented
52	#65683	C₂×C₃	1	1	yes	characteristic, complemented
53	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
61	C₃×#704	—	2	4	no	—
62	C₂×C₃×#170	—	2	4	no	—
63	C₂×C₃×#170	C₂³	1	1	yes	characteristic
64	C₂×C₃×#170	C₂³	1	1	yes	characteristic
65	C₂×C₃×#170	C₂³	1	2	yes	—
66	C₂×C₃×#170	C₂³	1	2	yes	—
67	C₂×C₃×#170	C₂³	1	1	yes	characteristic
68	C₂×C₃×#170	C₂³	1	1	yes	characteristic
69	C₃×D₅⋊C₈	—	2	2	no	—
70	C₃×D₅⋊C₈	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
75	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
76	C₃×#685	C₂×C₄	1	2	yes	—
77	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
80	C₃×#683	C₂×C₄	1	2	yes	—
81	C₃×#683	C₂×C₄	1	2	yes	—
82	C₃×#683	C₂×C₄	1	2	yes	—
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	2	no	—
93	C₃×C₈×D₄	—	5	1	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	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
101	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×#124	C₃×C₄	1	1	yes	characteristic
103	#4092	C₃×C₄	1	1	yes	characteristic
104	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
105	#4084	C₃×C₄	1	1	yes	characteristic
106	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
107	#4029	C₃×C₄	1	2	yes	—
108	#4027	C₂²×C₃	1	2	yes	—
109	#4025	C₃×C₄	1	2	yes	—
110	#4023	C₂²×C₃	1	2	yes	—
111	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
112	#4016	C₃×C₄	1	1	yes	characteristic
113	C₂²⋊#170	C₂²×C₃	1	2	yes	—
114	C₂²⋊#170	C₂²×C₃	1	2	yes	—
115	#4004	C₂²×C₃	1	2	yes	—
116	#4003	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	1	yes	characteristic
120	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
121	C₄⋊#170	C₂²×C₃	1	2	yes	—
122	C₄×#170	C₂²×C₃	1	1	yes	characteristic
123	C₄×#170	C₂²×C₃	1	1	yes	characteristic
124	C₄×#170	C₂²×C₃	1	1	yes	characteristic
125	C₄×#170	C₂²×C₃	1	1	yes	characteristic
126	C₄×#170	C₂²×C₃	1	2	yes	—
127	#2966	—	5	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₃×C₂²⋊D₅	—	2	4	no	—
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
144	C₃×C₄×D₅	—	2	2	no	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	1	no	—
147	C₃×C₄×D₅	—	2	1	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	AGL(1,𝔽₅)	1	1	yes	characteristic
161	C₃×#123	—	5	2	no	—
162	C₃×C₂²⋊Q₈	—	5	1	no	—
163	C₃×#121	—	5	1	no	—
164	C₃×C₄×Q₈	—	5	1	no	—
165	C₃×C₄×D₄	—	5	1	no	—
166	C₃×C₄×D₄	—	5	2	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×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
185	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
186	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
187	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
189	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
190	#704	—	2	4	no	—
191	C₂×#170	—	2	4	no	—
192	C₂×#170	C₂³×C₃	1	1	yes	characteristic
193	C₂×#170	C₂³×C₃	1	1	yes	characteristic
194	C₂×#170	C₂³×C₃	1	2	yes	—
195	C₂×#170	C₂³×C₃	1	2	yes	—
196	C₂×#170	C₂³×C₃	1	1	yes	characteristic
197	C₂×#170	C₂³×C₃	1	1	yes	characteristic
198	D₅⋊C₈	—	2	2	no	—
199	D₅⋊C₈	—	2	2	no	—
200	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
201	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
202	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
204	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
205	#685	C₂×C₃×C₄	1	2	yes	—
206	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
209	#683	C₂×C₃×C₄	1	2	yes	—
210	#683	C₂×C₃×C₄	1	2	yes	—
211	#683	C₂×C₃×C₄	1	2	yes	—
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	2	no	—
222	C₈×D₄	—	5	1	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	2	no	—
228	C₂²×C₃×C₅	—	2	2	no	—
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₃×D₅	—	2	1	no	—
232	C₂×C₃×D₅	—	2	1	no	—
233	C₂×C₃×D₅	#131	1	2	yes	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	#131	1	2	yes	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	2	1	no	—
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
243	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
244	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
245	C₂×C₃×D₄	—	5	2	no	—
246	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
247	C₂²×C₃×C₄	—	5	2	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
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	2	no	—
260	C₂×C₃×C₈	—	10	4	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	1	no	—
266	C₃×C₄⋊C₄	—	5	2	no	—
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	C₂×AGL(1,𝔽₅)	1	2	yes	—
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	2	no	—
276	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
277	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
278	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₅×Q₈	—	2	2	no	—
280	C₅×D₄	—	2	2	no	—
281	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
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	C₂²⋊D₅	—	2	4	no	—
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	—	2	2	no	—
288	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
289	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
290	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
291	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
292	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
293	C₄×D₅	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	1	no	—
296	C₄×D₅	—	2	1	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	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
310	#123	—	5	2	no	—
311	C₂²⋊Q₈	—	5	1	no	—
312	#121	—	5	1	no	—
313	C₄×Q₈	—	5	1	no	—
314	C₄×D₄	—	5	1	no	—
315	C₄×D₄	—	5	2	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	—	4	2	no	—
333	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₃×D₅	—	2	2	no	—
337	C₂³×C₃	—	5	1	no	—
338	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
339	C₃×Q₈	—	2	2	no	—
340	C₃×D₄	—	2	2	no	—
341	C₃×D₄	—	10	4	no	—
342	C₂×C₃×C₄	—	5	1	no	—
343	C₂×C₃×C₄	—	5	1	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	5	2	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	10	1	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	10	2	no	—
351	C₂×C₃×C₄	—	10	2	no	—
352	C₂×C₃×C₄	—	10	2	no	—
353	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
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	2	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
367	C₂×D₅	—	2	1	no	—
368	C₂×D₅	—	2	1	no	—
369	C₂×D₅	C₃×#131	1	2	yes	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	C₃×#131	1	2	yes	—
374	Dic₅	—	2	1	no	—
375	Dic₅	—	2	1	no	—
376	Dic₅	—	2	2	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	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₂×D₄	—	5	2	no	—
382	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₂²×C₄	—	5	2	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
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	2	no	—
396	C₂×C₈	—	10	4	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	1	no	—
402	C₄⋊C₄	—	5	2	no	—
403	C₂²⋊C₄	—	5	2	no	—
404	C₂²⋊C₄	—	5	2	no	—
405	C₂²⋊C₄	—	5	2	no	—
406	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
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	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	5	2	no	—
418	C₂²×C₃	—	10	1	no	—
419	C₂²×C₃	—	10	1	no	—
420	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	5	1	no	—
425	C₃×C₄	—	5	1	no	—
426	C₃×C₄	—	10	1	no	—
427	C₃×C₄	—	10	1	no	—
428	C₃×C₄	—	10	2	no	—
429	C₃×C₄	—	10	2	no	—
430	C₃×C₄	#4131	1	2	yes	—
431	C₂×C₅	—	4	2	no	—
432	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
433	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
434	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
435	D₅	—	2	2	no	—
436	C₂³	—	5	1	no	—
437	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
438	Q₈	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	10	4	no	—
441	C₂×C₄	—	5	1	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	5	2	no	—
446	C₂×C₄	—	10	1	no	—
447	C₂×C₄	—	10	1	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	4	2	no	—
463	C₂×C₃	—	10	2	no	—
464	C₂×C₃	C₂×#4131	1	1	yes	characteristic
465	C₂×C₃	D₅⋊#131	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	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	5	2	no	—
472	C₂²	—	10	1	no	—
473	C₂²	—	10	1	no	—
474	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	5	1	no	—
479	C₄	—	5	1	no	—
480	C₄	—	10	1	no	—
481	C₄	—	10	1	no	—
482	C₄	—	10	2	no	—
483	C₄	—	10	2	no	—
484	C₄	C₃×#4131	1	2	yes	—
485	C₃	#10617312	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	4	2	no	—
487	C₂	—	10	2	no	—
488	C₂	C₂×C₃×#4131	1	1	yes	characteristic
489	C₂	C₃×D₅⋊#131	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	C₃×C₅×#124	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#4084	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#124	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2966
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
2. C₃×#65788	C₂	semidirect
3. C₃×Q₈×#170	C₂	semidirect
4. C₃×#65774	C₂	semidirect
5. C₃×D₄×#170	C₂	semidirect
6. C₃×#65697	C₂	semidirect
7. C₃×#65694	C₂	semidirect
8. C₃×#65692	C₂	semidirect
9. C₃×#65691	C₂	semidirect
10. C₃×#65683	C₂	semidirect
11. C₃×C₄×D₅⋊C₈	C₂	semidirect
12. #10617312	C₃	direct (N × H)
44. #65788	C₂×C₃	semidirect
45. Q₈×#170	C₂×C₃	semidirect
46. #65774	C₂×C₃	semidirect
47. D₄×#170	C₂×C₃	semidirect
48. #65697	C₂×C₃	semidirect
49. #65694	C₂×C₃	semidirect
50. #65692	C₂×C₃	semidirect
51. #65691	C₂×C₃	semidirect
52. #65683	C₂×C₃	semidirect
53. C₄×D₅⋊C₈	C₂×C₃	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	C₃×#2966	semidirect
485. C₃	#10617312	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×#66014	2
C₃×#65788	2
C₃×Q₈×#170	2
C₃×#65774	2
C₃×D₄×#170	2
C₃×#65697	2
C₃×#65694	2
C₃×#65692	2
C₃×#65691	2
C₃×#65683	2
C₃×C₄×D₅⋊C₈	2
#10617312	3
C₃×#2966	5

Subgroups — C3×#10617312 #14419159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617312 #14419159