Subgroups — C₃×#10610769 #14413913

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65415	C₂	1	2	yes	maximal
4	C₃×M₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65124	C₂	1	4	yes	maximal, complemented
7	C₃×#65122	C₂	1	4	yes	maximal, complemented
8	#10610769	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	2	yes	—
16	C₃×C₄²×D₅	C₄	1	2	yes	—
17	C₃×C₄²×D₅	C₄	1	2	yes	—
18	C₃×C₄²×D₅	C₂²	1	2	yes	—
19	C₃×C₄²×D₅	C₂²	1	2	yes	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
21	C₃×#3952	C₂²	1	8	yes	—
22	C₃×#3947	C₂²	1	4	yes	complemented
23	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
24	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
25	C₃×#2920	—	5	1	no	maximal, Hall
26	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
27	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
28	#65415	C₂×C₃	1	2	yes	—
29	M₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
30	#65213	C₂×C₃	1	1	yes	characteristic, complemented
31	#65124	C₂×C₃	1	4	yes	complemented
32	#65122	C₂×C₃	1	4	yes	complemented
33	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	—	2	2	no	—
39	C₂×C₃×C₄×D₅	—	2	2	no	—
40	C₂×C₃×C₄×D₅	—	2	8	no	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	4	no	—
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
53	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
54	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
55	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
57	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
58	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
59	C₃×#681	—	2	4	no	—
60	C₂×C₃×#168	C₂³	1	4	yes	—
61	C₂²×C₃×C₄²	—	5	1	no	—
62	C₃×#432	—	5	4	no	—
63	C₃×#431	—	5	4	no	—
64	C₃×#423	—	5	1	no	—
65	C₃×#423	D₅	1	1	yes	characteristic, complemented
66	C₃×#407	—	5	2	no	—
67	C₃×C₄×M₁₆	—	5	2	no	—
68	C₂²×C₄×D₅	C₃×C₄	1	2	yes	—
69	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
73	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×#681	C₂²×C₃	1	2	yes	—
75	C₄²×D₅	C₃×C₄	1	2	yes	—
76	C₄²×D₅	C₃×C₄	1	2	yes	—
77	C₄²×D₅	C₂²×C₃	1	2	yes	—
78	C₄²×D₅	C₂²×C₃	1	2	yes	—
79	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
80	#3952	C₂²×C₃	1	8	yes	—
81	#3947	C₂²×C₃	1	4	yes	complemented
82	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
83	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
84	#2920	—	5	1	no	Sylow
85	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₃×D₅	—	2	2	no	—
87	C₂²×C₃×D₅	—	2	4	no	—
88	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	#41	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×Dic₅	—	2	2	no	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
101	C₃×C₄×D₅	—	2	4	no	—
102	C₃×C₄×D₅	—	2	4	no	—
103	C₃×C₄×D₅	—	2	4	no	—
104	C₃×C₄×D₅	—	2	2	no	—
105	C₃×C₄×D₅	—	2	2	no	—
106	C₃×C₄×D₅	—	2	4	no	—
107	C₃×C₄×D₅	M₁₆	1	8	yes	complemented
108	C₃×C₅×C₈	—	2	4	no	—
109	C₃×#168	—	2	4	no	—
110	C₂³×C₃×C₄	—	5	2	no	—
111	C₂³×C₃×C₄	—	5	1	no	—
112	C₂×C₃×M₁₆	—	5	2	no	—
113	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
114	C₂×C₃×C₄²	—	5	2	no	—
115	C₂×C₃×C₄²	—	5	1	no	—
116	C₂×C₃×C₄²	—	5	2	no	—
117	C₂×C₃×C₄²	—	5	2	no	—
118	C₂×C₃×C₄²	—	5	2	no	—
119	C₂×C₃×C₄²	—	5	2	no	—
120	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
121	C₃×C₄⋊C₈	—	5	4	no	—
122	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
123	C₃×C₂²⋊C₈	—	5	8	no	—
124	C₃×#97	—	5	4	no	—
125	C₃×C₄×C₈	—	5	4	no	—
126	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂×C₄×D₅	—	2	2	no	—
132	C₂×C₄×D₅	—	2	2	no	—
133	C₂×C₄×D₅	—	2	8	no	—
134	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
136	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
139	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
140	C₅×M₁₆	—	2	4	no	—
141	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
142	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
144	C₄²×C₅	C₂³×C₃	1	2	yes	—
145	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
146	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
147	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
148	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
149	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
150	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
151	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
152	#681	—	2	4	no	—
153	C₂×#168	C₂³×C₃	1	4	yes	—
154	C₂²×C₄²	—	5	1	no	—
155	#432	—	5	4	no	—
156	#431	—	5	4	no	—
157	#423	—	5	1	no	—
158	#423	C₃×D₅	1	1	yes	characteristic, complemented
159	#407	—	5	2	no	—
160	C₄×M₁₆	—	5	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	#117	1	2	yes	—
163	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₃×D₅	—	2	8	no	—
165	C₂×C₃×D₅	—	2	2	no	—
166	C₂×C₃×D₅	—	2	2	no	—
167	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	#117	1	2	yes	—
170	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
171	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
173	C₃×Dic₅	—	2	2	no	—
174	C₃×Dic₅	—	2	2	no	—
175	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
176	C₂⁴×C₃	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	2	no	—
178	C₂²×C₃×C₄	—	5	2	no	—
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	2	no	—
181	C₂²×C₃×C₄	—	5	2	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	—	5	2	no	—
184	C₂²×C₃×C₄	—	5	2	no	—
185	C₂²×C₃×C₄	—	10	8	no	—
186	C₂²×C₃×C₄	—	10	2	no	—
187	C₂²×C₃×C₄	—	10	2	no	—
188	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₃×M₁₆	—	2	4	no	—
191	C₃×M₁₆	—	10	4	no	—
192	C₂×C₃×C₈	—	5	4	no	—
193	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
194	C₃×C₄²	—	5	2	no	—
195	C₃×C₄²	—	5	2	no	—
196	C₃×C₄²	—	5	2	no	—
197	C₃×C₄²	—	5	2	no	—
198	C₃×C₄²	—	5	2	no	—
199	C₃×C₄²	—	5	1	no	—
200	C₃×C₄²	—	5	1	no	—
201	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
202	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
203	C₃×C₄²	C₂²×D₅	1	2	yes	—
204	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂²×D₅	—	2	2	no	—
206	C₂²×D₅	—	2	4	no	—
207	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
210	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
212	C₂×C₄×C₅	C₃×#41	1	2	yes	—
213	C₂×C₄×C₅	C₃×#41	1	2	yes	—
214	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	2	4	no	—
217	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
218	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
220	C₄×D₅	—	2	4	no	—
221	C₄×D₅	—	2	4	no	—
222	C₄×D₅	—	2	4	no	—
223	C₄×D₅	—	2	2	no	—
224	C₄×D₅	—	2	2	no	—
225	C₄×D₅	—	2	4	no	—
226	C₄×D₅	C₃×M₁₆	1	8	yes	complemented
227	C₅×C₈	—	2	4	no	—
228	#168	—	2	4	no	—
229	C₂³×C₄	—	5	2	no	—
230	C₂³×C₄	—	5	1	no	—
231	C₂×M₁₆	—	5	2	no	—
232	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
233	C₂×C₄²	—	5	2	no	—
234	C₂×C₄²	—	5	1	no	—
235	C₂×C₄²	—	5	2	no	—
236	C₂×C₄²	—	5	2	no	—
237	C₂×C₄²	—	5	2	no	—
238	C₂×C₄²	—	5	2	no	—
239	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
240	C₄⋊C₈	—	5	4	no	—
241	C₄⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
242	C₂²⋊C₈	—	5	8	no	—
243	#97	—	5	4	no	—
244	C₄×C₈	—	5	4	no	—
245	C₂×C₃×C₅	—	2	2	no	—
246	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
248	C₃×D₅	—	2	4	no	—
249	C₂³×C₃	—	5	2	no	—
250	C₂³×C₃	—	10	4	no	—
251	C₂³×C₃	—	10	2	no	—
252	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	5	2	no	—
255	C₂×C₃×C₄	—	5	8	no	—
256	C₂×C₃×C₄	—	5	2	no	—
257	C₂×C₃×C₄	—	5	2	no	—
258	C₂×C₃×C₄	—	10	4	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	10	4	no	—
261	C₂×C₃×C₄	—	10	2	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	10	2	no	—
264	C₂×C₃×C₄	—	10	4	no	—
265	C₂×C₃×C₄	—	10	4	no	—
266	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
267	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
269	C₂×C₃×C₄	#711	1	2	yes	—
270	C₂×C₃×C₄	#713	1	2	yes	—
271	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
272	C₃×C₈	—	2	4	no	—
273	C₃×C₈	—	10	4	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	C₃×#117	1	2	yes	—
276	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
277	C₂×D₅	—	2	8	no	—
278	C₂×D₅	—	2	2	no	—
279	C₂×D₅	—	2	2	no	—
280	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	C₃×#117	1	2	yes	—
283	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	—
284	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
285	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
286	Dic₅	—	2	2	no	—
287	Dic₅	—	2	2	no	—
288	Dic₅	C₂×C₃×M₁₆	1	4	yes	—
289	C₂⁴	—	5	1	no	—
290	C₂²×C₄	—	5	2	no	—
291	C₂²×C₄	—	5	2	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	2	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	5	2	no	—
296	C₂²×C₄	—	5	2	no	—
297	C₂²×C₄	—	5	2	no	—
298	C₂²×C₄	—	10	8	no	—
299	C₂²×C₄	—	10	2	no	—
300	C₂²×C₄	—	10	2	no	—
301	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
302	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
303	M₁₆	—	2	4	no	—
304	M₁₆	—	10	4	no	—
305	C₂×C₈	—	5	4	no	—
306	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
307	C₄²	—	5	2	no	—
308	C₄²	—	5	2	no	—
309	C₄²	—	5	2	no	—
310	C₄²	—	5	2	no	—
311	C₄²	—	5	2	no	—
312	C₄²	—	5	1	no	—
313	C₄²	—	5	1	no	—
314	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
315	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
316	C₄²	C₂²×C₃×D₅	1	2	yes	—
317	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	5	4	no	—
320	C₂²×C₃	—	10	8	no	—
321	C₂²×C₃	—	10	2	no	—
322	C₂²×C₃	—	10	2	no	—
323	C₂²×C₃	#4038	1	2	yes	—
324	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	5	4	no	—
327	C₃×C₄	—	10	2	no	—
328	C₃×C₄	—	10	2	no	—
329	C₃×C₄	#4038	1	2	yes	—
330	C₃×C₄	D₅×M₁₆	1	4	yes	—
331	C₃×C₄	C₂×#711	1	1	yes	characteristic
332	C₃×C₄	C₂×#713	1	1	yes	characteristic
333	C₂×C₅	—	2	2	no	—
334	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
335	C₂×C₅	C₂²×C₃×M₁₆	1	2	yes	—
336	D₅	—	2	4	no	—
337	C₂³	—	5	2	no	—
338	C₂³	—	10	4	no	—
339	C₂³	—	10	2	no	—
340	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	5	2	no	—
343	C₂×C₄	—	5	8	no	—
344	C₂×C₄	—	5	2	no	—
345	C₂×C₄	—	5	2	no	—
346	C₂×C₄	—	10	4	no	—
347	C₂×C₄	—	10	4	no	—
348	C₂×C₄	—	10	4	no	—
349	C₂×C₄	—	10	2	no	—
350	C₂×C₄	—	10	2	no	—
351	C₂×C₄	—	10	2	no	—
352	C₂×C₄	—	10	4	no	—
353	C₂×C₄	—	10	4	no	—
354	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
355	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
356	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
357	C₂×C₄	C₃×#711	1	2	yes	—
358	C₂×C₄	C₃×#713	1	2	yes	—
359	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	10	4	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	10	4	no	—
364	C₂×C₃	C₂×#4038	1	1	yes	characteristic
365	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
366	C₅	C₃×#2920	1	1	yes	characteristic, complemented, Sylow
367	C₂²	—	2	2	no	—
368	C₂²	—	5	4	no	—
369	C₂²	—	10	8	no	—
370	C₂²	—	10	2	no	—
371	C₂²	—	10	2	no	—
372	C₂²	C₃×#4038	1	2	yes	—
373	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	5	4	no	—
376	C₄	—	10	2	no	—
377	C₄	—	10	2	no	—
378	C₄	C₃×#4038	1	2	yes	—
379	C₄	C₃×D₅×M₁₆	1	4	yes	—
380	C₄	C₂×C₃×#711	1	1	yes	characteristic
381	C₄	C₂×C₃×#713	1	1	yes	characteristic
382	C₃	#10610769	1	1	yes	characteristic, direct product factor, Sylow
383	C₂	—	2	2	no	—
384	C₂	—	10	4	no	—
385	C₂	C₂×C₃×#4038	1	1	yes	characteristic
386	C₂	C₂×C₃×D₅×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#423	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#423	D₅
hypocenter	C₅	C₃×#2920
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#423	C₂	semidirect
4. C₃×M₁₆×Dic₅	C₂	semidirect
5. C₃×#65213	C₂	semidirect
6. C₃×#65124	C₂	semidirect
7. C₃×#65122	C₂	semidirect
8. #10610769	C₃	direct (N × H)
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
22. C₃×#3947	C₂²	semidirect
23. C₃×C₈×Dic₅	C₂²	semidirect
24. C₃×C₄⋊#168	C₂²	semidirect
27. C₅×#423	C₂×C₃	semidirect
29. M₁₆×Dic₅	C₂×C₃	semidirect
30. #65213	C₂×C₃	semidirect
31. #65124	C₂×C₃	semidirect
32. #65122	C₂×C₃	semidirect
65. C₃×#423	D₅	semidirect
79. C₅×C₄⋊C₈	C₂²×C₃	semidirect
81. #3947	C₂²×C₃	semidirect
82. C₈×Dic₅	C₂²×C₃	semidirect
83. C₄⋊#168	C₂²×C₃	semidirect
107. C₃×C₄×D₅	M₁₆	semidirect
122. C₃×C₄⋊C₈	C₂×D₅	semidirect
158. #423	C₃×D₅	semidirect
226. C₄×D₅	C₃×M₁₆	semidirect
241. C₄⋊C₈	C₂×C₃×D₅	semidirect
317. C₃×C₅	#2920	semidirect
366. C₅	C₃×#2920	semidirect
382. C₃	#10610769	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₄²×D₅	2
C₃×C₅×#423	2
C₃×#65415	2
C₃×M₁₆×Dic₅	2
C₃×#65213	2
C₃×#65124	2
C₃×#65122	2
#10610769	3
C₃×#2920	5

Subgroups — C3×#10610769 #14413913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610769 #14413913