Subgroups — C₃×#66042 #11755719

Order 960.

428 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4029	C₂	1	1	yes	maximal, characteristic
9	C₃×#4029	C₂	1	1	yes	maximal, characteristic
10	C₃×#4027	C₂	1	1	yes	maximal, characteristic
11	C₃×#4025	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
16	#66042	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
32	C₃×#685	C₂²	1	1	yes	characteristic
33	C₃×#685	C₂²	1	1	yes	characteristic
34	C₃×#685	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
39	C₃×#683	C₂²	1	1	yes	characteristic
40	C₃×#683	C₂²	1	1	yes	characteristic
41	C₃×#683	C₂²	1	1	yes	characteristic
42	C₃×#683	C₂²	1	1	yes	characteristic
43	C₃×#683	C₂²	1	1	yes	characteristic
44	C₃×#683	C₂²	1	1	yes	characteristic
45	C₃×#683	C₂²	1	1	yes	characteristic
46	C₃×#683	C₂²	1	1	yes	characteristic
47	C₃×#683	C₂²	1	1	yes	characteristic
48	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
52	C₃×#552	—	5	1	no	maximal, Hall
53	C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
54	#4042	C₂×C₃	1	1	yes	characteristic, complemented
55	#4038	C₂×C₃	1	1	yes	characteristic, complemented
56	D₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
57	#4036	C₂×C₃	1	1	yes	characteristic, complemented
58	#4035	C₂×C₃	1	1	yes	characteristic, complemented
59	#4035	C₂×C₃	1	1	yes	characteristic, complemented
60	#4029	C₂×C₃	1	1	yes	characteristic
61	#4029	C₂×C₃	1	1	yes	characteristic
62	#4027	C₂×C₃	1	1	yes	characteristic
63	#4025	C₂×C₃	1	1	yes	characteristic, complemented
64	#4024	C₂×C₃	1	1	yes	characteristic, complemented
65	#4023	C₂×C₃	1	1	yes	characteristic, complemented
66	#4018	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₂²⋊D₅	—	2	2	no	—
77	C₂×C₃×Dic₅	—	2	2	no	—
78	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄×D₅	—	2	2	no	—
86	C₃×C₄×D₅	—	2	2	no	—
87	C₃×C₄×D₅	—	2	2	no	—
88	C₃×Dic₁₀	—	2	2	no	—
89	C₃×#126	—	5	1	no	—
90	C₃×#126	D₅	1	1	yes	characteristic, complemented
91	C₃×#125	—	5	1	no	—
92	C₃×#125	—	5	1	no	—
93	C₃×#125	—	5	1	no	—
94	C₃×#123	—	5	1	no	—
95	C₃×#123	—	5	1	no	—
96	C₃×C₂²⋊Q₈	—	5	1	no	—
97	C₃×C₂²⋊Q₈	—	5	1	no	—
98	C₃×C₄×Q₈	—	5	1	no	—
99	C₃×C₄×D₄	—	5	1	no	—
100	C₃×#117	—	5	1	no	—
101	C₃×#117	—	5	1	no	—
102	C₃×#117	—	5	1	no	—
103	C₂×C₃×C₄⋊C₄	—	5	1	no	—
104	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
105	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
110	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
117	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
118	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
119	#685	C₂²×C₃	1	1	yes	characteristic
120	#685	C₂²×C₃	1	1	yes	characteristic
121	#685	C₂²×C₃	1	1	yes	characteristic
122	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
123	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
124	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
125	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
126	#683	C₂²×C₃	1	1	yes	characteristic
127	#683	C₂²×C₃	1	1	yes	characteristic
128	#683	C₂²×C₃	1	1	yes	characteristic
129	#683	C₂²×C₃	1	1	yes	characteristic
130	#683	C₂²×C₃	1	1	yes	characteristic
131	#683	C₂²×C₃	1	1	yes	characteristic
132	#683	C₂²×C₃	1	1	yes	characteristic
133	#683	C₂²×C₃	1	1	yes	characteristic
134	#683	C₂²×C₃	1	1	yes	characteristic
135	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
136	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
137	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
138	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
139	#552	—	5	1	no	Sylow
140	C₂²×C₃×C₅	—	2	1	no	—
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	2	1	no	—
143	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
144	C₂×C₃×D₅	—	2	1	no	—
145	C₂×C₃×D₅	—	2	1	no	—
146	C₂×C₃×D₅	#41	1	2	yes	—
147	C₃×C₄×C₅	—	2	1	no	—
148	C₃×C₄×C₅	—	2	1	no	—
149	C₃×C₄×C₅	—	2	1	no	—
150	C₃×C₄×C₅	—	2	1	no	—
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×Dic₅	—	2	1	no	—
154	C₃×Dic₅	—	2	1	no	—
155	C₃×Dic₅	—	2	1	no	—
156	C₃×Dic₅	—	2	1	no	—
157	C₃×Dic₅	—	2	1	no	—
158	C₃×Dic₅	—	2	1	no	—
159	C₃×Dic₅	#41	1	2	yes	—
160	C₂×C₃×Q₈	—	5	1	no	—
161	C₂×C₃×D₄	—	5	1	no	—
162	C₂²×C₃×C₄	—	5	1	no	—
163	C₂²×C₃×C₄	—	5	1	no	—
164	C₂²×C₃×C₄	—	5	1	no	—
165	C₂²×C₃×C₄	—	5	1	no	—
166	C₃×C₄⋊C₄	—	5	1	no	—
167	C₃×C₄⋊C₄	—	5	1	no	—
168	C₃×C₄⋊C₄	—	5	1	no	—
169	C₃×C₄⋊C₄	—	5	1	no	—
170	C₃×C₄⋊C₄	—	5	1	no	—
171	C₃×C₄⋊C₄	—	5	1	no	—
172	C₃×C₄⋊C₄	—	5	1	no	—
173	C₃×C₄⋊C₄	—	5	1	no	—
174	C₃×C₄⋊C₄	—	5	1	no	—
175	C₃×C₄⋊C₄	—	5	1	no	—
176	C₃×C₄⋊C₄	—	5	1	no	—
177	C₃×C₄⋊C₄	—	5	1	no	—
178	C₃×C₄⋊C₄	—	5	1	no	—
179	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
182	C₃×C₂²⋊C₄	—	5	1	no	—
183	C₃×C₂²⋊C₄	—	5	1	no	—
184	C₃×C₂²⋊C₄	—	5	1	no	—
185	C₃×C₂²⋊C₄	—	5	1	no	—
186	C₃×C₂²⋊C₄	—	5	1	no	—
187	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
190	C₃×C₄²	—	5	1	no	—
191	C₃×C₄²	—	5	1	no	—
192	C₃×C₄²	—	5	1	no	—
193	C₃×C₄²	—	5	1	no	—
194	C₃×C₄²	C₂×D₅	1	1	yes	characteristic
195	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₂²⋊D₅	—	2	2	no	—
204	C₂×Dic₅	—	2	2	no	—
205	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
206	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
210	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
212	C₄×D₅	—	2	2	no	—
213	C₄×D₅	—	2	2	no	—
214	C₄×D₅	—	2	2	no	—
215	Dic₁₀	—	2	2	no	—
216	#126	—	5	1	no	—
217	#126	C₃×D₅	1	1	yes	characteristic, complemented
218	#125	—	5	1	no	—
219	#125	—	5	1	no	—
220	#125	—	5	1	no	—
221	#123	—	5	1	no	—
222	#123	—	5	1	no	—
223	C₂²⋊Q₈	—	5	1	no	—
224	C₂²⋊Q₈	—	5	1	no	—
225	C₄×Q₈	—	5	1	no	—
226	C₄×D₄	—	5	1	no	—
227	#117	—	5	1	no	—
228	#117	—	5	1	no	—
229	#117	—	5	1	no	—
230	C₂×C₄⋊C₄	—	5	1	no	—
231	C₂×C₃×C₅	—	4	1	no	—
232	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
235	C₃×D₅	—	2	2	no	—
236	C₂³×C₃	—	5	1	no	—
237	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
238	C₃×Q₈	—	10	2	no	—
239	C₃×D₄	—	10	2	no	—
240	C₂×C₃×C₄	—	5	1	no	—
241	C₂×C₃×C₄	—	5	1	no	—
242	C₂×C₃×C₄	—	5	1	no	—
243	C₂×C₃×C₄	—	5	1	no	—
244	C₂×C₃×C₄	—	5	1	no	—
245	C₂×C₃×C₄	—	5	1	no	—
246	C₂×C₃×C₄	—	5	1	no	—
247	C₂×C₃×C₄	—	10	2	no	—
248	C₂×C₃×C₄	—	10	2	no	—
249	C₂×C₃×C₄	—	10	2	no	—
250	C₂×C₃×C₄	—	10	2	no	—
251	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×D₅	—	2	1	no	—
262	C₂×D₅	—	2	1	no	—
263	C₂×D₅	C₃×#41	1	2	yes	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	Dic₅	—	2	1	no	—
271	Dic₅	—	2	1	no	—
272	Dic₅	—	2	1	no	—
273	Dic₅	—	2	1	no	—
274	Dic₅	—	2	1	no	—
275	Dic₅	—	2	1	no	—
276	Dic₅	C₃×#41	1	2	yes	—
277	C₂×Q₈	—	5	1	no	—
278	C₂×D₄	—	5	1	no	—
279	C₂²×C₄	—	5	1	no	—
280	C₂²×C₄	—	5	1	no	—
281	C₂²×C₄	—	5	1	no	—
282	C₂²×C₄	—	5	1	no	—
283	C₄⋊C₄	—	5	1	no	—
284	C₄⋊C₄	—	5	1	no	—
285	C₄⋊C₄	—	5	1	no	—
286	C₄⋊C₄	—	5	1	no	—
287	C₄⋊C₄	—	5	1	no	—
288	C₄⋊C₄	—	5	1	no	—
289	C₄⋊C₄	—	5	1	no	—
290	C₄⋊C₄	—	5	1	no	—
291	C₄⋊C₄	—	5	1	no	—
292	C₄⋊C₄	—	5	1	no	—
293	C₄⋊C₄	—	5	1	no	—
294	C₄⋊C₄	—	5	1	no	—
295	C₄⋊C₄	—	5	1	no	—
296	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
297	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
298	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
299	C₂²⋊C₄	—	5	1	no	—
300	C₂²⋊C₄	—	5	1	no	—
301	C₂²⋊C₄	—	5	1	no	—
302	C₂²⋊C₄	—	5	1	no	—
303	C₂²⋊C₄	—	5	1	no	—
304	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
305	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
306	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
307	C₄²	—	5	1	no	—
308	C₄²	—	5	1	no	—
309	C₄²	—	5	1	no	—
310	C₄²	—	5	1	no	—
311	C₄²	C₂×C₃×D₅	1	1	yes	characteristic
312	C₃×C₅	#552	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	5	2	no	—
317	C₂²×C₃	—	10	1	no	—
318	C₂²×C₃	—	10	1	no	—
319	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	5	2	no	—
327	C₃×C₄	—	10	1	no	—
328	C₃×C₄	—	10	1	no	—
329	C₃×C₄	—	10	1	no	—
330	C₃×C₄	—	10	1	no	—
331	C₃×C₄	—	10	1	no	—
332	C₃×C₄	—	10	1	no	—
333	C₂×C₅	—	4	1	no	—
334	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
335	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
336	C₂×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
337	D₅	—	2	2	no	—
338	C₂³	—	5	1	no	—
339	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
340	Q₈	—	10	2	no	—
341	D₄	—	10	2	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	1	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	5	1	no	—
346	C₂×C₄	—	5	1	no	—
347	C₂×C₄	—	5	1	no	—
348	C₂×C₄	—	5	1	no	—
349	C₂×C₄	—	10	2	no	—
350	C₂×C₄	—	10	2	no	—
351	C₂×C₄	—	10	2	no	—
352	C₂×C₄	—	10	2	no	—
353	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
359	C₂×C₃	—	4	1	no	—
360	C₂×C₃	—	10	2	no	—
361	C₂×C₃	D₅×#41	1	1	yes	characteristic
362	C₂×C₃	D₅×#41	1	1	yes	characteristic
363	C₂×C₃	#4150	1	1	yes	characteristic
364	C₅	C₃×#552	1	1	yes	characteristic, complemented, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	5	2	no	—
369	C₂²	—	10	1	no	—
370	C₂²	—	10	1	no	—
371	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	5	2	no	—
379	C₄	—	10	1	no	—
380	C₄	—	10	1	no	—
381	C₄	—	10	1	no	—
382	C₄	—	10	1	no	—
383	C₄	—	10	1	no	—
384	C₄	—	10	1	no	—
385	C₃	#66042	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	4	1	no	—
387	C₂	—	10	2	no	—
388	C₂	C₃×D₅×#41	1	1	yes	characteristic
389	C₂	C₃×D₅×#41	1	1	yes	characteristic
390	C₂	C₃×#4150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×#126	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×C₃×C₂²⋊D₅	C₂²
hypercenter	C₃×#126	D₅
hypocenter	C₅	C₃×#552
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#126

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#126	C₂	semidirect
2. C₃×#4042	C₂	semidirect
3. C₃×#4038	C₂	semidirect
4. C₃×D₅×C₄⋊C₄	C₂	semidirect
5. C₃×#4036	C₂	semidirect
6. C₃×#4035	C₂	semidirect
7. C₃×#4035	C₂	semidirect
11. C₃×#4025	C₂	semidirect
12. C₃×#4024	C₂	semidirect
13. C₃×#4023	C₂	semidirect
14. C₃×#4018	C₂	semidirect
15. C₃×C₄×Dic₁₀	C₂	semidirect
16. #66042	C₃	direct (N × H)
53. C₅×#126	C₂×C₃	semidirect
54. #4042	C₂×C₃	semidirect
55. #4038	C₂×C₃	semidirect
56. D₅×C₄⋊C₄	C₂×C₃	semidirect
57. #4036	C₂×C₃	semidirect
58. #4035	C₂×C₃	semidirect
59. #4035	C₂×C₃	semidirect
63. #4025	C₂×C₃	semidirect
64. #4024	C₂×C₃	semidirect
65. #4023	C₂×C₃	semidirect
66. #4018	C₂×C₃	semidirect
67. C₄×Dic₁₀	C₂×C₃	semidirect
90. C₃×#126	D₅	semidirect
217. #126	C₃×D₅	semidirect
312. C₃×C₅	#552	semidirect
364. C₅	C₃×#552	semidirect
385. C₃	#66042	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×C₅×#126	2
C₃×#4042	2
C₃×#4038	2
C₃×D₅×C₄⋊C₄	2
C₃×#4036	2
C₃×#4035	2
C₃×#4029	2
C₃×#4027	2
C₃×#4025	2
C₃×#4024	2
C₃×#4023	2
C₃×#4018	2
C₃×C₄×Dic₁₀	2
#66042	3
C₃×#552	5

Subgroups — C3×#66042 #11755719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66042 #11755719