Subgroups — C₃×C₅×#3127 #14276161

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#485	C₂	1	2	yes	maximal
4	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	2	yes	maximal
7	C₃×C₅×#441	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic
10	C₅×#3127	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#126	—	2	2	no	—
16	C₃×C₅×#125	—	2	2	no	—
17	C₃×C₅×#125	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₄×C₅×Q₈	—	2	2	no	—
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#117	—	2	2	no	—
24	C₃×C₅×#117	C₂²	1	1	yes	characteristic
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₃×C₅×#107	C₂²	1	2	yes	—
27	C₃×C₅×#106	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃×C₅×#103	C₂²	1	2	yes	—
30	C₃×C₅×#103	C₂²	1	2	yes	—
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×#97	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₃×#3127	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#541	C₂×C₃	1	1	yes	characteristic
38	C₅×#519	C₂×C₃	1	1	yes	characteristic
39	C₅×#485	C₂×C₃	1	2	yes	—
40	C₅×#479	C₂×C₃	1	2	yes	complemented
41	C₅×#462	C₂×C₃	1	2	yes	complemented
42	C₅×#451	C₂×C₃	1	2	yes	—
43	C₅×#441	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×Q₁₆	C₂×C₃	1	2	yes	complemented
45	C₅×#433	C₂×C₃	1	1	yes	characteristic
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	—	2	1	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×Q₁₆	—	2	4	no	—
53	C₃×C₅×Q₁₆	—	2	4	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	—	2	1	no	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#541	C₂×C₅	1	1	yes	characteristic
75	C₃×#519	C₂×C₅	1	1	yes	characteristic
76	C₃×#485	C₂×C₅	1	2	yes	—
77	C₃×#479	C₂×C₅	1	2	yes	complemented
78	C₃×#462	C₂×C₅	1	2	yes	complemented
79	C₃×#451	C₂×C₅	1	2	yes	—
80	C₃×#441	C₂×C₅	1	2	yes	complemented
81	C₃×C₄×Q₁₆	C₂×C₅	1	2	yes	complemented
82	C₃×#433	C₂×C₅	1	1	yes	characteristic
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
85	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
86	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
87	C₅×#126	—	2	2	no	—
88	C₅×#125	—	2	2	no	—
89	C₅×#125	C₂²×C₃	1	1	yes	characteristic
90	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
93	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
94	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
95	C₅×#117	—	2	2	no	—
96	C₅×#117	C₂²×C₃	1	1	yes	characteristic
97	C₅×#117	C₂²×C₃	1	1	yes	characteristic
98	C₅×#107	C₂²×C₃	1	2	yes	—
99	C₅×#106	C₂²×C₃	1	2	yes	—
100	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
101	C₅×#103	C₂²×C₃	1	2	yes	—
102	C₅×#103	C₂²×C₃	1	2	yes	—
103	C₅×#103	C₂²×C₃	1	2	yes	—
104	C₅×#103	C₂²×C₃	1	2	yes	—
105	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₅×#97	C₂²×C₃	1	1	yes	characteristic
107	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
108	#3127	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×Q₈	#41	1	4	yes	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₃×C₅×C₈	—	2	2	no	—
126	C₃×C₅×C₈	—	2	2	no	—
127	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
129	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
130	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
131	C₃×#126	—	2	2	no	—
132	C₃×#125	—	2	2	no	—
133	C₃×#125	C₂²×C₅	1	1	yes	characteristic
134	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
135	C₃×C₄×Q₈	—	2	2	no	—
136	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
137	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
138	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
139	C₃×#117	—	2	2	no	—
140	C₃×#117	C₂²×C₅	1	1	yes	characteristic
141	C₃×#117	C₂²×C₅	1	1	yes	characteristic
142	C₃×#107	C₂²×C₅	1	2	yes	—
143	C₃×#106	C₂²×C₅	1	2	yes	—
144	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
145	C₃×#103	C₂²×C₅	1	2	yes	—
146	C₃×#103	C₂²×C₅	1	2	yes	—
147	C₃×#103	C₂²×C₅	1	2	yes	—
148	C₃×#103	C₂²×C₅	1	2	yes	—
149	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
150	C₃×#97	C₂²×C₅	1	1	yes	characteristic
151	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
155	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₅×Q₁₆	—	2	4	no	—
159	C₅×Q₁₆	—	2	4	no	—
160	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
161	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	—	2	2	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
169	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
170	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	2	2	no	—
173	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	2	no	—
178	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
180	#541	C₂×C₃×C₅	1	1	yes	characteristic
181	#519	C₂×C₃×C₅	1	1	yes	characteristic
182	#485	C₂×C₃×C₅	1	2	yes	—
183	#479	C₂×C₃×C₅	1	2	yes	complemented
184	#462	C₂×C₃×C₅	1	2	yes	complemented
185	#451	C₂×C₃×C₅	1	2	yes	—
186	#441	C₂×C₃×C₅	1	2	yes	complemented
187	C₄×Q₁₆	C₂×C₃×C₅	1	2	yes	complemented
188	#433	C₂×C₃×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₅	—	2	1	no	—
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	—	2	4	no	—
193	C₃×C₄×C₅	—	2	1	no	—
194	C₃×C₄×C₅	—	2	2	no	—
195	C₃×C₄×C₅	—	2	2	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	C₂×#41	1	2	yes	—
200	C₂×C₃×Q₈	—	2	4	no	—
201	C₂×C₃×Q₈	—	2	1	no	—
202	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
203	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₃×Q₁₆	—	2	4	no	—
207	C₃×Q₁₆	—	2	4	no	—
208	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
209	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
210	C₃×C₄⋊C₄	—	2	2	no	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	—	2	2	no	—
214	C₃×C₄⋊C₄	—	2	2	no	—
215	C₃×C₄⋊C₄	—	2	2	no	—
216	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
217	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
218	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₂²⋊C₄	—	2	2	no	—
221	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
222	C₃×C₄²	—	2	2	no	—
223	C₃×C₄²	—	2	2	no	—
224	C₃×C₄²	—	2	1	no	—
225	C₃×C₄²	—	2	2	no	—
226	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
227	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
228	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
229	C₅×Q₈	—	2	4	no	—
230	C₅×Q₈	—	2	2	no	—
231	C₅×Q₈	—	2	2	no	—
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	C₃×#41	1	4	yes	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	2	2	no	—
246	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
247	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
248	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
249	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	#126	—	2	2	no	—
251	#125	—	2	2	no	—
252	#125	C₂²×C₃×C₅	1	1	yes	characteristic
253	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
256	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
257	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
258	#117	—	2	2	no	—
259	#117	C₂²×C₃×C₅	1	1	yes	characteristic
260	#117	C₂²×C₃×C₅	1	1	yes	characteristic
261	#107	C₂²×C₃×C₅	1	2	yes	—
262	#106	C₂²×C₃×C₅	1	2	yes	—
263	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
264	#103	C₂²×C₃×C₅	1	2	yes	—
265	#103	C₂²×C₃×C₅	1	2	yes	—
266	#103	C₂²×C₃×C₅	1	2	yes	—
267	#103	C₂²×C₃×C₅	1	2	yes	—
268	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
269	#97	C₂²×C₃×C₅	1	1	yes	characteristic
270	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
271	C₂×C₃×C₅	—	4	1	no	—
272	C₂×C₃×C₅	#525	1	1	yes	characteristic
273	C₂×C₃×C₅	#578	1	2	yes	—
274	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
275	C₃×Q₈	—	2	4	no	—
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	2	2	no	—
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	C₅×#41	1	4	yes	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	2	4	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	C₂×C₃×#41	1	2	yes	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
306	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
309	Q₁₆	—	2	4	no	—
310	Q₁₆	—	2	4	no	—
311	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
312	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
320	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
321	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
330	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
331	C₃×C₅	#3127	1	1	yes	characteristic, direct product factor, Hall
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	4	2	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	C₂×C₅×#41	1	2	yes	—
343	C₂×C₅	—	4	1	no	—
344	C₂×C₅	C₃×#525	1	1	yes	characteristic
345	C₂×C₅	C₃×#578	1	2	yes	—
346	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	C₃×C₅×#41	1	4	yes	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
359	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
360	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₂×C₃	—	4	1	no	—
365	C₂×C₃	C₅×#525	1	1	yes	characteristic
366	C₂×C₃	C₅×#578	1	2	yes	—
367	C₅	C₃×#3127	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	—	2	1	no	—
369	C₂²	—	2	2	no	—
370	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	C₂×C₃×C₅×#41	1	2	yes	—
379	C₃	C₅×#3127	1	1	yes	characteristic, direct product factor, Sylow
380	C₂	—	4	1	no	—
381	C₂	C₃×C₅×#525	1	1	yes	characteristic
382	C₂	C₃×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#479	C₂	semidirect
5. C₃×C₅×#462	C₂	semidirect
7. C₃×C₅×#441	C₂	semidirect
8. C₃×C₄×C₅×Q₁₆	C₂	semidirect
10. C₅×#3127	C₃	direct (N × H)
36. C₃×#3127	C₅	direct (N × H)
40. C₅×#479	C₂×C₃	semidirect
41. C₅×#462	C₂×C₃	semidirect
43. C₅×#441	C₂×C₃	semidirect
44. C₄×C₅×Q₁₆	C₂×C₃	semidirect
77. C₃×#479	C₂×C₅	semidirect
78. C₃×#462	C₂×C₅	semidirect
80. C₃×#441	C₂×C₅	semidirect
81. C₃×C₄×Q₁₆	C₂×C₅	semidirect
108. #3127	C₃×C₅	direct (N × H)
183. #479	C₂×C₃×C₅	semidirect
184. #462	C₂×C₃×C₅	semidirect
186. #441	C₂×C₃×C₅	semidirect
187. C₄×Q₁₆	C₂×C₃×C₅	semidirect
331. C₃×C₅	#3127	direct (N × H)
367. C₅	C₃×#3127	direct (N × H)
379. C₃	C₅×#3127	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×#541	2
C₃×C₅×#519	2
C₃×C₅×#485	2
C₃×C₅×#479	2
C₃×C₅×#462	2
C₃×C₅×#451	2
C₃×C₅×#441	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×#433	2
C₅×#3127	3
C₃×#3127	5

Subgroups — C3×C5×#3127 #14276161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3127 #14276161