Subgroups — C₃×C₅×#2612 #14275646

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#398	C₂	1	2	yes	maximal
3	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	2	yes	maximal
5	C₃×C₅×#389	C₂	1	2	yes	maximal
6	C₃×C₅×#387	C₂	1	2	yes	maximal
7	C₃×C₅×#387	C₂	1	2	yes	maximal
8	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#376	C₂	1	2	yes	maximal
10	C₅×#2612	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×#2612	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#400	C₂×C₃	1	1	yes	characteristic
34	C₅×#398	C₂×C₃	1	2	yes	—
35	C₅×#395	C₂×C₃	1	1	yes	characteristic
36	C₅×#391	C₂×C₃	1	2	yes	—
37	C₅×#389	C₂×C₃	1	2	yes	—
38	C₅×#387	C₂×C₃	1	2	yes	—
39	C₅×#387	C₂×C₃	1	2	yes	—
40	C₅×#382	C₂×C₃	1	1	yes	characteristic
41	C₅×#376	C₂×C₃	1	2	yes	—
42	C₂×C₃×C₅×Q₈	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	—	4	1	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	4	1	no	—
57	C₃×C₅×C₄⋊C₄	—	4	1	no	—
58	C₃×C₅×C₄⋊C₄	—	4	2	no	—
59	C₃×C₅×C₄⋊C₄	—	4	1	no	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
63	C₃×#400	C₂×C₅	1	1	yes	characteristic
64	C₃×#398	C₂×C₅	1	2	yes	—
65	C₃×#395	C₂×C₅	1	1	yes	characteristic
66	C₃×#391	C₂×C₅	1	2	yes	—
67	C₃×#389	C₂×C₅	1	2	yes	—
68	C₃×#387	C₂×C₅	1	2	yes	—
69	C₃×#387	C₂×C₅	1	2	yes	—
70	C₃×#382	C₂×C₅	1	1	yes	characteristic
71	C₃×#376	C₂×C₅	1	2	yes	—
72	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
82	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
83	C₅×#95	C₂²×C₃	1	2	yes	—
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	2	yes	—
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	C₅×#95	C₂²×C₃	1	2	yes	—
88	C₅×#95	C₂²×C₃	1	2	yes	—
89	C₅×#95	C₂²×C₃	1	1	yes	characteristic
90	C₅×#95	C₂²×C₃	1	1	yes	characteristic
91	C₅×#95	C₂²×C₃	1	2	yes	—
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	#2612	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	4	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
119	C₂×C₃×C₄×C₅	#41	1	4	yes	—
120	C₂×C₃×C₄×C₅	#41	1	4	yes	—
121	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
132	C₃×#95	C₂²×C₅	1	2	yes	—
133	C₃×#95	C₂²×C₅	1	2	yes	—
134	C₃×#95	C₂²×C₅	1	2	yes	—
135	C₃×#95	C₂²×C₅	1	2	yes	—
136	C₃×#95	C₂²×C₅	1	2	yes	—
137	C₃×#95	C₂²×C₅	1	2	yes	—
138	C₃×#95	C₂²×C₅	1	1	yes	characteristic
139	C₃×#95	C₂²×C₅	1	1	yes	characteristic
140	C₃×#95	C₂²×C₅	1	2	yes	—
141	C₃×#95	C₂²×C₅	1	2	yes	—
142	C₂×C₅×Q₈	—	2	4	no	—
143	C₂×C₅×Q₈	—	4	1	no	—
144	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	4	1	no	—
157	C₅×C₄⋊C₄	—	4	1	no	—
158	C₅×C₄⋊C₄	—	4	2	no	—
159	C₅×C₄⋊C₄	—	4	1	no	—
160	C₄²×C₅	—	2	4	no	—
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	C₃×Q₈	1	4	yes	complemented
163	#400	C₂×C₃×C₅	1	1	yes	characteristic
164	#398	C₂×C₃×C₅	1	2	yes	—
165	#395	C₂×C₃×C₅	1	1	yes	characteristic
166	#391	C₂×C₃×C₅	1	2	yes	—
167	#389	C₂×C₃×C₅	1	2	yes	—
168	#387	C₂×C₃×C₅	1	2	yes	—
169	#387	C₂×C₃×C₅	1	2	yes	—
170	#382	C₂×C₃×C₅	1	1	yes	characteristic
171	#376	C₂×C₃×C₅	1	2	yes	—
172	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
174	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
175	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
177	C₃×C₄×C₅	—	2	4	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	4	no	—
180	C₃×C₄×C₅	—	2	4	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	—	4	1	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₂×C₃×Q₈	—	2	4	no	—
187	C₂×C₃×Q₈	—	4	1	no	—
188	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
189	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
193	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
194	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
197	C₃×C₄⋊C₄	—	2	4	no	—
198	C₃×C₄⋊C₄	—	2	4	no	—
199	C₃×C₄⋊C₄	—	2	4	no	—
200	C₃×C₄⋊C₄	—	4	1	no	—
201	C₃×C₄⋊C₄	—	4	1	no	—
202	C₃×C₄⋊C₄	—	4	2	no	—
203	C₃×C₄⋊C₄	—	4	1	no	—
204	C₃×C₄²	—	2	4	no	—
205	C₃×C₄²	—	2	4	no	—
206	C₃×C₄²	C₅×Q₈	1	4	yes	complemented
207	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
208	C₅×Q₈	—	4	4	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
231	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
232	C₂×C₄×C₅	C₃×#41	1	4	yes	—
233	C₂×C₄×C₅	C₃×#41	1	4	yes	—
234	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
236	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
237	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
238	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
242	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
243	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
244	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
245	#95	C₂²×C₃×C₅	1	2	yes	—
246	#95	C₂²×C₃×C₅	1	2	yes	—
247	#95	C₂²×C₃×C₅	1	2	yes	—
248	#95	C₂²×C₃×C₅	1	2	yes	—
249	#95	C₂²×C₃×C₅	1	2	yes	—
250	#95	C₂²×C₃×C₅	1	2	yes	—
251	#95	C₂²×C₃×C₅	1	1	yes	characteristic
252	#95	C₂²×C₃×C₅	1	1	yes	characteristic
253	#95	C₂²×C₃×C₅	1	2	yes	—
254	#95	C₂²×C₃×C₅	1	2	yes	—
255	C₂×C₃×C₅	#533	1	2	yes	—
256	C₂×C₃×C₅	#544	1	1	yes	characteristic
257	C₂×C₃×C₅	#551	1	1	yes	characteristic
258	C₂×C₃×C₅	#552	1	2	yes	—
259	C₂×C₃×C₅	#555	1	1	yes	characteristic
260	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
261	C₃×Q₈	—	4	4	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
284	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
285	C₂×C₃×C₄	C₅×#41	1	4	yes	—
286	C₂×C₃×C₄	C₅×#41	1	4	yes	—
287	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
288	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
289	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
290	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
292	C₄×C₅	—	2	4	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	2	4	no	—
295	C₄×C₅	—	2	4	no	—
296	C₄×C₅	—	4	1	no	—
297	C₄×C₅	—	4	1	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
304	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
305	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
306	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
308	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
309	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
311	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	4	no	—
321	C₄²	C₃×C₅×Q₈	1	4	yes	complemented
322	C₃×C₅	#2612	1	1	yes	characteristic, direct product factor, Hall
323	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
324	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
325	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
326	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
328	C₃×C₄	—	2	4	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	4	1	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	—	4	2	no	—
337	C₂×C₅	C₃×#533	1	2	yes	—
338	C₂×C₅	C₃×#544	1	1	yes	characteristic
339	C₂×C₅	C₃×#551	1	1	yes	characteristic
340	C₂×C₅	C₃×#552	1	2	yes	—
341	C₂×C₅	C₃×#555	1	1	yes	characteristic
342	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
343	Q₈	—	4	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	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	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
366	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
367	C₂×C₄	C₃×C₅×#41	1	4	yes	—
368	C₂×C₄	C₃×C₅×#41	1	4	yes	—
369	C₂×C₃	C₅×#533	1	2	yes	—
370	C₂×C₃	C₅×#544	1	1	yes	characteristic
371	C₂×C₃	C₅×#551	1	1	yes	characteristic
372	C₂×C₃	C₅×#552	1	2	yes	—
373	C₂×C₃	C₅×#555	1	1	yes	characteristic
374	C₅	C₃×#2612	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
376	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
377	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
378	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
380	C₄	—	2	4	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₃	C₅×#2612	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	C₃×C₅×#533	1	2	yes	—
391	C₂	C₃×C₅×#544	1	1	yes	characteristic
392	C₂	C₃×C₅×#551	1	1	yes	characteristic
393	C₂	C₃×C₅×#552	1	2	yes	—
394	C₂	C₃×C₅×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₅×#2612	C₃	direct (N × H)
32. C₃×#2612	C₅	direct (N × H)
62. C₃×C₄²×C₅	Q₈	semidirect
93. #2612	C₃×C₅	direct (N × H)
162. C₄²×C₅	C₃×Q₈	semidirect
206. C₃×C₄²	C₅×Q₈	semidirect
321. C₄²	C₃×C₅×Q₈	semidirect
322. C₃×C₅	#2612	direct (N × H)
374. C₅	C₃×#2612	direct (N × H)
389. C₃	C₅×#2612	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×#400	2
C₃×C₅×#398	2
C₃×C₅×#395	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#382	2
C₃×C₅×#376	2
C₅×#2612	3
C₃×#2612	5

Subgroups — C3×C5×#2612 #14275646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2612 #14275646