Subgroups — C₃×C₅×#2625 #14275659

Order 1920.

928 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	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#397	C₂	1	4	yes	maximal
6	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
9	C₅×#2625	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
13	C₃×C₅×#117	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	4	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2625	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
31	C₅×#400	C₂×C₃	1	2	yes	complemented
32	C₅×#398	C₂×C₃	1	2	yes	complemented
33	C₅×#397	C₂×C₃	1	4	yes	—
34	C₅×#391	C₂×C₃	1	2	yes	complemented
35	C₅×#389	C₂×C₃	1	2	yes	complemented
36	C₅×#380	C₂×C₃	1	1	yes	characteristic
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	4	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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	—	4	4	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
58	C₃×C₄²×C₅	—	2	4	no	—
59	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
60	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
61	C₃×#400	C₂×C₅	1	2	yes	complemented
62	C₃×#398	C₂×C₅	1	2	yes	complemented
63	C₃×#397	C₂×C₅	1	4	yes	—
64	C₃×#391	C₂×C₅	1	2	yes	complemented
65	C₃×#389	C₂×C₅	1	2	yes	complemented
66	C₃×#380	C₂×C₅	1	1	yes	characteristic
67	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₅×C₂²⋊Q₈	—	2	4	no	—
70	C₅×#117	—	2	4	no	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
77	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
81	C₅×#95	C₂²×C₃	1	2	yes	—
82	C₅×#95	C₂²×C₃	1	4	yes	—
83	C₅×#95	C₂²×C₃	1	4	yes	—
84	C₅×#95	C₂²×C₃	1	4	yes	—
85	#2625	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	1	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	4	4	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	8	no	—
95	C₂×C₃×C₄×C₅	—	2	2	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	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	4	yes	—
111	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
112	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
113	C₃×C₂²⋊Q₈	—	2	4	no	—
114	C₃×#117	—	2	4	no	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
125	C₃×#95	C₂²×C₅	1	2	yes	—
126	C₃×#95	C₂²×C₅	1	4	yes	—
127	C₃×#95	C₂²×C₅	1	4	yes	—
128	C₃×#95	C₂²×C₅	1	4	yes	—
129	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₅×Q₈	—	2	2	no	—
131	C₂×C₅×Q₈	—	2	4	no	—
132	C₂²×C₄×C₅	—	2	4	no	—
133	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	4	no	—
145	C₅×C₄⋊C₄	—	2	4	no	—
146	C₅×C₄⋊C₄	—	4	4	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	—	2	4	no	—
149	C₅×C₂²⋊C₄	—	4	2	no	—
150	C₄²×C₅	—	2	4	no	—
151	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
152	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
153	#400	C₂×C₃×C₅	1	2	yes	complemented
154	#398	C₂×C₃×C₅	1	2	yes	complemented
155	#397	C₂×C₃×C₅	1	4	yes	—
156	#391	C₂×C₃×C₅	1	2	yes	complemented
157	#389	C₂×C₃×C₅	1	2	yes	complemented
158	#380	C₂×C₃×C₅	1	1	yes	characteristic
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	—	4	2	no	—
164	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
166	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
168	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	4	2	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	2	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	—	4	4	no	—
175	C₃×C₄×C₅	#123	1	4	yes	—
176	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
177	C₂×C₃×Q₈	—	2	2	no	—
178	C₂×C₃×Q₈	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	4	no	—
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	4	4	no	—
194	C₃×C₂²⋊C₄	—	2	4	no	—
195	C₃×C₂²⋊C₄	—	2	4	no	—
196	C₃×C₂²⋊C₄	—	4	2	no	—
197	C₃×C₄²	—	2	4	no	—
198	C₂³×C₅	—	2	2	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	2	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
203	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₅×Q₈	—	4	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	8	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	4	no	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
222	C₂×C₄×C₅	C₃×#41	1	4	yes	—
223	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₂²⋊Q₈	—	2	4	no	—
226	#117	—	2	4	no	—
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
233	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
236	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
237	#95	C₂²×C₃×C₅	1	2	yes	—
238	#95	C₂²×C₃×C₅	1	4	yes	—
239	#95	C₂²×C₃×C₅	1	4	yes	—
240	#95	C₂²×C₃×C₅	1	4	yes	—
241	C₂×C₃×C₅	—	4	2	no	—
242	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
243	C₂×C₃×C₅	#536	1	1	yes	characteristic
244	C₂×C₃×C₅	#537	1	1	yes	characteristic
245	C₂×C₃×C₅	#541	1	2	yes	—
246	C₂×C₃×C₅	#542	1	2	yes	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
252	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
253	C₃×Q₈	—	4	4	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
271	C₂×C₃×C₄	C₅×#41	1	4	yes	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	4	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
279	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
281	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	4	2	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	C₃×#123	1	4	yes	—
289	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
295	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
297	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
298	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
299	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	4	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₄²	—	2	4	no	—
311	C₃×C₅	#2625	1	1	yes	characteristic, direct product factor, Hall
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	4	2	no	—
316	C₂²×C₃	—	4	2	no	—
317	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
319	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
320	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
321	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	4	2	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	4	2	no	—
326	C₃×C₄	—	4	2	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	C₅×#123	1	4	yes	—
329	C₂×C₅	—	4	2	no	—
330	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
331	C₂×C₅	C₃×#536	1	1	yes	characteristic
332	C₂×C₅	C₃×#537	1	1	yes	characteristic
333	C₂×C₅	C₃×#541	1	2	yes	—
334	C₂×C₅	C₃×#542	1	2	yes	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	1	no	—
339	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
340	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	8	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	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
358	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
359	C₂×C₄	C₃×C₅×#41	1	4	yes	—
360	C₂×C₃	—	4	2	no	—
361	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
362	C₂×C₃	C₅×#536	1	1	yes	characteristic
363	C₂×C₃	C₅×#537	1	1	yes	characteristic
364	C₂×C₃	C₅×#541	1	2	yes	—
365	C₂×C₃	C₅×#542	1	2	yes	—
366	C₅	C₃×#2625	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
373	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
374	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
376	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	4	no	—
383	C₄	C₃×C₅×#123	1	4	yes	—
384	C₃	C₅×#2625	1	1	yes	characteristic, direct product factor, Sylow
385	C₂	—	4	2	no	—
386	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
387	C₂	C₃×C₅×#536	1	1	yes	characteristic
388	C₂	C₃×C₅×#537	1	1	yes	characteristic
389	C₂	C₃×C₅×#541	1	2	yes	—
390	C₂	C₃×C₅×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
6. C₃×C₅×#391	C₂	semidirect
7. C₃×C₅×#389	C₂	semidirect
9. C₅×#2625	C₃	direct (N × H)
28. C₃×#2625	C₅	direct (N × H)
31. C₅×#400	C₂×C₃	semidirect
32. C₅×#398	C₂×C₃	semidirect
34. C₅×#391	C₂×C₃	semidirect
35. C₅×#389	C₂×C₃	semidirect
61. C₃×#400	C₂×C₅	semidirect
62. C₃×#398	C₂×C₅	semidirect
64. C₃×#391	C₂×C₅	semidirect
65. C₃×#389	C₂×C₅	semidirect
85. #2625	C₃×C₅	direct (N × H)
153. #400	C₂×C₃×C₅	semidirect
154. #398	C₂×C₃×C₅	semidirect
156. #391	C₂×C₃×C₅	semidirect
157. #389	C₂×C₃×C₅	semidirect
311. C₃×C₅	#2625	direct (N × H)
366. C₅	C₃×#2625	direct (N × H)
384. C₃	C₅×#2625	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×C₅×C₂²⋊Q₈	2
C₂×C₃×C₅×#117	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#380	2
C₅×#2625	3
C₃×#2625	5

Subgroups — C3×C5×#2625 #14275659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2625 #14275659