Subgroups — C₃×C₅×#2619 #14275653

Order 1920.

1456 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×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#392	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2619	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#127	—	2	4	no	—
14	C₃×C₅×#121	—	2	8	no	—
15	C₃×C₅×#117	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	4	yes	—
24	C₃×#2619	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#394	C₂×C₃	1	4	yes	complemented
29	C₅×#392	C₂×C₃	1	4	yes	complemented
30	C₅×#390	C₂×C₃	1	2	yes	complemented
31	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	8	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	8	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	4	8	no	—
40	C₂×C₃×C₅×D₄	—	4	8	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
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	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
53	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
54	C₃×C₄²×C₅	—	2	2	no	—
55	C₃×C₄²×C₅	D₄	1	4	yes	complemented
56	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
58	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
59	C₃×#394	C₂×C₅	1	4	yes	complemented
60	C₃×#392	C₂×C₅	1	4	yes	complemented
61	C₃×#390	C₂×C₅	1	2	yes	complemented
62	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
64	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
65	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
66	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₅×#127	—	2	4	no	—
68	C₅×#121	—	2	8	no	—
69	C₅×#117	—	2	4	no	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₅×#95	C₂²×C₃	1	4	yes	—
78	#2619	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	—	2	4	no	—
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	2	4	no	—
85	C₂³×C₃×C₅	—	2	8	no	—
86	C₂³×C₃×C₅	—	2	8	no	—
87	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₃×C₅×D₄	—	4	16	no	—
90	C₃×C₅×D₄	—	4	16	no	—
91	C₃×C₅×D₄	—	4	8	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	8	no	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
106	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
107	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
108	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
109	C₃×#127	—	2	4	no	—
110	C₃×#121	—	2	8	no	—
111	C₃×#117	—	2	4	no	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
117	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
119	C₃×#95	C₂²×C₅	1	4	yes	—
120	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
121	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂×C₅×D₄	—	2	8	no	—
123	C₂×C₅×D₄	—	2	4	no	—
124	C₂×C₅×D₄	—	2	8	no	—
125	C₂×C₅×D₄	—	2	4	no	—
126	C₂×C₅×D₄	—	2	4	no	—
127	C₂×C₅×D₄	—	4	8	no	—
128	C₂×C₅×D₄	—	4	8	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
132	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₂²⋊C₄	—	2	4	no	—
140	C₅×C₂²⋊C₄	—	2	8	no	—
141	C₅×C₂²⋊C₄	—	4	8	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	C₃×D₄	1	4	yes	complemented
144	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
146	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	#394	C₂×C₃×C₅	1	4	yes	complemented
148	#392	C₂×C₃×C₅	1	4	yes	complemented
149	#390	C₂×C₃×C₅	1	2	yes	complemented
150	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	4	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	4	no	—
156	C₂²×C₃×C₅	—	4	8	no	—
157	C₂²×C₃×C₅	—	4	4	no	—
158	C₂²×C₃×C₅	—	4	4	no	—
159	C₂²×C₃×C₅	—	4	8	no	—
160	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
163	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	—	4	2	no	—
167	C₃×C₄×C₅	—	4	4	no	—
168	C₃×C₄×C₅	#121	1	4	yes	—
169	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
170	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
171	C₂×C₃×D₄	—	2	8	no	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂×C₃×D₄	—	2	8	no	—
174	C₂×C₃×D₄	—	2	4	no	—
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	4	8	no	—
177	C₂×C₃×D₄	—	4	8	no	—
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
181	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	2	4	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₂²⋊C₄	—	2	4	no	—
189	C₃×C₂²⋊C₄	—	2	8	no	—
190	C₃×C₂²⋊C₄	—	4	8	no	—
191	C₃×C₄²	—	2	2	no	—
192	C₃×C₄²	C₅×D₄	1	4	yes	complemented
193	C₂³×C₅	—	2	1	no	—
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	2	4	no	—
198	C₂³×C₅	—	2	4	no	—
199	C₂³×C₅	—	2	8	no	—
200	C₂³×C₅	—	2	8	no	—
201	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
202	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
203	C₅×D₄	—	4	16	no	—
204	C₅×D₄	—	4	16	no	—
205	C₅×D₄	—	4	8	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	8	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	8	no	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×#41	1	2	yes	—
219	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
220	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
221	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
222	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	#127	—	2	4	no	—
224	#121	—	2	8	no	—
225	#117	—	2	4	no	—
226	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
231	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
232	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
233	#95	C₂²×C₃×C₅	1	4	yes	—
234	C₂×C₃×C₅	—	4	2	no	—
235	C₂×C₃×C₅	—	8	4	no	—
236	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
237	C₂×C₃×C₅	#535	1	2	yes	—
238	C₂×C₃×C₅	#535	1	2	yes	—
239	C₂×C₃×C₅	#540	1	2	yes	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	8	no	—
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
249	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
250	C₃×D₄	—	4	16	no	—
251	C₃×D₄	—	4	16	no	—
252	C₃×D₄	—	4	8	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	8	no	—
261	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₅×#41	1	2	yes	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	4	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	4	no	—
271	C₂²×C₅	—	4	8	no	—
272	C₂²×C₅	—	4	4	no	—
273	C₂²×C₅	—	4	4	no	—
274	C₂²×C₅	—	4	8	no	—
275	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
277	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
278	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	4	2	no	—
282	C₄×C₅	—	4	4	no	—
283	C₄×C₅	C₃×#121	1	4	yes	—
284	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
285	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
296	C₂²×C₄	C₂³×C₃×C₅	1	4	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	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	8	no	—
305	C₂²⋊C₄	—	4	8	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₃×C₅×D₄	1	4	yes	complemented
308	C₃×C₅	#2619	1	1	yes	characteristic, direct product factor, Hall
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	4	no	—
311	C₂²×C₃	—	4	2	no	—
312	C₂²×C₃	—	4	2	no	—
313	C₂²×C₃	—	4	4	no	—
314	C₂²×C₃	—	4	8	no	—
315	C₂²×C₃	—	4	4	no	—
316	C₂²×C₃	—	4	4	no	—
317	C₂²×C₃	—	4	8	no	—
318	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
319	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
321	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	4	4	no	—
326	C₃×C₄	C₅×#121	1	4	yes	—
327	C₂×C₅	—	4	2	no	—
328	C₂×C₅	—	8	4	no	—
329	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
330	C₂×C₅	C₃×#535	1	2	yes	—
331	C₂×C₅	C₃×#535	1	2	yes	—
332	C₂×C₅	C₃×#540	1	2	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	2	8	no	—
341	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
342	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
343	D₄	—	4	16	no	—
344	D₄	—	4	16	no	—
345	D₄	—	4	8	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
355	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
356	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
357	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
358	C₂×C₄	C₃×C₅×#41	1	2	yes	—
359	C₂×C₃	—	4	2	no	—
360	C₂×C₃	—	8	4	no	—
361	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
362	C₂×C₃	C₅×#535	1	2	yes	—
363	C₂×C₃	C₅×#535	1	2	yes	—
364	C₂×C₃	C₅×#540	1	2	yes	—
365	C₅	C₃×#2619	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²	—	2	2	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	8	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	4	8	no	—
375	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
376	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
377	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
378	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
379	C₄	—	2	2	no	—
380	C₄	—	2	4	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	2	no	—
383	C₄	C₃×C₅×#121	1	4	yes	—
384	C₃	C₅×#2619	1	1	yes	characteristic, direct product factor, Sylow
385	C₂	—	4	2	no	—
386	C₂	—	8	4	no	—
387	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
388	C₂	C₃×C₅×#535	1	2	yes	—
389	C₂	C₃×C₅×#535	1	2	yes	—
390	C₂	C₃×C₅×#540	1	2	yes	—

	subgroup	G/H
center, socle	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
1. C₂×C₃×C₅×#127	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#117	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#382	C₂	semidirect
8. C₅×#2619	C₃	direct (N × H)
24. C₃×#2619	C₅	direct (N × H)
25. C₂×C₅×#127	C₂×C₃	semidirect
26. C₂×C₅×#121	C₂×C₃	semidirect
27. C₂×C₅×#117	C₂×C₃	semidirect
28. C₅×#394	C₂×C₃	semidirect
29. C₅×#392	C₂×C₃	semidirect
30. C₅×#390	C₂×C₃	semidirect
31. C₅×#382	C₂×C₃	semidirect
43. C₂²×C₃×C₄×C₅	D₄	semidirect
55. C₃×C₄²×C₅	D₄	semidirect
56. C₂×C₃×#127	C₂×C₅	semidirect
57. C₂×C₃×#121	C₂×C₅	semidirect
58. C₂×C₃×#117	C₂×C₅	semidirect
59. C₃×#394	C₂×C₅	semidirect
60. C₃×#392	C₂×C₅	semidirect
61. C₃×#390	C₂×C₅	semidirect
62. C₃×#382	C₂×C₅	semidirect
78. #2619	C₃×C₅	direct (N × H)
131. C₂²×C₄×C₅	C₃×D₄	semidirect
143. C₄²×C₅	C₃×D₄	semidirect
144. C₂×#127	C₂×C₃×C₅	semidirect
145. C₂×#121	C₂×C₃×C₅	semidirect
146. C₂×#117	C₂×C₃×C₅	semidirect
147. #394	C₂×C₃×C₅	semidirect
148. #392	C₂×C₃×C₅	semidirect
149. #390	C₂×C₃×C₅	semidirect
150. #382	C₂×C₃×C₅	semidirect
180. C₂²×C₃×C₄	C₅×D₄	semidirect
192. C₃×C₄²	C₅×D₄	semidirect
295. C₂²×C₄	C₃×C₅×D₄	semidirect
307. C₄²	C₃×C₅×D₄	semidirect
308. C₃×C₅	#2619	direct (N × H)
365. C₅	C₃×#2619	direct (N × H)
384. C₃	C₅×#2619	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×#127	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#117	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#382	2
C₅×#2619	3
C₃×#2619	5

Subgroups — C3×C5×#2619 #14275653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2619 #14275653