Subgroups — C₃×C₅×#1852 #14274886

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#107	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	2	yes	maximal, complemented
6	C₅×#1852	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	—	2	1	no	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
11	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₅×#107	—	2	4	no	—
17	C₃×C₅×C₂²⋊C₈	C₄	1	4	yes	complemented
18	C₃×C₅×#95	—	2	1	no	—
19	C₃×#1852	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×#107	C₂×C₃	1	2	yes	complemented
22	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₅×#380	C₂×C₃	1	1	yes	characteristic
24	C₅×#340	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	4	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	1	no	—
31	C₂²×C₃×C₄×C₅	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	—	4	2	no	—
33	C₂²×C₃×C₄×C₅	—	4	2	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₂×C₃×C₅×C₈	—	2	2	no	—
40	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
46	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
47	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
48	C₂×C₃×#107	C₂×C₅	1	2	yes	complemented
49	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
50	C₃×#380	C₂×C₅	1	1	yes	characteristic
51	C₃×#340	C₂×C₅	1	2	yes	complemented
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	4	no	—
57	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
60	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
61	C₅×#107	—	2	4	no	—
62	C₅×C₂²⋊C₈	C₃×C₄	1	4	yes	complemented
63	C₅×#95	—	2	1	no	—
64	#1852	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₃×C₅	—	2	1	no	—
66	C₂³×C₃×C₅	—	2	1	no	—
67	C₂³×C₃×C₅	—	2	1	no	—
68	C₂³×C₃×C₅	—	2	1	no	—
69	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
70	C₂³×C₃×C₅	D₈	1	2	yes	—
71	C₂³×C₃×C₅	Q₁₆	1	2	yes	—
72	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	1	no	—
75	C₂×C₃×C₄×C₅	—	2	4	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	2	4	no	—
78	C₂×C₃×C₄×C₅	—	4	8	no	—
79	C₂×C₃×C₄×C₅	—	4	2	no	—
80	C₂×C₃×C₄×C₅	—	4	2	no	—
81	C₂×C₃×C₄×C₅	—	4	1	no	—
82	C₂×C₃×C₄×C₅	—	4	1	no	—
83	C₂×C₃×C₄×C₅	—	4	1	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	#41	1	2	yes	—
92	C₃×C₅×C₈	—	2	4	no	—
93	C₂³×C₃×C₄	—	2	1	no	—
94	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
95	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₃×C₄⋊C₄	—	2	4	no	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
102	C₃×#107	—	2	4	no	—
103	C₃×C₂²⋊C₈	C₄×C₅	1	4	yes	complemented
104	C₃×#95	—	2	1	no	—
105	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	4	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	4	2	no	—
113	C₂²×C₄×C₅	—	4	2	no	—
114	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
115	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
126	C₅×C₂²⋊C₄	—	4	2	no	—
127	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
128	C₂×#107	C₂×C₃×C₅	1	2	yes	complemented
129	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
130	#380	C₂×C₃×C₅	1	1	yes	characteristic
131	#340	C₂×C₃×C₅	1	2	yes	complemented
132	C₂²×C₃×C₅	—	2	2	no	—
133	C₂²×C₃×C₅	—	2	2	no	—
134	C₂²×C₃×C₅	—	2	2	no	—
135	C₂²×C₃×C₅	—	2	2	no	—
136	C₂²×C₃×C₅	—	2	2	no	—
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	#107	1	4	yes	complemented
139	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂²×C₃×C₅	#120	1	1	yes	characteristic
141	C₂²×C₃×C₅	#123	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
144	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂²×C₃×C₅	#137	1	1	yes	characteristic
146	C₃×C₄×C₅	—	2	2	no	—
147	C₃×C₄×C₅	—	4	4	no	—
148	C₃×C₄×C₅	—	8	1	no	—
149	C₃×C₄×C₅	—	8	1	no	—
150	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
151	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
152	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	—	2	1	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	4	2	no	—
160	C₂²×C₃×C₄	—	4	2	no	—
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
162	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	2	no	—
167	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
173	C₃×C₂²⋊C₄	—	4	2	no	—
174	C₂³×C₅	—	2	1	no	—
175	C₂³×C₅	—	2	1	no	—
176	C₂³×C₅	—	2	1	no	—
177	C₂³×C₅	—	2	1	no	—
178	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
179	C₂³×C₅	C₃×D₈	1	2	yes	—
180	C₂³×C₅	C₃×Q₁₆	1	2	yes	—
181	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	4	8	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	1	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×#41	1	2	yes	—
201	C₅×C₈	—	2	4	no	—
202	C₂³×C₄	—	2	1	no	—
203	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
210	C₂×C₂²⋊C₄	—	2	1	no	—
211	#107	—	2	4	no	—
212	C₂²⋊C₈	C₃×C₄×C₅	1	4	yes	complemented
213	#95	—	2	1	no	—
214	C₂×C₃×C₅	—	2	4	no	—
215	C₂×C₃×C₅	#385	1	1	yes	characteristic
216	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
217	C₂×C₃×C₅	#428	1	1	yes	characteristic
218	C₂×C₃×C₅	#447	1	1	yes	characteristic
219	C₂×C₃×C₅	#451	1	1	yes	characteristic
220	C₂×C₃×C₅	#480	1	1	yes	characteristic
221	C₂×C₃×C₅	#484	1	1	yes	characteristic
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	1	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
227	C₂³×C₃	C₅×D₈	1	2	yes	—
228	C₂³×C₃	C₅×Q₁₆	1	2	yes	—
229	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	4	8	no	—
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	4	1	no	—
239	C₂×C₃×C₄	—	4	1	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	1	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
248	C₂×C₃×C₄	C₅×#41	1	2	yes	—
249	C₃×C₈	—	2	4	no	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	2	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	2	2	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	C₃×#107	1	4	yes	complemented
257	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₅	C₃×#120	1	1	yes	characteristic
259	C₂²×C₅	C₃×#123	1	1	yes	characteristic
260	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
261	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
262	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₅	C₃×#137	1	1	yes	characteristic
264	C₄×C₅	—	2	2	no	—
265	C₄×C₅	—	4	4	no	—
266	C₄×C₅	—	8	1	no	—
267	C₄×C₅	—	8	1	no	—
268	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
269	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
270	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
280	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
282	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
291	C₂²⋊C₄	—	4	2	no	—
292	C₃×C₅	#1852	1	1	yes	characteristic, direct product factor, Hall
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	C₅×#107	1	4	yes	complemented
300	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₃	C₅×#120	1	1	yes	characteristic
302	C₂²×C₃	C₅×#123	1	1	yes	characteristic
303	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
304	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
305	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₂²×C₃	C₅×#137	1	1	yes	characteristic
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	4	4	no	—
309	C₃×C₄	—	8	1	no	—
310	C₃×C₄	—	8	1	no	—
311	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
312	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
313	C₂×C₅	—	2	4	no	—
314	C₂×C₅	C₃×#385	1	1	yes	characteristic
315	C₂×C₅	C₂×C₃×#107	1	1	yes	characteristic
316	C₂×C₅	C₃×#428	1	1	yes	characteristic
317	C₂×C₅	C₃×#447	1	1	yes	characteristic
318	C₂×C₅	C₃×#451	1	1	yes	characteristic
319	C₂×C₅	C₃×#480	1	1	yes	characteristic
320	C₂×C₅	C₃×#484	1	1	yes	characteristic
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₃×C₅×C₄⋊C₄	1	2	yes	—
326	C₂³	C₃×C₅×D₈	1	2	yes	—
327	C₂³	C₃×C₅×Q₁₆	1	2	yes	—
328	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
344	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
346	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
347	C₂×C₄	C₃×C₅×#41	1	2	yes	—
348	C₈	—	2	4	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	C₅×#385	1	1	yes	characteristic
351	C₂×C₃	C₂×C₅×#107	1	1	yes	characteristic
352	C₂×C₃	C₅×#428	1	1	yes	characteristic
353	C₂×C₃	C₅×#447	1	1	yes	characteristic
354	C₂×C₃	C₅×#451	1	1	yes	characteristic
355	C₂×C₃	C₅×#480	1	1	yes	characteristic
356	C₂×C₃	C₅×#484	1	1	yes	characteristic
357	C₅	C₃×#1852	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	C₃×C₅×#107	1	4	yes	complemented
365	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
366	C₂²	C₃×C₅×#120	1	1	yes	characteristic
367	C₂²	C₃×C₅×#123	1	1	yes	characteristic
368	C₂²	C₂×C₃×C₅×D₈	1	1	yes	characteristic
369	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
370	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
371	C₂²	C₃×C₅×#137	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	4	4	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	1	no	—
376	C₄	C₃×C₄×C₅×D₄	1	2	yes	—
377	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
378	C₃	C₅×#1852	1	1	yes	characteristic, direct product factor, Sylow
379	C₂	—	2	4	no	—
380	C₂	C₃×C₅×#385	1	1	yes	characteristic
381	C₂	C₂×C₃×C₅×#107	1	1	yes	characteristic
382	C₂	C₃×C₅×#428	1	1	yes	characteristic
383	C₂	C₃×C₅×#447	1	1	yes	characteristic
384	C₂	C₃×C₅×#451	1	1	yes	characteristic
385	C₂	C₃×C₅×#480	1	1	yes	characteristic
386	C₂	C₃×C₅×#484	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#107	C₂	semidirect
5. C₃×C₅×#340	C₂	semidirect
6. C₅×#1852	C₃	direct (N × H)
17. C₃×C₅×C₂²⋊C₈	C₄	semidirect
19. C₃×#1852	C₅	direct (N × H)
21. C₂×C₅×#107	C₂×C₃	semidirect
24. C₅×#340	C₂×C₃	semidirect
40. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
48. C₂×C₃×#107	C₂×C₅	semidirect
51. C₃×#340	C₂×C₅	semidirect
62. C₅×C₂²⋊C₈	C₃×C₄	semidirect
64. #1852	C₃×C₅	direct (N × H)
103. C₃×C₂²⋊C₈	C₄×C₅	semidirect
120. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
128. C₂×#107	C₂×C₃×C₅	semidirect
131. #340	C₂×C₃×C₅	semidirect
138. C₂²×C₃×C₅	#107	semidirect
167. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
212. C₂²⋊C₈	C₃×C₄×C₅	semidirect
256. C₂²×C₅	C₃×#107	semidirect
285. C₂×C₈	C₂×C₃×C₄×C₅	semidirect
292. C₃×C₅	#1852	direct (N × H)
299. C₂²×C₃	C₅×#107	semidirect
357. C₅	C₃×#1852	direct (N × H)
364. C₂²	C₃×C₅×#107	semidirect
378. C₃	C₅×#1852	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₅×#380	2
C₃×C₅×#340	2
C₅×#1852	3
C₃×#1852	5

Subgroups — C3×C5×#1852 #14274886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1852 #14274886