Subgroups — C₃×C₅×#1866 #14274900

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1866	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₃×C₅×#131	—	2	2	no	—
11	C₃×C₅×#131	—	2	2	no	—
12	C₂×C₃×C₅×M₁₆	—	2	1	no	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	—	2	1	no	—
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#108	—	2	2	no	—
21	C₃×C₅×C₄⋊C₈	—	2	1	no	—
22	C₃×C₅×C₄⋊C₈	—	2	1	no	—
23	C₃×C₅×#104	—	2	2	no	—
24	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
25	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
26	C₃×C₅×#102	C₄	1	1	yes	characteristic, complemented
27	C₃×C₅×#102	C₄	1	1	yes	characteristic, complemented
28	C₃×#1866	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₅×#104	C₂×C₃	1	1	yes	characteristic
33	C₅×#416	C₂×C₃	1	1	yes	characteristic
34	C₅×#339	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	—	2	1	no	—
38	C₃×C₅×#41	D₄	1	2	yes	—
39	C₃×C₅×#41	Q₈	1	2	yes	—
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×M₁₆	—	2	4	no	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	—	2	1	no	—
49	C₃×C₅×M₁₆	—	2	1	no	—
50	C₃×C₅×M₁₆	D₄	1	2	yes	—
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	—	2	1	no	—
57	C₂×C₃×C₅×C₈	—	2	1	no	—
58	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
65	C₃×C₄²×C₅	—	2	1	no	—
66	C₃×C₄²×C₅	—	2	1	no	—
67	C₃×C₄²×C₅	—	2	1	no	—
68	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
69	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic
72	C₃×#416	C₂×C₅	1	1	yes	characteristic
73	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
76	C₅×#131	—	2	2	no	—
77	C₅×#131	—	2	2	no	—
78	C₂×C₅×M₁₆	—	2	1	no	—
79	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₅×#117	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
86	C₅×#108	—	2	2	no	—
87	C₅×C₄⋊C₈	—	2	1	no	—
88	C₅×C₄⋊C₈	—	2	1	no	—
89	C₅×#104	—	2	2	no	—
90	C₅×#103	C₃×C₄	1	1	yes	characteristic, complemented
91	C₅×#103	C₃×C₄	1	1	yes	characteristic, complemented
92	C₅×#102	C₃×C₄	1	1	yes	characteristic, complemented
93	C₅×#102	C₃×C₄	1	1	yes	characteristic, complemented
94	#1866	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂³×C₃×C₅	#41	1	1	yes	characteristic
97	C₃×C₅×Q₈	—	2	1	no	—
98	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	—	2	1	no	—
102	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
108	C₂×C₃×C₄×C₅	—	2	1	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	—	4	1	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
117	C₃×C₅×C₈	—	2	1	no	—
118	C₃×C₅×C₈	—	2	1	no	—
119	C₃×C₅×C₈	—	2	1	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	—	2	1	no	—
122	C₃×C₅×C₈	—	4	1	no	—
123	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
124	C₃×#131	—	2	2	no	—
125	C₃×#131	—	2	2	no	—
126	C₂×C₃×M₁₆	—	2	1	no	—
127	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
129	C₂²×C₃×C₈	—	2	1	no	—
130	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×#117	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
134	C₃×#108	—	2	2	no	—
135	C₃×C₄⋊C₈	—	2	1	no	—
136	C₃×C₄⋊C₈	—	2	1	no	—
137	C₃×#104	—	2	2	no	—
138	C₃×#103	C₄×C₅	1	1	yes	characteristic, complemented
139	C₃×#103	C₄×C₅	1	1	yes	characteristic, complemented
140	C₃×#102	C₄×C₅	1	1	yes	characteristic, complemented
141	C₃×#102	C₄×C₅	1	1	yes	characteristic, complemented
142	C₅×#41	—	2	1	no	—
143	C₅×#41	—	2	1	no	—
144	C₅×#41	C₃×D₄	1	2	yes	—
145	C₅×#41	C₃×Q₈	1	2	yes	—
146	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₅×M₁₆	—	2	4	no	—
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	—	2	1	no	—
155	C₅×M₁₆	—	2	1	no	—
156	C₅×M₁₆	C₃×D₄	1	2	yes	—
157	C₂×C₅×C₈	—	2	4	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
167	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
175	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
176	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
177	C₂×#104	C₂×C₃×C₅	1	1	yes	characteristic
178	#416	C₂×C₃×C₅	1	1	yes	characteristic
179	#339	C₂×C₃×C₅	1	1	yes	characteristic, complemented
180	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	—	4	1	no	—
186	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂²×C₃×C₅	#123	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	1	no	—
192	C₃×C₄×C₅	—	4	1	no	—
193	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	#120	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	C₅×D₄	1	2	yes	—
200	C₃×#41	C₅×Q₈	1	2	yes	—
201	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₃×M₁₆	—	2	4	no	—
208	C₃×M₁₆	—	2	1	no	—
209	C₃×M₁₆	—	2	1	no	—
210	C₃×M₁₆	—	2	1	no	—
211	C₃×M₁₆	C₅×D₄	1	2	yes	—
212	C₂×C₃×C₈	—	2	4	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	—	2	1	no	—
216	C₂×C₃×C₈	—	2	1	no	—
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
222	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
223	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
224	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₃×C₂²⋊C₄	—	2	1	no	—
226	C₃×C₄²	—	2	1	no	—
227	C₃×C₄²	—	2	1	no	—
228	C₃×C₄²	—	2	1	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	C₃×#41	1	1	yes	characteristic
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	C₃×C₄⋊C₄	1	2	yes	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	C₃×C₄⋊C₄	1	2	yes	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
250	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	C₅×C₈	—	2	1	no	—
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	—	2	1	no	—
256	C₅×C₈	—	4	1	no	—
257	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
258	#131	—	2	2	no	—
259	#131	—	2	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
262	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
266	#117	C₂²×C₃×C₅	1	1	yes	characteristic
267	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
268	#108	—	2	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	#104	—	2	2	no	—
272	#103	C₃×C₄×C₅	1	1	yes	characteristic, complemented
273	#103	C₃×C₄×C₅	1	1	yes	characteristic, complemented
274	#102	C₃×C₄×C₅	1	1	yes	characteristic, complemented
275	#102	C₃×C₄×C₅	1	1	yes	characteristic, complemented
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	#385	1	1	yes	characteristic
280	C₂×C₃×C₅	#443	1	1	yes	characteristic
281	C₂×C₃×C₅	#444	1	1	yes	characteristic
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	C₅×#41	1	1	yes	characteristic
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₅×C₄⋊C₄	1	2	yes	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	1	no	—
289	C₃×D₄	C₅×C₄⋊C₄	1	2	yes	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	4	1	no	—
297	C₂×C₃×C₄	—	4	1	no	—
298	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
303	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃×C₈	—	2	1	no	—
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	—	2	1	no	—
309	C₃×C₈	—	4	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
316	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
317	C₂²×C₅	C₃×#123	1	1	yes	characteristic
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	—	4	1	no	—
322	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
323	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
324	C₄×C₅	C₃×#120	1	1	yes	characteristic
325	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
326	#41	—	2	1	no	—
327	#41	—	2	1	no	—
328	#41	C₃×C₅×D₄	1	2	yes	—
329	#41	C₃×C₅×Q₈	1	2	yes	—
330	C₂×Q₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
336	M₁₆	—	2	4	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	2	1	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	C₃×C₅×D₄	1	2	yes	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
349	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
350	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
351	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
352	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
353	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₃×C₅	#1866	1	1	yes	characteristic, direct product factor, Hall
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	4	1	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
365	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂²×C₃	C₅×#123	1	1	yes	characteristic
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	1	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
372	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
373	C₃×C₄	C₅×#120	1	1	yes	characteristic
374	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	4	2	no	—
378	C₂×C₅	C₃×#385	1	1	yes	characteristic
379	C₂×C₅	C₃×#443	1	1	yes	characteristic
380	C₂×C₅	C₃×#444	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	C₃×C₅×#41	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	1	no	—
388	D₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
398	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
400	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
402	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	2	no	—
407	C₈	—	2	1	no	—
408	C₈	—	4	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	C₅×#385	1	1	yes	characteristic
413	C₂×C₃	C₅×#443	1	1	yes	characteristic
414	C₂×C₃	C₅×#444	1	1	yes	characteristic
415	C₅	C₃×#1866	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
422	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
423	C₂²	C₃×C₅×#123	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
429	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
430	C₄	C₃×C₅×#120	1	1	yes	characteristic
431	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
432	C₃	C₅×#1866	1	1	yes	characteristic, direct product factor, Sylow
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	4	2	no	—
436	C₂	C₃×C₅×#385	1	1	yes	characteristic
437	C₂	C₃×C₅×#443	1	1	yes	characteristic
438	C₂	C₃×C₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂²×C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#108	C₂	semidirect
3. C₃×C₅×#424	C₂	semidirect
6. C₃×C₅×#339	C₂	semidirect
7. C₃×C₅×#336	C₂	semidirect
8. C₅×#1866	C₃	direct (N × H)
24. C₃×C₅×#103	C₄	semidirect
25. C₃×C₅×#103	C₄	semidirect
26. C₃×C₅×#102	C₄	semidirect
27. C₃×C₅×#102	C₄	semidirect
28. C₃×#1866	C₅	direct (N × H)
30. C₂×C₅×#108	C₂×C₃	semidirect
31. C₅×#424	C₂×C₃	semidirect
34. C₅×#339	C₂×C₃	semidirect
35. C₅×#336	C₂×C₃	semidirect
69. C₂×C₃×#108	C₂×C₅	semidirect
70. C₃×#424	C₂×C₅	semidirect
73. C₃×#339	C₂×C₅	semidirect
74. C₃×#336	C₂×C₅	semidirect
90. C₅×#103	C₃×C₄	semidirect
91. C₅×#103	C₃×C₄	semidirect
92. C₅×#102	C₃×C₄	semidirect
93. C₅×#102	C₃×C₄	semidirect
94. #1866	C₃×C₅	direct (N × H)
138. C₃×#103	C₄×C₅	semidirect
139. C₃×#103	C₄×C₅	semidirect
140. C₃×#102	C₄×C₅	semidirect
141. C₃×#102	C₄×C₅	semidirect
175. C₂×#108	C₂×C₃×C₅	semidirect
176. #424	C₂×C₃×C₅	semidirect
179. #339	C₂×C₃×C₅	semidirect
180. #336	C₂×C₃×C₅	semidirect
272. #103	C₃×C₄×C₅	semidirect
273. #103	C₃×C₄×C₅	semidirect
274. #102	C₃×C₄×C₅	semidirect
275. #102	C₃×C₄×C₅	semidirect
358. C₃×C₅	#1866	direct (N × H)
415. C₅	C₃×#1866	direct (N × H)
432. C₃	C₅×#1866	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×#131	2
C₂×C₃×C₅×#108	2
C₃×C₅×#424	2
C₂×C₃×C₅×#104	2
C₃×C₅×#416	2
C₃×C₅×#339	2
C₃×C₅×#336	2
C₅×#1866	3
C₃×#1866	5

Subgroups — C3×C5×#1866 #14274900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1866 #14274900