Subgroups — C₃×C₅×#2010 #14275044

Order 1920.

788 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×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#525	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#421	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2010	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×#137	—	2	2	no	—
10	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
11	C₃×C₅×#135	—	2	2	no	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#123	—	2	2	no	—
15	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
16	C₃×C₅×#121	—	2	2	no	—
17	C₃×C₅×#120	—	2	2	no	—
18	C₃×C₄×C₅×D₄	—	2	4	no	—
19	C₃×C₅×#117	C₂²	1	2	yes	—
20	C₃×C₅×#104	—	2	4	no	—
21	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
22	C₃×#2010	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×#575	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#525	C₂×C₃	1	2	yes	complemented
25	C₅×#421	C₂×C₃	1	2	yes	complemented
26	C₅×#407	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×H(3,ℤ/4)	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	—	2	2	no	—
32	C₃×C₅×#41	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	D₄	1	2	yes	complemented
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	—	2	2	no	—
36	C₂×C₃×C₅×D₄	D₄	1	2	yes	complemented
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×Q₁₆	—	2	2	no	—
45	C₃×C₅×SD₁₆	—	2	4	no	—
46	C₃×C₅×D₈	—	2	2	no	—
47	C₃×C₅×M₁₆	—	2	2	no	—
48	C₃×C₅×M₁₆	—	2	2	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	D₄	1	2	yes	complemented
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	2	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₄²×C₅	D₄	1	4	yes	complemented
57	C₃×#575	C₂×C₅	1	1	yes	characteristic, complemented
58	C₃×#525	C₂×C₅	1	2	yes	complemented
59	C₃×#421	C₂×C₅	1	2	yes	complemented
60	C₃×#407	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
63	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₅×#137	—	2	2	no	—
65	C₅×AGL(1,ℤ/8)	—	2	2	no	—
66	C₅×#135	—	2	2	no	—
67	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
69	C₅×#123	—	2	2	no	—
70	C₅×C₂²⋊Q₈	—	2	2	no	—
71	C₅×#121	—	2	2	no	—
72	C₅×#120	—	2	2	no	—
73	C₄×C₅×D₄	—	2	4	no	—
74	C₅×#117	C₂²×C₃	1	2	yes	—
75	C₅×#104	—	2	4	no	—
76	C₅×C₂²⋊C₈	—	2	2	no	—
77	#2010	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	—	2	2	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	2	2	no	—
84	C₃×C₅×Q₈	—	2	2	no	—
85	C₃×C₅×D₄	—	2	2	no	—
86	C₃×C₅×D₄	—	2	2	no	—
87	C₃×C₅×D₄	—	4	8	no	—
88	C₃×C₅×D₄	—	4	2	no	—
89	C₃×C₅×D₄	—	4	2	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	4	2	no	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₃×C₅×C₈	—	2	2	no	—
104	C₃×C₅×C₈	—	4	1	no	—
105	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
106	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
107	C₃×#137	—	2	2	no	—
108	C₃×AGL(1,ℤ/8)	—	2	2	no	—
109	C₃×#135	—	2	2	no	—
110	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
112	C₃×#123	—	2	2	no	—
113	C₃×C₂²⋊Q₈	—	2	2	no	—
114	C₃×#121	—	2	2	no	—
115	C₃×#120	—	2	2	no	—
116	C₃×C₄×D₄	—	2	4	no	—
117	C₃×#117	C₂²×C₅	1	2	yes	—
118	C₃×#104	—	2	4	no	—
119	C₃×C₂²⋊C₈	—	2	2	no	—
120	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
121	C₅×#41	—	2	2	no	—
122	C₅×#41	—	2	2	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	2	2	no	—
125	C₂×C₅×Q₈	C₃×D₄	1	2	yes	complemented
126	C₂×C₅×D₄	—	2	4	no	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	C₃×D₄	1	2	yes	complemented
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₅×Q₁₆	—	2	2	no	—
137	C₅×SD₁₆	—	2	4	no	—
138	C₅×D₈	—	2	2	no	—
139	C₅×M₁₆	—	2	2	no	—
140	C₅×M₁₆	—	2	2	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	C₃×D₄	1	2	yes	complemented
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₂²⋊C₄	—	2	4	no	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₄²×C₅	C₃×D₄	1	4	yes	complemented
149	#575	C₂×C₃×C₅	1	1	yes	characteristic, complemented
150	#525	C₂×C₃×C₅	1	2	yes	complemented
151	#421	C₂×C₃×C₅	1	2	yes	complemented
152	#407	C₂×C₃×C₅	1	1	yes	characteristic, complemented
153	H(3,ℤ/4)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
154	C₂²×C₃×C₅	—	2	4	no	—
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	—	4	1	no	—
157	C₂²×C₃×C₅	—	4	2	no	—
158	C₂²×C₃×C₅	—	4	1	no	—
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	—	4	1	no	—
161	C₂²×C₃×C₅	—	4	2	no	—
162	C₂²×C₃×C₅	#120	1	2	yes	—
163	C₂²×C₃×C₅	#121	1	1	yes	characteristic
164	C₃×C₄×C₅	—	4	4	no	—
165	C₃×C₄×C₅	—	4	1	no	—
166	C₃×C₄×C₅	—	4	2	no	—
167	C₃×C₄×C₅	#120	1	1	yes	characteristic
168	C₃×C₄×C₅	#121	1	2	yes	—
169	C₃×C₄×C₅	#127	1	1	yes	characteristic
170	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
171	C₃×#41	—	2	2	no	—
172	C₃×#41	—	2	2	no	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	—	2	2	no	—
175	C₂×C₃×Q₈	C₅×D₄	1	2	yes	complemented
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	2	2	no	—
178	C₂×C₃×D₄	C₅×D₄	1	2	yes	complemented
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	2	2	no	—
182	C₂²×C₃×C₄	—	2	2	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₃×Q₁₆	—	2	2	no	—
187	C₃×SD₁₆	—	2	4	no	—
188	C₃×D₈	—	2	2	no	—
189	C₃×M₁₆	—	2	2	no	—
190	C₃×M₁₆	—	2	2	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	C₅×D₄	1	2	yes	complemented
193	C₃×C₄⋊C₄	—	2	4	no	—
194	C₃×C₄⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	—	2	4	no	—
196	C₃×C₂²⋊C₄	—	2	4	no	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₄²	C₅×D₄	1	4	yes	complemented
199	C₂³×C₅	—	2	2	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
204	C₅×Q₈	—	2	2	no	—
205	C₅×Q₈	—	2	2	no	—
206	C₅×D₄	—	2	2	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	8	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	2	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
223	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	—	4	1	no	—
226	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
227	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
228	#137	—	2	2	no	—
229	AGL(1,ℤ/8)	—	2	2	no	—
230	#135	—	2	2	no	—
231	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
232	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
233	#123	—	2	2	no	—
234	C₂²⋊Q₈	—	2	2	no	—
235	#121	—	2	2	no	—
236	#120	—	2	2	no	—
237	C₄×D₄	—	2	4	no	—
238	#117	C₂²×C₃×C₅	1	2	yes	—
239	#104	—	2	4	no	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	—	2	1	no	—
243	C₂×C₃×C₅	—	4	2	no	—
244	C₂×C₃×C₅	—	8	2	no	—
245	C₂×C₃×C₅	#392	1	1	yes	characteristic
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	1	no	—
248	C₂³×C₃	—	2	2	no	—
249	C₂³×C₃	—	4	2	no	—
250	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
251	C₃×Q₈	—	2	2	no	—
252	C₃×Q₈	—	2	2	no	—
253	C₃×D₄	—	2	2	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	—	4	8	no	—
256	C₃×D₄	—	4	2	no	—
257	C₃×D₄	—	4	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	—	4	2	no	—
265	C₂×C₃×C₄	—	4	1	no	—
266	C₂×C₃×C₄	—	4	2	no	—
267	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	—	4	1	no	—
273	C₂²×C₅	—	2	4	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	—	4	4	no	—
279	C₂²×C₅	—	4	1	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	C₃×#120	1	2	yes	—
282	C₂²×C₅	C₃×#121	1	1	yes	characteristic
283	C₄×C₅	—	4	4	no	—
284	C₄×C₅	—	4	1	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	C₃×#120	1	1	yes	characteristic
287	C₄×C₅	C₃×#121	1	2	yes	—
288	C₄×C₅	C₃×#127	1	1	yes	characteristic
289	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	#41	—	2	2	no	—
294	C₂×Q₈	C₃×C₅×D₄	1	2	yes	complemented
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₃×C₅×D₄	1	2	yes	complemented
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
305	Q₁₆	—	2	2	no	—
306	SD₁₆	—	2	4	no	—
307	D₈	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	C₃×C₅×D₄	1	2	yes	complemented
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₄²	C₃×C₅×D₄	1	4	yes	complemented
318	C₃×C₅	#2010	1	1	yes	characteristic, direct product factor, Hall
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	—	4	4	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	—	4	2	no	—
327	C₂²×C₃	C₅×#120	1	2	yes	—
328	C₂²×C₃	C₅×#121	1	1	yes	characteristic
329	C₃×C₄	—	4	4	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	—	4	2	no	—
332	C₃×C₄	C₅×#120	1	1	yes	characteristic
333	C₃×C₄	C₅×#121	1	2	yes	—
334	C₃×C₄	C₅×#127	1	1	yes	characteristic
335	C₂×C₅	—	2	2	no	—
336	C₂×C₅	—	2	1	no	—
337	C₂×C₅	—	4	2	no	—
338	C₂×C₅	—	8	2	no	—
339	C₂×C₅	C₃×#392	1	1	yes	characteristic
340	C₂³	—	2	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
362	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
364	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	4	1	no	—
367	C₂×C₃	—	2	2	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	4	2	no	—
370	C₂×C₃	—	8	2	no	—
371	C₂×C₃	C₅×#392	1	1	yes	characteristic
372	C₅	C₃×#2010	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₃×C₅×#120	1	2	yes	—
382	C₂²	C₃×C₅×#121	1	1	yes	characteristic
383	C₄	—	4	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	C₃×C₅×#120	1	1	yes	characteristic
387	C₄	C₃×C₅×#121	1	2	yes	—
388	C₄	C₃×C₅×#127	1	1	yes	characteristic
389	C₃	C₅×#2010	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	2	2	no	—
391	C₂	—	2	1	no	—
392	C₂	—	4	2	no	—
393	C₂	—	8	2	no	—
394	C₂	C₃×C₅×#392	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂×C₃×C₅	#392
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#575	C₂	semidirect
2. C₃×C₅×#525	C₂	semidirect
3. C₃×C₅×#421	C₂	semidirect
4. C₃×C₅×#407	C₂	semidirect
5. C₃×C₅×H(3,ℤ/4)	C₂	semidirect
6. C₅×#2010	C₃	direct (N × H)
22. C₃×#2010	C₅	direct (N × H)
23. C₅×#575	C₂×C₃	semidirect
24. C₅×#525	C₂×C₃	semidirect
25. C₅×#421	C₂×C₃	semidirect
26. C₅×#407	C₂×C₃	semidirect
27. C₅×H(3,ℤ/4)	C₂×C₃	semidirect
33. C₂×C₃×C₅×Q₈	D₄	semidirect
36. C₂×C₃×C₅×D₄	D₄	semidirect
50. C₂×C₃×C₅×C₈	D₄	semidirect
56. C₃×C₄²×C₅	D₄	semidirect
57. C₃×#575	C₂×C₅	semidirect
58. C₃×#525	C₂×C₅	semidirect
59. C₃×#421	C₂×C₅	semidirect
60. C₃×#407	C₂×C₅	semidirect
61. C₃×H(3,ℤ/4)	C₂×C₅	semidirect
77. #2010	C₃×C₅	direct (N × H)
125. C₂×C₅×Q₈	C₃×D₄	semidirect
128. C₂×C₅×D₄	C₃×D₄	semidirect
142. C₂×C₅×C₈	C₃×D₄	semidirect
148. C₄²×C₅	C₃×D₄	semidirect
149. #575	C₂×C₃×C₅	semidirect
150. #525	C₂×C₃×C₅	semidirect
151. #421	C₂×C₃×C₅	semidirect
152. #407	C₂×C₃×C₅	semidirect
153. H(3,ℤ/4)	C₂×C₃×C₅	semidirect
175. C₂×C₃×Q₈	C₅×D₄	semidirect
178. C₂×C₃×D₄	C₅×D₄	semidirect
192. C₂×C₃×C₈	C₅×D₄	semidirect
198. C₃×C₄²	C₅×D₄	semidirect
294. C₂×Q₈	C₃×C₅×D₄	semidirect
297. C₂×D₄	C₃×C₅×D₄	semidirect
311. C₂×C₈	C₃×C₅×D₄	semidirect
317. C₄²	C₃×C₅×D₄	semidirect
318. C₃×C₅	#2010	direct (N × H)
372. C₅	C₃×#2010	direct (N × H)
389. C₃	C₅×#2010	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×#575	2
C₃×C₅×#525	2
C₃×C₅×#421	2
C₃×C₅×#407	2
C₃×C₅×H(3,ℤ/4)	2
C₅×#2010	3
C₃×#2010	5

Subgroups — C3×C5×#2010 #14275044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2010 #14275044