Subgroups — C₃×#10615528 #14412633

Order 1920.

1556 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×#4149	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66161	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65422	C₂	1	3	yes	maximal, complemented
5	C₃×#65420	C₂	1	3	yes	maximal, complemented
6	C₃×#65402	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#3953	C₂	1	3	yes	maximal, complemented
8	#10615528	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₃×#4149	—	2	4	no	—
11	C₃×#4149	C₄	1	8	yes	complemented
12	C₂×C₃×#713	—	2	1	no	—
13	C₂×C₃×D₄×D₅	—	2	3	no	—
14	C₂×C₃×#709	C₂²	1	3	yes	—
15	C₂²×C₃×D₂₀	C₂²	1	3	yes	—
16	C₃×C₅×#131	—	2	4	no	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	3	yes	complemented
18	C₂²×C₃×C₅×C₈	C₂²	1	3	yes	complemented
19	C₃×Q₈×Dic₅	—	2	1	no	—
20	C₃×D₄×Dic₅	—	2	3	no	—
21	C₃×#4072	C₂²	1	3	yes	complemented
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	complemented
23	C₃×#3953	C₂²	1	3	yes	complemented
24	C₃×#3953	C₂²	1	6	yes	complemented
25	C₃×#3953	C₂²	1	3	yes	complemented
26	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
27	C₃×#3948	C₂²	1	3	yes	complemented
28	C₃×#2897	—	5	1	no	maximal, Hall
29	C₂×#4149	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
31	#66161	C₂×C₃	1	1	yes	characteristic, complemented
32	#65422	C₂×C₃	1	3	yes	complemented
33	#65420	C₂×C₃	1	3	yes	complemented
34	#65402	C₂×C₃	1	3	yes	complemented
35	C₂×#3953	C₂×C₃	1	3	yes	complemented
36	C₂³×C₃×D₅	—	2	3	no	—
37	C₃×C₅×#41	C₂×C₄	1	4	yes	—
38	C₃×C₅×#41	D₄	1	4	yes	—
39	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
42	C₂×C₃×C₂²⋊D₅	—	2	3	no	—
43	C₂²×C₃×Dic₅	—	2	3	no	—
44	C₃×#713	—	2	8	no	—
45	C₃×D₄×D₅	—	2	24	no	—
46	C₃×#709	—	2	6	no	—
47	C₃×#709	C₂×C₄	1	12	yes	complemented
48	C₂×C₃×D₂₀	—	2	3	no	—
49	C₂×C₃×D₂₀	—	2	6	no	—
50	C₂×C₃×D₂₀	C₂×C₄	1	12	yes	complemented
51	C₂×C₃×D₂₀	C₂³	1	3	yes	—
52	C₂×C₃×C₄×D₅	—	2	3	no	—
53	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
54	C₃×C₅×M₁₆	—	2	6	no	—
55	C₂×C₃×C₅×C₈	—	2	6	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	3	yes	—
58	C₃×C₂²⋊Dic₅	—	2	3	no	—
59	C₃×C₄⋊Dic₅	—	2	3	no	—
60	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
61	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
62	C₃×C₄×Dic₅	—	2	3	no	—
63	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
64	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
65	C₃×#520	—	5	1	no	—
66	C₃×#418	—	5	3	no	—
67	C₃×#417	—	5	3	no	—
68	C₃×#416	—	5	3	no	—
69	C₂×C₃×#102	—	5	3	no	—
70	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
71	#4149	—	2	4	no	—
72	#4149	C₃×C₄	1	8	yes	complemented
73	C₂×#713	—	2	1	no	—
74	C₂×D₄×D₅	—	2	3	no	—
75	C₂×#709	C₂²×C₃	1	3	yes	—
76	C₂²×D₂₀	C₂²×C₃	1	3	yes	—
77	C₅×#131	—	2	4	no	—
78	C₂×C₅×M₁₆	C₂²×C₃	1	3	yes	complemented
79	C₂²×C₅×C₈	C₂²×C₃	1	3	yes	complemented
80	Q₈×Dic₅	—	2	1	no	—
81	D₄×Dic₅	—	2	3	no	—
82	#4072	C₂²×C₃	1	3	yes	complemented
83	C₂×C₄⋊Dic₅	C₂²×C₃	1	3	yes	complemented
84	#3953	C₂²×C₃	1	3	yes	complemented
85	#3953	C₂²×C₃	1	6	yes	complemented
86	#3953	C₂²×C₃	1	3	yes	complemented
87	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
88	#3948	C₂²×C₃	1	3	yes	complemented
89	#2897	—	5	1	no	Sylow
90	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
91	C₂²×C₃×D₅	—	2	3	no	—
92	C₂²×C₃×D₅	—	2	12	no	—
93	C₂²×C₃×D₅	—	8	3	no	—
94	C₂²×C₃×D₅	—	8	3	no	—
95	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
96	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₂²⋊D₅	—	2	12	no	—
102	C₂×C₃×Dic₅	—	2	1	no	—
103	C₂×C₃×Dic₅	—	2	1	no	—
104	C₂×C₃×Dic₅	—	2	3	no	—
105	C₂×C₃×Dic₅	—	8	3	no	—
106	C₃×D₂₀	—	2	12	no	—
107	C₃×D₂₀	—	2	3	no	—
108	C₃×D₂₀	C₂²×C₄	1	6	yes	—
109	C₃×C₄×D₅	—	2	12	no	—
110	C₃×Dic₁₀	—	2	1	no	—
111	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
112	C₃×C₅×C₈	—	2	1	no	—
113	C₃×C₅×C₈	—	2	3	no	—
114	C₃×H(5,𝔽₂)	—	5	8	no	—
115	C₃×H(5,𝔽₂)	—	10	4	no	—
116	C₂×C₃×#41	—	5	3	no	—
117	C₂×C₃×#41	—	10	1	no	—
118	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
119	C₂²×C₃×D₄	—	5	3	no	—
120	C₂²×C₃×D₄	—	10	3	no	—
121	C₃×#131	—	2	4	no	—
122	C₂×C₃×M₁₆	C₂×D₅	1	3	yes	complemented
123	C₂²×C₃×C₈	C₂×D₅	1	3	yes	complemented
124	C₃×C₄×Q₈	—	10	1	no	—
125	C₃×C₄×D₄	—	10	3	no	—
126	C₃×#117	—	5	3	no	—
127	C₂×C₃×C₄⋊C₄	—	5	3	no	—
128	C₃×#103	—	5	1	no	—
129	C₃×#103	—	5	3	no	—
130	C₃×#102	—	5	3	no	—
131	C₃×#102	—	5	6	no	—
132	C₃×#102	—	5	3	no	—
133	C₂³×D₅	—	2	3	no	—
134	C₅×#41	C₂×C₃×C₄	1	4	yes	—
135	C₅×#41	C₃×D₄	1	4	yes	—
136	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
137	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
139	C₂×C₂²⋊D₅	—	2	3	no	—
140	C₂²×Dic₅	—	2	3	no	—
141	#713	—	2	8	no	—
142	D₄×D₅	—	2	24	no	—
143	#709	—	2	6	no	—
144	#709	C₂×C₃×C₄	1	12	yes	complemented
145	C₂×D₂₀	—	2	3	no	—
146	C₂×D₂₀	—	2	6	no	—
147	C₂×D₂₀	C₂×C₃×C₄	1	12	yes	complemented
148	C₂×D₂₀	C₂³×C₃	1	3	yes	—
149	C₂×C₄×D₅	—	2	3	no	—
150	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
151	C₅×M₁₆	—	2	6	no	—
152	C₂×C₅×C₈	—	2	6	no	—
153	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂³×C₃	1	3	yes	—
155	C₂²⋊Dic₅	—	2	3	no	—
156	C₄⋊Dic₅	—	2	3	no	—
157	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
158	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
159	C₄×Dic₅	—	2	3	no	—
160	C₂×H(5,𝔽₂)	—	5	1	no	—
161	C₂×#131	C₃×D₅	1	1	yes	characteristic, complemented
162	#520	—	5	1	no	—
163	#418	—	5	3	no	—
164	#417	—	5	3	no	—
165	#416	—	5	3	no	—
166	C₂×#102	—	5	3	no	—
167	C₂²×C₃×C₅	—	2	3	no	—
168	C₂²×C₃×C₅	—	2	3	no	—
169	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
170	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₃×D₅	—	2	6	no	—
172	C₂×C₃×D₅	—	4	3	no	—
173	C₂×C₃×D₅	—	4	3	no	—
174	C₂×C₃×D₅	—	8	12	no	—
175	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
176	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₃×Dic₅	—	2	2	no	—
179	C₃×Dic₅	—	4	3	no	—
180	C₃×Dic₅	—	4	1	no	—
181	C₂⁴×C₃	—	10	3	no	—
182	C₃×#41	—	5	12	no	—
183	C₃×#41	—	10	8	no	—
184	C₃×#41	—	10	6	no	—
185	C₃×#41	C₄×D₅	1	4	yes	—
186	C₃×#41	C₂²⋊D₅	1	4	yes	—
187	C₂×C₃×Q₈	—	5	1	no	—
188	C₂×C₃×Q₈	D₂₀	1	1	yes	characteristic
189	C₂×C₃×D₄	—	5	12	no	—
190	C₂×C₃×D₄	—	5	3	no	—
191	C₂×C₃×D₄	—	10	3	no	—
192	C₂×C₃×D₄	—	10	24	no	—
193	C₂×C₃×D₄	—	10	3	no	—
194	C₂×C₃×D₄	—	10	6	no	—
195	C₂×C₃×D₄	D₂₀	1	3	yes	—
196	C₂²×C₃×C₄	—	10	3	no	—
197	C₂²×C₃×C₄	—	10	3	no	—
198	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
199	C₃×M₁₆	—	2	6	no	—
200	C₂×C₃×C₈	—	2	6	no	—
201	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
202	C₂×C₃×C₈	C₂²×D₅	1	3	yes	—
203	C₃×C₄⋊C₄	—	5	3	no	—
204	C₃×C₄⋊C₄	—	5	1	no	—
205	C₃×C₄⋊C₄	—	10	3	no	—
206	C₃×C₂²⋊C₄	—	10	3	no	—
207	C₃×C₄²	—	10	3	no	—
208	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
209	C₂²×D₅	—	2	3	no	—
210	C₂²×D₅	—	2	12	no	—
211	C₂²×D₅	—	8	3	no	—
212	C₂²×D₅	—	8	3	no	—
213	C₅×Q₈	C₃×C₂²⋊C₄	1	4	yes	—
214	C₅×D₄	C₃×C₂²⋊C₄	1	12	yes	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
218	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
219	C₂²⋊D₅	—	2	12	no	—
220	C₂×Dic₅	—	2	1	no	—
221	C₂×Dic₅	—	2	1	no	—
222	C₂×Dic₅	—	2	3	no	—
223	C₂×Dic₅	—	8	3	no	—
224	D₂₀	—	2	12	no	—
225	D₂₀	—	2	3	no	—
226	D₂₀	C₂²×C₃×C₄	1	6	yes	—
227	C₄×D₅	—	2	12	no	—
228	Dic₁₀	—	2	1	no	—
229	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
230	C₅×C₈	—	2	1	no	—
231	C₅×C₈	—	2	3	no	—
232	H(5,𝔽₂)	—	5	8	no	—
233	H(5,𝔽₂)	—	10	4	no	—
234	C₂×#41	—	5	3	no	—
235	C₂×#41	—	10	1	no	—
236	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
237	C₂²×D₄	—	5	3	no	—
238	C₂²×D₄	—	10	3	no	—
239	#131	—	2	4	no	—
240	C₂×M₁₆	C₂×C₃×D₅	1	3	yes	complemented
241	C₂²×C₈	C₂×C₃×D₅	1	3	yes	complemented
242	C₄×Q₈	—	10	1	no	—
243	C₄×D₄	—	10	3	no	—
244	#117	—	5	3	no	—
245	C₂×C₄⋊C₄	—	5	3	no	—
246	#103	—	5	1	no	—
247	#103	—	5	3	no	—
248	#102	—	5	3	no	—
249	#102	—	5	6	no	—
250	#102	—	5	3	no	—
251	C₂×C₃×C₅	—	2	6	no	—
252	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₅	#576	1	1	yes	characteristic
254	C₂×C₃×C₅	#577	1	1	yes	characteristic
255	C₃×D₅	—	4	6	no	—
256	C₂³×C₃	—	10	3	no	—
257	C₂³×C₃	—	10	12	no	—
258	C₂³×C₃	—	40	3	no	—
259	C₂³×C₃	—	40	3	no	—
260	C₂³×C₃	C₂×D₂₀	1	3	yes	—
261	C₃×Q₈	—	5	2	no	—
262	C₃×Q₈	—	10	1	no	—
263	C₃×Q₈	#685	1	4	yes	—
264	C₃×D₄	—	5	6	no	—
265	C₃×D₄	—	10	12	no	—
266	C₃×D₄	—	10	3	no	—
267	C₃×D₄	—	10	12	no	—
268	C₃×D₄	#685	1	12	yes	—
269	C₂×C₃×C₄	—	10	1	no	—
270	C₂×C₃×C₄	—	10	12	no	—
271	C₂×C₃×C₄	—	10	1	no	—
272	C₂×C₃×C₄	—	10	3	no	—
273	C₂×C₃×C₄	—	40	3	no	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	6	yes	—
275	C₂×C₃×C₄	C₂×D₂₀	1	3	yes	—
276	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	6	yes	—
277	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
278	C₃×C₈	—	2	1	no	—
279	C₃×C₈	—	2	3	no	—
280	C₂²×C₅	—	2	3	no	—
281	C₂²×C₅	—	2	3	no	—
282	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
283	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
284	C₂×D₅	—	2	6	no	—
285	C₂×D₅	—	4	3	no	—
286	C₂×D₅	—	4	3	no	—
287	C₂×D₅	—	8	12	no	—
288	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
289	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
290	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
291	Dic₅	—	2	2	no	—
292	Dic₅	—	4	3	no	—
293	Dic₅	—	4	1	no	—
294	C₂⁴	—	10	3	no	—
295	#41	—	5	12	no	—
296	#41	—	10	8	no	—
297	#41	—	10	6	no	—
298	#41	C₃×C₄×D₅	1	4	yes	—
299	#41	C₃×C₂²⋊D₅	1	4	yes	—
300	C₂×Q₈	—	5	1	no	—
301	C₂×Q₈	C₃×D₂₀	1	1	yes	characteristic
302	C₂×D₄	—	5	12	no	—
303	C₂×D₄	—	5	3	no	—
304	C₂×D₄	—	10	3	no	—
305	C₂×D₄	—	10	24	no	—
306	C₂×D₄	—	10	3	no	—
307	C₂×D₄	—	10	6	no	—
308	C₂×D₄	C₃×D₂₀	1	3	yes	—
309	C₂²×C₄	—	10	3	no	—
310	C₂²×C₄	—	10	3	no	—
311	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
312	M₁₆	—	2	6	no	—
313	C₂×C₈	—	2	6	no	—
314	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
315	C₂×C₈	C₂²×C₃×D₅	1	3	yes	—
316	C₄⋊C₄	—	5	3	no	—
317	C₄⋊C₄	—	5	1	no	—
318	C₄⋊C₄	—	10	3	no	—
319	C₂²⋊C₄	—	10	3	no	—
320	C₄²	—	10	3	no	—
321	C₃×C₅	#2897	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	—	2	3	no	—
323	C₂²×C₃	—	2	3	no	—
324	C₂²×C₃	—	10	6	no	—
325	C₂²×C₃	—	20	3	no	—
326	C₂²×C₃	—	20	3	no	—
327	C₂²×C₃	—	40	12	no	—
328	C₂²×C₃	C₂×#685	1	6	yes	—
329	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
330	C₃×C₄	—	10	2	no	—
331	C₃×C₄	—	20	1	no	—
332	C₃×C₄	—	20	3	no	—
333	C₃×C₄	C₂×#685	1	6	yes	—
334	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
335	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
336	C₂×C₅	—	2	6	no	—
337	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₅	C₃×#576	1	1	yes	characteristic
339	C₂×C₅	C₃×#577	1	1	yes	characteristic
340	D₅	—	4	6	no	—
341	C₂³	—	10	3	no	—
342	C₂³	—	10	12	no	—
343	C₂³	—	40	3	no	—
344	C₂³	—	40	3	no	—
345	C₂³	C₂×C₃×D₂₀	1	3	yes	—
346	Q₈	—	5	2	no	—
347	Q₈	—	10	1	no	—
348	Q₈	C₃×#685	1	4	yes	—
349	D₄	—	5	6	no	—
350	D₄	—	10	12	no	—
351	D₄	—	10	3	no	—
352	D₄	—	10	12	no	—
353	D₄	C₃×#685	1	12	yes	—
354	C₂×C₄	—	10	1	no	—
355	C₂×C₄	—	10	12	no	—
356	C₂×C₄	—	10	1	no	—
357	C₂×C₄	—	10	3	no	—
358	C₂×C₄	—	40	3	no	—
359	C₂×C₄	C₂×C₃×C₄×D₅	1	6	yes	—
360	C₂×C₄	C₂×C₃×D₂₀	1	3	yes	—
361	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	6	yes	—
362	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	3	no	—
365	C₂×C₃	—	2	6	no	—
366	C₂×C₃	—	20	6	no	—
367	C₂×C₃	#66085	1	1	yes	characteristic
368	C₂×C₃	#66086	1	1	yes	characteristic
369	C₂×C₃	C₂²×#685	1	1	yes	characteristic
370	C₅	C₃×#2897	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	3	no	—
372	C₂²	—	2	3	no	—
373	C₂²	—	10	6	no	—
374	C₂²	—	20	3	no	—
375	C₂²	—	20	3	no	—
376	C₂²	—	40	12	no	—
377	C₂²	C₂×C₃×#685	1	6	yes	—
378	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
379	C₄	—	10	2	no	—
380	C₄	—	20	1	no	—
381	C₄	—	20	3	no	—
382	C₄	C₂×C₃×#685	1	6	yes	—
383	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
384	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
385	C₃	#10615528	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	2	6	no	—
387	C₂	—	20	6	no	—
388	C₂	C₃×#66085	1	1	yes	characteristic
389	C₂	C₃×#66086	1	1	yes	characteristic
390	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4149	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₅
hypocenter	C₅	C₃×#2897
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₃×#66161	C₂	semidirect
4. C₃×#65422	C₂	semidirect
5. C₃×#65420	C₂	semidirect
6. C₃×#65402	C₂	semidirect
7. C₂×C₃×#3953	C₂	semidirect
8. #10615528	C₃	direct (N × H)
11. C₃×#4149	C₄	semidirect
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₂²×C₃×C₅×C₈	C₂²	semidirect
21. C₃×#4072	C₂²	semidirect
22. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
23. C₃×#3953	C₂²	semidirect
24. C₃×#3953	C₂²	semidirect
25. C₃×#3953	C₂²	semidirect
26. C₃×#3948	C₂²	semidirect
27. C₃×#3948	C₂²	semidirect
30. C₂×C₅×#131	C₂×C₃	semidirect
31. #66161	C₂×C₃	semidirect
32. #65422	C₂×C₃	semidirect
33. #65420	C₂×C₃	semidirect
34. #65402	C₂×C₃	semidirect
35. C₂×#3953	C₂×C₃	semidirect
47. C₃×#709	C₂×C₄	semidirect
50. C₂×C₃×D₂₀	C₂×C₄	semidirect
64. C₂×C₃×#131	D₅	semidirect
72. #4149	C₃×C₄	semidirect
78. C₂×C₅×M₁₆	C₂²×C₃	semidirect
79. C₂²×C₅×C₈	C₂²×C₃	semidirect
82. #4072	C₂²×C₃	semidirect
83. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
84. #3953	C₂²×C₃	semidirect
85. #3953	C₂²×C₃	semidirect
86. #3953	C₂²×C₃	semidirect
87. #3948	C₂²×C₃	semidirect
88. #3948	C₂²×C₃	semidirect
122. C₂×C₃×M₁₆	C₂×D₅	semidirect
123. C₂²×C₃×C₈	C₂×D₅	semidirect
144. #709	C₂×C₃×C₄	semidirect
147. C₂×D₂₀	C₂×C₃×C₄	semidirect
161. C₂×#131	C₃×D₅	semidirect
240. C₂×M₁₆	C₂×C₃×D₅	semidirect
241. C₂²×C₈	C₂×C₃×D₅	semidirect
321. C₃×C₅	#2897	semidirect
370. C₅	C₃×#2897	semidirect
385. C₃	#10615528	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×#4149	2
C₂×C₃×C₅×#131	2
C₃×#66161	2
C₃×#65422	2
C₃×#65420	2
C₃×#65402	2
C₂×C₃×#3953	2
#10615528	3
C₃×#2897	5

Subgroups — C3×#10615528 #14412633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615528 #14412633