Subgroups — C₂×C₃×#66032 #14481098

Order 1920.

2520 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×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66032	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4041	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4041	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×#4040	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4039	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66032	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
12	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
15	C₃×C₅×#125	C₂²	1	8	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#685	C₂²	1	2	yes	—
20	C₂×C₃×#685	C₂²	1	4	yes	—
21	C₂×C₃×#685	C₂²	1	4	yes	—
22	C₂×C₃×#683	C₂²	1	2	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₃×#4041	C₂²	1	32	yes	complemented
25	C₃×#4041	C₂²	1	16	yes	complemented
26	C₃×#4040	C₂²	1	32	yes	complemented
27	C₃×#4039	C₂²	1	16	yes	complemented
28	C₃×#4020	C₂²	1	8	yes	complemented
29	C₃×#4018	C₂²	1	8	yes	complemented
30	C₂×C₃×#540	—	5	1	no	maximal, Hall
31	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
32	#66032	C₂×C₃	1	16	yes	direct product factor
33	C₂×#4041	C₂×C₃	1	2	yes	complemented
34	C₂×#4041	C₂×C₃	1	4	yes	complemented
35	C₂×#4040	C₂×C₃	1	4	yes	complemented
36	C₂×#4039	C₂×C₃	1	2	yes	complemented
37	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
40	C₂³×C₃×D₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×D₂₀	—	2	8	no	—
47	C₂×C₃×D₂₀	—	4	8	no	—
48	C₂×C₃×D₂₀	—	4	8	no	—
49	C₂×C₃×D₂₀	C₂³	1	8	yes	—
50	C₂×C₃×D₂₀	C₂³	1	16	yes	—
51	C₂×C₃×D₂₀	C₂³	1	16	yes	—
52	C₂×C₃×C₄×D₅	—	2	4	no	—
53	C₂×C₃×C₄×D₅	—	4	8	no	—
54	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
55	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
58	C₃×C₄²×C₅	C₂³	1	4	yes	—
59	C₃×#685	C₂³	1	8	yes	—
60	C₃×#685	C₂³	1	16	yes	—
61	C₃×#685	C₂³	1	16	yes	—
62	C₃×#683	C₂³	1	8	yes	—
63	C₃×C₄×Dic₅	C₂³	1	4	yes	—
64	C₃×#540	—	5	16	no	—
65	C₂×C₃×#127	—	5	1	no	—
66	C₂×C₃×#125	D₅	1	1	yes	characteristic, complemented
67	C₂×C₃×#123	—	5	4	no	—
68	C₂×C₃×#121	—	5	4	no	—
69	C₂×C₃×#121	—	5	2	no	—
70	C₂×C₃×C₄×D₄	—	5	2	no	—
71	C₂×C₃×#117	—	5	1	no	—
72	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
73	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
74	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
75	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
77	C₅×#125	C₂²×C₃	1	8	yes	complemented
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₂×#685	C₂²×C₃	1	2	yes	—
82	C₂×#685	C₂²×C₃	1	4	yes	—
83	C₂×#685	C₂²×C₃	1	4	yes	—
84	C₂×#683	C₂²×C₃	1	2	yes	—
85	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
86	#4041	C₂²×C₃	1	32	yes	complemented
87	#4041	C₂²×C₃	1	16	yes	complemented
88	#4040	C₂²×C₃	1	32	yes	complemented
89	#4039	C₂²×C₃	1	16	yes	complemented
90	#4020	C₂²×C₃	1	8	yes	complemented
91	#4018	C₂²×C₃	1	8	yes	complemented
92	C₂×#540	—	5	1	no	Sylow
93	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
94	C₂²×C₃×D₅	—	2	2	no	—
95	C₂²×C₃×D₅	—	2	8	no	—
96	C₂²×C₃×D₅	—	2	8	no	—
97	C₂²×C₃×D₅	—	2	4	no	—
98	C₂²×C₃×D₅	—	2	8	no	—
99	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
100	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
101	C₂×C₃×C₄×C₅	—	2	8	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	4	no	—
109	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
110	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
111	C₃×D₂₀	—	2	16	no	—
112	C₃×D₂₀	—	4	16	no	—
113	C₃×D₂₀	—	4	16	no	—
114	C₃×C₄×D₅	—	2	8	no	—
115	C₃×C₄×D₅	—	4	16	no	—
116	C₂²×C₃×D₄	—	5	2	no	—
117	C₂²×C₃×D₄	—	5	4	no	—
118	C₂²×C₃×D₄	—	5	4	no	—
119	C₂³×C₃×C₄	—	5	1	no	—
120	C₂³×C₃×C₄	—	5	4	no	—
121	C₃×#127	—	5	8	no	—
122	C₃×#125	C₂×D₅	1	8	yes	complemented
123	C₃×#123	—	5	32	no	—
124	C₃×#121	—	5	32	no	—
125	C₃×#121	—	5	16	no	—
126	C₃×C₄×D₄	—	5	16	no	—
127	C₃×#117	—	5	8	no	—
128	C₂×C₃×C₄⋊C₄	—	5	2	no	—
129	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	—
131	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
132	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
133	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
134	C₂×C₃×C₄²	—	5	1	no	—
135	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
136	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
137	C₂³×D₅	C₂³×C₃	1	4	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
142	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
143	C₂×D₂₀	—	2	8	no	—
144	C₂×D₂₀	—	4	8	no	—
145	C₂×D₂₀	—	4	8	no	—
146	C₂×D₂₀	C₂³×C₃	1	8	yes	—
147	C₂×D₂₀	C₂³×C₃	1	16	yes	—
148	C₂×D₂₀	C₂³×C₃	1	16	yes	—
149	C₂×C₄×D₅	—	2	4	no	—
150	C₂×C₄×D₅	—	4	8	no	—
151	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
152	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
153	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
154	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
155	C₄²×C₅	C₂³×C₃	1	4	yes	—
156	#685	C₂³×C₃	1	8	yes	—
157	#685	C₂³×C₃	1	16	yes	—
158	#685	C₂³×C₃	1	16	yes	—
159	#683	C₂³×C₃	1	8	yes	—
160	C₄×Dic₅	C₂³×C₃	1	4	yes	—
161	#540	—	5	16	no	—
162	C₂×#127	—	5	1	no	—
163	C₂×#125	C₃×D₅	1	1	yes	characteristic, complemented
164	C₂×#123	—	5	4	no	—
165	C₂×#121	—	5	4	no	—
166	C₂×#121	—	5	2	no	—
167	C₂×C₄×D₄	—	5	2	no	—
168	C₂×#117	—	5	1	no	—
169	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
170	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
171	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
172	C₂×C₃×D₅	—	2	2	no	—
173	C₂×C₃×D₅	—	2	8	no	—
174	C₂×C₃×D₅	—	2	8	no	—
175	C₂×C₃×D₅	—	2	4	no	—
176	C₂×C₃×D₅	—	2	8	no	—
177	C₂×C₃×D₅	—	4	4	no	—
178	C₂×C₃×D₅	—	4	16	no	—
179	C₃×C₄×C₅	—	2	8	no	—
180	C₃×C₄×C₅	—	2	4	no	—
181	C₃×C₄×C₅	C₂×#41	1	4	yes	—
182	C₃×Dic₅	—	2	2	no	—
183	C₃×Dic₅	—	2	4	no	—
184	C₂⁴×C₃	—	5	1	no	—
185	C₂⁴×C₃	—	5	4	no	—
186	C₂×C₃×D₄	—	5	8	no	—
187	C₂×C₃×D₄	—	5	16	no	—
188	C₂×C₃×D₄	—	5	16	no	—
189	C₂×C₃×D₄	—	10	8	no	—
190	C₂×C₃×D₄	—	20	8	no	—
191	C₂×C₃×D₄	—	20	8	no	—
192	C₂²×C₃×C₄	—	5	2	no	—
193	C₂²×C₃×C₄	—	5	1	no	—
194	C₂²×C₃×C₄	—	5	4	no	—
195	C₂²×C₃×C₄	—	5	16	no	—
196	C₂²×C₃×C₄	—	10	4	no	—
197	C₂²×C₃×C₄	—	20	8	no	—
198	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
199	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
200	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
201	C₃×C₄⋊C₄	—	5	8	no	—
202	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
203	C₃×C₄⋊C₄	C₂²×D₅	1	16	yes	—
204	C₃×C₂²⋊C₄	—	5	8	no	—
205	C₃×C₂²⋊C₄	—	5	16	no	—
206	C₃×C₂²⋊C₄	—	5	16	no	—
207	C₃×C₄²	—	5	4	no	—
208	C₃×C₄²	C₂²×D₅	1	4	yes	—
209	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
210	C₂²×D₅	—	2	2	no	—
211	C₂²×D₅	—	2	8	no	—
212	C₂²×D₅	—	2	8	no	—
213	C₂²×D₅	—	2	4	no	—
214	C₂²×D₅	—	2	8	no	—
215	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
216	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
217	C₂×C₄×C₅	—	2	8	no	—
218	C₂×C₄×C₅	—	2	4	no	—
219	C₂×C₄×C₅	C₃×#41	1	4	yes	—
220	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
221	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
222	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
223	C₂×Dic₅	—	2	2	no	—
224	C₂×Dic₅	—	2	4	no	—
225	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
226	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
227	D₂₀	—	2	16	no	—
228	D₂₀	—	4	16	no	—
229	D₂₀	—	4	16	no	—
230	C₄×D₅	—	2	8	no	—
231	C₄×D₅	—	4	16	no	—
232	C₂²×D₄	—	5	2	no	—
233	C₂²×D₄	—	5	4	no	—
234	C₂²×D₄	—	5	4	no	—
235	C₂³×C₄	—	5	1	no	—
236	C₂³×C₄	—	5	4	no	—
237	#127	—	5	8	no	—
238	#125	C₂×C₃×D₅	1	8	yes	complemented
239	#123	—	5	32	no	—
240	#121	—	5	32	no	—
241	#121	—	5	16	no	—
242	C₄×D₄	—	5	16	no	—
243	#117	—	5	8	no	—
244	C₂×C₄⋊C₄	—	5	2	no	—
245	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
246	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	—
247	C₂×C₂²⋊C₄	—	5	2	no	—
248	C₂×C₂²⋊C₄	—	5	4	no	—
249	C₂×C₂²⋊C₄	—	5	4	no	—
250	C₂×C₄²	—	5	1	no	—
251	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
252	C₂×C₃×C₅	#540	1	4	yes	complemented
253	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
254	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
255	C₃×D₅	—	4	2	no	—
256	C₃×D₅	—	4	8	no	—
257	C₂³×C₃	—	5	2	no	—
258	C₂³×C₃	—	5	8	no	—
259	C₂³×C₃	—	10	2	no	—
260	C₂³×C₃	—	10	8	no	—
261	C₂³×C₃	—	10	8	no	—
262	C₂³×C₃	—	10	4	no	—
263	C₂³×C₃	—	10	8	no	—
264	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
265	C₃×D₄	—	10	16	no	—
266	C₃×D₄	—	20	16	no	—
267	C₃×D₄	—	20	16	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	5	4	no	—
271	C₂×C₃×C₄	—	5	2	no	—
272	C₂×C₃×C₄	—	10	2	no	—
273	C₂×C₃×C₄	—	10	4	no	—
274	C₂×C₃×C₄	—	10	8	no	—
275	C₂×C₃×C₄	—	20	16	no	—
276	C₂×C₃×C₄	#713	1	4	yes	—
277	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
278	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
279	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
280	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
281	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
282	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
283	C₂×D₅	—	2	2	no	—
284	C₂×D₅	—	2	8	no	—
285	C₂×D₅	—	2	8	no	—
286	C₂×D₅	—	2	4	no	—
287	C₂×D₅	—	2	8	no	—
288	C₂×D₅	—	4	4	no	—
289	C₂×D₅	—	4	16	no	—
290	C₄×C₅	—	2	8	no	—
291	C₄×C₅	—	2	4	no	—
292	C₄×C₅	C₂×C₃×#41	1	4	yes	—
293	Dic₅	—	2	2	no	—
294	Dic₅	—	2	4	no	—
295	C₂⁴	—	5	1	no	—
296	C₂⁴	—	5	4	no	—
297	C₂×D₄	—	5	8	no	—
298	C₂×D₄	—	5	16	no	—
299	C₂×D₄	—	5	16	no	—
300	C₂×D₄	—	10	8	no	—
301	C₂×D₄	—	20	8	no	—
302	C₂×D₄	—	20	8	no	—
303	C₂²×C₄	—	5	2	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	4	no	—
306	C₂²×C₄	—	5	16	no	—
307	C₂²×C₄	—	10	4	no	—
308	C₂²×C₄	—	20	8	no	—
309	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
310	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
311	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
312	C₄⋊C₄	—	5	8	no	—
313	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
314	C₄⋊C₄	C₂²×C₃×D₅	1	16	yes	—
315	C₂²⋊C₄	—	5	8	no	—
316	C₂²⋊C₄	—	5	16	no	—
317	C₂²⋊C₄	—	5	16	no	—
318	C₄²	—	5	4	no	—
319	C₄²	C₂²×C₃×D₅	1	4	yes	—
320	C₃×C₅	C₂×#540	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	—	10	2	no	—
322	C₂²×C₃	—	10	8	no	—
323	C₂²×C₃	—	10	8	no	—
324	C₂²×C₃	—	10	4	no	—
325	C₂²×C₃	—	10	8	no	—
326	C₂²×C₃	—	20	4	no	—
327	C₂²×C₃	—	20	16	no	—
328	C₂²×C₃	C₂×#713	1	2	yes	—
329	C₂²×C₃	#4149	1	4	yes	—
330	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
331	C₃×C₄	—	2	8	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	10	2	no	—
334	C₃×C₄	—	10	4	no	—
335	C₃×C₄	C₂×#713	1	4	yes	—
336	C₂×C₅	C₃×#540	1	4	yes	complemented
337	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
338	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
339	D₅	—	4	2	no	—
340	D₅	—	4	8	no	—
341	C₂³	—	5	2	no	—
342	C₂³	—	5	8	no	—
343	C₂³	—	10	2	no	—
344	C₂³	—	10	8	no	—
345	C₂³	—	10	8	no	—
346	C₂³	—	10	4	no	—
347	C₂³	—	10	8	no	—
348	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
349	D₄	—	10	16	no	—
350	D₄	—	20	16	no	—
351	D₄	—	20	16	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	5	4	no	—
355	C₂×C₄	—	5	2	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	10	8	no	—
359	C₂×C₄	—	20	16	no	—
360	C₂×C₄	C₃×#713	1	4	yes	—
361	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
362	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
363	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
364	C₂×C₃	—	20	2	no	—
365	C₂×C₃	—	20	8	no	—
366	C₂×C₃	#66032	1	4	yes	direct product factor
367	C₂×C₃	C₂²×#713	1	1	yes	characteristic
368	C₂×C₃	C₂×#4149	1	2	yes	—
369	C₅	C₂×C₃×#540	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	10	2	no	—
371	C₂²	—	10	8	no	—
372	C₂²	—	10	8	no	—
373	C₂²	—	10	4	no	—
374	C₂²	—	10	8	no	—
375	C₂²	—	20	4	no	—
376	C₂²	—	20	16	no	—
377	C₂²	C₂×C₃×#713	1	2	yes	—
378	C₂²	C₃×#4149	1	4	yes	—
379	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
380	C₄	—	2	8	no	—
381	C₄	—	2	4	no	—
382	C₄	—	10	2	no	—
383	C₄	—	10	4	no	—
384	C₄	C₂×C₃×#713	1	4	yes	—
385	C₃	C₂×#66032	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	20	2	no	—
387	C₂	—	20	8	no	—
388	C₂	C₃×#66032	1	4	yes	direct product factor
389	C₂	C₂²×C₃×#713	1	1	yes	characteristic
390	C₂	C₂×C₃×#4149	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#125	D₅
hypocenter	C₅	C₂×C₃×#540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₃×#66032	C₂	direct (N × H)
3. C₂×C₃×#4041	C₂	semidirect
4. C₂×C₃×#4041	C₂	semidirect
5. C₂×C₃×#4040	C₂	semidirect
6. C₂×C₃×#4039	C₂	semidirect
7. C₂×C₃×#4020	C₂	semidirect
8. C₂×C₃×#4018	C₂	semidirect
9. C₂×#66032	C₃	direct (N × H)
15. C₃×C₅×#125	C₂²	semidirect
24. C₃×#4041	C₂²	semidirect
25. C₃×#4041	C₂²	semidirect
26. C₃×#4040	C₂²	semidirect
27. C₃×#4039	C₂²	semidirect
28. C₃×#4020	C₂²	semidirect
29. C₃×#4018	C₂²	semidirect
31. C₂×C₅×#125	C₂×C₃	semidirect
32. #66032	C₂×C₃	direct (N × H)
33. C₂×#4041	C₂×C₃	semidirect
34. C₂×#4041	C₂×C₃	semidirect
35. C₂×#4040	C₂×C₃	semidirect
36. C₂×#4039	C₂×C₃	semidirect
37. C₂×#4020	C₂×C₃	semidirect
38. C₂×#4018	C₂×C₃	semidirect
66. C₂×C₃×#125	D₅	semidirect
77. C₅×#125	C₂²×C₃	semidirect
86. #4041	C₂²×C₃	semidirect
87. #4041	C₂²×C₃	semidirect
88. #4040	C₂²×C₃	semidirect
89. #4039	C₂²×C₃	semidirect
90. #4020	C₂²×C₃	semidirect
91. #4018	C₂²×C₃	semidirect
122. C₃×#125	C₂×D₅	semidirect
163. C₂×#125	C₃×D₅	semidirect
238. #125	C₂×C₃×D₅	semidirect
252. C₂×C₃×C₅	#540	semidirect
320. C₃×C₅	C₂×#540	semidirect
336. C₂×C₅	C₃×#540	semidirect
366. C₂×C₃	#66032	direct (N × H)
369. C₅	C₂×C₃×#540	semidirect
385. C₃	C₂×#66032	direct (N × H)
388. C₂	C₃×#66032	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×#125	2
C₃×#66032	2
C₂×C₃×#4041	2
C₂×C₃×#4040	2
C₂×C₃×#4039	2
C₂×C₃×#4020	2
C₂×C₃×#4018	2
C₂×#66032	3
C₂×C₃×#540	5

Subgroups — C2×C3×#66032 #14481098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66032 #14481098