Subgroups — C₂×C₃×#66053 #14481092

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×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4085	C₂	1	4	yes	maximal, complemented
3	C₂×C₃×#4084	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4081	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×D₄×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₃×#66053	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66053	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	—
13	C₂³×C₃×Dic₅	C₂²	1	4	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	8	yes	complemented
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
18	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
19	C₃×#4085	C₂²	1	32	yes	complemented
20	C₃×#4084	C₂²	1	16	yes	complemented
21	C₃×#4081	C₂²	1	32	yes	complemented
22	C₃×D₄×Dic₅	C₂²	1	16	yes	complemented
23	C₂×C₃×#685	C₂²	1	2	yes	—
24	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×#683	C₂²	1	2	yes	—
26	C₂×C₃×#683	C₂²	1	4	yes	—
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₃×#4018	C₂²	1	8	yes	complemented
29	C₃×#4016	C₂²	1	8	yes	complemented
30	C₂×C₃×#540	—	5	1	no	maximal, Hall
31	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#4085	C₂×C₃	1	4	yes	complemented
33	C₂×#4084	C₂×C₃	1	2	yes	complemented
34	C₂×#4081	C₂×C₃	1	4	yes	complemented
35	C₂×D₄×Dic₅	C₂×C₃	1	2	yes	complemented
36	#66053	C₂×C₃	1	16	yes	direct product factor
37	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#4016	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
40	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₅×D₄	—	2	8	no	—
42	C₂×C₃×C₅×D₄	—	4	8	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
44	C₂×C₃×C₅×D₄	C₂³	1	16	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
48	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
49	C₂²×C₃×Dic₅	—	4	8	no	—
50	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
53	C₂²×C₃×Dic₅	C₂³	1	16	yes	—
54	C₂×C₃×C₄×D₅	—	2	4	no	—
55	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
56	C₃×C₄²×C₅	C₂³	1	4	yes	—
57	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	—
58	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	—
59	C₃×#685	C₂³	1	8	yes	—
60	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
61	C₃×#683	C₂³	1	8	yes	—
62	C₃×#683	C₂³	1	16	yes	—
63	C₃×C₄×Dic₅	C₂³	1	4	yes	—
64	C₃×#540	—	5	16	no	—
65	C₂×C₃×#127	D₅	1	1	yes	characteristic, complemented
66	C₂×C₃×#125	—	5	1	no	—
67	C₂×C₃×#123	—	5	4	no	—
68	C₂×C₃×#121	—	5	2	no	—
69	C₂×C₃×#121	—	5	4	no	—
70	C₂×C₃×C₄×D₄	—	5	2	no	—
71	C₂×C₃×#117	—	5	1	no	—
72	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
73	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
74	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
75	C₂³×Dic₅	C₂²×C₃	1	4	yes	—
76	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
77	C₅×#127	C₂²×C₃	1	8	yes	complemented
78	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
80	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
81	#4085	C₂²×C₃	1	32	yes	complemented
82	#4084	C₂²×C₃	1	16	yes	complemented
83	#4081	C₂²×C₃	1	32	yes	complemented
84	D₄×Dic₅	C₂²×C₃	1	16	yes	complemented
85	C₂×#685	C₂²×C₃	1	2	yes	—
86	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
87	C₂×#683	C₂²×C₃	1	4	yes	—
88	C₂×#683	C₂²×C₃	1	2	yes	—
89	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
90	#4018	C₂²×C₃	1	8	yes	complemented
91	#4016	C₂²×C₃	1	8	yes	complemented
92	C₂×#540	—	5	1	no	Sylow
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	8	no	—
95	C₂³×C₃×C₅	—	2	8	no	—
96	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
97	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	2	4	no	—
100	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
101	C₃×C₅×D₄	—	2	16	no	—
102	C₃×C₅×D₄	—	4	16	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	#41	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
107	C₃×C₂²⋊D₅	—	4	16	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	4	no	—
110	C₂×C₃×Dic₅	—	2	8	no	—
111	C₂×C₃×Dic₅	—	4	16	no	—
112	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
113	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
114	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
115	C₃×C₄×D₅	—	2	8	no	—
116	C₂²×C₃×D₄	—	5	4	no	—
117	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
118	C₂²×C₃×D₄	C₂×D₅	1	4	yes	—
119	C₂³×C₃×C₄	—	5	4	no	—
120	C₂³×C₃×C₄	—	5	1	no	—
121	C₃×#127	C₂×D₅	1	8	yes	complemented
122	C₃×#125	—	5	8	no	—
123	C₃×#123	—	5	32	no	—
124	C₃×#121	—	5	16	no	—
125	C₃×#121	—	5	32	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	—	5	2	no	—
130	C₂×C₃×C₄⋊C₄	—	5	4	no	—
131	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
132	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
133	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
134	C₂×C₃×C₄²	—	5	1	no	—
135	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
136	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
137	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
138	C₂×C₅×D₄	—	2	8	no	—
139	C₂×C₅×D₄	—	4	8	no	—
140	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
141	C₂×C₅×D₄	C₂³×C₃	1	16	yes	—
142	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₂²⋊D₅	—	4	8	no	—
145	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
146	C₂²×Dic₅	—	4	8	no	—
147	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
148	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
149	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
150	C₂²×Dic₅	C₂³×C₃	1	16	yes	—
151	C₂×C₄×D₅	—	2	4	no	—
152	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
153	C₄²×C₅	C₂³×C₃	1	4	yes	—
154	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	—
155	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	—
156	#685	C₂³×C₃	1	8	yes	—
157	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
158	#683	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	C₃×D₅	1	1	yes	characteristic, complemented
163	C₂×#125	—	5	1	no	—
164	C₂×#123	—	5	4	no	—
165	C₂×#121	—	5	2	no	—
166	C₂×#121	—	5	4	no	—
167	C₂×C₄×D₄	—	5	2	no	—
168	C₂×#117	—	5	1	no	—
169	C₂²×C₃×C₅	—	2	8	no	—
170	C₂²×C₃×C₅	—	2	8	no	—
171	C₂²×C₃×C₅	—	2	8	no	—
172	C₂²×C₃×C₅	—	4	16	no	—
173	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
174	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
175	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
176	C₂×C₃×D₅	—	2	2	no	—
177	C₂×C₃×D₅	—	2	4	no	—
178	C₂×C₃×D₅	—	4	4	no	—
179	C₃×C₄×C₅	—	2	4	no	—
180	C₃×C₄×C₅	C₂×#41	1	4	yes	—
181	C₃×Dic₅	—	2	2	no	—
182	C₃×Dic₅	—	2	4	no	—
183	C₃×Dic₅	—	2	8	no	—
184	C₂⁴×C₃	—	5	1	no	—
185	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
186	C₂×C₃×D₄	—	2	8	no	—
187	C₂×C₃×D₄	—	4	8	no	—
188	C₂×C₃×D₄	—	5	16	no	—
189	C₂×C₃×D₄	—	20	8	no	—
190	C₂×C₃×D₄	C₂²×D₅	1	8	yes	—
191	C₂×C₃×D₄	C₂²×D₅	1	16	yes	—
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	—	5	4	no	—
197	C₂²×C₃×C₄	—	10	4	no	—
198	C₂²×C₃×C₄	—	20	8	no	—
199	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
200	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
201	C₃×C₄⋊C₄	—	5	8	no	—
202	C₃×C₄⋊C₄	—	5	16	no	—
203	C₃×C₄⋊C₄	—	5	8	no	—
204	C₃×C₂²⋊C₄	—	5	16	no	—
205	C₃×C₂²⋊C₄	—	5	16	no	—
206	C₃×C₂²⋊C₄	—	5	8	no	—
207	C₃×C₄²	—	5	4	no	—
208	C₃×C₄²	C₂²×D₅	1	4	yes	—
209	C₂³×C₅	—	2	8	no	—
210	C₂³×C₅	—	2	8	no	—
211	C₂³×C₅	—	2	8	no	—
212	C₂³×C₅	C₂⁴×C₃	1	8	yes	—
213	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₂²×D₅	—	2	2	no	—
215	C₂²×D₅	—	2	4	no	—
216	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
217	C₅×D₄	—	2	16	no	—
218	C₅×D₄	—	4	16	no	—
219	C₂×C₄×C₅	—	2	4	no	—
220	C₂×C₄×C₅	C₃×#41	1	4	yes	—
221	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
222	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
223	C₂²⋊D₅	—	4	16	no	—
224	C₂×Dic₅	—	2	2	no	—
225	C₂×Dic₅	—	2	4	no	—
226	C₂×Dic₅	—	2	8	no	—
227	C₂×Dic₅	—	4	16	no	—
228	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
229	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
230	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
231	C₄×D₅	—	2	8	no	—
232	C₂²×D₄	—	5	4	no	—
233	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
234	C₂²×D₄	C₂×C₃×D₅	1	4	yes	—
235	C₂³×C₄	—	5	4	no	—
236	C₂³×C₄	—	5	1	no	—
237	#127	C₂×C₃×D₅	1	8	yes	complemented
238	#125	—	5	8	no	—
239	#123	—	5	32	no	—
240	#121	—	5	16	no	—
241	#121	—	5	32	no	—
242	C₄×D₄	—	5	16	no	—
243	#117	—	5	8	no	—
244	C₂×C₄⋊C₄	—	5	2	no	—
245	C₂×C₄⋊C₄	—	5	2	no	—
246	C₂×C₄⋊C₄	—	5	4	no	—
247	C₂×C₂²⋊C₄	—	5	4	no	—
248	C₂×C₂²⋊C₄	—	5	4	no	—
249	C₂×C₂²⋊C₄	—	5	2	no	—
250	C₂×C₄²	—	5	1	no	—
251	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
252	C₂×C₃×C₅	—	4	8	no	—
253	C₂×C₃×C₅	#540	1	4	yes	complemented
254	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
255	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₃×D₅	—	4	2	no	—
257	C₂³×C₃	—	2	8	no	—
258	C₂³×C₃	—	2	8	no	—
259	C₂³×C₃	—	2	8	no	—
260	C₂³×C₃	—	5	2	no	—
261	C₂³×C₃	—	10	2	no	—
262	C₂³×C₃	—	10	4	no	—
263	C₂³×C₃	C₂³×D₅	1	8	yes	—
264	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
265	C₃×D₄	—	2	16	no	—
266	C₃×D₄	—	4	16	no	—
267	C₃×D₄	—	20	16	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	5	4	no	—
270	C₂×C₃×C₄	—	5	2	no	—
271	C₂×C₃×C₄	—	5	8	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	—	10	8	no	—
276	C₂×C₃×C₄	—	20	16	no	—
277	C₂×C₃×C₄	#711	1	4	yes	—
278	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
279	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
280	C₂²×C₅	—	2	8	no	—
281	C₂²×C₅	—	2	8	no	—
282	C₂²×C₅	—	2	8	no	—
283	C₂²×C₅	—	4	16	no	—
284	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
285	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
286	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
287	C₂×D₅	—	2	2	no	—
288	C₂×D₅	—	2	4	no	—
289	C₂×D₅	—	4	4	no	—
290	C₄×C₅	—	2	4	no	—
291	C₄×C₅	C₂×C₃×#41	1	4	yes	—
292	Dic₅	—	2	2	no	—
293	Dic₅	—	2	4	no	—
294	Dic₅	—	2	8	no	—
295	C₂⁴	—	5	1	no	—
296	C₂⁴	C₂²×C₃×D₅	1	4	yes	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	—	5	16	no	—
300	C₂×D₄	—	20	8	no	—
301	C₂×D₄	C₂²×C₃×D₅	1	8	yes	—
302	C₂×D₄	C₂²×C₃×D₅	1	16	yes	—
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	—	5	4	no	—
308	C₂²×C₄	—	10	4	no	—
309	C₂²×C₄	—	20	8	no	—
310	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
311	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
312	C₄⋊C₄	—	5	8	no	—
313	C₄⋊C₄	—	5	8	no	—
314	C₄⋊C₄	—	5	16	no	—
315	C₂²⋊C₄	—	5	16	no	—
316	C₂²⋊C₄	—	5	16	no	—
317	C₂²⋊C₄	—	5	8	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	—	2	8	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	4	16	no	—
325	C₂²×C₃	—	10	2	no	—
326	C₂²×C₃	—	10	4	no	—
327	C₂²×C₃	—	20	4	no	—
328	C₂²×C₃	C₂×#711	1	2	yes	—
329	C₂²×C₃	#4144	1	4	yes	—
330	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	10	2	no	—
333	C₃×C₄	—	10	4	no	—
334	C₃×C₄	—	10	8	no	—
335	C₃×C₄	C₂×#711	1	4	yes	—
336	C₂×C₅	—	4	8	no	—
337	C₂×C₅	C₃×#540	1	4	yes	complemented
338	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
339	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
340	D₅	—	4	2	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	5	2	no	—
345	C₂³	—	10	2	no	—
346	C₂³	—	10	4	no	—
347	C₂³	C₂³×C₃×D₅	1	8	yes	—
348	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
349	D₄	—	2	16	no	—
350	D₄	—	4	16	no	—
351	D₄	—	20	16	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	5	4	no	—
354	C₂×C₄	—	5	2	no	—
355	C₂×C₄	—	5	8	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	10	8	no	—
359	C₂×C₄	—	10	8	no	—
360	C₂×C₄	—	20	16	no	—
361	C₂×C₄	C₃×#711	1	4	yes	—
362	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
363	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
364	C₂×C₃	—	4	8	no	—
365	C₂×C₃	—	20	2	no	—
366	C₂×C₃	#66053	1	4	yes	direct product factor
367	C₂×C₃	C₂²×#711	1	1	yes	characteristic
368	C₂×C₃	C₂×#4144	1	2	yes	—
369	C₅	C₂×C₃×#540	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	2	8	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	4	16	no	—
374	C₂²	—	10	2	no	—
375	C₂²	—	10	4	no	—
376	C₂²	—	20	4	no	—
377	C₂²	C₂×C₃×#711	1	2	yes	—
378	C₂²	C₃×#4144	1	4	yes	—
379	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
380	C₄	—	2	4	no	—
381	C₄	—	10	2	no	—
382	C₄	—	10	4	no	—
383	C₄	—	10	8	no	—
384	C₄	C₂×C₃×#711	1	4	yes	—
385	C₃	C₂×#66053	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	4	8	no	—
387	C₂	—	20	2	no	—
388	C₂	C₃×#66053	1	4	yes	direct product factor
389	C₂	C₂²×C₃×#711	1	1	yes	characteristic
390	C₂	C₂×C₃×#4144	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×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#127	D₅
hypocenter	C₅	C₂×C₃×#540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#127	C₂	semidirect
2. C₂×C₃×#4085	C₂	semidirect
3. C₂×C₃×#4084	C₂	semidirect
4. C₂×C₃×#4081	C₂	semidirect
5. C₂×C₃×D₄×Dic₅	C₂	semidirect
6. C₃×#66053	C₂	direct (N × H)
7. C₂×C₃×#4018	C₂	semidirect
8. C₂×C₃×#4016	C₂	semidirect
9. C₂×#66053	C₃	direct (N × H)
15. C₃×C₅×#127	C₂²	semidirect
19. C₃×#4085	C₂²	semidirect
20. C₃×#4084	C₂²	semidirect
21. C₃×#4081	C₂²	semidirect
22. C₃×D₄×Dic₅	C₂²	semidirect
28. C₃×#4018	C₂²	semidirect
29. C₃×#4016	C₂²	semidirect
31. C₂×C₅×#127	C₂×C₃	semidirect
32. C₂×#4085	C₂×C₃	semidirect
33. C₂×#4084	C₂×C₃	semidirect
34. C₂×#4081	C₂×C₃	semidirect
35. C₂×D₄×Dic₅	C₂×C₃	semidirect
36. #66053	C₂×C₃	direct (N × H)
37. C₂×#4018	C₂×C₃	semidirect
38. C₂×#4016	C₂×C₃	semidirect
65. C₂×C₃×#127	D₅	semidirect
77. C₅×#127	C₂²×C₃	semidirect
81. #4085	C₂²×C₃	semidirect
82. #4084	C₂²×C₃	semidirect
83. #4081	C₂²×C₃	semidirect
84. D₄×Dic₅	C₂²×C₃	semidirect
90. #4018	C₂²×C₃	semidirect
91. #4016	C₂²×C₃	semidirect
121. C₃×#127	C₂×D₅	semidirect
162. C₂×#127	C₃×D₅	semidirect
237. #127	C₂×C₃×D₅	semidirect
253. C₂×C₃×C₅	#540	semidirect
320. C₃×C₅	C₂×#540	semidirect
337. C₂×C₅	C₃×#540	semidirect
366. C₂×C₃	#66053	direct (N × H)
369. C₅	C₂×C₃×#540	semidirect
385. C₃	C₂×#66053	direct (N × H)
388. C₂	C₃×#66053	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×#127	2
C₂×C₃×#4085	2
C₂×C₃×#4084	2
C₂×C₃×#4081	2
C₂×C₃×D₄×Dic₅	2
C₃×#66053	2
C₂×C₃×#4018	2
C₂×C₃×#4016	2
C₂×#66053	3
C₂×C₃×#540	5

Subgroups — C2×C3×#66053 #14481092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66053 #14481092