Subgroups — C₂×C₃×#65827 #14480303

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4076	C₂	1	4	yes	maximal, complemented
4	C₃×#65827	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4032	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4028	C₂	1	4	yes	maximal, complemented
7	C₂×#65827	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂⁴×C₃×D₅	C₂²	1	2	yes	complemented
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
11	C₂²×C₃×C₂²⋊D₅	—	2	16	no	—
12	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	—
13	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	complemented
14	C₂²×C₃×C₂²⋊D₅	C₂²	1	16	yes	complemented
15	C₂³×C₃×Dic₅	C₂²	1	2	yes	complemented
16	C₂²×C₃×D₂₀	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
19	C₃×#4076	C₂²	1	32	yes	complemented
20	C₂×C₃×#685	C₂²	1	8	yes	complemented
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	complemented
22	C₃×#4032	C₂²	1	32	yes	complemented
23	C₃×#4028	C₂²	1	32	yes	complemented
24	C₂×C₃×#534	—	5	1	no	maximal, Hall
25	C₂³×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
26	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#4076	C₂×C₃	1	4	yes	complemented
28	#65827	C₂×C₃	1	16	yes	direct product factor
29	C₂×#4032	C₂×C₃	1	4	yes	complemented
30	C₂×#4028	C₂×C₃	1	4	yes	complemented
31	C₂⁴×C₃×C₅	—	4	4	no	—
32	C₂⁴×C₃×C₅	D₄	1	8	yes	complemented
33	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
36	C₂³×C₃×D₅	—	2	8	no	—
37	C₂³×C₃×D₅	—	4	8	no	—
38	C₂³×C₃×D₅	C₂³	1	4	yes	—
39	C₂³×C₃×D₅	C₂³	1	8	yes	complemented
40	C₂²×C₃×C₄×C₅	—	4	4	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	complemented
43	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
44	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
45	C₂×C₃×C₂²⋊D₅	—	2	64	no	—
46	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
47	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	complemented
48	C₂²×C₃×Dic₅	—	2	8	no	—
49	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	8	yes	complemented
51	C₂×C₃×D₂₀	—	4	8	no	—
52	C₂×C₃×D₂₀	C₂³	1	16	yes	complemented
53	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
54	C₃×#685	C₂³	1	32	yes	complemented
55	C₃×C₄⋊Dic₅	C₂³	1	16	yes	complemented
56	C₂³×C₃×D₄	—	5	2	no	—
57	C₃×#534	—	5	16	no	—
58	C₂×C₃×#123	—	5	4	no	—
59	C₂×C₃×#121	—	5	4	no	—
60	C₂×C₃×#120	—	5	4	no	—
61	C₂²×C₃×C₂²⋊C₄	D₅	1	1	yes	characteristic, complemented
62	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂⁴×D₅	C₂²×C₃	1	2	yes	complemented
64	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	complemented
65	C₂²×C₂²⋊D₅	—	2	16	no	—
66	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
67	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
68	C₂²×C₂²⋊D₅	C₂²×C₃	1	16	yes	complemented
69	C₂³×Dic₅	C₂²×C₃	1	2	yes	complemented
70	C₂²×D₂₀	C₂²×C₃	1	4	yes	complemented
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
72	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
73	#4076	C₂²×C₃	1	32	yes	complemented
74	C₂×#685	C₂²×C₃	1	8	yes	complemented
75	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	complemented
76	#4032	C₂²×C₃	1	32	yes	complemented
77	#4028	C₂²×C₃	1	32	yes	complemented
78	C₂×#534	—	5	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	—	2	8	no	—
81	C₂³×C₃×C₅	—	4	16	no	—
82	C₂³×C₃×C₅	—	4	8	no	—
83	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	16	yes	complemented
86	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₂²×C₃×D₅	—	2	8	no	—
90	C₂²×C₃×D₅	—	2	16	no	—
91	C₂²×C₃×D₅	—	2	16	no	—
92	C₂²×C₃×D₅	—	4	16	no	—
93	C₂²×C₃×D₅	—	4	32	no	—
94	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	4	8	no	—
97	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
98	C₃×C₂²⋊D₅	—	2	32	no	—
99	C₃×C₂²⋊D₅	—	2	32	no	—
100	C₂×C₃×Dic₅	—	2	8	no	—
101	C₂×C₃×Dic₅	—	2	16	no	—
102	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
103	C₃×D₂₀	—	4	16	no	—
104	C₂⁵×C₃	—	5	2	no	—
105	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
106	C₂²×C₃×D₄	—	5	4	no	—
107	C₂²×C₃×D₄	—	5	4	no	—
108	C₂²×C₃×D₄	—	5	16	no	—
109	C₂²×C₃×D₄	—	5	4	no	—
110	C₂²×C₃×D₄	—	10	16	no	—
111	C₂³×C₃×C₄	—	5	2	no	—
112	C₂³×C₃×C₄	C₂×D₅	1	2	yes	complemented
113	C₃×#123	—	5	32	no	—
114	C₃×#121	—	5	32	no	—
115	C₃×#120	—	5	32	no	—
116	C₂×C₃×C₄⋊C₄	—	5	4	no	—
117	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
118	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	4	yes	complemented
119	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	8	yes	complemented
120	C₂⁴×C₅	—	4	4	no	—
121	C₂⁴×C₅	C₃×D₄	1	8	yes	complemented
122	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
123	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
125	C₂³×D₅	—	2	8	no	—
126	C₂³×D₅	—	4	8	no	—
127	C₂³×D₅	C₂³×C₃	1	4	yes	—
128	C₂³×D₅	C₂³×C₃	1	8	yes	complemented
129	C₂²×C₄×C₅	—	4	4	no	—
130	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	complemented
132	C₂×C₂²⋊D₅	—	2	16	no	—
133	C₂×C₂²⋊D₅	—	2	16	no	—
134	C₂×C₂²⋊D₅	—	2	64	no	—
135	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
136	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	complemented
137	C₂²×Dic₅	—	2	8	no	—
138	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
139	C₂²×Dic₅	C₂³×C₃	1	8	yes	complemented
140	C₂×D₂₀	—	4	8	no	—
141	C₂×D₂₀	C₂³×C₃	1	16	yes	complemented
142	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
143	#685	C₂³×C₃	1	32	yes	complemented
144	C₄⋊Dic₅	C₂³×C₃	1	16	yes	complemented
145	C₂³×D₄	—	5	2	no	—
146	#534	—	5	16	no	—
147	C₂×#123	—	5	4	no	—
148	C₂×#121	—	5	4	no	—
149	C₂×#120	—	5	4	no	—
150	C₂²×C₂²⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
151	C₂²×C₃×C₅	—	2	16	no	—
152	C₂²×C₃×C₅	—	2	8	no	—
153	C₂²×C₃×C₅	—	2	4	no	—
154	C₂²×C₃×C₅	—	2	8	no	—
155	C₂²×C₃×C₅	—	4	16	no	—
156	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	—
157	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
158	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
159	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
160	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×D₅	—	2	8	no	—
162	C₂×C₃×D₅	—	2	16	no	—
163	C₂×C₃×D₅	—	4	32	no	—
164	C₂×C₃×D₅	—	4	16	no	—
165	C₃×C₄×C₅	—	2	8	no	—
166	C₃×Dic₅	—	2	8	no	—
167	C₂⁴×C₃	—	4	4	no	—
168	C₂⁴×C₃	—	5	4	no	—
169	C₂⁴×C₃	—	5	8	no	—
170	C₂⁴×C₃	—	10	8	no	—
171	C₂⁴×C₃	—	20	8	no	—
172	C₂⁴×C₃	D₂₀	1	8	yes	complemented
173	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
174	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
175	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
176	C₂×C₃×D₄	—	5	16	no	—
177	C₂×C₃×D₄	—	5	16	no	—
178	C₂×C₃×D₄	—	5	16	no	—
179	C₂×C₃×D₄	—	10	16	no	—
180	C₂×C₃×D₄	—	10	16	no	—
181	C₂×C₃×D₄	—	10	64	no	—
182	C₂×C₃×D₄	—	20	8	no	—
183	C₂²×C₃×C₄	—	4	4	no	—
184	C₂²×C₃×C₄	—	5	8	no	—
185	C₂²×C₃×C₄	—	5	4	no	—
186	C₂²×C₃×C₄	—	10	8	no	—
187	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
188	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	complemented
189	C₃×C₄⋊C₄	—	5	16	no	—
190	C₃×C₂²⋊C₄	—	5	32	no	—
191	C₃×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	—	2	8	no	—
194	C₂³×C₅	—	4	16	no	—
195	C₂³×C₅	—	4	8	no	—
196	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
197	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
198	C₂³×C₅	C₂×C₃×D₄	1	16	yes	complemented
199	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
200	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
201	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₂²×D₅	—	2	8	no	—
203	C₂²×D₅	—	2	16	no	—
204	C₂²×D₅	—	2	16	no	—
205	C₂²×D₅	—	4	16	no	—
206	C₂²×D₅	—	4	32	no	—
207	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
208	C₂×C₄×C₅	—	2	8	no	—
209	C₂×C₄×C₅	—	4	8	no	—
210	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
211	C₂²⋊D₅	—	2	32	no	—
212	C₂²⋊D₅	—	2	32	no	—
213	C₂×Dic₅	—	2	8	no	—
214	C₂×Dic₅	—	2	16	no	—
215	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
216	D₂₀	—	4	16	no	—
217	C₂⁵	—	5	2	no	—
218	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
219	C₂²×D₄	—	5	4	no	—
220	C₂²×D₄	—	5	4	no	—
221	C₂²×D₄	—	5	16	no	—
222	C₂²×D₄	—	5	4	no	—
223	C₂²×D₄	—	10	16	no	—
224	C₂³×C₄	—	5	2	no	—
225	C₂³×C₄	C₂×C₃×D₅	1	2	yes	complemented
226	#123	—	5	32	no	—
227	#121	—	5	32	no	—
228	#120	—	5	32	no	—
229	C₂×C₄⋊C₄	—	5	4	no	—
230	C₂×C₂²⋊C₄	—	5	8	no	—
231	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
232	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	8	yes	complemented
233	C₂×C₃×C₅	—	2	8	no	—
234	C₂×C₃×C₅	—	2	4	no	—
235	C₂×C₃×C₅	#534	1	4	yes	complemented
236	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₃×D₅	—	4	8	no	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	2	8	no	—
241	C₂³×C₃	—	4	16	no	—
242	C₂³×C₃	—	4	8	no	—
243	C₂³×C₃	—	5	8	no	—
244	C₂³×C₃	—	10	16	no	—
245	C₂³×C₃	—	10	8	no	—
246	C₂³×C₃	—	10	16	no	—
247	C₂³×C₃	—	20	16	no	—
248	C₂³×C₃	—	20	32	no	—
249	C₂³×C₃	C₂×D₂₀	1	8	yes	—
250	C₂³×C₃	C₂×D₂₀	1	4	yes	—
251	C₂³×C₃	C₂×D₂₀	1	16	yes	complemented
252	C₂³×C₃	C₂³×D₅	1	4	yes	—
253	C₂³×C₃	C₂³×D₅	1	2	yes	—
254	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
255	C₃×D₄	—	10	32	no	—
256	C₃×D₄	—	10	32	no	—
257	C₃×D₄	—	20	16	no	—
258	C₂×C₃×C₄	—	2	8	no	—
259	C₂×C₃×C₄	—	4	8	no	—
260	C₂×C₃×C₄	—	5	8	no	—
261	C₂×C₃×C₄	—	10	16	no	—
262	C₂×C₃×C₄	—	10	8	no	—
263	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	2	8	no	—
266	C₂²×C₅	—	2	16	no	—
267	C₂²×C₅	—	2	8	no	—
268	C₂²×C₅	—	4	16	no	—
269	C₂²×C₅	C₂²×C₃×D₄	1	8	yes	—
270	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
271	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
272	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
273	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
274	C₂×D₅	—	2	8	no	—
275	C₂×D₅	—	2	16	no	—
276	C₂×D₅	—	4	32	no	—
277	C₂×D₅	—	4	16	no	—
278	C₄×C₅	—	2	8	no	—
279	Dic₅	—	2	8	no	—
280	C₂⁴	—	4	4	no	—
281	C₂⁴	—	5	4	no	—
282	C₂⁴	—	5	8	no	—
283	C₂⁴	—	10	8	no	—
284	C₂⁴	—	20	8	no	—
285	C₂⁴	C₃×D₂₀	1	8	yes	complemented
286	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
287	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
288	C₂⁴	C₂²×C₃×D₅	1	4	yes	—
289	C₂×D₄	—	5	16	no	—
290	C₂×D₄	—	5	16	no	—
291	C₂×D₄	—	5	16	no	—
292	C₂×D₄	—	10	16	no	—
293	C₂×D₄	—	10	16	no	—
294	C₂×D₄	—	10	64	no	—
295	C₂×D₄	—	20	8	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	5	4	no	—
298	C₂²×C₄	—	5	8	no	—
299	C₂²×C₄	—	10	8	no	—
300	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
301	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	complemented
302	C₄⋊C₄	—	5	16	no	—
303	C₂²⋊C₄	—	5	32	no	—
304	C₂²⋊C₄	C₂²×C₃×D₅	1	16	yes	complemented
305	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	16	no	—
307	C₂²×C₃	—	2	8	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	4	16	no	—
311	C₂²×C₃	—	10	8	no	—
312	C₂²×C₃	—	10	16	no	—
313	C₂²×C₃	—	20	32	no	—
314	C₂²×C₃	—	20	16	no	—
315	C₂²×C₃	C₂²×D₂₀	1	8	yes	—
316	C₂²×C₃	C₂²×D₂₀	1	4	yes	—
317	C₂²×C₃	C₂²×D₂₀	1	2	yes	—
318	C₂²×C₃	#4144	1	4	yes	—
319	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
320	C₃×C₄	—	2	8	no	—
321	C₃×C₄	—	10	8	no	—
322	C₂×C₅	—	2	8	no	—
323	C₂×C₅	—	2	4	no	—
324	C₂×C₅	C₃×#534	1	4	yes	complemented
325	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
326	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
327	D₅	—	4	8	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	8	no	—
330	C₂³	—	4	16	no	—
331	C₂³	—	4	8	no	—
332	C₂³	—	5	8	no	—
333	C₂³	—	10	16	no	—
334	C₂³	—	10	8	no	—
335	C₂³	—	10	16	no	—
336	C₂³	—	20	16	no	—
337	C₂³	—	20	32	no	—
338	C₂³	C₂×C₃×D₂₀	1	8	yes	—
339	C₂³	C₂×C₃×D₂₀	1	4	yes	—
340	C₂³	C₂×C₃×D₂₀	1	16	yes	complemented
341	C₂³	C₂³×C₃×D₅	1	4	yes	—
342	C₂³	C₂³×C₃×D₅	1	2	yes	—
343	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
344	D₄	—	10	32	no	—
345	D₄	—	10	32	no	—
346	D₄	—	20	16	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	5	8	no	—
350	C₂×C₄	—	10	16	no	—
351	C₂×C₄	—	10	8	no	—
352	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
353	C₂×C₃	—	2	8	no	—
354	C₂×C₃	—	2	4	no	—
355	C₂×C₃	—	20	8	no	—
356	C₂×C₃	#65827	1	4	yes	direct product factor
357	C₂×C₃	C₂³×D₂₀	1	1	yes	characteristic
358	C₂×C₃	C₂×#4144	1	2	yes	—
359	C₅	C₂×C₃×#534	1	1	yes	characteristic, complemented, Sylow
360	C₂²	—	2	4	no	—
361	C₂²	—	2	8	no	—
362	C₂²	—	2	16	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	4	16	no	—
365	C₂²	—	10	8	no	—
366	C₂²	—	10	16	no	—
367	C₂²	—	20	32	no	—
368	C₂²	—	20	16	no	—
369	C₂²	C₂²×C₃×D₂₀	1	8	yes	—
370	C₂²	C₂²×C₃×D₂₀	1	4	yes	—
371	C₂²	C₂²×C₃×D₂₀	1	2	yes	—
372	C₂²	C₃×#4144	1	4	yes	—
373	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
374	C₄	—	2	8	no	—
375	C₄	—	10	8	no	—
376	C₃	C₂×#65827	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	8	no	—
378	C₂	—	2	4	no	—
379	C₂	—	20	8	no	—
380	C₂	C₃×#65827	1	4	yes	direct product factor
381	C₂	C₂³×C₃×D₂₀	1	1	yes	characteristic
382	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	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₃×C₂²⋊C₄	D₅
hypocenter	C₅	C₂×C₃×#534
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₂²⋊D₅	C₂	semidirect
2. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
3. C₂×C₃×#4076	C₂	semidirect
4. C₃×#65827	C₂	direct (N × H)
5. C₂×C₃×#4032	C₂	semidirect
6. C₂×C₃×#4028	C₂	semidirect
7. C₂×#65827	C₃	direct (N × H)
9. C₂⁴×C₃×D₅	C₂²	semidirect
10. C₂³×C₃×C₄×C₅	C₂²	semidirect
13. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
14. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
15. C₂³×C₃×Dic₅	C₂²	semidirect
16. C₂²×C₃×D₂₀	C₂²	semidirect
17. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
19. C₃×#4076	C₂²	semidirect
20. C₂×C₃×#685	C₂²	semidirect
21. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
22. C₃×#4032	C₂²	semidirect
23. C₃×#4028	C₂²	semidirect
25. C₂³×C₂²⋊D₅	C₂×C₃	semidirect
26. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
27. C₂×#4076	C₂×C₃	semidirect
28. #65827	C₂×C₃	direct (N × H)
29. C₂×#4032	C₂×C₃	semidirect
30. C₂×#4028	C₂×C₃	semidirect
32. C₂⁴×C₃×C₅	D₄	semidirect
39. C₂³×C₃×D₅	C₂³	semidirect
42. C₂²×C₃×C₄×C₅	C₂³	semidirect
47. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
50. C₂²×C₃×Dic₅	C₂³	semidirect
52. C₂×C₃×D₂₀	C₂³	semidirect
53. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
54. C₃×#685	C₂³	semidirect
55. C₃×C₄⋊Dic₅	C₂³	semidirect
61. C₂²×C₃×C₂²⋊C₄	D₅	semidirect
63. C₂⁴×D₅	C₂²×C₃	semidirect
64. C₂³×C₄×C₅	C₂²×C₃	semidirect
67. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
68. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
69. C₂³×Dic₅	C₂²×C₃	semidirect
70. C₂²×D₂₀	C₂²×C₃	semidirect
71. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
72. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
73. #4076	C₂²×C₃	semidirect
74. C₂×#685	C₂²×C₃	semidirect
75. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
76. #4032	C₂²×C₃	semidirect
77. #4028	C₂²×C₃	semidirect
85. C₂³×C₃×C₅	C₂×D₄	semidirect
112. C₂³×C₃×C₄	C₂×D₅	semidirect
118. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
119. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
121. C₂⁴×C₅	C₃×D₄	semidirect
128. C₂³×D₅	C₂³×C₃	semidirect
131. C₂²×C₄×C₅	C₂³×C₃	semidirect
136. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
139. C₂²×Dic₅	C₂³×C₃	semidirect
141. C₂×D₂₀	C₂³×C₃	semidirect
142. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
143. #685	C₂³×C₃	semidirect
144. C₄⋊Dic₅	C₂³×C₃	semidirect
150. C₂²×C₂²⋊C₄	C₃×D₅	semidirect
172. C₂⁴×C₃	D₂₀	semidirect
188. C₂²×C₃×C₄	C₂²×D₅	semidirect
191. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
198. C₂³×C₅	C₂×C₃×D₄	semidirect
225. C₂³×C₄	C₂×C₃×D₅	semidirect
231. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
232. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
235. C₂×C₃×C₅	#534	semidirect
251. C₂³×C₃	C₂×D₂₀	semidirect
285. C₂⁴	C₃×D₂₀	semidirect
301. C₂²×C₄	C₂²×C₃×D₅	semidirect
304. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
305. C₃×C₅	C₂×#534	semidirect
324. C₂×C₅	C₃×#534	semidirect
340. C₂³	C₂×C₃×D₂₀	semidirect
356. C₂×C₃	#65827	direct (N × H)
359. C₅	C₂×C₃×#534	semidirect
376. C₃	C₂×#65827	direct (N × H)
380. C₂	C₃×#65827	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₂²⋊D₅	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂×C₃×#4076	2
C₃×#65827	2
C₂×C₃×#4032	2
C₂×C₃×#4028	2
C₂×#65827	3
C₂×C₃×#534	5

Subgroups — C2×C3×#65827 #14480303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65827 #14480303