Subgroups — C₂×C₅×#4848 #14426019

Order 1920.

1168 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	C₂²×C₅×#204	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#821	C₂	1	2	yes	maximal, complemented
6	C₅×#4848	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#460	—	3	1	no	maximal, Hall
8	C₂²×C₅×D₁₂	—	2	1	no	—
9	C₂²×C₅×D₁₂	—	2	1	no	—
10	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
11	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
16	C₂×C₄×C₅×Dic₃	—	2	1	no	—
17	C₂×C₅×#204	—	2	8	no	—
18	C₂×C₅×#204	C₂²	1	8	yes	complemented
19	C₅×#874	—	2	2	no	—
20	C₅×#874	C₂²	1	4	yes	—
21	C₄×C₅×Dic₆	—	2	2	no	—
22	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
23	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
24	C₅×#821	C₂²	1	8	yes	complemented
25	C₂×#4848	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×SD₁₆	—	3	2	no	—
27	C₂×C₅×#127	—	3	1	no	—
28	C₂×C₄×C₅×Q₈	—	3	1	no	—
29	C₅×#460	—	3	8	no	—
30	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
31	C₂×C₅×#102	—	3	2	no	—
32	C₂³×C₅×D₃	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₂²×C₅×Dic₃	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	4	no	—
39	C₂×C₅×D₁₂	—	2	4	no	—
40	C₂×C₅×D₁₂	—	2	2	no	—
41	C₂×C₅×D₁₂	—	2	4	no	—
42	C₂×C₅×D₁₂	—	2	4	no	—
43	C₂×C₅×D₁₂	—	4	4	no	—
44	C₂×C₅×D₁₂	—	4	4	no	—
45	C₂×C₅×D₁₂	C₂³	1	4	yes	—
46	C₂×C₅×Dic₆	—	2	1	no	—
47	C₂×C₅×Dic₆	—	2	2	no	—
48	C₂×C₅×Dic₆	D₄	1	4	yes	complemented
49	C₂×C₅×Dic₆	C₂³	1	2	yes	—
50	C₂×C₃×C₅×C₈	—	2	4	no	—
51	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
52	C₃×C₄²×C₅	D₄	1	2	yes	—
53	C₃×C₄²×C₅	C₂³	1	2	yes	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
56	C₅×Dic₃⋊C₄	—	2	4	no	—
57	C₄×C₅×Dic₃	—	2	4	no	—
58	C₅×#204	—	2	16	no	—
59	C₂²×#204	C₂×C₅	1	2	yes	complemented
60	C₂×#874	C₂×C₅	1	1	yes	characteristic
61	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#821	C₂×C₅	1	2	yes	complemented
64	#4848	C₂×C₅	1	8	yes	direct product factor
65	C₂²×C₅×Q₈	—	3	1	no	—
66	C₂²×C₅×D₄	—	3	2	no	—
67	C₂²×C₅×D₄	—	6	1	no	—
68	C₂²×C₅×D₄	—	6	1	no	—
69	C₂×C₅×SD₁₆	—	3	8	no	—
70	C₂×C₅×SD₁₆	—	6	8	no	—
71	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
72	C₅×#127	—	3	4	no	—
73	C₅×#127	—	6	2	no	—
74	C₄×C₅×Q₈	—	3	4	no	—
75	C₄×C₅×Q₈	—	6	2	no	—
76	C₂×C₅×C₄⋊C₄	—	3	1	no	—
77	C₂×C₅×C₄⋊C₄	—	6	1	no	—
78	C₂×C₄²×C₅	—	6	1	no	—
79	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
80	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
81	C₅×#102	—	3	8	no	—
82	C₂×#460	—	3	1	no	Sylow
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₅×D₃	—	2	4	no	—
85	C₂²×C₅×D₃	—	4	4	no	—
86	C₂²×C₅×D₃	—	4	4	no	—
87	C₂²×C₅×D₃	—	4	4	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₅×Dic₃	—	2	4	no	—
97	C₂×C₅×Dic₃	—	2	2	no	—
98	C₂×C₅×Dic₃	—	2	2	no	—
99	C₂×C₅×Dic₃	—	4	2	no	—
100	C₅×D₁₂	—	2	4	no	—
101	C₅×D₁₂	—	2	4	no	—
102	C₅×D₁₂	—	4	8	no	—
103	C₅×D₁₂	—	4	4	no	—
104	C₅×D₁₂	—	4	8	no	—
105	C₅×Dic₆	—	2	4	no	—
106	C₅×Dic₆	—	2	2	no	—
107	C₅×Dic₆	C₂×D₄	1	4	yes	complemented
108	C₃×C₅×C₈	—	2	4	no	—
109	C₂²×D₁₂	—	2	1	no	—
110	C₂²×D₁₂	—	2	1	no	—
111	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
112	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
116	C₂×Dic₃⋊C₄	—	2	1	no	—
117	C₂×C₄×Dic₃	—	2	1	no	—
118	C₂×#204	—	2	8	no	—
119	C₂×#204	C₂²×C₅	1	8	yes	complemented
120	#874	—	2	2	no	—
121	#874	C₂²×C₅	1	4	yes	—
122	C₄×Dic₆	—	2	2	no	—
123	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
124	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
125	#821	C₂²×C₅	1	8	yes	complemented
126	C₂⁴×C₅	—	6	2	no	—
127	C₂×C₅×Q₈	—	3	4	no	—
128	C₂×C₅×Q₈	—	3	2	no	—
129	C₂×C₅×Q₈	—	6	1	no	—
130	C₂×C₅×Q₈	—	6	2	no	—
131	C₂×C₅×D₄	—	3	4	no	—
132	C₂×C₅×D₄	—	6	4	no	—
133	C₂×C₅×D₄	—	6	4	no	—
134	C₂×C₅×D₄	—	6	2	no	—
135	C₂×C₅×D₄	—	6	4	no	—
136	C₂×C₅×D₄	—	6	4	no	—
137	C₂×C₅×D₄	—	12	4	no	—
138	C₂×C₅×D₄	—	12	4	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₂²×C₄×C₅	—	6	1	no	—
141	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
142	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×SD₁₆	—	6	16	no	—
145	C₂×C₅×C₈	—	2	4	no	—
146	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
147	C₅×C₄⋊C₄	—	3	2	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₄⋊C₄	—	6	4	no	—
150	C₄²×C₅	—	6	4	no	—
151	C₄²×C₅	D₁₂	1	2	yes	—
152	C₄²×C₅	C₂²×D₃	1	2	yes	—
153	C₂²×SD₁₆	—	3	2	no	—
154	C₂×#127	—	3	1	no	—
155	C₂×C₄×Q₈	—	3	1	no	—
156	#460	—	3	8	no	—
157	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
158	C₂×#102	—	3	2	no	—
159	C₂²×C₃×C₅	#121	1	2	yes	—
160	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
161	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
162	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₅×D₃	—	4	4	no	—
164	C₂×C₅×D₃	—	4	4	no	—
165	C₂×C₅×D₃	—	4	4	no	—
166	C₂×C₅×D₃	—	8	8	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	#121	1	2	yes	—
169	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
170	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
172	C₅×Dic₃	—	2	4	no	—
173	C₅×Dic₃	—	4	2	no	—
174	C₂³×D₃	—	2	2	no	—
175	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
178	C₂²×Dic₃	—	2	1	no	—
179	C₂²×Dic₃	—	2	1	no	—
180	C₂×D₁₂	—	2	4	no	—
181	C₂×D₁₂	—	2	4	no	—
182	C₂×D₁₂	—	2	2	no	—
183	C₂×D₁₂	—	2	4	no	—
184	C₂×D₁₂	—	2	4	no	—
185	C₂×D₁₂	—	4	4	no	—
186	C₂×D₁₂	—	4	4	no	—
187	C₂×D₁₂	C₂³×C₅	1	4	yes	—
188	C₂×Dic₆	—	2	1	no	—
189	C₂×Dic₆	—	2	2	no	—
190	C₂×Dic₆	C₅×D₄	1	4	yes	complemented
191	C₂×Dic₆	C₂³×C₅	1	2	yes	—
192	C₂×C₃×C₈	—	2	4	no	—
193	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
194	C₃×C₄²	C₅×D₄	1	2	yes	—
195	C₃×C₄²	C₂³×C₅	1	2	yes	—
196	C₄⋊Dic₃	—	2	1	no	—
197	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
198	Dic₃⋊C₄	—	2	4	no	—
199	C₄×Dic₃	—	2	4	no	—
200	#204	—	2	16	no	—
201	C₂³×C₅	—	6	4	no	—
202	C₂³×C₅	—	12	4	no	—
203	C₂³×C₅	—	12	4	no	—
204	C₂³×C₅	—	12	4	no	—
205	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
206	C₅×Q₈	—	3	4	no	—
207	C₅×Q₈	—	6	4	no	—
208	C₅×Q₈	—	6	2	no	—
209	C₅×D₄	—	6	4	no	—
210	C₅×D₄	—	6	4	no	—
211	C₅×D₄	—	12	8	no	—
212	C₅×D₄	—	12	4	no	—
213	C₅×D₄	—	12	8	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	6	4	no	—
216	C₂×C₄×C₅	—	6	2	no	—
217	C₂×C₄×C₅	—	6	2	no	—
218	C₂×C₄×C₅	—	12	2	no	—
219	C₂×C₄×C₅	#204	1	4	yes	complemented
220	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
221	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
223	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
224	C₂×C₄×C₅	#239	1	2	yes	—
225	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
226	C₅×C₈	—	2	4	no	—
227	C₂²×Q₈	—	3	1	no	—
228	C₂²×D₄	—	3	2	no	—
229	C₂²×D₄	—	6	1	no	—
230	C₂²×D₄	—	6	1	no	—
231	C₂×SD₁₆	—	3	8	no	—
232	C₂×SD₁₆	—	6	8	no	—
233	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
234	#127	—	3	4	no	—
235	#127	—	6	2	no	—
236	C₄×Q₈	—	3	4	no	—
237	C₄×Q₈	—	6	2	no	—
238	C₂×C₄⋊C₄	—	3	1	no	—
239	C₂×C₄⋊C₄	—	6	1	no	—
240	C₂×C₄²	—	6	1	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
242	C₄⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
243	#102	—	3	8	no	—
244	C₂×C₃×C₅	#460	1	4	yes	complemented
245	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₅×D₃	—	8	4	no	—
249	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂²×D₃	—	2	4	no	—
251	C₂²×D₃	—	4	4	no	—
252	C₂²×D₃	—	4	4	no	—
253	C₂²×D₃	—	4	4	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
260	C₂×C₃×C₄	C₅×#41	1	2	yes	—
261	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
262	C₂×Dic₃	—	2	4	no	—
263	C₂×Dic₃	—	2	2	no	—
264	C₂×Dic₃	—	2	2	no	—
265	C₂×Dic₃	—	4	2	no	—
266	D₁₂	—	2	4	no	—
267	D₁₂	—	2	4	no	—
268	D₁₂	—	4	8	no	—
269	D₁₂	—	4	4	no	—
270	D₁₂	—	4	8	no	—
271	Dic₆	—	2	4	no	—
272	Dic₆	—	2	2	no	—
273	Dic₆	C₂×C₅×D₄	1	4	yes	complemented
274	C₃×C₈	—	2	4	no	—
275	C₂²×C₅	—	12	4	no	—
276	C₂²×C₅	—	12	4	no	—
277	C₂²×C₅	—	12	4	no	—
278	C₂²×C₅	—	24	8	no	—
279	C₂²×C₅	#895	1	2	yes	—
280	C₂²×C₅	C₂×#204	1	2	yes	—
281	C₂²×C₅	#908	1	2	yes	—
282	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	6	4	no	—
285	C₄×C₅	—	12	2	no	—
286	C₄×C₅	#895	1	2	yes	—
287	C₄×C₅	C₂×#204	1	4	yes	complemented
288	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
289	C₄×C₅	C₂×#239	1	1	yes	characteristic
290	C₂⁴	—	6	2	no	—
291	C₂×Q₈	—	3	4	no	—
292	C₂×Q₈	—	3	2	no	—
293	C₂×Q₈	—	6	1	no	—
294	C₂×Q₈	—	6	2	no	—
295	C₂×D₄	—	3	4	no	—
296	C₂×D₄	—	6	4	no	—
297	C₂×D₄	—	6	4	no	—
298	C₂×D₄	—	6	2	no	—
299	C₂×D₄	—	6	4	no	—
300	C₂×D₄	—	6	4	no	—
301	C₂×D₄	—	12	4	no	—
302	C₂×D₄	—	12	4	no	—
303	C₂²×C₄	—	6	1	no	—
304	C₂²×C₄	—	6	1	no	—
305	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
306	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
308	SD₁₆	—	6	16	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
311	C₄⋊C₄	—	3	2	no	—
312	C₄⋊C₄	—	6	1	no	—
313	C₄⋊C₄	—	6	4	no	—
314	C₄²	—	6	4	no	—
315	C₄²	C₅×D₁₂	1	2	yes	—
316	C₄²	C₂²×C₅×D₃	1	2	yes	—
317	C₃×C₅	C₂×#460	1	1	yes	characteristic, complemented, Hall
318	C₂²×C₃	C₅×#121	1	2	yes	—
319	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
320	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
321	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
322	C₂×D₃	—	4	4	no	—
323	C₂×D₃	—	4	4	no	—
324	C₂×D₃	—	4	4	no	—
325	C₂×D₃	—	8	8	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	C₅×#121	1	2	yes	—
328	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	complemented
329	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
331	Dic₃	—	2	4	no	—
332	Dic₃	—	4	2	no	—
333	C₂×C₅	—	24	4	no	—
334	C₂×C₅	#4848	1	4	yes	direct product factor
335	C₂×C₅	C₂×#895	1	1	yes	characteristic
336	C₂×C₅	C₂²×#204	1	1	yes	characteristic
337	C₂×C₅	C₂×#908	1	1	yes	characteristic
338	C₂³	—	6	4	no	—
339	C₂³	—	12	4	no	—
340	C₂³	—	12	4	no	—
341	C₂³	—	12	4	no	—
342	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
343	Q₈	—	3	4	no	—
344	Q₈	—	6	4	no	—
345	Q₈	—	6	2	no	—
346	D₄	—	6	4	no	—
347	D₄	—	6	4	no	—
348	D₄	—	12	8	no	—
349	D₄	—	12	4	no	—
350	D₄	—	12	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	6	4	no	—
353	C₂×C₄	—	6	2	no	—
354	C₂×C₄	—	6	2	no	—
355	C₂×C₄	—	12	2	no	—
356	C₂×C₄	C₅×#204	1	4	yes	complemented
357	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
358	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
360	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
361	C₂×C₄	C₅×#239	1	2	yes	—
362	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₂×C₃	C₅×#460	1	4	yes	complemented
365	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
366	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
367	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
368	D₃	—	8	4	no	—
369	C₅	C₂×#4848	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	12	4	no	—
371	C₂²	—	12	4	no	—
372	C₂²	—	12	4	no	—
373	C₂²	—	24	8	no	—
374	C₂²	C₅×#895	1	2	yes	—
375	C₂²	C₂×C₅×#204	1	2	yes	—
376	C₂²	C₅×#908	1	2	yes	—
377	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	6	4	no	—
380	C₄	—	12	2	no	—
381	C₄	C₅×#895	1	2	yes	—
382	C₄	C₂×C₅×#204	1	4	yes	complemented
383	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
384	C₄	C₂×C₅×#239	1	1	yes	characteristic
385	C₃	C₂×C₅×#460	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	24	4	no	—
387	C₂	C₅×#4848	1	4	yes	direct product factor
388	C₂	C₂×C₅×#895	1	1	yes	characteristic
389	C₂	C₂²×C₅×#204	1	1	yes	characteristic
390	C₂	C₂×C₅×#908	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#874	C₂
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#460
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#204	C₂	semidirect
3. C₂×C₄×C₅×Dic₆	C₂	semidirect
4. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₂×C₅×#821	C₂	semidirect
6. C₅×#4848	C₂	direct (N × H)
18. C₂×C₅×#204	C₂²	semidirect
22. C₄×C₅×Dic₆	C₂²	semidirect
23. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₅×#821	C₂²	semidirect
25. C₂×#4848	C₅	direct (N × H)
30. C₂×C₅×C₄⋊C₈	D₃	semidirect
48. C₂×C₅×Dic₆	D₄	semidirect
59. C₂²×#204	C₂×C₅	semidirect
61. C₂×C₄×Dic₆	C₂×C₅	semidirect
62. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
63. C₂×#821	C₂×C₅	semidirect
64. #4848	C₂×C₅	direct (N × H)
80. C₅×C₄⋊C₈	C₂×D₃	semidirect
89. C₂×C₃×C₄×C₅	SD₁₆	semidirect
107. C₅×Dic₆	C₂×D₄	semidirect
119. C₂×#204	C₂²×C₅	semidirect
123. C₄×Dic₆	C₂²×C₅	semidirect
124. C₃×C₄⋊C₈	C₂²×C₅	semidirect
125. #821	C₂²×C₅	semidirect
157. C₂×C₄⋊C₈	C₅×D₃	semidirect
169. C₃×C₄×C₅	C₂×SD₁₆	semidirect
190. C₂×Dic₆	C₅×D₄	semidirect
219. C₂×C₄×C₅	#204	semidirect
242. C₄⋊C₈	C₂×C₅×D₃	semidirect
244. C₂×C₃×C₅	#460	semidirect
255. C₂×C₃×C₄	C₅×SD₁₆	semidirect
273. Dic₆	C₂×C₅×D₄	semidirect
287. C₄×C₅	C₂×#204	semidirect
317. C₃×C₅	C₂×#460	semidirect
328. C₃×C₄	C₂×C₅×SD₁₆	semidirect
334. C₂×C₅	#4848	direct (N × H)
356. C₂×C₄	C₅×#204	semidirect
364. C₂×C₃	C₅×#460	semidirect
369. C₅	C₂×#4848	direct (N × H)
382. C₄	C₂×C₅×#204	semidirect
385. C₃	C₂×C₅×#460	semidirect
387. C₂	C₅×#4848	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#204	2
C₂×C₅×#874	2
C₂×C₄×C₅×Dic₆	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₅×#821	2
C₅×#4848	2
C₂×C₅×#460	3
C₂×#4848	5

Subgroups — C2×C5×#4848 #14426019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4848 #14426019