Subgroups — C₂×C₅×#5027 #14426016

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	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#215	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic
4	C₅×#5027	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#809	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#460	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₅×D₁₂	—	2	1	no	—
10	C₂²×C₅×D₁₂	—	2	1	no	—
11	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
12	C₃×C₄×C₅×Q₈	—	2	2	no	—
13	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×#215	—	2	8	no	—
19	C₂×C₅×#215	C₂²	1	8	yes	complemented
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₅×#874	—	2	2	no	—
22	C₅×#874	C₂²	1	4	yes	—
23	C₅×#809	C₂²	1	8	yes	complemented
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂×#5027	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	D₃	1	1	yes	characteristic, complemented
29	C₅×#460	—	3	8	no	—
30	C₂×C₅×C₄⋊C₈	—	3	1	no	—
31	C₂×C₅×#102	—	3	2	no	—
32	C₂³×C₅×D₃	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
36	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×D₁₂	—	2	4	no	—
43	C₂×C₅×D₁₂	—	2	4	no	—
44	C₂×C₅×D₁₂	—	2	2	no	—
45	C₂×C₅×D₁₂	—	2	4	no	—
46	C₂×C₅×D₁₂	—	2	4	no	—
47	C₂×C₅×D₁₂	—	4	4	no	—
48	C₂×C₅×D₁₂	—	4	4	no	—
49	C₂×C₅×D₁₂	C₂³	1	4	yes	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₃×C₄²×C₅	D₄	1	2	yes	—
55	C₃×C₄²×C₅	C₂³	1	2	yes	—
56	C₅×#215	—	2	16	no	—
57	C₂×C₅×C₃⋊C₈	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
59	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×#215	C₂×C₅	1	2	yes	complemented
61	C₂×#874	C₂×C₅	1	1	yes	characteristic
62	#5027	C₂×C₅	1	8	yes	direct product factor
63	C₂×#809	C₂×C₅	1	2	yes	complemented
64	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
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	—	3	2	no	—
72	C₅×#127	—	3	4	no	—
73	C₅×#127	—	6	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	C₂×D₃	1	4	yes	complemented
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₄²×C₅	—	2	1	no	—
79	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
80	C₅×C₄⋊C₈	—	3	4	no	—
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	C₃×C₅×Q₈	—	2	4	no	—
89	C₃×C₅×Q₈	—	2	2	no	—
90	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	#41	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
103	C₅×D₁₂	—	2	4	no	—
104	C₅×D₁₂	—	2	4	no	—
105	C₅×D₁₂	—	4	8	no	—
106	C₅×D₁₂	—	4	4	no	—
107	C₅×D₁₂	—	4	8	no	—
108	C₅×C₃⋊C₈	—	2	4	no	—
109	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
110	C₂²×D₁₂	—	2	1	no	—
111	C₂²×D₁₂	—	2	1	no	—
112	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
113	C₃×C₄×Q₈	—	2	2	no	—
114	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	complemented
115	C₂×C₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄²	—	2	1	no	—
118	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
119	C₂×#215	—	2	8	no	—
120	C₂×#215	C₂²×C₅	1	8	yes	complemented
121	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
122	#874	—	2	2	no	—
123	#874	C₂²×C₅	1	4	yes	—
124	#809	C₂²×C₅	1	8	yes	complemented
125	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
126	C₂⁴×C₅	—	6	2	no	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	D₁₂	1	4	yes	complemented
130	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
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	4	no	—
135	C₂×C₅×D₄	—	6	4	no	—
136	C₂×C₅×D₄	—	6	2	no	—
137	C₂×C₅×D₄	—	12	4	no	—
138	C₂×C₅×D₄	—	12	4	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	#67	1	1	yes	characteristic
142	C₂²×C₄×C₅	#67	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×SD₁₆	—	6	16	no	—
145	C₂×C₅×C₈	—	3	4	no	—
146	C₂×C₅×C₈	—	6	4	no	—
147	C₅×C₄⋊C₄	—	2	4	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
150	C₄²×C₅	—	2	4	no	—
151	C₄²×C₅	#67	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	C₅×D₃	1	1	yes	characteristic, complemented
156	#460	—	3	8	no	—
157	C₂×C₄⋊C₈	—	3	1	no	—
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	4	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	#121	1	2	yes	—
171	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
172	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
174	C₂³×D₃	—	2	2	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	—	2	2	no	—
177	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
178	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂×D₁₂	—	2	4	no	—
185	C₂×D₁₂	—	2	4	no	—
186	C₂×D₁₂	—	2	2	no	—
187	C₂×D₁₂	—	2	4	no	—
188	C₂×D₁₂	—	2	4	no	—
189	C₂×D₁₂	—	4	4	no	—
190	C₂×D₁₂	—	4	4	no	—
191	C₂×D₁₂	C₂³×C₅	1	4	yes	—
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
195	C₃×C₄²	—	2	4	no	—
196	C₃×C₄²	C₅×D₄	1	2	yes	—
197	C₃×C₄²	C₂³×C₅	1	2	yes	—
198	#215	—	2	16	no	—
199	C₂×C₃⋊C₈	—	2	4	no	—
200	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
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×#67	1	1	yes	characteristic
206	C₅×Q₈	—	2	4	no	—
207	C₅×Q₈	—	2	2	no	—
208	C₅×Q₈	C₂×D₁₂	1	4	yes	complemented
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	4	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	#215	1	4	yes	complemented
220	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
221	C₂×C₄×C₅	#235	1	2	yes	—
222	C₂×C₄×C₅	C₂×#67	1	2	yes	—
223	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#67	1	2	yes	—
225	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
226	C₅×C₈	—	6	4	no	—
227	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
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	—	3	2	no	—
234	#127	—	3	4	no	—
235	#127	—	6	2	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	C₂×C₅×D₃	1	4	yes	complemented
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
242	C₄⋊C₈	—	3	4	no	—
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	C₃×Q₈	—	2	4	no	—
255	C₃×Q₈	—	2	2	no	—
256	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
267	C₂×C₃×C₄	C₅×#41	1	2	yes	—
268	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
269	D₁₂	—	2	4	no	—
270	D₁₂	—	2	4	no	—
271	D₁₂	—	4	8	no	—
272	D₁₂	—	4	4	no	—
273	D₁₂	—	4	8	no	—
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	#930	1	2	yes	—
280	C₂²×C₅	C₂×#215	1	2	yes	—
281	C₂²×C₅	#949	1	2	yes	—
282	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	#930	1	2	yes	—
287	C₄×C₅	C₂×#215	1	4	yes	complemented
288	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
289	C₄×C₅	C₂×#235	1	1	yes	characteristic
290	C₂⁴	—	6	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	C₅×D₁₂	1	4	yes	complemented
294	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
295	C₂×D₄	—	3	4	no	—
296	C₂×D₄	—	6	4	no	—
297	C₂×D₄	—	6	4	no	—
298	C₂×D₄	—	6	4	no	—
299	C₂×D₄	—	6	4	no	—
300	C₂×D₄	—	6	2	no	—
301	C₂×D₄	—	12	4	no	—
302	C₂×D₄	—	12	4	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	C₅×#67	1	1	yes	characteristic
306	C₂²×C₄	C₅×#67	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
308	SD₁₆	—	6	16	no	—
309	C₂×C₈	—	3	4	no	—
310	C₂×C₈	—	6	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
314	C₄²	—	2	4	no	—
315	C₄²	C₅×#67	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	4	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	4	2	no	—
329	C₃×C₄	C₅×#121	1	2	yes	—
330	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	complemented
331	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
332	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
333	C₂×C₅	—	24	4	no	—
334	C₂×C₅	#5027	1	4	yes	direct product factor
335	C₂×C₅	C₂×#930	1	1	yes	characteristic
336	C₂×C₅	C₂²×#215	1	1	yes	characteristic
337	C₂×C₅	C₂×#949	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×#67	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	2	2	no	—
345	Q₈	C₂×C₅×D₁₂	1	4	yes	complemented
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	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	C₅×#215	1	4	yes	complemented
357	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
358	C₂×C₄	C₅×#235	1	2	yes	—
359	C₂×C₄	C₂×C₅×#67	1	2	yes	—
360	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
361	C₂×C₄	C₂×C₅×#67	1	2	yes	—
362	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
363	C₈	—	6	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×#5027	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×#930	1	2	yes	—
375	C₂²	C₂×C₅×#215	1	2	yes	—
376	C₂²	C₅×#949	1	2	yes	—
377	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	2	no	—
381	C₄	C₅×#930	1	2	yes	—
382	C₄	C₂×C₅×#215	1	4	yes	complemented
383	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
384	C₄	C₂×C₅×#235	1	1	yes	characteristic
385	C₃	C₂×C₅×#460	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	24	4	no	—
387	C₂	C₅×#5027	1	4	yes	direct product factor
388	C₂	C₂×C₅×#930	1	1	yes	characteristic
389	C₂	C₂²×C₅×#215	1	1	yes	characteristic
390	C₂	C₂×C₅×#949	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#874	C₂
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×#460
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
2. C₂²×C₅×#215	C₂	semidirect
4. C₅×#5027	C₂	direct (N × H)
5. C₂×C₅×#809	C₂	semidirect
6. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
13. C₃×C₄×C₅×Q₈	C₂²	semidirect
19. C₂×C₅×#215	C₂²	semidirect
23. C₅×#809	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₂×#5027	C₅	direct (N × H)
28. C₂×C₄×C₅×Q₈	D₃	semidirect
35. C₂×C₃×C₅×Q₈	D₄	semidirect
59. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
60. C₂²×#215	C₂×C₅	semidirect
62. #5027	C₂×C₅	direct (N × H)
63. C₂×#809	C₂×C₅	semidirect
64. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
75. C₄×C₅×Q₈	C₂×D₃	semidirect
90. C₃×C₅×Q₈	C₂×D₄	semidirect
96. C₂×C₃×C₄×C₅	SD₁₆	semidirect
114. C₃×C₄×Q₈	C₂²×C₅	semidirect
120. C₂×#215	C₂²×C₅	semidirect
124. #809	C₂²×C₅	semidirect
125. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
129. C₂×C₅×Q₈	D₁₂	semidirect
155. C₂×C₄×Q₈	C₅×D₃	semidirect
171. C₃×C₄×C₅	C₂×SD₁₆	semidirect
177. C₂×C₃×Q₈	C₅×D₄	semidirect
208. C₅×Q₈	C₂×D₁₂	semidirect
219. C₂×C₄×C₅	#215	semidirect
237. C₄×Q₈	C₂×C₅×D₃	semidirect
244. C₂×C₃×C₅	#460	semidirect
256. C₃×Q₈	C₂×C₅×D₄	semidirect
262. C₂×C₃×C₄	C₅×SD₁₆	semidirect
287. C₄×C₅	C₂×#215	semidirect
293. C₂×Q₈	C₅×D₁₂	semidirect
317. C₃×C₅	C₂×#460	semidirect
330. C₃×C₄	C₂×C₅×SD₁₆	semidirect
334. C₂×C₅	#5027	direct (N × H)
345. Q₈	C₂×C₅×D₁₂	semidirect
356. C₂×C₄	C₅×#215	semidirect
364. C₂×C₃	C₅×#460	semidirect
369. C₅	C₂×#5027	direct (N × H)
382. C₄	C₂×C₅×#215	semidirect
385. C₃	C₂×C₅×#460	semidirect
387. C₂	C₅×#5027	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×C₄×C₅×Q₈	2
C₂²×C₅×#215	2
C₂×C₅×#874	2
C₅×#5027	2
C₂×C₅×#809	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#460	3
C₂×#5027	5

Subgroups — C2×C5×#5027 #14426016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5027 #14426016