Subgroups — C₂×C₅×#5075 #14426007

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×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#214	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
5	C₅×#5075	C₂	1	8	yes	maximal, direct product factor
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×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
12	C₃×C₅×#127	—	2	2	no	—
13	C₃×C₅×#127	C₂²	1	4	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#214	—	2	8	no	—
16	C₂×C₅×#214	C₂²	1	8	yes	complemented
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	—	2	1	no	—
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₄×C₅×Dic₆	—	2	2	no	—
22	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
23	C₅×#832	C₂²	1	8	yes	complemented
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂×#5075	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×SD₁₆	—	3	2	no	—
27	C₂×C₅×#127	D₃	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	—	3	1	no	—
29	C₅×#460	—	3	8	no	—
30	C₂×C₅×C₄⋊C₈	—	3	1	no	—
31	C₂×C₅×#102	—	3	2	no	—
32	C₂⁴×C₃×C₅	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	4	4	no	—
39	C₂×C₃×C₅×D₄	—	4	4	no	—
40	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	2	1	no	—
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	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₅×#214	—	2	16	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
55	C₅×Dic₃⋊C₄	—	2	4	no	—
56	C₄×C₅×Dic₃	—	2	4	no	—
57	C₂×C₅×C₃⋊C₈	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
59	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
60	C₂²×#214	C₂×C₅	1	2	yes	complemented
61	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×#832	C₂×C₅	1	2	yes	complemented
63	#5075	C₂×C₅	1	8	yes	direct product factor
64	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂²×C₅×Q₈	—	3	1	no	—
66	C₂²×C₅×D₄	—	2	1	no	—
67	C₂²×C₅×D₄	—	2	1	no	—
68	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
69	C₂×C₅×SD₁₆	—	3	8	no	—
70	C₂×C₅×SD₁₆	—	6	8	no	—
71	C₂²×C₅×C₈	—	3	2	no	—
72	C₅×#127	—	2	2	no	—
73	C₅×#127	C₂×D₃	1	4	yes	—
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	—	3	4	no	—
81	C₅×#102	—	3	8	no	—
82	C₂×#460	—	3	1	no	Sylow
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	4	4	no	—
85	C₂³×C₃×C₅	—	4	4	no	—
86	C₂³×C₃×C₅	—	4	4	no	—
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₃×C₅×D₄	—	2	4	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	4	8	no	—
91	C₃×C₅×D₄	—	4	4	no	—
92	C₃×C₅×D₄	—	4	8	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	4	2	no	—
105	C₅×Dic₆	—	2	4	no	—
106	C₅×Dic₆	—	2	2	no	—
107	C₅×Dic₆	C₂×D₄	1	4	yes	complemented
108	C₅×C₃⋊C₈	—	2	4	no	—
109	C₂²×C₃×D₄	—	2	1	no	—
110	C₂²×C₃×D₄	—	2	1	no	—
111	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
112	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
113	C₃×#127	—	2	2	no	—
114	C₃×#127	C₂²×C₅	1	4	yes	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₂×#214	—	2	8	no	—
117	C₂×#214	C₂²×C₅	1	8	yes	complemented
118	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂×Dic₃⋊C₄	—	2	1	no	—
120	C₂×C₄×Dic₃	—	2	1	no	—
121	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
122	C₄×Dic₆	—	2	2	no	—
123	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
124	#832	C₂²×C₅	1	8	yes	complemented
125	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
126	C₂⁴×C₅	—	2	2	no	—
127	C₂×C₅×Q₈	—	3	4	no	—
128	C₂×C₅×Q₈	—	3	2	no	—
129	C₂×C₅×Q₈	—	6	2	no	—
130	C₂×C₅×Q₈	—	6	1	no	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	4	no	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	—	4	4	no	—
137	C₂×C₅×D₄	—	4	4	no	—
138	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₂²×C₄×C₅	—	6	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	—	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	#67	1	2	yes	—
152	C₄²×C₅	C₂²×D₃	1	2	yes	—
153	C₂²×SD₁₆	—	3	2	no	—
154	C₂×#127	C₅×D₃	1	1	yes	characteristic
155	C₂×C₄×Q₈	—	3	1	no	—
156	#460	—	3	8	no	—
157	C₂×C₄⋊C₈	—	3	1	no	—
158	C₂×#102	—	3	2	no	—
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	—	8	8	no	—
163	C₂²×C₃×C₅	#121	1	2	yes	—
164	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
165	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
166	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
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	C₂⁴×C₃	—	2	2	no	—
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	2	2	no	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	—	4	4	no	—
181	C₂×C₃×D₄	—	4	4	no	—
182	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂²×Dic₃	—	2	1	no	—
187	C₂²×Dic₃	—	2	1	no	—
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	C₃×C₄²	C₅×D₄	1	2	yes	—
193	C₃×C₄²	C₂³×C₅	1	2	yes	—
194	#214	—	2	16	no	—
195	C₄⋊Dic₃	—	2	1	no	—
196	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
197	Dic₃⋊C₄	—	2	4	no	—
198	C₄×Dic₃	—	2	4	no	—
199	C₂×C₃⋊C₈	—	2	4	no	—
200	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
201	C₂³×C₅	—	2	4	no	—
202	C₂³×C₅	—	4	4	no	—
203	C₂³×C₅	—	4	4	no	—
204	C₂³×C₅	—	4	4	no	—
205	C₂³×C₅	C₂×#67	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	—	2	4	no	—
210	C₅×D₄	—	2	4	no	—
211	C₅×D₄	—	4	8	no	—
212	C₅×D₄	—	4	8	no	—
213	C₅×D₄	—	4	4	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	#214	1	4	yes	complemented
220	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	#237	1	2	yes	—
222	C₂×C₄×C₅	C₂×#67	1	2	yes	—
223	C₂×C₄×C₅	C₂×#67	1	2	yes	—
224	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
226	C₅×C₈	—	6	4	no	—
227	C₂²×Q₈	—	3	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
231	C₂×SD₁₆	—	3	8	no	—
232	C₂×SD₁₆	—	6	8	no	—
233	C₂²×C₈	—	3	2	no	—
234	#127	—	2	2	no	—
235	#127	C₂×C₅×D₃	1	4	yes	—
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	—	3	4	no	—
243	#102	—	3	8	no	—
244	C₂×C₃×C₅	—	8	4	no	—
245	C₂×C₃×C₅	#460	1	4	yes	complemented
246	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	4	4	no	—
251	C₂³×C₃	—	4	4	no	—
252	C₂³×C₃	—	4	4	no	—
253	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
254	C₃×D₄	—	2	4	no	—
255	C₃×D₄	—	2	4	no	—
256	C₃×D₄	—	4	8	no	—
257	C₃×D₄	—	4	4	no	—
258	C₃×D₄	—	4	8	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
261	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₅×#41	1	2	yes	—
266	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
267	C₂×Dic₃	—	2	4	no	—
268	C₂×Dic₃	—	2	2	no	—
269	C₂×Dic₃	—	2	2	no	—
270	C₂×Dic₃	—	4	2	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	—	4	4	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	4	4	no	—
278	C₂²×C₅	—	8	8	no	—
279	C₂²×C₅	#932	1	2	yes	—
280	C₂²×C₅	C₂×#214	1	2	yes	—
281	C₂²×C₅	#938	1	2	yes	—
282	C₂²×C₅	C₂²×#67	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	C₂×#214	1	4	yes	complemented
287	C₄×C₅	#938	1	2	yes	—
288	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
289	C₄×C₅	C₂×#237	1	1	yes	characteristic
290	C₂⁴	—	2	2	no	—
291	C₂×Q₈	—	3	4	no	—
292	C₂×Q₈	—	3	2	no	—
293	C₂×Q₈	—	6	2	no	—
294	C₂×Q₈	—	6	1	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
303	C₂²×C₄	—	6	1	no	—
304	C₂²×C₄	—	6	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	—	3	2	no	—
312	C₄⋊C₄	—	6	1	no	—
313	C₄⋊C₄	—	6	4	no	—
314	C₄²	—	6	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	—	4	4	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	—	4	4	no	—
321	C₂²×C₃	—	8	8	no	—
322	C₂²×C₃	C₅×#121	1	2	yes	—
323	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
324	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
325	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
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	—	8	4	no	—
334	C₂×C₅	#5075	1	4	yes	direct product factor
335	C₂×C₅	C₂×#932	1	1	yes	characteristic
336	C₂×C₅	C₂²×#214	1	1	yes	characteristic
337	C₂×C₅	C₂×#938	1	1	yes	characteristic
338	C₂³	—	2	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₅×#67	1	1	yes	characteristic
343	Q₈	—	3	4	no	—
344	Q₈	—	6	4	no	—
345	Q₈	—	6	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	4	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×#214	1	4	yes	complemented
357	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
358	C₂×C₄	C₅×#237	1	2	yes	—
359	C₂×C₄	C₂×C₅×#67	1	2	yes	—
360	C₂×C₄	C₂×C₅×#67	1	2	yes	—
361	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
362	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
363	C₈	—	6	4	no	—
364	C₂×C₃	—	8	4	no	—
365	C₂×C₃	C₅×#460	1	4	yes	complemented
366	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
367	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
368	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₅	C₂×#5075	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	8	no	—
374	C₂²	C₅×#932	1	2	yes	—
375	C₂²	C₂×C₅×#214	1	2	yes	—
376	C₂²	C₅×#938	1	2	yes	—
377	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	6	4	no	—
380	C₄	—	12	2	no	—
381	C₄	C₂×C₅×#214	1	4	yes	complemented
382	C₄	C₅×#938	1	2	yes	—
383	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
384	C₄	C₂×C₅×#237	1	1	yes	characteristic
385	C₃	C₂×C₅×#460	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	8	4	no	—
387	C₂	C₅×#5075	1	4	yes	direct product factor
388	C₂	C₂×C₅×#932	1	1	yes	characteristic
389	C₂	C₂²×C₅×#214	1	1	yes	characteristic
390	C₂	C₂×C₅×#938	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, prime radical	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#127	D₃
hypocenter	C₃	C₂×C₅×#460
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#127

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#214	C₂	semidirect
3. C₂×C₄×C₅×Dic₆	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5075	C₂	direct (N × H)
6. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
16. C₂×C₅×#214	C₂²	semidirect
22. C₄×C₅×Dic₆	C₂²	semidirect
23. C₅×#832	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₂×#5075	C₅	direct (N × H)
48. C₂×C₅×Dic₆	D₄	semidirect
60. C₂²×#214	C₂×C₅	semidirect
61. C₂×C₄×Dic₆	C₂×C₅	semidirect
62. C₂×#832	C₂×C₅	semidirect
63. #5075	C₂×C₅	direct (N × H)
64. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
94. C₂×C₃×C₄×C₅	SD₁₆	semidirect
107. C₅×Dic₆	C₂×D₄	semidirect
117. C₂×#214	C₂²×C₅	semidirect
123. C₄×Dic₆	C₂²×C₅	semidirect
124. #832	C₂²×C₅	semidirect
125. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
169. C₃×C₄×C₅	C₂×SD₁₆	semidirect
190. C₂×Dic₆	C₅×D₄	semidirect
219. C₂×C₄×C₅	#214	semidirect
245. C₂×C₃×C₅	#460	semidirect
260. C₂×C₃×C₄	C₅×SD₁₆	semidirect
273. Dic₆	C₂×C₅×D₄	semidirect
286. C₄×C₅	C₂×#214	semidirect
317. C₃×C₅	C₂×#460	semidirect
328. C₃×C₄	C₂×C₅×SD₁₆	semidirect
334. C₂×C₅	#5075	direct (N × H)
356. C₂×C₄	C₅×#214	semidirect
365. C₂×C₃	C₅×#460	semidirect
369. C₅	C₂×#5075	direct (N × H)
381. C₄	C₂×C₅×#214	semidirect
385. C₃	C₂×C₅×#460	semidirect
387. C₂	C₅×#5075	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
C₂²×C₅×#214	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#832	2
C₅×#5075	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#460	3
C₂×#5075	5

Subgroups — C2×C5×#5075 #14426007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5075 #14426007