Subgroups — C₂×C₅×#5719 #14481091

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×C₅×#939	C₂	1	4	yes	maximal, complemented
3	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#935	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
6	C₅×#5719	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#540	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂³×C₅×Dic₃	C₂²	1	4	yes	—
14	C₂²×C₄×C₅×D₃	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×C₅×#217	C₂²	1	4	yes	—
18	C₂×C₅×#217	C₂²	1	4	yes	—
19	C₅×#939	C₂²	1	32	yes	complemented
20	C₅×#938	C₂²	1	16	yes	complemented
21	C₅×#935	C₂²	1	32	yes	complemented
22	C₅×D₄×Dic₃	C₂²	1	16	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₅×#872	C₂²	1	8	yes	complemented
29	C₅×#870	C₂²	1	8	yes	complemented
30	C₂×#5719	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#540	—	3	16	no	—
32	C₂×C₅×#127	D₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#125	—	3	1	no	—
34	C₂×C₅×#123	—	3	4	no	—
35	C₂×C₅×#121	—	3	2	no	—
36	C₂×C₅×#121	—	3	4	no	—
37	C₂×C₄×C₅×D₄	—	3	2	no	—
38	C₂×C₅×#117	—	3	1	no	—
39	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
40	C₂³×C₅×D₃	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×C₅×#67	—	4	8	no	—
48	C₂×C₅×#67	C₂³	1	16	yes	—
49	C₂²×C₅×Dic₃	—	4	8	no	—
50	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
52	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
53	C₂²×C₅×Dic₃	C₂³	1	16	yes	—
54	C₂×C₄×C₅×D₃	—	2	4	no	—
55	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
56	C₃×C₄²×C₅	C₂³	1	4	yes	—
57	C₅×#217	C₂³	1	16	yes	—
58	C₅×#217	C₂³	1	16	yes	—
59	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
60	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
61	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
62	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
63	C₄×C₅×Dic₃	C₂³	1	4	yes	—
64	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#939	C₂×C₅	1	4	yes	complemented
66	C₂×#938	C₂×C₅	1	2	yes	complemented
67	C₂×#935	C₂×C₅	1	4	yes	complemented
68	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	complemented
69	#5719	C₂×C₅	1	16	yes	direct product factor
70	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#870	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×C₅×D₄	—	3	4	no	—
73	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
74	C₂²×C₅×D₄	C₂×D₃	1	4	yes	—
75	C₂³×C₄×C₅	—	3	4	no	—
76	C₂³×C₄×C₅	—	3	1	no	—
77	C₅×#127	C₂×D₃	1	8	yes	complemented
78	C₅×#125	—	3	8	no	—
79	C₅×#123	—	3	32	no	—
80	C₅×#121	—	3	16	no	—
81	C₅×#121	—	3	32	no	—
82	C₄×C₅×D₄	—	3	16	no	—
83	C₅×#117	—	3	8	no	—
84	C₂×C₅×C₄⋊C₄	—	3	2	no	—
85	C₂×C₅×C₄⋊C₄	—	3	4	no	—
86	C₂×C₅×C₄⋊C₄	—	3	2	no	—
87	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
90	C₂×C₄²×C₅	—	3	1	no	—
91	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
92	C₂×#540	—	3	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×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	2	4	no	—
100	C₂²×C₅×D₃	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	C₅×#67	—	4	16	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	4	no	—
110	C₂×C₅×Dic₃	—	2	8	no	—
111	C₂×C₅×Dic₃	—	4	16	no	—
112	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
113	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
114	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
115	C₄×C₅×D₃	—	2	8	no	—
116	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
117	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
118	C₂²×#67	C₂²×C₅	1	4	yes	—
119	C₂³×Dic₃	C₂²×C₅	1	4	yes	—
120	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
121	C₃×#127	C₂²×C₅	1	8	yes	complemented
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₂×#217	C₂²×C₅	1	4	yes	—
124	C₂×#217	C₂²×C₅	1	4	yes	—
125	#939	C₂²×C₅	1	32	yes	complemented
126	#938	C₂²×C₅	1	16	yes	complemented
127	#935	C₂²×C₅	1	32	yes	complemented
128	D₄×Dic₃	C₂²×C₅	1	16	yes	complemented
129	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
131	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
132	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
134	#872	C₂²×C₅	1	8	yes	complemented
135	#870	C₂²×C₅	1	8	yes	complemented
136	C₂⁴×C₅	—	3	1	no	—
137	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
138	C₂×C₅×D₄	—	2	8	no	—
139	C₂×C₅×D₄	—	3	16	no	—
140	C₂×C₅×D₄	—	4	8	no	—
141	C₂×C₅×D₄	—	12	8	no	—
142	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
143	C₂×C₅×D₄	C₂²×D₃	1	16	yes	—
144	C₂²×C₄×C₅	—	3	2	no	—
145	C₂²×C₄×C₅	—	3	1	no	—
146	C₂²×C₄×C₅	—	3	4	no	—
147	C₂²×C₄×C₅	—	3	16	no	—
148	C₂²×C₄×C₅	—	3	4	no	—
149	C₂²×C₄×C₅	—	6	4	no	—
150	C₂²×C₄×C₅	—	12	8	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	3	8	no	—
154	C₅×C₄⋊C₄	—	3	8	no	—
155	C₅×C₄⋊C₄	—	3	16	no	—
156	C₅×C₂²⋊C₄	—	3	16	no	—
157	C₅×C₂²⋊C₄	—	3	16	no	—
158	C₅×C₂²⋊C₄	—	3	8	no	—
159	C₄²×C₅	—	3	4	no	—
160	C₄²×C₅	C₂²×D₃	1	4	yes	—
161	#540	—	3	16	no	—
162	C₂×#127	C₅×D₃	1	1	yes	characteristic, complemented
163	C₂×#125	—	3	1	no	—
164	C₂×#123	—	3	4	no	—
165	C₂×#121	—	3	2	no	—
166	C₂×#121	—	3	4	no	—
167	C₂×C₄×D₄	—	3	2	no	—
168	C₂×#117	—	3	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×C₅×D₃	—	2	2	no	—
177	C₂×C₅×D₃	—	2	4	no	—
178	C₂×C₅×D₃	—	4	4	no	—
179	C₃×C₄×C₅	—	2	4	no	—
180	C₃×C₄×C₅	C₂×#41	1	4	yes	—
181	C₅×Dic₃	—	2	2	no	—
182	C₅×Dic₃	—	2	4	no	—
183	C₅×Dic₃	—	2	8	no	—
184	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
185	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
186	C₂×C₃×D₄	—	2	8	no	—
187	C₂×C₃×D₄	—	4	8	no	—
188	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
189	C₂×C₃×D₄	C₂³×C₅	1	16	yes	—
190	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂×#67	—	4	8	no	—
193	C₂×#67	C₂³×C₅	1	16	yes	—
194	C₂²×Dic₃	—	4	8	no	—
195	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
196	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
197	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
198	C₂²×Dic₃	C₂³×C₅	1	16	yes	—
199	C₂×C₄×D₃	—	2	4	no	—
200	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
201	C₃×C₄²	C₂³×C₅	1	4	yes	—
202	#217	C₂³×C₅	1	16	yes	—
203	#217	C₂³×C₅	1	16	yes	—
204	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
205	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
206	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
207	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
208	C₄×Dic₃	C₂³×C₅	1	4	yes	—
209	C₂³×C₅	—	2	8	no	—
210	C₂³×C₅	—	2	8	no	—
211	C₂³×C₅	—	2	8	no	—
212	C₂³×C₅	—	3	2	no	—
213	C₂³×C₅	—	6	2	no	—
214	C₂³×C₅	—	6	4	no	—
215	C₂³×C₅	C₂³×D₃	1	8	yes	—
216	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
217	C₅×D₄	—	2	16	no	—
218	C₅×D₄	—	4	16	no	—
219	C₅×D₄	—	12	16	no	—
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	—	3	4	no	—
222	C₂×C₄×C₅	—	3	2	no	—
223	C₂×C₄×C₅	—	3	8	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	4	no	—
226	C₂×C₄×C₅	—	6	8	no	—
227	C₂×C₄×C₅	—	6	8	no	—
228	C₂×C₄×C₅	—	12	16	no	—
229	C₂×C₄×C₅	#237	1	4	yes	—
230	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
231	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
232	C₂²×D₄	—	3	4	no	—
233	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
234	C₂²×D₄	C₂×C₅×D₃	1	4	yes	—
235	C₂³×C₄	—	3	4	no	—
236	C₂³×C₄	—	3	1	no	—
237	#127	C₂×C₅×D₃	1	8	yes	complemented
238	#125	—	3	8	no	—
239	#123	—	3	32	no	—
240	#121	—	3	16	no	—
241	#121	—	3	32	no	—
242	C₄×D₄	—	3	16	no	—
243	#117	—	3	8	no	—
244	C₂×C₄⋊C₄	—	3	2	no	—
245	C₂×C₄⋊C₄	—	3	2	no	—
246	C₂×C₄⋊C₄	—	3	4	no	—
247	C₂×C₂²⋊C₄	—	3	4	no	—
248	C₂×C₂²⋊C₄	—	3	4	no	—
249	C₂×C₂²⋊C₄	—	3	2	no	—
250	C₂×C₄²	—	3	1	no	—
251	C₂×C₄²	C₂×C₅×D₃	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	C₅×D₃	—	4	2	no	—
257	C₂³×C₃	—	2	8	no	—
258	C₂³×C₃	—	2	8	no	—
259	C₂³×C₃	—	2	8	no	—
260	C₂³×C₃	C₂⁴×C₅	1	8	yes	—
261	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
262	C₂²×D₃	—	2	2	no	—
263	C₂²×D₃	—	2	4	no	—
264	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
265	C₃×D₄	—	2	16	no	—
266	C₃×D₄	—	4	16	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	C₅×#41	1	4	yes	—
269	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
270	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
271	#67	—	4	16	no	—
272	C₂×Dic₃	—	2	2	no	—
273	C₂×Dic₃	—	2	4	no	—
274	C₂×Dic₃	—	2	8	no	—
275	C₂×Dic₃	—	4	16	no	—
276	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
277	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
278	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
279	C₄×D₃	—	2	8	no	—
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	—	6	2	no	—
285	C₂²×C₅	—	6	4	no	—
286	C₂²×C₅	—	12	4	no	—
287	C₂²×C₅	C₂×#237	1	2	yes	—
288	C₂²×C₅	#1004	1	4	yes	—
289	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
290	C₄×C₅	—	2	4	no	—
291	C₄×C₅	—	6	2	no	—
292	C₄×C₅	—	6	4	no	—
293	C₄×C₅	—	6	8	no	—
294	C₄×C₅	C₂×#237	1	4	yes	—
295	C₂⁴	—	3	1	no	—
296	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	3	16	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	12	8	no	—
301	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
302	C₂×D₄	C₂²×C₅×D₃	1	16	yes	—
303	C₂²×C₄	—	3	2	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	4	no	—
306	C₂²×C₄	—	3	16	no	—
307	C₂²×C₄	—	3	4	no	—
308	C₂²×C₄	—	6	4	no	—
309	C₂²×C₄	—	12	8	no	—
310	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
311	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
312	C₄⋊C₄	—	3	8	no	—
313	C₄⋊C₄	—	3	8	no	—
314	C₄⋊C₄	—	3	16	no	—
315	C₂²⋊C₄	—	3	16	no	—
316	C₂²⋊C₄	—	3	16	no	—
317	C₂²⋊C₄	—	3	8	no	—
318	C₄²	—	3	4	no	—
319	C₄²	C₂²×C₅×D₃	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	C₂×C₅×#41	1	2	yes	—
326	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
327	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
328	C₂×D₃	—	2	2	no	—
329	C₂×D₃	—	2	4	no	—
330	C₂×D₃	—	4	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	C₂×C₅×#41	1	4	yes	—
333	Dic₃	—	2	2	no	—
334	Dic₃	—	2	4	no	—
335	Dic₃	—	2	8	no	—
336	C₂×C₅	—	4	8	no	—
337	C₂×C₅	—	12	2	no	—
338	C₂×C₅	#5719	1	4	yes	direct product factor
339	C₂×C₅	C₂²×#237	1	1	yes	characteristic
340	C₂×C₅	C₂×#1004	1	2	yes	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	3	2	no	—
345	C₂³	—	6	2	no	—
346	C₂³	—	6	4	no	—
347	C₂³	C₂³×C₅×D₃	1	8	yes	—
348	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
349	D₄	—	2	16	no	—
350	D₄	—	4	16	no	—
351	D₄	—	12	16	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	3	4	no	—
354	C₂×C₄	—	3	2	no	—
355	C₂×C₄	—	3	8	no	—
356	C₂×C₄	—	6	2	no	—
357	C₂×C₄	—	6	4	no	—
358	C₂×C₄	—	6	8	no	—
359	C₂×C₄	—	6	8	no	—
360	C₂×C₄	—	12	16	no	—
361	C₂×C₄	C₅×#237	1	4	yes	—
362	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
363	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
364	C₂×C₃	—	4	8	no	—
365	C₂×C₃	C₅×#540	1	4	yes	complemented
366	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
367	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
368	D₃	—	4	2	no	—
369	C₅	C₂×#5719	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	2	8	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	4	16	no	—
374	C₂²	—	6	2	no	—
375	C₂²	—	6	4	no	—
376	C₂²	—	12	4	no	—
377	C₂²	C₂×C₅×#237	1	2	yes	—
378	C₂²	C₅×#1004	1	4	yes	—
379	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
380	C₄	—	2	4	no	—
381	C₄	—	6	2	no	—
382	C₄	—	6	4	no	—
383	C₄	—	6	8	no	—
384	C₄	C₂×C₅×#237	1	4	yes	—
385	C₃	C₂×C₅×#540	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	4	8	no	—
387	C₂	—	12	2	no	—
388	C₂	C₅×#5719	1	4	yes	direct product factor
389	C₂	C₂²×C₅×#237	1	1	yes	characteristic
390	C₂	C₂×C₅×#1004	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#127	D₃
hypocenter	C₃	C₂×C₅×#540
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#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×C₅×#939	C₂	semidirect
3. C₂×C₅×#938	C₂	semidirect
4. C₂×C₅×#935	C₂	semidirect
5. C₂×C₅×D₄×Dic₃	C₂	semidirect
6. C₅×#5719	C₂	direct (N × H)
7. C₂×C₅×#872	C₂	semidirect
8. C₂×C₅×#870	C₂	semidirect
15. C₃×C₅×#127	C₂²	semidirect
19. C₅×#939	C₂²	semidirect
20. C₅×#938	C₂²	semidirect
21. C₅×#935	C₂²	semidirect
22. C₅×D₄×Dic₃	C₂²	semidirect
28. C₅×#872	C₂²	semidirect
29. C₅×#870	C₂²	semidirect
30. C₂×#5719	C₅	direct (N × H)
32. C₂×C₅×#127	D₃	semidirect
64. C₂×C₃×#127	C₂×C₅	semidirect
65. C₂×#939	C₂×C₅	semidirect
66. C₂×#938	C₂×C₅	semidirect
67. C₂×#935	C₂×C₅	semidirect
68. C₂×D₄×Dic₃	C₂×C₅	semidirect
69. #5719	C₂×C₅	direct (N × H)
70. C₂×#872	C₂×C₅	semidirect
71. C₂×#870	C₂×C₅	semidirect
77. C₅×#127	C₂×D₃	semidirect
121. C₃×#127	C₂²×C₅	semidirect
125. #939	C₂²×C₅	semidirect
126. #938	C₂²×C₅	semidirect
127. #935	C₂²×C₅	semidirect
128. D₄×Dic₃	C₂²×C₅	semidirect
134. #872	C₂²×C₅	semidirect
135. #870	C₂²×C₅	semidirect
162. C₂×#127	C₅×D₃	semidirect
237. #127	C₂×C₅×D₃	semidirect
253. C₂×C₃×C₅	#540	semidirect
320. C₃×C₅	C₂×#540	semidirect
338. C₂×C₅	#5719	direct (N × H)
365. C₂×C₃	C₅×#540	semidirect
369. C₅	C₂×#5719	direct (N × H)
385. C₃	C₂×C₅×#540	semidirect
388. C₂	C₅×#5719	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×C₅×#939	2
C₂×C₅×#938	2
C₂×C₅×#935	2
C₂×C₅×D₄×Dic₃	2
C₅×#5719	2
C₂×C₅×#872	2
C₂×C₅×#870	2
C₂×C₅×#540	3
C₂×#5719	5

Subgroups — C2×C5×#5719 #14481091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5719 #14481091