Subgroups — C₂×C₅×#4891 #14429937

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4891	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#478	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	—	2	1	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₅×#893	—	2	2	no	—
22	C₅×#893	C₂²	1	4	yes	—
23	C₅×#890	—	2	2	no	—
24	C₅×#890	C₂²	1	4	yes	complemented
25	C₃×C₅×#107	C₂²	1	4	yes	complemented
26	C₅×#821	C₂²	1	4	yes	—
27	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
28	C₅×#809	C₂²	1	4	yes	—
29	C₅×#808	C₂²	1	4	yes	complemented
30	C₂×#4891	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#125	—	3	1	no	—
32	C₂×C₄×C₅×D₄	—	3	1	no	—
33	C₅×#478	—	3	8	no	—
34	C₂×C₅×#107	D₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#106	—	3	1	no	—
36	C₂×C₅×C₄⋊C₈	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂³×C₅×D₃	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	2	no	—
48	C₂×C₅×D₁₂	Q₈	1	4	yes	—
49	C₂×C₅×D₁₂	C₂³	1	2	yes	—
50	C₂×C₄×C₅×D₃	—	2	4	no	—
51	C₂×C₄×C₅×D₃	—	4	4	no	—
52	C₂×C₃×C₅×C₈	—	2	2	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
59	C₅×C₄⋊Dic₃	—	2	1	no	—
60	C₅×C₄⋊Dic₃	—	2	4	no	—
61	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
62	C₅×Dic₃⋊C₄	—	2	4	no	—
63	C₄×C₅×Dic₃	D₄	1	2	yes	—
64	C₄×C₅×Dic₃	C₂³	1	2	yes	—
65	C₂×C₅×C₃⋊C₈	—	2	2	no	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₂×#893	C₂×C₅	1	1	yes	characteristic
68	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#821	C₂×C₅	1	1	yes	characteristic
71	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#809	C₂×C₅	1	1	yes	characteristic
73	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
74	#4891	C₂×C₅	1	8	yes	direct product factor
75	C₂²×C₅×D₄	—	3	1	no	—
76	C₂³×C₄×C₅	—	6	1	no	—
77	C₂²×C₅×C₈	—	3	1	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×#125	—	3	4	no	—
80	C₅×#125	—	6	2	no	—
81	C₄×C₅×D₄	—	3	4	no	—
82	C₄×C₅×D₄	—	6	2	no	—
83	C₂×C₅×C₄⋊C₄	—	3	1	no	—
84	C₂×C₅×C₄⋊C₄	—	6	1	no	—
85	C₂×C₅×C₄⋊C₄	—	6	1	no	—
86	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
89	C₂×C₄²×C₅	—	3	1	no	—
90	C₅×#107	C₂×D₃	1	4	yes	complemented
91	C₅×#106	—	3	4	no	—
92	C₅×C₄⋊C₈	—	3	4	no	—
93	C₅×#102	—	3	4	no	—
94	C₅×#102	—	3	4	no	—
95	C₂×#478	—	3	1	no	Sylow
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	4	no	—
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	4	2	no	—
100	C₂²×C₅×D₃	—	4	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	2	no	—
104	C₂×C₃×C₄×C₅	—	4	2	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	4	2	no	—
113	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
114	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
115	C₅×D₁₂	—	2	4	no	—
116	C₅×D₁₂	—	2	2	no	—
117	C₅×D₁₂	C₂×Q₈	1	4	yes	—
118	C₄×C₅×D₃	—	4	8	no	—
119	C₃×C₅×C₈	—	2	2	no	—
120	C₅×C₃⋊C₈	—	2	2	no	—
121	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₄×D₃	—	2	1	no	—
123	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₂×C₄⋊Dic₃	—	2	1	no	—
128	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
129	C₂×Dic₃⋊C₄	—	2	1	no	—
130	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
132	#893	—	2	2	no	—
133	#893	C₂²×C₅	1	4	yes	—
134	#890	—	2	2	no	—
135	#890	C₂²×C₅	1	4	yes	complemented
136	C₃×#107	C₂²×C₅	1	4	yes	complemented
137	#821	C₂²×C₅	1	4	yes	—
138	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
139	#809	C₂²×C₅	1	4	yes	—
140	#808	C₂²×C₅	1	4	yes	complemented
141	C₂⁴×C₅	—	6	1	no	—
142	C₂×C₅×D₄	—	3	4	no	—
143	C₂×C₅×D₄	—	3	2	no	—
144	C₂×C₅×D₄	—	6	2	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	3	1	no	—
150	C₂²×C₄×C₅	—	6	4	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂²×C₄×C₅	—	12	4	no	—
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	3	2	no	—
156	C₂×C₅×C₈	—	6	2	no	—
157	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	3	2	no	—
161	C₅×C₄⋊C₄	—	6	4	no	—
162	C₅×C₄⋊C₄	—	6	4	no	—
163	C₅×C₄⋊C₄	—	6	1	no	—
164	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
165	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
166	C₅×C₂²⋊C₄	—	6	4	no	—
167	C₄²×C₅	—	3	2	no	—
168	C₄²×C₅	—	3	2	no	—
169	C₂×#125	—	3	1	no	—
170	C₂×C₄×D₄	—	3	1	no	—
171	#478	—	3	8	no	—
172	C₂×#107	C₅×D₃	1	1	yes	characteristic, complemented
173	C₂×#106	—	3	1	no	—
174	C₂×C₄⋊C₈	—	3	1	no	—
175	C₂×#102	—	3	1	no	—
176	C₂×#102	—	3	1	no	—
177	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
178	C₂²×C₃×C₅	#135	1	2	yes	—
179	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
180	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	4	no	—
182	C₂×C₅×D₃	—	4	2	no	—
183	C₂×C₅×D₃	—	4	2	no	—
184	C₂×C₅×D₃	—	4	8	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	—	4	2	no	—
187	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
188	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
190	C₅×Dic₃	—	2	2	no	—
191	C₅×Dic₃	—	2	2	no	—
192	C₅×Dic₃	—	4	2	no	—
193	C₂³×D₃	—	2	1	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂²×Dic₃	—	2	1	no	—
198	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
199	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
200	C₂×D₁₂	—	2	1	no	—
201	C₂×D₁₂	—	2	2	no	—
202	C₂×D₁₂	C₅×Q₈	1	4	yes	—
203	C₂×D₁₂	C₂³×C₅	1	2	yes	—
204	C₂×C₄×D₃	—	2	4	no	—
205	C₂×C₄×D₃	—	4	4	no	—
206	C₂×C₃×C₈	—	2	2	no	—
207	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
211	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
212	(C₂×D₃)⋊C₄	—	2	4	no	—
213	C₄⋊Dic₃	—	2	1	no	—
214	C₄⋊Dic₃	—	2	4	no	—
215	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
216	Dic₃⋊C₄	—	2	4	no	—
217	C₄×Dic₃	C₅×D₄	1	2	yes	—
218	C₄×Dic₃	C₂³×C₅	1	2	yes	—
219	C₂×C₃⋊C₈	—	2	2	no	—
220	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
221	C₂³×C₅	—	6	4	no	—
222	C₂³×C₅	—	6	2	no	—
223	C₂³×C₅	—	12	2	no	—
224	C₂³×C₅	—	12	2	no	—
225	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
226	C₅×D₄	—	3	4	no	—
227	C₅×D₄	—	6	4	no	—
228	C₅×D₄	—	6	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	3	2	no	—
232	C₂×C₄×C₅	—	3	2	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	6	2	no	—
237	C₂×C₄×C₅	—	6	2	no	—
238	C₂×C₄×C₅	—	12	8	no	—
239	C₂×C₄×C₅	—	12	2	no	—
240	C₂×C₄×C₅	#235	1	2	yes	—
241	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
243	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	6	2	no	—
246	C₂²×D₄	—	3	1	no	—
247	C₂³×C₄	—	6	1	no	—
248	C₂²×C₈	—	3	1	no	—
249	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
250	#125	—	3	4	no	—
251	#125	—	6	2	no	—
252	C₄×D₄	—	3	4	no	—
253	C₄×D₄	—	6	2	no	—
254	C₂×C₄⋊C₄	—	3	1	no	—
255	C₂×C₄⋊C₄	—	6	1	no	—
256	C₂×C₄⋊C₄	—	6	1	no	—
257	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	6	1	no	—
260	C₂×C₄²	—	3	1	no	—
261	#107	C₂×C₅×D₃	1	4	yes	complemented
262	#106	—	3	4	no	—
263	C₄⋊C₈	—	3	4	no	—
264	#102	—	3	4	no	—
265	#102	—	3	4	no	—
266	C₂×C₃×C₅	#478	1	4	yes	complemented
267	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₅×D₃	—	4	4	no	—
271	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂²×D₃	—	2	4	no	—
273	C₂²×D₃	—	2	2	no	—
274	C₂²×D₃	—	4	2	no	—
275	C₂²×D₃	—	4	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	4	2	no	—
279	C₂×C₃×C₄	—	4	2	no	—
280	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
282	C₂×C₃×C₄	C₅×#41	1	2	yes	—
283	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	—	2	2	no	—
286	C₂×Dic₃	—	2	2	no	—
287	C₂×Dic₃	—	4	2	no	—
288	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
289	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
290	D₁₂	—	2	4	no	—
291	D₁₂	—	2	2	no	—
292	D₁₂	C₂×C₅×Q₈	1	4	yes	—
293	C₄×D₃	—	4	8	no	—
294	C₃×C₈	—	2	2	no	—
295	C₃⋊C₈	—	2	2	no	—
296	C₂²×C₅	—	6	4	no	—
297	C₂²×C₅	—	12	8	no	—
298	C₂²×C₅	—	12	2	no	—
299	C₂²×C₅	—	12	2	no	—
300	C₂²×C₅	#896	1	2	yes	—
301	C₂²×C₅	#911	1	2	yes	—
302	C₂²×C₅	#919	1	2	yes	—
303	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	6	2	no	—
307	C₄×C₅	—	6	2	no	—
308	C₄×C₅	—	12	2	no	—
309	C₄×C₅	#896	1	2	yes	—
310	C₄×C₅	C₂×#235	1	1	yes	characteristic
311	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
312	C₂⁴	—	6	1	no	—
313	C₂×D₄	—	3	4	no	—
314	C₂×D₄	—	3	2	no	—
315	C₂×D₄	—	6	2	no	—
316	C₂×D₄	—	6	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	3	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	6	4	no	—
322	C₂²×C₄	—	6	1	no	—
323	C₂²×C₄	—	12	4	no	—
324	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	3	2	no	—
327	C₂×C₈	—	6	2	no	—
328	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	3	2	no	—
332	C₄⋊C₄	—	6	4	no	—
333	C₄⋊C₄	—	6	4	no	—
334	C₄⋊C₄	—	6	1	no	—
335	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
336	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
337	C₂²⋊C₄	—	6	4	no	—
338	C₄²	—	3	2	no	—
339	C₄²	—	3	2	no	—
340	C₃×C₅	C₂×#478	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
342	C₂²×C₃	C₅×#135	1	2	yes	—
343	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
344	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
345	C₂×D₃	—	2	4	no	—
346	C₂×D₃	—	4	8	no	—
347	C₂×D₃	—	4	2	no	—
348	C₂×D₃	—	4	2	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	—	4	2	no	—
351	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
352	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
353	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
354	Dic₃	—	2	2	no	—
355	Dic₃	—	2	2	no	—
356	Dic₃	—	4	2	no	—
357	C₂×C₅	—	12	4	no	—
358	C₂×C₅	#4891	1	4	yes	direct product factor
359	C₂×C₅	C₂×#896	1	1	yes	characteristic
360	C₂×C₅	C₂×#911	1	1	yes	characteristic
361	C₂×C₅	C₂×#919	1	1	yes	characteristic
362	C₂³	—	6	4	no	—
363	C₂³	—	6	2	no	—
364	C₂³	—	12	2	no	—
365	C₂³	—	12	2	no	—
366	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
367	D₄	—	3	4	no	—
368	D₄	—	6	4	no	—
369	D₄	—	6	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	3	2	no	—
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	6	2	no	—
379	C₂×C₄	—	12	8	no	—
380	C₂×C₄	—	12	2	no	—
381	C₂×C₄	C₅×#235	1	2	yes	—
382	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
383	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
384	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	6	2	no	—
387	C₂×C₃	C₅×#478	1	4	yes	complemented
388	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
389	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
390	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
391	D₃	—	4	4	no	—
392	C₅	C₂×#4891	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	—	6	4	no	—
394	C₂²	—	12	2	no	—
395	C₂²	—	12	2	no	—
396	C₂²	—	12	8	no	—
397	C₂²	C₅×#896	1	2	yes	—
398	C₂²	C₅×#911	1	2	yes	—
399	C₂²	C₅×#919	1	2	yes	—
400	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	6	2	no	—
404	C₄	—	6	2	no	—
405	C₄	—	12	2	no	—
406	C₄	C₅×#896	1	2	yes	—
407	C₄	C₂×C₅×#235	1	1	yes	characteristic
408	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
409	C₃	C₂×C₅×#478	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	12	4	no	—
411	C₂	C₅×#4891	1	4	yes	direct product factor
412	C₂	C₂×C₅×#896	1	1	yes	characteristic
413	C₂	C₂×C₅×#911	1	1	yes	characteristic
414	C₂	C₂×C₅×#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×#107	D₃
hypocenter	C₃	C₂×C₅×#478
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#890	C₂	semidirect
3. C₂×C₃×C₅×#107	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
7. C₂×C₅×#808	C₂	semidirect
8. C₅×#4891	C₂	direct (N × H)
24. C₅×#890	C₂²	semidirect
25. C₃×C₅×#107	C₂²	semidirect
27. C₅×Dic₃⋊C₈	C₂²	semidirect
29. C₅×#808	C₂²	semidirect
30. C₂×#4891	C₅	direct (N × H)
34. C₂×C₅×#107	D₃	semidirect
68. C₂×#890	C₂×C₅	semidirect
69. C₂×C₃×#107	C₂×C₅	semidirect
71. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
73. C₂×#808	C₂×C₅	semidirect
74. #4891	C₂×C₅	direct (N × H)
90. C₅×#107	C₂×D₃	semidirect
135. #890	C₂²×C₅	semidirect
136. C₃×#107	C₂²×C₅	semidirect
138. Dic₃⋊C₈	C₂²×C₅	semidirect
140. #808	C₂²×C₅	semidirect
172. C₂×#107	C₅×D₃	semidirect
261. #107	C₂×C₅×D₃	semidirect
266. C₂×C₃×C₅	#478	semidirect
340. C₃×C₅	C₂×#478	semidirect
358. C₂×C₅	#4891	direct (N × H)
387. C₂×C₃	C₅×#478	semidirect
392. C₅	C₂×#4891	direct (N × H)
409. C₃	C₂×C₅×#478	semidirect
411. C₂	C₅×#4891	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×C₅×#893	2
C₂×C₅×#890	2
C₂×C₃×C₅×#107	2
C₂×C₅×#821	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₅×#4891	2
C₂×C₅×#478	3
C₂×#4891	5

Subgroups — C2×C5×#4891 #14429937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4891 #14429937