Subgroups — C₂×C₅×#4843 #14425818

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₂₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×D₁₂	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×#4843	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#459	—	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×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	1	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₂₄	—	2	8	no	—
18	C₂×C₅×D₂₄	C₂²	1	8	yes	complemented
19	C₅×#874	—	2	2	no	—
20	C₅×#874	C₂²	1	4	yes	complemented
21	C₄×C₅×D₁₂	—	2	2	no	—
22	C₄×C₅×D₁₂	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×#4843	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×D₈	—	3	2	no	—
27	C₂×C₅×#127	—	3	1	no	—
28	C₂×C₄×C₅×D₄	—	3	1	no	—
29	C₅×#459	—	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	1	no	—
33	C₂³×C₅×D₃	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	2	no	—
40	C₂×C₅×D₁₂	—	2	4	no	—
41	C₂×C₅×D₁₂	—	2	4	no	—
42	C₂×C₅×D₁₂	—	2	2	no	—
43	C₂×C₅×D₁₂	—	2	4	no	—
44	C₂×C₅×D₁₂	—	2	4	no	—
45	C₂×C₅×D₁₂	—	4	4	no	—
46	C₂×C₅×D₁₂	—	4	4	no	—
47	C₂×C₅×D₁₂	D₄	1	4	yes	complemented
48	C₂×C₅×D₁₂	C₂³	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	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₃×C₄²×C₅	D₄	1	2	yes	—
55	C₃×C₄²×C₅	C₂³	1	2	yes	—
56	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
59	C₅×D₂₄	—	2	16	no	—
60	C₂²×D₂₄	C₂×C₅	1	2	yes	complemented
61	C₂×#874	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×#821	C₂×C₅	1	2	yes	complemented
65	#4843	C₂×C₅	1	8	yes	direct product factor
66	C₂²×C₅×D₄	—	3	1	no	—
67	C₂²×C₅×D₄	—	3	2	no	—
68	C₂²×C₅×D₄	—	6	1	no	—
69	C₂²×C₅×D₄	—	6	1	no	—
70	C₂³×C₄×C₅	—	6	1	no	—
71	C₂×C₅×D₈	—	3	8	no	—
72	C₂×C₅×D₈	—	6	8	no	—
73	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
74	C₅×#127	—	3	4	no	—
75	C₅×#127	—	6	2	no	—
76	C₄×C₅×D₄	—	3	4	no	—
77	C₄×C₅×D₄	—	6	2	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
82	C₅×#102	—	3	8	no	—
83	C₂×#459	—	3	1	no	Sylow
84	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₅×D₃	—	2	4	no	—
86	C₂²×C₅×D₃	—	2	2	no	—
87	C₂²×C₅×D₃	—	2	4	no	—
88	C₂²×C₅×D₃	—	4	2	no	—
89	C₂²×C₅×D₃	—	4	2	no	—
90	C₂²×C₅×D₃	—	4	4	no	—
91	C₂²×C₅×D₃	—	4	4	no	—
92	C₂²×C₅×D₃	—	4	4	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	D₈	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	2	no	—
102	C₂×C₅×Dic₃	—	4	2	no	—
103	C₅×D₁₂	—	2	4	no	—
104	C₅×D₁₂	—	2	4	no	—
105	C₅×D₁₂	—	2	2	no	—
106	C₅×D₁₂	—	2	4	no	—
107	C₅×D₁₂	—	4	8	no	—
108	C₅×D₁₂	—	4	4	no	—
109	C₅×D₁₂	—	4	8	no	—
110	C₅×D₁₂	C₂×D₄	1	4	yes	complemented
111	C₄×C₅×D₃	—	4	8	no	—
112	C₃×C₅×C₈	—	2	4	no	—
113	C₂²×D₁₂	—	2	1	no	—
114	C₂²×D₁₂	—	2	1	no	—
115	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
116	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₄×D₃	—	2	1	no	—
118	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
120	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
122	C₂×D₂₄	—	2	8	no	—
123	C₂×D₂₄	C₂²×C₅	1	8	yes	complemented
124	#874	—	2	2	no	—
125	#874	C₂²×C₅	1	4	yes	complemented
126	C₄×D₁₂	—	2	2	no	—
127	C₄×D₁₂	C₂²×C₅	1	4	yes	complemented
128	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
129	#821	C₂²×C₅	1	8	yes	complemented
130	C₂⁴×C₅	—	6	1	no	—
131	C₂⁴×C₅	—	6	2	no	—
132	C₂×C₅×D₄	—	3	4	no	—
133	C₂×C₅×D₄	—	3	2	no	—
134	C₂×C₅×D₄	—	3	4	no	—
135	C₂×C₅×D₄	—	6	1	no	—
136	C₂×C₅×D₄	—	6	4	no	—
137	C₂×C₅×D₄	—	6	4	no	—
138	C₂×C₅×D₄	—	6	2	no	—
139	C₂×C₅×D₄	—	6	4	no	—
140	C₂×C₅×D₄	—	6	2	no	—
141	C₂×C₅×D₄	—	6	4	no	—
142	C₂×C₅×D₄	—	12	4	no	—
143	C₂×C₅×D₄	—	12	4	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	4	no	—
146	C₂²×C₄×C₅	—	12	4	no	—
147	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
148	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₅×D₈	—	6	16	no	—
151	C₂×C₅×C₈	—	2	4	no	—
152	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
153	C₅×C₄⋊C₄	—	3	2	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₂²⋊C₄	—	6	4	no	—
156	C₄²×C₅	D₁₂	1	2	yes	—
157	C₄²×C₅	C₂²×D₃	1	2	yes	—
158	C₂²×D₈	—	3	2	no	—
159	C₂×#127	—	3	1	no	—
160	C₂×C₄×D₄	—	3	1	no	—
161	#459	—	3	8	no	—
162	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
163	C₂×#102	—	3	2	no	—
164	C₂²×C₃×C₅	#121	1	2	yes	—
165	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
166	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
167	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₅×D₃	—	2	4	no	—
169	C₂×C₅×D₃	—	4	2	no	—
170	C₂×C₅×D₃	—	4	2	no	—
171	C₂×C₅×D₃	—	4	8	no	—
172	C₂×C₅×D₃	—	4	4	no	—
173	C₂×C₅×D₃	—	4	4	no	—
174	C₂×C₅×D₃	—	4	4	no	—
175	C₂×C₅×D₃	—	8	8	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	#121	1	2	yes	—
178	C₃×C₄×C₅	C₂×D₈	1	4	yes	complemented
179	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
181	C₅×Dic₃	—	4	2	no	—
182	C₂³×D₃	—	2	1	no	—
183	C₂³×D₃	—	2	2	no	—
184	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×Dic₃	—	2	1	no	—
188	C₂×D₁₂	—	2	1	no	—
189	C₂×D₁₂	—	2	2	no	—
190	C₂×D₁₂	—	2	4	no	—
191	C₂×D₁₂	—	2	4	no	—
192	C₂×D₁₂	—	2	2	no	—
193	C₂×D₁₂	—	2	4	no	—
194	C₂×D₁₂	—	2	4	no	—
195	C₂×D₁₂	—	4	4	no	—
196	C₂×D₁₂	—	4	4	no	—
197	C₂×D₁₂	C₅×D₄	1	4	yes	complemented
198	C₂×D₁₂	C₂³×C₅	1	4	yes	—
199	C₂×D₁₂	C₂³×C₅	1	2	yes	—
200	C₂×C₄×D₃	—	2	4	no	—
201	C₂×C₄×D₃	—	4	4	no	—
202	C₂×C₃×C₈	—	2	4	no	—
203	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
204	C₃×C₄²	C₅×D₄	1	2	yes	—
205	C₃×C₄²	C₂³×C₅	1	2	yes	—
206	(C₂×D₃)⋊C₄	—	2	4	no	—
207	C₄⋊Dic₃	—	2	1	no	—
208	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
209	D₂₄	—	2	16	no	—
210	C₂³×C₅	—	6	4	no	—
211	C₂³×C₅	—	6	2	no	—
212	C₂³×C₅	—	6	4	no	—
213	C₂³×C₅	—	12	2	no	—
214	C₂³×C₅	—	12	2	no	—
215	C₂³×C₅	—	12	4	no	—
216	C₂³×C₅	—	12	4	no	—
217	C₂³×C₅	—	12	4	no	—
218	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
219	C₅×D₄	—	3	4	no	—
220	C₅×D₄	—	6	4	no	—
221	C₅×D₄	—	6	4	no	—
222	C₅×D₄	—	6	2	no	—
223	C₅×D₄	—	6	4	no	—
224	C₅×D₄	—	12	8	no	—
225	C₅×D₄	—	12	4	no	—
226	C₅×D₄	—	12	8	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	6	2	no	—
229	C₂×C₄×C₅	—	12	2	no	—
230	C₂×C₄×C₅	—	12	8	no	—
231	C₂×C₄×C₅	D₂₄	1	4	yes	complemented
232	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
233	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
235	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
236	C₂×C₄×C₅	#239	1	2	yes	—
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×C₈	—	2	4	no	—
239	C₂²×D₄	—	3	1	no	—
240	C₂²×D₄	—	3	2	no	—
241	C₂²×D₄	—	6	1	no	—
242	C₂²×D₄	—	6	1	no	—
243	C₂³×C₄	—	6	1	no	—
244	C₂×D₈	—	3	8	no	—
245	C₂×D₈	—	6	8	no	—
246	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
247	#127	—	3	4	no	—
248	#127	—	6	2	no	—
249	C₄×D₄	—	3	4	no	—
250	C₄×D₄	—	6	2	no	—
251	C₂×C₄⋊C₄	—	3	1	no	—
252	C₂×C₂²⋊C₄	—	6	1	no	—
253	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
254	C₄⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
255	#102	—	3	8	no	—
256	C₂×C₃×C₅	#459	1	4	yes	complemented
257	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
258	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₅×D₃	—	4	4	no	—
261	C₅×D₃	—	8	4	no	—
262	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×D₃	—	2	4	no	—
264	C₂²×D₃	—	2	2	no	—
265	C₂²×D₃	—	2	4	no	—
266	C₂²×D₃	—	4	2	no	—
267	C₂²×D₃	—	4	2	no	—
268	C₂²×D₃	—	4	4	no	—
269	C₂²×D₃	—	4	4	no	—
270	C₂²×D₃	—	4	4	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	C₅×D₈	1	4	yes	complemented
273	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
276	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
277	C₂×C₃×C₄	C₅×#41	1	2	yes	—
278	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
279	C₂×Dic₃	—	2	2	no	—
280	C₂×Dic₃	—	4	2	no	—
281	D₁₂	—	2	4	no	—
282	D₁₂	—	2	4	no	—
283	D₁₂	—	2	2	no	—
284	D₁₂	—	2	4	no	—
285	D₁₂	—	4	8	no	—
286	D₁₂	—	4	4	no	—
287	D₁₂	—	4	8	no	—
288	D₁₂	C₂×C₅×D₄	1	4	yes	complemented
289	C₄×D₃	—	4	8	no	—
290	C₃×C₈	—	2	4	no	—
291	C₂²×C₅	—	6	4	no	—
292	C₂²×C₅	—	12	2	no	—
293	C₂²×C₅	—	12	2	no	—
294	C₂²×C₅	—	12	8	no	—
295	C₂²×C₅	—	12	4	no	—
296	C₂²×C₅	—	12	4	no	—
297	C₂²×C₅	—	12	4	no	—
298	C₂²×C₅	—	24	8	no	—
299	C₂²×C₅	#895	1	2	yes	—
300	C₂²×C₅	C₂×D₂₄	1	2	yes	—
301	C₂²×C₅	#908	1	2	yes	—
302	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	12	2	no	—
305	C₄×C₅	#895	1	2	yes	—
306	C₄×C₅	C₂×D₂₄	1	4	yes	complemented
307	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
308	C₄×C₅	C₂×#239	1	1	yes	characteristic
309	C₂⁴	—	6	1	no	—
310	C₂⁴	—	6	2	no	—
311	C₂×D₄	—	3	4	no	—
312	C₂×D₄	—	3	2	no	—
313	C₂×D₄	—	3	4	no	—
314	C₂×D₄	—	6	1	no	—
315	C₂×D₄	—	6	4	no	—
316	C₂×D₄	—	6	4	no	—
317	C₂×D₄	—	6	2	no	—
318	C₂×D₄	—	6	4	no	—
319	C₂×D₄	—	6	2	no	—
320	C₂×D₄	—	6	4	no	—
321	C₂×D₄	—	12	4	no	—
322	C₂×D₄	—	12	4	no	—
323	C₂²×C₄	—	6	1	no	—
324	C₂²×C₄	—	6	4	no	—
325	C₂²×C₄	—	12	4	no	—
326	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
327	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
329	D₈	—	6	16	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
332	C₄⋊C₄	—	3	2	no	—
333	C₄⋊C₄	—	6	1	no	—
334	C₂²⋊C₄	—	6	4	no	—
335	C₄²	C₅×D₁₂	1	2	yes	—
336	C₄²	C₂²×C₅×D₃	1	2	yes	—
337	C₃×C₅	C₂×#459	1	1	yes	characteristic, complemented, Hall
338	C₂²×C₃	C₅×#121	1	2	yes	—
339	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
340	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
341	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
342	C₂×D₃	—	2	4	no	—
343	C₂×D₃	—	4	8	no	—
344	C₂×D₃	—	4	2	no	—
345	C₂×D₃	—	4	2	no	—
346	C₂×D₃	—	4	4	no	—
347	C₂×D₃	—	4	4	no	—
348	C₂×D₃	—	4	4	no	—
349	C₂×D₃	—	8	8	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	C₅×#121	1	2	yes	—
352	C₃×C₄	C₂×C₅×D₈	1	4	yes	complemented
353	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
355	Dic₃	—	4	2	no	—
356	C₂×C₅	—	12	4	no	—
357	C₂×C₅	—	24	4	no	—
358	C₂×C₅	#4843	1	4	yes	direct product factor
359	C₂×C₅	C₂×#895	1	1	yes	characteristic
360	C₂×C₅	C₂²×D₂₄	1	1	yes	characteristic
361	C₂×C₅	C₂×#908	1	1	yes	characteristic
362	C₂³	—	6	4	no	—
363	C₂³	—	6	2	no	—
364	C₂³	—	6	4	no	—
365	C₂³	—	12	2	no	—
366	C₂³	—	12	2	no	—
367	C₂³	—	12	4	no	—
368	C₂³	—	12	4	no	—
369	C₂³	—	12	4	no	—
370	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
371	D₄	—	3	4	no	—
372	D₄	—	6	4	no	—
373	D₄	—	6	4	no	—
374	D₄	—	6	2	no	—
375	D₄	—	6	4	no	—
376	D₄	—	12	8	no	—
377	D₄	—	12	4	no	—
378	D₄	—	12	8	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	12	2	no	—
382	C₂×C₄	—	12	8	no	—
383	C₂×C₄	C₅×D₂₄	1	4	yes	complemented
384	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
385	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
386	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
387	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
388	C₂×C₄	C₅×#239	1	2	yes	—
389	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₂×C₃	C₅×#459	1	4	yes	complemented
392	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
393	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
394	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
395	D₃	—	4	4	no	—
396	D₃	—	8	4	no	—
397	C₅	C₂×#4843	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	6	4	no	—
399	C₂²	—	12	2	no	—
400	C₂²	—	12	2	no	—
401	C₂²	—	12	8	no	—
402	C₂²	—	12	4	no	—
403	C₂²	—	12	4	no	—
404	C₂²	—	12	4	no	—
405	C₂²	—	24	8	no	—
406	C₂²	C₅×#895	1	2	yes	—
407	C₂²	C₂×C₅×D₂₄	1	2	yes	—
408	C₂²	C₅×#908	1	2	yes	—
409	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	12	2	no	—
412	C₄	C₅×#895	1	2	yes	—
413	C₄	C₂×C₅×D₂₄	1	4	yes	complemented
414	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
415	C₄	C₂×C₅×#239	1	1	yes	characteristic
416	C₃	C₂×C₅×#459	1	1	yes	characteristic, complemented, Sylow
417	C₂	—	12	4	no	—
418	C₂	—	24	4	no	—
419	C₂	C₅×#4843	1	4	yes	direct product factor
420	C₂	C₂×C₅×#895	1	1	yes	characteristic
421	C₂	C₂²×C₅×D₂₄	1	1	yes	characteristic
422	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
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#459
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×D₂₄	C₂	semidirect
2. C₂×C₅×#874	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₂×C₅×#821	C₂	semidirect
6. C₅×#4843	C₂	direct (N × H)
18. C₂×C₅×D₂₄	C₂²	semidirect
20. C₅×#874	C₂²	semidirect
22. C₄×C₅×D₁₂	C₂²	semidirect
23. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₅×#821	C₂²	semidirect
25. C₂×#4843	C₅	direct (N × H)
30. C₂×C₅×C₄⋊C₈	D₃	semidirect
47. C₂×C₅×D₁₂	D₄	semidirect
60. C₂²×D₂₄	C₂×C₅	semidirect
61. C₂×#874	C₂×C₅	semidirect
62. C₂×C₄×D₁₂	C₂×C₅	semidirect
63. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
64. C₂×#821	C₂×C₅	semidirect
65. #4843	C₂×C₅	direct (N × H)
81. C₅×C₄⋊C₈	C₂×D₃	semidirect
94. C₂×C₃×C₄×C₅	D₈	semidirect
110. C₅×D₁₂	C₂×D₄	semidirect
123. C₂×D₂₄	C₂²×C₅	semidirect
125. #874	C₂²×C₅	semidirect
127. C₄×D₁₂	C₂²×C₅	semidirect
128. C₃×C₄⋊C₈	C₂²×C₅	semidirect
129. #821	C₂²×C₅	semidirect
162. C₂×C₄⋊C₈	C₅×D₃	semidirect
178. C₃×C₄×C₅	C₂×D₈	semidirect
197. C₂×D₁₂	C₅×D₄	semidirect
231. C₂×C₄×C₅	D₂₄	semidirect
254. C₄⋊C₈	C₂×C₅×D₃	semidirect
256. C₂×C₃×C₅	#459	semidirect
272. C₂×C₃×C₄	C₅×D₈	semidirect
288. D₁₂	C₂×C₅×D₄	semidirect
306. C₄×C₅	C₂×D₂₄	semidirect
337. C₃×C₅	C₂×#459	semidirect
352. C₃×C₄	C₂×C₅×D₈	semidirect
358. C₂×C₅	#4843	direct (N × H)
383. C₂×C₄	C₅×D₂₄	semidirect
391. C₂×C₃	C₅×#459	semidirect
397. C₅	C₂×#4843	direct (N × H)
413. C₄	C₂×C₅×D₂₄	semidirect
416. C₃	C₂×C₅×#459	semidirect
419. C₂	C₅×#4843	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×D₂₄	2
C₂×C₅×#874	2
C₂×C₄×C₅×D₁₂	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₅×#821	2
C₅×#4843	2
C₂×C₅×#459	3
C₂×#4843	5

Subgroups — C2×C5×#4843 #14425818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4843 #14425818