Subgroups — C₂×C₅×#4737 #14431524

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4737	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#482	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	—	2	1	no	—
12	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#217	—	2	1	no	—
16	C₅×#930	—	2	2	no	—
17	C₅×#930	C₂²	1	4	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₅×#926	—	2	2	no	—
20	C₅×#926	C₂²	1	4	yes	complemented
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Dic₃	—	2	1	no	—
25	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
26	C₅×#821	C₂²	1	4	yes	complemented
27	C₅×#821	C₂²	1	4	yes	complemented
28	C₅×#818	C₂²	1	4	yes	complemented
29	C₅×#817	C₂²	1	4	yes	complemented
30	C₂×#4737	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#121	—	3	1	no	—
32	C₂×C₅×#117	—	3	1	no	—
33	C₅×#482	—	3	8	no	—
34	C₂×C₅×#107	—	3	1	no	—
35	C₂×C₅×#106	—	3	1	no	—
36	C₂×C₅×#102	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
40	C₂³×C₅×D₃	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×#67	—	2	4	no	—
48	C₂×C₅×#67	—	4	4	no	—
49	C₂²×C₅×Dic₃	—	2	1	no	—
50	C₂²×C₅×Dic₃	—	2	1	no	—
51	C₂²×C₅×Dic₃	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	2	no	—
53	C₂×C₅×D₁₂	—	2	2	no	—
54	C₂×C₅×D₁₂	—	2	1	no	—
55	C₂×C₅×D₁₂	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	—	2	2	no	—
57	C₂×C₃×C₅×C₈	—	2	2	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₅×#217	—	2	4	no	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×C₄⋊Dic₃	—	2	1	no	—
63	C₅×C₄⋊Dic₃	—	2	1	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
68	C₄×C₅×Dic₃	—	2	4	no	—
69	C₂×#930	C₂×C₅	1	1	yes	characteristic
70	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
76	#4737	C₂×C₅	1	8	yes	direct product factor
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂²×C₅×D₄	—	6	1	no	—
79	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
82	C₅×#121	—	3	4	no	—
83	C₅×#121	—	6	2	no	—
84	C₅×#117	—	3	4	no	—
85	C₅×#117	—	6	2	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	—	3	1	no	—
88	C₂×C₅×C₄⋊C₄	—	3	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
91	C₂×C₄²×C₅	—	6	1	no	—
92	C₅×#107	—	3	4	no	—
93	C₅×#106	—	3	4	no	—
94	C₅×#102	—	3	4	no	—
95	C₅×#102	—	3	4	no	—
96	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	complemented
97	C₂×#482	—	3	1	no	Sylow
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	4	2	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂²×C₅×D₃	—	4	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₅×#67	—	4	8	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	4	2	no	—
121	C₂×C₅×Dic₃	—	4	2	no	—
122	C₂×C₅×Dic₃	—	4	2	no	—
123	C₅×D₁₂	—	2	2	no	—
124	C₅×D₁₂	—	2	2	no	—
125	C₅×D₁₂	—	4	2	no	—
126	C₃×C₅×C₈	—	2	2	no	—
127	C₃×C₅×C₈	—	2	2	no	—
128	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂²×#67	—	2	1	no	—
130	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
133	C₂×#217	—	2	1	no	—
134	#930	—	2	2	no	—
135	#930	C₂²×C₅	1	4	yes	—
136	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
137	#926	—	2	2	no	—
138	#926	C₂²×C₅	1	4	yes	complemented
139	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄×Dic₃	—	2	1	no	—
143	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
144	#821	C₂²×C₅	1	4	yes	complemented
145	#821	C₂²×C₅	1	4	yes	complemented
146	#818	C₂²×C₅	1	4	yes	complemented
147	#817	C₂²×C₅	1	4	yes	complemented
148	C₂⁴×C₅	—	6	1	no	—
149	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	6	4	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	2	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	12	4	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	6	1	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	D₁₂	1	2	yes	—
162	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
168	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
169	C₅×C₄⋊C₄	—	3	2	no	—
170	C₅×C₄⋊C₄	—	3	2	no	—
171	C₅×C₄⋊C₄	—	3	2	no	—
172	C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×C₄⋊C₄	—	6	1	no	—
174	C₅×C₄⋊C₄	—	6	1	no	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₅×C₂²⋊C₄	—	6	4	no	—
177	C₄²×C₅	—	6	4	no	—
178	C₂×#121	—	3	1	no	—
179	C₂×#117	—	3	1	no	—
180	#482	—	3	8	no	—
181	C₂×#107	—	3	1	no	—
182	C₂×#106	—	3	1	no	—
183	C₂×#102	—	3	1	no	—
184	C₂×#102	—	3	1	no	—
185	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	2	2	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	4	4	no	—
190	C₂²×C₃×C₅	#123	1	2	yes	—
191	C₂²×C₃×C₅	#135	1	2	yes	—
192	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	4	2	no	—
197	C₂×C₅×D₃	—	8	4	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	#123	1	2	yes	—
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
202	C₅×Dic₃	—	4	2	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
206	C₂³×D₃	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	—	2	2	no	—
209	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂×#67	—	2	4	no	—
214	C₂×#67	—	4	4	no	—
215	C₂²×Dic₃	—	2	1	no	—
216	C₂²×Dic₃	—	2	1	no	—
217	C₂²×Dic₃	—	2	1	no	—
218	C₂×D₁₂	—	2	2	no	—
219	C₂×D₁₂	—	2	2	no	—
220	C₂×D₁₂	—	2	1	no	—
221	C₂×D₁₂	C₂³×C₅	1	2	yes	—
222	C₂×C₃×C₈	—	2	2	no	—
223	C₂×C₃×C₈	—	2	2	no	—
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
226	#217	—	2	4	no	—
227	(C₂×D₃)⋊C₄	—	2	4	no	—
228	C₄⋊Dic₃	—	2	1	no	—
229	C₄⋊Dic₃	—	2	1	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
232	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
233	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
234	C₄×Dic₃	—	2	4	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	—	12	2	no	—
240	C₂³×C₅	—	12	2	no	—
241	C₂³×C₅	—	12	2	no	—
242	C₂³×C₅	C₂×D₁₂	1	2	yes	—
243	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
244	C₅×D₄	—	6	2	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	12	8	no	—
247	C₅×D₄	—	12	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	6	2	no	—
255	C₂×C₄×C₅	—	12	2	no	—
256	C₂×C₄×C₅	—	12	2	no	—
257	C₂×C₄×C₅	—	12	2	no	—
258	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
259	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
260	C₂×C₄×C₅	#237	1	2	yes	—
261	C₂×C₄×C₅	#237	1	2	yes	—
262	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	2	2	no	—
265	C₂²×D₄	—	3	1	no	—
266	C₂²×D₄	—	6	1	no	—
267	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
270	#121	—	3	4	no	—
271	#121	—	6	2	no	—
272	#117	—	3	4	no	—
273	#117	—	6	2	no	—
274	C₂×C₄⋊C₄	—	3	1	no	—
275	C₂×C₄⋊C₄	—	3	1	no	—
276	C₂×C₄⋊C₄	—	3	1	no	—
277	C₂×C₂²⋊C₄	—	6	1	no	—
278	C₂×C₂²⋊C₄	—	6	1	no	—
279	C₂×C₄²	—	6	1	no	—
280	#107	—	3	4	no	—
281	#106	—	3	4	no	—
282	#102	—	3	4	no	—
283	#102	—	3	4	no	—
284	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
285	C₂×C₃×C₅	—	4	2	no	—
286	C₂×C₃×C₅	#482	1	4	yes	complemented
287	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₅×D₃	—	8	2	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
295	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂²×D₃	—	2	2	no	—
297	C₂²×D₃	—	4	2	no	—
298	C₂²×D₃	—	4	2	no	—
299	C₂²×D₃	—	4	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₅×#41	1	2	yes	—
307	C₂×C₃×C₄	C₅×#41	1	2	yes	—
308	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
309	#67	—	4	8	no	—
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	2	2	no	—
312	C₂×Dic₃	—	2	2	no	—
313	C₂×Dic₃	—	4	2	no	—
314	C₂×Dic₃	—	4	2	no	—
315	C₂×Dic₃	—	4	2	no	—
316	D₁₂	—	2	2	no	—
317	D₁₂	—	2	2	no	—
318	D₁₂	—	4	2	no	—
319	C₃×C₈	—	2	2	no	—
320	C₃×C₈	—	2	2	no	—
321	C₂²×C₅	—	2	2	no	—
322	C₂²×C₅	—	2	2	no	—
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	4	4	no	—
325	C₂²×C₅	—	12	2	no	—
326	C₂²×C₅	—	12	2	no	—
327	C₂²×C₅	—	12	2	no	—
328	C₂²×C₅	—	24	4	no	—
329	C₂²×C₅	#886	1	2	yes	—
330	C₂²×C₅	#904	1	2	yes	—
331	C₂²×C₅	#908	1	2	yes	—
332	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	12	2	no	—
335	C₄×C₅	—	12	2	no	—
336	C₄×C₅	—	12	2	no	—
337	C₄×C₅	#886	1	2	yes	—
338	C₄×C₅	C₂×#237	1	1	yes	characteristic
339	C₄×C₅	C₂×#237	1	1	yes	characteristic
340	C₂⁴	—	6	1	no	—
341	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
342	C₂×D₄	—	3	2	no	—
343	C₂×D₄	—	6	4	no	—
344	C₂×D₄	—	6	1	no	—
345	C₂×D₄	—	6	2	no	—
346	C₂×D₄	—	6	2	no	—
347	C₂×D₄	—	12	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	6	1	no	—
351	C₂²×C₄	—	6	1	no	—
352	C₂²×C₄	—	6	1	no	—
353	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
354	C₂²×C₄	C₅×D₁₂	1	2	yes	—
355	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
360	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
361	C₄⋊C₄	—	3	2	no	—
362	C₄⋊C₄	—	3	2	no	—
363	C₄⋊C₄	—	3	2	no	—
364	C₄⋊C₄	—	6	1	no	—
365	C₄⋊C₄	—	6	1	no	—
366	C₄⋊C₄	—	6	1	no	—
367	C₂²⋊C₄	—	6	4	no	—
368	C₂²⋊C₄	—	6	4	no	—
369	C₄²	—	6	4	no	—
370	C₃×C₅	C₂×#482	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	4	4	no	—
375	C₂²×C₃	C₅×#123	1	2	yes	—
376	C₂²×C₃	C₅×#135	1	2	yes	—
377	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
378	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
379	C₂×D₃	—	4	2	no	—
380	C₂×D₃	—	4	2	no	—
381	C₂×D₃	—	4	2	no	—
382	C₂×D₃	—	8	4	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	C₅×#123	1	2	yes	—
385	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
386	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	Dic₃	—	4	2	no	—
388	Dic₃	—	4	2	no	—
389	Dic₃	—	4	2	no	—
390	C₂×C₅	—	4	2	no	—
391	C₂×C₅	—	24	2	no	—
392	C₂×C₅	#4737	1	4	yes	direct product factor
393	C₂×C₅	C₂×#886	1	1	yes	characteristic
394	C₂×C₅	C₂×#904	1	1	yes	characteristic
395	C₂×C₅	C₂×#908	1	1	yes	characteristic
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	6	2	no	—
400	C₂³	—	12	2	no	—
401	C₂³	—	12	2	no	—
402	C₂³	—	12	2	no	—
403	C₂³	C₂×C₅×D₁₂	1	2	yes	—
404	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
405	D₄	—	6	2	no	—
406	D₄	—	6	2	no	—
407	D₄	—	12	8	no	—
408	D₄	—	12	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	—	6	2	no	—
415	C₂×C₄	—	6	2	no	—
416	C₂×C₄	—	12	2	no	—
417	C₂×C₄	—	12	2	no	—
418	C₂×C₄	—	12	2	no	—
419	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
420	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
421	C₂×C₄	C₅×#237	1	2	yes	—
422	C₂×C₄	C₅×#237	1	2	yes	—
423	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	2	no	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	C₅×#482	1	4	yes	complemented
428	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
429	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
430	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
431	D₃	—	8	2	no	—
432	C₅	C₂×#4737	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	12	2	no	—
438	C₂²	—	12	2	no	—
439	C₂²	—	12	2	no	—
440	C₂²	—	24	4	no	—
441	C₂²	C₅×#886	1	2	yes	—
442	C₂²	C₅×#904	1	2	yes	—
443	C₂²	C₅×#908	1	2	yes	—
444	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	12	2	no	—
447	C₄	—	12	2	no	—
448	C₄	—	12	2	no	—
449	C₄	C₅×#886	1	2	yes	—
450	C₄	C₂×C₅×#237	1	1	yes	characteristic
451	C₄	C₂×C₅×#237	1	1	yes	characteristic
452	C₃	C₂×C₅×#482	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	4	2	no	—
454	C₂	—	24	2	no	—
455	C₂	C₅×#4737	1	4	yes	direct product factor
456	C₂	C₂×C₅×#886	1	1	yes	characteristic
457	C₂	C₂×C₅×#904	1	1	yes	characteristic
458	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×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#930	C₂
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#482
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#926	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
4. C₂×C₅×#821	C₂	semidirect
5. C₂×C₅×#821	C₂	semidirect
6. C₂×C₅×#818	C₂	semidirect
7. C₂×C₅×#817	C₂	semidirect
8. C₅×#4737	C₂	direct (N × H)
20. C₅×#926	C₂²	semidirect
25. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
26. C₅×#821	C₂²	semidirect
27. C₅×#821	C₂²	semidirect
28. C₅×#818	C₂²	semidirect
29. C₅×#817	C₂²	semidirect
30. C₂×#4737	C₅	direct (N × H)
38. C₂×C₅×C₂²⋊C₈	D₃	semidirect
70. C₂×#926	C₂×C₅	semidirect
71. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
72. C₂×#821	C₂×C₅	semidirect
73. C₂×#821	C₂×C₅	semidirect
74. C₂×#818	C₂×C₅	semidirect
75. C₂×#817	C₂×C₅	semidirect
76. #4737	C₂×C₅	direct (N × H)
96. C₅×C₂²⋊C₈	C₂×D₃	semidirect
138. #926	C₂²×C₅	semidirect
143. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
144. #821	C₂²×C₅	semidirect
145. #821	C₂²×C₅	semidirect
146. #818	C₂²×C₅	semidirect
147. #817	C₂²×C₅	semidirect
185. C₂×C₂²⋊C₈	C₅×D₃	semidirect
284. C₂²⋊C₈	C₂×C₅×D₃	semidirect
286. C₂×C₃×C₅	#482	semidirect
370. C₃×C₅	C₂×#482	semidirect
392. C₂×C₅	#4737	direct (N × H)
427. C₂×C₃	C₅×#482	semidirect
432. C₅	C₂×#4737	direct (N × H)
452. C₃	C₂×C₅×#482	semidirect
455. C₂	C₅×#4737	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×#930	2
C₂×C₅×#926	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#821	2
C₂×C₅×#818	2
C₂×C₅×#817	2
C₅×#4737	2
C₂×C₅×#482	3
C₂×#4737	5

Subgroups — C2×C5×#4737 #14431524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4737 #14431524