Subgroups — C₅×#70153 #14297627

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1802	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×#217	—	2	1	no	—
14	C₅×D₄×Dic₃	—	2	2	no	—
15	C₅×D₄×Dic₃	C₄	1	4	yes	complemented
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
19	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#102	—	2	2	no	—
23	C₅×#832	—	2	2	no	—
24	C₅×Dic₃⋊C₈	—	2	2	no	—
25	#70153	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₂×C₅×C₄⋊C₈	—	3	1	no	—
28	C₂×C₅×#102	—	3	1	no	—
29	C₂×C₅×#102	D₃	1	1	yes	characteristic
30	C₅×#384	—	3	1	no	—
31	C₅×#340	—	3	1	no	—
32	C₅×#340	—	3	1	no	—
33	C₂⁴×C₃×C₅	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	4	no	—
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	4	2	no	—
46	C₂²×C₅×Dic₃	—	4	2	no	—
47	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
48	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₅×#217	—	2	4	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
59	C₅×Dic₃⋊C₄	—	4	2	no	—
60	C₅×Dic₃⋊C₄	—	4	2	no	—
61	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
62	C₄×C₅×Dic₃	D₄	1	2	yes	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic
68	C₂×#832	C₂×C₅	1	1	yes	characteristic
69	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
70	#4975	C₂×C₅	1	1	yes	characteristic, complemented
71	#4551	C₂×C₅	1	1	yes	characteristic, complemented
72	#4529	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
74	C₂³×C₄×C₅	—	6	1	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×D₄	—	3	4	no	—
78	C₄×C₅×D₄	—	6	2	no	—
79	C₂×C₅×C₄⋊C₄	—	3	1	no	—
80	C₂×C₅×C₄⋊C₄	—	3	1	no	—
81	C₂×C₅×C₄⋊C₄	—	6	1	no	—
82	C₂×C₅×C₄⋊C₄	—	6	1	no	—
83	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₅×C₄⋊C₈	—	6	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	—	6	2	no	—
89	#1802	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	4	1	no	—
94	C₂³×C₃×C₅	—	4	1	no	—
95	C₂³×C₃×C₅	—	4	1	no	—
96	C₂³×C₃×C₅	—	4	1	no	—
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	C₄⋊C₄	1	4	yes	complemented
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₅×Dic₃	—	2	1	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	8	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₂×C₅×Dic₃	—	4	1	no	—
119	C₂×C₅×Dic₃	—	4	1	no	—
120	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
121	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
122	C₂×C₅×Dic₃	D₈	1	2	yes	—
123	C₂×C₅×Dic₃	SD₁₆	1	2	yes	—
124	C₃×C₅×C₈	—	4	1	no	—
125	C₅×C₃⋊C₈	—	4	1	no	—
126	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
127	C₂³×Dic₃	—	2	1	no	—
128	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×#217	—	2	1	no	—
131	D₄×Dic₃	—	2	2	no	—
132	D₄×Dic₃	C₄×C₅	1	4	yes	complemented
133	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
135	C₂×Dic₃⋊C₄	—	2	1	no	—
136	C₂×Dic₃⋊C₄	—	2	1	no	—
137	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
139	C₃×#102	—	2	2	no	—
140	#832	—	2	2	no	—
141	Dic₃⋊C₈	—	2	2	no	—
142	C₂⁴×C₅	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	Dic₆	1	2	yes	—
147	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
148	C₂×C₅×D₄	#67	1	2	yes	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	3	1	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	6	4	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	—	6	1	no	—
155	C₂²×C₄×C₅	—	12	2	no	—
156	C₂²×C₄×C₅	—	12	2	no	—
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	6	1	no	—
162	C₂×C₅×C₈	—	6	1	no	—
163	C₂×C₅×C₈	—	6	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	3	2	no	—
167	C₅×C₄⋊C₄	—	6	1	no	—
168	C₅×C₄⋊C₄	—	6	1	no	—
169	C₅×C₄⋊C₄	—	6	1	no	—
170	C₅×C₄⋊C₄	—	12	2	no	—
171	C₅×C₄⋊C₄	—	12	2	no	—
172	C₅×C₂²⋊C₄	—	6	4	no	—
173	C₄²×C₅	—	3	2	no	—
174	C₄²×C₅	—	3	2	no	—
175	C₂×C₄×D₄	—	3	1	no	—
176	C₂×C₄⋊C₈	—	3	1	no	—
177	C₂×#102	—	3	1	no	—
178	C₂×#102	C₅×D₃	1	1	yes	characteristic
179	#384	—	3	1	no	—
180	#340	—	3	1	no	—
181	#340	—	3	1	no	—
182	C₂²×C₃×C₅	—	2	4	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	—	4	2	no	—
185	C₂²×C₃×C₅	—	4	2	no	—
186	C₂²×C₃×C₅	—	4	2	no	—
187	C₂²×C₃×C₅	—	4	2	no	—
188	C₂²×C₃×C₅	—	4	2	no	—
189	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	#121	1	1	yes	characteristic
191	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
194	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×C₃×C₅	#137	1	1	yes	characteristic
196	C₃×C₄×C₅	—	8	1	no	—
197	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₃×C₄×C₅	#117	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
201	C₅×Dic₃	—	2	2	no	—
202	C₅×Dic₃	—	4	2	no	—
203	C₅×Dic₃	—	8	1	no	—
204	C₅×Dic₃	#102	1	4	yes	complemented
205	C₂⁴×C₃	—	2	1	no	—
206	C₂×C₃×D₄	—	2	1	no	—
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	—	2	1	no	—
209	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
210	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
211	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂²×Dic₃	—	2	1	no	—
215	C₂²×Dic₃	—	2	4	no	—
216	C₂²×Dic₃	—	2	1	no	—
217	C₂²×Dic₃	—	4	2	no	—
218	C₂²×Dic₃	—	4	2	no	—
219	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
220	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
221	C₂×C₃×C₈	—	2	1	no	—
222	C₂×C₃×C₈	—	2	1	no	—
223	C₂×C₃×C₈	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	#217	—	2	4	no	—
227	C₄⋊Dic₃	—	2	1	no	—
228	C₄⋊Dic₃	—	2	1	no	—
229	C₄⋊Dic₃	—	2	1	no	—
230	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
231	Dic₃⋊C₄	—	4	2	no	—
232	Dic₃⋊C₄	—	4	2	no	—
233	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
234	C₄×Dic₃	C₅×D₄	1	2	yes	—
235	C₂×C₃⋊C₈	—	2	1	no	—
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂×C₃⋊C₈	—	2	1	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	4	1	no	—
242	C₂³×C₅	—	4	1	no	—
243	C₂³×C₅	—	4	1	no	—
244	C₂³×C₅	—	4	1	no	—
245	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	2	2	no	—
249	C₅×D₄	Dic₃⋊C₄	1	4	yes	complemented
250	C₂×C₄×C₅	—	3	2	no	—
251	C₂×C₄×C₅	—	3	2	no	—
252	C₂×C₄×C₅	—	3	2	no	—
253	C₂×C₄×C₅	—	3	2	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	6	1	no	—
258	C₂×C₄×C₅	—	6	1	no	—
259	C₂×C₄×C₅	—	6	2	no	—
260	C₂×C₄×C₅	—	12	8	no	—
261	C₂×C₄×C₅	—	12	1	no	—
262	C₂×C₄×C₅	—	12	1	no	—
263	C₂×C₄×C₅	—	12	1	no	—
264	C₂×C₄×C₅	—	12	1	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
268	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	#237	1	1	yes	characteristic
270	C₂×C₄×C₅	#237	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
272	C₅×C₈	—	4	1	no	—
273	C₅×C₈	—	12	1	no	—
274	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂³×C₄	—	6	1	no	—
276	C₂²×C₈	—	3	1	no	—
277	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
278	C₄×D₄	—	3	4	no	—
279	C₄×D₄	—	6	2	no	—
280	C₂×C₄⋊C₄	—	3	1	no	—
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₄⋊C₄	—	6	1	no	—
283	C₂×C₄⋊C₄	—	6	1	no	—
284	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	6	1	no	—
286	C₂×C₄²	—	3	1	no	—
287	C₄⋊C₈	—	6	2	no	—
288	#102	—	2	2	no	—
289	#102	—	6	2	no	—
290	C₂×C₃×C₅	—	4	4	no	—
291	C₂×C₃×C₅	#380	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
293	C₂×C₃×C₅	#417	1	1	yes	characteristic
294	C₂×C₃×C₅	#459	1	1	yes	characteristic
295	C₂×C₃×C₅	#461	1	1	yes	characteristic
296	C₂×C₃×C₅	#474	1	1	yes	characteristic
297	C₂×C₃×C₅	#476	1	1	yes	characteristic
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	—	4	1	no	—
302	C₂³×C₃	—	4	1	no	—
303	C₂³×C₃	—	4	1	no	—
304	C₂³×C₃	—	4	1	no	—
305	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
306	C₃×D₄	—	2	2	no	—
307	C₃×D₄	—	2	2	no	—
308	C₃×D₄	—	2	2	no	—
309	C₃×D₄	C₅×C₄⋊C₄	1	4	yes	complemented
310	C₂×C₃×C₄	—	4	1	no	—
311	C₂×C₃×C₄	—	4	1	no	—
312	C₂×C₃×C₄	—	4	1	no	—
313	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
317	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
318	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
319	C₂×Dic₃	—	2	1	no	—
320	C₂×Dic₃	—	2	1	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	4	1	no	—
323	C₂×Dic₃	—	4	1	no	—
324	C₂×Dic₃	—	4	8	no	—
325	C₂×Dic₃	—	4	1	no	—
326	C₂×Dic₃	—	4	1	no	—
327	C₂×Dic₃	—	4	1	no	—
328	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
329	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
330	C₂×Dic₃	C₅×D₈	1	2	yes	—
331	C₂×Dic₃	C₅×SD₁₆	1	2	yes	—
332	C₃×C₈	—	4	1	no	—
333	C₃⋊C₈	—	4	1	no	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	—	4	2	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	4	2	no	—
341	C₂²×C₅	#878	1	1	yes	characteristic
342	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
344	C₂²×C₅	#911	1	1	yes	characteristic
345	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
346	C₂²×C₅	#915	1	1	yes	characteristic
347	C₂²×C₅	#939	1	1	yes	characteristic
348	C₄×C₅	—	3	4	no	—
349	C₄×C₅	—	6	2	no	—
350	C₄×C₅	—	8	1	no	—
351	C₄×C₅	—	12	2	no	—
352	C₄×C₅	—	24	1	no	—
353	C₄×C₅	#877	1	1	yes	characteristic
354	C₄×C₅	#878	1	1	yes	characteristic
355	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
356	C₄×C₅	#939	1	1	yes	characteristic
357	C₂⁴	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	C₅×Dic₆	1	2	yes	—
362	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
363	C₂×D₄	C₅×#67	1	2	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	6	4	no	—
368	C₂²×C₄	—	6	1	no	—
369	C₂²×C₄	—	6	1	no	—
370	C₂²×C₄	—	12	2	no	—
371	C₂²×C₄	—	12	2	no	—
372	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	6	1	no	—
377	C₂×C₈	—	6	1	no	—
378	C₂×C₈	—	6	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	—	6	1	no	—
383	C₄⋊C₄	—	6	1	no	—
384	C₄⋊C₄	—	6	1	no	—
385	C₄⋊C₄	—	12	2	no	—
386	C₄⋊C₄	—	12	2	no	—
387	C₂²⋊C₄	—	6	4	no	—
388	C₄²	—	3	2	no	—
389	C₄²	—	3	2	no	—
390	C₃×C₅	#1802	1	1	yes	characteristic, complemented, Hall
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
399	C₂²×C₃	C₅×#121	1	1	yes	characteristic
400	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
402	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
403	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂²×C₃	C₅×#137	1	1	yes	characteristic
405	C₃×C₄	—	8	1	no	—
406	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
407	C₃×C₄	C₅×#117	1	1	yes	characteristic
408	C₃×C₄	C₅×#121	1	1	yes	characteristic
409	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
410	Dic₃	—	2	2	no	—
411	Dic₃	—	4	2	no	—
412	Dic₃	—	8	1	no	—
413	Dic₃	C₅×#102	1	4	yes	complemented
414	C₂×C₅	—	4	4	no	—
415	C₂×C₅	#4759	1	1	yes	characteristic
416	C₂×C₅	#4761	1	1	yes	characteristic
417	C₂×C₅	D₃×#102	1	1	yes	characteristic
418	C₂×C₅	#4771	1	1	yes	characteristic
419	C₂×C₅	#4942	1	1	yes	characteristic
420	C₂×C₅	#5150	1	1	yes	characteristic
421	C₂×C₅	#5162	1	1	yes	characteristic
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
430	D₄	—	2	2	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	C₅×Dic₃⋊C₄	1	4	yes	complemented
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	3	2	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	6	1	no	—
442	C₂×C₄	—	6	1	no	—
443	C₂×C₄	—	6	2	no	—
444	C₂×C₄	—	12	8	no	—
445	C₂×C₄	—	12	1	no	—
446	C₂×C₄	—	12	1	no	—
447	C₂×C₄	—	12	1	no	—
448	C₂×C₄	—	12	1	no	—
449	C₂×C₄	—	12	1	no	—
450	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
452	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
453	C₂×C₄	C₅×#237	1	1	yes	characteristic
454	C₂×C₄	C₅×#237	1	1	yes	characteristic
455	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
456	C₈	—	4	1	no	—
457	C₈	—	12	1	no	—
458	C₂×C₃	—	4	4	no	—
459	C₂×C₃	C₅×#380	1	1	yes	characteristic
460	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
461	C₂×C₃	C₅×#417	1	1	yes	characteristic
462	C₂×C₃	C₅×#459	1	1	yes	characteristic
463	C₂×C₃	C₅×#461	1	1	yes	characteristic
464	C₂×C₃	C₅×#474	1	1	yes	characteristic
465	C₂×C₃	C₅×#476	1	1	yes	characteristic
466	C₅	#70153	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	C₅×#878	1	1	yes	characteristic
475	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
476	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
477	C₂²	C₅×#911	1	1	yes	characteristic
478	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
479	C₂²	C₅×#915	1	1	yes	characteristic
480	C₂²	C₅×#939	1	1	yes	characteristic
481	C₄	—	3	4	no	—
482	C₄	—	6	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	12	2	no	—
485	C₄	—	24	1	no	—
486	C₄	C₅×#877	1	1	yes	characteristic
487	C₄	C₅×#878	1	1	yes	characteristic
488	C₄	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
489	C₄	C₅×#939	1	1	yes	characteristic
490	C₃	C₅×#1802	1	1	yes	characteristic, complemented, Sylow
491	C₂	—	4	4	no	—
492	C₂	C₅×#4759	1	1	yes	characteristic
493	C₂	C₅×#4761	1	1	yes	characteristic
494	C₂	C₅×D₃×#102	1	1	yes	characteristic
495	C₂	C₅×#4771	1	1	yes	characteristic
496	C₂	C₅×#4942	1	1	yes	characteristic
497	C₂	C₅×#5150	1	1	yes	characteristic
498	C₂	C₅×#5162	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₅×#1802
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#102

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
5. C₅×#4975	C₂	semidirect
6. C₅×#4551	C₂	semidirect
7. C₅×#4529	C₂	semidirect
15. C₅×D₄×Dic₃	C₄	semidirect
25. #70153	C₅	direct (N × H)
69. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
70. #4975	C₂×C₅	semidirect
71. #4551	C₂×C₅	semidirect
72. #4529	C₂×C₅	semidirect
101. C₃×C₅×D₄	C₄⋊C₄	semidirect
132. D₄×Dic₃	C₄×C₅	semidirect
204. C₅×Dic₃	#102	semidirect
249. C₅×D₄	Dic₃⋊C₄	semidirect
309. C₃×D₄	C₅×C₄⋊C₄	semidirect
390. C₃×C₅	#1802	semidirect
413. Dic₃	C₅×#102	semidirect
433. D₄	C₅×Dic₃⋊C₄	semidirect
466. C₅	#70153	direct (N × H)
490. C₃	C₅×#1802	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×D₄×Dic₃	2
C₂×C₃×C₅×#102	2
C₂×C₅×#832	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#4975	2
C₅×#4551	2
C₅×#4529	2
C₅×#1802	3
#70153	5

Subgroups — C5×#70153 #14297627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70153 #14297627