Subgroups — C₅×#78560 #14417009

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic
2	C₅×#5523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5521	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5113	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4711	C₂	1	2	yes	maximal, complemented
9	C₅×#4710	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₂₄	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#204	C₂	1	2	yes	maximal, complemented
12	C₅×#2946	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₅×#926	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#908	C₄	1	8	yes	complemented
21	C₂×C₅×D₂₄	C₂²	1	2	yes	—
22	C₂×C₅×#204	C₂²	1	2	yes	—
23	C₅×#893	—	2	1	no	—
24	C₅×#893	—	2	1	no	—
25	C₅×#892	—	2	1	no	—
26	C₅×D₃×C₄⋊C₄	—	2	1	no	—
27	C₅×#67⋊C₄	—	2	2	no	—
28	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
29	C₄×C₅×D₁₂	C₂²	1	2	yes	—
30	C₄×C₅×D₁₂	C₂²	1	2	yes	—
31	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
32	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
33	C₃×C₅×#97	C₂²	1	2	yes	complemented
34	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
35	C₅×#821	C₂²	1	2	yes	—
36	C₅×#821	C₂²	1	2	yes	—
37	C₅×#821	C₂²	1	1	yes	characteristic, complemented
38	C₅×#821	C₂²	1	1	yes	characteristic, complemented
39	C₅×#818	C₂²	1	2	yes	complemented
40	C₅×#817	C₂²	1	2	yes	complemented
41	C₅×#816	C₂²	1	1	yes	characteristic, complemented
42	C₅×#816	C₂²	1	1	yes	characteristic, complemented
43	#78560	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
45	C₅×#520	—	3	1	no	—
46	C₅×#518	—	3	1	no	—
47	C₅×#442	—	3	2	no	—
48	C₅×#440	—	3	2	no	—
49	C₄×C₅×SD₁₆	—	3	2	no	—
50	C₄×C₅×D₈	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#416	—	3	1	no	—
53	C₂×C₅×#102	—	3	1	no	—
54	C₅×#405	D₃	1	1	yes	characteristic, complemented
55	C₂³×C₅×D₃	—	2	1	no	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	2	1	no	—
58	C₂²×C₅×Dic₃	—	2	1	no	—
59	C₅×#235	—	2	2	no	—
60	C₅×#235	C₂×C₄	1	4	yes	complemented
61	C₂×C₅×D₁₂	—	2	1	no	—
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
64	C₂×C₅×D₁₂	C₂³	1	2	yes	—
65	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₄×C₅×D₃	—	2	2	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
71	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
78	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
79	C₃×C₄²×C₅	C₂³	1	2	yes	—
80	C₅×#217	—	2	1	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₅×C₄⋊Dic₃	—	2	1	no	—
85	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
86	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
88	C₅×Dic₃⋊C₄	—	2	2	no	—
89	C₄×C₅×Dic₃	—	2	2	no	—
90	C₄×C₅×Dic₃	—	2	1	no	—
91	C₅×D₂₄	C₂×C₄	1	8	yes	complemented
92	C₅×#204	C₂×C₄	1	8	yes	complemented
93	C₂×#908	C₂×C₅	1	1	yes	characteristic
94	#5523	C₂×C₅	1	1	yes	characteristic, complemented
95	#5521	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
97	#5121	C₂×C₅	1	1	yes	characteristic, complemented
98	#5113	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
100	#4711	C₂×C₅	1	2	yes	complemented
101	#4710	C₂×C₅	1	2	yes	complemented
102	C₄×D₂₄	C₂×C₅	1	2	yes	complemented
103	C₄×#204	C₂×C₅	1	2	yes	complemented
104	C₂×C₅×#41	—	3	1	no	—
105	C₂²×C₅×D₄	—	3	1	no	—
106	C₅×AGL(1,ℤ/8)	—	3	8	no	—
107	C₂×C₅×SD₁₆	—	3	2	no	—
108	C₂×C₅×D₈	—	3	2	no	—
109	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
110	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
111	C₄×C₅×Q₈	—	3	2	no	—
112	C₄×C₅×D₄	—	3	2	no	—
113	C₄×C₅×D₄	—	3	2	no	—
114	C₄×C₅×D₄	—	3	2	no	—
115	C₄×C₅×D₄	—	6	1	no	—
116	C₄×C₅×D₄	—	6	1	no	—
117	C₄×C₅×D₄	—	6	2	no	—
118	C₅×#117	—	3	1	no	—
119	C₅×#117	—	6	1	no	—
120	C₅×#117	C₂×D₃	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	—	3	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
124	C₅×#107	—	3	2	no	—
125	C₅×#106	—	3	2	no	—
126	C₅×#103	—	3	1	no	—
127	C₅×#103	—	3	1	no	—
128	C₅×#102	—	3	2	no	—
129	C₅×#102	—	3	2	no	—
130	C₅×#102	—	3	1	no	—
131	C₅×#102	—	3	1	no	—
132	C₅×#97	C₂×D₃	1	2	yes	complemented
133	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
134	#2946	—	3	1	no	Sylow
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₅×D₃	—	2	1	no	—
137	C₂²×C₅×D₃	—	2	2	no	—
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	—	8	1	no	—
140	C₂²×C₅×D₃	—	8	1	no	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	#41	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×#67	—	2	4	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	—	2	1	no	—
151	C₂×C₅×Dic₃	—	2	1	no	—
152	C₂×C₅×Dic₃	—	8	1	no	—
153	C₅×D₁₂	—	2	4	no	—
154	C₅×D₁₂	—	2	2	no	—
155	C₅×D₁₂	—	2	1	no	—
156	C₅×D₁₂	C₂²×C₄	1	4	yes	—
157	C₅×D₁₂	C₂²×C₄	1	2	yes	—
158	C₄×C₅×D₃	—	2	4	no	—
159	C₄×C₅×D₃	—	8	2	no	—
160	C₄×C₅×D₃	—	8	2	no	—
161	C₄×C₅×D₃	—	8	2	no	—
162	C₅×Dic₆	—	2	1	no	—
163	C₅×Dic₆	C₂²×C₄	1	2	yes	—
164	C₃×C₅×C₈	—	2	1	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
167	C₂×#235	C₂²×C₅	1	1	yes	characteristic
168	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×#117	C₂²×C₅	1	1	yes	characteristic
172	#926	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
174	#908	C₄×C₅	1	8	yes	complemented
175	C₂×D₂₄	C₂²×C₅	1	2	yes	—
176	C₂×#204	C₂²×C₅	1	2	yes	—
177	#893	—	2	1	no	—
178	#893	—	2	1	no	—
179	#892	—	2	1	no	—
180	D₃×C₄⋊C₄	—	2	1	no	—
181	#67⋊C₄	—	2	2	no	—
182	D₃×C₂²⋊C₄	—	2	2	no	—
183	C₄×D₁₂	C₂²×C₅	1	2	yes	—
184	C₄×D₁₂	C₂²×C₅	1	2	yes	—
185	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
186	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
187	C₃×#97	C₂²×C₅	1	2	yes	complemented
188	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
189	#821	C₂²×C₅	1	2	yes	—
190	#821	C₂²×C₅	1	2	yes	—
191	#821	C₂²×C₅	1	1	yes	characteristic, complemented
192	#821	C₂²×C₅	1	1	yes	characteristic, complemented
193	#818	C₂²×C₅	1	2	yes	complemented
194	#817	C₂²×C₅	1	2	yes	complemented
195	#816	C₂²×C₅	1	1	yes	characteristic, complemented
196	#816	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂⁴×C₅	—	6	1	no	—
198	C₅×#41	—	3	4	no	—
199	C₅×#41	—	6	2	no	—
200	C₂×C₅×Q₈	—	3	1	no	—
201	C₂×C₅×D₄	—	3	4	no	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	3	2	no	—
204	C₂×C₅×D₄	—	6	1	no	—
205	C₂×C₅×D₄	—	6	1	no	—
206	C₂×C₅×D₄	—	6	2	no	—
207	C₂²×C₄×C₅	—	6	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	—	6	2	no	—
210	C₂²×C₄×C₅	—	6	2	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×SD₁₆	—	3	8	no	—
214	C₅×D₈	—	3	8	no	—
215	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
216	C₂×C₅×C₈	—	2	2	no	—
217	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
220	C₅×C₄⋊C₄	—	3	2	no	—
221	C₅×C₄⋊C₄	—	3	1	no	—
222	C₅×C₄⋊C₄	—	3	1	no	—
223	C₅×C₄⋊C₄	—	6	1	no	—
224	C₅×C₄⋊C₄	—	6	2	no	—
225	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
226	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
227	C₅×C₂²⋊C₄	—	6	1	no	—
228	C₅×C₂²⋊C₄	—	6	2	no	—
229	C₅×C₂²⋊C₄	—	6	2	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
232	C₄²×C₅	—	6	1	no	—
233	C₄²×C₅	—	6	2	no	—
234	C₄²×C₅	C₂²×D₃	1	2	yes	—
235	C₂×AGL(1,ℤ/8)	—	3	1	no	—
236	#520	—	3	1	no	—
237	#518	—	3	1	no	—
238	#442	—	3	2	no	—
239	#440	—	3	2	no	—
240	C₄×SD₁₆	—	3	2	no	—
241	C₄×D₈	—	3	2	no	—
242	#428	—	3	1	no	—
243	#416	—	3	1	no	—
244	C₂×#102	—	3	1	no	—
245	#405	C₅×D₃	1	1	yes	characteristic, complemented
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	2	no	—
251	C₂×C₅×D₃	—	2	4	no	—
252	C₂×C₅×D₃	—	4	1	no	—
253	C₂×C₅×D₃	—	4	2	no	—
254	C₂×C₅×D₃	—	4	2	no	—
255	C₂×C₅×D₃	—	4	1	no	—
256	C₂×C₅×D₃	—	8	4	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
260	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
261	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₅×Dic₃	—	2	2	no	—
263	C₅×Dic₃	—	4	1	no	—
264	C₅×Dic₃	—	4	2	no	—
265	C₅×Dic₃	—	4	1	no	—
266	C₂³×D₃	—	2	1	no	—
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂×#67	—	2	1	no	—
269	C₂²×Dic₃	—	2	1	no	—
270	#235	—	2	2	no	—
271	#235	C₂×C₄×C₅	1	4	yes	complemented
272	C₂×D₁₂	—	2	1	no	—
273	C₂×D₁₂	—	2	2	no	—
274	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
275	C₂×D₁₂	C₂³×C₅	1	2	yes	—
276	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄×D₃	—	2	1	no	—
278	C₂×C₄×D₃	—	2	2	no	—
279	C₂×C₄×D₃	—	2	2	no	—
280	C₂×C₄×D₃	—	2	2	no	—
281	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
282	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
283	C₂×C₃×C₈	—	2	2	no	—
284	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
287	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
288	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
290	C₃×C₄²	C₂³×C₅	1	2	yes	—
291	#217	—	2	1	no	—
292	(C₂×D₃)⋊C₄	—	2	2	no	—
293	(C₂×D₃)⋊C₄	—	2	2	no	—
294	(C₂×D₃)⋊C₄	—	2	2	no	—
295	C₄⋊Dic₃	—	2	1	no	—
296	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
297	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
298	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
299	Dic₃⋊C₄	—	2	2	no	—
300	C₄×Dic₃	—	2	2	no	—
301	C₄×Dic₃	—	2	1	no	—
302	D₂₄	C₂×C₄×C₅	1	8	yes	complemented
303	#204	C₂×C₄×C₅	1	8	yes	complemented
304	C₂³×C₅	—	6	1	no	—
305	C₂³×C₅	—	6	2	no	—
306	C₂³×C₅	—	6	4	no	—
307	C₂³×C₅	—	24	1	no	—
308	C₂³×C₅	—	24	1	no	—
309	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
310	C₅×Q₈	—	3	2	no	—
311	C₅×Q₈	—	6	1	no	—
312	C₅×D₄	—	3	2	no	—
313	C₅×D₄	—	3	4	no	—
314	C₅×D₄	—	6	4	no	—
315	C₅×D₄	—	6	4	no	—
316	C₅×D₄	—	6	2	no	—
317	C₅×D₄	—	6	1	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	4	no	—
320	C₂×C₄×C₅	—	6	1	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	24	2	no	—
324	C₂×C₄×C₅	—	24	2	no	—
325	C₂×C₄×C₅	—	24	2	no	—
326	C₂×C₄×C₅	—	24	1	no	—
327	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
328	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
329	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
330	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
331	C₂×C₄×C₅	#235	1	2	yes	—
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
336	C₂×#41	—	3	1	no	—
337	C₂²×D₄	—	3	1	no	—
338	AGL(1,ℤ/8)	—	3	8	no	—
339	C₂×SD₁₆	—	3	2	no	—
340	C₂×D₈	—	3	2	no	—
341	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
342	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
343	C₄×Q₈	—	3	2	no	—
344	C₄×D₄	—	3	2	no	—
345	C₄×D₄	—	3	2	no	—
346	C₄×D₄	—	3	2	no	—
347	C₄×D₄	—	6	1	no	—
348	C₄×D₄	—	6	1	no	—
349	C₄×D₄	—	6	2	no	—
350	#117	—	3	1	no	—
351	#117	—	6	1	no	—
352	#117	C₂×C₅×D₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	—	3	1	no	—
354	C₂×C₄⋊C₄	—	6	1	no	—
355	C₂×C₂²⋊C₄	—	6	2	no	—
356	#107	—	3	2	no	—
357	#106	—	3	2	no	—
358	#103	—	3	1	no	—
359	#103	—	3	1	no	—
360	#102	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	—	3	1	no	—
363	#102	—	3	1	no	—
364	#97	C₂×C₅×D₃	1	2	yes	complemented
365	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
368	C₂×C₃×C₅	#576	1	1	yes	characteristic
369	C₂×C₃×C₅	#577	1	1	yes	characteristic
370	C₅×D₃	—	4	2	no	—
371	C₅×D₃	—	4	4	no	—
372	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×D₃	—	2	1	no	—
374	C₂²×D₃	—	2	2	no	—
375	C₂²×D₃	—	2	4	no	—
376	C₂²×D₃	—	8	1	no	—
377	C₂²×D₃	—	8	1	no	—
378	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
380	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
381	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₅×#41	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	#67	—	2	4	no	—
385	C₂×Dic₃	—	2	1	no	—
386	C₂×Dic₃	—	2	2	no	—
387	C₂×Dic₃	—	2	1	no	—
388	C₂×Dic₃	—	2	1	no	—
389	C₂×Dic₃	—	8	1	no	—
390	D₁₂	—	2	4	no	—
391	D₁₂	—	2	2	no	—
392	D₁₂	—	2	1	no	—
393	D₁₂	C₂²×C₄×C₅	1	4	yes	—
394	D₁₂	C₂²×C₄×C₅	1	2	yes	—
395	C₄×D₃	—	2	4	no	—
396	C₄×D₃	—	8	2	no	—
397	C₄×D₃	—	8	2	no	—
398	C₄×D₃	—	8	2	no	—
399	Dic₆	—	2	1	no	—
400	Dic₆	C₂²×C₄×C₅	1	2	yes	—
401	C₃×C₈	—	2	1	no	—
402	C₃×C₈	—	2	1	no	—
403	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	6	2	no	—
407	C₂²×C₅	—	6	4	no	—
408	C₂²×C₅	—	12	2	no	—
409	C₂²×C₅	—	12	1	no	—
410	C₂²×C₅	—	12	1	no	—
411	C₂²×C₅	—	12	2	no	—
412	C₂²×C₅	—	24	4	no	—
413	C₂²×C₅	C₄×D₁₂	1	2	yes	—
414	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	6	2	no	—
418	C₄×C₅	—	12	1	no	—
419	C₄×C₅	—	12	1	no	—
420	C₄×C₅	—	12	2	no	—
421	C₄×C₅	C₄×D₁₂	1	2	yes	—
422	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
423	C₄×C₅	C₂×#235	1	1	yes	characteristic
424	C₂⁴	—	6	1	no	—
425	#41	—	3	4	no	—
426	#41	—	6	2	no	—
427	C₂×Q₈	—	3	1	no	—
428	C₂×D₄	—	3	4	no	—
429	C₂×D₄	—	3	1	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	6	1	no	—
432	C₂×D₄	—	6	1	no	—
433	C₂×D₄	—	6	2	no	—
434	C₂²×C₄	—	6	1	no	—
435	C₂²×C₄	—	6	1	no	—
436	C₂²×C₄	—	6	2	no	—
437	C₂²×C₄	—	6	2	no	—
438	C₂²×C₄	—	6	2	no	—
439	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
440	SD₁₆	—	3	8	no	—
441	D₈	—	3	8	no	—
442	M₁₆	C₄×C₅×D₃	1	4	yes	complemented
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
445	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
446	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	1	no	—
450	C₄⋊C₄	—	6	1	no	—
451	C₄⋊C₄	—	6	2	no	—
452	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
453	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
454	C₂²⋊C₄	—	6	1	no	—
455	C₂²⋊C₄	—	6	2	no	—
456	C₂²⋊C₄	—	6	2	no	—
457	C₂²⋊C₄	—	6	2	no	—
458	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
459	C₄²	—	6	1	no	—
460	C₄²	—	6	2	no	—
461	C₄²	C₂²×C₅×D₃	1	2	yes	—
462	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
466	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	2	4	no	—
469	C₂×D₃	—	4	1	no	—
470	C₂×D₃	—	4	2	no	—
471	C₂×D₃	—	4	2	no	—
472	C₂×D₃	—	4	1	no	—
473	C₂×D₃	—	8	4	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
477	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
478	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
479	Dic₃	—	2	2	no	—
480	Dic₃	—	4	1	no	—
481	Dic₃	—	4	2	no	—
482	Dic₃	—	4	1	no	—
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	12	4	no	—
485	C₂×C₅	—	12	2	no	—
486	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
487	C₂×C₅	#5751	1	1	yes	characteristic
488	C₂×C₅	#5752	1	1	yes	characteristic
489	C₂³	—	6	1	no	—
490	C₂³	—	6	2	no	—
491	C₂³	—	6	4	no	—
492	C₂³	—	24	1	no	—
493	C₂³	—	24	1	no	—
494	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
495	Q₈	—	3	2	no	—
496	Q₈	—	6	1	no	—
497	D₄	—	3	2	no	—
498	D₄	—	3	4	no	—
499	D₄	—	6	4	no	—
500	D₄	—	6	4	no	—
501	D₄	—	6	2	no	—
502	D₄	—	6	1	no	—
503	C₂×C₄	—	6	1	no	—
504	C₂×C₄	—	6	4	no	—
505	C₂×C₄	—	6	1	no	—
506	C₂×C₄	—	6	1	no	—
507	C₂×C₄	—	6	2	no	—
508	C₂×C₄	—	24	2	no	—
509	C₂×C₄	—	24	2	no	—
510	C₂×C₄	—	24	2	no	—
511	C₂×C₄	—	24	1	no	—
512	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
513	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
514	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
515	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
516	C₂×C₄	C₅×#235	1	2	yes	—
517	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
523	C₂×C₃	C₅×#576	1	1	yes	characteristic
524	C₂×C₃	C₅×#577	1	1	yes	characteristic
525	D₃	—	4	4	no	—
526	D₃	—	4	2	no	—
527	C₅	#78560	1	1	yes	characteristic, direct product factor, Sylow
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	6	2	no	—
531	C₂²	—	6	4	no	—
532	C₂²	—	12	2	no	—
533	C₂²	—	12	1	no	—
534	C₂²	—	12	1	no	—
535	C₂²	—	12	2	no	—
536	C₂²	—	24	4	no	—
537	C₂²	C₄×C₅×D₁₂	1	2	yes	—
538	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	6	2	no	—
542	C₄	—	12	1	no	—
543	C₄	—	12	1	no	—
544	C₄	—	12	2	no	—
545	C₄	C₄×C₅×D₁₂	1	2	yes	—
546	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
547	C₄	C₂×C₅×#235	1	1	yes	characteristic
548	C₃	C₅×#2946	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	12	4	no	—
551	C₂	—	12	2	no	—
552	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
553	C₂	C₅×#5751	1	1	yes	characteristic
554	C₂	C₅×#5752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#908	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2946
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
2. C₅×#5523	C₂	semidirect
3. C₅×#5521	C₂	semidirect
4. C₃×C₅×#405	C₂	semidirect
5. C₅×#5121	C₂	semidirect
6. C₅×#5113	C₂	semidirect
7. C₂×C₅×#821	C₂	semidirect
8. C₅×#4711	C₂	semidirect
9. C₅×#4710	C₂	semidirect
10. C₄×C₅×D₂₄	C₂	semidirect
11. C₄×C₅×#204	C₂	semidirect
20. C₅×#908	C₄	semidirect
31. C₄×C₅×D₁₂	C₂²	semidirect
32. C₄×C₅×Dic₆	C₂²	semidirect
33. C₃×C₅×#97	C₂²	semidirect
34. C₃×C₄×C₅×C₈	C₂²	semidirect
37. C₅×#821	C₂²	semidirect
38. C₅×#821	C₂²	semidirect
39. C₅×#818	C₂²	semidirect
40. C₅×#817	C₂²	semidirect
41. C₅×#816	C₂²	semidirect
42. C₅×#816	C₂²	semidirect
43. #78560	C₅	direct (N × H)
54. C₅×#405	D₃	semidirect
60. C₅×#235	C₂×C₄	semidirect
63. C₂×C₅×D₁₂	C₂×C₄	semidirect
71. C₃×C₅×M₁₆	C₂×C₄	semidirect
91. C₅×D₂₄	C₂×C₄	semidirect
92. C₅×#204	C₂×C₄	semidirect
94. #5523	C₂×C₅	semidirect
95. #5521	C₂×C₅	semidirect
96. C₃×#405	C₂×C₅	semidirect
97. #5121	C₂×C₅	semidirect
98. #5113	C₂×C₅	semidirect
99. C₂×#821	C₂×C₅	semidirect
100. #4711	C₂×C₅	semidirect
101. #4710	C₂×C₅	semidirect
102. C₄×D₂₄	C₂×C₅	semidirect
103. C₄×#204	C₂×C₅	semidirect
132. C₅×#97	C₂×D₃	semidirect
133. C₄×C₅×C₈	C₂×D₃	semidirect
174. #908	C₄×C₅	semidirect
185. C₄×D₁₂	C₂²×C₅	semidirect
186. C₄×Dic₆	C₂²×C₅	semidirect
187. C₃×#97	C₂²×C₅	semidirect
188. C₃×C₄×C₈	C₂²×C₅	semidirect
191. #821	C₂²×C₅	semidirect
192. #821	C₂²×C₅	semidirect
193. #818	C₂²×C₅	semidirect
194. #817	C₂²×C₅	semidirect
195. #816	C₂²×C₅	semidirect
196. #816	C₂²×C₅	semidirect
215. C₅×M₁₆	C₄×D₃	semidirect
245. #405	C₅×D₃	semidirect
271. #235	C₂×C₄×C₅	semidirect
274. C₂×D₁₂	C₂×C₄×C₅	semidirect
282. C₃×M₁₆	C₂×C₄×C₅	semidirect
302. D₂₄	C₂×C₄×C₅	semidirect
303. #204	C₂×C₄×C₅	semidirect
364. #97	C₂×C₅×D₃	semidirect
365. C₄×C₈	C₂×C₅×D₃	semidirect
442. M₁₆	C₄×C₅×D₃	semidirect
462. C₃×C₅	#2946	semidirect
527. C₅	#78560	direct (N × H)
548. C₃	C₅×#2946	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#908	2
C₅×#5523	2
C₅×#5521	2
C₃×C₅×#405	2
C₅×#5121	2
C₅×#5113	2
C₂×C₅×#821	2
C₅×#4711	2
C₅×#4710	2
C₄×C₅×D₂₄	2
C₄×C₅×#204	2
C₅×#2946	3
#78560	5

Subgroups — C5×#78560 #14417009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78560 #14417009