Subgroups — C₅×#79721 #14417626

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#919	C₂	1	1	yes	maximal, characteristic
2	C₅×#5574	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5026	C₂	1	2	yes	maximal, complemented
6	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4817	C₂	1	2	yes	maximal, complemented
9	C₅×#4803	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2951	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#215	C₂²	1	2	yes	—
18	C₅×#919	C₄	1	8	yes	complemented
19	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₅×#893	—	2	2	no	—
23	C₅×#893	C₂²	1	2	yes	—
24	C₅×D₃×C₄⋊C₄	—	2	2	no	—
25	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₄×C₅×D₁₂	—	2	2	no	—
27	C₄×C₅×D₁₂	C₂²	1	2	yes	—
28	C₅×#872	—	2	2	no	—
29	C₅×#872	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	2	yes	—
35	C₅×#818	C₂²	1	1	yes	characteristic
36	C₅×#815	C₂²	1	1	yes	characteristic
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₅×#809	C₂²	1	2	yes	—
39	C₅×#807	C₂²	1	2	yes	—
40	C₅×#803	C₂²	1	1	yes	characteristic
41	#79721	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#135	—	3	1	no	—
43	C₅×#520	—	3	2	no	—
44	C₅×#440	—	3	2	no	—
45	C₅×#440	—	3	2	no	—
46	C₄×C₅×Q₁₆	—	3	1	no	—
47	C₄×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
48	C₄×C₅×D₈	—	3	1	no	—
49	C₄×C₅×D₈	—	3	1	no	—
50	C₂×C₅×#107	—	3	1	no	—
51	C₅×#417	—	3	2	no	—
52	C₅×#405	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₅×#239	—	2	4	no	—
55	C₅×#239	C₂×C₄	1	8	yes	complemented
56	C₂×C₅×D₁₂	—	2	2	no	—
57	C₂×C₅×D₁₂	C₂³	1	2	yes	—
58	C₂×C₄×C₅×D₃	—	2	2	no	—
59	C₂×C₄×C₅×D₃	—	2	2	no	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#215	C₂×C₄	1	8	yes	complemented
71	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
74	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
75	C₅×C₄⋊Dic₃	—	2	2	no	—
76	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
77	C₅×Dic₃⋊C₄	—	2	2	no	—
78	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
79	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	—	2	2	no	—
81	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
85	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
86	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
87	C₂×#919	C₂×C₅	1	1	yes	characteristic
88	#5574	C₂×C₅	1	2	yes	complemented
89	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
90	Dic₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	#5026	C₂×C₅	1	2	yes	complemented
92	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
93	#4872	C₂×C₅	1	1	yes	characteristic, complemented
94	#4817	C₂×C₅	1	2	yes	complemented
95	#4803	C₂×C₅	1	2	yes	complemented
96	C₄×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
97	#4689	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₅×#41	—	3	2	no	—
99	C₅×#135	—	3	8	no	—
100	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×SD₁₆	—	3	2	no	—
102	C₂×C₅×D₈	—	3	1	no	—
103	C₂×C₅×M₁₆	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₄×C₅×Q₈	—	3	2	no	—
106	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	6	2	no	—
110	C₄×C₅×D₄	—	6	2	no	—
111	C₅×#117	—	3	1	no	—
112	C₅×#117	—	6	2	no	—
113	C₂×C₅×C₄⋊C₄	—	3	2	no	—
114	C₂×C₅×C₄⋊C₄	—	6	2	no	—
115	C₅×#107	—	3	1	no	—
116	C₅×#107	—	3	2	no	—
117	C₅×#107	C₂×D₃	1	1	yes	characteristic
118	C₅×#103	—	3	2	no	—
119	C₅×#103	C₂×D₃	1	2	yes	—
120	C₅×#102	—	3	2	no	—
121	C₅×#102	—	3	2	no	—
122	C₅×#97	—	3	1	no	—
123	C₅×#97	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
126	#2951	—	3	1	no	Sylow
127	C₂²×C₅×D₃	—	2	2	no	—
128	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
140	C₅×D₁₂	—	2	8	no	—
141	C₅×D₁₂	—	2	2	no	—
142	C₅×D₁₂	C₂²×C₄	1	4	yes	—
143	C₄×C₅×D₃	—	2	8	no	—
144	C₄×C₅×D₃	—	8	2	no	—
145	C₄×C₅×D₃	—	8	2	no	—
146	C₄×C₅×D₃	—	8	2	no	—
147	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
148	C₄×C₅×D₃	#41	1	2	yes	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₅×C₃⋊C₈	—	2	1	no	—
152	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×#239	C₂²×C₅	1	2	yes	—
154	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
155	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
156	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
157	C₂×#215	C₂²×C₅	1	2	yes	—
158	#919	C₄×C₅	1	8	yes	complemented
159	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
160	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
161	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
162	#893	—	2	2	no	—
163	#893	C₂²×C₅	1	2	yes	—
164	D₃×C₄⋊C₄	—	2	2	no	—
165	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
166	C₄×D₁₂	—	2	2	no	—
167	C₄×D₁₂	C₂²×C₅	1	2	yes	—
168	#872	—	2	2	no	—
169	#872	C₂²×C₅	1	1	yes	characteristic
170	C₃×#107	C₂²×C₅	1	1	yes	characteristic
171	C₃×#103	C₂²×C₅	1	2	yes	—
172	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
173	#835	C₂²×C₅	1	2	yes	—
174	#821	C₂²×C₅	1	2	yes	—
175	#818	C₂²×C₅	1	1	yes	characteristic
176	#815	C₂²×C₅	1	1	yes	characteristic
177	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
178	#809	C₂²×C₅	1	2	yes	—
179	#807	C₂²×C₅	1	2	yes	—
180	#803	C₂²×C₅	1	1	yes	characteristic
181	C₅×#41	—	3	8	no	—
182	C₅×#41	—	6	4	no	—
183	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
184	C₂×C₅×D₄	—	3	2	no	—
185	C₂×C₅×D₄	—	6	2	no	—
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	6	2	no	—
188	C₂²×C₄×C₅	—	6	2	no	—
189	C₂²×C₄×C₅	—	6	2	no	—
190	C₂²×C₄×C₅	—	6	2	no	—
191	C₅×Q₁₆	C₄×D₃	1	4	yes	complemented
192	C₅×SD₁₆	—	3	8	no	—
193	C₅×D₈	—	3	4	no	—
194	C₅×M₁₆	—	6	2	no	—
195	C₂×C₅×C₈	—	3	1	no	—
196	C₂×C₅×C₈	—	3	4	no	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×C₄⋊C₄	—	3	2	no	—
204	C₅×C₄⋊C₄	—	6	2	no	—
205	C₅×C₄⋊C₄	—	6	2	no	—
206	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
207	C₅×C₂²⋊C₄	—	3	1	no	—
208	C₅×C₂²⋊C₄	—	3	1	no	—
209	C₅×C₂²⋊C₄	—	6	2	no	—
210	C₅×C₂²⋊C₄	—	6	2	no	—
211	C₄²×C₅	—	2	2	no	—
212	C₄²×C₅	—	3	1	no	—
213	C₄²×C₅	—	6	2	no	—
214	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₂×#135	—	3	1	no	—
216	#520	—	3	2	no	—
217	#440	—	3	2	no	—
218	#440	—	3	2	no	—
219	C₄×Q₁₆	—	3	1	no	—
220	C₄×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
221	C₄×D₈	—	3	1	no	—
222	C₄×D₈	—	3	1	no	—
223	C₂×#107	—	3	1	no	—
224	#417	—	3	2	no	—
225	#405	—	3	1	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₅×D₃	—	2	1	no	—
228	C₂×C₅×D₃	—	2	1	no	—
229	C₂×C₅×D₃	—	2	4	no	—
230	C₂×C₅×D₃	—	4	2	no	—
231	C₂×C₅×D₃	—	4	2	no	—
232	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
233	C₃×C₄×C₅	—	2	4	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
238	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₅×Dic₃	—	2	1	no	—
240	C₅×Dic₃	—	2	1	no	—
241	C₅×Dic₃	—	4	2	no	—
242	C₅×Dic₃	C₄×D₄	1	2	yes	—
243	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
244	#239	—	2	4	no	—
245	#239	C₂×C₄×C₅	1	8	yes	complemented
246	C₂×D₁₂	—	2	2	no	—
247	C₂×D₁₂	C₂³×C₅	1	2	yes	—
248	C₂×C₄×D₃	—	2	2	no	—
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×C₄×D₃	—	2	2	no	—
251	C₂×C₄×D₃	—	2	2	no	—
252	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
253	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
254	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
258	C₃×C₄²	—	2	2	no	—
259	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
260	#215	C₂×C₄×C₅	1	8	yes	complemented
261	(C₂×D₃)⋊C₄	—	2	2	no	—
262	(C₂×D₃)⋊C₄	—	2	2	no	—
263	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
264	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
265	C₄⋊Dic₃	—	2	2	no	—
266	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
267	Dic₃⋊C₄	—	2	2	no	—
268	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
269	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
270	C₄×Dic₃	—	2	2	no	—
271	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
275	ΓL(1,𝔽₂₅)	—	2	2	no	—
276	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
277	C₂³×C₅	—	3	1	no	—
278	C₂³×C₅	—	6	2	no	—
279	C₅×Q₈	—	2	2	no	—
280	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
281	C₅×D₄	—	3	4	no	—
282	C₅×D₄	—	6	8	no	—
283	C₅×D₄	—	6	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	3	1	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	3	2	no	—
289	C₂×C₄×C₅	—	3	1	no	—
290	C₂×C₄×C₅	—	3	1	no	—
291	C₂×C₄×C₅	—	6	8	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	24	2	no	—
294	C₂×C₄×C₅	—	24	2	no	—
295	C₂×C₄×C₅	—	24	2	no	—
296	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
299	C₅×C₈	—	2	1	no	—
300	C₅×C₈	—	3	2	no	—
301	C₅×C₈	—	6	1	no	—
302	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
303	C₂×#41	—	3	2	no	—
304	#135	—	3	8	no	—
305	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂×SD₁₆	—	3	2	no	—
307	C₂×D₈	—	3	1	no	—
308	C₂×M₁₆	—	3	1	no	—
309	C₂²×C₈	—	3	1	no	—
310	C₄×Q₈	—	3	2	no	—
311	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
312	C₄×D₄	—	3	2	no	—
313	C₄×D₄	—	3	2	no	—
314	C₄×D₄	—	6	2	no	—
315	C₄×D₄	—	6	2	no	—
316	#117	—	3	1	no	—
317	#117	—	6	2	no	—
318	C₂×C₄⋊C₄	—	3	2	no	—
319	C₂×C₄⋊C₄	—	6	2	no	—
320	#107	—	3	1	no	—
321	#107	—	3	2	no	—
322	#107	C₂×C₅×D₃	1	1	yes	characteristic
323	#103	—	3	2	no	—
324	#103	C₂×C₅×D₃	1	2	yes	—
325	#102	—	3	2	no	—
326	#102	—	3	2	no	—
327	#97	—	3	1	no	—
328	#97	—	3	1	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂×C₃×C₅	#576	1	1	yes	characteristic
333	C₂×C₃×C₅	#578	1	1	yes	characteristic
334	C₅×D₃	—	2	2	no	—
335	C₅×D₃	—	4	4	no	—
336	C₂²×D₃	—	2	2	no	—
337	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
338	C₃×Q₈	—	2	2	no	—
339	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	C₂×Dic₃	—	2	2	no	—
346	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
349	D₁₂	—	2	8	no	—
350	D₁₂	—	2	2	no	—
351	D₁₂	C₂²×C₄×C₅	1	4	yes	—
352	C₄×D₃	—	2	8	no	—
353	C₄×D₃	—	8	2	no	—
354	C₄×D₃	—	8	2	no	—
355	C₄×D₃	—	8	2	no	—
356	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
357	C₄×D₃	C₅×#41	1	2	yes	—
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
360	C₃⋊C₈	—	2	1	no	—
361	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
362	C₂²×C₅	—	3	2	no	—
363	C₂²×C₅	—	6	1	no	—
364	C₂²×C₅	—	6	1	no	—
365	C₂²×C₅	—	6	4	no	—
366	C₂²×C₅	—	12	2	no	—
367	C₂²×C₅	—	12	2	no	—
368	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
369	C₄×C₅	—	2	1	no	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	4	no	—
372	C₄×C₅	—	3	2	no	—
373	C₄×C₅	—	4	2	no	—
374	C₄×C₅	—	6	1	no	—
375	C₄×C₅	—	6	1	no	—
376	C₄×C₅	—	12	2	no	—
377	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
378	C₄×C₅	D₃×#41	1	1	yes	characteristic
379	#41	—	3	8	no	—
380	#41	—	6	4	no	—
381	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
382	C₂×D₄	—	3	2	no	—
383	C₂×D₄	—	6	2	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	6	2	no	—
386	C₂²×C₄	—	6	2	no	—
387	C₂²×C₄	—	6	2	no	—
388	C₂²×C₄	—	6	2	no	—
389	Q₁₆	C₄×C₅×D₃	1	4	yes	complemented
390	SD₁₆	—	3	8	no	—
391	D₈	—	3	4	no	—
392	M₁₆	—	6	2	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	—	3	4	no	—
395	C₂×C₈	—	3	1	no	—
396	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
397	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	3	1	no	—
400	C₄⋊C₄	—	3	1	no	—
401	C₄⋊C₄	—	3	2	no	—
402	C₄⋊C₄	—	6	2	no	—
403	C₄⋊C₄	—	6	2	no	—
404	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
405	C₂²⋊C₄	—	3	1	no	—
406	C₂²⋊C₄	—	3	1	no	—
407	C₂²⋊C₄	—	6	2	no	—
408	C₂²⋊C₄	—	6	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	3	1	no	—
411	C₄²	—	6	2	no	—
412	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
413	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
415	C₂×D₃	—	2	1	no	—
416	C₂×D₃	—	2	1	no	—
417	C₂×D₃	—	2	4	no	—
418	C₂×D₃	—	4	2	no	—
419	C₂×D₃	—	4	2	no	—
420	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
421	C₃×C₄	—	2	4	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	4	2	no	—
425	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
426	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
427	Dic₃	—	2	1	no	—
428	Dic₃	—	2	1	no	—
429	Dic₃	—	4	2	no	—
430	Dic₃	C₄×C₅×D₄	1	2	yes	—
431	C₂×C₅	—	6	2	no	—
432	C₂×C₅	—	12	4	no	—
433	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
434	C₂×C₅	#5766	1	1	yes	characteristic
435	C₂×C₅	#5769	1	1	yes	characteristic
436	C₂³	—	3	1	no	—
437	C₂³	—	6	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
440	D₄	—	3	4	no	—
441	D₄	—	6	8	no	—
442	D₄	—	6	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	3	1	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	3	2	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	6	8	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	24	2	no	—
453	C₂×C₄	—	24	2	no	—
454	C₂×C₄	—	24	2	no	—
455	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
456	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
458	C₈	—	2	1	no	—
459	C₈	—	3	2	no	—
460	C₈	—	6	1	no	—
461	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
462	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
463	C₂×C₃	C₅×#576	1	1	yes	characteristic
464	C₂×C₃	C₅×#578	1	1	yes	characteristic
465	D₃	—	2	2	no	—
466	D₃	—	4	4	no	—
467	C₅	#79721	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	3	2	no	—
469	C₂²	—	6	1	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	6	4	no	—
472	C₂²	—	12	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	4	no	—
478	C₄	—	3	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	6	1	no	—
481	C₄	—	6	1	no	—
482	C₄	—	12	2	no	—
483	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
484	C₄	C₅×D₃×#41	1	1	yes	characteristic
485	C₃	C₅×#2951	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	6	2	no	—
487	C₂	—	12	4	no	—
488	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
489	C₂	C₅×#5766	1	1	yes	characteristic
490	C₂	C₅×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#919	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#2951
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#5574	C₂	semidirect
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×Dic₃×Q₁₆	C₂	semidirect
5. C₅×#5026	C₂	semidirect
6. C₅×D₃×#107	C₂	semidirect
7. C₅×#4872	C₂	semidirect
8. C₅×#4817	C₂	semidirect
9. C₅×#4803	C₂	semidirect
10. C₄×C₅×D₂₄	C₂	semidirect
11. C₅×#4689	C₂	semidirect
18. C₅×#919	C₄	semidirect
41. #79721	C₅	direct (N × H)
47. C₄×C₅×Q₁₆	D₃	semidirect
55. C₅×#239	C₂×C₄	semidirect
63. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₅×#215	C₂×C₄	semidirect
84. C₅×D₂₄	C₂×C₄	semidirect
86. C₅×D₃×C₈	C₂×C₄	semidirect
88. #5574	C₂×C₅	semidirect
89. C₃×C₄×Q₁₆	C₂×C₅	semidirect
90. Dic₃×Q₁₆	C₂×C₅	semidirect
91. #5026	C₂×C₅	semidirect
92. D₃×#107	C₂×C₅	semidirect
93. #4872	C₂×C₅	semidirect
94. #4817	C₂×C₅	semidirect
95. #4803	C₂×C₅	semidirect
96. C₄×D₂₄	C₂×C₅	semidirect
97. #4689	C₂×C₅	semidirect
158. #919	C₄×C₅	semidirect
191. C₅×Q₁₆	C₄×D₃	semidirect
220. C₄×Q₁₆	C₅×D₃	semidirect
245. #239	C₂×C₄×C₅	semidirect
253. C₃×Q₁₆	C₂×C₄×C₅	semidirect
260. #215	C₂×C₄×C₅	semidirect
274. D₂₄	C₂×C₄×C₅	semidirect
276. D₃×C₈	C₂×C₄×C₅	semidirect
389. Q₁₆	C₄×C₅×D₃	semidirect
413. C₃×C₅	#2951	semidirect
467. C₅	#79721	direct (N × H)
485. C₃	C₅×#2951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#919	2
C₅×#5574	2
C₃×C₄×C₅×Q₁₆	2
C₅×Dic₃×Q₁₆	2
C₅×#5026	2
C₅×D₃×#107	2
C₅×#4872	2
C₅×#4817	2
C₅×#4803	2
C₄×C₅×D₂₄	2
C₅×#4689	2
C₅×#2951	3
#79721	5

Subgroups — C5×#79721 #14417626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79721 #14417626