Subgroups — C₅×#78660 #14415828

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5832	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5129	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4730	C₂	1	2	yes	maximal, complemented
9	C₅×#4729	C₂	1	2	yes	maximal, complemented
10	C₅×#4728	C₂	1	2	yes	maximal, complemented
11	C₅×#67⋊C₈	C₂	1	2	yes	maximal, complemented
12	C₅×#2935	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	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	C₅×#948	—	2	4	no	—
18	C₅×#947	C₄	1	1	yes	characteristic
19	C₅×#944	C₄	1	1	yes	characteristic
20	C₅×#940	C₄	1	1	yes	characteristic
21	C₅×#939	C₄	1	2	yes	—
22	C₅×#939	C₄	1	2	yes	—
23	C₅×#936	C₄	1	1	yes	characteristic
24	C₄×C₅×#67	C₂²	1	2	yes	—
25	C₄×C₅×#67	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×#208	C₂²	1	2	yes	—
28	C₂×C₅×#208	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₅×#901	—	2	4	no	—
32	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
33	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
34	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
37	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
38	C₅×#815	C₂²	1	2	yes	—
39	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×C₈×Dic₃	C₂²	1	2	yes	—
44	#78660	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#131	—	3	1	no	—
46	C₂×C₅×#131	—	3	1	no	—
47	C₅×#532	—	3	1	no	—
48	C₅×#436	—	3	2	no	—
49	C₅×#435	—	3	2	no	—
50	C₅×#435	—	3	2	no	—
51	C₅×C₈×D₄	—	3	2	no	—
52	C₂×C₅×C₄⋊C₈	—	3	1	no	—
53	C₅×#408	—	3	1	no	—
54	C₅×#408	D₃	1	1	yes	characteristic, complemented
55	C₄×C₅×M₁₆	—	3	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₅×#67	C₂×C₄	1	2	yes	—
64	C₂×C₅×#67	C₂×C₄	1	2	yes	—
65	C₂×C₅×#67	C₂×C₄	1	2	yes	—
66	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
68	C₅×#235	—	2	2	no	—
69	C₅×#235	—	2	2	no	—
70	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
72	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
73	C₃×C₅×M₁₆	—	2	2	no	—
74	C₂×C₃×C₅×C₈	—	2	2	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₅×#217	C₂×C₄	1	2	yes	—
79	C₅×#217	C₂×C₄	1	2	yes	—
80	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
81	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
82	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
83	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
84	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₅×#208	—	2	4	no	—
89	C₅×#208	D₄	1	4	yes	complemented
90	C₂×C₅×C₃⋊C₈	—	2	2	no	—
91	C₂×C₅×C₃⋊C₈	—	2	4	no	—
92	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
96	C₅×D₃×C₈	—	2	4	no	—
97	#5832	C₂×C₅	1	1	yes	characteristic
98	C₂×#948	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×#901	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
101	#5129	C₂×C₅	1	1	yes	characteristic, complemented
102	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
104	#4730	C₂×C₅	1	2	yes	complemented
105	#4729	C₂×C₅	1	2	yes	complemented
106	#4728	C₂×C₅	1	2	yes	complemented
107	#67⋊C₈	C₂×C₅	1	2	yes	complemented
108	C₂×C₅×#41	—	3	1	no	—
109	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
110	C₅×#131	—	6	4	no	—
111	C₅×#131	—	6	4	no	—
112	C₂×C₅×M₁₆	—	3	1	no	—
113	C₂×C₅×M₁₆	—	3	2	no	—
114	C₂×C₅×M₁₆	—	3	2	no	—
115	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₅×C₈	—	3	1	no	—
117	C₂²×C₅×C₈	—	3	2	no	—
118	C₂²×C₅×C₈	—	3	2	no	—
119	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
120	C₅×C₄⋊Q₈	—	3	1	no	—
121	C₅×#127	—	3	1	no	—
122	C₅×#124	—	3	1	no	—
123	C₅×#124	—	3	1	no	—
124	C₅×#121	—	3	2	no	—
125	C₅×#121	—	3	2	no	—
126	C₄×C₅×D₄	—	3	2	no	—
127	C₄×C₅×D₄	—	3	2	no	—
128	C₂×C₄²×C₅	—	3	1	no	—
129	C₅×C₄⋊C₈	—	3	1	no	—
130	C₅×C₄⋊C₈	—	3	1	no	—
131	C₅×C₄⋊C₈	—	3	1	no	—
132	C₅×C₄⋊C₈	—	3	1	no	—
133	C₅×C₂²⋊C₈	—	3	2	no	—
134	C₅×C₂²⋊C₈	—	3	2	no	—
135	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
136	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
137	C₅×#97	—	3	2	no	—
138	C₄×C₅×C₈	—	3	2	no	—
139	#2935	—	3	1	no	Sylow
140	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
141	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
143	C₃×C₅×Q₈	—	2	2	no	—
144	C₃×C₅×D₄	—	2	4	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₅×#67	—	2	4	no	—
154	C₅×#67	—	2	4	no	—
155	C₅×#67	—	4	2	no	—
156	C₂×C₅×Dic₃	—	2	2	no	—
157	C₂×C₅×Dic₃	—	4	1	no	—
158	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
162	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
163	C₅×D₁₂	—	2	2	no	—
164	C₄×C₅×D₃	—	2	2	no	—
165	C₄×C₅×D₃	—	2	2	no	—
166	C₅×Dic₆	—	2	2	no	—
167	C₃×C₅×C₈	—	2	1	no	—
168	C₃×C₅×C₈	—	2	1	no	—
169	C₃×C₅×C₈	—	2	2	no	—
170	C₅×C₃⋊C₈	—	2	1	no	—
171	C₅×C₃⋊C₈	—	2	1	no	—
172	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
173	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
174	C₂×#235	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
177	#948	—	2	4	no	—
178	#947	C₄×C₅	1	1	yes	characteristic
179	#944	C₄×C₅	1	1	yes	characteristic
180	#940	C₄×C₅	1	1	yes	characteristic
181	#939	C₄×C₅	1	2	yes	—
182	#939	C₄×C₅	1	2	yes	—
183	#936	C₄×C₅	1	1	yes	characteristic
184	C₄×#67	C₂²×C₅	1	2	yes	—
185	C₄×#67	C₂²×C₅	1	2	yes	—
186	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
187	C₂×#208	C₂²×C₅	1	2	yes	—
188	C₂×#208	C₂²×C₅	1	1	yes	characteristic
189	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
190	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
191	#901	—	2	4	no	—
192	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
193	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
194	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
195	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
196	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
197	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
198	#815	C₂²×C₅	1	2	yes	—
199	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
200	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
201	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
202	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
203	C₈×Dic₃	C₂²×C₅	1	2	yes	—
204	C₅×#41	—	2	2	no	—
205	C₅×#41	—	2	2	no	—
206	C₅×#41	—	6	2	no	—
207	C₅×#41	—	6	2	no	—
208	C₂×C₅×Q₈	—	3	1	no	—
209	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
210	C₂×C₅×D₄	—	3	2	no	—
211	C₂×C₅×D₄	—	3	2	no	—
212	C₂×C₅×D₄	—	3	2	no	—
213	C₂×C₅×D₄	—	3	1	no	—
214	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
215	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	—	3	1	no	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	2	no	—
219	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₅×M₁₆	—	2	2	no	—
222	C₅×M₁₆	—	3	4	no	—
223	C₅×M₁₆	—	6	4	no	—
224	C₅×M₁₆	—	6	4	no	—
225	C₂×C₅×C₈	—	2	2	no	—
226	C₂×C₅×C₈	—	3	2	no	—
227	C₂×C₅×C₈	—	3	1	no	—
228	C₂×C₅×C₈	—	3	1	no	—
229	C₂×C₅×C₈	—	6	4	no	—
230	C₂×C₅×C₈	—	6	4	no	—
231	C₂×C₅×C₈	—	6	2	no	—
232	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
235	C₅×C₄⋊C₄	—	3	2	no	—
236	C₅×C₄⋊C₄	—	3	2	no	—
237	C₅×C₂²⋊C₄	—	3	2	no	—
238	C₅×C₂²⋊C₄	—	3	2	no	—
239	C₅×C₂²⋊C₄	—	3	2	no	—
240	C₅×C₂²⋊C₄	—	3	2	no	—
241	C₄²×C₅	—	3	1	no	—
242	C₄²×C₅	—	3	1	no	—
243	C₄²×C₅	—	3	1	no	—
244	C₄²×C₅	—	3	1	no	—
245	C₂×#131	—	3	1	no	—
246	C₂×#131	—	3	1	no	—
247	#532	—	3	1	no	—
248	#436	—	3	2	no	—
249	#435	—	3	2	no	—
250	#435	—	3	2	no	—
251	C₈×D₄	—	3	2	no	—
252	C₂×C₄⋊C₈	—	3	1	no	—
253	#408	—	3	1	no	—
254	#408	C₅×D₃	1	1	yes	characteristic, complemented
255	C₄×M₁₆	—	3	1	no	—
256	C₂²×C₃×C₅	—	2	1	no	—
257	C₂²×C₃×C₅	—	2	1	no	—
258	C₂²×C₃×C₅	—	2	2	no	—
259	C₂²×C₃×C₅	—	2	2	no	—
260	C₂²×C₃×C₅	—	2	2	no	—
261	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₅×D₃	—	2	2	no	—
264	C₂×C₅×D₃	—	2	2	no	—
265	C₂×C₅×D₃	—	2	2	no	—
266	C₃×C₄×C₅	—	2	2	no	—
267	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
268	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
270	C₅×Dic₃	—	2	2	no	—
271	C₅×Dic₃	—	2	1	no	—
272	C₅×Dic₃	—	2	1	no	—
273	C₅×Dic₃	—	2	1	no	—
274	C₅×Dic₃	#131	1	2	yes	complemented
275	C₃×#41	—	2	2	no	—
276	C₃×#41	—	2	2	no	—
277	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂×#67	C₂×C₄×C₅	1	2	yes	—
283	C₂×#67	C₂×C₄×C₅	1	2	yes	—
284	C₂×#67	C₂×C₄×C₅	1	2	yes	—
285	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
287	#235	—	2	2	no	—
288	#235	—	2	2	no	—
289	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
291	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
292	C₃×M₁₆	—	2	2	no	—
293	C₂×C₃×C₈	—	2	2	no	—
294	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
295	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
297	#217	C₂×C₄×C₅	1	2	yes	—
298	#217	C₂×C₄×C₅	1	2	yes	—
299	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
300	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
301	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
302	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
303	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
304	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
305	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
306	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
307	#208	—	2	4	no	—
308	#208	C₅×D₄	1	4	yes	complemented
309	C₂×C₃⋊C₈	—	2	2	no	—
310	C₂×C₃⋊C₈	—	2	4	no	—
311	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
313	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
314	ΓL(1,𝔽₂₅)	—	2	4	no	—
315	D₃×C₈	—	2	4	no	—
316	C₂³×C₅	—	3	2	no	—
317	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
318	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
319	C₅×Q₈	—	2	2	no	—
320	C₅×Q₈	—	6	2	no	—
321	C₅×D₄	—	2	4	no	—
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	6	4	no	—
324	C₅×D₄	—	6	4	no	—
325	C₅×D₄	—	6	2	no	—
326	C₅×D₄	—	12	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	3	1	no	—
330	C₂×C₄×C₅	—	3	1	no	—
331	C₂×C₄×C₅	—	3	1	no	—
332	C₂×C₄×C₅	—	3	1	no	—
333	C₂×C₄×C₅	—	3	2	no	—
334	C₂×C₄×C₅	—	6	2	no	—
335	C₂×C₄×C₅	—	6	2	no	—
336	C₂×C₄×C₅	—	6	2	no	—
337	C₂×C₄×C₅	—	12	1	no	—
338	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
339	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
340	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
341	C₂×C₄×C₅	#237	1	2	yes	—
342	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	2	1	no	—
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	—	3	4	no	—
347	C₅×C₈	—	6	1	no	—
348	C₅×C₈	—	6	1	no	—
349	C₂×#41	—	3	1	no	—
350	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
351	#131	—	6	4	no	—
352	#131	—	6	4	no	—
353	C₂×M₁₆	—	3	1	no	—
354	C₂×M₁₆	—	3	2	no	—
355	C₂×M₁₆	—	3	2	no	—
356	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
357	C₂²×C₈	—	3	1	no	—
358	C₂²×C₈	—	3	2	no	—
359	C₂²×C₈	—	3	2	no	—
360	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
361	C₄⋊Q₈	—	3	1	no	—
362	#127	—	3	1	no	—
363	#124	—	3	1	no	—
364	#124	—	3	1	no	—
365	#121	—	3	2	no	—
366	#121	—	3	2	no	—
367	C₄×D₄	—	3	2	no	—
368	C₄×D₄	—	3	2	no	—
369	C₂×C₄²	—	3	1	no	—
370	C₄⋊C₈	—	3	1	no	—
371	C₄⋊C₈	—	3	1	no	—
372	C₄⋊C₈	—	3	1	no	—
373	C₄⋊C₈	—	3	1	no	—
374	C₂²⋊C₈	—	3	2	no	—
375	C₂²⋊C₈	—	3	2	no	—
376	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
377	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
378	#97	—	3	2	no	—
379	C₄×C₈	—	3	2	no	—
380	C₂×C₃×C₅	—	2	2	no	—
381	C₂×C₃×C₅	—	4	2	no	—
382	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
383	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
384	C₂×C₃×C₅	#568	1	1	yes	characteristic
385	C₅×D₃	—	4	2	no	—
386	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
387	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
389	C₃×Q₈	—	2	2	no	—
390	C₃×D₄	—	2	4	no	—
391	C₃×D₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
395	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
397	C₂×C₃×C₄	C₅×#41	1	2	yes	—
398	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
399	#67	—	2	4	no	—
400	#67	—	2	4	no	—
401	#67	—	4	2	no	—
402	C₂×Dic₃	—	2	2	no	—
403	C₂×Dic₃	—	4	1	no	—
404	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
405	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
406	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
407	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
408	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
409	D₁₂	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	2	2	no	—
412	Dic₆	—	2	2	no	—
413	C₃×C₈	—	2	1	no	—
414	C₃×C₈	—	2	1	no	—
415	C₃×C₈	—	2	2	no	—
416	C₃⋊C₈	—	2	1	no	—
417	C₃⋊C₈	—	2	1	no	—
418	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	6	2	no	—
425	C₂²×C₅	—	6	2	no	—
426	C₂²×C₅	—	6	2	no	—
427	C₂²×C₅	#67⋊C₄	1	2	yes	—
428	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	3	2	no	—
431	C₄×C₅	—	6	2	no	—
432	C₄×C₅	—	6	1	no	—
433	C₄×C₅	—	6	1	no	—
434	C₄×C₅	—	6	1	no	—
435	C₄×C₅	#67⋊C₄	1	2	yes	—
436	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
437	C₄×C₅	C₂×#237	1	1	yes	characteristic
438	#41	—	2	2	no	—
439	#41	—	2	2	no	—
440	#41	—	6	2	no	—
441	#41	—	6	2	no	—
442	C₂×Q₈	—	3	1	no	—
443	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	1	no	—
448	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
449	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
454	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
455	M₁₆	—	2	2	no	—
456	M₁₆	—	3	4	no	—
457	M₁₆	—	6	4	no	—
458	M₁₆	—	6	4	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	3	2	no	—
461	C₂×C₈	—	3	1	no	—
462	C₂×C₈	—	3	1	no	—
463	C₂×C₈	—	6	4	no	—
464	C₂×C₈	—	6	4	no	—
465	C₂×C₈	—	6	2	no	—
466	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
467	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₄²	—	3	1	no	—
476	C₄²	—	3	1	no	—
477	C₄²	—	3	1	no	—
478	C₄²	—	3	1	no	—
479	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
486	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
487	C₂×D₃	—	2	2	no	—
488	C₂×D₃	—	2	2	no	—
489	C₂×D₃	—	2	2	no	—
490	C₃×C₄	—	2	2	no	—
491	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
492	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
493	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
494	Dic₃	—	2	2	no	—
495	Dic₃	—	2	1	no	—
496	Dic₃	—	2	1	no	—
497	Dic₃	—	2	1	no	—
498	Dic₃	C₅×#131	1	2	yes	complemented
499	C₂×C₅	—	2	2	no	—
500	C₂×C₅	—	4	2	no	—
501	C₂×C₅	—	12	2	no	—
502	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
503	C₂×C₅	D₃×#131	1	1	yes	characteristic
504	C₂×C₅	#5750	1	1	yes	characteristic
505	C₂³	—	3	2	no	—
506	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
507	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
508	Q₈	—	2	2	no	—
509	Q₈	—	6	2	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	2	no	—
512	D₄	—	6	4	no	—
513	D₄	—	6	4	no	—
514	D₄	—	6	2	no	—
515	D₄	—	12	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	3	1	no	—
519	C₂×C₄	—	3	1	no	—
520	C₂×C₄	—	3	1	no	—
521	C₂×C₄	—	3	1	no	—
522	C₂×C₄	—	3	2	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	—	6	2	no	—
525	C₂×C₄	—	6	2	no	—
526	C₂×C₄	—	12	1	no	—
527	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
528	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
529	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
530	C₂×C₄	C₅×#237	1	2	yes	—
531	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	2	no	—
535	C₈	—	3	4	no	—
536	C₈	—	6	1	no	—
537	C₈	—	6	1	no	—
538	C₂×C₃	—	2	2	no	—
539	C₂×C₃	—	4	2	no	—
540	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
541	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
542	C₂×C₃	C₅×#568	1	1	yes	characteristic
543	D₃	—	4	2	no	—
544	C₅	#78660	1	1	yes	characteristic, direct product factor, Sylow
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	6	2	no	—
551	C₂²	—	6	2	no	—
552	C₂²	—	6	2	no	—
553	C₂²	C₅×#67⋊C₄	1	2	yes	—
554	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	3	2	no	—
557	C₄	—	6	2	no	—
558	C₄	—	6	1	no	—
559	C₄	—	6	1	no	—
560	C₄	—	6	1	no	—
561	C₄	C₅×#67⋊C₄	1	2	yes	—
562	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
563	C₄	C₂×C₅×#237	1	1	yes	characteristic
564	C₃	C₅×#2935	1	1	yes	characteristic, complemented, Sylow
565	C₂	—	2	2	no	—
566	C₂	—	4	2	no	—
567	C₂	—	12	2	no	—
568	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
569	C₂	C₅×D₃×#131	1	1	yes	characteristic
570	C₂	C₅×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#408	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₅×#5832	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#408	D₃
hypocenter	C₃	C₅×#2935
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂×C₅×#901	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₅×#5129	C₂	semidirect
6. C₅×Dic₃×M₁₆	C₂	semidirect
7. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
8. C₅×#4730	C₂	semidirect
9. C₅×#4729	C₂	semidirect
10. C₅×#4728	C₂	semidirect
11. C₅×#67⋊C₈	C₂	semidirect
44. #78660	C₅	direct (N × H)
54. C₅×#408	D₃	semidirect
89. C₅×#208	D₄	semidirect
98. C₂×#948	C₂×C₅	semidirect
99. C₂×#901	C₂×C₅	semidirect
100. C₃×#408	C₂×C₅	semidirect
101. #5129	C₂×C₅	semidirect
102. Dic₃×M₁₆	C₂×C₅	semidirect
103. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
104. #4730	C₂×C₅	semidirect
105. #4729	C₂×C₅	semidirect
106. #4728	C₂×C₅	semidirect
107. #67⋊C₈	C₂×C₅	semidirect
254. #408	C₅×D₃	semidirect
274. C₅×Dic₃	#131	semidirect
308. #208	C₅×D₄	semidirect
479. C₃×C₅	#2935	semidirect
498. Dic₃	C₅×#131	semidirect
544. C₅	#78660	direct (N × H)
564. C₃	C₅×#2935	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5832	2
C₂×C₅×#948	2
C₂×C₅×#901	2
C₃×C₅×#408	2
C₅×#5129	2
C₅×Dic₃×M₁₆	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#4730	2
C₅×#4729	2
C₅×#4728	2
C₅×#67⋊C₈	2
C₅×#2935	3
#78660	5

Subgroups — C5×#78660 #14415828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78660 #14415828