Subgroups — C₅×#78600 #14411800

Order 1920.

1548 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#901	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5110	C₂	1	2	yes	maximal, complemented
6	C₅×#4727	C₂	1	4	yes	maximal, complemented
7	C₅×#4726	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₅×#2880	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₄	1	2	yes	—
12	C₂×C₅×#235	—	2	8	no	—
13	C₂×C₅×#235	C₄	1	2	yes	—
14	C₂×C₅×#235	C₄	1	1	yes	characteristic
15	C₂×C₅×#235	C₄	1	1	yes	characteristic
16	C₂×C₅×#235	C₂²	1	2	yes	—
17	C₂×C₅×#235	C₂²	1	1	yes	characteristic
18	C₂×C₅×#235	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
21	C₂²×C₅×Dic₆	C₄	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
23	C₂×C₅×#208	C₂²	1	2	yes	complemented
24	C₅×#901	—	2	8	no	—
25	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
26	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
27	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
30	C₅×#830	C₂²	1	2	yes	—
31	C₅×#830	C₂²	1	2	yes	complemented
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
33	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
34	#78600	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₅×#41	—	3	1	no	—
36	C₂×C₅×#131	—	3	2	no	—
37	C₅×#408	—	3	4	no	—
38	C₅×#408	—	3	2	no	—
39	C₅×#407	—	3	2	no	—
40	C₅×#407	—	3	1	no	—
41	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
42	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
43	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₅×#67	—	2	8	no	—
53	C₂×C₅×#67	C₂×C₄	1	2	yes	—
54	C₂×C₅×#67	C₂×C₄	1	2	yes	—
55	C₂×C₅×#67	C₂×C₄	1	2	yes	—
56	C₂×C₅×#67	C₂×C₄	1	2	yes	—
57	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
58	C₅×#235	—	2	4	no	—
59	C₅×#235	—	2	8	no	—
60	C₅×#235	—	2	4	no	—
61	C₅×#235	—	2	8	no	—
62	C₅×#235	—	2	4	no	—
63	C₅×#235	D₄	1	8	yes	—
64	C₂×C₅×D₁₂	—	2	4	no	—
65	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
66	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
67	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	—	2	8	no	—
69	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
70	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
71	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
72	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
73	C₂×C₅×Dic₆	—	2	4	no	—
74	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
76	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	—	2	4	no	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₅×#208	—	2	4	no	—
81	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
82	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
83	C₅×D₃×C₈	—	2	8	no	—
84	C₂²×#235	C₂×C₅	1	1	yes	characteristic
85	C₂×#901	C₂×C₅	1	2	yes	complemented
86	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
87	#5207	C₂×C₅	1	1	yes	characteristic, complemented
88	#5110	C₂×C₅	1	2	yes	complemented
89	#4727	C₂×C₅	1	4	yes	complemented
90	#4726	C₂×C₅	1	2	yes	complemented
91	D₃×C₂²⋊C₈	C₂×C₅	1	2	yes	complemented
92	C₂×C₅×#41	—	3	2	no	—
93	C₂×C₅×#41	—	3	1	no	—
94	C₂×C₅×#41	—	3	1	no	—
95	C₂×C₅×#41	—	3	1	no	—
96	C₂×C₅×#41	—	3	2	no	—
97	C₂×C₅×#41	—	3	1	no	—
98	C₂×C₅×#41	—	6	8	no	—
99	C₂²×C₅×Q₈	—	3	1	no	—
100	C₂²×C₅×D₄	—	3	2	no	—
101	C₂²×C₅×D₄	—	3	1	no	—
102	C₂³×C₄×C₅	—	3	2	no	—
103	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
104	C₅×#131	—	6	8	no	—
105	C₂×C₅×M₁₆	—	3	2	no	—
106	C₂×C₅×M₁₆	—	3	4	no	—
107	C₂²×C₅×C₈	—	3	4	no	—
108	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
109	C₅×C₂²⋊C₈	—	3	2	no	—
110	C₅×C₂²⋊C₈	—	3	2	no	—
111	C₅×C₂²⋊C₈	—	3	4	no	—
112	C₅×C₂²⋊C₈	—	3	4	no	—
113	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
114	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
116	#2880	—	3	1	no	Sylow
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	4	1	no	—
120	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₅×D₃	—	2	4	no	—
124	C₂²×C₅×D₃	—	2	4	no	—
125	C₂²×C₅×D₃	—	4	2	no	—
126	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₅×#67	—	2	4	no	—
139	C₅×#67	—	2	4	no	—
140	C₅×#67	—	2	4	no	—
141	C₅×#67	C₂²⋊C₄	1	8	yes	—
142	C₂×C₅×Dic₃	—	2	4	no	—
143	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
144	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
145	C₅×D₁₂	—	2	4	no	—
146	C₅×D₁₂	—	2	2	no	—
147	C₅×D₁₂	C₂²⋊C₄	1	4	yes	—
148	C₄×C₅×D₃	—	2	4	no	—
149	C₄×C₅×D₃	—	2	4	no	—
150	C₄×C₅×D₃	—	2	4	no	—
151	C₄×C₅×D₃	C₂×D₄	1	8	yes	—
152	C₅×Dic₆	—	2	2	no	—
153	C₅×Dic₆	—	2	4	no	—
154	C₅×Dic₆	C₂²⋊C₄	1	4	yes	—
155	C₃×C₅×C₈	—	2	2	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₅×C₃⋊C₈	—	2	4	no	—
158	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
159	C₂²×#67	C₄×C₅	1	2	yes	—
160	C₂×#235	—	2	8	no	—
161	C₂×#235	C₄×C₅	1	2	yes	—
162	C₂×#235	C₄×C₅	1	1	yes	characteristic
163	C₂×#235	C₄×C₅	1	1	yes	characteristic
164	C₂×#235	C₂²×C₅	1	2	yes	—
165	C₂×#235	C₂²×C₅	1	1	yes	characteristic
166	C₂×#235	C₂²×C₅	1	1	yes	characteristic
167	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
168	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
169	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
171	C₂×#208	C₂²×C₅	1	2	yes	complemented
172	#901	—	2	8	no	—
173	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	complemented
174	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
175	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
178	#830	C₂²×C₅	1	2	yes	—
179	#830	C₂²×C₅	1	2	yes	complemented
180	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
181	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
182	C₂⁴×C₅	—	3	2	no	—
183	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
184	C₅×#41	—	3	8	no	—
185	C₅×#41	—	6	8	no	—
186	C₅×#41	—	6	8	no	—
187	C₅×#41	—	6	4	no	—
188	C₅×#41	—	6	4	no	—
189	C₅×#41	—	6	4	no	—
190	C₂×C₅×Q₈	—	3	1	no	—
191	C₂×C₅×Q₈	—	3	2	no	—
192	C₂×C₅×Q₈	—	3	1	no	—
193	C₂×C₅×Q₈	—	6	4	no	—
194	C₂×C₅×D₄	—	3	2	no	—
195	C₂×C₅×D₄	—	3	2	no	—
196	C₂×C₅×D₄	—	3	2	no	—
197	C₂×C₅×D₄	—	3	2	no	—
198	C₂×C₅×D₄	—	3	1	no	—
199	C₂×C₅×D₄	—	3	2	no	—
200	C₂×C₅×D₄	—	3	1	no	—
201	C₂×C₅×D₄	—	6	4	no	—
202	C₂×C₅×D₄	—	6	8	no	—
203	C₂²×C₄×C₅	—	2	4	no	—
204	C₂²×C₄×C₅	—	3	2	no	—
205	C₂²×C₄×C₅	—	3	2	no	—
206	C₂²×C₄×C₅	—	3	2	no	—
207	C₂²×C₄×C₅	—	3	2	no	—
208	C₂²×C₄×C₅	—	3	2	no	—
209	C₂²×C₄×C₅	—	6	8	no	—
210	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₅×M₁₆	—	6	8	no	—
217	C₅×M₁₆	—	6	4	no	—
218	C₂×C₅×C₈	—	2	4	no	—
219	C₂×C₅×C₈	—	3	4	no	—
220	C₂×C₅×C₈	—	6	8	no	—
221	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
222	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
223	C₂²×#41	—	3	1	no	—
224	C₂×#131	—	3	2	no	—
225	#408	—	3	2	no	—
226	#408	—	3	4	no	—
227	#407	—	3	1	no	—
228	#407	—	3	2	no	—
229	C₂×C₂²⋊C₈	—	3	2	no	—
230	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
231	C₂²×C₃×C₅	—	2	1	no	—
232	C₂²×C₃×C₅	—	2	1	no	—
233	C₂²×C₃×C₅	—	2	1	no	—
234	C₂²×C₃×C₅	—	2	1	no	—
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	1	no	—
237	C₂²×C₃×C₅	—	2	1	no	—
238	C₂²×C₃×C₅	—	4	4	no	—
239	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂²×C₃×C₅	#131	1	2	yes	complemented
241	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₂×C₅×D₃	—	2	2	no	—
243	C₂×C₅×D₃	—	2	2	no	—
244	C₂×C₅×D₃	—	2	2	no	—
245	C₂×C₅×D₃	—	2	2	no	—
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	4	8	no	—
248	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
249	C₃×C₄×C₅	—	2	1	no	—
250	C₃×C₄×C₅	—	2	1	no	—
251	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
252	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
253	C₅×Dic₃	—	2	2	no	—
254	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
255	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
256	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
257	C₂²×C₃×C₄	—	2	4	no	—
258	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂×#67	—	2	8	no	—
265	C₂×#67	C₂×C₄×C₅	1	2	yes	—
266	C₂×#67	C₂×C₄×C₅	1	2	yes	—
267	C₂×#67	C₂×C₄×C₅	1	2	yes	—
268	C₂×#67	C₂×C₄×C₅	1	2	yes	—
269	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
270	#235	—	2	4	no	—
271	#235	—	2	8	no	—
272	#235	—	2	4	no	—
273	#235	—	2	8	no	—
274	#235	—	2	4	no	—
275	#235	C₅×D₄	1	8	yes	—
276	C₂×D₁₂	—	2	4	no	—
277	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
278	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂×C₄×D₃	—	2	8	no	—
281	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
282	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
283	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
284	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
285	C₂×Dic₆	—	2	4	no	—
286	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
287	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
288	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
289	C₂×C₃×C₈	—	2	4	no	—
290	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
291	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
292	#208	—	2	4	no	—
293	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
294	ΓL(1,𝔽₂₅)	—	2	8	no	—
295	D₃×C₈	—	2	8	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	3	2	no	—
299	C₂³×C₅	—	3	2	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	6	4	no	—
302	C₂³×C₅	—	6	4	no	—
303	C₂³×C₅	—	12	2	no	—
304	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
305	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
306	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
307	C₅×Q₈	—	3	4	no	—
308	C₅×Q₈	—	6	4	no	—
309	C₅×Q₈	—	6	2	no	—
310	C₅×D₄	—	3	8	no	—
311	C₅×D₄	—	3	4	no	—
312	C₅×D₄	—	6	4	no	—
313	C₅×D₄	—	6	4	no	—
314	C₅×D₄	—	6	4	no	—
315	C₅×D₄	—	6	4	no	—
316	C₅×D₄	—	6	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	3	2	no	—
323	C₂×C₄×C₅	—	3	8	no	—
324	C₂×C₄×C₅	—	3	2	no	—
325	C₂×C₄×C₅	—	6	4	no	—
326	C₂×C₄×C₅	—	6	4	no	—
327	C₂×C₄×C₅	—	6	4	no	—
328	C₂×C₄×C₅	—	6	4	no	—
329	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
332	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
333	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
334	C₅×C₈	—	2	2	no	—
335	C₅×C₈	—	2	2	no	—
336	C₅×C₈	—	6	4	no	—
337	C₂×#41	—	3	2	no	—
338	C₂×#41	—	3	1	no	—
339	C₂×#41	—	3	1	no	—
340	C₂×#41	—	3	1	no	—
341	C₂×#41	—	3	2	no	—
342	C₂×#41	—	3	1	no	—
343	C₂×#41	—	6	8	no	—
344	C₂²×Q₈	—	3	1	no	—
345	C₂²×D₄	—	3	2	no	—
346	C₂²×D₄	—	3	1	no	—
347	C₂³×C₄	—	3	2	no	—
348	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
349	#131	—	6	8	no	—
350	C₂×M₁₆	—	3	2	no	—
351	C₂×M₁₆	—	3	4	no	—
352	C₂²×C₈	—	3	4	no	—
353	C₂²×C₈	C₂×C₅×D₃	1	2	yes	complemented
354	C₂²⋊C₈	—	3	2	no	—
355	C₂²⋊C₈	—	3	2	no	—
356	C₂²⋊C₈	—	3	4	no	—
357	C₂²⋊C₈	—	3	4	no	—
358	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
359	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
360	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
361	C₂×C₃×C₅	—	2	2	no	—
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	—	4	1	no	—
364	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
366	C₂×C₃×C₅	#568	1	1	yes	characteristic
367	C₅×D₃	—	2	4	no	—
368	C₅×D₃	—	4	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	—	4	1	no	—
372	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
374	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
375	C₂²×D₃	—	2	4	no	—
376	C₂²×D₃	—	2	4	no	—
377	C₂²×D₃	—	4	2	no	—
378	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
379	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
389	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
390	#67	—	2	4	no	—
391	#67	—	2	4	no	—
392	#67	—	2	4	no	—
393	#67	C₅×C₂²⋊C₄	1	8	yes	—
394	C₂×Dic₃	—	2	4	no	—
395	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
396	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
397	D₁₂	—	2	4	no	—
398	D₁₂	—	2	2	no	—
399	D₁₂	C₅×C₂²⋊C₄	1	4	yes	—
400	C₄×D₃	—	2	4	no	—
401	C₄×D₃	—	2	4	no	—
402	C₄×D₃	—	2	4	no	—
403	C₄×D₃	C₂×C₅×D₄	1	8	yes	—
404	Dic₆	—	2	2	no	—
405	Dic₆	—	2	4	no	—
406	Dic₆	C₅×C₂²⋊C₄	1	4	yes	—
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	2	no	—
409	C₃⋊C₈	—	2	4	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	1	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	3	4	no	—
418	C₂²×C₅	—	4	4	no	—
419	C₂²×C₅	—	6	2	no	—
420	C₂²×C₅	—	6	2	no	—
421	C₂²×C₅	—	6	2	no	—
422	C₂²×C₅	—	6	2	no	—
423	C₂²×C₅	—	6	2	no	—
424	C₂²×C₅	—	12	8	no	—
425	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
426	C₂²×C₅	#901	1	2	yes	complemented
427	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	3	4	no	—
431	C₄×C₅	—	6	2	no	—
432	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
433	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
434	C₂⁴	—	3	2	no	—
435	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
436	#41	—	3	8	no	—
437	#41	—	6	8	no	—
438	#41	—	6	8	no	—
439	#41	—	6	4	no	—
440	#41	—	6	4	no	—
441	#41	—	6	4	no	—
442	C₂×Q₈	—	3	1	no	—
443	C₂×Q₈	—	3	2	no	—
444	C₂×Q₈	—	3	1	no	—
445	C₂×Q₈	—	6	4	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	2	no	—
448	C₂×D₄	—	3	2	no	—
449	C₂×D₄	—	3	2	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	3	1	no	—
453	C₂×D₄	—	6	4	no	—
454	C₂×D₄	—	6	8	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	3	2	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	2	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	6	8	no	—
462	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
463	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
464	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
468	M₁₆	—	6	8	no	—
469	M₁₆	—	6	4	no	—
470	C₂×C₈	—	2	4	no	—
471	C₂×C₈	—	3	4	no	—
472	C₂×C₈	—	6	8	no	—
473	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
474	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
475	C₃×C₅	#2880	1	1	yes	characteristic, complemented, Hall
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	4	4	no	—
484	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
485	C₂²×C₃	C₅×#131	1	2	yes	complemented
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	C₂×D₃	—	2	2	no	—
491	C₂×D₃	—	2	2	no	—
492	C₂×D₃	—	4	8	no	—
493	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
497	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
498	Dic₃	—	2	2	no	—
499	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
500	C₂×C₅	—	2	2	no	—
501	C₂×C₅	—	2	2	no	—
502	C₂×C₅	—	4	1	no	—
503	C₂×C₅	—	6	4	no	—
504	C₂×C₅	—	12	2	no	—
505	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
506	C₂×C₅	C₂×#901	1	1	yes	characteristic
507	C₂×C₅	#5745	1	1	yes	characteristic
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	3	2	no	—
511	C₂³	—	3	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	6	4	no	—
514	C₂³	—	6	4	no	—
515	C₂³	—	12	2	no	—
516	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
517	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
518	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
519	Q₈	—	3	4	no	—
520	Q₈	—	6	4	no	—
521	Q₈	—	6	2	no	—
522	D₄	—	3	8	no	—
523	D₄	—	3	4	no	—
524	D₄	—	6	4	no	—
525	D₄	—	6	4	no	—
526	D₄	—	6	4	no	—
527	D₄	—	6	4	no	—
528	D₄	—	6	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	3	2	no	—
535	C₂×C₄	—	3	8	no	—
536	C₂×C₄	—	3	2	no	—
537	C₂×C₄	—	6	4	no	—
538	C₂×C₄	—	6	4	no	—
539	C₂×C₄	—	6	4	no	—
540	C₂×C₄	—	6	4	no	—
541	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
542	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
543	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
544	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
545	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	6	4	no	—
549	C₂×C₃	—	2	2	no	—
550	C₂×C₃	—	2	2	no	—
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
553	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
554	C₂×C₃	C₅×#568	1	1	yes	characteristic
555	D₃	—	2	4	no	—
556	D₃	—	4	2	no	—
557	C₅	#78600	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	3	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	6	2	no	—
568	C₂²	—	6	2	no	—
569	C₂²	—	6	2	no	—
570	C₂²	—	6	2	no	—
571	C₂²	—	6	2	no	—
572	C₂²	—	12	8	no	—
573	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
574	C₂²	C₅×#901	1	2	yes	complemented
575	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	3	4	no	—
579	C₄	—	6	2	no	—
580	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
581	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
582	C₃	C₅×#2880	1	1	yes	characteristic, complemented, Sylow
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	6	4	no	—
587	C₂	—	12	2	no	—
588	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
589	C₂	C₂×C₅×#901	1	1	yes	characteristic
590	C₂	C₅×#5745	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	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₅×#2880
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×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×#901	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
4. C₅×#5207	C₂	semidirect
5. C₅×#5110	C₂	semidirect
6. C₅×#4727	C₂	semidirect
7. C₅×#4726	C₂	semidirect
8. C₅×D₃×C₂²⋊C₈	C₂	semidirect
22. C₂²×C₃×C₅×C₈	C₂²	semidirect
23. C₂×C₅×#208	C₂²	semidirect
25. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
26. C₂×C₅×D₃×C₈	C₂²	semidirect
29. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
31. C₅×#830	C₂²	semidirect
32. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
33. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
34. #78600	C₅	direct (N × H)
42. C₂×C₅×C₂²⋊C₈	D₃	semidirect
85. C₂×#901	C₂×C₅	semidirect
86. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
87. #5207	C₂×C₅	semidirect
88. #5110	C₂×C₅	semidirect
89. #4727	C₂×C₅	semidirect
90. #4726	C₂×C₅	semidirect
91. D₃×C₂²⋊C₈	C₂×C₅	semidirect
108. C₂²×C₅×C₈	C₂×D₃	semidirect
115. C₅×C₂²⋊C₈	C₂×D₃	semidirect
170. C₂²×C₃×C₈	C₂²×C₅	semidirect
171. C₂×#208	C₂²×C₅	semidirect
173. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
174. C₂×D₃×C₈	C₂²×C₅	semidirect
177. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
179. #830	C₂²×C₅	semidirect
180. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
181. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
230. C₂×C₂²⋊C₈	C₅×D₃	semidirect
240. C₂²×C₃×C₅	#131	semidirect
353. C₂²×C₈	C₂×C₅×D₃	semidirect
360. C₂²⋊C₈	C₂×C₅×D₃	semidirect
426. C₂²×C₅	#901	semidirect
475. C₃×C₅	#2880	semidirect
485. C₂²×C₃	C₅×#131	semidirect
557. C₅	#78600	direct (N × H)
574. C₂²	C₅×#901	semidirect
582. C₃	C₅×#2880	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×C₅×#901	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#5207	2
C₅×#5110	2
C₅×#4727	2
C₅×#4726	2
C₅×D₃×C₂²⋊C₈	2
C₅×#2880	3
#78600	5

Subgroups — C5×#78600 #14411800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78600 #14411800