Subgroups — C₅×#80714 #14427795

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#912	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5606	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5157	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5116	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5041	C₂	1	2	yes	maximal, complemented
8	C₅×#4887	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4880	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4778	C₂	1	2	yes	maximal, complemented
11	C₅×#4772	C₂	1	2	yes	maximal, complemented
12	C₅×#3050	—	3	1	no	maximal, Hall
13	C₂×C₅×#237	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#121	C₂²	1	2	yes	—
18	C₅×#938	C₂²	1	2	yes	—
19	C₅×#937	—	2	2	no	—
20	C₅×D₄×Dic₃	—	2	2	no	—
21	C₂×C₅×#214	C₂²	1	2	yes	complemented
22	C₅×#924	C₂²	1	2	yes	—
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₅×#912	—	2	4	no	—
25	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₃×C₈	—	2	4	no	—
27	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
31	C₅×#897	C₂²	1	2	yes	—
32	C₅×#892	C₂²	1	2	yes	—
33	C₅×#883	—	2	2	no	—
34	C₅×#67⋊C₄	—	2	2	no	—
35	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₅×#832	C₂²	1	2	yes	complemented
38	C₅×#818	C₂²	1	1	yes	characteristic, complemented
39	C₅×#816	C₂²	1	2	yes	complemented
40	C₅×#810	C₂²	1	2	yes	complemented
41	C₅×#808	C₂²	1	2	yes	complemented
42	#80714	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂×C₅×#135	—	3	1	no	—
44	C₂³×C₅×C₈	—	3	1	no	—
45	C₅×#525	—	3	2	no	—
46	C₅×#467	—	3	1	no	—
47	C₅×#467	—	3	1	no	—
48	C₅×#466	—	3	1	no	—
49	C₅×#466	D₃	1	1	yes	characteristic, complemented
50	C₅×#465	—	3	2	no	—
51	C₅×#465	—	3	2	no	—
52	C₅×#427	—	3	1	no	—
53	C₅×#416	—	3	2	no	—
54	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×#67	—	2	2	no	—
59	C₂×C₅×#67	—	2	2	no	—
60	C₂²×C₅×Dic₃	—	2	2	no	—
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₅×#237	—	2	4	no	—
63	C₅×#237	—	2	4	no	—
64	C₂×C₄×C₅×D₃	—	2	2	no	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂×C₅×Dic₆	C₂³	1	2	yes	—
71	C₃×C₅×D₈	—	2	2	no	—
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	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₅×#217	—	2	2	no	—
78	C₅×#217	—	2	2	no	—
79	C₅×#214	—	2	4	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₅×C₄⋊Dic₃	—	2	2	no	—
83	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₄×C₅×Dic₃	—	2	2	no	—
86	C₂×C₅×C₃⋊C₈	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×Dic₁₂	—	2	2	no	—
90	C₅×D₃×C₈	—	2	2	no	—
91	C₅×D₃×C₈	—	2	2	no	—
92	C₅×D₃×C₈	—	2	2	no	—
93	C₅×D₃×C₈	D₄	1	4	yes	complemented
94	C₂×#912	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
96	#5606	C₂×C₅	1	2	yes	complemented
97	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
98	#5157	C₂×C₅	1	1	yes	characteristic, complemented
99	#5116	C₂×C₅	1	1	yes	characteristic, complemented
100	#5041	C₂×C₅	1	2	yes	complemented
101	#4887	C₂×C₅	1	1	yes	characteristic, complemented
102	#4880	C₂×C₅	1	1	yes	characteristic, complemented
103	#4778	C₂×C₅	1	2	yes	complemented
104	#4772	C₂×C₅	1	2	yes	complemented
105	C₂×C₅×#41	—	3	2	no	—
106	C₂³×C₄×C₅	—	3	1	no	—
107	C₅×#135	—	6	4	no	—
108	C₂×C₅×Q₁₆	—	3	1	no	—
109	C₂×C₅×SD₁₆	—	3	2	no	—
110	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
111	C₂²×C₅×C₈	—	3	1	no	—
112	C₂²×C₅×C₈	—	3	1	no	—
113	C₂²×C₅×C₈	—	3	1	no	—
114	C₂²×C₅×C₈	—	3	1	no	—
115	C₂²×C₅×C₈	—	3	1	no	—
116	C₂²×C₅×C₈	—	6	4	no	—
117	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	C₅×#123	—	6	2	no	—
119	C₅×C₂²⋊Q₈	—	3	2	no	—
120	C₅×C₂²⋊Q₈	—	3	2	no	—
121	C₅×#121	—	3	2	no	—
122	C₅×#121	C₂×D₃	1	2	yes	—
123	C₅×#120	—	6	2	no	—
124	C₄×C₅×D₄	—	6	2	no	—
125	C₄×C₅×D₄	—	6	2	no	—
126	C₅×#117	—	3	2	no	—
127	C₅×#107	—	3	1	no	—
128	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
129	C₅×#106	—	3	2	no	—
130	C₅×#103	—	3	2	no	—
131	C₅×#103	—	3	2	no	—
132	C₅×#102	—	3	2	no	—
133	C₅×#102	C₂×D₃	1	2	yes	complemented
134	#3050	—	3	1	no	Sylow
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₅×D₃	—	2	2	no	—
138	C₂²×C₅×D₃	—	2	2	no	—
139	C₂²×C₅×D₃	—	2	2	no	—
140	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	4	4	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₅×#67	—	4	4	no	—
151	C₅×#67	—	4	4	no	—
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₂×C₅×Dic₃	—	2	2	no	—
154	C₂×C₅×Dic₃	—	2	2	no	—
155	C₂×C₅×Dic₃	—	4	4	no	—
156	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
158	C₄×C₅×D₃	—	2	2	no	—
159	C₄×C₅×D₃	—	2	1	no	—
160	C₄×C₅×D₃	—	2	1	no	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
163	C₄×C₅×D₃	#41	1	2	yes	—
164	C₅×Dic₆	—	2	2	no	—
165	C₅×Dic₆	—	2	2	no	—
166	C₃×C₅×C₈	—	2	1	no	—
167	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
168	C₅×C₃⋊C₈	—	2	1	no	—
169	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×#237	C₂²×C₅	1	2	yes	—
171	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
174	C₃×#121	C₂²×C₅	1	2	yes	—
175	#938	C₂²×C₅	1	2	yes	—
176	#937	—	2	2	no	—
177	D₄×Dic₃	—	2	2	no	—
178	C₂×#214	C₂²×C₅	1	2	yes	complemented
179	#924	C₂²×C₅	1	2	yes	—
180	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
181	#912	—	2	4	no	—
182	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂×D₃×C₈	—	2	4	no	—
184	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
185	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
187	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
188	#897	C₂²×C₅	1	2	yes	—
189	#892	C₂²×C₅	1	2	yes	—
190	#883	—	2	2	no	—
191	#67⋊C₄	—	2	2	no	—
192	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₃×#102	C₂²×C₅	1	2	yes	complemented
194	#832	C₂²×C₅	1	2	yes	complemented
195	#818	C₂²×C₅	1	1	yes	characteristic, complemented
196	#816	C₂²×C₅	1	2	yes	complemented
197	#810	C₂²×C₅	1	2	yes	complemented
198	#808	C₂²×C₅	1	2	yes	complemented
199	C₂⁴×C₅	—	3	1	no	—
200	C₅×#41	—	6	4	no	—
201	C₅×#41	—	6	4	no	—
202	C₂×C₅×Q₈	—	3	2	no	—
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	6	2	no	—
206	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	3	1	no	—
209	C₂²×C₄×C₅	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	1	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	6	2	no	—
213	C₂²×C₄×C₅	—	6	2	no	—
214	C₂²×C₄×C₅	—	6	2	no	—
215	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₅×Q₁₆	—	6	2	no	—
217	C₅×SD₁₆	—	6	4	no	—
218	C₅×D₈	—	2	2	no	—
219	C₂×C₅×C₈	—	2	2	no	—
220	C₂×C₅×C₈	—	3	1	no	—
221	C₂×C₅×C₈	—	3	4	no	—
222	C₂×C₅×C₈	—	3	1	no	—
223	C₂×C₅×C₈	—	6	2	no	—
224	C₂×C₅×C₈	—	6	2	no	—
225	C₂×C₅×C₈	—	6	2	no	—
226	C₂×C₅×C₈	—	6	2	no	—
227	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
229	C₅×C₄⋊C₄	—	3	2	no	—
230	C₅×C₄⋊C₄	—	6	2	no	—
231	C₅×C₄⋊C₄	—	6	2	no	—
232	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	6	2	no	—
235	C₅×C₂²⋊C₄	—	6	2	no	—
236	C₅×C₂²⋊C₄	—	6	2	no	—
237	C₅×C₂²⋊C₄	—	6	2	no	—
238	C₄²×C₅	—	6	2	no	—
239	C₂×#135	—	3	1	no	—
240	C₂³×C₈	—	3	1	no	—
241	#525	—	3	2	no	—
242	#467	—	3	1	no	—
243	#467	—	3	1	no	—
244	#466	—	3	1	no	—
245	#466	C₅×D₃	1	1	yes	characteristic, complemented
246	#465	—	3	2	no	—
247	#465	—	3	2	no	—
248	#427	—	3	1	no	—
249	#416	—	3	2	no	—
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	—	4	2	no	—
254	C₂²×C₃×C₅	—	4	2	no	—
255	C₂²×C₃×C₅	#135	1	2	yes	complemented
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₅×D₃	—	2	8	no	—
258	C₂×C₅×D₃	—	2	1	no	—
259	C₂×C₅×D₃	—	2	1	no	—
260	C₂×C₅×D₃	—	2	1	no	—
261	C₂×C₅×D₃	—	2	1	no	—
262	C₂×C₅×D₃	#121	1	2	yes	—
263	C₂×C₅×D₃	#135	1	2	yes	complemented
264	C₃×C₄×C₅	—	2	1	no	—
265	C₃×C₄×C₅	—	4	2	no	—
266	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
268	C₅×Dic₃	—	2	1	no	—
269	C₅×Dic₃	—	4	2	no	—
270	C₅×Dic₃	—	4	2	no	—
271	C₅×Dic₃	#121	1	2	yes	—
272	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
275	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂×#67	—	2	2	no	—
277	C₂×#67	—	2	2	no	—
278	C₂²×Dic₃	—	2	2	no	—
279	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
280	#237	—	2	4	no	—
281	#237	—	2	4	no	—
282	C₂×C₄×D₃	—	2	2	no	—
283	C₂×C₄×D₃	—	2	2	no	—
284	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
285	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
288	C₂×Dic₆	C₂³×C₅	1	2	yes	—
289	C₃×D₈	—	2	2	no	—
290	C₂×C₃×C₈	—	2	2	no	—
291	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
294	C₃×C₂²⋊C₄	—	2	2	no	—
295	#217	—	2	2	no	—
296	#217	—	2	2	no	—
297	#214	—	2	4	no	—
298	(C₂×D₃)⋊C₄	—	2	2	no	—
299	(C₂×D₃)⋊C₄	—	2	2	no	—
300	C₄⋊Dic₃	—	2	2	no	—
301	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
302	Dic₃⋊C₄	—	2	2	no	—
303	C₄×Dic₃	—	2	2	no	—
304	C₂×C₃⋊C₈	—	2	2	no	—
305	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
307	Dic₁₂	—	2	2	no	—
308	D₃×C₈	—	2	2	no	—
309	D₃×C₈	—	2	2	no	—
310	D₃×C₈	—	2	2	no	—
311	D₃×C₈	C₅×D₄	1	4	yes	complemented
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	—	3	1	no	—
314	C₂³×C₅	—	3	1	no	—
315	C₂³×C₅	—	6	2	no	—
316	C₂³×C₅	—	6	2	no	—
317	C₂³×C₅	—	6	2	no	—
318	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
319	C₅×Q₈	—	6	2	no	—
320	C₅×Q₈	—	6	2	no	—
321	C₅×D₄	—	2	2	no	—
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	4	4	no	—
324	C₅×D₄	—	12	4	no	—
325	C₅×D₄	—	12	4	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	3	1	no	—
330	C₂×C₄×C₅	—	3	2	no	—
331	C₂×C₄×C₅	—	3	2	no	—
332	C₂×C₄×C₅	—	3	1	no	—
333	C₂×C₄×C₅	—	6	2	no	—
334	C₂×C₄×C₅	—	6	2	no	—
335	C₂×C₄×C₅	—	6	2	no	—
336	C₂×C₄×C₅	—	6	1	no	—
337	C₂×C₄×C₅	—	6	1	no	—
338	C₂×C₄×C₅	—	6	2	no	—
339	C₂×C₄×C₅	—	6	2	no	—
340	C₂×C₄×C₅	—	12	4	no	—
341	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	3	2	no	—
345	C₅×C₈	—	6	1	no	—
346	C₅×C₈	D₃×D₄	1	2	yes	—
347	C₂×#41	—	3	2	no	—
348	C₂³×C₄	—	3	1	no	—
349	#135	—	6	4	no	—
350	C₂×Q₁₆	—	3	1	no	—
351	C₂×SD₁₆	—	3	2	no	—
352	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
353	C₂²×C₈	—	3	1	no	—
354	C₂²×C₈	—	3	1	no	—
355	C₂²×C₈	—	3	1	no	—
356	C₂²×C₈	—	3	1	no	—
357	C₂²×C₈	—	3	1	no	—
358	C₂²×C₈	—	6	4	no	—
359	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
360	#123	—	6	2	no	—
361	C₂²⋊Q₈	—	3	2	no	—
362	C₂²⋊Q₈	—	3	2	no	—
363	#121	—	3	2	no	—
364	#121	C₂×C₅×D₃	1	2	yes	—
365	#120	—	6	2	no	—
366	C₄×D₄	—	6	2	no	—
367	C₄×D₄	—	6	2	no	—
368	#117	—	3	2	no	—
369	#107	—	3	1	no	—
370	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
371	#106	—	3	2	no	—
372	#103	—	3	2	no	—
373	#103	—	3	2	no	—
374	#102	—	3	2	no	—
375	#102	C₂×C₅×D₃	1	2	yes	complemented
376	C₂×C₃×C₅	—	2	2	no	—
377	C₂×C₃×C₅	—	8	2	no	—
378	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
379	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
380	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
381	C₅×D₃	—	2	2	no	—
382	C₅×D₃	—	2	2	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂²×D₃	—	2	2	no	—
386	C₂²×D₃	—	2	2	no	—
387	C₂²×D₃	—	2	2	no	—
388	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₃×D₄	—	2	2	no	—
391	C₃×D₄	—	2	2	no	—
392	C₃×D₄	—	4	4	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
398	#67	—	4	4	no	—
399	#67	—	4	4	no	—
400	C₂×Dic₃	—	2	2	no	—
401	C₂×Dic₃	—	2	2	no	—
402	C₂×Dic₃	—	2	2	no	—
403	C₂×Dic₃	—	4	4	no	—
404	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	2	1	no	—
408	C₄×D₃	—	2	1	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
411	C₄×D₃	C₅×#41	1	2	yes	—
412	Dic₆	—	2	2	no	—
413	Dic₆	—	2	2	no	—
414	C₃×C₈	—	2	1	no	—
415	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
416	C₃⋊C₈	—	2	1	no	—
417	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	3	2	no	—
421	C₂²×C₅	—	3	2	no	—
422	C₂²×C₅	—	4	2	no	—
423	C₂²×C₅	—	4	2	no	—
424	C₂²×C₅	—	4	2	no	—
425	C₂²×C₅	—	6	8	no	—
426	C₂²×C₅	—	6	1	no	—
427	C₂²×C₅	—	6	1	no	—
428	C₂²×C₅	—	6	1	no	—
429	C₂²×C₅	—	6	1	no	—
430	C₂²×C₅	#912	1	2	yes	complemented
431	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	3	2	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	—	6	1	no	—
436	C₄×C₅	—	12	2	no	—
437	C₄×C₅	—	12	2	no	—
438	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
439	C₄×C₅	D₃×#41	1	1	yes	characteristic
440	C₂⁴	—	3	1	no	—
441	#41	—	6	4	no	—
442	#41	—	6	4	no	—
443	C₂×Q₈	—	3	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	6	2	no	—
446	C₂×D₄	—	6	2	no	—
447	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	6	2	no	—
454	C₂²×C₄	—	6	2	no	—
455	C₂²×C₄	—	6	2	no	—
456	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
457	Q₁₆	—	6	2	no	—
458	SD₁₆	—	6	4	no	—
459	D₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	3	1	no	—
462	C₂×C₈	—	3	4	no	—
463	C₂×C₈	—	3	1	no	—
464	C₂×C₈	—	6	2	no	—
465	C₂×C₈	—	6	2	no	—
466	C₂×C₈	—	6	2	no	—
467	C₂×C₈	—	6	2	no	—
468	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	6	2	no	—
472	C₄⋊C₄	—	6	2	no	—
473	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	6	2	no	—
476	C₂²⋊C₄	—	6	2	no	—
477	C₂²⋊C₄	—	6	2	no	—
478	C₂²⋊C₄	—	6	2	no	—
479	C₄²	—	6	2	no	—
480	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	C₅×#135	1	2	yes	complemented
487	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₂×D₃	—	2	8	no	—
489	C₂×D₃	—	2	1	no	—
490	C₂×D₃	—	2	1	no	—
491	C₂×D₃	—	2	1	no	—
492	C₂×D₃	—	2	1	no	—
493	C₂×D₃	C₅×#121	1	2	yes	—
494	C₂×D₃	C₅×#135	1	2	yes	complemented
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	4	2	no	—
497	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
499	Dic₃	—	2	1	no	—
500	Dic₃	—	4	2	no	—
501	Dic₃	—	4	2	no	—
502	Dic₃	C₅×#121	1	2	yes	—
503	C₂×C₅	—	2	2	no	—
504	C₂×C₅	—	6	2	no	—
505	C₂×C₅	—	6	2	no	—
506	C₂×C₅	—	8	2	no	—
507	C₂×C₅	D₃×#121	1	1	yes	characteristic
508	C₂×C₅	C₂×#912	1	1	yes	characteristic
509	C₂×C₅	D₃×#135	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	3	1	no	—
512	C₂³	—	3	1	no	—
513	C₂³	—	6	2	no	—
514	C₂³	—	6	2	no	—
515	C₂³	—	6	2	no	—
516	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
517	Q₈	—	6	2	no	—
518	Q₈	—	6	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	12	4	no	—
523	D₄	—	12	4	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	3	1	no	—
528	C₂×C₄	—	3	2	no	—
529	C₂×C₄	—	3	2	no	—
530	C₂×C₄	—	3	1	no	—
531	C₂×C₄	—	6	2	no	—
532	C₂×C₄	—	6	2	no	—
533	C₂×C₄	—	6	2	no	—
534	C₂×C₄	—	6	1	no	—
535	C₂×C₄	—	6	1	no	—
536	C₂×C₄	—	6	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	12	4	no	—
539	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
540	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
541	C₈	—	2	1	no	—
542	C₈	—	3	2	no	—
543	C₈	—	6	1	no	—
544	C₈	C₅×D₃×D₄	1	2	yes	—
545	C₂×C₃	—	2	2	no	—
546	C₂×C₃	—	8	2	no	—
547	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
548	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
549	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
550	D₃	—	2	2	no	—
551	D₃	—	2	2	no	—
552	C₅	#80714	1	1	yes	characteristic, direct product factor, Sylow
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	3	2	no	—
556	C₂²	—	3	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	6	8	no	—
561	C₂²	—	6	1	no	—
562	C₂²	—	6	1	no	—
563	C₂²	—	6	1	no	—
564	C₂²	—	6	1	no	—
565	C₂²	C₅×#912	1	2	yes	complemented
566	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	3	2	no	—
569	C₄	—	4	2	no	—
570	C₄	—	6	1	no	—
571	C₄	—	12	2	no	—
572	C₄	—	12	2	no	—
573	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
574	C₄	C₅×D₃×#41	1	1	yes	characteristic
575	C₃	C₅×#3050	1	1	yes	characteristic, complemented, Sylow
576	C₂	—	2	2	no	—
577	C₂	—	6	2	no	—
578	C₂	—	6	2	no	—
579	C₂	—	8	2	no	—
580	C₂	C₅×D₃×#121	1	1	yes	characteristic
581	C₂	C₂×C₅×#912	1	1	yes	characteristic
582	C₂	C₅×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#466	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#466	D₃
hypocenter	C₃	C₅×#3050
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#466

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#912	C₂	semidirect
2. C₂²×C₅×D₃×C₈	C₂	semidirect
3. C₅×#5606	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₅×#5157	C₂	semidirect
6. C₅×#5116	C₂	semidirect
7. C₅×#5041	C₂	semidirect
8. C₅×#4887	C₂	semidirect
9. C₅×#4880	C₂	semidirect
10. C₅×#4778	C₂	semidirect
11. C₅×#4772	C₂	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
21. C₂×C₅×#214	C₂²	semidirect
25. C₂×C₅×Dic₁₂	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₅×#832	C₂²	semidirect
38. C₅×#818	C₂²	semidirect
39. C₅×#816	C₂²	semidirect
40. C₅×#810	C₂²	semidirect
41. C₅×#808	C₂²	semidirect
42. #80714	C₅	direct (N × H)
49. C₅×#466	D₃	semidirect
93. C₅×D₃×C₈	D₄	semidirect
94. C₂×#912	C₂×C₅	semidirect
95. C₂²×D₃×C₈	C₂×C₅	semidirect
96. #5606	C₂×C₅	semidirect
97. C₃×#466	C₂×C₅	semidirect
98. #5157	C₂×C₅	semidirect
99. #5116	C₂×C₅	semidirect
100. #5041	C₂×C₅	semidirect
101. #4887	C₂×C₅	semidirect
102. #4880	C₂×C₅	semidirect
103. #4778	C₂×C₅	semidirect
104. #4772	C₂×C₅	semidirect
110. C₂×C₅×D₈	C₂×D₃	semidirect
128. C₅×#107	C₂×D₃	semidirect
133. C₅×#102	C₂×D₃	semidirect
172. C₂×C₃×D₈	C₂²×C₅	semidirect
178. C₂×#214	C₂²×C₅	semidirect
182. C₂×Dic₁₂	C₂²×C₅	semidirect
192. C₃×#107	C₂²×C₅	semidirect
193. C₃×#102	C₂²×C₅	semidirect
194. #832	C₂²×C₅	semidirect
195. #818	C₂²×C₅	semidirect
196. #816	C₂²×C₅	semidirect
197. #810	C₂²×C₅	semidirect
198. #808	C₂²×C₅	semidirect
245. #466	C₅×D₃	semidirect
255. C₂²×C₃×C₅	#135	semidirect
263. C₂×C₅×D₃	#135	semidirect
311. D₃×C₈	C₅×D₄	semidirect
352. C₂×D₈	C₂×C₅×D₃	semidirect
370. #107	C₂×C₅×D₃	semidirect
375. #102	C₂×C₅×D₃	semidirect
430. C₂²×C₅	#912	semidirect
480. C₃×C₅	#3050	semidirect
486. C₂²×C₃	C₅×#135	semidirect
494. C₂×D₃	C₅×#135	semidirect
552. C₅	#80714	direct (N × H)
565. C₂²	C₅×#912	semidirect
575. C₃	C₅×#3050	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#912	2
C₂²×C₅×D₃×C₈	2
C₅×#5606	2
C₃×C₅×#466	2
C₅×#5157	2
C₅×#5116	2
C₅×#5041	2
C₅×#4887	2
C₅×#4880	2
C₅×#4778	2
C₅×#4772	2
C₅×#3050	3
#80714	5

Subgroups — C5×#80714 #14427795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80714 #14427795