Subgroups — C₅×#79200 #14416823

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#909	C₂	1	1	yes	maximal, characteristic
2	C₅×#5522	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5004	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4966	C₂	1	1	yes	maximal, characteristic
8	C₅×#4889	C₂	1	2	yes	maximal, complemented
9	C₅×#4873	C₂	1	2	yes	maximal, complemented
10	C₅×#4853	C₂	1	2	yes	maximal, complemented
11	C₅×#4852	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#137	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	—	2	1	no	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₅×#909	C₄	1	8	yes	complemented
23	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
24	C₂×C₅×#204	C₂²	1	2	yes	—
25	C₅×#893	C₂²	1	1	yes	characteristic
26	C₅×#893	C₂²	1	1	yes	characteristic
27	C₅×#887	—	2	1	no	—
28	C₅×#887	—	2	1	no	—
29	C₅×#887	C₂²	1	2	yes	—
30	C₅×#887	C₂²	1	2	yes	—
31	C₅×#887	C₂²	1	1	yes	characteristic
32	C₅×#887	C₂²	1	1	yes	characteristic
33	C₅×#67⋊C₄	—	2	1	no	—
34	C₅×#67⋊C₄	—	2	1	no	—
35	C₅×#872	—	2	1	no	—
36	C₄²×C₅×D₃	—	2	1	no	—
37	C₃×C₅×#107	C₂²	1	2	yes	—
38	C₃×C₅×#106	C₂²	1	2	yes	—
39	C₅×#815	C₂²	1	2	yes	—
40	C₅×C₈×Dic₃	C₂²	1	2	yes	—
41	C₅×#810	C₂²	1	2	yes	—
42	C₅×#810	C₂²	1	2	yes	—
43	C₅×#810	C₂²	1	2	yes	—
44	C₅×#809	C₂²	1	2	yes	—
45	#79200	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×#137	—	3	1	no	—
47	C₄×C₅×#41	—	3	1	no	—
48	C₂×C₄×C₅×Q₈	—	3	1	no	—
49	C₅×#441	—	3	2	no	—
50	C₅×#440	—	3	2	no	—
51	C₄×C₅×Q₁₆	—	3	2	no	—
52	C₄×C₅×SD₁₆	—	3	2	no	—
53	C₅×#428	D₃	1	1	yes	characteristic, complemented
54	C₅×#419	—	3	1	no	—
55	C₅×#417	—	3	1	no	—
56	C₄×C₅×M₁₆	—	3	1	no	—
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	1	no	—
60	C₂²×C₅×Dic₃	—	2	1	no	—
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₅×#235	—	2	2	no	—
64	C₅×#235	C₂×C₄	1	4	yes	—
65	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	—	2	1	no	—
68	C₂×C₄×C₅×D₃	—	2	1	no	—
69	C₂×C₅×Dic₆	—	2	1	no	—
70	C₂×C₅×Dic₆	—	2	2	no	—
71	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₅×Dic₆	C₂³	1	2	yes	—
73	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
74	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₄²×C₅	—	2	1	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
84	C₅×Dic₃⋊C₄	—	2	1	no	—
85	C₅×Dic₃⋊C₄	—	2	1	no	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₅×Dic₃⋊C₄	—	2	2	no	—
88	C₄×C₅×Dic₃	—	2	1	no	—
89	C₄×C₅×Dic₃	—	2	1	no	—
90	C₄×C₅×Dic₃	—	2	2	no	—
91	C₄×C₅×Dic₃	—	2	2	no	—
92	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
93	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
94	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₅×#208	—	2	2	no	—
97	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
98	C₅×Dic₁₂	C₂×C₄	1	8	yes	complemented
99	C₅×#204	C₂×C₄	1	8	yes	complemented
100	C₂×#909	C₂×C₅	1	1	yes	characteristic
101	#5522	C₂×C₅	1	1	yes	characteristic
102	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
104	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
105	#5004	C₂×C₅	1	1	yes	characteristic, complemented
106	#4966	C₂×C₅	1	1	yes	characteristic
107	#4889	C₂×C₅	1	2	yes	complemented
108	#4873	C₂×C₅	1	2	yes	complemented
109	#4853	C₂×C₅	1	2	yes	complemented
110	#4852	C₂×C₅	1	2	yes	complemented
111	C₂×C₅×#41	—	3	1	no	—
112	C₂²×C₅×Q₈	—	3	1	no	—
113	C₅×#137	—	3	8	no	—
114	C₂×C₅×Q₁₆	—	3	2	no	—
115	C₂×C₅×SD₁₆	—	3	2	no	—
116	C₂×C₅×M₁₆	—	3	1	no	—
117	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
118	C₄×C₅×Q₈	—	3	2	no	—
119	C₄×C₅×Q₈	—	3	1	no	—
120	C₄×C₅×Q₈	—	3	2	no	—
121	C₄×C₅×Q₈	—	3	1	no	—
122	C₄×C₅×Q₈	—	6	1	no	—
123	C₄×C₅×Q₈	—	6	1	no	—
124	C₄×C₅×D₄	—	3	1	no	—
125	C₄×C₅×D₄	—	3	1	no	—
126	C₄×C₅×D₄	—	6	1	no	—
127	C₄×C₅×D₄	—	6	1	no	—
128	C₅×#117	—	6	1	no	—
129	C₅×#117	C₂×D₃	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	—	6	1	no	—
131	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₂×C₄²×C₅	—	3	1	no	—
133	C₂×C₄²×C₅	—	6	1	no	—
134	C₂×C₄²×C₅	—	6	1	no	—
135	C₅×#107	C₂×D₃	1	2	yes	—
136	C₅×#106	C₂×D₃	1	2	yes	—
137	C₅×#103	—	3	2	no	—
138	C₅×#103	—	3	2	no	—
139	C₅×#103	—	3	2	no	—
140	C₅×#102	—	3	2	no	—
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	C₄×#137	—	3	1	no	Sylow
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₅×D₃	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	4	2	no	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	#41	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	2	4	no	—
155	C₂×C₅×Dic₃	—	2	4	no	—
156	C₂×C₅×Dic₃	—	2	2	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	—	4	1	no	—
160	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
164	C₅×D₁₂	—	2	1	no	—
165	C₅×D₁₂	C₂²×C₄	1	2	yes	—
166	C₄×C₅×D₃	—	2	4	no	—
167	C₄×C₅×D₃	—	4	2	no	—
168	C₄×C₅×D₃	—	4	2	no	—
169	C₅×Dic₆	—	2	4	no	—
170	C₅×Dic₆	—	2	2	no	—
171	C₅×Dic₆	—	2	1	no	—
172	C₅×Dic₆	C₂²×C₄	1	4	yes	—
173	C₅×Dic₆	C₂²×C₄	1	2	yes	—
174	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
175	C₅×C₃⋊C₈	—	2	2	no	—
176	C₂×#235	C₂²×C₅	1	1	yes	characteristic
177	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
179	C₃×#117	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×Dic₃⋊C₄	—	2	1	no	—
182	C₂×C₄×Dic₃	—	2	1	no	—
183	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
184	C₂×#208	C₂²×C₅	1	1	yes	characteristic
185	#909	C₄×C₅	1	8	yes	complemented
186	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
187	C₂×#204	C₂²×C₅	1	2	yes	—
188	#893	C₂²×C₅	1	1	yes	characteristic
189	#893	C₂²×C₅	1	1	yes	characteristic
190	#887	—	2	1	no	—
191	#887	—	2	1	no	—
192	#887	C₂²×C₅	1	1	yes	characteristic
193	#887	C₂²×C₅	1	2	yes	—
194	#887	C₂²×C₅	1	2	yes	—
195	#887	C₂²×C₅	1	1	yes	characteristic
196	#67⋊C₄	—	2	1	no	—
197	#67⋊C₄	—	2	1	no	—
198	#872	—	2	1	no	—
199	C₄²×D₃	—	2	1	no	—
200	C₃×#107	C₂²×C₅	1	2	yes	—
201	C₃×#106	C₂²×C₅	1	2	yes	—
202	#815	C₂²×C₅	1	2	yes	—
203	C₈×Dic₃	C₂²×C₅	1	2	yes	—
204	#810	C₂²×C₅	1	2	yes	—
205	#810	C₂²×C₅	1	2	yes	—
206	#810	C₂²×C₅	1	2	yes	—
207	#809	C₂²×C₅	1	2	yes	—
208	C₅×#41	—	3	4	no	—
209	C₅×#41	—	6	2	no	—
210	C₂×C₅×Q₈	—	3	4	no	—
211	C₂×C₅×Q₈	—	3	2	no	—
212	C₂×C₅×Q₈	—	3	1	no	—
213	C₂×C₅×Q₈	—	6	1	no	—
214	C₂×C₅×Q₈	—	6	2	no	—
215	C₂×C₅×D₄	—	3	1	no	—
216	C₂×C₅×D₄	—	6	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	3	1	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	6	1	no	—
221	C₂²×C₄×C₅	—	6	1	no	—
222	C₂²×C₄×C₅	—	6	1	no	—
223	C₂²×C₄×C₅	—	6	1	no	—
224	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₅×Q₁₆	—	3	8	no	—
226	C₅×SD₁₆	—	3	8	no	—
227	C₅×M₁₆	—	6	2	no	—
228	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
229	C₂×C₅×C₈	—	3	2	no	—
230	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	6	2	no	—
233	C₅×C₄⋊C₄	—	6	2	no	—
234	C₅×C₄⋊C₄	—	6	1	no	—
235	C₅×C₄⋊C₄	—	6	1	no	—
236	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
237	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
238	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
239	C₅×C₂²⋊C₄	—	2	1	no	—
240	C₅×C₂²⋊C₄	—	6	1	no	—
241	C₅×C₂²⋊C₄	—	6	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	—	3	1	no	—
244	C₄²×C₅	—	3	1	no	—
245	C₄²×C₅	—	3	1	no	—
246	C₄²×C₅	—	3	1	no	—
247	C₄²×C₅	—	6	1	no	—
248	C₄²×C₅	—	6	1	no	—
249	C₄²×C₅	—	6	2	no	—
250	C₄²×C₅	—	6	2	no	—
251	C₂×#137	—	3	1	no	—
252	C₄×#41	—	3	1	no	—
253	C₂×C₄×Q₈	—	3	1	no	—
254	#441	—	3	2	no	—
255	#440	—	3	2	no	—
256	C₄×Q₁₆	—	3	2	no	—
257	C₄×SD₁₆	—	3	2	no	—
258	#428	C₅×D₃	1	1	yes	characteristic, complemented
259	#419	—	3	1	no	—
260	#417	—	3	1	no	—
261	C₄×M₁₆	—	3	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
265	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₅×D₃	—	2	2	no	—
267	C₂×C₅×D₃	—	4	1	no	—
268	C₂×C₅×D₃	—	4	1	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	—	4	1	no	—
271	C₃×C₄×C₅	—	4	2	no	—
272	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
273	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
274	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₅×Dic₃	—	2	4	no	—
276	C₅×Dic₃	—	2	2	no	—
277	C₅×Dic₃	—	2	1	no	—
278	C₅×Dic₃	—	2	1	no	—
279	C₅×Dic₃	—	2	1	no	—
280	C₅×Dic₃	#137	1	2	yes	complemented
281	C₂²×C₃×C₄	—	2	1	no	—
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×#67	—	2	1	no	—
284	C₂²×Dic₃	—	2	1	no	—
285	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
286	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
287	#235	—	2	2	no	—
288	#235	C₂×C₄×C₅	1	4	yes	—
289	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄×D₃	—	2	1	no	—
291	C₂×C₄×D₃	—	2	1	no	—
292	C₂×C₄×D₃	—	2	1	no	—
293	C₂×Dic₆	—	2	1	no	—
294	C₂×Dic₆	—	2	2	no	—
295	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
296	C₂×Dic₆	C₂³×C₅	1	2	yes	—
297	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
298	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
299	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
302	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
303	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
304	C₃×C₂²⋊C₄	—	2	1	no	—
305	C₃×C₄²	—	2	1	no	—
306	(C₂×D₃)⋊C₄	—	2	1	no	—
307	(C₂×D₃)⋊C₄	—	2	1	no	—
308	Dic₃⋊C₄	—	2	1	no	—
309	Dic₃⋊C₄	—	2	1	no	—
310	Dic₃⋊C₄	—	2	2	no	—
311	Dic₃⋊C₄	—	2	2	no	—
312	C₄×Dic₃	—	2	1	no	—
313	C₄×Dic₃	—	2	1	no	—
314	C₄×Dic₃	—	2	2	no	—
315	C₄×Dic₃	—	2	2	no	—
316	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
317	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
318	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
319	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
320	#208	—	2	2	no	—
321	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
322	Dic₁₂	C₂×C₄×C₅	1	8	yes	complemented
323	#204	C₂×C₄×C₅	1	8	yes	complemented
324	C₂³×C₅	—	6	1	no	—
325	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
326	C₅×Q₈	—	3	4	no	—
327	C₅×Q₈	—	3	2	no	—
328	C₅×Q₈	—	6	4	no	—
329	C₅×Q₈	—	6	2	no	—
330	C₅×Q₈	—	6	1	no	—
331	C₅×D₄	—	3	2	no	—
332	C₅×D₄	—	6	4	no	—
333	C₅×D₄	—	6	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	3	1	no	—
338	C₂×C₄×C₅	—	3	1	no	—
339	C₂×C₄×C₅	—	3	1	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	4	2	no	—
342	C₂×C₄×C₅	—	6	2	no	—
343	C₂×C₄×C₅	—	6	4	no	—
344	C₂×C₄×C₅	—	6	1	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	—	6	4	no	—
347	C₂×C₄×C₅	—	12	2	no	—
348	C₂×C₄×C₅	—	12	2	no	—
349	C₂×C₄×C₅	—	12	1	no	—
350	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
351	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	#239	1	2	yes	—
353	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
354	C₅×C₈	—	6	2	no	—
355	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
356	C₂×#41	—	3	1	no	—
357	C₂²×Q₈	—	3	1	no	—
358	#137	—	3	8	no	—
359	C₂×Q₁₆	—	3	2	no	—
360	C₂×SD₁₆	—	3	2	no	—
361	C₂×M₁₆	—	3	1	no	—
362	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
363	C₄×Q₈	—	3	2	no	—
364	C₄×Q₈	—	3	2	no	—
365	C₄×Q₈	—	3	1	no	—
366	C₄×Q₈	—	3	1	no	—
367	C₄×Q₈	—	6	1	no	—
368	C₄×Q₈	—	6	1	no	—
369	C₄×D₄	—	3	1	no	—
370	C₄×D₄	—	3	1	no	—
371	C₄×D₄	—	6	1	no	—
372	C₄×D₄	—	6	1	no	—
373	#117	—	6	1	no	—
374	#117	C₂×C₅×D₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	—	6	1	no	—
376	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
377	C₂×C₄²	—	3	1	no	—
378	C₂×C₄²	—	6	1	no	—
379	C₂×C₄²	—	6	1	no	—
380	#107	C₂×C₅×D₃	1	2	yes	—
381	#106	C₂×C₅×D₃	1	2	yes	—
382	#103	—	3	2	no	—
383	#103	—	3	2	no	—
384	#103	—	3	2	no	—
385	#102	—	3	2	no	—
386	#97	—	3	2	no	—
387	C₄×C₈	—	3	2	no	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
391	C₂×C₃×C₅	#575	1	1	yes	characteristic
392	C₅×D₃	—	4	2	no	—
393	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂²×D₃	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	4	2	no	—
399	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
400	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₅×#41	1	2	yes	—
402	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
403	#67	—	2	4	no	—
404	C₂×Dic₃	—	2	4	no	—
405	C₂×Dic₃	—	2	2	no	—
406	C₂×Dic₃	—	2	1	no	—
407	C₂×Dic₃	—	2	2	no	—
408	C₂×Dic₃	—	4	1	no	—
409	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
413	D₁₂	—	2	1	no	—
414	D₁₂	C₂²×C₄×C₅	1	2	yes	—
415	C₄×D₃	—	2	4	no	—
416	C₄×D₃	—	4	2	no	—
417	C₄×D₃	—	4	2	no	—
418	Dic₆	—	2	4	no	—
419	Dic₆	—	2	2	no	—
420	Dic₆	—	2	1	no	—
421	Dic₆	C₂²×C₄×C₅	1	4	yes	—
422	Dic₆	C₂²×C₄×C₅	1	2	yes	—
423	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
424	C₃⋊C₈	—	2	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	6	2	no	—
428	C₂²×C₅	—	12	1	no	—
429	C₂²×C₅	—	12	1	no	—
430	C₂²×C₅	#893	1	2	yes	—
431	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
432	C₄×C₅	—	3	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	6	2	no	—
437	C₄×C₅	—	6	4	no	—
438	C₄×C₅	—	6	1	no	—
439	C₄×C₅	—	6	1	no	—
440	C₄×C₅	—	6	1	no	—
441	C₄×C₅	#893	1	2	yes	—
442	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
443	C₄×C₅	C₂×#239	1	1	yes	characteristic
444	#41	—	3	4	no	—
445	#41	—	6	2	no	—
446	C₂×Q₈	—	3	4	no	—
447	C₂×Q₈	—	3	2	no	—
448	C₂×Q₈	—	3	1	no	—
449	C₂×Q₈	—	6	1	no	—
450	C₂×Q₈	—	6	2	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	6	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	6	1	no	—
457	C₂²×C₄	—	6	1	no	—
458	C₂²×C₄	—	6	1	no	—
459	C₂²×C₄	—	6	1	no	—
460	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
461	Q₁₆	—	3	8	no	—
462	SD₁₆	—	3	8	no	—
463	M₁₆	—	6	2	no	—
464	M₁₆	C₄×C₅×D₃	1	4	yes	complemented
465	C₂×C₈	—	3	2	no	—
466	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	6	2	no	—
469	C₄⋊C₄	—	6	2	no	—
470	C₄⋊C₄	—	6	1	no	—
471	C₄⋊C₄	—	6	1	no	—
472	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
473	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	6	1	no	—
477	C₂²⋊C₄	—	6	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	3	1	no	—
480	C₄²	—	3	1	no	—
481	C₄²	—	3	1	no	—
482	C₄²	—	3	1	no	—
483	C₄²	—	6	1	no	—
484	C₄²	—	6	1	no	—
485	C₄²	—	6	2	no	—
486	C₄²	—	6	2	no	—
487	C₃×C₅	C₄×#137	1	1	yes	characteristic, complemented, Hall
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
491	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	4	1	no	—
494	C₂×D₃	—	4	1	no	—
495	C₃×C₄	—	4	1	no	—
496	C₃×C₄	—	4	1	no	—
497	C₃×C₄	—	4	2	no	—
498	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
499	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
500	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
501	Dic₃	—	2	4	no	—
502	Dic₃	—	2	2	no	—
503	Dic₃	—	2	1	no	—
504	Dic₃	—	2	1	no	—
505	Dic₃	—	2	1	no	—
506	Dic₃	C₅×#137	1	2	yes	complemented
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	12	2	no	—
509	C₂×C₅	C₂×#893	1	1	yes	characteristic
510	C₂×C₅	#5773	1	1	yes	characteristic
511	C₂×C₅	D₃×#137	1	1	yes	characteristic
512	C₂³	—	6	1	no	—
513	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
514	Q₈	—	3	4	no	—
515	Q₈	—	3	2	no	—
516	Q₈	—	6	4	no	—
517	Q₈	—	6	2	no	—
518	Q₈	—	6	1	no	—
519	D₄	—	3	2	no	—
520	D₄	—	6	4	no	—
521	D₄	—	6	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	3	1	no	—
526	C₂×C₄	—	3	1	no	—
527	C₂×C₄	—	3	1	no	—
528	C₂×C₄	—	3	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	6	2	no	—
531	C₂×C₄	—	6	4	no	—
532	C₂×C₄	—	6	1	no	—
533	C₂×C₄	—	6	2	no	—
534	C₂×C₄	—	6	4	no	—
535	C₂×C₄	—	12	2	no	—
536	C₂×C₄	—	12	2	no	—
537	C₂×C₄	—	12	1	no	—
538	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
539	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
540	C₂×C₄	C₅×#239	1	2	yes	—
541	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
542	C₈	—	6	2	no	—
543	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
544	C₂×C₃	—	2	2	no	—
545	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
546	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
547	C₂×C₃	C₅×#575	1	1	yes	characteristic
548	D₃	—	4	2	no	—
549	C₅	#79200	1	1	yes	characteristic, direct product factor, Sylow
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	6	2	no	—
553	C₂²	—	12	1	no	—
554	C₂²	—	12	1	no	—
555	C₂²	C₅×#893	1	2	yes	—
556	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
557	C₄	—	3	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	6	2	no	—
562	C₄	—	6	4	no	—
563	C₄	—	6	1	no	—
564	C₄	—	6	1	no	—
565	C₄	—	6	1	no	—
566	C₄	C₅×#893	1	2	yes	—
567	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
568	C₄	C₂×C₅×#239	1	1	yes	characteristic
569	C₃	C₄×C₅×#137	1	1	yes	characteristic, complemented, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	12	2	no	—
572	C₂	C₂×C₅×#893	1	1	yes	characteristic
573	C₂	C₅×#5773	1	1	yes	characteristic
574	C₂	C₅×D₃×#137	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×C₅×#428	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#428	D₃
hypocenter	C₃	C₄×C₅×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#428

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#887	C₂	semidirect
4. C₃×C₅×#428	C₂	semidirect
5. C₅×Dic₃×M₁₆	C₂	semidirect
6. C₅×#5004	C₂	semidirect
8. C₅×#4889	C₂	semidirect
9. C₅×#4873	C₂	semidirect
10. C₅×#4853	C₂	semidirect
11. C₅×#4852	C₂	semidirect
22. C₅×#909	C₄	semidirect
45. #79200	C₅	direct (N × H)
53. C₅×#428	D₃	semidirect
71. C₂×C₅×Dic₆	C₂×C₄	semidirect
74. C₃×C₅×M₁₆	C₂×C₄	semidirect
98. C₅×Dic₁₂	C₂×C₄	semidirect
99. C₅×#204	C₂×C₄	semidirect
102. C₂×#887	C₂×C₅	semidirect
103. C₃×#428	C₂×C₅	semidirect
104. Dic₃×M₁₆	C₂×C₅	semidirect
105. #5004	C₂×C₅	semidirect
107. #4889	C₂×C₅	semidirect
108. #4873	C₂×C₅	semidirect
109. #4853	C₂×C₅	semidirect
110. #4852	C₂×C₅	semidirect
185. #909	C₄×C₅	semidirect
228. C₅×M₁₆	C₄×D₃	semidirect
258. #428	C₅×D₃	semidirect
280. C₅×Dic₃	#137	semidirect
295. C₂×Dic₆	C₂×C₄×C₅	semidirect
298. C₃×M₁₆	C₂×C₄×C₅	semidirect
322. Dic₁₂	C₂×C₄×C₅	semidirect
323. #204	C₂×C₄×C₅	semidirect
464. M₁₆	C₄×C₅×D₃	semidirect
487. C₃×C₅	C₄×#137	semidirect
506. Dic₃	C₅×#137	semidirect
549. C₅	#79200	direct (N × H)
569. C₃	C₄×C₅×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#909	2
C₅×#5522	2
C₂×C₅×#887	2
C₃×C₅×#428	2
C₅×Dic₃×M₁₆	2
C₅×#5004	2
C₅×#4966	2
C₅×#4889	2
C₅×#4873	2
C₅×#4853	2
C₅×#4852	2
C₄×C₅×#137	3
#79200	5

Subgroups — C5×#79200 #14416823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79200 #14416823