Subgroups — C₅×#78564 #14439393

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 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, complemented
2	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5526	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5525	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4715	C₂	1	2	yes	maximal, complemented
9	C₅×#4712	C₂	1	2	yes	maximal, complemented
10	C₅×#4696	C₂	1	2	yes	maximal, complemented
11	C₅×#4693	C₂	1	2	yes	maximal, complemented
12	C₅×#3154	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₅×#909	—	2	4	no	—
21	C₅×#908	—	2	4	no	—
22	C₂×C₅×Dic₁₂	C₂²	1	2	yes	complemented
23	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
24	C₅×#904	—	2	4	no	—
25	C₂×C₅×D₂₄	C₂²	1	2	yes	—
26	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#204	—	2	4	no	—
28	C₂×C₅×#204	C₂²	1	2	yes	—
29	C₂×C₅×#204	C₂²	1	2	yes	—
30	C₂×C₅×#204	C₂²	1	2	yes	—
31	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#204	C₂²	1	2	yes	complemented
33	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
34	C₅×#897	—	2	2	no	—
35	C₅×#895	—	2	2	no	—
36	C₅×#886	—	2	2	no	—
37	C₅×#882	—	2	2	no	—
38	C₅×#875	C₂²	1	2	yes	—
39	C₅×#875	C₂²	1	2	yes	complemented
40	C₅×#874	C₂²	1	2	yes	—
41	C₅×#869	C₂²	1	2	yes	complemented
42	C₃×C₅×#97	C₂²	1	2	yes	complemented
43	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
44	#78564	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	—	3	1	no	—
46	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
47	C₂×C₅×#135	—	3	1	no	—
48	C₂²×C₅×SD₁₆	—	3	1	no	—
49	C₅×#536	—	3	1	no	—
50	C₅×#535	—	3	1	no	—
51	C₅×#497	—	3	2	no	—
52	C₅×#496	—	3	2	no	—
53	C₅×#495	—	3	2	no	—
54	C₅×#492	—	3	2	no	—
55	C₅×#405	D₃	1	1	yes	characteristic, complemented
56	C₂³×C₅×D₃	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×#67	—	2	1	no	—
59	C₂×C₅×#67	—	2	1	no	—
60	C₂²×C₅×Dic₃	—	2	1	no	—
61	C₅×#235	—	2	2	no	—
62	C₅×#235	—	2	2	no	—
63	C₅×#235	—	2	2	no	—
64	C₅×#235	—	2	2	no	—
65	C₂×C₅×D₁₂	—	2	2	no	—
66	C₂×C₅×D₁₂	—	2	2	no	—
67	C₂×C₅×D₁₂	—	2	1	no	—
68	C₂×C₅×D₁₂	—	2	4	no	—
69	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
70	C₂×C₅×D₁₂	C₂³	1	2	yes	—
71	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	—	2	1	no	—
73	C₂×C₄×C₅×D₃	—	2	1	no	—
74	C₂×C₅×Dic₆	—	2	2	no	—
75	C₂×C₅×Dic₆	—	2	2	no	—
76	C₂×C₅×Dic₆	—	2	1	no	—
77	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×Dic₆	C₂³	1	2	yes	—
79	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
80	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
81	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
82	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
86	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
87	C₃×C₄²×C₅	C₂³	1	2	yes	—
88	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
89	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
90	C₅×C₄⋊Dic₃	—	2	4	no	—
91	C₅×Dic₁₂	—	2	2	no	—
92	C₅×Dic₁₂	—	2	4	no	—
93	C₅×D₂₄	—	2	4	no	—
94	C₅×D₂₄	—	2	2	no	—
95	C₅×#204	—	2	4	no	—
96	C₅×#204	—	2	4	no	—
97	C₅×#204	—	2	4	no	—
98	C₅×#204	—	2	2	no	—
99	C₅×#204	—	2	2	no	—
100	C₅×#204	—	2	4	no	—
101	C₂×#909	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#908	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂²×#204	C₂×C₅	1	1	yes	characteristic, complemented
105	#5526	C₂×C₅	1	1	yes	characteristic, complemented
106	#5525	C₂×C₅	1	1	yes	characteristic, complemented
107	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
108	#4715	C₂×C₅	1	2	yes	complemented
109	#4712	C₂×C₅	1	2	yes	complemented
110	#4696	C₂×C₅	1	2	yes	complemented
111	#4693	C₂×C₅	1	2	yes	complemented
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	—	3	1	no	—
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×D₄	—	3	1	no	—
116	C₅×#137	—	6	4	no	—
117	C₅×AGL(1,ℤ/8)	—	6	4	no	—
118	C₅×#135	—	6	4	no	—
119	C₂×C₅×Q₁₆	—	3	2	no	—
120	C₂×C₅×Q₁₆	—	3	1	no	—
121	C₂×C₅×SD₁₆	—	3	2	no	—
122	C₂×C₅×SD₁₆	—	3	2	no	—
123	C₂×C₅×SD₁₆	—	3	2	no	—
124	C₂×C₅×SD₁₆	—	3	1	no	—
125	C₂×C₅×SD₁₆	—	3	2	no	—
126	C₂×C₅×SD₁₆	—	3	1	no	—
127	C₂×C₅×SD₁₆	—	6	4	no	—
128	C₂×C₅×D₈	—	3	2	no	—
129	C₂×C₅×D₈	—	3	1	no	—
130	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
131	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
132	C₅×C₄⋊Q₈	—	3	2	no	—
133	C₅×#127	—	3	2	no	—
134	C₅×#124	—	3	2	no	—
135	C₅×#124	—	3	2	no	—
136	C₅×#123	—	6	2	no	—
137	C₅×C₂²⋊Q₈	—	6	2	no	—
138	C₅×#121	—	6	2	no	—
139	C₅×#120	—	6	2	no	—
140	C₅×#117	C₂×D₃	1	1	yes	characteristic
141	C₅×#97	C₂×D₃	1	2	yes	complemented
142	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
143	#3154	—	3	1	no	Sylow
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₅×D₃	—	2	1	no	—
146	C₂²×C₅×D₃	—	2	2	no	—
147	C₂²×C₅×D₃	—	2	1	no	—
148	C₂²×C₅×D₃	—	4	2	no	—
149	C₂²×C₅×D₃	—	8	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₅×#67	—	4	2	no	—
156	C₅×#67	—	4	2	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	—	2	1	no	—
160	C₂×C₅×Dic₃	—	4	2	no	—
161	C₅×D₁₂	—	2	2	no	—
162	C₅×D₁₂	—	2	1	no	—
163	C₅×D₁₂	—	2	2	no	—
164	C₅×D₁₂	—	2	1	no	—
165	C₅×D₁₂	—	2	1	no	—
166	C₅×D₁₂	—	2	1	no	—
167	C₅×D₁₂	—	4	2	no	—
168	C₅×D₁₂	—	8	4	no	—
169	C₄×C₅×D₃	—	4	2	no	—
170	C₄×C₅×D₃	—	4	2	no	—
171	C₅×Dic₆	—	2	2	no	—
172	C₅×Dic₆	—	2	1	no	—
173	C₅×Dic₆	—	2	2	no	—
174	C₅×Dic₆	—	2	1	no	—
175	C₅×Dic₆	—	2	1	no	—
176	C₅×Dic₆	—	2	1	no	—
177	C₅×Dic₆	—	4	2	no	—
178	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
179	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
180	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
181	C₂×#235	C₂²×C₅	1	1	yes	characteristic
182	C₂×#235	C₂²×C₅	1	1	yes	characteristic
183	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
184	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
187	C₃×#117	C₂²×C₅	1	1	yes	characteristic
188	#909	—	2	4	no	—
189	#908	—	2	4	no	—
190	C₂×Dic₁₂	C₂²×C₅	1	2	yes	complemented
191	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
192	#904	—	2	4	no	—
193	C₂×D₂₄	C₂²×C₅	1	2	yes	—
194	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×#204	—	2	4	no	—
196	C₂×#204	C₂²×C₅	1	2	yes	—
197	C₂×#204	C₂²×C₅	1	2	yes	—
198	C₂×#204	C₂²×C₅	1	2	yes	—
199	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
200	C₂×#204	C₂²×C₅	1	2	yes	complemented
201	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
202	#897	—	2	2	no	—
203	#895	—	2	2	no	—
204	#886	—	2	2	no	—
205	#882	—	2	2	no	—
206	#875	C₂²×C₅	1	2	yes	—
207	#875	C₂²×C₅	1	2	yes	complemented
208	#874	C₂²×C₅	1	2	yes	—
209	#869	C₂²×C₅	1	2	yes	complemented
210	C₃×#97	C₂²×C₅	1	2	yes	complemented
211	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
212	C₂⁴×C₅	—	6	1	no	—
213	C₅×#41	—	6	2	no	—
214	C₅×#41	—	6	2	no	—
215	C₅×#41	—	6	2	no	—
216	C₅×#41	—	6	2	no	—
217	C₂×C₅×Q₈	—	3	1	no	—
218	C₂×C₅×Q₈	—	3	2	no	—
219	C₂×C₅×Q₈	—	3	1	no	—
220	C₂×C₅×Q₈	—	6	1	no	—
221	C₂×C₅×Q₈	—	6	2	no	—
222	C₂×C₅×Q₈	—	6	2	no	—
223	C₂×C₅×D₄	—	3	1	no	—
224	C₂×C₅×D₄	—	3	2	no	—
225	C₂×C₅×D₄	—	3	1	no	—
226	C₂×C₅×D₄	—	6	1	no	—
227	C₂×C₅×D₄	—	6	1	no	—
228	C₂×C₅×D₄	—	6	2	no	—
229	C₂×C₅×D₄	—	6	2	no	—
230	C₂×C₅×D₄	—	6	1	no	—
231	C₂×C₅×D₄	—	6	4	no	—
232	C₂²×C₄×C₅	—	6	1	no	—
233	C₂²×C₄×C₅	—	6	1	no	—
234	C₂²×C₄×C₅	—	6	1	no	—
235	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
236	C₅×Q₁₆	—	6	2	no	—
237	C₅×Q₁₆	—	6	4	no	—
238	C₅×SD₁₆	—	6	4	no	—
239	C₅×SD₁₆	—	6	4	no	—
240	C₅×SD₁₆	—	6	2	no	—
241	C₅×SD₁₆	—	6	2	no	—
242	C₅×SD₁₆	—	6	4	no	—
243	C₅×SD₁₆	—	6	4	no	—
244	C₅×D₈	—	6	2	no	—
245	C₅×D₈	—	6	4	no	—
246	C₅×M₁₆	D₁₂	1	4	yes	complemented
247	C₂×C₅×C₈	D₁₂	1	4	yes	complemented
248	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
249	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
250	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
251	C₅×C₄⋊C₄	—	6	4	no	—
252	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
253	C₅×C₂²⋊C₄	—	6	4	no	—
254	C₅×C₂²⋊C₄	—	6	4	no	—
255	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
256	C₄²×C₅	C₂²×D₃	1	2	yes	—
257	C₂×#137	—	3	1	no	—
258	C₂×AGL(1,ℤ/8)	—	3	1	no	—
259	C₂×#135	—	3	1	no	—
260	C₂²×SD₁₆	—	3	1	no	—
261	#536	—	3	1	no	—
262	#535	—	3	1	no	—
263	#497	—	3	2	no	—
264	#496	—	3	2	no	—
265	#495	—	3	2	no	—
266	#492	—	3	2	no	—
267	#405	C₅×D₃	1	1	yes	characteristic, complemented
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	#127	1	2	yes	—
270	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₅×D₃	—	4	1	no	—
272	C₂×C₅×D₃	—	4	1	no	—
273	C₂×C₅×D₃	—	4	2	no	—
274	C₂×C₅×D₃	—	4	2	no	—
275	C₂×C₅×D₃	—	4	4	no	—
276	C₂×C₅×D₃	—	4	2	no	—
277	C₂×C₅×D₃	—	8	4	no	—
278	C₃×C₄×C₅	—	2	4	no	—
279	C₃×C₄×C₅	#127	1	2	yes	—
280	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₅×Dic₃	—	4	2	no	—
283	C₅×Dic₃	—	4	1	no	—
284	C₅×Dic₃	—	4	1	no	—
285	C₂³×D₃	—	2	1	no	—
286	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂×#67	—	2	1	no	—
288	C₂×#67	—	2	1	no	—
289	C₂²×Dic₃	—	2	1	no	—
290	#235	—	2	2	no	—
291	#235	—	2	2	no	—
292	#235	—	2	2	no	—
293	#235	—	2	2	no	—
294	C₂×D₁₂	—	2	2	no	—
295	C₂×D₁₂	—	2	2	no	—
296	C₂×D₁₂	—	2	1	no	—
297	C₂×D₁₂	—	2	4	no	—
298	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
299	C₂×D₁₂	C₂³×C₅	1	2	yes	—
300	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄×D₃	—	2	1	no	—
302	C₂×C₄×D₃	—	2	1	no	—
303	C₂×Dic₆	—	2	2	no	—
304	C₂×Dic₆	—	2	2	no	—
305	C₂×Dic₆	—	2	1	no	—
306	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
307	C₂×Dic₆	C₂³×C₅	1	2	yes	—
308	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
309	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
310	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
311	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
313	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
314	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
315	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
316	C₃×C₄²	C₂³×C₅	1	2	yes	—
317	(C₂×D₃)⋊C₄	—	2	4	no	—
318	(C₂×D₃)⋊C₄	—	2	4	no	—
319	C₄⋊Dic₃	—	2	4	no	—
320	Dic₁₂	—	2	2	no	—
321	Dic₁₂	—	2	4	no	—
322	D₂₄	—	2	4	no	—
323	D₂₄	—	2	2	no	—
324	#204	—	2	4	no	—
325	#204	—	2	4	no	—
326	#204	—	2	4	no	—
327	#204	—	2	2	no	—
328	#204	—	2	2	no	—
329	#204	—	2	4	no	—
330	C₂³×C₅	—	6	1	no	—
331	C₂³×C₅	—	6	2	no	—
332	C₂³×C₅	—	6	1	no	—
333	C₂³×C₅	—	12	2	no	—
334	C₂³×C₅	—	24	2	no	—
335	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
336	C₅×Q₈	—	6	2	no	—
337	C₅×Q₈	—	6	1	no	—
338	C₅×Q₈	—	6	2	no	—
339	C₅×Q₈	—	6	1	no	—
340	C₅×Q₈	—	6	1	no	—
341	C₅×Q₈	—	6	1	no	—
342	C₅×Q₈	—	12	2	no	—
343	C₅×D₄	—	6	1	no	—
344	C₅×D₄	—	6	2	no	—
345	C₅×D₄	—	6	1	no	—
346	C₅×D₄	—	6	1	no	—
347	C₅×D₄	—	6	2	no	—
348	C₅×D₄	—	6	1	no	—
349	C₅×D₄	—	12	2	no	—
350	C₅×D₄	—	12	2	no	—
351	C₅×D₄	—	12	2	no	—
352	C₅×D₄	—	24	4	no	—
353	C₂×C₄×C₅	—	6	1	no	—
354	C₂×C₄×C₅	—	6	2	no	—
355	C₂×C₄×C₅	—	6	1	no	—
356	C₂×C₄×C₅	—	12	2	no	—
357	C₂×C₄×C₅	—	12	2	no	—
358	C₂×C₄×C₅	—	12	2	no	—
359	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
360	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
362	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
363	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
364	C₅×C₈	C₂×D₁₂	1	2	yes	—
365	C₅×C₈	C₂×D₁₂	1	2	yes	—
366	C₅×C₈	C₂×D₁₂	1	4	yes	—
367	C₂×#41	—	3	1	no	—
368	C₂×#41	—	3	1	no	—
369	C₂²×Q₈	—	3	1	no	—
370	C₂²×D₄	—	3	1	no	—
371	#137	—	6	4	no	—
372	AGL(1,ℤ/8)	—	6	4	no	—
373	#135	—	6	4	no	—
374	C₂×Q₁₆	—	3	1	no	—
375	C₂×Q₁₆	—	3	2	no	—
376	C₂×SD₁₆	—	3	2	no	—
377	C₂×SD₁₆	—	3	2	no	—
378	C₂×SD₁₆	—	3	1	no	—
379	C₂×SD₁₆	—	3	1	no	—
380	C₂×SD₁₆	—	3	2	no	—
381	C₂×SD₁₆	—	3	2	no	—
382	C₂×SD₁₆	—	6	4	no	—
383	C₂×D₈	—	3	1	no	—
384	C₂×D₈	—	3	2	no	—
385	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
386	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
387	C₄⋊Q₈	—	3	2	no	—
388	#127	—	3	2	no	—
389	#124	—	3	2	no	—
390	#124	—	3	2	no	—
391	#123	—	6	2	no	—
392	C₂²⋊Q₈	—	6	2	no	—
393	#121	—	6	2	no	—
394	#120	—	6	2	no	—
395	#117	C₂×C₅×D₃	1	1	yes	characteristic
396	#97	C₂×C₅×D₃	1	2	yes	complemented
397	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
398	C₂×C₃×C₅	—	2	2	no	—
399	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
400	C₂×C₃×C₅	#577	1	2	yes	—
401	C₅×D₃	—	8	1	no	—
402	C₅×D₃	—	8	1	no	—
403	C₅×D₃	—	8	2	no	—
404	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂²×D₃	—	2	1	no	—
406	C₂²×D₃	—	2	2	no	—
407	C₂²×D₃	—	2	1	no	—
408	C₂²×D₃	—	4	2	no	—
409	C₂²×D₃	—	8	2	no	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
413	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
415	#67	—	4	2	no	—
416	#67	—	4	2	no	—
417	C₂×Dic₃	—	2	1	no	—
418	C₂×Dic₃	—	2	2	no	—
419	C₂×Dic₃	—	2	1	no	—
420	C₂×Dic₃	—	4	2	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	—	2	1	no	—
423	D₁₂	—	2	2	no	—
424	D₁₂	—	2	1	no	—
425	D₁₂	—	2	1	no	—
426	D₁₂	—	2	1	no	—
427	D₁₂	—	4	2	no	—
428	D₁₂	—	8	4	no	—
429	C₄×D₃	—	4	2	no	—
430	C₄×D₃	—	4	2	no	—
431	Dic₆	—	2	2	no	—
432	Dic₆	—	2	1	no	—
433	Dic₆	—	2	2	no	—
434	Dic₆	—	2	1	no	—
435	Dic₆	—	2	1	no	—
436	Dic₆	—	2	1	no	—
437	Dic₆	—	4	2	no	—
438	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
439	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
440	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	12	1	no	—
443	C₂²×C₅	—	12	1	no	—
444	C₂²×C₅	—	12	2	no	—
445	C₂²×C₅	—	12	2	no	—
446	C₂²×C₅	—	12	4	no	—
447	C₂²×C₅	—	12	2	no	—
448	C₂²×C₅	—	24	4	no	—
449	C₂²×C₅	#874	1	2	yes	—
450	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
451	C₄×C₅	—	2	4	no	—
452	C₄×C₅	—	12	1	no	—
453	C₄×C₅	—	12	1	no	—
454	C₄×C₅	—	12	2	no	—
455	C₄×C₅	#874	1	2	yes	—
456	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
457	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
458	C₂⁴	—	6	1	no	—
459	#41	—	6	2	no	—
460	#41	—	6	2	no	—
461	#41	—	6	2	no	—
462	#41	—	6	2	no	—
463	C₂×Q₈	—	3	1	no	—
464	C₂×Q₈	—	3	2	no	—
465	C₂×Q₈	—	3	1	no	—
466	C₂×Q₈	—	6	1	no	—
467	C₂×Q₈	—	6	2	no	—
468	C₂×Q₈	—	6	2	no	—
469	C₂×D₄	—	3	1	no	—
470	C₂×D₄	—	3	2	no	—
471	C₂×D₄	—	3	1	no	—
472	C₂×D₄	—	6	1	no	—
473	C₂×D₄	—	6	1	no	—
474	C₂×D₄	—	6	2	no	—
475	C₂×D₄	—	6	2	no	—
476	C₂×D₄	—	6	1	no	—
477	C₂×D₄	—	6	4	no	—
478	C₂²×C₄	—	6	1	no	—
479	C₂²×C₄	—	6	1	no	—
480	C₂²×C₄	—	6	1	no	—
481	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
482	Q₁₆	—	6	2	no	—
483	Q₁₆	—	6	4	no	—
484	SD₁₆	—	6	4	no	—
485	SD₁₆	—	6	4	no	—
486	SD₁₆	—	6	2	no	—
487	SD₁₆	—	6	2	no	—
488	SD₁₆	—	6	4	no	—
489	SD₁₆	—	6	4	no	—
490	D₈	—	6	2	no	—
491	D₈	—	6	4	no	—
492	M₁₆	C₅×D₁₂	1	4	yes	complemented
493	C₂×C₈	C₅×D₁₂	1	4	yes	complemented
494	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
495	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
496	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
497	C₄⋊C₄	—	6	4	no	—
498	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
499	C₂²⋊C₄	—	6	4	no	—
500	C₂²⋊C₄	—	6	4	no	—
501	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
502	C₄²	C₂²×C₅×D₃	1	2	yes	—
503	C₃×C₅	#3154	1	1	yes	characteristic, complemented, Hall
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	C₅×#127	1	2	yes	—
506	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
507	C₂×D₃	—	4	1	no	—
508	C₂×D₃	—	4	1	no	—
509	C₂×D₃	—	4	2	no	—
510	C₂×D₃	—	4	2	no	—
511	C₂×D₃	—	4	4	no	—
512	C₂×D₃	—	4	2	no	—
513	C₂×D₃	—	8	4	no	—
514	C₃×C₄	—	2	4	no	—
515	C₃×C₄	C₅×#127	1	2	yes	—
516	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
517	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
518	Dic₃	—	4	2	no	—
519	Dic₃	—	4	1	no	—
520	Dic₃	—	4	1	no	—
521	C₂×C₅	—	2	2	no	—
522	C₂×C₅	—	24	2	no	—
523	C₂×C₅	—	24	1	no	—
524	C₂×C₅	—	24	1	no	—
525	C₂×C₅	C₂×#874	1	1	yes	characteristic
526	C₂×C₅	#5751	1	2	yes	—
527	C₂³	—	6	1	no	—
528	C₂³	—	6	2	no	—
529	C₂³	—	6	1	no	—
530	C₂³	—	12	2	no	—
531	C₂³	—	24	2	no	—
532	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
533	Q₈	—	6	2	no	—
534	Q₈	—	6	1	no	—
535	Q₈	—	6	2	no	—
536	Q₈	—	6	1	no	—
537	Q₈	—	6	1	no	—
538	Q₈	—	6	1	no	—
539	Q₈	—	12	2	no	—
540	D₄	—	6	1	no	—
541	D₄	—	6	2	no	—
542	D₄	—	6	1	no	—
543	D₄	—	6	1	no	—
544	D₄	—	6	2	no	—
545	D₄	—	6	1	no	—
546	D₄	—	12	2	no	—
547	D₄	—	12	2	no	—
548	D₄	—	12	2	no	—
549	D₄	—	24	4	no	—
550	C₂×C₄	—	6	1	no	—
551	C₂×C₄	—	6	2	no	—
552	C₂×C₄	—	6	1	no	—
553	C₂×C₄	—	12	2	no	—
554	C₂×C₄	—	12	2	no	—
555	C₂×C₄	—	12	2	no	—
556	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
557	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
558	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
559	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
560	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
561	C₈	C₂×C₅×D₁₂	1	2	yes	—
562	C₈	C₂×C₅×D₁₂	1	2	yes	—
563	C₈	C₂×C₅×D₁₂	1	4	yes	—
564	C₂×C₃	—	2	2	no	—
565	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
566	C₂×C₃	C₅×#577	1	2	yes	—
567	D₃	—	8	2	no	—
568	D₃	—	8	1	no	—
569	D₃	—	8	1	no	—
570	C₅	#78564	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	2	2	no	—
572	C₂²	—	12	1	no	—
573	C₂²	—	12	1	no	—
574	C₂²	—	12	2	no	—
575	C₂²	—	12	2	no	—
576	C₂²	—	12	4	no	—
577	C₂²	—	12	2	no	—
578	C₂²	—	24	4	no	—
579	C₂²	C₅×#874	1	2	yes	—
580	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
581	C₄	—	2	4	no	—
582	C₄	—	12	1	no	—
583	C₄	—	12	1	no	—
584	C₄	—	12	2	no	—
585	C₄	C₅×#874	1	2	yes	—
586	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
587	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
588	C₃	C₅×#3154	1	1	yes	characteristic, complemented, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	24	2	no	—
591	C₂	—	24	1	no	—
592	C₂	—	24	1	no	—
593	C₂	C₂×C₅×#874	1	1	yes	characteristic
594	C₂	C₅×#5751	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#3154
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#909	C₂	semidirect
2. C₂×C₅×#908	C₂	semidirect
3. C₂×C₅×#904	C₂	semidirect
4. C₂²×C₅×#204	C₂	semidirect
5. C₅×#5526	C₂	semidirect
6. C₅×#5525	C₂	semidirect
7. C₃×C₅×#405	C₂	semidirect
8. C₅×#4715	C₂	semidirect
9. C₅×#4712	C₂	semidirect
10. C₅×#4696	C₂	semidirect
11. C₅×#4693	C₂	semidirect
22. C₂×C₅×Dic₁₂	C₂²	semidirect
23. C₂×C₅×Dic₁₂	C₂²	semidirect
26. C₂×C₅×D₂₄	C₂²	semidirect
31. C₂×C₅×#204	C₂²	semidirect
32. C₂×C₅×#204	C₂²	semidirect
33. C₂×C₅×#204	C₂²	semidirect
39. C₅×#875	C₂²	semidirect
41. C₅×#869	C₂²	semidirect
42. C₃×C₅×#97	C₂²	semidirect
43. C₃×C₄×C₅×C₈	C₂²	semidirect
44. #78564	C₅	direct (N × H)
55. C₅×#405	D₃	semidirect
80. C₃×C₅×M₁₆	D₄	semidirect
81. C₂×C₃×C₅×C₈	D₄	semidirect
101. C₂×#909	C₂×C₅	semidirect
102. C₂×#908	C₂×C₅	semidirect
103. C₂×#904	C₂×C₅	semidirect
104. C₂²×#204	C₂×C₅	semidirect
105. #5526	C₂×C₅	semidirect
106. #5525	C₂×C₅	semidirect
107. C₃×#405	C₂×C₅	semidirect
108. #4715	C₂×C₅	semidirect
109. #4712	C₂×C₅	semidirect
110. #4696	C₂×C₅	semidirect
111. #4693	C₂×C₅	semidirect
141. C₅×#97	C₂×D₃	semidirect
142. C₄×C₅×C₈	C₂×D₃	semidirect
190. C₂×Dic₁₂	C₂²×C₅	semidirect
191. C₂×Dic₁₂	C₂²×C₅	semidirect
194. C₂×D₂₄	C₂²×C₅	semidirect
199. C₂×#204	C₂²×C₅	semidirect
200. C₂×#204	C₂²×C₅	semidirect
201. C₂×#204	C₂²×C₅	semidirect
207. #875	C₂²×C₅	semidirect
209. #869	C₂²×C₅	semidirect
210. C₃×#97	C₂²×C₅	semidirect
211. C₃×C₄×C₈	C₂²×C₅	semidirect
246. C₅×M₁₆	D₁₂	semidirect
247. C₂×C₅×C₈	D₁₂	semidirect
267. #405	C₅×D₃	semidirect
309. C₃×M₁₆	C₅×D₄	semidirect
310. C₂×C₃×C₈	C₅×D₄	semidirect
396. #97	C₂×C₅×D₃	semidirect
397. C₄×C₈	C₂×C₅×D₃	semidirect
492. M₁₆	C₅×D₁₂	semidirect
493. C₂×C₈	C₅×D₁₂	semidirect
503. C₃×C₅	#3154	semidirect
570. C₅	#78564	direct (N × H)
588. C₃	C₅×#3154	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
C₂×C₅×#908	2
C₂×C₅×#904	2
C₂²×C₅×#204	2
C₅×#5526	2
C₅×#5525	2
C₃×C₅×#405	2
C₅×#4715	2
C₅×#4712	2
C₅×#4696	2
C₅×#4693	2
C₅×#3154	3
#78564	5

Subgroups — C5×#78564 #14439393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78564 #14439393