Subgroups — C₅×#84113 #14424429

Order 1920.

1464 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×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5830	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5238	C₂	1	4	yes	maximal, complemented
6	C₅×#5234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5233	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5227	C₂	1	4	yes	maximal, complemented
9	C₅×#5225	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3010	—	3	1	no	maximal, Hall
11	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
12	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
13	C₂×C₃×C₅×#41	—	2	2	no	—
14	C₂×C₃×C₅×#41	—	2	1	no	—
15	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₅×Q₈	—	2	1	no	—
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
21	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₅×#949	—	2	4	no	—
23	C₅×#947	—	2	1	no	—
24	C₂×C₅×#215	—	2	4	no	—
25	C₂×C₅×#215	C₂²	1	2	yes	—
26	C₂×C₅×#215	C₂²	1	4	yes	—
27	C₅×#940	—	2	1	no	—
28	C₅×#937	—	2	2	no	—
29	C₂×C₅×#213	C₂²	1	2	yes	—
30	C₅×#930	C₂²	1	4	yes	—
31	C₅×#926	C₂²	1	1	yes	characteristic
32	C₂×C₅×#208	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₅×#835	C₂²	1	4	yes	complemented
35	C₅×#835	C₂²	1	2	yes	complemented
36	C₅×#832	C₂²	1	2	yes	complemented
37	C₅×#830	C₂²	1	4	yes	complemented
38	#84113	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×2₋¹⁺⁴	D₃	1	1	yes	characteristic, complemented
40	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
41	C₂²×C₅×SD₁₆	—	3	1	no	—
42	C₅×#535	—	3	1	no	—
43	C₅×#449	—	3	4	no	—
44	C₅×#448	—	3	4	no	—
45	C₅×#419	—	3	1	no	—
46	C₅×#416	—	3	1	no	—
47	C₅×#408	—	3	1	no	—
48	C₂³×C₅×D₃	—	2	1	no	—
49	C₃×C₅×#41	—	2	16	no	—
50	C₃×C₅×#41	—	2	8	no	—
51	C₃×C₅×#41	—	2	4	no	—
52	C₃×C₅×#41	—	2	4	no	—
53	C₃×C₅×#41	—	2	2	no	—
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	D₄	1	4	yes	complemented
57	C₂×C₃×C₅×Q₈	—	2	8	no	—
58	C₂×C₃×C₅×Q₈	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	—	2	4	no	—
60	C₂×C₃×C₅×Q₈	—	2	1	no	—
61	C₂×C₃×C₅×Q₈	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	—	2	2	no	—
63	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
65	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×D₄	—	2	1	no	—
68	C₂×C₃×C₅×D₄	—	2	2	no	—
69	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
70	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
71	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	—	2	1	no	—
73	C₂²×C₃×C₄×C₅	—	2	2	no	—
74	C₂²×C₃×C₄×C₅	—	2	1	no	—
75	C₂²×C₃×C₄×C₅	—	2	2	no	—
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₅×#67	—	2	4	no	—
79	C₂×C₅×D₁₂	—	2	2	no	—
80	C₂×C₅×D₁₂	—	2	2	no	—
81	C₂×C₅×D₁₂	—	2	1	no	—
82	C₂×C₅×D₁₂	C₂³	1	2	yes	—
83	C₅×#217	—	2	1	no	—
84	C₅×#215	—	2	8	no	—
85	C₅×#215	—	2	4	no	—
86	C₅×#213	—	2	4	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
88	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
89	C₄×C₅×Dic₃	—	2	1	no	—
90	C₅×#208	—	2	2	no	—
91	C₂×C₅×C₃⋊C₈	—	2	2	no	—
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
94	C₂×C₃×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic, complemented
95	#5830	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#949	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
98	#5238	C₂×C₅	1	4	yes	complemented
99	#5234	C₂×C₅	1	1	yes	characteristic, complemented
100	#5233	C₂×C₅	1	1	yes	characteristic, complemented
101	#5227	C₂×C₅	1	4	yes	complemented
102	#5225	C₂×C₅	1	1	yes	characteristic, complemented
103	C₅×2₋¹⁺⁴	—	2	4	no	—
104	C₅×2₋¹⁺⁴	—	2	4	no	—
105	C₂×C₅×#41	—	2	2	no	—
106	C₂×C₅×#41	—	2	1	no	—
107	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
108	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
109	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
110	C₂²×C₅×Q₈	—	2	1	no	—
111	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	complemented
113	C₂²×C₅×D₄	—	3	1	no	—
114	C₅×AGL(1,ℤ/8)	—	6	4	no	—
115	C₂×C₅×SD₁₆	—	3	2	no	—
116	C₂×C₅×SD₁₆	—	3	4	no	—
117	C₂×C₅×SD₁₆	—	6	4	no	—
118	C₂×C₅×D₈	—	3	2	no	—
119	C₂×C₅×M₁₆	—	3	1	no	—
120	C₂²×C₅×C₈	—	3	1	no	—
121	C₅×#127	—	6	1	no	—
122	C₅×#124	—	6	1	no	—
123	C₅×#121	—	3	4	no	—
124	C₅×#120	—	6	2	no	—
125	C₅×#117	—	3	1	no	—
126	C₅×#103	—	3	2	no	—
127	C₅×#103	—	3	4	no	—
128	C₅×#102	—	3	2	no	—
129	C₅×C₂²⋊C₈	—	3	4	no	—
130	#3010	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₅×D₃	—	2	2	no	—
135	C₂²×C₅×D₃	—	4	2	no	—
136	C₂²×C₅×D₃	—	8	2	no	—
137	C₃×C₅×Q₈	—	2	8	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	4	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
143	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
144	C₃×C₅×D₄	—	2	8	no	—
145	C₃×C₅×D₄	—	2	4	no	—
146	C₃×C₅×D₄	—	2	4	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	1	no	—
149	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	—	2	8	no	—
151	C₂×C₃×C₄×C₅	—	2	8	no	—
152	C₂×C₃×C₄×C₅	—	2	4	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	4	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₅×#67	—	8	4	no	—
164	C₂×C₅×Dic₃	—	2	2	no	—
165	C₅×D₁₂	—	2	2	no	—
166	C₅×D₁₂	—	2	2	no	—
167	C₅×D₁₂	—	4	2	no	—
168	C₅×C₃⋊C₈	—	2	2	no	—
169	C₅×C₃⋊C₈	—	2	2	no	—
170	C₃×2₋¹⁺⁴	—	2	4	no	—
171	C₃×2₋¹⁺⁴	—	2	4	no	—
172	C₂×C₃×#41	—	2	2	no	—
173	C₂×C₃×#41	—	2	1	no	—
174	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
177	C₂²×C₃×Q₈	—	2	1	no	—
178	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	complemented
180	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
181	#949	—	2	4	no	—
182	#947	—	2	1	no	—
183	C₂×#215	—	2	4	no	—
184	C₂×#215	C₂²×C₅	1	2	yes	—
185	C₂×#215	C₂²×C₅	1	4	yes	—
186	#940	—	2	1	no	—
187	#937	—	2	2	no	—
188	C₂×#213	C₂²×C₅	1	2	yes	—
189	#930	C₂²×C₅	1	4	yes	—
190	#926	C₂²×C₅	1	1	yes	characteristic
191	C₂×#208	C₂²×C₅	1	1	yes	characteristic
192	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
193	#835	C₂²×C₅	1	4	yes	complemented
194	#835	C₂²×C₅	1	2	yes	complemented
195	#832	C₂²×C₅	1	2	yes	complemented
196	#830	C₂²×C₅	1	4	yes	complemented
197	C₂⁴×C₅	—	6	1	no	—
198	C₅×#41	—	2	16	no	—
199	C₅×#41	—	2	8	no	—
200	C₅×#41	—	2	4	no	—
201	C₅×#41	—	2	4	no	—
202	C₅×#41	—	2	2	no	—
203	C₅×#41	—	2	2	no	—
204	C₅×#41	—	2	2	no	—
205	C₅×#41	#67	1	4	yes	complemented
206	C₂×C₅×Q₈	—	2	8	no	—
207	C₂×C₅×Q₈	—	2	4	no	—
208	C₂×C₅×Q₈	—	2	4	no	—
209	C₂×C₅×Q₈	—	2	1	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	2	2	no	—
212	C₂×C₅×Q₈	#67	1	1	yes	characteristic
213	C₂×C₅×Q₈	#67	1	4	yes	complemented
214	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
215	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	3	2	no	—
219	C₂×C₅×D₄	—	6	4	no	—
220	C₂×C₅×D₄	—	6	2	no	—
221	C₂×C₅×D₄	—	6	2	no	—
222	C₂×C₅×D₄	—	6	1	no	—
223	C₂×C₅×D₄	#67	1	2	yes	—
224	C₂×C₅×D₄	#67	1	1	yes	characteristic
225	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
226	C₂²×C₄×C₅	—	2	1	no	—
227	C₂²×C₄×C₅	—	2	2	no	—
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	—	2	2	no	—
230	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
231	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₅×SD₁₆	—	6	8	no	—
233	C₅×SD₁₆	—	6	4	no	—
234	C₅×D₈	—	6	4	no	—
235	C₅×M₁₆	—	6	2	no	—
236	C₂×C₅×C₈	—	3	2	no	—
237	C₂×C₅×C₈	—	3	2	no	—
238	C₂×C₅×C₈	—	6	2	no	—
239	C₅×C₄⋊C₄	—	3	2	no	—
240	C₅×C₂²⋊C₄	—	6	1	no	—
241	C₅×C₂²⋊C₄	—	6	4	no	—
242	C₄²×C₅	—	6	1	no	—
243	C₂×2₋¹⁺⁴	C₅×D₃	1	1	yes	characteristic, complemented
244	C₂×AGL(1,ℤ/8)	—	3	1	no	—
245	C₂²×SD₁₆	—	3	1	no	—
246	#535	—	3	1	no	—
247	#449	—	3	4	no	—
248	#448	—	3	4	no	—
249	#419	—	3	1	no	—
250	#416	—	3	1	no	—
251	#408	—	3	1	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	2	2	no	—
254	C₂²×C₃×C₅	—	2	2	no	—
255	C₂²×C₃×C₅	—	2	4	no	—
256	C₂²×C₃×C₅	—	4	2	no	—
257	C₂²×C₃×C₅	#120	1	2	yes	—
258	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₅×D₃	—	4	2	no	—
260	C₂×C₅×D₃	—	4	4	no	—
261	C₂×C₅×D₃	—	8	4	no	—
262	C₃×C₄×C₅	—	2	4	no	—
263	C₃×C₄×C₅	—	2	2	no	—
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	#120	1	2	yes	—
266	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₅×Dic₃	—	4	2	no	—
269	C₂³×D₃	—	2	1	no	—
270	C₃×#41	—	2	16	no	—
271	C₃×#41	—	2	8	no	—
272	C₃×#41	—	2	4	no	—
273	C₃×#41	—	2	4	no	—
274	C₃×#41	—	2	2	no	—
275	C₃×#41	—	2	2	no	—
276	C₃×#41	—	2	2	no	—
277	C₃×#41	C₅×D₄	1	4	yes	complemented
278	C₂×C₃×Q₈	—	2	8	no	—
279	C₂×C₃×Q₈	—	2	4	no	—
280	C₂×C₃×Q₈	—	2	4	no	—
281	C₂×C₃×Q₈	—	2	1	no	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
286	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
287	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	—	2	2	no	—
290	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
291	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
292	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	2	2	no	—
295	C₂²×C₃×C₄	—	2	1	no	—
296	C₂²×C₃×C₄	—	2	2	no	—
297	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂×#67	—	2	4	no	—
300	C₂×D₁₂	—	2	2	no	—
301	C₂×D₁₂	—	2	2	no	—
302	C₂×D₁₂	—	2	1	no	—
303	C₂×D₁₂	C₂³×C₅	1	2	yes	—
304	#217	—	2	1	no	—
305	#215	—	2	8	no	—
306	#215	—	2	4	no	—
307	#213	—	2	4	no	—
308	(C₂×D₃)⋊C₄	—	2	4	no	—
309	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
310	C₄×Dic₃	—	2	1	no	—
311	#208	—	2	2	no	—
312	C₂×C₃⋊C₈	—	2	2	no	—
313	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
314	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	—	6	2	no	—
317	C₂³×C₅	—	12	2	no	—
318	C₂³×C₅	—	24	2	no	—
319	C₂³×C₅	C₂×#67	1	2	yes	—
320	C₂³×C₅	C₂×#67	1	1	yes	characteristic
321	C₅×Q₈	—	2	8	no	—
322	C₅×Q₈	—	2	2	no	—
323	C₅×Q₈	—	2	4	no	—
324	C₅×Q₈	—	2	1	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	C₂×#67	1	2	yes	—
327	C₅×Q₈	C₂×#67	1	4	yes	—
328	C₅×D₄	—	2	8	no	—
329	C₅×D₄	—	2	4	no	—
330	C₅×D₄	—	2	4	no	—
331	C₅×D₄	—	2	2	no	—
332	C₅×D₄	—	2	1	no	—
333	C₅×D₄	—	6	2	no	—
334	C₅×D₄	—	6	2	no	—
335	C₅×D₄	—	12	2	no	—
336	C₅×D₄	—	24	4	no	—
337	C₅×D₄	C₂×#67	1	2	yes	—
338	C₂×C₄×C₅	—	2	8	no	—
339	C₂×C₄×C₅	—	2	8	no	—
340	C₂×C₄×C₅	—	2	4	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	4	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	6	2	no	—
347	C₂×C₄×C₅	C₂×#67	1	2	yes	—
348	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#67	1	2	yes	—
350	C₂×C₄×C₅	C₂×#67	1	2	yes	—
351	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
352	C₅×C₈	—	6	2	no	—
353	C₅×C₈	—	6	2	no	—
354	2₋¹⁺⁴	—	2	4	no	—
355	2₋¹⁺⁴	—	2	4	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
359	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
360	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
363	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	complemented
364	C₂²×D₄	—	3	1	no	—
365	AGL(1,ℤ/8)	—	6	4	no	—
366	C₂×SD₁₆	—	3	4	no	—
367	C₂×SD₁₆	—	3	2	no	—
368	C₂×SD₁₆	—	6	4	no	—
369	C₂×D₈	—	3	2	no	—
370	C₂×M₁₆	—	3	1	no	—
371	C₂²×C₈	—	3	1	no	—
372	#127	—	6	1	no	—
373	#124	—	6	1	no	—
374	#121	—	3	4	no	—
375	#120	—	6	2	no	—
376	#117	—	3	1	no	—
377	#103	—	3	2	no	—
378	#103	—	3	4	no	—
379	#102	—	3	2	no	—
380	C₂²⋊C₈	—	3	4	no	—
381	C₂×C₃×C₅	—	2	2	no	—
382	C₂×C₃×C₅	—	4	2	no	—
383	C₂×C₃×C₅	—	4	2	no	—
384	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
385	C₂×C₃×C₅	#577	1	2	yes	—
386	C₅×D₃	—	8	2	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
389	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂²×D₃	—	2	2	no	—
391	C₂²×D₃	—	4	2	no	—
392	C₂²×D₃	—	8	2	no	—
393	C₃×Q₈	—	2	8	no	—
394	C₃×Q₈	—	2	2	no	—
395	C₃×Q₈	—	2	4	no	—
396	C₃×Q₈	—	2	1	no	—
397	C₃×Q₈	—	2	2	no	—
398	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
399	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
400	C₃×D₄	—	2	8	no	—
401	C₃×D₄	—	2	4	no	—
402	C₃×D₄	—	2	4	no	—
403	C₃×D₄	—	2	2	no	—
404	C₃×D₄	—	2	1	no	—
405	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
406	C₂×C₃×C₄	—	2	8	no	—
407	C₂×C₃×C₄	—	2	8	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	4	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
415	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
417	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
418	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	#67	—	8	4	no	—
420	C₂×Dic₃	—	2	2	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	—	2	2	no	—
423	D₁₂	—	4	2	no	—
424	C₃⋊C₈	—	2	2	no	—
425	C₃⋊C₈	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	4	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	12	4	no	—
432	C₂²×C₅	—	12	2	no	—
433	C₂²×C₅	—	24	4	no	—
434	C₂²×C₅	#953	1	2	yes	—
435	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
436	C₄×C₅	—	2	4	no	—
437	C₄×C₅	—	2	2	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	12	2	no	—
440	C₄×C₅	#953	1	2	yes	—
441	C₄×C₅	C₂²×#67	1	1	yes	characteristic
442	C₄×C₅	C₂²×#67	1	1	yes	characteristic
443	C₂⁴	—	6	1	no	—
444	#41	—	2	16	no	—
445	#41	—	2	8	no	—
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	C₅×#67	1	4	yes	complemented
452	C₂×Q₈	—	2	8	no	—
453	C₂×Q₈	—	2	4	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	C₅×#67	1	1	yes	characteristic
459	C₂×Q₈	C₅×#67	1	4	yes	complemented
460	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
461	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	3	2	no	—
465	C₂×D₄	—	6	4	no	—
466	C₂×D₄	—	6	2	no	—
467	C₂×D₄	—	6	2	no	—
468	C₂×D₄	—	6	1	no	—
469	C₂×D₄	C₅×#67	1	2	yes	—
470	C₂×D₄	C₅×#67	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
477	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
478	SD₁₆	—	6	8	no	—
479	SD₁₆	—	6	4	no	—
480	D₈	—	6	4	no	—
481	M₁₆	—	6	2	no	—
482	C₂×C₈	—	3	2	no	—
483	C₂×C₈	—	3	2	no	—
484	C₂×C₈	—	6	2	no	—
485	C₄⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	6	1	no	—
487	C₂²⋊C₄	—	6	4	no	—
488	C₄²	—	6	1	no	—
489	C₃×C₅	#3010	1	1	yes	characteristic, complemented, Hall
490	C₂²×C₃	—	2	2	no	—
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	—	2	4	no	—
494	C₂²×C₃	—	4	2	no	—
495	C₂²×C₃	C₅×#120	1	2	yes	—
496	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
497	C₂×D₃	—	4	2	no	—
498	C₂×D₃	—	4	4	no	—
499	C₂×D₃	—	8	4	no	—
500	C₃×C₄	—	2	4	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	C₅×#120	1	2	yes	—
504	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
505	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
506	Dic₃	—	4	2	no	—
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	4	2	no	—
509	C₂×C₅	—	4	2	no	—
510	C₂×C₅	—	24	2	no	—
511	C₂×C₅	#5837	1	2	yes	—
512	C₂×C₅	C₂×#953	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	6	2	no	—
515	C₂³	—	12	2	no	—
516	C₂³	—	24	2	no	—
517	C₂³	C₂×C₅×#67	1	2	yes	—
518	C₂³	C₂×C₅×#67	1	1	yes	characteristic
519	Q₈	—	2	8	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	4	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	2	2	no	—
524	Q₈	C₂×C₅×#67	1	2	yes	—
525	Q₈	C₂×C₅×#67	1	4	yes	—
526	D₄	—	2	8	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	1	no	—
531	D₄	—	6	2	no	—
532	D₄	—	6	2	no	—
533	D₄	—	12	2	no	—
534	D₄	—	24	4	no	—
535	D₄	C₂×C₅×#67	1	2	yes	—
536	C₂×C₄	—	2	8	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	6	2	no	—
545	C₂×C₄	C₂×C₅×#67	1	2	yes	—
546	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
547	C₂×C₄	C₂×C₅×#67	1	2	yes	—
548	C₂×C₄	C₂×C₅×#67	1	2	yes	—
549	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
550	C₈	—	6	2	no	—
551	C₈	—	6	2	no	—
552	C₂×C₃	—	2	2	no	—
553	C₂×C₃	—	4	2	no	—
554	C₂×C₃	—	4	2	no	—
555	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
556	C₂×C₃	C₅×#577	1	2	yes	—
557	D₃	—	8	2	no	—
558	C₅	#84113	1	1	yes	characteristic, direct product factor, Sylow
559	C₂²	—	2	2	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	12	4	no	—
565	C₂²	—	12	2	no	—
566	C₂²	—	24	4	no	—
567	C₂²	C₅×#953	1	2	yes	—
568	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
569	C₄	—	2	4	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	12	2	no	—
573	C₄	C₅×#953	1	2	yes	—
574	C₄	C₂²×C₅×#67	1	1	yes	characteristic
575	C₄	C₂²×C₅×#67	1	1	yes	characteristic
576	C₃	C₅×#3010	1	1	yes	characteristic, complemented, Sylow
577	C₂	—	2	2	no	—
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	—	24	2	no	—
581	C₂	C₅×#5837	1	2	yes	—
582	C₂	C₂×C₅×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×2₋¹⁺⁴	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×2₋¹⁺⁴	D₃
hypocenter	C₃	C₅×#3010
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×2₋¹⁺⁴	C₂	semidirect
2. C₅×#5830	C₂	semidirect
3. C₂×C₅×#949	C₂	semidirect
4. C₂²×C₅×#215	C₂	semidirect
5. C₅×#5238	C₂	semidirect
6. C₅×#5234	C₂	semidirect
7. C₅×#5233	C₂	semidirect
8. C₅×#5227	C₂	semidirect
9. C₅×#5225	C₂	semidirect
17. C₂×C₃×C₅×#41	C₂²	semidirect
20. C₂²×C₃×C₅×Q₈	C₂²	semidirect
34. C₅×#835	C₂²	semidirect
35. C₅×#835	C₂²	semidirect
36. C₅×#832	C₂²	semidirect
37. C₅×#830	C₂²	semidirect
38. #84113	C₅	direct (N × H)
39. C₂×C₅×2₋¹⁺⁴	D₃	semidirect
56. C₃×C₅×#41	D₄	semidirect
64. C₂×C₃×C₅×Q₈	D₄	semidirect
94. C₂×C₃×2₋¹⁺⁴	C₂×C₅	semidirect
95. #5830	C₂×C₅	semidirect
96. C₂×#949	C₂×C₅	semidirect
97. C₂²×#215	C₂×C₅	semidirect
98. #5238	C₂×C₅	semidirect
99. #5234	C₂×C₅	semidirect
100. #5233	C₂×C₅	semidirect
101. #5227	C₂×C₅	semidirect
102. #5225	C₂×C₅	semidirect
109. C₂×C₅×#41	C₂×D₃	semidirect
112. C₂²×C₅×Q₈	C₂×D₃	semidirect
176. C₂×C₃×#41	C₂²×C₅	semidirect
179. C₂²×C₃×Q₈	C₂²×C₅	semidirect
193. #835	C₂²×C₅	semidirect
194. #835	C₂²×C₅	semidirect
195. #832	C₂²×C₅	semidirect
196. #830	C₂²×C₅	semidirect
205. C₅×#41	#67	semidirect
213. C₂×C₅×Q₈	#67	semidirect
243. C₂×2₋¹⁺⁴	C₅×D₃	semidirect
277. C₃×#41	C₅×D₄	semidirect
285. C₂×C₃×Q₈	C₅×D₄	semidirect
360. C₂×#41	C₂×C₅×D₃	semidirect
363. C₂²×Q₈	C₂×C₅×D₃	semidirect
451. #41	C₅×#67	semidirect
459. C₂×Q₈	C₅×#67	semidirect
489. C₃×C₅	#3010	semidirect
558. C₅	#84113	direct (N × H)
576. C₃	C₅×#3010	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×2₋¹⁺⁴	2
C₅×#5830	2
C₂×C₅×#949	2
C₂²×C₅×#215	2
C₅×#5238	2
C₅×#5234	2
C₅×#5233	2
C₅×#5227	2
C₅×#5225	2
C₅×#3010	3
#84113	5

Subgroups — C5×#84113 #14424429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#84113 #14424429