Subgroups — C₅×#84122 #14425455

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5830	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#949	C₂	1	2	yes	maximal, complemented
4	C₅×#5245	C₂	1	4	yes	maximal, complemented
5	C₅×#5241	C₂	1	4	yes	maximal, complemented
6	C₅×#5237	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5236	C₂	1	2	yes	maximal, complemented
8	C₅×#3021	—	3	1	no	maximal, Hall
9	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
10	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	complemented
11	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
12	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
13	C₃×C₅×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂×C₃×C₅×#41	—	2	4	no	—
15	C₂×C₃×C₅×#41	—	2	2	no	—
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
19	C₅×#949	—	2	4	no	—
20	C₅×#949	C₂²	1	8	yes	complemented
21	C₅×#947	C₂²	1	2	yes	complemented
22	C₂×C₅×#215	—	2	2	no	—
23	C₅×#940	C₂²	1	2	yes	complemented
24	C₅×#937	—	2	2	no	—
25	C₂×C₅×#213	—	2	2	no	—
26	C₅×#930	—	2	2	no	—
27	C₅×#926	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#208	C₂²	1	2	yes	complemented
29	C₅×#837	C₂²	1	8	yes	complemented
30	C₅×#836	C₂²	1	2	yes	complemented
31	C₅×#833	C₂²	1	2	yes	complemented
32	#84122	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#585	D₃	1	1	yes	characteristic, complemented
34	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
35	C₅×#535	—	3	1	no	—
36	C₅×#454	—	3	4	no	—
37	C₅×#453	—	3	4	no	—
38	C₅×#421	—	3	2	no	—
39	C₅×#413	—	3	1	no	—
40	C₂³×C₅×D₃	—	2	1	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	8	no	—
43	C₃×C₅×#41	—	2	4	no	—
44	C₃×C₅×#41	—	2	4	no	—
45	C₃×C₅×#41	—	2	4	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	—	2	2	no	—
48	C₃×C₅×#41	—	2	4	no	—
49	C₃×C₅×#41	—	2	2	no	—
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	D₄	1	4	yes	complemented
52	C₃×C₅×#41	C₂³	1	4	yes	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	—	2	4	no	—
55	C₂×C₃×C₅×Q₈	D₄	1	2	yes	complemented
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	—	2	8	no	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	4	no	—
62	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
63	C₂×C₃×C₅×D₄	D₄	1	2	yes	complemented
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	4	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×#67	—	2	4	no	—
70	C₂×C₅×D₁₂	—	2	2	no	—
71	C₂×C₅×D₁₂	—	2	2	no	—
72	C₂×C₅×D₁₂	—	2	1	no	—
73	C₂×C₅×D₁₂	C₂³	1	2	yes	—
74	C₅×#217	—	2	1	no	—
75	C₅×#215	—	2	8	no	—
76	C₅×#213	—	2	8	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
78	C₅×C₄⋊Dic₃	—	2	1	no	—
79	C₄×C₅×Dic₃	C₂³	1	2	yes	—
80	C₅×#208	—	2	2	no	—
81	C₅×#208	C₂³	1	4	yes	—
82	C₂×C₅×C₃⋊C₈	—	2	2	no	—
83	C₃×#585	C₂×C₅	1	1	yes	characteristic, complemented
84	#5830	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×#949	C₂×C₅	1	2	yes	complemented
86	#5245	C₂×C₅	1	4	yes	complemented
87	#5241	C₂×C₅	1	4	yes	complemented
88	#5237	C₂×C₅	1	1	yes	characteristic, complemented
89	#5236	C₂×C₅	1	2	yes	complemented
90	C₅×2₋¹⁺⁴	—	2	2	no	—
91	C₅×2₋¹⁺⁴	C₂×D₃	1	2	yes	complemented
92	C₅×H(5,𝔽₂)	—	2	2	no	—
93	C₅×H(5,𝔽₂)	—	2	2	no	—
94	C₅×H(5,𝔽₂)	C₂×D₃	1	2	yes	complemented
95	C₂×C₅×#41	—	2	4	no	—
96	C₂×C₅×#41	—	2	2	no	—
97	C₂×C₅×#41	C₂×D₃	1	2	yes	—
98	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₅×D₄	—	3	1	no	—
100	C₅×AGL(1,ℤ/8)	—	3	8	no	—
101	C₅×AGL(1,ℤ/8)	—	6	4	no	—
102	C₂×C₅×SD₁₆	—	6	2	no	—
103	C₂×C₅×D₈	—	6	2	no	—
104	C₂×C₅×M₁₆	—	3	2	no	—
105	C₅×#127	—	3	2	no	—
106	C₅×#124	—	3	2	no	—
107	C₅×#121	—	6	2	no	—
108	C₅×#120	—	6	2	no	—
109	C₅×#117	—	3	1	no	—
110	C₅×#104	—	3	8	no	—
111	C₅×#101	—	3	2	no	—
112	C₅×#100	—	3	2	no	—
113	#3021	—	3	1	no	Sylow
114	C₂³×C₃×C₅	—	2	4	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
117	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₅×D₃	—	2	2	no	—
119	C₂²×C₅×D₃	—	4	2	no	—
120	C₂²×C₅×D₃	—	8	2	no	—
121	C₃×C₅×Q₈	—	2	4	no	—
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×Q₈	—	2	2	no	—
124	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
125	C₃×C₅×D₄	—	2	8	no	—
126	C₃×C₅×D₄	—	2	4	no	—
127	C₃×C₅×D₄	—	2	4	no	—
128	C₃×C₅×D₄	—	2	4	no	—
129	C₃×C₅×D₄	—	2	4	no	—
130	C₃×C₅×D₄	—	2	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	—	2	4	no	—
134	C₂×C₃×C₄×C₅	—	2	8	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	4	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×#67	—	8	4	no	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₅×D₁₂	—	2	4	no	—
148	C₅×D₁₂	—	4	1	no	—
149	C₅×D₁₂	—	4	1	no	—
150	C₅×C₃⋊C₈	—	2	4	no	—
151	C₃×2₋¹⁺⁴	—	2	2	no	—
152	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	complemented
153	C₃×H(5,𝔽₂)	—	2	2	no	—
154	C₃×H(5,𝔽₂)	—	2	2	no	—
155	C₃×H(5,𝔽₂)	C₂²×C₅	1	2	yes	complemented
156	C₂×C₃×#41	—	2	4	no	—
157	C₂×C₃×#41	—	2	2	no	—
158	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
159	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
160	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
161	#949	—	2	4	no	—
162	#949	C₂²×C₅	1	8	yes	complemented
163	#947	C₂²×C₅	1	2	yes	complemented
164	C₂×#215	—	2	2	no	—
165	#940	C₂²×C₅	1	2	yes	complemented
166	#937	—	2	2	no	—
167	C₂×#213	—	2	2	no	—
168	#930	—	2	2	no	—
169	#926	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₂×#208	C₂²×C₅	1	2	yes	complemented
171	#837	C₂²×C₅	1	8	yes	complemented
172	#836	C₂²×C₅	1	2	yes	complemented
173	#833	C₂²×C₅	1	2	yes	complemented
174	C₂⁴×C₅	—	6	1	no	—
175	C₅×#41	—	2	4	no	—
176	C₅×#41	—	2	8	no	—
177	C₅×#41	—	2	4	no	—
178	C₅×#41	—	2	4	no	—
179	C₅×#41	—	2	4	no	—
180	C₅×#41	—	2	2	no	—
181	C₅×#41	—	2	2	no	—
182	C₅×#41	—	2	4	no	—
183	C₅×#41	—	2	2	no	—
184	C₅×#41	—	2	2	no	—
185	C₅×#41	#67	1	4	yes	complemented
186	C₅×#41	C₂²×D₃	1	4	yes	—
187	C₂×C₅×Q₈	—	2	2	no	—
188	C₂×C₅×Q₈	—	2	4	no	—
189	C₂×C₅×Q₈	#67	1	2	yes	complemented
190	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₅×D₄	—	2	8	no	—
192	C₂×C₅×D₄	—	2	2	no	—
193	C₂×C₅×D₄	—	2	4	no	—
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	2	4	no	—
196	C₂×C₅×D₄	—	3	2	no	—
197	C₂×C₅×D₄	—	6	4	no	—
198	C₂×C₅×D₄	—	6	2	no	—
199	C₂×C₅×D₄	—	6	2	no	—
200	C₂×C₅×D₄	—	6	1	no	—
201	C₂×C₅×D₄	#67	1	2	yes	—
202	C₂×C₅×D₄	#67	1	2	yes	complemented
203	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	2	4	no	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	#67	1	2	yes	—
207	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₅×SD₁₆	—	6	8	no	—
209	C₅×D₈	—	6	8	no	—
210	C₅×M₁₆	—	3	4	no	—
211	C₅×M₁₆	—	6	2	no	—
212	C₂×C₅×C₈	—	6	2	no	—
213	C₅×C₄⋊C₄	—	6	1	no	—
214	C₅×C₂²⋊C₄	—	6	1	no	—
215	C₅×C₂²⋊C₄	—	6	4	no	—
216	C₄²×C₅	—	3	2	no	—
217	#585	C₅×D₃	1	1	yes	characteristic, complemented
218	C₂×AGL(1,ℤ/8)	—	3	2	no	—
219	#535	—	3	1	no	—
220	#454	—	3	4	no	—
221	#453	—	3	4	no	—
222	#421	—	3	2	no	—
223	#413	—	3	1	no	—
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	2	4	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	—	4	2	no	—
228	C₂²×C₃×C₅	—	8	2	no	—
229	C₂²×C₃×C₅	—	8	4	no	—
230	C₂²×C₃×C₅	#120	1	2	yes	—
231	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₅×D₃	—	4	4	no	—
233	C₂×C₅×D₃	—	4	2	no	—
234	C₂×C₅×D₃	—	8	4	no	—
235	C₃×C₄×C₅	—	2	4	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	#120	1	1	yes	characteristic
238	C₃×C₄×C₅	#120	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
240	C₅×Dic₃	—	4	2	no	—
241	C₂³×D₃	—	2	1	no	—
242	C₃×#41	—	2	4	no	—
243	C₃×#41	—	2	8	no	—
244	C₃×#41	—	2	4	no	—
245	C₃×#41	—	2	4	no	—
246	C₃×#41	—	2	4	no	—
247	C₃×#41	—	2	2	no	—
248	C₃×#41	—	2	2	no	—
249	C₃×#41	—	2	4	no	—
250	C₃×#41	—	2	2	no	—
251	C₃×#41	—	2	2	no	—
252	C₃×#41	C₅×D₄	1	4	yes	complemented
253	C₃×#41	C₂³×C₅	1	4	yes	—
254	C₂×C₃×Q₈	—	2	2	no	—
255	C₂×C₃×Q₈	—	2	4	no	—
256	C₂×C₃×Q₈	C₅×D₄	1	2	yes	complemented
257	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₃×D₄	—	2	8	no	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	2	4	no	—
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	—	2	4	no	—
263	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
264	C₂×C₃×D₄	C₅×D₄	1	2	yes	complemented
265	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₄	—	2	4	no	—
267	C₂²×C₃×C₄	—	2	2	no	—
268	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×#67	—	2	4	no	—
271	C₂×D₁₂	—	2	2	no	—
272	C₂×D₁₂	—	2	2	no	—
273	C₂×D₁₂	—	2	1	no	—
274	C₂×D₁₂	C₂³×C₅	1	2	yes	—
275	#217	—	2	1	no	—
276	#215	—	2	8	no	—
277	#213	—	2	8	no	—
278	(C₂×D₃)⋊C₄	—	2	4	no	—
279	C₄⋊Dic₃	—	2	1	no	—
280	C₄×Dic₃	C₂³×C₅	1	2	yes	—
281	#208	—	2	2	no	—
282	#208	C₂³×C₅	1	4	yes	—
283	C₂×C₃⋊C₈	—	2	2	no	—
284	C₂³×C₅	—	2	4	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	6	2	no	—
287	C₂³×C₅	—	12	2	no	—
288	C₂³×C₅	—	24	2	no	—
289	C₂³×C₅	C₂×#67	1	2	yes	—
290	C₂³×C₅	C₂×#67	1	1	yes	characteristic
291	C₅×Q₈	—	2	4	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	C₂×#67	1	4	yes	—
295	C₅×D₄	—	2	8	no	—
296	C₅×D₄	—	2	4	no	—
297	C₅×D₄	—	2	4	no	—
298	C₅×D₄	—	2	4	no	—
299	C₅×D₄	—	2	4	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	6	4	no	—
303	C₅×D₄	—	12	1	no	—
304	C₅×D₄	—	12	1	no	—
305	C₅×D₄	—	24	4	no	—
306	C₅×D₄	C₂×#67	1	4	yes	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	8	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	4	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	6	2	no	—
315	C₂×C₄×C₅	C₂×#67	1	2	yes	—
316	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×#67	1	2	yes	—
318	C₂×C₄×C₅	C₂×#67	1	2	yes	—
319	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
320	C₅×C₈	—	6	4	no	—
321	2₋¹⁺⁴	—	2	2	no	—
322	2₋¹⁺⁴	C₂×C₅×D₃	1	2	yes	complemented
323	H(5,𝔽₂)	—	2	2	no	—
324	H(5,𝔽₂)	—	2	2	no	—
325	H(5,𝔽₂)	C₂×C₅×D₃	1	2	yes	complemented
326	C₂×#41	—	2	4	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	C₂×C₅×D₃	1	2	yes	—
329	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
330	C₂²×D₄	—	3	1	no	—
331	AGL(1,ℤ/8)	—	3	8	no	—
332	AGL(1,ℤ/8)	—	6	4	no	—
333	C₂×SD₁₆	—	6	2	no	—
334	C₂×D₈	—	6	2	no	—
335	C₂×M₁₆	—	3	2	no	—
336	#127	—	3	2	no	—
337	#124	—	3	2	no	—
338	#121	—	6	2	no	—
339	#120	—	6	2	no	—
340	#117	—	3	1	no	—
341	#104	—	3	8	no	—
342	#101	—	3	2	no	—
343	#100	—	3	2	no	—
344	C₂×C₃×C₅	—	2	1	no	—
345	C₂×C₃×C₅	—	2	2	no	—
346	C₂×C₃×C₅	—	4	2	no	—
347	C₂×C₃×C₅	—	4	4	no	—
348	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
349	C₅×D₃	—	8	2	no	—
350	C₂³×C₃	—	2	4	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
353	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	—	8	2	no	—
357	C₃×Q₈	—	2	4	no	—
358	C₃×Q₈	—	2	2	no	—
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
361	C₃×D₄	—	2	8	no	—
362	C₃×D₄	—	2	4	no	—
363	C₃×D₄	—	2	4	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	8	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	4	no	—
376	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
379	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
380	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
381	#67	—	8	4	no	—
382	C₂×Dic₃	—	2	2	no	—
383	D₁₂	—	2	4	no	—
384	D₁₂	—	4	1	no	—
385	D₁₂	—	4	1	no	—
386	C₃⋊C₈	—	2	4	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	4	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	—	8	2	no	—
392	C₂²×C₅	—	8	4	no	—
393	C₂²×C₅	—	12	4	no	—
394	C₂²×C₅	—	12	2	no	—
395	C₂²×C₅	—	24	4	no	—
396	C₂²×C₅	#953	1	2	yes	—
397	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
398	C₄×C₅	—	2	4	no	—
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	12	2	no	—
401	C₄×C₅	#953	1	1	yes	characteristic
402	C₄×C₅	#953	1	1	yes	characteristic
403	C₄×C₅	C₂²×#67	1	2	yes	—
404	C₂⁴	—	6	1	no	—
405	#41	—	2	4	no	—
406	#41	—	2	8	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	4	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	C₅×#67	1	4	yes	complemented
416	#41	C₂²×C₅×D₃	1	4	yes	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	C₅×#67	1	2	yes	complemented
420	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	6	4	no	—
428	C₂×D₄	—	6	2	no	—
429	C₂×D₄	—	6	2	no	—
430	C₂×D₄	—	6	1	no	—
431	C₂×D₄	C₅×#67	1	2	yes	—
432	C₂×D₄	C₅×#67	1	2	yes	complemented
433	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	C₅×#67	1	2	yes	—
437	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
438	SD₁₆	—	6	8	no	—
439	D₈	—	6	8	no	—
440	M₁₆	—	3	4	no	—
441	M₁₆	—	6	2	no	—
442	C₂×C₈	—	6	2	no	—
443	C₄⋊C₄	—	6	1	no	—
444	C₂²⋊C₄	—	6	1	no	—
445	C₂²⋊C₄	—	6	4	no	—
446	C₄²	—	3	2	no	—
447	C₃×C₅	#3021	1	1	yes	characteristic, complemented, Hall
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	4	no	—
450	C₂²×C₃	—	4	1	no	—
451	C₂²×C₃	—	4	2	no	—
452	C₂²×C₃	—	8	2	no	—
453	C₂²×C₃	—	8	4	no	—
454	C₂²×C₃	C₅×#120	1	2	yes	—
455	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
456	C₂×D₃	—	4	4	no	—
457	C₂×D₃	—	4	2	no	—
458	C₂×D₃	—	8	4	no	—
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	C₅×#120	1	1	yes	characteristic
462	C₃×C₄	C₅×#120	1	1	yes	characteristic
463	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
464	Dic₃	—	4	2	no	—
465	C₂×C₅	—	2	1	no	—
466	C₂×C₅	—	2	2	no	—
467	C₂×C₅	—	4	2	no	—
468	C₂×C₅	—	4	4	no	—
469	C₂×C₅	—	24	2	no	—
470	C₂×C₅	C₂×#953	1	1	yes	characteristic
471	C₂³	—	2	4	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	6	2	no	—
474	C₂³	—	12	2	no	—
475	C₂³	—	24	2	no	—
476	C₂³	C₂×C₅×#67	1	2	yes	—
477	C₂³	C₂×C₅×#67	1	1	yes	characteristic
478	Q₈	—	2	4	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	C₂×C₅×#67	1	4	yes	—
482	D₄	—	2	8	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	6	4	no	—
490	D₄	—	12	1	no	—
491	D₄	—	12	1	no	—
492	D₄	—	24	4	no	—
493	D₄	C₂×C₅×#67	1	4	yes	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	6	2	no	—
502	C₂×C₄	C₂×C₅×#67	1	2	yes	—
503	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
504	C₂×C₄	C₂×C₅×#67	1	2	yes	—
505	C₂×C₄	C₂×C₅×#67	1	2	yes	—
506	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
507	C₈	—	6	4	no	—
508	C₂×C₃	—	2	1	no	—
509	C₂×C₃	—	2	2	no	—
510	C₂×C₃	—	4	2	no	—
511	C₂×C₃	—	4	4	no	—
512	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
513	D₃	—	8	2	no	—
514	C₅	#84122	1	1	yes	characteristic, direct product factor, Sylow
515	C₂²	—	2	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	4	no	—
521	C₂²	—	12	4	no	—
522	C₂²	—	12	2	no	—
523	C₂²	—	24	4	no	—
524	C₂²	C₅×#953	1	2	yes	—
525	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
526	C₄	—	2	4	no	—
527	C₄	—	2	2	no	—
528	C₄	—	12	2	no	—
529	C₄	C₅×#953	1	1	yes	characteristic
530	C₄	C₅×#953	1	1	yes	characteristic
531	C₄	C₂²×C₅×#67	1	2	yes	—
532	C₃	C₅×#3021	1	1	yes	characteristic, complemented, Sylow
533	C₂	—	2	1	no	—
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	—	4	4	no	—
537	C₂	—	24	2	no	—
538	C₂	C₂×C₅×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#953
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#585	C₂
socle	C₂×C₃×C₅	C₂×#120
hypercenter	C₅×#585	D₃
hypocenter	C₃	C₅×#3021
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#585

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#585	C₂	semidirect
2. C₅×#5830	C₂	semidirect
3. C₂×C₅×#949	C₂	semidirect
4. C₅×#5245	C₂	semidirect
5. C₅×#5241	C₂	semidirect
6. C₅×#5237	C₂	semidirect
7. C₅×#5236	C₂	semidirect
10. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
13. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₅×D₁₂	C₂²	semidirect
20. C₅×#949	C₂²	semidirect
21. C₅×#947	C₂²	semidirect
23. C₅×#940	C₂²	semidirect
27. C₅×#926	C₂²	semidirect
28. C₂×C₅×#208	C₂²	semidirect
29. C₅×#837	C₂²	semidirect
30. C₅×#836	C₂²	semidirect
31. C₅×#833	C₂²	semidirect
32. #84122	C₅	direct (N × H)
33. C₅×#585	D₃	semidirect
51. C₃×C₅×#41	D₄	semidirect
55. C₂×C₃×C₅×Q₈	D₄	semidirect
63. C₂×C₃×C₅×D₄	D₄	semidirect
83. C₃×#585	C₂×C₅	semidirect
84. #5830	C₂×C₅	semidirect
85. C₂×#949	C₂×C₅	semidirect
86. #5245	C₂×C₅	semidirect
87. #5241	C₂×C₅	semidirect
88. #5237	C₂×C₅	semidirect
89. #5236	C₂×C₅	semidirect
91. C₅×2₋¹⁺⁴	C₂×D₃	semidirect
94. C₅×H(5,𝔽₂)	C₂×D₃	semidirect
152. C₃×2₋¹⁺⁴	C₂²×C₅	semidirect
155. C₃×H(5,𝔽₂)	C₂²×C₅	semidirect
160. C₂²×D₁₂	C₂²×C₅	semidirect
162. #949	C₂²×C₅	semidirect
163. #947	C₂²×C₅	semidirect
165. #940	C₂²×C₅	semidirect
169. #926	C₂²×C₅	semidirect
170. C₂×#208	C₂²×C₅	semidirect
171. #837	C₂²×C₅	semidirect
172. #836	C₂²×C₅	semidirect
173. #833	C₂²×C₅	semidirect
185. C₅×#41	#67	semidirect
189. C₂×C₅×Q₈	#67	semidirect
202. C₂×C₅×D₄	#67	semidirect
217. #585	C₅×D₃	semidirect
252. C₃×#41	C₅×D₄	semidirect
256. C₂×C₃×Q₈	C₅×D₄	semidirect
264. C₂×C₃×D₄	C₅×D₄	semidirect
322. 2₋¹⁺⁴	C₂×C₅×D₃	semidirect
325. H(5,𝔽₂)	C₂×C₅×D₃	semidirect
415. #41	C₅×#67	semidirect
419. C₂×Q₈	C₅×#67	semidirect
432. C₂×D₄	C₅×#67	semidirect
447. C₃×C₅	#3021	semidirect
514. C₅	#84122	direct (N × H)
532. C₃	C₅×#3021	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#585	2
C₅×#5830	2
C₂×C₅×#949	2
C₅×#5245	2
C₅×#5241	2
C₅×#5237	2
C₅×#5236	2
C₅×#3021	3
#84122	5

Subgroups — C5×#84122 #14425455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#84122 #14425455