Subgroups — C₃×C₅×#3019 #14276053

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#575	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#455	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#453	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#421	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3019	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
10	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
11	C₃×C₅×H(5,𝔽₂)	C₂²	1	4	yes	—
12	C₂×C₃×C₅×#41	—	2	2	no	—
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅×D₄	—	2	2	no	—
16	C₂²×C₃×C₅×D₄	—	2	2	no	—
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₃×C₅×#137	—	2	2	no	—
19	C₃×C₅×#137	C₂²	1	4	yes	complemented
20	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
21	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₃×C₅×#135	—	2	4	no	—
23	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
24	C₃×C₅×#127	C₂²	1	2	yes	complemented
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#121	—	2	2	no	—
27	C₃×C₅×#120	—	2	2	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#104	C₂²	1	8	yes	complemented
30	C₃×C₅×#100	C₂²	1	4	yes	complemented
31	C₃×#3019	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#575	C₂×C₃	1	2	yes	complemented
34	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#455	C₂×C₃	1	4	yes	complemented
36	C₅×#453	C₂×C₃	1	4	yes	complemented
37	C₅×#421	C₂×C₃	1	2	yes	complemented
38	C₂×C₅×#100	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	—	2	2	no	—
40	C₂⁴×C₃×C₅	D₄	1	2	yes	—
41	C₃×C₅×#41	—	2	8	no	—
42	C₃×C₅×#41	—	2	8	no	—
43	C₃×C₅×#41	—	2	2	no	—
44	C₃×C₅×#41	—	2	2	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	D₄	1	4	yes	complemented
48	C₃×C₅×#41	C₂³	1	4	yes	—
49	C₂×C₃×C₅×Q₈	D₄	1	2	yes	complemented
50	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
51	C₂×C₃×C₅×D₄	—	2	4	no	—
52	C₂×C₃×C₅×D₄	—	2	8	no	—
53	C₂×C₃×C₅×D₄	—	2	8	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	2	8	no	—
56	C₂×C₃×C₅×D₄	—	2	8	no	—
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
62	C₂×C₃×C₅×D₄	D₄	1	2	yes	complemented
63	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₅×Q₁₆	—	2	4	no	—
70	C₃×C₅×SD₁₆	—	2	4	no	—
71	C₃×C₅×SD₁₆	—	2	4	no	—
72	C₃×C₅×D₈	—	2	4	no	—
73	C₃×C₅×M₁₆	—	2	2	no	—
74	C₃×C₅×M₁₆	C₂³	1	4	yes	complemented
75	C₂×C₃×C₅×C₈	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
80	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#575	C₂×C₅	1	2	yes	complemented
82	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#455	C₂×C₅	1	4	yes	complemented
84	C₃×#453	C₂×C₅	1	4	yes	complemented
85	C₃×#421	C₂×C₅	1	2	yes	complemented
86	C₂×C₃×#100	C₂×C₅	1	1	yes	characteristic, complemented
87	C₅×H(5,𝔽₂)	—	2	4	no	—
88	C₅×H(5,𝔽₂)	—	2	2	no	—
89	C₅×H(5,𝔽₂)	C₂²×C₃	1	4	yes	—
90	C₂×C₅×#41	—	2	2	no	—
91	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
92	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₂²×C₅×D₄	—	2	2	no	—
94	C₂²×C₅×D₄	—	2	2	no	—
95	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₅×#137	—	2	2	no	—
97	C₅×#137	C₂²×C₃	1	4	yes	complemented
98	C₅×AGL(1,ℤ/8)	—	2	2	no	—
99	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	complemented
100	C₅×#135	—	2	4	no	—
101	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
102	C₅×#127	C₂²×C₃	1	2	yes	complemented
103	C₅×#124	C₂²×C₃	1	2	yes	complemented
104	C₅×#121	—	2	2	no	—
105	C₅×#120	—	2	2	no	—
106	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₅×#104	C₂²×C₃	1	8	yes	complemented
108	C₅×#100	C₂²×C₃	1	4	yes	complemented
109	#3019	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³×C₃×C₅	—	2	8	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	1	no	—
115	C₂³×C₃×C₅	—	8	2	no	—
116	C₂³×C₃×C₅	—	8	4	no	—
117	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
118	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
119	C₃×C₅×Q₈	—	2	2	no	—
120	C₃×C₅×Q₈	—	2	2	no	—
121	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
122	C₃×C₅×D₄	—	2	16	no	—
123	C₃×C₅×D₄	—	2	4	no	—
124	C₃×C₅×D₄	—	2	4	no	—
125	C₃×C₅×D₄	—	2	4	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	2	4	no	—
128	C₃×C₅×D₄	—	2	2	no	—
129	C₃×C₅×D₄	—	4	1	no	—
130	C₃×C₅×D₄	—	4	1	no	—
131	C₃×C₅×D₄	—	8	4	no	—
132	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	—	2	8	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	4	no	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	4	2	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₃×C₅×C₈	—	2	4	no	—
145	C₃×H(5,𝔽₂)	—	2	4	no	—
146	C₃×H(5,𝔽₂)	—	2	2	no	—
147	C₃×H(5,𝔽₂)	C₂²×C₅	1	4	yes	—
148	C₂×C₃×#41	—	2	2	no	—
149	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
150	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
151	C₂²×C₃×D₄	—	2	2	no	—
152	C₂²×C₃×D₄	—	2	2	no	—
153	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
154	C₃×#137	—	2	2	no	—
155	C₃×#137	C₂²×C₅	1	4	yes	complemented
156	C₃×AGL(1,ℤ/8)	—	2	2	no	—
157	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	4	yes	complemented
158	C₃×#135	—	2	4	no	—
159	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
160	C₃×#127	C₂²×C₅	1	2	yes	complemented
161	C₃×#124	C₂²×C₅	1	2	yes	complemented
162	C₃×#121	—	2	2	no	—
163	C₃×#120	—	2	2	no	—
164	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
165	C₃×#104	C₂²×C₅	1	8	yes	complemented
166	C₃×#100	C₂²×C₅	1	4	yes	complemented
167	C₂⁴×C₅	—	2	2	no	—
168	C₂⁴×C₅	C₃×D₄	1	2	yes	—
169	C₅×#41	—	2	8	no	—
170	C₅×#41	—	2	8	no	—
171	C₅×#41	—	2	2	no	—
172	C₅×#41	—	2	2	no	—
173	C₅×#41	—	2	2	no	—
174	C₅×#41	—	2	2	no	—
175	C₅×#41	C₃×D₄	1	4	yes	complemented
176	C₅×#41	C₂³×C₃	1	4	yes	—
177	C₂×C₅×Q₈	C₃×D₄	1	2	yes	complemented
178	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
179	C₂×C₅×D₄	—	2	4	no	—
180	C₂×C₅×D₄	—	2	8	no	—
181	C₂×C₅×D₄	—	2	8	no	—
182	C₂×C₅×D₄	—	2	2	no	—
183	C₂×C₅×D₄	—	2	8	no	—
184	C₂×C₅×D₄	—	2	8	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	4	no	—
187	C₂×C₅×D₄	—	2	2	no	—
188	C₂×C₅×D₄	—	2	2	no	—
189	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
190	C₂×C₅×D₄	C₃×D₄	1	2	yes	complemented
191	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
192	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
193	C₂²×C₄×C₅	—	2	2	no	—
194	C₂²×C₄×C₅	—	2	2	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₅×Q₁₆	—	2	4	no	—
198	C₅×SD₁₆	—	2	4	no	—
199	C₅×SD₁₆	—	2	4	no	—
200	C₅×D₈	—	2	4	no	—
201	C₅×M₁₆	—	2	2	no	—
202	C₅×M₁₆	C₂³×C₃	1	4	yes	complemented
203	C₂×C₅×C₈	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₄²×C₅	C₂³×C₃	1	2	yes	complemented
208	C₂×H(5,𝔽₂)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	#575	C₂×C₃×C₅	1	2	yes	complemented
210	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
211	#455	C₂×C₃×C₅	1	4	yes	complemented
212	#453	C₂×C₃×C₅	1	4	yes	complemented
213	#421	C₂×C₃×C₅	1	2	yes	complemented
214	C₂×#100	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	C₂²×C₃×C₅	—	2	4	no	—
216	C₂²×C₃×C₅	—	2	4	no	—
217	C₂²×C₃×C₅	—	4	1	no	—
218	C₂²×C₃×C₅	—	4	4	no	—
219	C₂²×C₃×C₅	—	4	4	no	—
220	C₂²×C₃×C₅	—	4	4	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	1	no	—
223	C₂²×C₃×C₅	—	8	2	no	—
224	C₂²×C₃×C₅	—	8	8	no	—
225	C₂²×C₃×C₅	#120	1	1	yes	characteristic
226	C₂²×C₃×C₅	#120	1	1	yes	characteristic
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₃×C₄×C₅	—	2	4	no	—
229	C₃×C₄×C₅	—	4	2	no	—
230	C₃×C₄×C₅	—	4	1	no	—
231	C₃×C₄×C₅	#120	1	2	yes	—
232	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
233	C₂⁴×C₃	—	2	2	no	—
234	C₂⁴×C₃	C₅×D₄	1	2	yes	—
235	C₃×#41	—	2	8	no	—
236	C₃×#41	—	2	8	no	—
237	C₃×#41	—	2	2	no	—
238	C₃×#41	—	2	2	no	—
239	C₃×#41	—	2	2	no	—
240	C₃×#41	—	2	2	no	—
241	C₃×#41	C₅×D₄	1	4	yes	complemented
242	C₃×#41	C₂³×C₅	1	4	yes	—
243	C₂×C₃×Q₈	C₅×D₄	1	2	yes	complemented
244	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic, complemented
245	C₂×C₃×D₄	—	2	4	no	—
246	C₂×C₃×D₄	—	2	8	no	—
247	C₂×C₃×D₄	—	2	8	no	—
248	C₂×C₃×D₄	—	2	2	no	—
249	C₂×C₃×D₄	—	2	8	no	—
250	C₂×C₃×D₄	—	2	8	no	—
251	C₂×C₃×D₄	—	2	1	no	—
252	C₂×C₃×D₄	—	2	4	no	—
253	C₂×C₃×D₄	—	2	2	no	—
254	C₂×C₃×D₄	—	2	2	no	—
255	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
256	C₂×C₃×D₄	C₅×D₄	1	2	yes	complemented
257	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
258	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic, complemented
259	C₂²×C₃×C₄	—	2	2	no	—
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	—	2	1	no	—
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₃×Q₁₆	—	2	4	no	—
264	C₃×SD₁₆	—	2	4	no	—
265	C₃×SD₁₆	—	2	4	no	—
266	C₃×D₈	—	2	4	no	—
267	C₃×M₁₆	—	2	2	no	—
268	C₃×M₁₆	C₂³×C₅	1	4	yes	complemented
269	C₂×C₃×C₈	—	2	2	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₂²⋊C₄	—	2	1	no	—
272	C₃×C₂²⋊C₄	—	2	4	no	—
273	C₃×C₄²	C₂³×C₅	1	2	yes	complemented
274	C₂³×C₅	—	2	8	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	2	no	—
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	8	2	no	—
280	C₂³×C₅	—	8	4	no	—
281	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
282	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₅×Q₈	—	2	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
286	C₅×D₄	—	2	16	no	—
287	C₅×D₄	—	2	4	no	—
288	C₅×D₄	—	2	4	no	—
289	C₅×D₄	—	2	4	no	—
290	C₅×D₄	—	2	2	no	—
291	C₅×D₄	—	2	4	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₅×D₄	—	8	4	no	—
296	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
297	C₂×C₄×C₅	—	2	8	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	4	2	no	—
304	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
306	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
307	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
308	C₅×C₈	—	2	4	no	—
309	H(5,𝔽₂)	—	2	4	no	—
310	H(5,𝔽₂)	—	2	2	no	—
311	H(5,𝔽₂)	C₂²×C₃×C₅	1	4	yes	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
314	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
318	#137	—	2	2	no	—
319	#137	C₂²×C₃×C₅	1	4	yes	complemented
320	AGL(1,ℤ/8)	—	2	2	no	—
321	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	4	yes	complemented
322	#135	—	2	4	no	—
323	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
324	#127	C₂²×C₃×C₅	1	2	yes	complemented
325	#124	C₂²×C₃×C₅	1	2	yes	complemented
326	#121	—	2	2	no	—
327	#120	—	2	2	no	—
328	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
329	#104	C₂²×C₃×C₅	1	8	yes	complemented
330	#100	C₂²×C₃×C₅	1	4	yes	complemented
331	C₂×C₃×C₅	—	2	1	no	—
332	C₂×C₃×C₅	—	2	1	no	—
333	C₂×C₃×C₅	—	2	1	no	—
334	C₂×C₃×C₅	—	4	4	no	—
335	C₂×C₃×C₅	—	4	4	no	—
336	C₂×C₃×C₅	—	8	1	no	—
337	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
338	C₂³×C₃	—	2	8	no	—
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	2	2	no	—
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	8	2	no	—
344	C₂³×C₃	—	8	4	no	—
345	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
346	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	2	2	no	—
349	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
350	C₃×D₄	—	2	16	no	—
351	C₃×D₄	—	2	4	no	—
352	C₃×D₄	—	2	4	no	—
353	C₃×D₄	—	2	4	no	—
354	C₃×D₄	—	2	2	no	—
355	C₃×D₄	—	2	4	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	4	1	no	—
358	C₃×D₄	—	4	1	no	—
359	C₃×D₄	—	8	4	no	—
360	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
361	C₂×C₃×C₄	—	2	8	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	4	no	—
364	C₂×C₃×C₄	—	2	4	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	4	2	no	—
368	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
370	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
371	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
372	C₃×C₈	—	2	4	no	—
373	C₂²×C₅	—	2	4	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	4	1	no	—
376	C₂²×C₅	—	4	4	no	—
377	C₂²×C₅	—	4	4	no	—
378	C₂²×C₅	—	4	4	no	—
379	C₂²×C₅	—	4	2	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	8	2	no	—
382	C₂²×C₅	—	8	8	no	—
383	C₂²×C₅	C₃×#120	1	1	yes	characteristic
384	C₂²×C₅	C₃×#120	1	1	yes	characteristic
385	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
386	C₄×C₅	—	2	4	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	C₃×#120	1	2	yes	—
390	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	C₃×C₅×D₄	1	2	yes	—
393	#41	—	2	8	no	—
394	#41	—	2	8	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	C₃×C₅×D₄	1	4	yes	complemented
400	#41	C₂³×C₃×C₅	1	4	yes	—
401	C₂×Q₈	C₃×C₅×D₄	1	2	yes	complemented
402	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic, complemented
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
414	C₂×D₄	C₃×C₅×D₄	1	2	yes	complemented
415	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
416	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic, complemented
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
421	Q₁₆	—	2	4	no	—
422	SD₁₆	—	2	4	no	—
423	SD₁₆	—	2	4	no	—
424	D₈	—	2	4	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	C₂³×C₃×C₅	1	4	yes	complemented
427	C₂×C₈	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₄²	C₂³×C₃×C₅	1	2	yes	complemented
432	C₃×C₅	#3019	1	1	yes	characteristic, direct product factor, Hall
433	C₂²×C₃	—	2	4	no	—
434	C₂²×C₃	—	2	4	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	—	4	4	no	—
437	C₂²×C₃	—	4	4	no	—
438	C₂²×C₃	—	4	4	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	8	2	no	—
442	C₂²×C₃	—	8	8	no	—
443	C₂²×C₃	C₅×#120	1	1	yes	characteristic
444	C₂²×C₃	C₅×#120	1	1	yes	characteristic
445	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
446	C₃×C₄	—	2	4	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	4	1	no	—
449	C₃×C₄	C₅×#120	1	2	yes	—
450	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	1	no	—
454	C₂×C₅	—	4	4	no	—
455	C₂×C₅	—	4	4	no	—
456	C₂×C₅	—	8	1	no	—
457	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
458	C₂³	—	2	8	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	8	2	no	—
464	C₂³	—	8	4	no	—
465	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
466	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
470	D₄	—	2	16	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	2	no	—
477	D₄	—	4	1	no	—
478	D₄	—	4	1	no	—
479	D₄	—	8	4	no	—
480	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
490	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
491	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
492	C₈	—	2	4	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	2	1	no	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	4	4	no	—
497	C₂×C₃	—	4	4	no	—
498	C₂×C₃	—	8	1	no	—
499	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
500	C₅	C₃×#3019	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₃×C₅×#120	1	1	yes	characteristic
512	C₂²	C₃×C₅×#120	1	1	yes	characteristic
513	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
514	C₄	—	2	4	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	C₃×C₅×#120	1	2	yes	—
518	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
519	C₃	C₅×#3019	1	1	yes	characteristic, direct product factor, Sylow
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	4	no	—
524	C₂	—	4	4	no	—
525	C₂	—	8	1	no	—
526	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×H(5,𝔽₂)	C₂	semidirect
2. C₃×C₅×#575	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₃×C₅×#455	C₂	semidirect
5. C₃×C₅×#453	C₂	semidirect
6. C₃×C₅×#421	C₂	semidirect
7. C₂×C₃×C₅×#100	C₂	semidirect
8. C₅×#3019	C₃	direct (N × H)
14. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₃×C₅×#137	C₂²	semidirect
21. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₃×C₅×#127	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
28. C₃×C₅×#117	C₂²	semidirect
29. C₃×C₅×#104	C₂²	semidirect
30. C₃×C₅×#100	C₂²	semidirect
31. C₃×#3019	C₅	direct (N × H)
32. C₂×C₅×H(5,𝔽₂)	C₂×C₃	semidirect
33. C₅×#575	C₂×C₃	semidirect
34. C₅×#535	C₂×C₃	semidirect
35. C₅×#455	C₂×C₃	semidirect
36. C₅×#453	C₂×C₃	semidirect
37. C₅×#421	C₂×C₃	semidirect
38. C₂×C₅×#100	C₂×C₃	semidirect
47. C₃×C₅×#41	D₄	semidirect
49. C₂×C₃×C₅×Q₈	D₄	semidirect
50. C₂×C₃×C₅×Q₈	C₂³	semidirect
62. C₂×C₃×C₅×D₄	D₄	semidirect
64. C₂×C₃×C₅×D₄	C₂³	semidirect
74. C₃×C₅×M₁₆	C₂³	semidirect
79. C₃×C₄²×C₅	C₂³	semidirect
80. C₂×C₃×H(5,𝔽₂)	C₂×C₅	semidirect
81. C₃×#575	C₂×C₅	semidirect
82. C₃×#535	C₂×C₅	semidirect
83. C₃×#455	C₂×C₅	semidirect
84. C₃×#453	C₂×C₅	semidirect
85. C₃×#421	C₂×C₅	semidirect
86. C₂×C₃×#100	C₂×C₅	semidirect
92. C₂×C₅×#41	C₂²×C₃	semidirect
97. C₅×#137	C₂²×C₃	semidirect
99. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
101. C₂×C₅×M₁₆	C₂²×C₃	semidirect
102. C₅×#127	C₂²×C₃	semidirect
103. C₅×#124	C₂²×C₃	semidirect
106. C₅×#117	C₂²×C₃	semidirect
107. C₅×#104	C₂²×C₃	semidirect
108. C₅×#100	C₂²×C₃	semidirect
109. #3019	C₃×C₅	direct (N × H)
150. C₂×C₃×#41	C₂²×C₅	semidirect
155. C₃×#137	C₂²×C₅	semidirect
157. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
159. C₂×C₃×M₁₆	C₂²×C₅	semidirect
160. C₃×#127	C₂²×C₅	semidirect
161. C₃×#124	C₂²×C₅	semidirect
164. C₃×#117	C₂²×C₅	semidirect
165. C₃×#104	C₂²×C₅	semidirect
166. C₃×#100	C₂²×C₅	semidirect
175. C₅×#41	C₃×D₄	semidirect
177. C₂×C₅×Q₈	C₃×D₄	semidirect
178. C₂×C₅×Q₈	C₂³×C₃	semidirect
190. C₂×C₅×D₄	C₃×D₄	semidirect
192. C₂×C₅×D₄	C₂³×C₃	semidirect
202. C₅×M₁₆	C₂³×C₃	semidirect
207. C₄²×C₅	C₂³×C₃	semidirect
208. C₂×H(5,𝔽₂)	C₂×C₃×C₅	semidirect
209. #575	C₂×C₃×C₅	semidirect
210. #535	C₂×C₃×C₅	semidirect
211. #455	C₂×C₃×C₅	semidirect
212. #453	C₂×C₃×C₅	semidirect
213. #421	C₂×C₃×C₅	semidirect
214. C₂×#100	C₂×C₃×C₅	semidirect
241. C₃×#41	C₅×D₄	semidirect
243. C₂×C₃×Q₈	C₅×D₄	semidirect
244. C₂×C₃×Q₈	C₂³×C₅	semidirect
256. C₂×C₃×D₄	C₅×D₄	semidirect
258. C₂×C₃×D₄	C₂³×C₅	semidirect
268. C₃×M₁₆	C₂³×C₅	semidirect
273. C₃×C₄²	C₂³×C₅	semidirect
314. C₂×#41	C₂²×C₃×C₅	semidirect
319. #137	C₂²×C₃×C₅	semidirect
321. AGL(1,ℤ/8)	C₂²×C₃×C₅	semidirect
323. C₂×M₁₆	C₂²×C₃×C₅	semidirect
324. #127	C₂²×C₃×C₅	semidirect
325. #124	C₂²×C₃×C₅	semidirect
328. #117	C₂²×C₃×C₅	semidirect
329. #104	C₂²×C₃×C₅	semidirect
330. #100	C₂²×C₃×C₅	semidirect
399. #41	C₃×C₅×D₄	semidirect
401. C₂×Q₈	C₃×C₅×D₄	semidirect
402. C₂×Q₈	C₂³×C₃×C₅	semidirect
414. C₂×D₄	C₃×C₅×D₄	semidirect
416. C₂×D₄	C₂³×C₃×C₅	semidirect
426. M₁₆	C₂³×C₃×C₅	semidirect
431. C₄²	C₂³×C₃×C₅	semidirect
432. C₃×C₅	#3019	direct (N × H)
500. C₅	C₃×#3019	direct (N × H)
519. C₃	C₅×#3019	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×H(5,𝔽₂)	2
C₃×C₅×#575	2
C₃×C₅×#535	2
C₃×C₅×#455	2
C₃×C₅×#453	2
C₃×C₅×#421	2
C₂×C₃×C₅×#100	2
C₅×#3019	3
C₃×#3019	5

Subgroups — C3×C5×#3019 #14276053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3019 #14276053