Subgroups — C₃×C₅×#3041 #14276075

Order 1920.

1052 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#463	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#459	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3041	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×D₈	—	2	4	no	—
17	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#127	C₂²	1	2	yes	complemented
22	C₃×C₅×#124	C₂²	1	2	yes	complemented
23	C₃×C₅×#121	—	2	2	no	—
24	C₃×C₅×#120	—	2	2	no	—
25	C₃×C₄×C₅×D₄	—	2	2	no	—
26	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
27	C₃×C₅×#117	C₂²	1	1	yes	characteristic
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
31	C₃×C₅×#103	C₂²	1	2	yes	complemented
32	C₃×C₅×#102	C₂²	1	2	yes	complemented
33	C₃×C₅×#102	C₂²	1	4	yes	complemented
34	C₃×#3041	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#518	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#463	C₂×C₃	1	4	yes	complemented
40	C₅×#459	C₂×C₃	1	4	yes	complemented
41	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	—	2	1	no	—
45	C₂⁴×C₃×C₅	—	2	1	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	—	2	2	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	2	1	no	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	1	no	—
53	C₂×C₃×C₅×D₄	—	2	4	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	4	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₃×C₅×D₈	—	2	8	no	—
65	C₃×C₅×D₈	—	2	4	no	—
66	C₃×C₅×M₁₆	—	2	2	no	—
67	C₂×C₃×C₅×C₈	—	2	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#463	C₂×C₅	1	4	yes	complemented
83	C₃×#459	C₂×C₅	1	4	yes	complemented
84	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₅×AGL(1,ℤ/8)	—	2	4	no	—
91	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
92	C₂×C₅×D₈	—	2	4	no	—
93	C₂×C₅×D₈	C₂²×C₃	1	4	yes	—
94	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
95	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₅×#127	C₂²×C₃	1	2	yes	complemented
98	C₅×#124	C₂²×C₃	1	2	yes	complemented
99	C₅×#121	—	2	2	no	—
100	C₅×#120	—	2	2	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
103	C₅×#117	C₂²×C₃	1	1	yes	characteristic
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
107	C₅×#103	C₂²×C₃	1	2	yes	complemented
108	C₅×#102	C₂²×C₃	1	2	yes	complemented
109	C₅×#102	C₂²×C₃	1	4	yes	complemented
110	#3041	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	4	no	—
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	1	no	—
115	C₂³×C₃×C₅	—	4	2	no	—
116	C₂³×C₃×C₅	—	8	2	no	—
117	C₂³×C₃×C₅	—	8	2	no	—
118	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
119	C₃×C₅×Q₈	—	2	1	no	—
120	C₃×C₅×Q₈	—	2	1	no	—
121	C₃×C₅×D₄	—	2	4	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	2	1	no	—
124	C₃×C₅×D₄	—	2	2	no	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	2	1	no	—
127	C₃×C₅×D₄	—	4	2	no	—
128	C₃×C₅×D₄	—	4	2	no	—
129	C₃×C₅×D₄	—	8	4	no	—
130	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	4	2	no	—
134	C₂×C₃×C₄×C₅	—	8	4	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	#41	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₅×C₈	—	2	2	no	—
141	C₃×C₅×C₈	—	2	2	no	—
142	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
143	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₃×AGL(1,ℤ/8)	—	2	4	no	—
146	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
147	C₂×C₃×D₈	—	2	4	no	—
148	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
149	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
150	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
152	C₃×#127	C₂²×C₅	1	2	yes	complemented
153	C₃×#124	C₂²×C₅	1	2	yes	complemented
154	C₃×#121	—	2	2	no	—
155	C₃×#120	—	2	2	no	—
156	C₃×C₄×D₄	—	2	2	no	—
157	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
158	C₃×#117	C₂²×C₅	1	1	yes	characteristic
159	C₃×#117	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
161	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
162	C₃×#103	C₂²×C₅	1	2	yes	complemented
163	C₃×#102	C₂²×C₅	1	2	yes	complemented
164	C₃×#102	C₂²×C₅	1	4	yes	complemented
165	C₂⁴×C₅	—	2	1	no	—
166	C₂⁴×C₅	—	2	1	no	—
167	C₅×#41	—	2	2	no	—
168	C₅×#41	—	2	2	no	—
169	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	4	no	—
175	C₂×C₅×D₄	—	2	2	no	—
176	C₂×C₅×D₄	—	2	2	no	—
177	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
178	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
179	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	4	no	—
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₅×SD₁₆	—	2	4	no	—
185	C₅×D₈	—	2	8	no	—
186	C₅×D₈	—	2	4	no	—
187	C₅×M₁₆	—	2	2	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
190	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
191	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
192	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
193	C₅×C₂²⋊C₄	—	2	1	no	—
194	C₅×C₂²⋊C₄	—	2	4	no	—
195	C₅×C₂²⋊C₄	—	2	4	no	—
196	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	C₂³×C₃	1	2	yes	—
199	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
200	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
201	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#518	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#463	C₂×C₃×C₅	1	4	yes	complemented
204	#459	C₂×C₃×C₅	1	4	yes	complemented
205	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
207	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	4	no	—
210	C₂²×C₃×C₅	—	4	4	no	—
211	C₂²×C₃×C₅	—	4	1	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	—	4	4	no	—
215	C₂²×C₃×C₅	—	8	4	no	—
216	C₂²×C₃×C₅	—	8	4	no	—
217	C₂²×C₃×C₅	#121	1	2	yes	—
218	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₃×C₄×C₅	—	2	4	no	—
220	C₃×C₄×C₅	—	4	1	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	#121	1	2	yes	—
223	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₂⁴×C₃	—	2	1	no	—
226	C₂⁴×C₃	—	2	1	no	—
227	C₃×#41	—	2	2	no	—
228	C₃×#41	—	2	2	no	—
229	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
230	C₂×C₃×D₄	—	2	1	no	—
231	C₂×C₃×D₄	—	2	1	no	—
232	C₂×C₃×D₄	—	2	2	no	—
233	C₂×C₃×D₄	—	2	1	no	—
234	C₂×C₃×D₄	—	2	4	no	—
235	C₂×C₃×D₄	—	2	2	no	—
236	C₂×C₃×D₄	—	2	2	no	—
237	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
238	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
239	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₃×SD₁₆	—	2	4	no	—
245	C₃×D₈	—	2	8	no	—
246	C₃×D₈	—	2	4	no	—
247	C₃×M₁₆	—	2	2	no	—
248	C₂×C₃×C₈	—	2	2	no	—
249	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
250	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
251	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
252	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₃×C₂²⋊C₄	—	2	1	no	—
254	C₃×C₂²⋊C₄	—	2	4	no	—
255	C₃×C₂²⋊C₄	—	2	4	no	—
256	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
257	C₃×C₄²	—	2	1	no	—
258	C₃×C₄²	C₂³×C₅	1	2	yes	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	2	4	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	4	2	no	—
264	C₂³×C₅	—	8	2	no	—
265	C₂³×C₅	—	8	2	no	—
266	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
267	C₅×Q₈	—	2	1	no	—
268	C₅×Q₈	—	2	1	no	—
269	C₅×D₄	—	2	4	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	2	1	no	—
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	2	2	no	—
274	C₅×D₄	—	2	1	no	—
275	C₅×D₄	—	4	2	no	—
276	C₅×D₄	—	4	2	no	—
277	C₅×D₄	—	8	4	no	—
278	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	4	2	no	—
282	C₂×C₄×C₅	—	8	4	no	—
283	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₄×C₅	C₃×#41	1	2	yes	—
287	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
288	C₅×C₈	—	2	2	no	—
289	C₅×C₈	—	2	2	no	—
290	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
291	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
293	AGL(1,ℤ/8)	—	2	4	no	—
294	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
295	C₂×D₈	—	2	4	no	—
296	C₂×D₈	C₂²×C₃×C₅	1	4	yes	—
297	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
298	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
300	#127	C₂²×C₃×C₅	1	2	yes	complemented
301	#124	C₂²×C₃×C₅	1	2	yes	complemented
302	#121	—	2	2	no	—
303	#120	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
306	#117	C₂²×C₃×C₅	1	1	yes	characteristic
307	#117	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
310	#103	C₂²×C₃×C₅	1	2	yes	complemented
311	#102	C₂²×C₃×C₅	1	2	yes	complemented
312	#102	C₂²×C₃×C₅	1	4	yes	complemented
313	C₂×C₃×C₅	—	2	2	no	—
314	C₂×C₃×C₅	—	4	4	no	—
315	C₂×C₃×C₅	—	8	1	no	—
316	C₂×C₃×C₅	—	8	2	no	—
317	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
318	C₂×C₃×C₅	#576	1	2	yes	—
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	2	4	no	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	1	no	—
323	C₂³×C₃	—	4	2	no	—
324	C₂³×C₃	—	8	2	no	—
325	C₂³×C₃	—	8	2	no	—
326	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
327	C₃×Q₈	—	2	1	no	—
328	C₃×Q₈	—	2	1	no	—
329	C₃×D₄	—	2	4	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	2	1	no	—
332	C₃×D₄	—	2	2	no	—
333	C₃×D₄	—	2	2	no	—
334	C₃×D₄	—	2	1	no	—
335	C₃×D₄	—	4	2	no	—
336	C₃×D₄	—	4	2	no	—
337	C₃×D₄	—	8	4	no	—
338	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	4	2	no	—
342	C₂×C₃×C₄	—	8	4	no	—
343	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
346	C₂×C₃×C₄	C₅×#41	1	2	yes	—
347	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
348	C₃×C₈	—	2	2	no	—
349	C₃×C₈	—	2	2	no	—
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	—	2	4	no	—
352	C₂²×C₅	—	4	4	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	—	4	4	no	—
355	C₂²×C₅	—	4	1	no	—
356	C₂²×C₅	—	4	2	no	—
357	C₂²×C₅	—	8	4	no	—
358	C₂²×C₅	—	8	4	no	—
359	C₂²×C₅	C₃×#121	1	2	yes	—
360	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₄×C₅	—	2	4	no	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	—	4	1	no	—
364	C₄×C₅	C₃×#121	1	2	yes	—
365	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
367	C₂⁴	—	2	1	no	—
368	C₂⁴	—	2	1	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
380	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
381	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
382	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
386	SD₁₆	—	2	4	no	—
387	D₈	—	2	8	no	—
388	D₈	—	2	4	no	—
389	M₁₆	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
392	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
393	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
394	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
399	C₄²	—	2	1	no	—
400	C₄²	C₂³×C₃×C₅	1	2	yes	—
401	C₃×C₅	#3041	1	1	yes	characteristic, direct product factor, Hall
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	2	4	no	—
404	C₂²×C₃	—	4	4	no	—
405	C₂²×C₃	—	4	1	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	4	2	no	—
408	C₂²×C₃	—	4	4	no	—
409	C₂²×C₃	—	8	4	no	—
410	C₂²×C₃	—	8	4	no	—
411	C₂²×C₃	C₅×#121	1	2	yes	—
412	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
413	C₃×C₄	—	2	4	no	—
414	C₃×C₄	—	4	1	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	C₅×#121	1	2	yes	—
417	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
418	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
419	C₂×C₅	—	2	2	no	—
420	C₂×C₅	—	4	4	no	—
421	C₂×C₅	—	8	2	no	—
422	C₂×C₅	—	8	1	no	—
423	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
424	C₂×C₅	C₃×#576	1	2	yes	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	8	2	no	—
431	C₂³	—	8	2	no	—
432	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	2	1	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	1	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	8	4	no	—
444	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
450	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
451	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
452	C₂×C₄	C₃×C₅×#41	1	2	yes	—
453	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₂×C₃	—	2	2	no	—
457	C₂×C₃	—	4	4	no	—
458	C₂×C₃	—	8	2	no	—
459	C₂×C₃	—	8	1	no	—
460	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
461	C₂×C₃	C₅×#576	1	2	yes	—
462	C₅	C₃×#3041	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	2	2	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	C₃×C₅×#121	1	2	yes	—
473	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	C₃×C₅×#121	1	2	yes	—
478	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
479	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
480	C₃	C₅×#3041	1	1	yes	characteristic, direct product factor, Sylow
481	C₂	—	2	2	no	—
482	C₂	—	4	4	no	—
483	C₂	—	8	2	no	—
484	C₂	—	8	1	no	—
485	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
486	C₂	C₃×C₅×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₃×C₅×D₈	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₃×C₅×#518	C₂	semidirect
5. C₃×C₅×#463	C₂	semidirect
6. C₃×C₅×#459	C₂	semidirect
7. C₃×C₅×#424	C₂	semidirect
8. C₃×C₅×#418	C₂	semidirect
9. C₃×C₅×#416	C₂	semidirect
10. C₅×#3041	C₃	direct (N × H)
15. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₂×C₃×C₅×D₈	C₂²	semidirect
21. C₃×C₅×#127	C₂²	semidirect
22. C₃×C₅×#124	C₂²	semidirect
26. C₃×C₄×C₅×D₄	C₂²	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×#103	C₂²	semidirect
32. C₃×C₅×#102	C₂²	semidirect
33. C₃×C₅×#102	C₂²	semidirect
34. C₃×#3041	C₅	direct (N × H)
35. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
36. C₂²×C₅×D₈	C₂×C₃	semidirect
37. C₅×#535	C₂×C₃	semidirect
38. C₅×#518	C₂×C₃	semidirect
39. C₅×#463	C₂×C₃	semidirect
40. C₅×#459	C₂×C₃	semidirect
41. C₅×#424	C₂×C₃	semidirect
42. C₅×#418	C₂×C₃	semidirect
43. C₅×#416	C₂×C₃	semidirect
56. C₂×C₃×C₅×D₄	D₄	semidirect
78. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
79. C₂²×C₃×D₈	C₂×C₅	semidirect
80. C₃×#535	C₂×C₅	semidirect
81. C₃×#518	C₂×C₅	semidirect
82. C₃×#463	C₂×C₅	semidirect
83. C₃×#459	C₂×C₅	semidirect
84. C₃×#424	C₂×C₅	semidirect
85. C₃×#418	C₂×C₅	semidirect
86. C₃×#416	C₂×C₅	semidirect
91. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
94. C₂×C₅×D₈	C₂²×C₃	semidirect
97. C₅×#127	C₂²×C₃	semidirect
98. C₅×#124	C₂²×C₃	semidirect
102. C₄×C₅×D₄	C₂²×C₃	semidirect
106. C₅×C₄⋊C₈	C₂²×C₃	semidirect
107. C₅×#103	C₂²×C₃	semidirect
108. C₅×#102	C₂²×C₃	semidirect
109. C₅×#102	C₂²×C₃	semidirect
110. #3041	C₃×C₅	direct (N × H)
146. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
149. C₂×C₃×D₈	C₂²×C₅	semidirect
152. C₃×#127	C₂²×C₅	semidirect
153. C₃×#124	C₂²×C₅	semidirect
157. C₃×C₄×D₄	C₂²×C₅	semidirect
161. C₃×C₄⋊C₈	C₂²×C₅	semidirect
162. C₃×#103	C₂²×C₅	semidirect
163. C₃×#102	C₂²×C₅	semidirect
164. C₃×#102	C₂²×C₅	semidirect
177. C₂×C₅×D₄	C₃×D₄	semidirect
199. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
200. C₂²×D₈	C₂×C₃×C₅	semidirect
201. #535	C₂×C₃×C₅	semidirect
202. #518	C₂×C₃×C₅	semidirect
203. #463	C₂×C₃×C₅	semidirect
204. #459	C₂×C₃×C₅	semidirect
205. #424	C₂×C₃×C₅	semidirect
206. #418	C₂×C₃×C₅	semidirect
207. #416	C₂×C₃×C₅	semidirect
237. C₂×C₃×D₄	C₅×D₄	semidirect
294. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
297. C₂×D₈	C₂²×C₃×C₅	semidirect
300. #127	C₂²×C₃×C₅	semidirect
301. #124	C₂²×C₃×C₅	semidirect
305. C₄×D₄	C₂²×C₃×C₅	semidirect
309. C₄⋊C₈	C₂²×C₃×C₅	semidirect
310. #103	C₂²×C₃×C₅	semidirect
311. #102	C₂²×C₃×C₅	semidirect
312. #102	C₂²×C₃×C₅	semidirect
379. C₂×D₄	C₃×C₅×D₄	semidirect
401. C₃×C₅	#3041	direct (N × H)
462. C₅	C₃×#3041	direct (N × H)
480. C₃	C₅×#3041	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×AGL(1,ℤ/8)	2
C₂²×C₃×C₅×D₈	2
C₃×C₅×#535	2
C₃×C₅×#518	2
C₃×C₅×#463	2
C₃×C₅×#459	2
C₃×C₅×#424	2
C₃×C₅×#418	2
C₃×C₅×#416	2
C₅×#3041	3
C₃×#3041	5

Subgroups — C3×C5×#3041 #14276075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3041 #14276075