Subgroups — C₃×C₅×#3273 #14276307

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 500 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	2	yes	maximal, complemented
2	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#447	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3273	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
13	C₃×C₅×AGL(1,ℤ/8)	—	2	8	no	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
21	C₃×C₅×#124	C₂²	1	2	yes	complemented
22	C₃×C₅×#123	—	2	2	no	—
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
24	C₃×C₅×#121	—	2	2	no	—
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₃×C₅×#120	—	2	2	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
29	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#103	C₂²	1	2	yes	complemented
33	C₃×C₅×#102	C₂²	1	2	yes	complemented
34	C₃×C₅×#102	C₂²	1	2	yes	complemented
35	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
36	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3273	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
39	C₅×#546	C₂×C₃	1	2	yes	complemented
40	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#468	C₂×C₃	1	2	yes	complemented
42	C₅×#463	C₂×C₃	1	2	yes	complemented
43	C₅×#452	C₂×C₃	1	2	yes	complemented
44	C₅×#447	C₂×C₃	1	2	yes	complemented
45	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂⁴×C₃×C₅	—	2	2	no	—
48	C₃×C₅×#41	—	2	4	no	—
49	C₃×C₅×#41	—	4	2	no	—
50	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×D₄	—	2	4	no	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	—	2	2	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	4	2	no	—
56	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₃×C₅×Q₁₆	—	4	1	no	—
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₃×C₅×SD₁₆	—	2	4	no	—
65	C₃×C₅×D₈	—	2	4	no	—
66	C₃×C₅×D₈	—	4	1	no	—
67	C₃×C₅×D₈	D₄	1	4	yes	complemented
68	C₃×C₅×M₁₆	—	2	4	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
83	C₃×#546	C₂×C₅	1	2	yes	complemented
84	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#468	C₂×C₅	1	2	yes	complemented
86	C₃×#463	C₂×C₅	1	2	yes	complemented
87	C₃×#452	C₂×C₅	1	2	yes	complemented
88	C₃×#447	C₂×C₅	1	2	yes	complemented
89	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
93	C₅×AGL(1,ℤ/8)	—	2	8	no	—
94	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
96	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
97	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
98	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
101	C₅×#124	C₂²×C₃	1	2	yes	complemented
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
104	C₅×#121	—	2	2	no	—
105	C₅×#121	C₂²×C₃	1	2	yes	—
106	C₅×#120	—	2	2	no	—
107	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
109	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₅×#103	C₂²×C₃	1	2	yes	complemented
113	C₅×#102	C₂²×C₃	1	2	yes	complemented
114	C₅×#102	C₂²×C₃	1	2	yes	complemented
115	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
116	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
117	#3273	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	4	4	no	—
121	C₂³×C₃×C₅	—	4	4	no	—
122	C₂³×C₃×C₅	—	8	2	no	—
123	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×Q₈	—	2	2	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	—	2	2	no	—
129	C₃×C₅×D₄	—	4	1	no	—
130	C₃×C₅×D₄	—	4	4	no	—
131	C₃×C₅×D₄	—	4	4	no	—
132	C₃×C₅×D₄	—	8	2	no	—
133	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	4	4	no	—
139	C₂×C₃×C₄×C₅	—	8	2	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
144	C₃×C₅×C₈	—	2	2	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
148	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
149	C₃×AGL(1,ℤ/8)	—	2	8	no	—
150	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
151	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
152	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
153	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
154	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
157	C₃×#124	C₂²×C₅	1	2	yes	complemented
158	C₃×#123	—	2	2	no	—
159	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
160	C₃×#121	—	2	2	no	—
161	C₃×#121	C₂²×C₅	1	2	yes	—
162	C₃×#120	—	2	2	no	—
163	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
164	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
165	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
166	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
167	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₃×#103	C₂²×C₅	1	2	yes	complemented
169	C₃×#102	C₂²×C₅	1	2	yes	complemented
170	C₃×#102	C₂²×C₅	1	2	yes	complemented
171	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
172	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂⁴×C₅	—	2	2	no	—
174	C₅×#41	—	2	4	no	—
175	C₅×#41	—	4	2	no	—
176	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
177	C₂×C₅×D₄	—	2	4	no	—
178	C₂×C₅×D₄	—	2	2	no	—
179	C₂×C₅×D₄	—	2	2	no	—
180	C₂×C₅×D₄	—	2	2	no	—
181	C₂×C₅×D₄	—	4	2	no	—
182	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
183	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
184	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
185	C₂²×C₄×C₅	—	2	2	no	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₅×Q₁₆	—	4	1	no	—
189	C₅×SD₁₆	—	2	4	no	—
190	C₅×SD₁₆	—	2	4	no	—
191	C₅×D₈	—	2	4	no	—
192	C₅×D₈	—	4	1	no	—
193	C₅×D₈	C₃×D₄	1	4	yes	complemented
194	C₅×M₁₆	—	2	4	no	—
195	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
196	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₅×C₂²⋊C₄	—	2	2	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
207	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
209	#546	C₂×C₃×C₅	1	2	yes	complemented
210	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
211	#468	C₂×C₃×C₅	1	2	yes	complemented
212	#463	C₂×C₃×C₅	1	2	yes	complemented
213	#452	C₂×C₃×C₅	1	2	yes	complemented
214	#447	C₂×C₃×C₅	1	2	yes	complemented
215	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	#436	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	C₂²×C₃×C₅	—	2	2	no	—
218	C₂²×C₃×C₅	—	2	4	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	—	2	2	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	—	4	2	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	8	8	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₃×C₄×C₅	—	2	2	no	—
229	C₃×C₄×C₅	—	2	1	no	—
230	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂⁴×C₃	—	2	2	no	—
236	C₃×#41	—	2	4	no	—
237	C₃×#41	—	4	2	no	—
238	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
239	C₂×C₃×D₄	—	2	4	no	—
240	C₂×C₃×D₄	—	2	2	no	—
241	C₂×C₃×D₄	—	2	2	no	—
242	C₂×C₃×D₄	—	2	2	no	—
243	C₂×C₃×D₄	—	4	2	no	—
244	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
245	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
246	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
247	C₂²×C₃×C₄	—	2	2	no	—
248	C₂²×C₃×C₄	—	2	2	no	—
249	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
250	C₃×Q₁₆	—	4	1	no	—
251	C₃×SD₁₆	—	2	4	no	—
252	C₃×SD₁₆	—	2	4	no	—
253	C₃×D₈	—	2	4	no	—
254	C₃×D₈	—	4	1	no	—
255	C₃×D₈	C₅×D₄	1	4	yes	complemented
256	C₃×M₁₆	—	2	4	no	—
257	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
259	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	2	2	no	—
265	C₃×C₂²⋊C₄	—	2	2	no	—
266	C₃×C₂²⋊C₄	—	2	2	no	—
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
269	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	2	no	—
272	C₂³×C₅	—	4	4	no	—
273	C₂³×C₅	—	4	4	no	—
274	C₂³×C₅	—	8	2	no	—
275	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	2	2	no	—
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	4	1	no	—
282	C₅×D₄	—	4	4	no	—
283	C₅×D₄	—	4	4	no	—
284	C₅×D₄	—	8	2	no	—
285	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	4	4	no	—
291	C₂×C₄×C₅	—	8	2	no	—
292	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
296	C₅×C₈	—	2	2	no	—
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
299	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
300	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
301	AGL(1,ℤ/8)	—	2	8	no	—
302	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
303	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
304	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
305	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
306	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
307	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
309	#124	C₂²×C₃×C₅	1	2	yes	complemented
310	#123	—	2	2	no	—
311	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
312	#121	—	2	2	no	—
313	#121	C₂²×C₃×C₅	1	2	yes	—
314	#120	—	2	2	no	—
315	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
319	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
320	#103	C₂²×C₃×C₅	1	2	yes	complemented
321	#102	C₂²×C₃×C₅	1	2	yes	complemented
322	#102	C₂²×C₃×C₅	1	2	yes	complemented
323	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
324	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
325	C₂×C₃×C₅	—	4	2	no	—
326	C₂×C₃×C₅	—	4	4	no	—
327	C₂×C₃×C₅	—	8	2	no	—
328	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
329	C₂×C₃×C₅	#575	1	1	yes	characteristic
330	C₂×C₃×C₅	#576	1	1	yes	characteristic
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	2	no	—
333	C₂³×C₃	—	4	4	no	—
334	C₂³×C₃	—	4	4	no	—
335	C₂³×C₃	—	8	2	no	—
336	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
337	C₃×Q₈	—	2	2	no	—
338	C₃×Q₈	—	2	2	no	—
339	C₃×D₄	—	2	2	no	—
340	C₃×D₄	—	2	2	no	—
341	C₃×D₄	—	2	2	no	—
342	C₃×D₄	—	4	1	no	—
343	C₃×D₄	—	4	4	no	—
344	C₃×D₄	—	4	4	no	—
345	C₃×D₄	—	8	2	no	—
346	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	4	4	no	—
352	C₂×C₃×C₄	—	8	2	no	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
356	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	C₃×C₈	—	2	2	no	—
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
360	C₂²×C₅	—	2	2	no	—
361	C₂²×C₅	—	2	2	no	—
362	C₂²×C₅	—	2	2	no	—
363	C₂²×C₅	—	2	4	no	—
364	C₂²×C₅	—	4	2	no	—
365	C₂²×C₅	—	4	2	no	—
366	C₂²×C₅	—	4	2	no	—
367	C₂²×C₅	—	4	2	no	—
368	C₂²×C₅	—	4	2	no	—
369	C₂²×C₅	—	8	8	no	—
370	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	2	no	—
374	C₄×C₅	—	4	2	no	—
375	C₄×C₅	—	4	2	no	—
376	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
377	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂⁴	—	2	2	no	—
379	#41	—	2	4	no	—
380	#41	—	4	2	no	—
381	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
388	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
389	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
393	Q₁₆	—	4	1	no	—
394	SD₁₆	—	2	4	no	—
395	SD₁₆	—	2	4	no	—
396	D₈	—	2	4	no	—
397	D₈	—	4	1	no	—
398	D₈	C₃×C₅×D₄	1	4	yes	complemented
399	M₁₆	—	2	4	no	—
400	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
402	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
412	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
413	C₃×C₅	#3273	1	1	yes	characteristic, direct product factor, Hall
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	4	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	2	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	—	4	2	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	2	no	—
422	C₂²×C₃	—	4	2	no	—
423	C₂²×C₃	—	8	8	no	—
424	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	1	no	—
428	C₃×C₄	—	4	2	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
431	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₅	—	4	2	no	—
433	C₂×C₅	—	4	4	no	—
434	C₂×C₅	—	8	2	no	—
435	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
436	C₂×C₅	C₃×#575	1	1	yes	characteristic
437	C₂×C₅	C₃×#576	1	1	yes	characteristic
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	8	2	no	—
443	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	—	8	2	no	—
453	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
461	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
463	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
464	C₈	—	2	2	no	—
465	C₈	—	2	1	no	—
466	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
467	C₂×C₃	—	4	2	no	—
468	C₂×C₃	—	4	4	no	—
469	C₂×C₃	—	8	2	no	—
470	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
471	C₂×C₃	C₅×#575	1	1	yes	characteristic
472	C₂×C₃	C₅×#576	1	1	yes	characteristic
473	C₅	C₃×#3273	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²	—	2	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	8	no	—
484	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
491	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
492	C₃	C₅×#3273	1	1	yes	characteristic, direct product factor, Sylow
493	C₂	—	4	2	no	—
494	C₂	—	4	4	no	—
495	C₂	—	8	2	no	—
496	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
497	C₂	C₃×C₅×#575	1	1	yes	characteristic
498	C₂	C₃×C₅×#576	1	1	yes	characteristic

	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×C₄×C₅×D₄ ◁ 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. C₃×C₅×#546	C₂	semidirect
3. C₃×C₅×#495	C₂	semidirect
4. C₃×C₅×#468	C₂	semidirect
5. C₃×C₅×#463	C₂	semidirect
6. C₃×C₅×#452	C₂	semidirect
7. C₃×C₅×#447	C₂	semidirect
8. C₃×C₄×C₅×D₈	C₂	semidirect
9. C₃×C₅×#436	C₂	semidirect
10. C₅×#3273	C₃	direct (N × H)
12. C₂²×C₃×C₅×D₄	C₂²	semidirect
14. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
15. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
20. C₂×C₃×C₅×M₁₆	C₂²	semidirect
21. C₃×C₅×#124	C₂²	semidirect
23. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₃×C₄×C₅×D₄	C₂²	semidirect
30. C₃×C₅×#107	C₂²	semidirect
31. C₃×C₅×C₄⋊C₈	C₂²	semidirect
32. C₃×C₅×#103	C₂²	semidirect
33. C₃×C₅×#102	C₂²	semidirect
34. C₃×C₅×#102	C₂²	semidirect
35. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
36. C₃×C₄×C₅×C₈	C₂²	semidirect
37. C₃×#3273	C₅	direct (N × H)
38. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
39. C₅×#546	C₂×C₃	semidirect
40. C₅×#495	C₂×C₃	semidirect
41. C₅×#468	C₂×C₃	semidirect
42. C₅×#463	C₂×C₃	semidirect
43. C₅×#452	C₂×C₃	semidirect
44. C₅×#447	C₂×C₃	semidirect
45. C₄×C₅×D₈	C₂×C₃	semidirect
46. C₅×#436	C₂×C₃	semidirect
67. C₃×C₅×D₈	D₄	semidirect
82. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
83. C₃×#546	C₂×C₅	semidirect
84. C₃×#495	C₂×C₅	semidirect
85. C₃×#468	C₂×C₅	semidirect
86. C₃×#463	C₂×C₅	semidirect
87. C₃×#452	C₂×C₅	semidirect
88. C₃×#447	C₂×C₅	semidirect
89. C₃×C₄×D₈	C₂×C₅	semidirect
90. C₃×#436	C₂×C₅	semidirect
92. C₂²×C₅×D₄	C₂²×C₃	semidirect
94. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
95. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
96. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
100. C₂×C₅×M₁₆	C₂²×C₃	semidirect
101. C₅×#124	C₂²×C₃	semidirect
103. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
108. C₄×C₅×D₄	C₂²×C₃	semidirect
110. C₅×#107	C₂²×C₃	semidirect
111. C₅×C₄⋊C₈	C₂²×C₃	semidirect
112. C₅×#103	C₂²×C₃	semidirect
113. C₅×#102	C₂²×C₃	semidirect
114. C₅×#102	C₂²×C₃	semidirect
115. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
116. C₄×C₅×C₈	C₂²×C₃	semidirect
117. #3273	C₃×C₅	direct (N × H)
148. C₂²×C₃×D₄	C₂²×C₅	semidirect
150. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
151. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
152. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
156. C₂×C₃×M₁₆	C₂²×C₅	semidirect
157. C₃×#124	C₂²×C₅	semidirect
159. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
164. C₃×C₄×D₄	C₂²×C₅	semidirect
166. C₃×#107	C₂²×C₅	semidirect
167. C₃×C₄⋊C₈	C₂²×C₅	semidirect
168. C₃×#103	C₂²×C₅	semidirect
169. C₃×#102	C₂²×C₅	semidirect
170. C₃×#102	C₂²×C₅	semidirect
171. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
172. C₃×C₄×C₈	C₂²×C₅	semidirect
193. C₅×D₈	C₃×D₄	semidirect
208. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
209. #546	C₂×C₃×C₅	semidirect
210. #495	C₂×C₃×C₅	semidirect
211. #468	C₂×C₃×C₅	semidirect
212. #463	C₂×C₃×C₅	semidirect
213. #452	C₂×C₃×C₅	semidirect
214. #447	C₂×C₃×C₅	semidirect
215. C₄×D₈	C₂×C₃×C₅	semidirect
216. #436	C₂×C₃×C₅	semidirect
255. C₃×D₈	C₅×D₄	semidirect
300. C₂²×D₄	C₂²×C₃×C₅	semidirect
302. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
303. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
304. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
308. C₂×M₁₆	C₂²×C₃×C₅	semidirect
309. #124	C₂²×C₃×C₅	semidirect
311. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
316. C₄×D₄	C₂²×C₃×C₅	semidirect
318. #107	C₂²×C₃×C₅	semidirect
319. C₄⋊C₈	C₂²×C₃×C₅	semidirect
320. #103	C₂²×C₃×C₅	semidirect
321. #102	C₂²×C₃×C₅	semidirect
322. #102	C₂²×C₃×C₅	semidirect
323. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
324. C₄×C₈	C₂²×C₃×C₅	semidirect
398. D₈	C₃×C₅×D₄	semidirect
413. C₃×C₅	#3273	direct (N × H)
473. C₅	C₃×#3273	direct (N × H)
492. C₃	C₅×#3273	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
C₃×C₅×#546	2
C₃×C₅×#495	2
C₃×C₅×#468	2
C₃×C₅×#463	2
C₃×C₅×#452	2
C₃×C₅×#447	2
C₃×C₄×C₅×D₈	2
C₃×C₅×#436	2
C₅×#3273	3
C₃×#3273	5

Subgroups — C3×C5×#3273 #14276307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3273 #14276307