Subgroups — C₃×C₅×#3171 #14276205

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#490	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×D₈	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3171	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	—	2	1	no	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₅×#126	—	2	1	no	—
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic
21	C₃×C₅×#124	—	2	1	no	—
22	C₃×C₅×#124	C₂²	1	1	yes	characteristic
23	C₃×C₅×#123	—	2	1	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#121	—	2	1	no	—
26	C₃×C₅×#121	C₂²	1	2	yes	—
27	C₃×C₅×#121	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	—	2	1	no	—
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₃×C₅×#117	—	2	1	no	—
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₃×C₅×#107	C₂²	1	2	yes	—
36	C₃×C₅×#106	C₂²	1	2	yes	—
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×#97	C₂²	1	1	yes	characteristic
42	C₃×C₅×#97	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
44	C₃×#3171	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#501	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#490	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#469	C₂×C₃	1	2	yes	complemented
52	C₅×#468	C₂×C₃	1	2	yes	complemented
53	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
54	C₄×C₅×D₈	C₂×C₃	1	2	yes	complemented
55	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	4	4	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₅×SD₁₆	—	2	4	no	—
71	C₃×C₅×D₈	—	2	4	no	—
72	C₃×C₅×M₁₆	—	2	4	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₃×C₄²×C₅	—	2	1	no	—
91	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#501	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#490	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#469	C₂×C₅	1	2	yes	complemented
102	C₃×#468	C₂×C₅	1	2	yes	complemented
103	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
104	C₃×C₄×D₈	C₂×C₅	1	2	yes	complemented
105	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×C₅×#41	—	2	1	no	—
107	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
109	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
110	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
111	C₅×#127	C₂²×C₃	1	1	yes	characteristic
112	C₅×#126	—	2	1	no	—
113	C₅×#125	C₂²×C₃	1	1	yes	characteristic
114	C₅×#124	—	2	1	no	—
115	C₅×#124	C₂²×C₃	1	1	yes	characteristic
116	C₅×#123	—	2	1	no	—
117	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₅×#121	—	2	1	no	—
119	C₅×#121	C₂²×C₃	1	2	yes	—
120	C₅×#121	C₂²×C₃	1	1	yes	characteristic
121	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
122	C₄×C₅×D₄	—	2	1	no	—
123	C₄×C₅×D₄	—	2	1	no	—
124	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
126	C₅×#117	—	2	1	no	—
127	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
128	C₅×#107	C₂²×C₃	1	2	yes	—
129	C₅×#106	C₂²×C₃	1	2	yes	—
130	C₅×#103	C₂²×C₃	1	2	yes	—
131	C₅×#102	C₂²×C₃	1	2	yes	—
132	C₅×#102	C₂²×C₃	1	2	yes	—
133	C₅×#102	C₂²×C₃	1	2	yes	—
134	C₅×#97	C₂²×C₃	1	1	yes	characteristic
135	C₅×#97	C₂²×C₃	1	1	yes	characteristic
136	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
137	#3171	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
138	C₂³×C₃×C₅	—	2	1	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	4	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	4	2	no	—
147	C₃×C₅×D₄	—	4	2	no	—
148	C₃×C₅×D₄	—	4	2	no	—
149	C₃×C₅×D₄	—	4	4	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	4	1	no	—
157	C₂×C₃×C₄×C₅	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	4	4	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₃×C₅×C₈	—	2	2	no	—
166	C₃×C₅×C₈	#41	1	4	yes	complemented
167	C₂×C₃×#41	—	2	1	no	—
168	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
169	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
170	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
171	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
172	C₃×#127	C₂²×C₅	1	1	yes	characteristic
173	C₃×#126	—	2	1	no	—
174	C₃×#125	C₂²×C₅	1	1	yes	characteristic
175	C₃×#124	—	2	1	no	—
176	C₃×#124	C₂²×C₅	1	1	yes	characteristic
177	C₃×#123	—	2	1	no	—
178	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₃×#121	—	2	1	no	—
180	C₃×#121	C₂²×C₅	1	2	yes	—
181	C₃×#121	C₂²×C₅	1	1	yes	characteristic
182	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₃×C₄×D₄	—	2	1	no	—
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
187	C₃×#117	—	2	1	no	—
188	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
189	C₃×#107	C₂²×C₅	1	2	yes	—
190	C₃×#106	C₂²×C₅	1	2	yes	—
191	C₃×#103	C₂²×C₅	1	2	yes	—
192	C₃×#102	C₂²×C₅	1	2	yes	—
193	C₃×#102	C₂²×C₅	1	2	yes	—
194	C₃×#102	C₂²×C₅	1	2	yes	—
195	C₃×#97	C₂²×C₅	1	1	yes	characteristic
196	C₃×#97	C₂²×C₅	1	1	yes	characteristic
197	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
198	C₅×#41	—	4	4	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	2	2	no	—
209	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₅×SD₁₆	—	2	4	no	—
213	C₅×D₈	—	2	4	no	—
214	C₅×M₁₆	—	2	4	no	—
215	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
216	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
223	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	2	1	no	—
230	C₅×C₂²⋊C₄	—	2	2	no	—
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
234	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
235	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
237	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	#501	C₂×C₃×C₅	1	1	yes	characteristic, complemented
240	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#469	C₂×C₃×C₅	1	2	yes	complemented
244	#468	C₂×C₃×C₅	1	2	yes	complemented
245	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
246	C₄×D₈	C₂×C₃×C₅	1	2	yes	complemented
247	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	2	1	no	—
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	—	4	1	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	—	4	2	no	—
254	C₂²×C₃×C₅	—	4	1	no	—
255	C₂²×C₃×C₅	—	4	2	no	—
256	C₂²×C₃×C₅	—	4	1	no	—
257	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₃×C₄×C₅	—	2	1	no	—
259	C₃×C₄×C₅	—	2	1	no	—
260	C₃×C₄×C₅	—	2	1	no	—
261	C₃×C₄×C₅	—	2	1	no	—
262	C₃×C₄×C₅	—	4	1	no	—
263	C₃×C₄×C₅	—	4	1	no	—
264	C₃×C₄×C₅	—	4	2	no	—
265	C₃×C₄×C₅	—	4	1	no	—
266	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
267	C₃×C₄×C₅	C₂×#41	1	2	yes	—
268	C₃×#41	—	4	4	no	—
269	C₂×C₃×Q₈	—	2	1	no	—
270	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	—	2	1	no	—
274	C₂×C₃×D₄	—	2	1	no	—
275	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×SD₁₆	—	2	4	no	—
283	C₃×D₈	—	2	4	no	—
284	C₃×M₁₆	—	2	4	no	—
285	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
286	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
287	C₃×C₄⋊C₄	—	2	1	no	—
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	2	1	no	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
293	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
294	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
295	C₃×C₂²⋊C₄	—	2	1	no	—
296	C₃×C₂²⋊C₄	—	2	1	no	—
297	C₃×C₂²⋊C₄	—	2	1	no	—
298	C₃×C₂²⋊C₄	—	2	2	no	—
299	C₃×C₂²⋊C₄	—	2	1	no	—
300	C₃×C₂²⋊C₄	—	2	2	no	—
301	C₃×C₂²⋊C₄	—	2	1	no	—
302	C₃×C₄²	—	2	1	no	—
303	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
304	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
305	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
306	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₅×Q₈	—	2	2	no	—
311	C₅×Q₈	—	4	2	no	—
312	C₅×D₄	—	2	2	no	—
313	C₅×D₄	—	2	2	no	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	—	4	2	no	—
316	C₅×D₄	—	4	2	no	—
317	C₅×D₄	—	4	2	no	—
318	C₅×D₄	—	4	4	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	2	no	—
327	C₂×C₄×C₅	—	4	4	no	—
328	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
334	C₅×C₈	—	2	2	no	—
335	C₅×C₈	C₃×#41	1	4	yes	complemented
336	C₂×#41	—	2	1	no	—
337	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
338	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
339	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
340	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
341	#127	C₂²×C₃×C₅	1	1	yes	characteristic
342	#126	—	2	1	no	—
343	#125	C₂²×C₃×C₅	1	1	yes	characteristic
344	#124	—	2	1	no	—
345	#124	C₂²×C₃×C₅	1	1	yes	characteristic
346	#123	—	2	1	no	—
347	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
348	#121	—	2	1	no	—
349	#121	C₂²×C₃×C₅	1	1	yes	characteristic
350	#121	C₂²×C₃×C₅	1	2	yes	—
351	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
356	#117	—	2	1	no	—
357	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
358	#107	C₂²×C₃×C₅	1	2	yes	—
359	#106	C₂²×C₃×C₅	1	2	yes	—
360	#103	C₂²×C₃×C₅	1	2	yes	—
361	#102	C₂²×C₃×C₅	1	2	yes	—
362	#102	C₂²×C₃×C₅	1	2	yes	—
363	#102	C₂²×C₃×C₅	1	2	yes	—
364	#97	C₂²×C₃×C₅	1	1	yes	characteristic
365	#97	C₂²×C₃×C₅	1	1	yes	characteristic
366	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
367	C₂×C₃×C₅	—	4	1	no	—
368	C₂×C₃×C₅	—	8	2	no	—
369	C₂×C₃×C₅	—	8	1	no	—
370	C₂×C₃×C₅	#532	1	1	yes	characteristic
371	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂×C₃×C₅	#575	1	1	yes	characteristic
373	C₂³×C₃	—	2	1	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
376	C₃×Q₈	—	2	2	no	—
377	C₃×Q₈	—	4	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	2	2	no	—
380	C₃×D₄	—	2	2	no	—
381	C₃×D₄	—	4	2	no	—
382	C₃×D₄	—	4	2	no	—
383	C₃×D₄	—	4	2	no	—
384	C₃×D₄	—	4	4	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	4	1	no	—
392	C₂×C₃×C₄	—	4	2	no	—
393	C₂×C₃×C₄	—	4	4	no	—
394	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
400	C₃×C₈	—	2	2	no	—
401	C₃×C₈	C₅×#41	1	4	yes	complemented
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	4	2	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	4	2	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	4	1	no	—
417	C₄×C₅	—	4	2	no	—
418	C₄×C₅	—	4	1	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
421	C₄×C₅	C₂×C₃×#41	1	2	yes	—
422	#41	—	4	4	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
430	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
435	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
436	SD₁₆	—	2	4	no	—
437	D₈	—	2	4	no	—
438	M₁₆	—	2	4	no	—
439	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
440	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
447	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
448	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
449	C₂²⋊C₄	—	2	1	no	—
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
458	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
459	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
460	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
461	C₃×C₅	#3171	1	1	yes	characteristic, direct product factor, Hall
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	4	1	no	—
466	C₂²×C₃	—	4	2	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	4	1	no	—
469	C₂²×C₃	—	4	2	no	—
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₃×C₄	—	2	1	no	—
473	C₃×C₄	—	2	1	no	—
474	C₃×C₄	—	2	1	no	—
475	C₃×C₄	—	2	1	no	—
476	C₃×C₄	—	4	1	no	—
477	C₃×C₄	—	4	1	no	—
478	C₃×C₄	—	4	2	no	—
479	C₃×C₄	—	4	1	no	—
480	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
481	C₃×C₄	C₂×C₅×#41	1	2	yes	—
482	C₂×C₅	—	4	1	no	—
483	C₂×C₅	—	8	2	no	—
484	C₂×C₅	—	8	1	no	—
485	C₂×C₅	C₃×#532	1	1	yes	characteristic
486	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂×C₅	C₃×#575	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	—	2	2	no	—
490	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
491	Q₈	—	2	2	no	—
492	Q₈	—	4	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
511	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	C₃×C₅×#41	1	4	yes	complemented
517	C₂×C₃	—	4	1	no	—
518	C₂×C₃	—	8	2	no	—
519	C₂×C₃	—	8	1	no	—
520	C₂×C₃	C₅×#532	1	1	yes	characteristic
521	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
522	C₂×C₃	C₅×#575	1	1	yes	characteristic
523	C₅	C₃×#3171	1	1	yes	characteristic, direct product factor, Sylow
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
543	C₄	C₂×C₃×C₅×#41	1	2	yes	—
544	C₃	C₅×#3171	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	4	1	no	—
546	C₂	—	8	2	no	—
547	C₂	—	8	1	no	—
548	C₂	C₃×C₅×#532	1	1	yes	characteristic
549	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
550	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₃×C₅×#529	C₂	semidirect
3. C₃×C₅×#501	C₂	semidirect
4. C₃×C₅×#496	C₂	semidirect
5. C₃×C₅×#490	C₂	semidirect
6. C₃×C₅×#489	C₂	semidirect
7. C₃×C₅×#469	C₂	semidirect
8. C₃×C₅×#468	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₄×C₅×D₈	C₂	semidirect
11. C₃×C₄×C₅×M₁₆	C₂	semidirect
12. C₅×#3171	C₃	direct (N × H)
44. C₃×#3171	C₅	direct (N × H)
45. C₅×#532	C₂×C₃	semidirect
46. C₅×#529	C₂×C₃	semidirect
47. C₅×#501	C₂×C₃	semidirect
48. C₅×#496	C₂×C₃	semidirect
49. C₅×#490	C₂×C₃	semidirect
50. C₅×#489	C₂×C₃	semidirect
51. C₅×#469	C₂×C₃	semidirect
52. C₅×#468	C₂×C₃	semidirect
53. C₄×C₅×SD₁₆	C₂×C₃	semidirect
54. C₄×C₅×D₈	C₂×C₃	semidirect
55. C₄×C₅×M₁₆	C₂×C₃	semidirect
95. C₃×#532	C₂×C₅	semidirect
96. C₃×#529	C₂×C₅	semidirect
97. C₃×#501	C₂×C₅	semidirect
98. C₃×#496	C₂×C₅	semidirect
99. C₃×#490	C₂×C₅	semidirect
100. C₃×#489	C₂×C₅	semidirect
101. C₃×#469	C₂×C₅	semidirect
102. C₃×#468	C₂×C₅	semidirect
103. C₃×C₄×SD₁₆	C₂×C₅	semidirect
104. C₃×C₄×D₈	C₂×C₅	semidirect
105. C₃×C₄×M₁₆	C₂×C₅	semidirect
137. #3171	C₃×C₅	direct (N × H)
166. C₃×C₅×C₈	#41	semidirect
237. #532	C₂×C₃×C₅	semidirect
238. #529	C₂×C₃×C₅	semidirect
239. #501	C₂×C₃×C₅	semidirect
240. #496	C₂×C₃×C₅	semidirect
241. #490	C₂×C₃×C₅	semidirect
242. #489	C₂×C₃×C₅	semidirect
243. #469	C₂×C₃×C₅	semidirect
244. #468	C₂×C₃×C₅	semidirect
245. C₄×SD₁₆	C₂×C₃×C₅	semidirect
246. C₄×D₈	C₂×C₃×C₅	semidirect
247. C₄×M₁₆	C₂×C₃×C₅	semidirect
335. C₅×C₈	C₃×#41	semidirect
401. C₃×C₈	C₅×#41	semidirect
461. C₃×C₅	#3171	direct (N × H)
516. C₈	C₃×C₅×#41	semidirect
523. C₅	C₃×#3171	direct (N × H)
544. C₃	C₅×#3171	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₃×C₅×#529	2
C₃×C₅×#501	2
C₃×C₅×#496	2
C₃×C₅×#490	2
C₃×C₅×#489	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₄×C₅×D₈	2
C₃×C₄×C₅×M₁₆	2
C₅×#3171	3
C₃×#3171	5

Subgroups — C3×C5×#3171 #14276205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3171 #14276205