Subgroups — C₃×C₅×#3251 #14276285

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 568 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×#478	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3251	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
40	C₃×C₅×#103	C₂²	1	2	yes	—
41	C₃×C₅×#102	C₂²	1	2	yes	—
42	C₃×C₅×#102	C₂²	1	2	yes	—
43	C₃×C₅×#102	C₂²	1	2	yes	—
44	C₃×#3251	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×#478	C₂×C₃	1	2	yes	complemented
48	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#469	C₂×C₃	1	2	yes	complemented
51	C₅×#468	C₂×C₃	1	2	yes	complemented
52	C₅×#463	C₂×C₃	1	2	yes	complemented
53	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#423	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	—	4	2	no	—
71	C₃×C₅×D₈	—	4	2	no	—
72	C₃×C₅×M₁₆	—	4	2	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×#478	C₂×C₅	1	2	yes	complemented
98	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#469	C₂×C₅	1	2	yes	complemented
101	C₃×#468	C₂×C₅	1	2	yes	complemented
102	C₃×#463	C₂×C₅	1	2	yes	complemented
103	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#423	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×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
131	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
132	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
133	C₅×#103	C₂²×C₃	1	2	yes	—
134	C₅×#102	C₂²×C₃	1	2	yes	—
135	C₅×#102	C₂²×C₃	1	2	yes	—
136	C₅×#102	C₂²×C₃	1	2	yes	—
137	#3251	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	1	no	—
142	C₃×C₅×Q₈	—	2	1	no	—
143	C₃×C₅×Q₈	—	4	2	no	—
144	C₃×C₅×D₄	—	2	1	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	4	2	no	—
149	C₃×C₅×D₄	—	4	2	no	—
150	C₃×C₅×D₄	—	4	4	no	—
151	C₃×C₅×D₄	—	4	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	1	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	4	1	no	—
160	C₂×C₃×C₄×C₅	—	4	4	no	—
161	C₂×C₃×C₄×C₅	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₃×C₅×C₈	—	2	2	no	—
169	C₃×C₅×C₈	—	2	2	no	—
170	C₂×C₃×#41	—	2	1	no	—
171	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
172	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
173	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
174	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
175	C₃×#127	C₂²×C₅	1	1	yes	characteristic
176	C₃×#126	—	2	1	no	—
177	C₃×#125	C₂²×C₅	1	1	yes	characteristic
178	C₃×#124	—	2	1	no	—
179	C₃×#124	C₂²×C₅	1	1	yes	characteristic
180	C₃×#123	—	2	1	no	—
181	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
182	C₃×#121	—	2	1	no	—
183	C₃×#121	C₂²×C₅	1	2	yes	—
184	C₃×#121	C₂²×C₅	1	1	yes	characteristic
185	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₄×D₄	—	2	1	no	—
187	C₃×C₄×D₄	—	2	1	no	—
188	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
189	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
190	C₃×#117	—	2	1	no	—
191	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
192	C₃×#107	C₂²×C₅	1	2	yes	—
193	C₃×#106	C₂²×C₅	1	2	yes	—
194	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
196	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
197	C₃×#103	C₂²×C₅	1	2	yes	—
198	C₃×#102	C₂²×C₅	1	2	yes	—
199	C₃×#102	C₂²×C₅	1	2	yes	—
200	C₃×#102	C₂²×C₅	1	2	yes	—
201	C₅×#41	—	4	4	no	—
202	C₂×C₅×Q₈	—	2	1	no	—
203	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	—	2	2	no	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	—	2	1	no	—
208	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	2	no	—
212	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₅×SD₁₆	—	4	2	no	—
216	C₅×D₈	—	4	2	no	—
217	C₅×M₁₆	—	4	2	no	—
218	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
219	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
226	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
227	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
228	C₅×C₂²⋊C₄	—	2	1	no	—
229	C₅×C₂²⋊C₄	—	2	1	no	—
230	C₅×C₂²⋊C₄	—	2	1	no	—
231	C₅×C₂²⋊C₄	—	2	2	no	—
232	C₅×C₂²⋊C₄	—	2	1	no	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	2	1	no	—
235	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
237	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
238	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
239	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
240	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	#478	C₂×C₃×C₅	1	2	yes	complemented
243	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	#469	C₂×C₃×C₅	1	2	yes	complemented
246	#468	C₂×C₃×C₅	1	2	yes	complemented
247	#463	C₂×C₃×C₅	1	2	yes	complemented
248	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	2	1	no	—
253	C₂²×C₃×C₅	—	2	1	no	—
254	C₂²×C₃×C₅	—	4	1	no	—
255	C₂²×C₃×C₅	—	4	2	no	—
256	C₂²×C₃×C₅	—	4	2	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	—	4	1	no	—
260	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₃×C₄×C₅	—	2	1	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	—	2	1	no	—
264	C₃×C₄×C₅	—	2	1	no	—
265	C₃×C₄×C₅	—	4	1	no	—
266	C₃×C₄×C₅	—	4	1	no	—
267	C₃×C₄×C₅	—	4	2	no	—
268	C₃×C₄×C₅	—	4	1	no	—
269	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
270	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
271	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
272	C₃×#41	—	4	4	no	—
273	C₂×C₃×Q₈	—	2	1	no	—
274	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₃×D₄	—	2	1	no	—
276	C₂×C₃×D₄	—	2	2	no	—
277	C₂×C₃×D₄	—	2	1	no	—
278	C₂×C₃×D₄	—	2	1	no	—
279	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	—	2	1	no	—
282	C₂²×C₃×C₄	—	2	2	no	—
283	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₃×SD₁₆	—	4	2	no	—
287	C₃×D₈	—	4	2	no	—
288	C₃×M₁₆	—	4	2	no	—
289	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
290	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	—	2	1	no	—
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
299	C₃×C₂²⋊C₄	—	2	1	no	—
300	C₃×C₂²⋊C₄	—	2	1	no	—
301	C₃×C₂²⋊C₄	—	2	1	no	—
302	C₃×C₂²⋊C₄	—	2	2	no	—
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₂²⋊C₄	—	2	2	no	—
305	C₃×C₂²⋊C₄	—	2	1	no	—
306	C₃×C₄²	—	2	1	no	—
307	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
308	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
309	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
310	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₅×Q₈	—	2	1	no	—
315	C₅×Q₈	—	2	1	no	—
316	C₅×Q₈	—	4	2	no	—
317	C₅×D₄	—	2	1	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	2	1	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	4	2	no	—
322	C₅×D₄	—	4	2	no	—
323	C₅×D₄	—	4	4	no	—
324	C₅×D₄	—	4	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	4	no	—
334	C₂×C₄×C₅	—	4	2	no	—
335	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	2	2	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
345	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
346	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
347	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
348	#127	C₂²×C₃×C₅	1	1	yes	characteristic
349	#126	—	2	1	no	—
350	#125	C₂²×C₃×C₅	1	1	yes	characteristic
351	#124	—	2	1	no	—
352	#124	C₂²×C₃×C₅	1	1	yes	characteristic
353	#123	—	2	1	no	—
354	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
355	#121	—	2	1	no	—
356	#121	C₂²×C₃×C₅	1	1	yes	characteristic
357	#121	C₂²×C₃×C₅	1	2	yes	—
358	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
362	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
363	#117	—	2	1	no	—
364	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
365	#107	C₂²×C₃×C₅	1	2	yes	—
366	#106	C₂²×C₃×C₅	1	2	yes	—
367	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
368	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
370	#103	C₂²×C₃×C₅	1	2	yes	—
371	#102	C₂²×C₃×C₅	1	2	yes	—
372	#102	C₂²×C₃×C₅	1	2	yes	—
373	#102	C₂²×C₃×C₅	1	2	yes	—
374	C₂×C₃×C₅	—	4	1	no	—
375	C₂×C₃×C₅	—	8	2	no	—
376	C₂×C₃×C₅	—	8	1	no	—
377	C₂×C₃×C₅	#537	1	1	yes	characteristic
378	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂×C₃×C₅	#575	1	1	yes	characteristic
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	—	2	2	no	—
382	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
383	C₃×Q₈	—	2	1	no	—
384	C₃×Q₈	—	2	1	no	—
385	C₃×Q₈	—	4	2	no	—
386	C₃×D₄	—	2	1	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	2	1	no	—
389	C₃×D₄	—	2	2	no	—
390	C₃×D₄	—	4	2	no	—
391	C₃×D₄	—	4	2	no	—
392	C₃×D₄	—	4	4	no	—
393	C₃×D₄	—	4	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	4	1	no	—
402	C₂×C₃×C₄	—	4	4	no	—
403	C₂×C₃×C₄	—	4	2	no	—
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
410	C₃×C₈	—	2	2	no	—
411	C₃×C₈	—	2	2	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	4	2	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	2	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	2	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
431	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
432	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
433	#41	—	4	4	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
447	SD₁₆	—	4	2	no	—
448	D₈	—	4	2	no	—
449	M₁₆	—	4	2	no	—
450	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
451	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
458	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
469	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
470	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
471	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
472	C₃×C₅	#3251	1	1	yes	characteristic, direct product factor, Hall
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	2	no	—
478	C₂²×C₃	—	4	2	no	—
479	C₂²×C₃	—	4	1	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	1	no	—
482	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	—	2	1	no	—
487	C₃×C₄	—	4	1	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	2	no	—
490	C₃×C₄	—	4	1	no	—
491	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
492	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
493	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
494	C₂×C₅	—	4	1	no	—
495	C₂×C₅	—	8	2	no	—
496	C₂×C₅	—	8	1	no	—
497	C₂×C₅	C₃×#537	1	1	yes	characteristic
498	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
499	C₂×C₅	C₃×#575	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	4	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
530	C₈	—	2	2	no	—
531	C₈	—	2	2	no	—
532	C₂×C₃	—	4	1	no	—
533	C₂×C₃	—	8	2	no	—
534	C₂×C₃	—	8	1	no	—
535	C₂×C₃	C₅×#537	1	1	yes	characteristic
536	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
537	C₂×C₃	C₅×#575	1	1	yes	characteristic
538	C₅	C₃×#3251	1	1	yes	characteristic, direct product factor, Sylow
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
558	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
559	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
560	C₃	C₅×#3251	1	1	yes	characteristic, direct product factor, Sylow
561	C₂	—	4	1	no	—
562	C₂	—	8	2	no	—
563	C₂	—	8	1	no	—
564	C₂	C₃×C₅×#537	1	1	yes	characteristic
565	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
566	C₂	C₃×C₅×#575	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 ◁ 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×#478	C₂	semidirect
4. C₃×C₅×#475	C₂	semidirect
5. C₃×C₅×#474	C₂	semidirect
6. C₃×C₅×#469	C₂	semidirect
7. C₃×C₅×#468	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#460	C₂	semidirect
10. C₃×C₅×#459	C₂	semidirect
11. C₃×C₅×#423	C₂	semidirect
12. C₅×#3251	C₃	direct (N × H)
44. C₃×#3251	C₅	direct (N × H)
45. C₅×#532	C₂×C₃	semidirect
46. C₅×#529	C₂×C₃	semidirect
47. C₅×#478	C₂×C₃	semidirect
48. C₅×#475	C₂×C₃	semidirect
49. C₅×#474	C₂×C₃	semidirect
50. C₅×#469	C₂×C₃	semidirect
51. C₅×#468	C₂×C₃	semidirect
52. C₅×#463	C₂×C₃	semidirect
53. C₅×#460	C₂×C₃	semidirect
54. C₅×#459	C₂×C₃	semidirect
55. C₅×#423	C₂×C₃	semidirect
95. C₃×#532	C₂×C₅	semidirect
96. C₃×#529	C₂×C₅	semidirect
97. C₃×#478	C₂×C₅	semidirect
98. C₃×#475	C₂×C₅	semidirect
99. C₃×#474	C₂×C₅	semidirect
100. C₃×#469	C₂×C₅	semidirect
101. C₃×#468	C₂×C₅	semidirect
102. C₃×#463	C₂×C₅	semidirect
103. C₃×#460	C₂×C₅	semidirect
104. C₃×#459	C₂×C₅	semidirect
105. C₃×#423	C₂×C₅	semidirect
137. #3251	C₃×C₅	direct (N × H)
240. #532	C₂×C₃×C₅	semidirect
241. #529	C₂×C₃×C₅	semidirect
242. #478	C₂×C₃×C₅	semidirect
243. #475	C₂×C₃×C₅	semidirect
244. #474	C₂×C₃×C₅	semidirect
245. #469	C₂×C₃×C₅	semidirect
246. #468	C₂×C₃×C₅	semidirect
247. #463	C₂×C₃×C₅	semidirect
248. #460	C₂×C₃×C₅	semidirect
249. #459	C₂×C₃×C₅	semidirect
250. #423	C₂×C₃×C₅	semidirect
472. C₃×C₅	#3251	direct (N × H)
538. C₅	C₃×#3251	direct (N × H)
560. C₃	C₅×#3251	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×#478	2
C₃×C₅×#475	2
C₃×C₅×#474	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#463	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#423	2
C₅×#3251	3
C₃×#3251	5

Subgroups — C3×C5×#3251 #14276285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3251 #14276285