Subgroups — C₃×C₅×#3207 #14276241

Order 1920.

876 conjugacy classes of subgroups.

The subgroup lattice has 484 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×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#463	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#449	C₂	1	4	yes	maximal, complemented
9	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3207	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	—	2	1	no	—
12	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#127	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	—	2	1	no	—
20	C₃×C₅×#124	C₂²	1	2	yes	—
21	C₃×C₅×#121	—	2	1	no	—
22	C₃×C₅×#121	—	2	1	no	—
23	C₃×C₅×#121	—	2	1	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₄×C₅×D₄	—	2	1	no	—
26	C₃×C₄×C₅×D₄	—	2	1	no	—
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×#103	C₂²	1	4	yes	—
32	C₃×C₅×#102	C₂²	1	4	yes	—
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₃×#3207	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#463	C₂×C₃	1	4	yes	complemented
44	C₅×#449	C₂×C₃	1	4	yes	complemented
45	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×C₅×#41	—	4	4	no	—
47	C₃×C₅×#41	—	4	4	no	—
48	C₂×C₃×C₅×Q₈	—	2	1	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	1	no	—
53	C₂×C₃×C₅×D₄	—	2	1	no	—
54	C₂×C₃×C₅×D₄	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×SD₁₆	—	4	4	no	—
64	C₃×C₅×D₈	—	4	4	no	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#463	C₂×C₅	1	4	yes	complemented
86	C₃×#449	C₂×C₅	1	4	yes	complemented
87	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×C₅×#41	—	2	1	no	—
89	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
90	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
91	C₂×C₅×D₈	C₂²×C₃	1	4	yes	—
92	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₅×#127	C₂²×C₃	1	1	yes	characteristic
95	C₅×#127	C₂²×C₃	1	1	yes	characteristic
96	C₅×#124	—	2	1	no	—
97	C₅×#124	C₂²×C₃	1	2	yes	—
98	C₅×#121	—	2	1	no	—
99	C₅×#121	—	2	1	no	—
100	C₅×#121	—	2	1	no	—
101	C₅×#121	C₂²×C₃	1	2	yes	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	1	no	—
105	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
106	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
107	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
108	C₅×#103	C₂²×C₃	1	4	yes	—
109	C₅×#102	C₂²×C₃	1	4	yes	—
110	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
111	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
113	#3207	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
117	C₃×C₅×Q₈	—	2	4	no	—
118	C₃×C₅×Q₈	—	4	2	no	—
119	C₃×C₅×D₄	—	2	4	no	—
120	C₃×C₅×D₄	—	2	4	no	—
121	C₃×C₅×D₄	—	4	4	no	—
122	C₃×C₅×D₄	—	4	4	no	—
123	C₃×C₅×D₄	—	4	2	no	—
124	C₃×C₅×D₄	—	4	2	no	—
125	C₃×C₅×D₄	—	4	2	no	—
126	C₃×C₅×D₄	—	4	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	4	4	no	—
133	C₂×C₃×C₄×C₅	—	4	4	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
143	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
144	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
145	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
146	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
147	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
148	C₃×#127	C₂²×C₅	1	1	yes	characteristic
149	C₃×#127	C₂²×C₅	1	1	yes	characteristic
150	C₃×#124	—	2	1	no	—
151	C₃×#124	C₂²×C₅	1	2	yes	—
152	C₃×#121	—	2	1	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	—	2	1	no	—
155	C₃×#121	C₂²×C₅	1	2	yes	—
156	C₃×C₄×D₄	—	2	1	no	—
157	C₃×C₄×D₄	—	2	1	no	—
158	C₃×C₄×D₄	—	2	1	no	—
159	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
161	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
162	C₃×#103	C₂²×C₅	1	4	yes	—
163	C₃×#102	C₂²×C₅	1	4	yes	—
164	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
165	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
166	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₅×#41	—	4	4	no	—
168	C₅×#41	—	4	4	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
178	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
179	C₂²×C₄×C₅	—	2	2	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₅×SD₁₆	—	4	4	no	—
185	C₅×D₈	—	4	4	no	—
186	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
187	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
197	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
198	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
199	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
200	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
201	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
204	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	#463	C₂×C₃×C₅	1	4	yes	complemented
207	#449	C₂×C₃×C₅	1	4	yes	complemented
208	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₂²×C₃×C₅	—	2	1	no	—
210	C₂²×C₃×C₅	—	2	1	no	—
211	C₂²×C₃×C₅	—	2	1	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	—	4	2	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₃×C₄×C₅	—	2	1	no	—
220	C₃×C₄×C₅	—	2	1	no	—
221	C₃×C₄×C₅	—	2	1	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	#135	1	2	yes	—
225	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
226	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
227	C₃×#41	—	4	4	no	—
228	C₃×#41	—	4	4	no	—
229	C₂×C₃×Q₈	—	2	1	no	—
230	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	—	2	2	no	—
233	C₂×C₃×D₄	—	2	1	no	—
234	C₂×C₃×D₄	—	2	1	no	—
235	C₂×C₃×D₄	—	2	1	no	—
236	C₂×C₃×D₄	—	2	1	no	—
237	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
238	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₃×SD₁₆	—	4	4	no	—
245	C₃×D₈	—	4	4	no	—
246	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
247	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	—	2	1	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	—	2	2	no	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
257	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
258	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
259	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
263	C₅×Q₈	—	2	4	no	—
264	C₅×Q₈	—	4	2	no	—
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	—	2	4	no	—
267	C₅×D₄	—	4	4	no	—
268	C₅×D₄	—	4	4	no	—
269	C₅×D₄	—	4	2	no	—
270	C₅×D₄	—	4	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	4	4	no	—
279	C₂×C₄×C₅	—	4	4	no	—
280	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
286	C₅×C₈	—	2	2	no	—
287	C₅×C₈	—	2	2	no	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
290	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
291	C₂×D₈	C₂²×C₃×C₅	1	4	yes	—
292	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
294	#127	C₂²×C₃×C₅	1	1	yes	characteristic
295	#127	C₂²×C₃×C₅	1	1	yes	characteristic
296	#124	—	2	1	no	—
297	#124	C₂²×C₃×C₅	1	2	yes	—
298	#121	—	2	1	no	—
299	#121	—	2	1	no	—
300	#121	—	2	1	no	—
301	#121	C₂²×C₃×C₅	1	2	yes	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
306	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
308	#103	C₂²×C₃×C₅	1	4	yes	—
309	#102	C₂²×C₃×C₅	1	4	yes	—
310	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
311	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
313	C₂×C₃×C₅	—	4	1	no	—
314	C₂×C₃×C₅	—	8	2	no	—
315	C₂×C₃×C₅	—	8	2	no	—
316	C₂×C₃×C₅	#535	1	1	yes	characteristic
317	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
318	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	2	2	no	—
321	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
322	C₃×Q₈	—	2	4	no	—
323	C₃×Q₈	—	4	2	no	—
324	C₃×D₄	—	2	4	no	—
325	C₃×D₄	—	2	4	no	—
326	C₃×D₄	—	4	4	no	—
327	C₃×D₄	—	4	4	no	—
328	C₃×D₄	—	4	2	no	—
329	C₃×D₄	—	4	2	no	—
330	C₃×D₄	—	4	2	no	—
331	C₃×D₄	—	4	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	4	4	no	—
338	C₂×C₃×C₄	—	4	4	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	C₃×C₈	—	2	2	no	—
346	C₃×C₈	—	2	2	no	—
347	C₂²×C₅	—	2	1	no	—
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	—	4	2	no	—
355	C₂²×C₅	—	4	2	no	—
356	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	4	2	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	C₃×#135	1	2	yes	—
363	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
364	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
365	#41	—	4	4	no	—
366	#41	—	4	4	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
376	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
381	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
382	SD₁₆	—	4	4	no	—
383	D₈	—	4	4	no	—
384	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
385	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
395	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
396	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₃×C₅	#3207	1	1	yes	characteristic, direct product factor, Hall
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	—	4	2	no	—
405	C₂²×C₃	—	4	2	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	4	2	no	—
408	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	—	4	2	no	—
414	C₃×C₄	C₅×#135	1	2	yes	—
415	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
416	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
417	C₂×C₅	—	4	1	no	—
418	C₂×C₅	—	8	2	no	—
419	C₂×C₅	—	8	2	no	—
420	C₂×C₅	C₃×#535	1	1	yes	characteristic
421	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
422	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	4	2	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
444	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
447	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₂×C₃	—	4	1	no	—
452	C₂×C₃	—	8	2	no	—
453	C₂×C₃	—	8	2	no	—
454	C₂×C₃	C₅×#535	1	1	yes	characteristic
455	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
456	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
457	C₅	C₃×#3207	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	C₃×C₅×#135	1	2	yes	—
474	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
475	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
476	C₃	C₅×#3207	1	1	yes	characteristic, direct product factor, Sylow
477	C₂	—	4	1	no	—
478	C₂	—	8	2	no	—
479	C₂	—	8	2	no	—
480	C₂	C₃×C₅×#535	1	1	yes	characteristic
481	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
482	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	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×#532	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×C₅×#487	C₂	semidirect
6. C₃×C₅×#486	C₂	semidirect
7. C₃×C₅×#463	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₅×#431	C₂	semidirect
10. C₅×#3207	C₃	direct (N × H)
36. C₃×#3207	C₅	direct (N × H)
37. C₅×#532	C₂×C₃	semidirect
38. C₅×#532	C₂×C₃	semidirect
39. C₅×#493	C₂×C₃	semidirect
40. C₅×#492	C₂×C₃	semidirect
41. C₅×#487	C₂×C₃	semidirect
42. C₅×#486	C₂×C₃	semidirect
43. C₅×#463	C₂×C₃	semidirect
44. C₅×#449	C₂×C₃	semidirect
45. C₅×#431	C₂×C₃	semidirect
79. C₃×#532	C₂×C₅	semidirect
80. C₃×#532	C₂×C₅	semidirect
81. C₃×#493	C₂×C₅	semidirect
82. C₃×#492	C₂×C₅	semidirect
83. C₃×#487	C₂×C₅	semidirect
84. C₃×#486	C₂×C₅	semidirect
85. C₃×#463	C₂×C₅	semidirect
86. C₃×#449	C₂×C₅	semidirect
87. C₃×#431	C₂×C₅	semidirect
113. #3207	C₃×C₅	direct (N × H)
200. #532	C₂×C₃×C₅	semidirect
201. #532	C₂×C₃×C₅	semidirect
202. #493	C₂×C₃×C₅	semidirect
203. #492	C₂×C₃×C₅	semidirect
204. #487	C₂×C₃×C₅	semidirect
205. #486	C₂×C₃×C₅	semidirect
206. #463	C₂×C₃×C₅	semidirect
207. #449	C₂×C₃×C₅	semidirect
208. #431	C₂×C₃×C₅	semidirect
398. C₃×C₅	#3207	direct (N × H)
457. C₅	C₃×#3207	direct (N × H)
476. C₃	C₅×#3207	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×#493	2
C₃×C₅×#492	2
C₃×C₅×#487	2
C₃×C₅×#486	2
C₃×C₅×#463	2
C₃×C₅×#449	2
C₃×C₅×#431	2
C₅×#3207	3
C₃×#3207	5

Subgroups — C3×C5×#3207 #14276241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3207 #14276241