Subgroups — C₃×C₅×#3228 #14276262

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#482	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#478	C₂	1	4	yes	maximal, complemented
9	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3228	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₃×C₅×#125	C₂²	1	2	yes	—
17	C₃×C₅×#124	—	2	1	no	—
18	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
20	C₃×C₅×#121	—	2	1	no	—
21	C₃×C₅×#121	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×Q₈	—	2	1	no	—
24	C₃×C₄×C₅×D₄	—	2	1	no	—
25	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
26	C₃×C₅×#117	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#107	C₂²	1	4	yes	—
29	C₃×C₅×#106	C₂²	1	4	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×#102	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×#3228	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#532	C₂×C₃	1	1	yes	characteristic
39	C₅×#500	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#498	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#482	C₂×C₃	1	4	yes	complemented
44	C₅×#478	C₂×C₃	1	4	yes	complemented
45	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×C₅×#41	—	4	4	no	—
47	C₂×C₃×C₅×Q₈	—	2	1	no	—
48	C₂×C₃×C₅×Q₈	—	2	1	no	—
49	C₂×C₃×C₅×Q₈	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	1	no	—
52	C₂×C₃×C₅×D₄	—	2	1	no	—
53	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#532	C₂×C₅	1	1	yes	characteristic
78	C₃×#500	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#498	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#482	C₂×C₅	1	4	yes	complemented
83	C₃×#478	C₂×C₅	1	4	yes	complemented
84	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×C₅×#41	—	2	1	no	—
86	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
87	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
88	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#127	C₂²×C₃	1	1	yes	characteristic
90	C₅×#125	C₂²×C₃	1	2	yes	—
91	C₅×#124	—	2	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×C₂²⋊Q₈	—	2	1	no	—
94	C₅×#121	—	2	1	no	—
95	C₅×#121	C₂²×C₃	1	2	yes	—
96	C₄×C₅×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	—	2	1	no	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
100	C₅×#117	C₂²×C₃	1	2	yes	—
101	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
102	C₅×#107	C₂²×C₃	1	4	yes	—
103	C₅×#106	C₂²×C₃	1	4	yes	—
104	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₅×#102	C₂²×C₃	1	4	yes	—
106	C₅×#102	C₂²×C₃	1	4	yes	—
107	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
108	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
110	#3228	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₅×Q₈	—	4	2	no	—
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₃×C₅×Q₈	—	4	2	no	—
116	C₃×C₅×D₄	—	2	4	no	—
117	C₃×C₅×D₄	—	4	4	no	—
118	C₃×C₅×D₄	—	4	2	no	—
119	C₃×C₅×D₄	—	4	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	4	4	no	—
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₃×C₅×C₈	—	2	2	no	—
134	C₃×C₅×C₈	—	2	2	no	—
135	C₂×C₃×#41	—	2	1	no	—
136	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
139	C₃×#127	C₂²×C₅	1	1	yes	characteristic
140	C₃×#125	C₂²×C₅	1	2	yes	—
141	C₃×#124	—	2	1	no	—
142	C₃×C₂²⋊Q₈	—	2	1	no	—
143	C₃×C₂²⋊Q₈	—	2	1	no	—
144	C₃×#121	—	2	1	no	—
145	C₃×#121	C₂²×C₅	1	2	yes	—
146	C₃×C₄×Q₈	—	2	1	no	—
147	C₃×C₄×Q₈	—	2	1	no	—
148	C₃×C₄×D₄	—	2	1	no	—
149	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
150	C₃×#117	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
152	C₃×#107	C₂²×C₅	1	4	yes	—
153	C₃×#106	C₂²×C₅	1	4	yes	—
154	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
155	C₃×#102	C₂²×C₅	1	4	yes	—
156	C₃×#102	C₂²×C₅	1	4	yes	—
157	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
158	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
159	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
160	C₅×#41	—	4	4	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×D₄	—	2	2	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
173	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	2	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
180	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
181	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
182	C₅×C₂²⋊C₄	—	2	2	no	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₅×C₂²⋊C₄	—	2	2	no	—
185	C₄²×C₅	—	2	2	no	—
186	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
187	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
188	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
190	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
191	#532	C₂×C₃×C₅	1	1	yes	characteristic
192	#500	C₂×C₃×C₅	1	1	yes	characteristic, complemented
193	#498	C₂×C₃×C₅	1	1	yes	characteristic, complemented
194	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
196	#482	C₂×C₃×C₅	1	4	yes	complemented
197	#478	C₂×C₃×C₅	1	4	yes	complemented
198	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	C₂²×C₃×C₅	—	2	1	no	—
200	C₂²×C₃×C₅	—	2	1	no	—
201	C₂²×C₃×C₅	—	2	1	no	—
202	C₂²×C₃×C₅	—	4	2	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₃×C₄×C₅	—	2	1	no	—
207	C₃×C₄×C₅	—	2	1	no	—
208	C₃×C₄×C₅	—	2	1	no	—
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	#135	1	2	yes	—
213	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
214	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
215	C₃×#41	—	4	4	no	—
216	C₂×C₃×Q₈	—	2	1	no	—
217	C₂×C₃×Q₈	—	2	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	2	1	no	—
221	C₂×C₃×D₄	—	2	1	no	—
222	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	—	2	2	no	—
224	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
228	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₄⋊C₄	—	2	2	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
235	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
236	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
237	C₃×C₂²⋊C₄	—	2	2	no	—
238	C₃×C₂²⋊C₄	—	2	2	no	—
239	C₃×C₂²⋊C₄	—	2	2	no	—
240	C₃×C₄²	—	2	2	no	—
241	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
242	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
243	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
244	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₂³×C₅	—	2	2	no	—
246	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₅×Q₈	—	4	2	no	—
248	C₅×Q₈	—	4	2	no	—
249	C₅×Q₈	—	4	2	no	—
250	C₅×D₄	—	2	4	no	—
251	C₅×D₄	—	4	4	no	—
252	C₅×D₄	—	4	2	no	—
253	C₅×D₄	—	4	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	4	4	no	—
261	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
267	C₅×C₈	—	2	2	no	—
268	C₅×C₈	—	2	2	no	—
269	C₂×#41	—	2	1	no	—
270	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
271	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
272	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
273	#127	C₂²×C₃×C₅	1	1	yes	characteristic
274	#125	C₂²×C₃×C₅	1	2	yes	—
275	#124	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	C₂²×C₃×C₅	1	2	yes	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
284	#117	C₂²×C₃×C₅	1	2	yes	—
285	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
286	#107	C₂²×C₃×C₅	1	4	yes	—
287	#106	C₂²×C₃×C₅	1	4	yes	—
288	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
289	#102	C₂²×C₃×C₅	1	4	yes	—
290	#102	C₂²×C₃×C₅	1	4	yes	—
291	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
292	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
294	C₂×C₃×C₅	—	4	1	no	—
295	C₂×C₃×C₅	—	8	2	no	—
296	C₂×C₃×C₅	#536	1	1	yes	characteristic
297	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
298	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
301	C₃×Q₈	—	4	2	no	—
302	C₃×Q₈	—	4	2	no	—
303	C₃×Q₈	—	4	2	no	—
304	C₃×D₄	—	2	4	no	—
305	C₃×D₄	—	4	4	no	—
306	C₃×D₄	—	4	2	no	—
307	C₃×D₄	—	4	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	4	4	no	—
315	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
321	C₃×C₈	—	2	2	no	—
322	C₃×C₈	—	2	2	no	—
323	C₂²×C₅	—	2	1	no	—
324	C₂²×C₅	—	2	1	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	4	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	C₃×#135	1	2	yes	—
337	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
338	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
339	#41	—	4	4	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
349	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
351	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
352	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
359	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
360	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
366	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
367	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
368	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
369	C₃×C₅	#3228	1	1	yes	characteristic, direct product factor, Hall
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	4	2	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	4	2	no	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	C₅×#135	1	2	yes	—
384	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
385	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
386	C₂×C₅	—	4	1	no	—
387	C₂×C₅	—	8	2	no	—
388	C₂×C₅	C₃×#536	1	1	yes	characteristic
389	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
390	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₂³	—	2	2	no	—
392	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
408	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
409	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
410	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₂×C₃	—	4	1	no	—
416	C₂×C₃	—	8	2	no	—
417	C₂×C₃	C₅×#536	1	1	yes	characteristic
418	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
419	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₅	C₃×#3228	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	C₃×C₅×#135	1	2	yes	—
435	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
436	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
437	C₃	C₅×#3228	1	1	yes	characteristic, direct product factor, Sylow
438	C₂	—	4	1	no	—
439	C₂	—	8	2	no	—
440	C₂	C₃×C₅×#536	1	1	yes	characteristic
441	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
442	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
prime radical	C₃×C₅×#532	C₂
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×#533	C₂	semidirect
3. C₃×C₅×#500	C₂	semidirect
4. C₃×C₅×#498	C₂	semidirect
5. C₃×C₅×#486	C₂	semidirect
6. C₃×C₅×#486	C₂	semidirect
7. C₃×C₅×#482	C₂	semidirect
8. C₃×C₅×#478	C₂	semidirect
9. C₃×C₅×#431	C₂	semidirect
10. C₅×#3228	C₃	direct (N × H)
36. C₃×#3228	C₅	direct (N × H)
37. C₅×#533	C₂×C₃	semidirect
39. C₅×#500	C₂×C₃	semidirect
40. C₅×#498	C₂×C₃	semidirect
41. C₅×#486	C₂×C₃	semidirect
42. C₅×#486	C₂×C₃	semidirect
43. C₅×#482	C₂×C₃	semidirect
44. C₅×#478	C₂×C₃	semidirect
45. C₅×#431	C₂×C₃	semidirect
76. C₃×#533	C₂×C₅	semidirect
78. C₃×#500	C₂×C₅	semidirect
79. C₃×#498	C₂×C₅	semidirect
80. C₃×#486	C₂×C₅	semidirect
81. C₃×#486	C₂×C₅	semidirect
82. C₃×#482	C₂×C₅	semidirect
83. C₃×#478	C₂×C₅	semidirect
84. C₃×#431	C₂×C₅	semidirect
110. #3228	C₃×C₅	direct (N × H)
190. #533	C₂×C₃×C₅	semidirect
192. #500	C₂×C₃×C₅	semidirect
193. #498	C₂×C₃×C₅	semidirect
194. #486	C₂×C₃×C₅	semidirect
195. #486	C₂×C₃×C₅	semidirect
196. #482	C₂×C₃×C₅	semidirect
197. #478	C₂×C₃×C₅	semidirect
198. #431	C₂×C₃×C₅	semidirect
369. C₃×C₅	#3228	direct (N × H)
420. C₅	C₃×#3228	direct (N × H)
437. C₃	C₅×#3228	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×#533	2
C₃×C₅×#532	2
C₃×C₅×#500	2
C₃×C₅×#498	2
C₃×C₅×#486	2
C₃×C₅×#482	2
C₃×C₅×#478	2
C₃×C₅×#431	2
C₅×#3228	3
C₃×#3228	5

Subgroups — C3×C5×#3228 #14276262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3228 #14276262