Subgroups — C₃×C₅×#3167 #14276201

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#498	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×#465	C₂	1	4	yes	maximal, complemented
8	C₃×C₄×C₅×SD₁₆	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3167	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	—	2	1	no	—
12	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
13	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
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×#125	—	2	1	no	—
19	C₃×C₅×#124	—	2	1	no	—
20	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₅×#121	—	2	1	no	—
23	C₃×C₅×#121	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	—	2	1	no	—
25	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₃×C₄×C₅×D₄	—	2	1	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₃×C₅×#117	—	2	1	no	—
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	4	yes	—
31	C₃×C₅×#103	C₂²	1	4	yes	—
32	C₃×C₅×#102	C₂²	1	4	yes	—
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
36	C₃×#3167	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×#498	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×#465	C₂×C₃	1	4	yes	complemented
44	C₄×C₅×SD₁₆	C₂×C₃	1	4	yes	complemented
45	C₂×C₄×C₅×C₈	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	C₂³	1	2	yes	—
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	C₃×C₅×SD₁₆	—	2	8	no	—
59	C₂×C₃×C₅×C₈	—	2	4	no	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₄²×C₅	—	2	2	no	—
74	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#532	C₂×C₅	1	1	yes	characteristic
80	C₃×#498	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#465	C₂×C₅	1	4	yes	complemented
85	C₃×C₄×SD₁₆	C₂×C₅	1	4	yes	complemented
86	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₅×#41	—	2	1	no	—
88	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
89	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
90	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₅×#127	C₂²×C₃	1	1	yes	characteristic
94	C₅×#125	—	2	1	no	—
95	C₅×#124	—	2	1	no	—
96	C₅×C₂²⋊Q₈	—	2	1	no	—
97	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
98	C₅×#121	—	2	1	no	—
99	C₅×#121	C₂²×C₃	1	2	yes	—
100	C₄×C₅×Q₈	—	2	1	no	—
101	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
104	C₅×#117	—	2	1	no	—
105	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
106	C₅×#106	C₂²×C₃	1	4	yes	—
107	C₅×#103	C₂²×C₃	1	4	yes	—
108	C₅×#102	C₂²×C₃	1	4	yes	—
109	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
110	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
111	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
112	#3167	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
115	C₃×C₅×Q₈	—	2	4	no	—
116	C₃×C₅×Q₈	—	4	2	no	—
117	C₃×C₅×Q₈	—	4	2	no	—
118	C₃×C₅×D₄	—	2	4	no	—
119	C₃×C₅×D₄	—	4	4	no	—
120	C₃×C₅×D₄	—	4	2	no	—
121	C₃×C₅×D₄	—	4	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	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	4	4	no	—
128	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
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	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₃×C₅×C₈	—	2	2	no	—
136	C₃×C₅×C₈	#41	1	4	yes	complemented
137	C₂×C₃×#41	—	2	1	no	—
138	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
139	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
140	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
141	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
142	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
143	C₃×#127	C₂²×C₅	1	1	yes	characteristic
144	C₃×#125	—	2	1	no	—
145	C₃×#124	—	2	1	no	—
146	C₃×C₂²⋊Q₈	—	2	1	no	—
147	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
148	C₃×#121	—	2	1	no	—
149	C₃×#121	C₂²×C₅	1	2	yes	—
150	C₃×C₄×Q₈	—	2	1	no	—
151	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
152	C₃×C₄×D₄	—	2	1	no	—
153	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
154	C₃×#117	—	2	1	no	—
155	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
156	C₃×#106	C₂²×C₅	1	4	yes	—
157	C₃×#103	C₂²×C₅	1	4	yes	—
158	C₃×#102	C₂²×C₅	1	4	yes	—
159	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
160	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
162	C₅×#41	—	4	4	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
166	C₂×C₅×D₄	—	2	2	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₅×SD₁₆	—	2	8	no	—
175	C₂×C₅×C₈	—	2	4	no	—
176	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
177	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
185	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
186	C₅×C₂²⋊C₄	—	2	2	no	—
187	C₅×C₂²⋊C₄	—	2	2	no	—
188	C₅×C₂²⋊C₄	—	2	2	no	—
189	C₄²×C₅	—	2	2	no	—
190	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
191	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
194	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	#532	C₂×C₃×C₅	1	1	yes	characteristic
196	#498	C₂×C₃×C₅	1	1	yes	characteristic, complemented
197	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
198	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
200	#465	C₂×C₃×C₅	1	4	yes	complemented
201	C₄×SD₁₆	C₂×C₃×C₅	1	4	yes	complemented
202	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	C₂²×C₃×C₅	—	2	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	4	2	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
209	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₃×C₄×C₅	—	2	1	no	—
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	—	4	2	no	—
215	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
216	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
217	C₃×C₄×C₅	#135	1	2	yes	—
218	C₃×C₄×C₅	C₂×#41	1	2	yes	—
219	C₃×#41	—	4	4	no	—
220	C₂×C₃×Q₈	—	2	1	no	—
221	C₂×C₃×Q₈	—	2	1	no	—
222	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
223	C₂×C₃×D₄	—	2	2	no	—
224	C₂×C₃×D₄	—	2	1	no	—
225	C₂×C₃×D₄	—	2	1	no	—
226	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	—	2	2	no	—
228	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₃×SD₁₆	—	2	8	no	—
232	C₂×C₃×C₈	—	2	4	no	—
233	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
234	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
235	C₃×C₄⋊C₄	—	2	1	no	—
236	C₃×C₄⋊C₄	—	2	1	no	—
237	C₃×C₄⋊C₄	—	2	1	no	—
238	C₃×C₄⋊C₄	—	2	1	no	—
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
242	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
243	C₃×C₂²⋊C₄	—	2	2	no	—
244	C₃×C₂²⋊C₄	—	2	2	no	—
245	C₃×C₂²⋊C₄	—	2	2	no	—
246	C₃×C₄²	—	2	2	no	—
247	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
248	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
249	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
250	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
251	C₂³×C₅	—	2	2	no	—
252	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
253	C₅×Q₈	—	2	4	no	—
254	C₅×Q₈	—	4	2	no	—
255	C₅×Q₈	—	4	2	no	—
256	C₅×D₄	—	2	4	no	—
257	C₅×D₄	—	4	4	no	—
258	C₅×D₄	—	4	2	no	—
259	C₅×D₄	—	4	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	4	no	—
266	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
267	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
273	C₅×C₈	—	2	2	no	—
274	C₅×C₈	C₃×#41	1	4	yes	complemented
275	C₂×#41	—	2	1	no	—
276	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
277	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
278	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
281	#127	C₂²×C₃×C₅	1	1	yes	characteristic
282	#125	—	2	1	no	—
283	#124	—	2	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
286	#121	—	2	1	no	—
287	#121	C₂²×C₃×C₅	1	2	yes	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
292	#117	—	2	1	no	—
293	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
294	#106	C₂²×C₃×C₅	1	4	yes	—
295	#103	C₂²×C₃×C₅	1	4	yes	—
296	#102	C₂²×C₃×C₅	1	4	yes	—
297	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
298	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	8	2	no	—
302	C₂×C₃×C₅	#532	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
304	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
307	C₃×Q₈	—	2	4	no	—
308	C₃×Q₈	—	4	2	no	—
309	C₃×Q₈	—	4	2	no	—
310	C₃×D₄	—	2	4	no	—
311	C₃×D₄	—	4	4	no	—
312	C₃×D₄	—	4	2	no	—
313	C₃×D₄	—	4	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	4	4	no	—
320	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
321	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
327	C₃×C₈	—	2	2	no	—
328	C₃×C₈	C₅×#41	1	4	yes	complemented
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	4	2	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
335	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	4	2	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
342	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
343	C₄×C₅	C₃×#135	1	2	yes	—
344	C₄×C₅	C₂×C₃×#41	1	2	yes	—
345	#41	—	4	4	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
357	SD₁₆	—	2	8	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
360	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
368	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
374	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
375	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₃×C₅	#3167	1	1	yes	characteristic, direct product factor, Hall
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
384	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
391	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
392	C₃×C₄	C₅×#135	1	2	yes	—
393	C₃×C₄	C₂×C₅×#41	1	2	yes	—
394	C₂×C₅	—	2	2	no	—
395	C₂×C₅	—	8	2	no	—
396	C₂×C₅	C₃×#532	1	1	yes	characteristic
397	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
398	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
399	C₂³	—	2	2	no	—
400	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
401	Q₈	—	2	4	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	complemented
415	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
420	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	C₃×C₅×#41	1	4	yes	complemented
423	C₂×C₃	—	2	2	no	—
424	C₂×C₃	—	8	2	no	—
425	C₂×C₃	C₅×#532	1	1	yes	characteristic
426	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
427	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
428	C₅	C₃×#3167	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
435	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
442	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
443	C₄	C₃×C₅×#135	1	2	yes	—
444	C₄	C₂×C₃×C₅×#41	1	2	yes	—
445	C₃	C₅×#3167	1	1	yes	characteristic, direct product factor, Sylow
446	C₂	—	2	2	no	—
447	C₂	—	8	2	no	—
448	C₂	C₃×C₅×#532	1	1	yes	characteristic
449	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
450	C₂	C₂×C₃×C₅×#135	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
prime radical	C₃×C₅×#532	C₂
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×#533	C₂	semidirect
3. C₃×C₅×#498	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×C₅×#487	C₂	semidirect
6. C₃×C₅×#486	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₄×C₅×SD₁₆	C₂	semidirect
9. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
10. C₅×#3167	C₃	direct (N × H)
36. C₃×#3167	C₅	direct (N × H)
37. C₅×#533	C₂×C₃	semidirect
39. C₅×#498	C₂×C₃	semidirect
40. C₅×#492	C₂×C₃	semidirect
41. C₅×#487	C₂×C₃	semidirect
42. C₅×#486	C₂×C₃	semidirect
43. C₅×#465	C₂×C₃	semidirect
44. C₄×C₅×SD₁₆	C₂×C₃	semidirect
45. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
78. C₃×#533	C₂×C₅	semidirect
80. C₃×#498	C₂×C₅	semidirect
81. C₃×#492	C₂×C₅	semidirect
82. C₃×#487	C₂×C₅	semidirect
83. C₃×#486	C₂×C₅	semidirect
84. C₃×#465	C₂×C₅	semidirect
85. C₃×C₄×SD₁₆	C₂×C₅	semidirect
86. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
112. #3167	C₃×C₅	direct (N × H)
128. C₂×C₃×C₄×C₅	SD₁₆	semidirect
136. C₃×C₅×C₈	#41	semidirect
194. #533	C₂×C₃×C₅	semidirect
196. #498	C₂×C₃×C₅	semidirect
197. #492	C₂×C₃×C₅	semidirect
198. #487	C₂×C₃×C₅	semidirect
199. #486	C₂×C₃×C₅	semidirect
200. #465	C₂×C₃×C₅	semidirect
201. C₄×SD₁₆	C₂×C₃×C₅	semidirect
202. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
266. C₂×C₄×C₅	C₃×SD₁₆	semidirect
274. C₅×C₈	C₃×#41	semidirect
320. C₂×C₃×C₄	C₅×SD₁₆	semidirect
328. C₃×C₈	C₅×#41	semidirect
377. C₃×C₅	#3167	direct (N × H)
414. C₂×C₄	C₃×C₅×SD₁₆	semidirect
422. C₈	C₃×C₅×#41	semidirect
428. C₅	C₃×#3167	direct (N × H)
445. C₃	C₅×#3167	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×#498	2
C₃×C₅×#492	2
C₃×C₅×#487	2
C₃×C₅×#486	2
C₃×C₅×#465	2
C₃×C₄×C₅×SD₁₆	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#3167	3
C₃×#3167	5

Subgroups — C3×C5×#3167 #14276201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3167 #14276201