Subgroups — C₃×C₅×#3173 #14276207

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#489	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3173	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₅×#126	—	2	2	no	—
20	C₃×C₅×#124	—	2	2	no	—
21	C₃×C₅×#124	C₂²	1	2	yes	—
22	C₃×C₅×#123	—	2	2	no	—
23	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
27	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₃×C₅×#106	C₂²	1	2	yes	—
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#106	C₂²	1	1	yes	characteristic
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×C₅×#97	C₂²	1	1	yes	characteristic
37	C₃×C₅×#97	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₃×#3173	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#542	C₂×C₃	1	2	yes	complemented
42	C₅×#498	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#489	C₂×C₃	1	2	yes	complemented
45	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#469	C₂×C₃	1	1	yes	characteristic
47	C₅×#465	C₂×C₃	1	2	yes	complemented
48	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
50	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
51	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×Q₁₆	—	2	2	no	—
59	C₃×C₅×SD₁₆	—	2	4	no	—
60	C₃×C₅×D₈	—	2	2	no	—
61	C₃×C₅×M₁₆	—	2	2	no	—
62	C₂×C₃×C₅×C₈	—	2	2	no	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
79	C₃×C₄²×C₅	—	2	2	no	—
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₃×#542	C₂×C₅	1	2	yes	complemented
83	C₃×#498	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#489	C₂×C₅	1	2	yes	complemented
86	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#469	C₂×C₅	1	1	yes	characteristic
88	C₃×#465	C₂×C₅	1	2	yes	complemented
89	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
92	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
95	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
98	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
99	C₅×#126	—	2	2	no	—
100	C₅×#124	—	2	2	no	—
101	C₅×#124	C₂²×C₃	1	2	yes	—
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	—	2	2	no	—
104	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
105	C₅×#121	C₂²×C₃	1	2	yes	—
106	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
107	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
108	C₅×#117	C₂²×C₃	1	1	yes	characteristic
109	C₅×#106	C₂²×C₃	1	2	yes	—
110	C₅×#106	C₂²×C₃	1	1	yes	characteristic
111	C₅×#106	C₂²×C₃	1	1	yes	characteristic
112	C₅×#103	C₂²×C₃	1	2	yes	—
113	C₅×#103	C₂²×C₃	1	2	yes	—
114	C₅×#102	C₂²×C₃	1	2	yes	—
115	C₅×#102	C₂²×C₃	1	2	yes	—
116	C₅×#97	C₂²×C₃	1	1	yes	characteristic
117	C₅×#97	C₂²×C₃	1	1	yes	characteristic
118	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
119	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
120	#3173	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
123	C₃×C₅×Q₈	—	2	2	no	—
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×Q₈	—	8	2	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	—	8	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	1	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	8	2	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₃×C₅×C₈	—	2	1	no	—
140	C₃×C₅×C₈	—	2	1	no	—
141	C₃×C₅×C₈	#41	1	2	yes	—
142	C₃×C₅×C₈	#41	1	2	yes	—
143	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
145	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
147	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
148	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
149	C₃×#126	—	2	2	no	—
150	C₃×#124	—	2	2	no	—
151	C₃×#124	C₂²×C₅	1	2	yes	—
152	C₃×#123	—	2	2	no	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
155	C₃×#121	C₂²×C₅	1	2	yes	—
156	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
157	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
158	C₃×#117	C₂²×C₅	1	1	yes	characteristic
159	C₃×#106	C₂²×C₅	1	2	yes	—
160	C₃×#106	C₂²×C₅	1	1	yes	characteristic
161	C₃×#106	C₂²×C₅	1	1	yes	characteristic
162	C₃×#103	C₂²×C₅	1	2	yes	—
163	C₃×#103	C₂²×C₅	1	2	yes	—
164	C₃×#102	C₂²×C₅	1	2	yes	—
165	C₃×#102	C₂²×C₅	1	2	yes	—
166	C₃×#97	C₂²×C₅	1	1	yes	characteristic
167	C₃×#97	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₅×Q₈	—	2	2	no	—
171	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₅×Q₁₆	—	2	2	no	—
177	C₅×SD₁₆	—	2	4	no	—
178	C₅×D₈	—	2	2	no	—
179	C₅×M₁₆	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
189	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
190	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
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	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
197	C₄²×C₅	—	2	2	no	—
198	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
199	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
200	#542	C₂×C₃×C₅	1	2	yes	complemented
201	#498	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#489	C₂×C₃×C₅	1	2	yes	complemented
204	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#469	C₂×C₃×C₅	1	1	yes	characteristic
206	#465	C₂×C₃×C₅	1	2	yes	complemented
207	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
208	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
210	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
211	C₂²×C₃×C₅	—	2	1	no	—
212	C₂²×C₃×C₅	—	2	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	C₂²×D₄	1	1	yes	characteristic
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₂×C₃×Q₈	—	2	2	no	—
226	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
227	C₂×C₃×D₄	—	2	2	no	—
228	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
229	C₂²×C₃×C₄	—	2	2	no	—
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₃×Q₁₆	—	2	2	no	—
232	C₃×SD₁₆	—	2	4	no	—
233	C₃×D₈	—	2	2	no	—
234	C₃×M₁₆	—	2	2	no	—
235	C₂×C₃×C₈	—	2	2	no	—
236	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	—	2	2	no	—
242	C₃×C₄⋊C₄	—	2	2	no	—
243	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
244	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₂²⋊C₄	—	2	2	no	—
248	C₃×C₂²⋊C₄	—	2	2	no	—
249	C₃×C₂²⋊C₄	—	2	2	no	—
250	C₃×C₂²⋊C₄	—	2	2	no	—
251	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
252	C₃×C₄²	—	2	2	no	—
253	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
254	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	2	2	no	—
259	C₅×Q₈	—	8	2	no	—
260	C₅×D₄	—	2	2	no	—
261	C₅×D₄	—	2	2	no	—
262	C₅×D₄	—	8	2	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	8	2	no	—
269	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
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	1	no	—
274	C₅×C₈	—	2	1	no	—
275	C₅×C₈	C₃×#41	1	2	yes	—
276	C₅×C₈	C₃×#41	1	2	yes	—
277	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
279	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
281	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
282	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
283	#126	—	2	2	no	—
284	#124	—	2	2	no	—
285	#124	C₂²×C₃×C₅	1	2	yes	—
286	#123	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
289	#121	C₂²×C₃×C₅	1	2	yes	—
290	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
291	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
292	#117	C₂²×C₃×C₅	1	1	yes	characteristic
293	#106	C₂²×C₃×C₅	1	2	yes	—
294	#106	C₂²×C₃×C₅	1	1	yes	characteristic
295	#106	C₂²×C₃×C₅	1	1	yes	characteristic
296	#103	C₂²×C₃×C₅	1	2	yes	—
297	#103	C₂²×C₃×C₅	1	2	yes	—
298	#102	C₂²×C₃×C₅	1	2	yes	—
299	#102	C₂²×C₃×C₅	1	2	yes	—
300	#97	C₂²×C₃×C₅	1	1	yes	characteristic
301	#97	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
303	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
304	C₂×C₃×C₅	—	4	1	no	—
305	C₂×C₃×C₅	—	8	2	no	—
306	C₂×C₃×C₅	#532	1	1	yes	characteristic
307	C₂×C₃×C₅	#577	1	2	yes	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	8	2	no	—
313	C₃×D₄	—	2	2	no	—
314	C₃×D₄	—	2	2	no	—
315	C₃×D₄	—	8	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	8	2	no	—
322	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
326	C₃×C₈	—	2	1	no	—
327	C₃×C₈	—	2	1	no	—
328	C₃×C₈	C₅×#41	1	2	yes	—
329	C₃×C₈	C₅×#41	1	2	yes	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
336	C₄×C₅	—	2	2	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₄×C₅	—	4	2	no	—
342	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
343	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
350	Q₁₆	—	2	2	no	—
351	SD₁₆	—	2	4	no	—
352	D₈	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
356	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
357	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
358	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
363	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
364	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
371	C₄²	—	2	2	no	—
372	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
373	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
374	C₃×C₅	#3173	1	1	yes	characteristic, direct product factor, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	4	2	no	—
378	C₂²×C₃	—	4	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	—	4	2	no	—
386	C₃×C₄	—	4	2	no	—
387	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
388	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
389	C₂×C₅	—	4	1	no	—
390	C₂×C₅	—	8	2	no	—
391	C₂×C₅	C₃×#532	1	1	yes	characteristic
392	C₂×C₅	C₃×#577	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	8	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
408	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
409	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
410	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	C₃×C₅×#41	1	2	yes	—
414	C₈	C₃×C₅×#41	1	2	yes	—
415	C₂×C₃	—	4	1	no	—
416	C₂×C₃	—	8	2	no	—
417	C₂×C₃	C₅×#532	1	1	yes	characteristic
418	C₂×C₃	C₅×#577	1	2	yes	—
419	C₅	C₃×#3173	1	1	yes	characteristic, direct product factor, Sylow
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
433	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
434	C₃	C₅×#3173	1	1	yes	characteristic, direct product factor, Sylow
435	C₂	—	4	1	no	—
436	C₂	—	8	2	no	—
437	C₂	C₃×C₅×#532	1	1	yes	characteristic
438	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₃×C₅×#498	C₂	semidirect
3. C₃×C₅×#495	C₂	semidirect
4. C₃×C₅×#489	C₂	semidirect
5. C₃×C₅×#470	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₅×#442	C₂	semidirect
9. C₃×C₅×#441	C₂	semidirect
10. C₃×C₄×C₅×SD₁₆	C₂	semidirect
11. C₃×C₅×#405	C₂	semidirect
12. C₅×#3173	C₃	direct (N × H)
40. C₃×#3173	C₅	direct (N × H)
41. C₅×#542	C₂×C₃	semidirect
42. C₅×#498	C₂×C₃	semidirect
43. C₅×#495	C₂×C₃	semidirect
44. C₅×#489	C₂×C₃	semidirect
45. C₅×#470	C₂×C₃	semidirect
47. C₅×#465	C₂×C₃	semidirect
48. C₅×#442	C₂×C₃	semidirect
49. C₅×#441	C₂×C₃	semidirect
50. C₄×C₅×SD₁₆	C₂×C₃	semidirect
51. C₅×#405	C₂×C₃	semidirect
82. C₃×#542	C₂×C₅	semidirect
83. C₃×#498	C₂×C₅	semidirect
84. C₃×#495	C₂×C₅	semidirect
85. C₃×#489	C₂×C₅	semidirect
86. C₃×#470	C₂×C₅	semidirect
88. C₃×#465	C₂×C₅	semidirect
89. C₃×#442	C₂×C₅	semidirect
90. C₃×#441	C₂×C₅	semidirect
91. C₃×C₄×SD₁₆	C₂×C₅	semidirect
92. C₃×#405	C₂×C₅	semidirect
120. #3173	C₃×C₅	direct (N × H)
200. #542	C₂×C₃×C₅	semidirect
201. #498	C₂×C₃×C₅	semidirect
202. #495	C₂×C₃×C₅	semidirect
203. #489	C₂×C₃×C₅	semidirect
204. #470	C₂×C₃×C₅	semidirect
206. #465	C₂×C₃×C₅	semidirect
207. #442	C₂×C₃×C₅	semidirect
208. #441	C₂×C₃×C₅	semidirect
209. C₄×SD₁₆	C₂×C₃×C₅	semidirect
210. #405	C₂×C₃×C₅	semidirect
374. C₃×C₅	#3173	direct (N × H)
419. C₅	C₃×#3173	direct (N × H)
434. C₃	C₅×#3173	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×#542	2
C₃×C₅×#498	2
C₃×C₅×#495	2
C₃×C₅×#489	2
C₃×C₅×#470	2
C₃×C₅×#469	2
C₃×C₅×#465	2
C₃×C₅×#442	2
C₃×C₅×#441	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#405	2
C₅×#3173	3
C₃×#3173	5

Subgroups — C3×C5×#3173 #14276207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3173 #14276207