Subgroups — C₃×C₅×#3172 #14276206

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 520 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×#529	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#468	C₂	1	2	yes	maximal
9	C₃×C₄×C₅×Q₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3172	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#126	—	2	1	no	—
19	C₃×C₅×#125	—	2	1	no	—
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic
21	C₃×C₅×#124	C₂²	1	1	yes	characteristic
22	C₃×C₅×#123	—	2	1	no	—
23	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×Q₈	—	2	1	no	—
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₃×C₅×#117	—	2	1	no	—
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×#103	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#103	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×#97	C₂²	1	1	yes	characteristic
42	C₃×C₅×#97	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
44	C₃×#3172	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#529	C₂×C₃	1	1	yes	characteristic
47	C₅×#501	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#470	C₂×C₃	1	2	yes	complemented
52	C₅×#468	C₂×C₃	1	2	yes	—
53	C₄×C₅×Q₁₆	C₂×C₃	1	2	yes	complemented
54	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
55	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₅×Q₁₆	—	2	4	no	—
66	C₃×C₅×SD₁₆	—	2	4	no	—
67	C₃×C₅×M₁₆	—	2	4	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	—	2	2	no	—
90	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
91	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#529	C₂×C₅	1	1	yes	characteristic
96	C₃×#501	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#491	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#470	C₂×C₅	1	2	yes	complemented
101	C₃×#468	C₂×C₅	1	2	yes	—
102	C₃×C₄×Q₁₆	C₂×C₅	1	2	yes	complemented
103	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
104	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
106	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
107	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
108	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₅×#126	—	2	1	no	—
111	C₅×#125	—	2	1	no	—
112	C₅×#125	C₂²×C₃	1	1	yes	characteristic
113	C₅×#124	C₂²×C₃	1	1	yes	characteristic
114	C₅×#123	—	2	1	no	—
115	C₅×C₂²⋊Q₈	—	2	1	no	—
116	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
117	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₅×#121	C₂²×C₃	1	1	yes	characteristic
119	C₄×C₅×Q₈	—	2	1	no	—
120	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
121	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
122	C₄×C₅×D₄	—	2	1	no	—
123	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
124	C₅×#117	—	2	1	no	—
125	C₅×#117	—	2	1	no	—
126	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
127	C₅×#107	C₂²×C₃	1	2	yes	—
128	C₅×#106	C₂²×C₃	1	2	yes	—
129	C₅×#103	C₂²×C₃	1	2	yes	—
130	C₅×#103	C₂²×C₃	1	2	yes	—
131	C₅×#103	C₂²×C₃	1	2	yes	—
132	C₅×#102	C₂²×C₃	1	2	yes	—
133	C₅×#97	C₂²×C₃	1	1	yes	characteristic
134	C₅×#97	C₂²×C₃	1	1	yes	characteristic
135	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
136	#3172	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	4	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	4	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	4	1	no	—
153	C₂×C₃×C₄×C₅	—	4	2	no	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₃×C₅×C₈	—	2	2	no	—
161	C₃×C₅×C₈	#41	1	4	yes	—
162	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
163	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
164	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
165	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₃×#126	—	2	1	no	—
168	C₃×#125	—	2	1	no	—
169	C₃×#125	C₂²×C₅	1	1	yes	characteristic
170	C₃×#124	C₂²×C₅	1	1	yes	characteristic
171	C₃×#123	—	2	1	no	—
172	C₃×C₂²⋊Q₈	—	2	1	no	—
173	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
174	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
175	C₃×#121	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₄×Q₈	—	2	1	no	—
177	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
178	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₃×C₄×D₄	—	2	1	no	—
180	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₃×#117	—	2	1	no	—
182	C₃×#117	—	2	1	no	—
183	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
184	C₃×#107	C₂²×C₅	1	2	yes	—
185	C₃×#106	C₂²×C₅	1	2	yes	—
186	C₃×#103	C₂²×C₅	1	2	yes	—
187	C₃×#103	C₂²×C₅	1	2	yes	—
188	C₃×#103	C₂²×C₅	1	2	yes	—
189	C₃×#102	C₂²×C₅	1	2	yes	—
190	C₃×#97	C₂²×C₅	1	1	yes	characteristic
191	C₃×#97	C₂²×C₅	1	1	yes	characteristic
192	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
193	C₂×C₅×Q₈	—	2	1	no	—
194	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
196	C₂×C₅×D₄	—	2	1	no	—
197	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₅×Q₁₆	—	2	4	no	—
203	C₅×SD₁₆	—	2	4	no	—
204	C₅×M₁₆	—	2	4	no	—
205	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
206	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	2	no	—
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
218	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	—	2	1	no	—
222	C₅×C₂²⋊C₄	—	2	1	no	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	2	no	—
227	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
228	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
229	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
230	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
231	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#529	C₂×C₃×C₅	1	1	yes	characteristic
233	#501	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#491	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#470	C₂×C₃×C₅	1	2	yes	complemented
238	#468	C₂×C₃×C₅	1	2	yes	—
239	C₄×Q₁₆	C₂×C₃×C₅	1	2	yes	complemented
240	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
241	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₄×C₅	—	2	1	no	—
250	C₃×C₄×C₅	—	2	1	no	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	—	4	2	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	—	4	1	no	—
257	C₃×C₄×C₅	—	4	2	no	—
258	C₃×C₄×C₅	#137	1	2	yes	—
259	C₃×C₄×C₅	C₂×#41	1	2	yes	—
260	C₂×C₃×Q₈	—	2	1	no	—
261	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₃×C₄	—	2	1	no	—
266	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₃×Q₁₆	—	2	4	no	—
270	C₃×SD₁₆	—	2	4	no	—
271	C₃×M₁₆	—	2	4	no	—
272	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
273	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	—	2	1	no	—
277	C₃×C₄⋊C₄	—	2	1	no	—
278	C₃×C₄⋊C₄	—	2	1	no	—
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	—	2	2	no	—
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
284	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	—	2	2	no	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	1	no	—
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₂²⋊C₄	—	2	1	no	—
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₄²	—	2	1	no	—
293	C₃×C₄²	—	2	2	no	—
294	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
295	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
296	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
297	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	2	2	no	—
302	C₅×Q₈	—	2	2	no	—
303	C₅×Q₈	—	4	2	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	4	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	2	no	—
315	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
321	C₅×C₈	—	2	2	no	—
322	C₅×C₈	C₃×#41	1	4	yes	—
323	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
324	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
325	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
326	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
327	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
328	#126	—	2	1	no	—
329	#125	—	2	1	no	—
330	#125	C₂²×C₃×C₅	1	1	yes	characteristic
331	#124	C₂²×C₃×C₅	1	1	yes	characteristic
332	#123	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
335	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
336	#121	C₂²×C₃×C₅	1	1	yes	characteristic
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
339	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
345	#107	C₂²×C₃×C₅	1	2	yes	—
346	#106	C₂²×C₃×C₅	1	2	yes	—
347	#103	C₂²×C₃×C₅	1	2	yes	—
348	#103	C₂²×C₃×C₅	1	2	yes	—
349	#103	C₂²×C₃×C₅	1	2	yes	—
350	#102	C₂²×C₃×C₅	1	2	yes	—
351	#97	C₂²×C₃×C₅	1	1	yes	characteristic
352	#97	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
354	C₂×C₃×C₅	—	4	1	no	—
355	C₂×C₃×C₅	—	8	1	no	—
356	C₂×C₃×C₅	#532	1	1	yes	characteristic
357	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
358	C₂×C₃×C₅	#575	1	1	yes	characteristic
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	4	2	no	—
365	C₃×D₄	—	2	2	no	—
366	C₃×D₄	—	4	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	4	1	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
382	C₃×C₈	—	2	2	no	—
383	C₃×C₈	C₅×#41	1	4	yes	—
384	C₂²×C₅	—	2	1	no	—
385	C₂²×C₅	—	2	1	no	—
386	C₂²×C₅	—	2	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	2	1	no	—
393	C₄×C₅	—	2	1	no	—
394	C₄×C₅	—	2	1	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	—	4	2	no	—
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	C₃×#137	1	2	yes	—
401	C₄×C₅	C₂×C₃×#41	1	2	yes	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
411	Q₁₆	—	2	4	no	—
412	SD₁₆	—	2	4	no	—
413	M₁₆	—	2	4	no	—
414	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
415	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
426	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
427	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	2	no	—
436	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
437	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
438	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
439	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
440	C₃×C₅	#3172	1	1	yes	characteristic, direct product factor, Hall
441	C₂²×C₃	—	2	1	no	—
442	C₂²×C₃	—	2	1	no	—
443	C₂²×C₃	—	2	1	no	—
444	C₂²×C₃	—	4	1	no	—
445	C₂²×C₃	—	4	1	no	—
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
448	C₃×C₄	—	2	1	no	—
449	C₃×C₄	—	2	1	no	—
450	C₃×C₄	—	2	1	no	—
451	C₃×C₄	—	2	1	no	—
452	C₃×C₄	—	4	1	no	—
453	C₃×C₄	—	4	2	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	4	2	no	—
457	C₃×C₄	C₅×#137	1	2	yes	—
458	C₃×C₄	C₂×C₅×#41	1	2	yes	—
459	C₂×C₅	—	4	1	no	—
460	C₂×C₅	—	8	1	no	—
461	C₂×C₅	C₃×#532	1	1	yes	characteristic
462	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
463	C₂×C₅	C₃×#575	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	4	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	4	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
483	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	C₃×C₅×#41	1	4	yes	—
489	C₂×C₃	—	4	1	no	—
490	C₂×C₃	—	8	1	no	—
491	C₂×C₃	C₅×#532	1	1	yes	characteristic
492	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
493	C₂×C₃	C₅×#575	1	1	yes	characteristic
494	C₅	C₃×#3172	1	1	yes	characteristic, direct product factor, Sylow
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	2	no	—
511	C₄	C₃×C₅×#137	1	2	yes	—
512	C₄	C₂×C₃×C₅×#41	1	2	yes	—
513	C₃	C₅×#3172	1	1	yes	characteristic, direct product factor, Sylow
514	C₂	—	4	1	no	—
515	C₂	—	8	1	no	—
516	C₂	C₃×C₅×#532	1	1	yes	characteristic
517	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
518	C₂	C₃×C₅×#575	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×#121	C₂²
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×#501	C₂	semidirect
4. C₃×C₅×#497	C₂	semidirect
5. C₃×C₅×#491	C₂	semidirect
6. C₃×C₅×#489	C₂	semidirect
7. C₃×C₅×#470	C₂	semidirect
9. C₃×C₄×C₅×Q₁₆	C₂	semidirect
10. C₃×C₄×C₅×SD₁₆	C₂	semidirect
11. C₃×C₄×C₅×M₁₆	C₂	semidirect
12. C₅×#3172	C₃	direct (N × H)
44. C₃×#3172	C₅	direct (N × H)
45. C₅×#533	C₂×C₃	semidirect
47. C₅×#501	C₂×C₃	semidirect
48. C₅×#497	C₂×C₃	semidirect
49. C₅×#491	C₂×C₃	semidirect
50. C₅×#489	C₂×C₃	semidirect
51. C₅×#470	C₂×C₃	semidirect
53. C₄×C₅×Q₁₆	C₂×C₃	semidirect
54. C₄×C₅×SD₁₆	C₂×C₃	semidirect
55. C₄×C₅×M₁₆	C₂×C₃	semidirect
94. C₃×#533	C₂×C₅	semidirect
96. C₃×#501	C₂×C₅	semidirect
97. C₃×#497	C₂×C₅	semidirect
98. C₃×#491	C₂×C₅	semidirect
99. C₃×#489	C₂×C₅	semidirect
100. C₃×#470	C₂×C₅	semidirect
102. C₃×C₄×Q₁₆	C₂×C₅	semidirect
103. C₃×C₄×SD₁₆	C₂×C₅	semidirect
104. C₃×C₄×M₁₆	C₂×C₅	semidirect
136. #3172	C₃×C₅	direct (N × H)
231. #533	C₂×C₃×C₅	semidirect
233. #501	C₂×C₃×C₅	semidirect
234. #497	C₂×C₃×C₅	semidirect
235. #491	C₂×C₃×C₅	semidirect
236. #489	C₂×C₃×C₅	semidirect
237. #470	C₂×C₃×C₅	semidirect
239. C₄×Q₁₆	C₂×C₃×C₅	semidirect
240. C₄×SD₁₆	C₂×C₃×C₅	semidirect
241. C₄×M₁₆	C₂×C₃×C₅	semidirect
440. C₃×C₅	#3172	direct (N × H)
494. C₅	C₃×#3172	direct (N × H)
513. C₃	C₅×#3172	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×#529	2
C₃×C₅×#501	2
C₃×C₅×#497	2
C₃×C₅×#491	2
C₃×C₅×#489	2
C₃×C₅×#470	2
C₃×C₅×#468	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₄×C₅×M₁₆	2
C₅×#3172	3
C₃×#3172	5

Subgroups — C3×C5×#3172 #14276206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3172 #14276206