Subgroups — C₃×C₅×#3096 #14276130

Order 1920.

836 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#481	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#480	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3096	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#127	—	2	1	no	—
18	C₃×C₅×#124	—	2	1	no	—
19	C₃×C₅×#121	C₂²	1	2	yes	—
20	C₃×C₅×#121	C₂²	1	2	yes	—
21	C₃×C₅×#120	—	2	2	no	—
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×D₄	—	2	1	no	—
24	C₃×C₄×C₅×D₄	—	2	2	no	—
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₃×C₅×#117	C₂²	1	1	yes	characteristic
27	C₃×C₅×#117	C₂²	1	2	yes	complemented
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#107	C₂²	1	2	yes	complemented
32	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#106	C₂²	1	2	yes	complemented
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×#102	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
41	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
42	C₃×#3096	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#535	C₂×C₃	1	1	yes	characteristic
44	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#482	C₂×C₃	1	2	yes	complemented
46	C₅×#482	C₂×C₃	1	2	yes	complemented
47	C₅×#481	C₂×C₃	1	2	yes	complemented
48	C₅×#480	C₂×C₃	1	2	yes	complemented
49	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂⁴×C₃×C₅	—	2	1	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
64	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	2	no	—
71	C₂×C₃×C₅×C₈	—	2	2	no	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
82	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₄²×C₅	—	2	1	no	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	—	2	2	no	—
90	C₃×#535	C₂×C₅	1	1	yes	characteristic
91	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#482	C₂×C₅	1	2	yes	complemented
93	C₃×#482	C₂×C₅	1	2	yes	complemented
94	C₃×#481	C₂×C₅	1	2	yes	complemented
95	C₃×#480	C₂×C₅	1	2	yes	complemented
96	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×#127	—	2	1	no	—
106	C₅×#124	—	2	1	no	—
107	C₅×#121	C₂²×C₃	1	2	yes	—
108	C₅×#121	C₂²×C₃	1	2	yes	—
109	C₅×#120	—	2	2	no	—
110	C₄×C₅×Q₈	—	2	1	no	—
111	C₄×C₅×D₄	—	2	1	no	—
112	C₄×C₅×D₄	—	2	2	no	—
113	C₅×#117	C₂²×C₃	1	1	yes	characteristic
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₅×#117	C₂²×C₃	1	2	yes	complemented
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
118	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₅×#107	C₂²×C₃	1	2	yes	complemented
121	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×#106	C₂²×C₃	1	2	yes	complemented
124	C₅×#102	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	2	yes	—
126	C₅×#102	C₂²×C₃	1	2	yes	—
127	C₅×#102	C₂²×C₃	1	2	yes	—
128	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
129	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
130	#3096	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	4	2	no	—
133	C₂³×C₃×C₅	—	8	1	no	—
134	C₂³×C₃×C₅	—	8	1	no	—
135	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₅×Q₈	—	2	2	no	—
138	C₃×C₅×D₄	—	2	4	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	4	2	no	—
143	C₃×C₅×D₄	—	8	2	no	—
144	C₃×C₅×D₄	—	8	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	1	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	8	1	no	—
153	C₂×C₃×C₄×C₅	—	8	2	no	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	#41	1	2	yes	—
157	C₂×C₃×C₄×C₅	#41	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₃×C₅×C₈	—	2	1	no	—
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	2	no	—
162	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
166	C₃×#127	—	2	1	no	—
167	C₃×#124	—	2	1	no	—
168	C₃×#121	C₂²×C₅	1	2	yes	—
169	C₃×#121	C₂²×C₅	1	2	yes	—
170	C₃×#120	—	2	2	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	—	2	2	no	—
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	C₃×#117	C₂²×C₅	1	1	yes	characteristic
176	C₃×#117	C₂²×C₅	1	2	yes	complemented
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
179	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₃×#107	C₂²×C₅	1	2	yes	complemented
182	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₃×#106	C₂²×C₅	1	2	yes	complemented
185	C₃×#102	C₂²×C₅	1	2	yes	—
186	C₃×#102	C₂²×C₅	1	2	yes	—
187	C₃×#102	C₂²×C₅	1	2	yes	—
188	C₃×#102	C₂²×C₅	1	2	yes	—
189	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
190	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
191	C₂⁴×C₅	—	2	1	no	—
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	2	2	no	—
194	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
195	C₂×C₅×D₄	—	2	2	no	—
196	C₂×C₅×D₄	—	2	2	no	—
197	C₂×C₅×D₄	—	2	1	no	—
198	C₂×C₅×D₄	—	2	2	no	—
199	C₂×C₅×D₄	—	2	2	no	—
200	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
201	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
202	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	2	no	—
205	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₅×M₁₆	—	2	2	no	—
208	C₂×C₅×C₈	—	2	2	no	—
209	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	2	no	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
215	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	—	2	2	no	—
222	C₅×C₂²⋊C₄	—	2	2	no	—
223	C₅×C₂²⋊C₄	—	2	2	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	2	no	—
227	#535	C₂×C₃×C₅	1	1	yes	characteristic
228	#520	C₂×C₃×C₅	1	1	yes	characteristic, complemented
229	#482	C₂×C₃×C₅	1	2	yes	complemented
230	#482	C₂×C₃×C₅	1	2	yes	complemented
231	#481	C₂×C₃×C₅	1	2	yes	complemented
232	#480	C₂×C₃×C₅	1	2	yes	complemented
233	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	C₂²×C₃×C₅	—	2	1	no	—
239	C₂²×C₃×C₅	—	2	1	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	4	2	no	—
244	C₂²×C₃×C₅	—	4	2	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	8	4	no	—
247	C₂²×C₃×C₅	#123	1	2	yes	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	4	1	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	#123	1	2	yes	—
256	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
257	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₂⁴×C₃	—	2	1	no	—
259	C₃×#41	—	2	2	no	—
260	C₃×#41	—	2	2	no	—
261	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×D₄	—	2	2	no	—
263	C₂×C₃×D₄	—	2	2	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
268	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₃×M₁₆	—	2	2	no	—
275	C₂×C₃×C₈	—	2	2	no	—
276	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
278	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	—	2	2	no	—
281	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
282	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
283	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	no	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	—	2	2	no	—
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₄²	—	2	1	no	—
292	C₃×C₄²	—	2	1	no	—
293	C₃×C₄²	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	4	2	no	—
296	C₂³×C₅	—	8	1	no	—
297	C₂³×C₅	—	8	1	no	—
298	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
299	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₅×Q₈	—	2	2	no	—
301	C₅×D₄	—	2	4	no	—
302	C₅×D₄	—	2	2	no	—
303	C₅×D₄	—	2	2	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	4	2	no	—
306	C₅×D₄	—	8	2	no	—
307	C₅×D₄	—	8	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	8	1	no	—
316	C₂×C₄×C₅	—	8	2	no	—
317	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
318	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₃×#41	1	2	yes	—
320	C₂×C₄×C₅	C₃×#41	1	2	yes	—
321	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	2	no	—
325	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
327	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
328	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
329	#127	—	2	1	no	—
330	#124	—	2	1	no	—
331	#121	C₂²×C₃×C₅	1	2	yes	—
332	#121	C₂²×C₃×C₅	1	2	yes	—
333	#120	—	2	2	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	2	no	—
337	#117	C₂²×C₃×C₅	1	1	yes	characteristic
338	#117	C₂²×C₃×C₅	1	1	yes	characteristic
339	#117	C₂²×C₃×C₅	1	2	yes	complemented
340	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
342	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
343	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
344	#107	C₂²×C₃×C₅	1	2	yes	complemented
345	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
346	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
347	#106	C₂²×C₃×C₅	1	2	yes	complemented
348	#102	C₂²×C₃×C₅	1	2	yes	—
349	#102	C₂²×C₃×C₅	1	2	yes	—
350	#102	C₂²×C₃×C₅	1	2	yes	—
351	#102	C₂²×C₃×C₅	1	2	yes	—
352	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
353	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
354	C₂×C₃×C₅	—	2	2	no	—
355	C₂×C₃×C₅	—	4	2	no	—
356	C₂×C₃×C₅	—	8	2	no	—
357	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
358	C₂×C₃×C₅	#576	1	1	yes	characteristic
359	C₂×C₃×C₅	#577	1	1	yes	characteristic
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	4	2	no	—
362	C₂³×C₃	—	8	1	no	—
363	C₂³×C₃	—	8	1	no	—
364	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
365	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
366	C₃×Q₈	—	2	2	no	—
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	4	2	no	—
372	C₃×D₄	—	8	2	no	—
373	C₃×D₄	—	8	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	8	1	no	—
382	C₂×C₃×C₄	—	8	2	no	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₅×#41	1	2	yes	—
386	C₂×C₃×C₄	C₅×#41	1	2	yes	—
387	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
388	C₃×C₈	—	2	1	no	—
389	C₃×C₈	—	2	1	no	—
390	C₃×C₈	—	2	2	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	—	2	1	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	—	4	2	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	8	4	no	—
400	C₂²×C₅	C₃×#123	1	2	yes	—
401	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	2	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	1	no	—
408	C₄×C₅	C₃×#123	1	2	yes	—
409	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
410	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
411	C₂⁴	—	2	1	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
421	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
422	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
426	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
427	M₁₆	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
430	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
431	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
435	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
436	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
438	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	2	no	—
447	C₃×C₅	#3096	1	1	yes	characteristic, direct product factor, Hall
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	—	2	1	no	—
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	4	2	no	—
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	—	8	4	no	—
457	C₂²×C₃	C₅×#123	1	2	yes	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₃×C₄	—	2	2	no	—
460	C₃×C₄	—	4	1	no	—
461	C₃×C₄	—	4	2	no	—
462	C₃×C₄	—	4	1	no	—
463	C₃×C₄	—	4	1	no	—
464	C₃×C₄	—	4	1	no	—
465	C₃×C₄	C₅×#123	1	2	yes	—
466	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
467	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
468	C₂×C₅	—	2	2	no	—
469	C₂×C₅	—	4	2	no	—
470	C₂×C₅	—	8	2	no	—
471	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
472	C₂×C₅	C₃×#576	1	1	yes	characteristic
473	C₂×C₅	C₃×#577	1	1	yes	characteristic
474	C₂³	—	2	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	8	1	no	—
477	C₂³	—	8	1	no	—
478	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
479	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
480	Q₈	—	2	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
498	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
499	C₂×C₄	C₃×C₅×#41	1	2	yes	—
500	C₂×C₄	C₃×C₅×#41	1	2	yes	—
501	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	2	no	—
505	C₂×C₃	—	2	2	no	—
506	C₂×C₃	—	4	2	no	—
507	C₂×C₃	—	8	2	no	—
508	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
509	C₂×C₃	C₅×#576	1	1	yes	characteristic
510	C₂×C₃	C₅×#577	1	1	yes	characteristic
511	C₅	C₃×#3096	1	1	yes	characteristic, direct product factor, Sylow
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	8	4	no	—
521	C₂²	C₃×C₅×#123	1	2	yes	—
522	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	C₃×C₅×#123	1	2	yes	—
530	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
531	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
532	C₃	C₅×#3096	1	1	yes	characteristic, direct product factor, Sylow
533	C₂	—	2	2	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	2	no	—
536	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
537	C₂	C₃×C₅×#576	1	1	yes	characteristic
538	C₂	C₃×C₅×#577	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×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#520	C₂	semidirect
3. C₃×C₅×#482	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#480	C₂	semidirect
7. C₃×C₅×#428	C₂	semidirect
8. C₃×C₅×#427	C₂	semidirect
9. C₃×C₅×#418	C₂	semidirect
10. C₂×C₃×C₅×#102	C₂	semidirect
11. C₃×C₅×#408	C₂	semidirect
12. C₅×#3096	C₃	direct (N × H)
27. C₃×C₅×#117	C₂²	semidirect
29. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₅×#107	C₂²	semidirect
31. C₃×C₅×#107	C₂²	semidirect
32. C₃×C₅×#107	C₂²	semidirect
33. C₃×C₅×#106	C₂²	semidirect
34. C₃×C₅×#106	C₂²	semidirect
35. C₃×C₅×#106	C₂²	semidirect
40. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
41. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
42. C₃×#3096	C₅	direct (N × H)
44. C₅×#520	C₂×C₃	semidirect
45. C₅×#482	C₂×C₃	semidirect
46. C₅×#482	C₂×C₃	semidirect
47. C₅×#481	C₂×C₃	semidirect
48. C₅×#480	C₂×C₃	semidirect
49. C₅×#428	C₂×C₃	semidirect
50. C₅×#427	C₂×C₃	semidirect
51. C₅×#418	C₂×C₃	semidirect
52. C₂×C₅×#102	C₂×C₃	semidirect
53. C₅×#408	C₂×C₃	semidirect
91. C₃×#520	C₂×C₅	semidirect
92. C₃×#482	C₂×C₅	semidirect
93. C₃×#482	C₂×C₅	semidirect
94. C₃×#481	C₂×C₅	semidirect
95. C₃×#480	C₂×C₅	semidirect
96. C₃×#428	C₂×C₅	semidirect
97. C₃×#427	C₂×C₅	semidirect
98. C₃×#418	C₂×C₅	semidirect
99. C₂×C₃×#102	C₂×C₅	semidirect
100. C₃×#408	C₂×C₅	semidirect
115. C₅×#117	C₂²×C₃	semidirect
117. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
118. C₅×#107	C₂²×C₃	semidirect
119. C₅×#107	C₂²×C₃	semidirect
120. C₅×#107	C₂²×C₃	semidirect
121. C₅×#106	C₂²×C₃	semidirect
122. C₅×#106	C₂²×C₃	semidirect
123. C₅×#106	C₂²×C₃	semidirect
128. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
129. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
130. #3096	C₃×C₅	direct (N × H)
176. C₃×#117	C₂²×C₅	semidirect
178. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
179. C₃×#107	C₂²×C₅	semidirect
180. C₃×#107	C₂²×C₅	semidirect
181. C₃×#107	C₂²×C₅	semidirect
182. C₃×#106	C₂²×C₅	semidirect
183. C₃×#106	C₂²×C₅	semidirect
184. C₃×#106	C₂²×C₅	semidirect
189. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
190. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
228. #520	C₂×C₃×C₅	semidirect
229. #482	C₂×C₃×C₅	semidirect
230. #482	C₂×C₃×C₅	semidirect
231. #481	C₂×C₃×C₅	semidirect
232. #480	C₂×C₃×C₅	semidirect
233. #428	C₂×C₃×C₅	semidirect
234. #427	C₂×C₃×C₅	semidirect
235. #418	C₂×C₃×C₅	semidirect
236. C₂×#102	C₂×C₃×C₅	semidirect
237. #408	C₂×C₃×C₅	semidirect
339. #117	C₂²×C₃×C₅	semidirect
341. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
342. #107	C₂²×C₃×C₅	semidirect
343. #107	C₂²×C₃×C₅	semidirect
344. #107	C₂²×C₃×C₅	semidirect
345. #106	C₂²×C₃×C₅	semidirect
346. #106	C₂²×C₃×C₅	semidirect
347. #106	C₂²×C₃×C₅	semidirect
352. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
353. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
447. C₃×C₅	#3096	direct (N × H)
511. C₅	C₃×#3096	direct (N × H)
532. C₃	C₅×#3096	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×#535	2
C₃×C₅×#520	2
C₃×C₅×#482	2
C₃×C₅×#481	2
C₃×C₅×#480	2
C₃×C₅×#428	2
C₃×C₅×#427	2
C₃×C₅×#418	2
C₂×C₃×C₅×#102	2
C₃×C₅×#408	2
C₅×#3096	3
C₃×#3096	5

Subgroups — C3×C5×#3096 #14276130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3096 #14276130