Subgroups — C₃×C₅×#3250 #14276284

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3250	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#126	—	2	2	no	—
17	C₃×C₅×#125	C₂²	1	2	yes	—
18	C₃×C₅×#124	C₂²	1	2	yes	—
19	C₃×C₅×#123	—	2	2	no	—
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₅×#121	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₃×C₄×C₅×D₄	—	2	2	no	—
24	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
25	C₃×C₅×#117	—	2	2	no	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×#107	C₂²	1	1	yes	characteristic
28	C₃×C₅×#107	C₂²	1	1	yes	characteristic
29	C₃×C₅×#106	C₂²	1	2	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
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×#3250	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#529	C₂×C₃	1	2	yes	complemented
38	C₅×#479	C₂×C₃	1	2	yes	complemented
39	C₅×#478	C₂×C₃	1	2	yes	complemented
40	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#466	C₂×C₃	1	1	yes	characteristic
42	C₅×#465	C₂×C₃	1	2	yes	complemented
43	C₅×#464	C₂×C₃	1	2	yes	complemented
44	C₅×#463	C₂×C₃	1	2	yes	complemented
45	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×Q₁₆	—	4	1	no	—
54	C₃×C₅×SD₁₆	—	4	2	no	—
55	C₃×C₅×D₈	—	4	1	no	—
56	C₂×C₃×C₅×C₈	—	4	1	no	—
57	C₂×C₃×C₅×C₈	—	4	1	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
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×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₄²×C₅	—	2	2	no	—
73	C₃×C₄²×C₅	D₄	1	2	yes	—
74	C₃×C₄²×C₅	C₂³	1	2	yes	—
75	C₃×#529	C₂×C₅	1	2	yes	complemented
76	C₃×#479	C₂×C₅	1	2	yes	complemented
77	C₃×#478	C₂×C₅	1	2	yes	complemented
78	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#466	C₂×C₅	1	1	yes	characteristic
80	C₃×#465	C₂×C₅	1	2	yes	complemented
81	C₃×#464	C₂×C₅	1	2	yes	complemented
82	C₃×#463	C₂×C₅	1	2	yes	complemented
83	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
86	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#126	—	2	2	no	—
90	C₅×#125	C₂²×C₃	1	2	yes	—
91	C₅×#124	C₂²×C₃	1	2	yes	—
92	C₅×#123	—	2	2	no	—
93	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
94	C₅×#121	C₂²×C₃	1	2	yes	—
95	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
98	C₅×#117	—	2	2	no	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×#107	C₂²×C₃	1	1	yes	characteristic
101	C₅×#107	C₂²×C₃	1	1	yes	characteristic
102	C₅×#106	C₂²×C₃	1	2	yes	—
103	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₅×#103	C₂²×C₃	1	2	yes	—
106	C₅×#103	C₂²×C₃	1	2	yes	—
107	C₅×#102	C₂²×C₃	1	2	yes	—
108	C₅×#102	C₂²×C₃	1	2	yes	—
109	#3250	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	—	4	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	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	—	4	1	no	—
124	C₂×C₃×C₄×C₅	—	4	4	no	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₃×C₅×C₈	—	2	1	no	—
130	C₃×C₅×C₈	—	2	2	no	—
131	C₃×C₅×C₈	—	2	1	no	—
132	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
134	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
135	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#126	—	2	2	no	—
138	C₃×#125	C₂²×C₅	1	2	yes	—
139	C₃×#124	C₂²×C₅	1	2	yes	—
140	C₃×#123	—	2	2	no	—
141	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
142	C₃×#121	C₂²×C₅	1	2	yes	—
143	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
144	C₃×C₄×D₄	—	2	2	no	—
145	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
146	C₃×#117	—	2	2	no	—
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₃×#107	C₂²×C₅	1	1	yes	characteristic
149	C₃×#107	C₂²×C₅	1	1	yes	characteristic
150	C₃×#106	C₂²×C₅	1	2	yes	—
151	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
152	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
153	C₃×#103	C₂²×C₅	1	2	yes	—
154	C₃×#103	C₂²×C₅	1	2	yes	—
155	C₃×#102	C₂²×C₅	1	2	yes	—
156	C₃×#102	C₂²×C₅	1	2	yes	—
157	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₅×Q₁₆	—	4	1	no	—
165	C₅×SD₁₆	—	4	2	no	—
166	C₅×D₈	—	4	1	no	—
167	C₂×C₅×C₈	—	4	1	no	—
168	C₂×C₅×C₈	—	4	1	no	—
169	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
171	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	—	2	2	no	—
176	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
177	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₅×C₂²⋊C₄	—	2	2	no	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₅×C₂²⋊C₄	—	2	2	no	—
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	C₃×D₄	1	2	yes	—
185	C₄²×C₅	C₂³×C₃	1	2	yes	—
186	#529	C₂×C₃×C₅	1	2	yes	complemented
187	#479	C₂×C₃×C₅	1	2	yes	complemented
188	#478	C₂×C₃×C₅	1	2	yes	complemented
189	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
190	#466	C₂×C₃×C₅	1	1	yes	characteristic
191	#465	C₂×C₃×C₅	1	2	yes	complemented
192	#464	C₂×C₃×C₅	1	2	yes	complemented
193	#463	C₂×C₃×C₅	1	2	yes	complemented
194	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	—	2	1	no	—
196	C₂²×C₃×C₅	—	2	1	no	—
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	#135	1	2	yes	—
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₃×C₄×C₅	—	2	1	no	—
203	C₃×C₄×C₅	—	2	2	no	—
204	C₃×C₄×C₅	—	2	2	no	—
205	C₃×C₄×C₅	—	4	2	no	—
206	C₃×C₄×C₅	—	4	2	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
209	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	—	2	2	no	—
214	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
217	C₃×Q₁₆	—	4	1	no	—
218	C₃×SD₁₆	—	4	2	no	—
219	C₃×D₈	—	4	1	no	—
220	C₂×C₃×C₈	—	4	1	no	—
221	C₂×C₃×C₈	—	4	1	no	—
222	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	2	no	—
229	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
230	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	2	2	no	—
233	C₃×C₂²⋊C₄	—	2	2	no	—
234	C₃×C₂²⋊C₄	—	2	2	no	—
235	C₃×C₂²⋊C₄	—	2	2	no	—
236	C₃×C₄²	—	2	2	no	—
237	C₃×C₄²	C₅×D₄	1	2	yes	—
238	C₃×C₄²	C₂³×C₅	1	2	yes	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
241	C₅×Q₈	—	2	2	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	—	2	2	no	—
245	C₅×D₄	—	4	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	4	no	—
254	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
255	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
257	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
258	C₅×C₈	—	2	1	no	—
259	C₅×C₈	—	2	2	no	—
260	C₅×C₈	—	2	1	no	—
261	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
262	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
263	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
264	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
266	#126	—	2	2	no	—
267	#125	C₂²×C₃×C₅	1	2	yes	—
268	#124	C₂²×C₃×C₅	1	2	yes	—
269	#123	—	2	2	no	—
270	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
271	#121	C₂²×C₃×C₅	1	2	yes	—
272	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
275	#117	—	2	2	no	—
276	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
277	#107	C₂²×C₃×C₅	1	1	yes	characteristic
278	#107	C₂²×C₃×C₅	1	1	yes	characteristic
279	#106	C₂²×C₃×C₅	1	2	yes	—
280	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
281	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
282	#103	C₂²×C₃×C₅	1	2	yes	—
283	#103	C₂²×C₃×C₅	1	2	yes	—
284	#102	C₂²×C₃×C₅	1	2	yes	—
285	#102	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₃×C₅	—	2	2	no	—
287	C₂×C₃×C₅	—	8	2	no	—
288	C₂×C₃×C₅	#537	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
290	C₂×C₃×C₅	#575	1	1	yes	characteristic
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
293	C₃×Q₈	—	2	2	no	—
294	C₃×Q₈	—	2	2	no	—
295	C₃×D₄	—	2	2	no	—
296	C₃×D₄	—	2	2	no	—
297	C₃×D₄	—	4	4	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	4	1	no	—
305	C₂×C₃×C₄	—	4	4	no	—
306	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₃×C₈	—	2	1	no	—
311	C₃×C₈	—	2	2	no	—
312	C₃×C₈	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	2	1	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	4	2	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	C₃×#135	1	2	yes	—
319	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	2	2	no	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
327	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
335	Q₁₆	—	4	1	no	—
336	SD₁₆	—	4	2	no	—
337	D₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
341	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
342	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
348	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	C₃×C₅×D₄	1	2	yes	—
356	C₄²	C₂³×C₃×C₅	1	2	yes	—
357	C₃×C₅	#3250	1	1	yes	characteristic, direct product factor, Hall
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	—	4	2	no	—
363	C₂²×C₃	C₅×#135	1	2	yes	—
364	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	2	no	—
371	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
372	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂×C₅	—	2	2	no	—
374	C₂×C₅	—	8	2	no	—
375	C₂×C₅	C₃×#537	1	1	yes	characteristic
376	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
377	C₂×C₅	C₃×#575	1	1	yes	characteristic
378	C₂³	—	2	2	no	—
379	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
394	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
396	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	8	2	no	—
402	C₂×C₃	C₅×#537	1	1	yes	characteristic
403	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
404	C₂×C₃	C₅×#575	1	1	yes	characteristic
405	C₅	C₃×#3250	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₃×C₅×#135	1	2	yes	—
412	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
420	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
421	C₃	C₅×#3250	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	C₃×C₅×#537	1	1	yes	characteristic
425	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
426	C₂	C₃×C₅×#575	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×#466	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×#529	C₂	semidirect
2. C₃×C₅×#479	C₂	semidirect
3. C₃×C₅×#478	C₂	semidirect
4. C₃×C₅×#467	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
10. C₅×#3250	C₃	direct (N × H)
36. C₃×#3250	C₅	direct (N × H)
37. C₅×#529	C₂×C₃	semidirect
38. C₅×#479	C₂×C₃	semidirect
39. C₅×#478	C₂×C₃	semidirect
40. C₅×#467	C₂×C₃	semidirect
42. C₅×#465	C₂×C₃	semidirect
43. C₅×#464	C₂×C₃	semidirect
44. C₅×#463	C₂×C₃	semidirect
45. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
75. C₃×#529	C₂×C₅	semidirect
76. C₃×#479	C₂×C₅	semidirect
77. C₃×#478	C₂×C₅	semidirect
78. C₃×#467	C₂×C₅	semidirect
80. C₃×#465	C₂×C₅	semidirect
81. C₃×#464	C₂×C₅	semidirect
82. C₃×#463	C₂×C₅	semidirect
83. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
109. #3250	C₃×C₅	direct (N × H)
186. #529	C₂×C₃×C₅	semidirect
187. #479	C₂×C₃×C₅	semidirect
188. #478	C₂×C₃×C₅	semidirect
189. #467	C₂×C₃×C₅	semidirect
191. #465	C₂×C₃×C₅	semidirect
192. #464	C₂×C₃×C₅	semidirect
193. #463	C₂×C₃×C₅	semidirect
194. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
357. C₃×C₅	#3250	direct (N × H)
405. C₅	C₃×#3250	direct (N × H)
421. C₃	C₅×#3250	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×#529	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#467	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₂×C₃×C₅×C₄⋊C₈	2
C₅×#3250	3
C₃×#3250	5

Subgroups — C3×C5×#3250 #14276284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3250 #14276284