Subgroups — C₂×C₃×C₅×#458 #14276058

Order 1920.

1588 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#123	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×#458	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#99	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×#458	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×H(5,𝔽₂)	—	2	6	no	—
7	C₃×C₅×H(5,𝔽₂)	C₂²	1	4	yes	—
8	C₂×C₃×C₅×#41	—	2	3	no	—
9	C₂²×C₃×C₅×D₄	—	2	3	no	—
10	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
12	C₃×C₅×#123	—	2	6	no	—
13	C₃×C₅×#123	C₂²	1	12	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	—	2	3	no	—
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	3	no	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
17	C₃×C₅×#99	C₂²	1	12	yes	complemented
18	C₂×C₃×#458	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
20	C₂×C₅×#123	C₂×C₃	1	3	yes	complemented
21	C₅×#458	C₂×C₃	1	8	yes	direct product factor
22	C₂×C₅×#99	C₂×C₃	1	3	yes	complemented
23	C₂⁴×C₃×C₅	—	2	1	no	—
24	C₂⁴×C₃×C₅	D₄	1	3	yes	—
25	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
26	C₃×C₅×#41	—	2	12	no	—
27	C₃×C₅×#41	—	2	12	no	—
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×D₄	—	2	3	no	—
30	C₂×C₃×C₅×D₄	—	2	12	no	—
31	C₂×C₃×C₅×D₄	—	2	6	no	—
32	C₂×C₃×C₅×D₄	—	2	12	no	—
33	C₂×C₃×C₅×D₄	—	2	6	no	—
34	C₂×C₃×C₅×D₄	D₄	1	6	yes	—
35	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
36	C₂²×C₃×C₄×C₅	—	2	3	no	—
37	C₂²×C₃×C₄×C₅	—	2	3	no	—
38	C₂²×C₃×C₄×C₅	—	2	3	no	—
39	C₂²×C₃×C₄×C₅	—	2	3	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
42	C₃×C₅×C₄⋊C₄	—	2	12	no	—
43	C₃×C₅×C₂²⋊C₄	—	2	12	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	3	no	—
45	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	complemented
46	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic
47	C₂×C₃×#123	C₂×C₅	1	3	yes	complemented
48	C₃×#458	C₂×C₅	1	8	yes	direct product factor
49	C₂×C₃×#99	C₂×C₅	1	3	yes	complemented
50	C₅×H(5,𝔽₂)	—	2	6	no	—
51	C₅×H(5,𝔽₂)	C₂²×C₃	1	4	yes	—
52	C₂×C₅×#41	—	2	3	no	—
53	C₂²×C₅×D₄	—	2	3	no	—
54	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
55	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
56	C₅×#123	—	2	6	no	—
57	C₅×#123	C₂²×C₃	1	12	yes	complemented
58	C₂×C₅×C₄⋊C₄	—	2	3	no	—
59	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
60	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
61	C₅×#99	C₂²×C₃	1	12	yes	complemented
62	C₂×#458	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³×C₃×C₅	—	2	4	no	—
64	C₂³×C₃×C₅	—	2	3	no	—
65	C₂³×C₃×C₅	—	2	3	no	—
66	C₂³×C₃×C₅	—	4	2	no	—
67	C₂³×C₃×C₅	—	4	6	no	—
68	C₂³×C₃×C₅	—	8	2	no	—
69	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
70	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
71	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
72	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
73	C₃×C₅×Q₈	—	2	4	no	—
74	C₃×C₅×D₄	—	2	12	no	—
75	C₃×C₅×D₄	—	2	12	no	—
76	C₃×C₅×D₄	—	2	12	no	—
77	C₂×C₃×C₄×C₅	—	2	12	no	—
78	C₂×C₃×C₄×C₅	—	2	3	no	—
79	C₂×C₃×C₄×C₅	—	2	3	no	—
80	C₂×C₃×C₄×C₅	—	2	6	no	—
81	C₂×C₃×C₄×C₅	—	2	6	no	—
82	C₂×C₃×C₄×C₅	—	4	6	no	—
83	C₂×C₃×C₄×C₅	—	4	3	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
86	C₃×H(5,𝔽₂)	—	2	6	no	—
87	C₃×H(5,𝔽₂)	C₂²×C₅	1	4	yes	—
88	C₂×C₃×#41	—	2	3	no	—
89	C₂²×C₃×D₄	—	2	3	no	—
90	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
91	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
92	C₃×#123	—	2	6	no	—
93	C₃×#123	C₂²×C₅	1	12	yes	complemented
94	C₂×C₃×C₄⋊C₄	—	2	3	no	—
95	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
96	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
97	C₃×#99	C₂²×C₅	1	12	yes	complemented
98	C₂⁴×C₅	—	2	1	no	—
99	C₂⁴×C₅	C₃×D₄	1	3	yes	—
100	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
101	C₅×#41	—	2	12	no	—
102	C₅×#41	—	2	12	no	—
103	C₂×C₅×Q₈	—	2	1	no	—
104	C₂×C₅×D₄	—	2	3	no	—
105	C₂×C₅×D₄	—	2	12	no	—
106	C₂×C₅×D₄	—	2	6	no	—
107	C₂×C₅×D₄	—	2	12	no	—
108	C₂×C₅×D₄	—	2	6	no	—
109	C₂×C₅×D₄	C₃×D₄	1	6	yes	—
110	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
111	C₂²×C₄×C₅	—	2	3	no	—
112	C₂²×C₄×C₅	—	2	3	no	—
113	C₂²×C₄×C₅	—	2	3	no	—
114	C₂²×C₄×C₅	—	2	3	no	—
115	C₂²×C₄×C₅	C₃×D₄	1	3	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	complemented
117	C₅×C₄⋊C₄	—	2	12	no	—
118	C₅×C₂²⋊C₄	—	2	12	no	—
119	C₅×C₂²⋊C₄	—	2	3	no	—
120	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	complemented
121	C₂×H(5,𝔽₂)	C₂×C₃×C₅	1	1	yes	characteristic
122	C₂×#123	C₂×C₃×C₅	1	3	yes	complemented
123	#458	C₂×C₃×C₅	1	8	yes	direct product factor
124	C₂×#99	C₂×C₃×C₅	1	3	yes	complemented
125	C₂²×C₃×C₅	—	2	6	no	—
126	C₂²×C₃×C₅	—	2	6	no	—
127	C₂²×C₃×C₅	—	4	3	no	—
128	C₂²×C₃×C₅	—	4	1	no	—
129	C₂²×C₃×C₅	—	4	6	no	—
130	C₂²×C₃×C₅	—	4	6	no	—
131	C₂²×C₃×C₅	—	8	3	no	—
132	C₂²×C₃×C₅	—	8	4	no	—
133	C₂²×C₃×C₅	#120	1	3	yes	—
134	C₂²×C₃×C₅	#120	1	1	yes	characteristic
135	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
136	C₃×C₄×C₅	—	2	6	no	—
137	C₃×C₄×C₅	—	4	6	no	—
138	C₃×C₄×C₅	—	4	2	no	—
139	C₂⁴×C₃	—	2	1	no	—
140	C₂⁴×C₃	C₅×D₄	1	3	yes	—
141	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
142	C₃×#41	—	2	12	no	—
143	C₃×#41	—	2	12	no	—
144	C₂×C₃×Q₈	—	2	1	no	—
145	C₂×C₃×D₄	—	2	3	no	—
146	C₂×C₃×D₄	—	2	12	no	—
147	C₂×C₃×D₄	—	2	6	no	—
148	C₂×C₃×D₄	—	2	12	no	—
149	C₂×C₃×D₄	—	2	6	no	—
150	C₂×C₃×D₄	C₅×D₄	1	6	yes	—
151	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
152	C₂²×C₃×C₄	—	2	3	no	—
153	C₂²×C₃×C₄	—	2	3	no	—
154	C₂²×C₃×C₄	—	2	3	no	—
155	C₂²×C₃×C₄	—	2	3	no	—
156	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
157	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	complemented
158	C₃×C₄⋊C₄	—	2	12	no	—
159	C₃×C₂²⋊C₄	—	2	12	no	—
160	C₃×C₂²⋊C₄	—	2	3	no	—
161	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	complemented
162	C₂³×C₅	—	2	4	no	—
163	C₂³×C₅	—	2	3	no	—
164	C₂³×C₅	—	2	3	no	—
165	C₂³×C₅	—	4	2	no	—
166	C₂³×C₅	—	4	6	no	—
167	C₂³×C₅	—	8	2	no	—
168	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
169	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
170	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
171	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
172	C₅×Q₈	—	2	4	no	—
173	C₅×D₄	—	2	12	no	—
174	C₅×D₄	—	2	12	no	—
175	C₅×D₄	—	2	12	no	—
176	C₂×C₄×C₅	—	2	12	no	—
177	C₂×C₄×C₅	—	2	3	no	—
178	C₂×C₄×C₅	—	2	3	no	—
179	C₂×C₄×C₅	—	2	6	no	—
180	C₂×C₄×C₅	—	2	6	no	—
181	C₂×C₄×C₅	—	4	6	no	—
182	C₂×C₄×C₅	—	4	3	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
185	H(5,𝔽₂)	—	2	6	no	—
186	H(5,𝔽₂)	C₂²×C₃×C₅	1	4	yes	—
187	C₂×#41	—	2	3	no	—
188	C₂²×D₄	—	2	3	no	—
189	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
190	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
191	#123	—	2	6	no	—
192	#123	C₂²×C₃×C₅	1	12	yes	complemented
193	C₂×C₄⋊C₄	—	2	3	no	—
194	C₂×C₂²⋊C₄	—	2	3	no	—
195	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
196	#99	C₂²×C₃×C₅	1	12	yes	complemented
197	C₂×C₃×C₅	—	2	3	no	—
198	C₂×C₃×C₅	—	2	3	no	—
199	C₂×C₃×C₅	—	4	6	no	—
200	C₂×C₃×C₅	#458	1	2	yes	direct product factor
201	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	—	2	3	no	—
204	C₂³×C₃	—	2	3	no	—
205	C₂³×C₃	—	4	2	no	—
206	C₂³×C₃	—	4	6	no	—
207	C₂³×C₃	—	8	2	no	—
208	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
209	C₂³×C₃	C₂×C₅×D₄	1	6	yes	—
210	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
211	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
212	C₃×Q₈	—	2	4	no	—
213	C₃×D₄	—	2	12	no	—
214	C₃×D₄	—	2	12	no	—
215	C₃×D₄	—	2	12	no	—
216	C₂×C₃×C₄	—	2	12	no	—
217	C₂×C₃×C₄	—	2	3	no	—
218	C₂×C₃×C₄	—	2	3	no	—
219	C₂×C₃×C₄	—	2	6	no	—
220	C₂×C₃×C₄	—	2	6	no	—
221	C₂×C₃×C₄	—	4	6	no	—
222	C₂×C₃×C₄	—	4	3	no	—
223	C₂×C₃×C₄	—	4	1	no	—
224	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
225	C₂²×C₅	—	2	6	no	—
226	C₂²×C₅	—	2	6	no	—
227	C₂²×C₅	—	4	3	no	—
228	C₂²×C₅	—	4	1	no	—
229	C₂²×C₅	—	4	6	no	—
230	C₂²×C₅	—	4	6	no	—
231	C₂²×C₅	—	8	3	no	—
232	C₂²×C₅	—	8	4	no	—
233	C₂²×C₅	C₃×#120	1	3	yes	—
234	C₂²×C₅	C₃×#120	1	1	yes	characteristic
235	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
236	C₄×C₅	—	2	6	no	—
237	C₄×C₅	—	4	6	no	—
238	C₄×C₅	—	4	2	no	—
239	C₂⁴	—	2	1	no	—
240	C₂⁴	C₃×C₅×D₄	1	3	yes	—
241	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
242	#41	—	2	12	no	—
243	#41	—	2	12	no	—
244	C₂×Q₈	—	2	1	no	—
245	C₂×D₄	—	2	3	no	—
246	C₂×D₄	—	2	12	no	—
247	C₂×D₄	—	2	6	no	—
248	C₂×D₄	—	2	12	no	—
249	C₂×D₄	—	2	6	no	—
250	C₂×D₄	C₃×C₅×D₄	1	6	yes	—
251	C₂×D₄	C₂³×C₃×C₅	1	6	yes	—
252	C₂²×C₄	—	2	3	no	—
253	C₂²×C₄	—	2	3	no	—
254	C₂²×C₄	—	2	3	no	—
255	C₂²×C₄	—	2	3	no	—
256	C₂²×C₄	C₃×C₅×D₄	1	3	yes	—
257	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	complemented
258	C₄⋊C₄	—	2	12	no	—
259	C₂²⋊C₄	—	2	12	no	—
260	C₂²⋊C₄	—	2	3	no	—
261	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	complemented
262	C₃×C₅	C₂×#458	1	1	yes	characteristic, direct product factor, Hall
263	C₂²×C₃	—	2	6	no	—
264	C₂²×C₃	—	2	6	no	—
265	C₂²×C₃	—	4	3	no	—
266	C₂²×C₃	—	4	1	no	—
267	C₂²×C₃	—	4	6	no	—
268	C₂²×C₃	—	4	6	no	—
269	C₂²×C₃	—	8	3	no	—
270	C₂²×C₃	—	8	4	no	—
271	C₂²×C₃	C₅×#120	1	3	yes	—
272	C₂²×C₃	C₅×#120	1	1	yes	characteristic
273	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
274	C₃×C₄	—	2	6	no	—
275	C₃×C₄	—	4	6	no	—
276	C₃×C₄	—	4	2	no	—
277	C₂×C₅	—	2	3	no	—
278	C₂×C₅	—	2	3	no	—
279	C₂×C₅	—	4	6	no	—
280	C₂×C₅	C₃×#458	1	2	yes	direct product factor
281	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
282	C₂³	—	2	4	no	—
283	C₂³	—	2	3	no	—
284	C₂³	—	2	3	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	6	no	—
287	C₂³	—	8	2	no	—
288	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
289	C₂³	C₂×C₃×C₅×D₄	1	6	yes	—
290	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
291	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
292	Q₈	—	2	4	no	—
293	D₄	—	2	12	no	—
294	D₄	—	2	12	no	—
295	D₄	—	2	12	no	—
296	C₂×C₄	—	2	12	no	—
297	C₂×C₄	—	2	3	no	—
298	C₂×C₄	—	2	3	no	—
299	C₂×C₄	—	2	6	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	4	6	no	—
302	C₂×C₄	—	4	3	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
305	C₂×C₃	—	2	3	no	—
306	C₂×C₃	—	2	3	no	—
307	C₂×C₃	—	4	6	no	—
308	C₂×C₃	C₅×#458	1	2	yes	direct product factor
309	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
310	C₅	C₂×C₃×#458	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²	—	2	6	no	—
312	C₂²	—	2	6	no	—
313	C₂²	—	4	3	no	—
314	C₂²	—	4	1	no	—
315	C₂²	—	4	6	no	—
316	C₂²	—	4	6	no	—
317	C₂²	—	8	3	no	—
318	C₂²	—	8	4	no	—
319	C₂²	C₃×C₅×#120	1	3	yes	—
320	C₂²	C₃×C₅×#120	1	1	yes	characteristic
321	C₂²	C₂²×C₃×C₅×D₄	1	3	yes	—
322	C₄	—	2	6	no	—
323	C₄	—	4	6	no	—
324	C₄	—	4	2	no	—
325	C₃	C₂×C₅×#458	1	1	yes	characteristic, direct product factor, Sylow
326	C₂	—	2	3	no	—
327	C₂	—	2	3	no	—
328	C₂	—	4	6	no	—
329	C₂	C₃×C₅×#458	1	2	yes	direct product factor
330	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×H(5,𝔽₂)	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#123	C₂	semidirect
3. C₃×C₅×#458	C₂	direct (N × H)
4. C₂×C₃×C₅×#99	C₂	semidirect
5. C₂×C₅×#458	C₃	direct (N × H)
11. C₂³×C₃×C₄×C₅	C₂²	semidirect
13. C₃×C₅×#123	C₂²	semidirect
16. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
17. C₃×C₅×#99	C₂²	semidirect
18. C₂×C₃×#458	C₅	direct (N × H)
20. C₂×C₅×#123	C₂×C₃	semidirect
21. C₅×#458	C₂×C₃	direct (N × H)
22. C₂×C₅×#99	C₂×C₃	semidirect
41. C₂²×C₃×C₄×C₅	C₂³	semidirect
45. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
47. C₂×C₃×#123	C₂×C₅	semidirect
48. C₃×#458	C₂×C₅	direct (N × H)
49. C₂×C₃×#99	C₂×C₅	semidirect
55. C₂³×C₄×C₅	C₂²×C₃	semidirect
57. C₅×#123	C₂²×C₃	semidirect
60. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
61. C₅×#99	C₂²×C₃	semidirect
62. C₂×#458	C₃×C₅	direct (N × H)
91. C₂³×C₃×C₄	C₂²×C₅	semidirect
93. C₃×#123	C₂²×C₅	semidirect
96. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
97. C₃×#99	C₂²×C₅	semidirect
116. C₂²×C₄×C₅	C₂³×C₃	semidirect
120. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
122. C₂×#123	C₂×C₃×C₅	semidirect
123. #458	C₂×C₃×C₅	direct (N × H)
124. C₂×#99	C₂×C₃×C₅	semidirect
157. C₂²×C₃×C₄	C₂³×C₅	semidirect
161. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
190. C₂³×C₄	C₂²×C₃×C₅	semidirect
192. #123	C₂²×C₃×C₅	semidirect
195. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
196. #99	C₂²×C₃×C₅	semidirect
200. C₂×C₃×C₅	#458	direct (N × H)
257. C₂²×C₄	C₂³×C₃×C₅	semidirect
261. C₂²⋊C₄	C₂³×C₃×C₅	semidirect
262. C₃×C₅	C₂×#458	direct (N × H)
280. C₂×C₅	C₃×#458	direct (N × H)
308. C₂×C₃	C₅×#458	direct (N × H)
310. C₅	C₂×C₃×#458	direct (N × H)
325. C₃	C₂×C₅×#458	direct (N × H)
329. C₂	C₃×C₅×#458	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×H(5,𝔽₂)	2
C₂×C₃×C₅×#123	2
C₃×C₅×#458	2
C₂×C₃×C₅×#99	2
C₂×C₅×#458	3
C₂×C₃×#458	5

Subgroups — C2×C3×C5×#458 #14276058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#458 #14276058